Zuoz, 18.7.2006 M.S. SozziK physics Kaon physics M. S. Sozzi University of Pisa PSI Summer School Zuoz, July 17-22, 2006

MS Sozzi K physics Zuoz 1872006

Kaon physics

M S SozziUniversity of Pisa

PSI Summer School Zuoz July 17-22 2006


Outline

bull Express review of K phenomenologybull Neutral K hadronic decays and CP violation bull The measurement of direct CP violationbull More CP violationbull Radiative decaysbull Non CPV physics from Kbull The new frontier ultra-rare FCNC K decays


Express review of Kaon phenomenology


K mesonsDiscovered in cosmic raysL Leprince-Ringuet M LrsquoHeritier (1944)

Existence probable drsquoune particule de masse 990 m0 dans le rayonnement cosmique [K+ scatters elastically on e- in a cloud chamber]

GD Rochester CC Butler (1947)Evidence for the existence of new unstable elementary particles [K0 π+π- and K+ μ+ν in a cloud chamber]

K0 π+π- K+ μ+ν


ldquoStrangerdquo particles

loz copiously produced σ(π ndash pK0Λ) asymp 1 mb asymp σtot40 STRONG

BUT

loz long lifetime τ(Λ π ndash p) asymp 10-10 s raquo 10-23 s ~ rc WEAK

Strangeness (S) hypotesis a quantum number conserved by strong interactions and not by weak interactions

bullAssociated production (strong) π ndash p Kndash p not observedrate of events with two V-particles above accidental

rate

bullS-violating decay (weak) Λ π ndashpπ0 π ndashp is as slow as π ndashp Λπ0

Strangenesshellip

A Pais Phys Rev 86 (1952) 663M Gell-Mann Phys Rev 92 (1953) 833T Nakano K Nishijima Prog Theor Phys 10 (1953) 581


bull Macroscopic physics laws are C-symmetric [later CP-]bull Two classes of neutral particles behaviour under C

1 θ0 θ0 (self C-conjugated ex γπ0)2 θ 0 θ0 (distinct by conserved quantum numbers ex n)

bull K0 mesons belong to class (2) with strong interactions only (strangeness conservation) but in weak interactions strangeness is not conservedPossible K0 K0 transitions common decay final states

M Gell-Mann and A Pais (1955)hellip and

weirdness


Change of basis K0 K0 described by a complex field

11 CCCC

Defining

2)(

2)(

2

1

K

K

One gets 21

211

1 KCCKKCCK

So C(K1) = +1 C(K2) = minus1

Physical states are K1 and K2 with no transitions among them with well-defined masses (not a particle-antiparticle pair) and widths (expected to be different because different final states available)

Use C to characterize physical states (later CP)

[After 1964 replace C with CP everywhere]


(1) Long-lived K mesons

23 V events in 1200 pictures all but one non-coplanar (at least 3 particles)

Exclude possible backgroundsmeson pair production π0e+eminusγlarge-angle lepton pairs and scattering of backward-moving particles

e and decay modes and occasionally 10-9 s 10-6 s

KS (short-lived) KL (long-lived)

τ(KS) = 08910ndash

10 sτ(KL) = 51710ndash8 s

=K1

=K2

For the time beinghellip

Accidental difference by a factor 600


Producing a state (K0 K0) of definite strangeness at t=0 its strangeness oscillates in time

)cos(24

1)]()0([

)cos(24

1)]()0([

2)(00

2)(00

2121

2121

mteeetKtKP

mteeetKtKP

ttt

ttt

Δm=m1-m2

(2) Strangeness oscillations

Can be observed because Δm ~ Γ


Strangeness oscillations can be measured exploiting flavour-specific decays which are allowed only for K0 or for K0 (flavour tagging)

Semi-leptonic decaysK0 π ndashe+νe but not K0 π ndashe+νe because of the ldquoΔS = ΔQ rulerdquo (quarks)

Positrons

Electrons

Start with K0 only

End up with equal mixture of K0 and K0

Non-exponential decay into strangeness eigenstates (not eigenstates of H) strangeness non-conservationIgnoring strangeness (lepton charge) exponential decay(s) recovered


(3) Regeneration

Strong interactions with matter are not strangeness-symmetricbesides K0p nK+ and K0n pKndash also K0p Λπ+ (hyperon production) gives σ(K0) raquo σ(K0)

Indeed K0p Λπ+ has no threshold whileK0p ΛK0K+ has 127 GeV kinetic energy threshold

[A Pais O Piccioni (1955)]

hellip even more bizarre manifestations of the mixing of K0 and K0(JD Jackson 1958)


[KS=K1 KL=K2]

K0 (or K0) K1 plusmn K2 K2 K0 removed in matter K1 + K2

Regeneration

ldquohellip the only instance where a forward coherently scattered beam can be distinguished from the original beamrdquo

(K0K0) and (KSKL) as

(SxSy) and (SLSR) optical activity or

(Sy=plusmnfrac12) and (Sx=plusmnfrac12) Stern-Gerlach


π minus on H2 target 670 MeVc neutral K beam at Berkeley

Travelling ~75 m (200 τS) before reaching a propane chamber containing an iron plate

200000 pictures half with 15 inch iron plate half with 6 inch iron plate

Look for 2-track events close (2τS) to plate with same momentum as incident beam

Regeneration15 inch plate

6 inch plate

combined

K1 rate

Diffraction by nuclei


M(K0) = 4977 MeVc2

I(JP) = frac12(0ndash)

[ π0 = (uu+dd)2 = π0 ]

K0 ne K0

In terms of quarks

K0 = (ds) S = +1 K0 = (ds) S = ndash1 which means

Two neutral K mesonsExample n ΛK0 and K0 n Λ occur (strongly) but if K0 n Λ would occur then nn nΛK0 ΛΛ would also occur (not observed)

The K meson system is the minimal flavour laboratory

Not the most obvious multiplet assignment


ldquoThe search for ordering principles at this moment may indeed ultimately have to be likened to a chemistrsquos attempt to build up the periodic system if he were given only a dozen odd elementsrdquo (A Pais 1952)

ldquoIt is by no means certain that if the complex ensemble of phenomena concerning the neutral K mesons were known without the benefit of the Gell-Mann ndash Pais theory we could even today correctly interpret the behavior of these particlesThat their theory published in 1955 actually preceded most of the experimental evidence known at present is one of the most astonishing and gratifying successes in the history of the elementary particlesrdquo(RH Good et al 1961)

ldquoEspecially interesting is the fact that we have taken the principle of superposition to its ultimately logical conclusionrdquoldquohellip one of the greatest achievements of theoretical physicsrdquo(R Feynman)

A bold profound and very fruitful conceptual step


Two-state formalism

Consider the (non complete) subspace spanned by K0K0 for times raquo the strong interaction time scale [Weisskopf-Wigner]

)0()( tiet H

ΓΓMM

ΓMH

)(2

)()( ti

ttdt

di

)(2 11

112

Kkkij

kKk

ijKij

mEjHkkHi

mE

jHkkHijHimM

H2 direct transitions K0 K0 (ΔS=2)

H1 weak Hamiltonian (ΔS=1)

LSLSLS

LSLSLS

im

tKtKi

2

)()(2

ΓM

Effective Hamiltonian H (non-Hermitian) decomposed into a Hermitian part (mass matrix M) and an anti-Hermitian part (i2 decay matrix Γ)


mm

HH

HH

K

KK HH

2221

1211

0

0

01

10CP If CP symmetry is valid [HCP] = 0

0

0

mmm

mmm

K

K

H Mass shift m0 and split Δm = 2δm

Case of CP symmetry

H11 = H22 = m0 H12 = H21 = δm

K0HK0 = K0H CPK0 = K0CP HK0 = K0HK0


Decays m0 and δm have an imaginary part


Eigenstates

22

11

KKCP

KKCP

21 KKKK LS

00 )1( KKCP Choose (arbitrary phase convention)

Since C is violated in Nature physical states need not be C eigenstates or members of a degenerate C-conjugate pairEnter CP instead

Since 00 LJJ

CPCP

Very different (Q-valuesmK) 0432 vs 0157 (Q = 215 MeV vs Q = 78 MeV) τ(ππ) laquo τ(πππ)

one identifiedCP conserved (commutes with H) physical states = CP eigenstates

K1K2 = 0

CP symmetric case



Time evolutionDual description(1) K0 and K0 strangeness eigenstates

π ndashp ΛK0 K+n pK [strong interactions]

(2) K1 and K2 physical states (definite mass and lifetime) and CP

[weak interactions])0()0()(

)0()0()(

2)(

22

1)(

11

222

111

KeKetK

KeKetKtimitiE

timitiE

002

001

2

12

1

KKK

KKK

Uncoupled time evolution

1212 Re2Re2 Mm

Δm = m(KL) - m(KS) = (3483 plusmn 0007) middot 10-

6 eV

Arises from tiny difference in (weak) interactions of K1K2

Measured through oscillations eg (K+n K0p) K0 K0 (K0p Λπ+) or regeneration

CP symmetric case


Neutral K hadronic decaysand CP violation


Brookhaven AD 1963

ldquoThe probability that the peak arises purely as a statistical fluctuation is asymp 10minus6 rdquoldquoThe possibility of interpreting the events as two-pion decays of K2

0 which would be allowed if CP invariance were violated is excluded by the result of observation of 411 K2

0 decays in cloud chambers56 none of which were consistent with two-pion decaysrdquo

A new coherent regeneration mechanism


The experimentbull 30 GeV p on Be target

neutral beam ~ 1 GeVc 30degbull Pb absorber collimator sweepingbull ldquoHe bagrdquo after 17 m

(βγcτ ~ 23 cm only KL left)bull Two-arm spark chamber

spectrometer triggered by H20 Čerenkov counter and scintillators

bull Measure invariant mass and pT of π+πminus pair (3-body decays do not give peak)

bull Calibration with thick tungsten regenerator and anti-coincidence

Experiment to study the anomalous forward regeneration found by Leipuner et al at the 30 GeV synchrotron

Secondary part of the program improve limits on KL ππ

JH Christenson JW Cronin

VL Fitch R Turlay (1964)

Spark chambers higher track resolution and selective triggering


(45 plusmn 9)22700

After 6 months of scrutiny reject alternative explanations Coherent regeneration in He 3-body πμν or πeν decay ππ decay

R Turlayrsquos first notice

fall 1963

Letter of Intent April 1963Agreement of BNL directorate May 1963Apparatus ready June 2nd 196340 days+nights of running end July 1963


Evidence of CP SYMMETRY

VIOLATIONNobel Prize 1980

There exists a pair (KSKL) of non-degenerate states (Δmne0) one of them decaying into two states with opposite CP

New York Times August 6th 1964 ldquoHigh energy physics experiment finds time reversal may affect physics lawsrdquo

Conclusive proof KS - KL interference studying the ππ decay rate in vacuum and with regenerator V Fitch et al (BNL 1965)

ldquohellip a purely experimental discovery a discovery for which there were no precursive indications either theoretical or experimentalrdquo (V Fitch)

310)4002()(

)(

chargedKBR

KBR

L

L


The new paradigm

K0

K0

K0

K0

Present in Nature Absent in Nature

CP

Physical states (definite mass lifetime) are not CP eigenstates KSKL ne K1K2

KL is a coherent superposition of strangeness eigenstates with a tiny (0002) unbalance in favour of K0

CP invariance as a near ldquomissrdquo


K0 K0 Eigenstates of strangeness produced by strong interactions particle anti-particle pair (equal masses by CPT) common decay modes (not orthogonal) not defined lifetime (non-exponential decay)

K1 K2 Eigenstates of CP almost coincident with physical states not particle-antiparticle pair different masses and (almost completely) decay modes almost orthogonal

KS KL Physical states not particle-antiparticle pair different masses and (almost completely) decay modes almost orthogonal

ldquohellip there is scarcely a physical system which contains so many of the elements of modern physicsrdquo(V Fitch 1980)


Physical states

00

22

00

22

)1()1(

12

1

)1()1(

12

1

KKK

KKK

L

S

00

2122

00

2212

)1()1(12

1

1

1

)1()1(12

1

1

1

KKKKK

KKKKK

LL

L

L

L

L

SS

S

S

S

S

2)(

2)(

SL

LS

The physical states (definite mass and lifetime) are still ldquoalmostrdquo CP eigenstates

If εSεL ne 0 CP symmetry is not valid (physical states ne CP eigenstates)

Im2Re2 iKK SL 7 parameters λSL(4) Re(ε) δ(2)


If ε ne 0 T symmetry is violated

M12 ne M21 Γ12 ne Γ21

)2(2

)()(

2

Im)2(Im 112211221212

im

iMM

mi

iM

Diagonalizing the effective Hamiltonian

Note 1 Definitions Δm mL-mS gt 0 and ΔΓ ΓS-ΓL gt 0

Note 2 the phase of ε is not physical only its real part is

If ε ne 0 or δ ne 0 CP symmetry is violated (physical states are not CP eigenstates)

If δ ne 0 CPT symmetryis violated

M11 ne M22 Γ11 ne Γ22

Re(ε) really

[δ=0 assumed herafter]


The measurement of direct CP violation


The superweak hypotesis

34

2

2102

p

p

F

F

FSW

m

m

G

G

m

G

m

G

L Wolfenstein (1964)A hypotetical new interaction inducing K0K0 transitions (ΔS=2) in first order with coupling ~ 10-7 GF () could explain the effect and be practically undetectable anywhere else

It would appear as a property of the physical states KSKL

(indirect CP violation)Not a real dynamical hypotesis more an ansatz which only failed after 35 years of scrutiny

2

Im)2(Im 1212

mi

iM


Types of CP violation (1)

CP violation in ΔS=2 transitions is called

INDIRECT CP VIOLATIONINDIRECT CP VIOLATION

CP violation in ΔS=1 interactions is calledDIRECT CP VIOLATIONDIRECT CP VIOLATION



CP violation due to the CP-impurity (ε) in the physical states determined by K0-K0 virtual transitions is named

CP VIOLATION IN THE MIXINGCP VIOLATION IN THE MIXING

It is indirect CP violation(arising in the effective Hamiltonian H)

KL K2+ ε K1

ππ

Actually proportional to Re(ε)


CP violation in a physical decay process is named

CP VIOLATION IN THE DECAYCP VIOLATION IN THE DECAY

It is direct CP violation (arising in the (weak) interaction driving the decay)

KL K2+ ε K1

ππ

Transition from a CP eigenstate to another one with opposite eigenvalue

K2 (CP=-1) ππ (CP=+1)

It reveals an intrinsic property of the weak interactions (as opposed to a property of the peculiar decaying states)

It requires at least 2 interfering amplitudes with different (weak) phases AND different FSI (strong) phases

of comparable magnitude to have large effects

Not present in the superweak scenario


This is named

CP VIOLATION IN THE INTERFERENCE CP VIOLATION IN THE INTERFERENCE OF MIXING AND DECAYOF MIXING AND DECAY

For a single decay mode it cannot be unambiguously called direct or indirect

K0 ππ

K0

A non flavour-specific final state is accessible to both K0 and K0

The decay can occur both with and without strangeness oscillation

If the mixing and decay phases are different the two amplitude can result in CP violation

Mixing phase(indirect)

Decay phase

(direct)


Different weak phases CP violation

Different strong phases interference

Isospin I=0

Isospin I=2

ISOSPIN BASISPHYSICAL

(CHARGE) BASIS

CPV in decay K0 ππ

The two decay amplitudes in I=0 I=2 final states can interfere

(if they have different phases) in different ways for π+πminus and π0π0

(1) Direct CP violation is intrinsically suppressed by ΔI=12 ldquorulerdquo

(2) If η+- ne η00 different CP violation in different decay modes

(3) The strong phases are actually known experimentally from Fermi-Watson theorem they are the ππ elastic scattering phase shifts


CP violation in K0 ππ

221

2

)(

)(

21

)(

)(

00

00

000000

S

Li

S

Li

KA

KAe

KA

KAe

)(

0

0

2

2

0

2

0

0

02

)Re(

)Im(

)Re(

)Im(

)Re(

)Re(

2

)Re(

)Im(

iea

a

a

a

a

ai

a

ai

221

)0(

)2(

IKA

IKA

S

S

ΔI=12 ldquorulerdquo hadronic amplitudes with

ΔI gt 12 are smaller Γ(K+π+π0) laquoΓ(KSπ+π-)


Direct CP violationFor 35 years 35 years CP violation seen only in K0ππ decays (despite impressive experimental campaign) and described by a single parameter (ε) related to K0-K0 virtual mixing

Compatible with a ldquosuperweakrdquo ansatzThe K0 system exhibits an extremely tiny mass difference

The SM (not superweak) emerged Still no other sign of CPV elsewhere

Questions

Is CP violation really a universal property of weak interactionsIs it a peculiarity of the bizarre K0 systemIs it something related to particle mixtures or does it occur in other weak processes (eg weak particle decays)Is the way CPV is ldquoaccomodatedrdquo in the SM (CKM) sound

ldquoAt present our experimental understanding of CP violation can be summarized by the statement of a single numberrdquo (J Cronin 10121980)


Searching for direct CPV

Any difference in CP violation to different final states cannot be ascribed to an intrinsic property of the decaying system

Search for a difference between KL π+π minus and KL π0π0 ie εrsquo ne 0

First comparisons of the two modes in the late 60s εrsquo ltlt ε

Late 70s theory says εrsquoε could be significantly large and measurable

Pioneering dedicated experiments (inconclusive)

Dedicated programs at FNAL (E731) and CERN (NA31) disagreement no firm conclusion

Late 80s realize that penguin cancellations for large top mass can suppress εrsquoε to very small values


p

Target

Multi-stageCollimationCharged

particle sweeping

Dump

Neutral beam

Collimator

Production

angle

Protonenergy Beam

acceptance

Collimatorbackgroun

d

KL (+KS) beams

High energy p (~ 10-500 GeV) largest yield for pK ~ 03 pp long decay beam line (up to ~ 100 m) long decay volumes (up to ~ 100 m) long ldquoskinnyrdquo experimental setups


KS by regeneration

Coherent regeneration (transmission) same momentum and angle as incident beam

Diffractive regeneration interaction on nuclei small angle

Inelastic regeneration interaction on nucleons any angle(scattered particles can be detected)

KTeV regenerator84 10x10x2 cm2 scintillator modules (fully active) 170 cm long|Ar| ~ 003Diffractivecoherent 009Inelasticcoherent 100 before veto

KL KL + Ar KS


The double ratio methodComparing the CP-violating KL decay widths Avoid isospin factors normalize to the CP-conserving KS decay widthsmeasure and |η00|2 and |η+minus|2

Need to measure accurately four decay widthsΓ(KS π+π minus) Γ(KS π0π0) Γ(KL π+π minus) Γ(KL π0π0)

(1) Statistics BR(KL ππ) ~ 1divide2middot10-3 requires intense KL beam

(2) Systematics exploit cancellations

If concurrent π+π minus and π0π0 the K fluxes (KS ne KL) do cancel

If concurrent KS and KL detector inefficiencies (π+π minus ne π0π0) do cancel

61)Re(612

2

00

)(

)(

)(

)(00

00

2

2

00

L

S

S

L

K

K

K

K


We needΓ(Kππ) = int |M(Kππ)|2 d(PS)

We measureN(Kππ) = intEXP |M(Kππ)|2 d(PS) dt =

intEXP dt [ intEXP d(PSext)] [intEXP |M(Kππ)|2 d(PSint)]

From widths to counts

Same cuts cancellatio

n

Time dependence of cuts and response

d(PSext) d3x d3ph3

DetectorFiducial decay volume

Decay position resolution and

distortionsGeometricalacceptance

Position scale

Momentum

scale

Transversemomentum cut


Direct CPV 1996 AD

FNAL E731

CERN NA31Re(εrsquoε) = (74plusmn60) middot 10-4

Not disproving superweak

Re(εrsquoε) = (230plusmn65) middot 10-4

Inconsistent with superweak


The presshellip


The new fixed-target experiments

bull KTeV at FNAL (evolution of E731) 12 institutions (USA Japan) about 100 physicists

bull NA48 at CERN (evolution of NA31) 16 European institutions about 130 physicists

bull Started at end of 80s data-taking in late 90s first results in 1999bull All 4 modes collected simultaneouslybull Higher beam intensitiesbull Faster detectors and readout (pile-up)bull Important RampD on several aspectsbull Higher-resolution detectors (calorimetry) stabilitybull Large DAQ bandwidths and fast triggersbull Goal reaching 1divide2middot10minus4 precision on εrsquoε


KTeV at Fermilab

Main Injector (120 GeV) pDouble KL beam (ltpgt=70 GeVc)Regenerated KS Pure CsI calorimeterData taking in 1997 and 1999


NA48 at CERN

SPS (450 GeV) pKS and KL beams (ltpgt=100 GeVc)KS tagging by time-of-flightLiquid Krypton calorimeterData-taking 1998-1999-2001


Direct CP violation rsquo

600

00

10)820045()()(

)()(

KK

KK

1999 proof of direct CP violation (after 36 years) at gt7 σ

NA48 (1997-2001) final resultKTeV (1997-1999) frac12 statistics (1997)KLOE working (interferometry)χ2=623 consistency 10Room for improvement

Re(rsquo) = (163plusmn 22) middot 10-

4

World average

After the KTeV and NA48 results the NA31 collaboration received the 2005 EPS prize for what is a posteriori recognized as the first evidence of direct CP violation


Date of new measurements

Theoretical predictions (SM)

rsquo why

TheoryConsistent with SMNo Yes MaybehellipSM is accidentally a quasi-superweak modelWaiting for lattice QCD rsquo may become a quantitative test of SM

The qualitative importance of rsquo ne 0 trascends the theoretical difficulties of computing such parameter in the Standard Model

bull CP violation no longer described by a single number

bull It is a property of weak interactions (no superweak)

bull It is not a peculiarity of neutral K mesons (see also B-mesons sin2β in 1999)

bull Qualitative confirmation of CKM paradigm


Other ways of measuringCP violation


K decays

Relatively few major branching ratios several in the 10 range (compare B)A ldquosimplerdquo system

(PDG2004)


Searching for CP violation

For kaons

Transitions among CP eigenstates with opposite eigenvalues

K2ππ

Search for physical states not being CP eigenstates (non-exponential decay of CP eigenstates)

KL ππ andKL πππ

Differences in the partial decay widths or decay properties of particles and antiparticles

ΔΓ(K3π)Δg(K3π)

Test of time-reversibility (plus CPT) P(K0K0) neP(K0K0)

Measure of non-zero CP-odd quantities PT(Kμ3)


ss pairs produced by strong and EM interactions

(1) Wider range of experimental approaches possible with K (experiments with flavour and physical eigenstates possibility of beams stopped K)

(2) Short B lifetime poses considerable experimental challenges

(3) Higher mass is an advantage for ldquofactoriesrdquo

(4) B have many more final states available (more rich more complicated much smaller BR higher backgrounds)

(5) CPV effects of the same size (in the SM) asymmetries on suppressed decays can be larger in B

(6) All 3 types of CPV observed in K ldquodecayrdquo and ldquointerferencerdquo types in B (ldquomixingrdquo type is dominant in K and negligible in B) TRV also observed in K

(7) In a larger number of cases the higher mass B allow better theoretical control and extraction of SM parameters (sin2β vs ε)

K vs B


(A) Experimenting with strangeness eigenstates

(Compare to B experiments at hadron machines CDFD0 LHC-b)


Hadronic production strangeness eigenstates

By exploiting specific reactions strangeness tagging at production is possiblepp K+K0πminus and pp KminusK0π+ (04 of σtot(pp) at rest)

200

200

200

200

KeKKeK

KeKKeKA

iHtiHt

iHtiHt

T

Known strangeness at production timeMeasure strangeness (πeν) or CP (ππ) at decay time

20

20

20

20

KefKef

KefKefA

iHtCP

iHtCP

iHtCP

iHtCP

CP

200

200

200

200

KeKKeK

KeKKeKA

iHtiHt

iHtiHt

CPT

T violation(Kabir test)

CPT violationCP violation parameters


CPLEAR experiment

(CERN 1990-96)

Lifetime resolution5-10 fs (with tracks)70 fs (π0π0)

5times109 events collected

Interaction at rest 4π detectorKaon ID Čerenkov dEdx time-of-flightTracking r ~ 20 λS ~ 60 cmMinimize material (regeneration)ldquoHighrdquo rate (1 MHz) fast trigger

26 GeV p on targetCollect 36 GeVc p store decelerate and cool them down to 200 MeVc106 ps in 1 h spills


tf

ft

f

iHtCP

iHtCP

iHtCP

iHtCP

CPLS

LS

e

mte

KefKef

KefKefA

)(2

2)(

20

20

20

20

1

)cos(2)Re(2

π+π

minus

π0π0

π+π minusπ0

π0π0π0

CPLEARAsymmetrie

s

Non flavour-specific final states

Rate difference

Acceptance cancellation

Measure η


(B) Experimenting with correlated K pairs

(Compare to B factory experiments Babar Belle)


Kaon factories

e+eminus Φ KK at resonance σ = 31 μbJPC(Φ) = 1minusminus C(KK) = -1 coherent state

(ΦKKγ opposite C negligible)Bose statistics Even with strangeness oscillations

the two K have to be always distinct (until one decays) ie KSKL or K0K0 (and K+Kminus) but never KSKS K0K0hellip

pppp 2

1SLSL KKKKi

bullTagging observation of KS(KL) signals presence of KL(KS) unique ldquoKS beamrdquo (almost monochromatic kinematical constraints)

Absolute BR measurementsRare KS decay searches

bullQM correlation allows interference measurements

[Lipkin (1968)]

EPR correlation


DAΦNE (Frascati)


DAΦNE (Frascati)

bull e+eminus collider s = m(Φ) = 10194 MeVbull 2 interaction regions (KLOE ndash DEARFINUDA)bull Separate e+ eminus rings to minimize beam-beam interactionsbull Crossing angle 125 mrad ( p(Φ) 125

MeVc)

Design luminosity 5middot1032 cmminus2 sminus1

(141 reached so far)

Integrated luminosity ~ 23 fb-1 1999-2006(7 middot 109 Φ decays)


Be beam pipeSpherical small (10 cm ) thin (05 mm)Instrumented permanent magnet quadrupoles Drift chamberLight (MS) large (tracking)

Electromagnetic calorimeter Inside coil hermeticity high resolution in E and time

Superconducting coil (B = 052 T)

KLOE experimentK+K- 15 106 pb-1

p = 127 MeVcλ = 95 cm

KLKS 106 pb-1

p = 110 MeVcλS = 6 mm KS decays near interaction point

λL = 34 m Need large detector (r ~ 03 λL)


KLOE physics

bullldquoKS beamrdquoRare decays (incl CP-violating KS π0π0π0 KS πℓν and its CP-violating charge asymmetry)Cabibbo angle

bullldquoKL beamrdquoBranching ratios lifetimeCabibbo angle

bullldquoKS and KLrdquoDirect CP violation (double ratio method)

bullldquoEntangled KS and KLrdquoCP T CPT tests QM tests

bullldquoKplusmn beamsrdquoBranching ratios lifetimeDirect CP violation searches

More indirect CP CPT tests


(C) Experimenting with charged K beams


CPV in charged K decays

Direct CP violation seen in K0look for CPV in charged particle decays (no mixing any CPV is direct)

Any difference among K+ and Kminus CP violation(except when equality is enforced by CPT eg total decay widths)


Hadronic production charged K

Kplusmn beams readily obtained as secondary beamsMagnetic selection based on charge and momentum

unseparated positive beam contains pπ+K+μ+e+hellip (πK ~ 01)

K can be tagged by velocity measurement eg TOF or ČerenkovBeams can be separated to enrich K component with

Electrostatic separators asymp 1 GeVcRF separators (Panofsky) asymp 10-60 GeVc

to obtain eg Kπ ~ 3 to 10

p

Target

Collimator

Charge-momentum selection

Focusing quadrupoles

Dump

Tagging Separation

Charged beam


CP violation in KCP violation in Kππ33 (why) (why)

No intrinsic ΔI=12 amplitude suppression (as for εrsquoε)

Buthellip

Hadronic uncertainties

Small rescattering phases

rarr Small in SM

Width asymmetries suppressed

2π (εrsquoε)

3π (Ag)

Kplusmn rarr μplusmn

ν

Kplusmn rarr πplusmn

π0

Kplusmn rarr 3π


KKππ33 decays decays

BR(Kplusmnplusmn+) = 557 BR(Kplusmnplusmn00) = 173

π1

π2

π3

K

Kplusmnplusmn+ g = minus02154 plusmn 00035Kplusmnplusmn00 g = 0652 plusmn 0031 |h| |k| ltlt |g|

Kinematics

si = (PKminusPi)2 i=123 (3=odd )s0 = (s1+s2+s3)3

u = (s3minuss0)m2 = 2mK (mK3minusEodd)m

2

v = (s2minuss1)m2 = 2mK(E1minusE2)m

2

Matrix element

|M(uv)|2 ~ 1 + gu + hu2 + kv2

ldquochargedrdquo ldquoneutralrdquo

Naiumlve Taylor expansion


CP violation in KCP violation in Kππ33

Ag = (g+minusgminus)(g++gminus) ne 0

Potentially large statisticsSimple selectionLow backgrounds

KminusK+

neNo absolute K flux measurement compare only Dalitz plot shapes

NA482 (2003-04) NA482 (2003-04) maximal cancellations (robustness)maximal cancellations (robustness)

ndash Simultaneous K+ and Kminus beams superimposed in space with narrow momentum spectra

ndash Detect asymmetry only from slopes of ratios of normalized u distributions

ndash Equalize averaged K+ and Kndash acceptances by frequently alternating polarities of relevant magnets


KKplusmnplusmn asymmetries status asymmetries status

10-6

NA482 OKA

10-5

10-4

10-3

10-2

SMSM

SUSYSUSYNewNew

physicsphysics

HyperCP prelim (2000) (ldquochargedrdquo)TNF (2004) (ldquoneutralrdquo)

Ford et al (1970) (ldquochargedrdquo)Smith et al (1975) (ldquoneutralrdquo)

|Ag|

bull Ag ~ 10minus5

Compatible with SMbull Ag gt 1∙10minus4

SUSY New Physics

THEORY

SM contribution many theoretical computations from several groupsLarge uncertainties (~1 order of magnitude)esp for ldquoneutralrdquo

Some enhancements possible beyond SM

C

N


SM contribution (Prades et al)

=Ag


NA482 beamsNA482 beamsPK spectra 603 GeVc

54 60 66

1cm

50 100

10 cm

200 250 m

He tank+ spectrometer

bull Momentum selection

bull Focusingbull sweeping

bull Cleaningbull Beam spectrometer (07)

~11012

ppp

K+

Kminus

Beams coincide within ~1mm

all along 114m decay volume

always in vacuum

focusing beams

BM

z

magnet

vacuum tank

not to scale

K+

K

2 divide 3 M Kspill (πK ~ 12) π decay products stay in

pipe

0ordm prodangle

1011 K decays per year collected


Detector asymmetry cancellationDetector asymmetry cancellation

N(A+B+K+)N(A+B-K-)RUS=

Detector left-riDetector left-rigght asymmetry cancelsht asymmetry cancelsin 4 ratios of in 4 ratios of KK++ over over KK u distributions u distributions

ZZ

XXYY

JuraJura

SaleveSaleve

Beam line K+ Up

Beam line Kminus Down

B+

Bminus

Indexes correspond to- beamline polarity (U D)- direction of kaon deviation in spectrometer (S J)

(same deviation by spectrometer in numerator and denominator)

N(A+B-K+)N(A+B+K-)RUJ=

N(A-B+K+)N(A-B-K-)RDS=

N(A-B-K+)N(A-B+K-)RDJ=

Spectrometer field

K+

Kminus

Reverse each day

Reverse each week

MS Sozzi K physics Zuoz 1872006U

|V| even pion

in beam pipe

Data-taking 2003-04 3x103x1099 events selected (K+ Kminus asymp 18)

KK+ +

KK

odd pionin beam pipe

MM=17 MeVc=17 MeVc22

No significant

background

Magnetic spectrometer only

NA482 ππplusmnplusmnππ++ππ-- modemode


NA482 NA482 ππplusmnplusmnππ00ππ00 mode modev

-15 -10 -05 0 05 10 u

0

-1

-2

1

2

3

Dalitz plot

Kplusmn πplusmnπ0π0 also available lower statistics comparable sensitivity

Kinematic variable reconstructed from π0π0 only calorimeter used ndash complementary

EM calorimeter only


NA482 CPV asymmetry results

Kplusmnπplusmnπ+πminus mode full statistics31middot109 decays

Preliminary result on full statistics (2003+04)

Ag = (-13plusmn23)middot10-4

2003 result in PLB 634 (2006) 474

Kplusmnπplusmnπ-π0 mode full statistics011middot109 decays


Ag = (21plusmn19)middot10-4

2003 result in PLB 638 (2006) 22

Errors dominated by statistics No CPV foundNP window ldquoclosedrdquo part of SUSY model parameter space

excluded


OKA at Protvino

Alternate beam charge

Program Vus radiative and rare decays 3π asymmetries T-odd correlations hellip

RF-separated charged K beam in preparation at U-70 PS in Protvino1013 ppp (70 GeV)8middot106 particlespulse (gt50 K)15 GeVc K+ or K- alternated Commissioning for OKA experiment

Using CERN-Karlsruhe SC cavities

(in preparation)


More CP violation


Indirect

Direct

CP violation

parameters

(2005)


(A) KS decays


CPV in KS decays

Recall π0π0π0 is CP-odd π+πminusπ0 is predominantly CP-oddKS π0π0π0 (I=13) would indicate (mostly indirect) CP violation

SM prediction ΓS(3π) asymp ΓL(3π)|η|2 or

BR(KS 3π0) asymp BR(KL 3π0) |ε|2 (τSτL) asymp 19middot10minus9

000000

000

000 )(

)(

L

S

KA

KA εrsquo000 estimated to be of same order of εrsquo


KS π0π0π0 at hadron machines K

S+KL

KL

NA48 ldquocloserdquo to production target look for interfering KSKLπ0π0π0

starting from a mixture of K0K0

Take ratio with a KL run (ldquofar targetrdquo) to cancel acceptance and efficiencies

000 000 00

1( )2 ( 2

0

)

( )

( ) 1 2 ( ) cos sinRe ImL SL S

tt

NEARf E t

FARA E e D E e mt mt

ldquoDilution factorrdquo )()(

)()()( 00

00

EKNEKN

EKNEKNED

(incoherent

production)

NA481 Near target beam 49middot106 3π0

Far target beam 109middot106 3π0

Assuming CPT

BR(KS30) lt 2310minus7 (90 CL)


KS π0π0π0 at KLOE

N2BR(KS 000) = BR(KS 00) lt 12 10minus7

N3

20

40

60

00

4 62

|η000| lt 18middot10minus2 at 90 CL

No CPV seen yet

450 pb-1 (2001+2002 data)Kinematic fit to 2π0 and 3π0

2 signal events w 313082stat037syst expected background N(3π0) lt 345 at 90 CL


(B) Semi-leptonic charge asymmetries


Semi-leptonic charge asymmetry

Also KS semi-leptonic decays first detected by KLOEBR(KSrarrπeν) asymp 7middot10-4 (KSrarrπμν also observed at KLOE)charge asymmetry expected to be equal to KL one by CPT

KLOE (2006) δS(e) = (15 plusmn 96 plusmn 29) middot 10-3

(410 pb-1 data still far from significative CPT test)

Indirect CP violation2divide3 middot108 events (KTeV NA48)L(e) = (332 007) 10-3

It measures ε (hard to compute input for

theory) systematics limited


(C) T-odd correlations


T-odd correlations (1)

Tri-linear quantities such as patimespbsa are odd under T

Muon polarization transverse to the decay plane in KL rarr π+μ-ν decay or K+ rarr π0μ+ν decay

Effect arises from relative phase of two form factors ξ = fndashf+ (Im ξ ne 0 is T-violating)

Muon decay mode because fndash is proportional to lepton mass

FSI can fake the effect more relevant for KL (limit reached in the 70s) K+ also allows stopped K technique


T- violation KEK E246

KEK E246 660 MeVc K+ stopped in active fibre targetFinal result (83M 0 decays 1996-2000)

PT() = (-17 23 11) 10-

3

Im = (-53 71 36) 10-3

Experiment concluded Also 105 decays (larger background different sensitivity to New Physics) in 1996-98 Plans for improved experiment (x10) at J-PARC

T-violation first measured by CPLEAR compatible with indirect CP violation

PT() orthogonal to decay plane in 3-body decays (T-odd correlation) Tiny FSI (EM) in SM sensitive to New PhysicsStopped K experiments systematics from detector mis-alignment magnetic fields asymmetries and (large) in-plane polarization

Im = (-53 71 36) 10-3


T-odd correlations (2)Tri-linear quantities such as patimespbsa are odd under TTo avoid measuring polarizations patimespbpc but need 4-body final state

Ke4 (Kππeν) BR asymp 4middot10minus5 or

Ke3γ (K πeνγ) BR asymp 3middot10minus4

Final State Interactions can contribute Aξ asymp (05-1)middot10minus4 in the SMNP models Aξ asymp few 10minus4

ISTRA+ (2005) Aξ = 0015 plusmn 0021 (1400 events)OKA NA482 gt104 eventsNA482 Cancellation of FSI effects by K+Kminus comparison ()

ISTRA+ (2006) BR(K πμνγ) asymp 9middot10minus5 Aξ = -003 plusmn 013 (400 events)

ppp

ppp

)0()0(

)0()0(

NN

NNA


Radiative decays


K ππTwo classes of contributions

Inner bremsstrahlung (IB)

Direct emission (DE)

IB computed by QED proportional to the corresponding ππ decay usually dominant 1q bremsstrahlung spectrum for peaked at low E

DE depends on the details of the K

Depending on the multipolarity of the EM radiation the decay can be CP-conserving or CP-violating MqppEqppqppqA

211221 )()(

ldquoelectricrdquo (IB+DE) ldquomagneticrdquo (DE)

IB DE

p1 p1

p2p2

q q


CP-violation asymmetries require two interfering amplitudes one CP-conserving and one CP-violating

When summing over (unmeasured) helicities E and M do not interfere IB can interfere with the electric part of DE

Considering lowest order (dipole E1 M1) ππ (electric) is CP-even

KS π+πminus dominated by IBππ (magnetic) is CP-odd

KL π+πminus the M1 DE can compete with the CP-violating IB

)(

)(

S

L

KA

violatingCPKA

KS-KL CPV interference arises largely from interference of the two E1 IBin this case η+minus = η+minus

If an E1 DE component (CP-violating) is present for KL it can interfere with the (CP-conserving) E1 IB and modify η+minus (direct CP violation)


KL π+πminus

FNAL E731 (1995)8K events fitted after regenerator

|η+minus| = (2359 plusmn 0062)middot10minus3

φ+minus = (438 plusmn 35)degFully consistent with η+minus|εrsquo+minus||ε| lt 03 (90 CL)

New KTeV direct measurement (2006 40 data sample) 112middot103 events

DE(IB+DE) = 0689 plusmn 0021for Eγ gt 20 MeV

IB

M1 DE


CPV inner bremsstrahlung CPC direct emission

CPV direct emission Charge radius

KL itself

Interference gives indirect CP-violating asymmetry in the orientation of and ee decay planes large ( 14) asymmetry predicted

If one would observe helicity interference among E1 IB (CPV) and M1 DE (CPC) ndash of comparable magnitude - could be observed

In e+eminus the lepton plane orientation is correlated to the photon helicity (cmp π0 parity determination)


KL ee

KTeV first observationand NA48

BR = (308 020) 10minus7

KTeV full data set5200 events(4 background)

E1 DE term (if any) is small

E1M1 lt 004 (90 CL)


KL ee and CPVAsymmetry in angle φ between ππ and ee planes in agreement with theory (indirect CPV)

φ

AΦ = (138 plusmn 22)

KTeV and NA48 average


KS ee

No asymmetry for KS

as expected

BR = (471 032) 10-

5

AΦ = (05 43)

NA48 first observation600 eventsBackground = 01


Kplusmn π+π0γBR ~ 3middot10minus4 Similar to previous cases IB dominates DE measured interference term not yet

INT term could give CPV asymmetry

|εrsquo+0γ| lt~ 10minus4

IBEE

dEA

)tan( 0


Kplusmn π+π0γ

)730810672()(

)250350353()(

800

800

syststatMeVT

syststatMeVT

INTFrac

DEFrac

NA482 (2006) First indication of INT

Separation by photon spectrum


KL π0π0γDE only lowest possible multipole is E2 Not observed yetExpectations BR ~ 7middot10minus11 at first O(p6) order in CHPT

New KTeV limit (2006) BR lt 252 middot 10-7 (90 CL)(0 events found 166 plusmn 059 expected background)


KL π+πndashπ0γ

Dominated by IBExpectations BR ~ 17 middot 10minus4 (Eγ gt 10 MeV)

First observation by KTeV (2006) BR = (170 plusmn 003 plusmn 004 plusmn 003) middot 10-4

(preliminary 5700 candidates)

KL π+πndashπ0e+endash

First observation by KTeV (2006) BR = (160 plusmn 018) middot 10-7



Radiative semileptonic decays

ndash KL and Ksemileptonic radiative decays give information on kaon structure

ndash Ratio R (with constraints to avoid divergences) is predicted to be between 095 and 099

ndash Theoretical approachesbull Current algebra (Fearing Fischbach Smith) (Doncel)

bull PT (continuosly improved) latest estimate (096001)

ndash A recent measurement from KTeV gives R=(09080008+0013

-0012) in disagreement with the prediction

)(

)2030(

3

3

e

ee

K

MeVEKR

In K also T-odd variables CPVhellip


Radiative semileptonicsndash NA48 results

bull 10K Ke3g events

bull 6M Ke3 events

bull Less than 1 background

ndash R=(0964plusmn0008+0011-0009)

ndash In full agreement with the predictions

ndash Analysis in progress by NA48 on Kplusmn radiative semileptonic decay


Non CPV physics from K


|Vud|2 + |Vus|2 + |Vub|2 ~ |Vud|2 + |Vus|2 1 ndash

|Vud|2 = 09483plusmn00010 (nuclear decays)

|Vus|2 = 00482plusmn00010 (K semi-leptonic decays)

|Vub|2 = 0000011plusmn0000003 (B meson decays)

Unitarity of CKM matrix tests existence of extra quark generations and possible existence of new physics

Most precise test of unitarity from 1st row

PDG 2004

|Vud|2 + |Vus|2 + |Vub|2 = 0 9965plusmn00015(~ 23 deviation)

Vus and CKM unitarity test

Situation called for more precise K (and nuclear) measurements


Vus (the Cabibbo angle)

Rate from experiment

]21[192 3

52

KmG

Form factor at 0 momentum

transferpurely from theory

EW Isospin-breaking EM corrections few percent

Form factor slopes from experiment

Phase space integral


Vus measurements

lsaquo |Vus|timesf+(0) rsaquo WORLD AVG = 02164(4)

CKM matrix unitary within ~ 1σ

Black pre-2004measurements


unitarity

Using fK f from Lattice QCD

(MILC 2005) and KLOE BR(K+ μ+ν) VusVud = 02294 00026

Fit of the above results Vus = 02242 00016 Vud = 097377 000027

Fit assuming unitarity Vus = 02264 00009

KLOE Kl 3

KLOE K2

copy A Antonelli

Vus some more


K+rarrπ+π-eν (Ke4) decays


Ke4 results

Extraction of well predicted (a2-a0) QCD parameter (difference of S-wave ππ scattering lengths)

using theoretical input

New NA482 prelim (350K events) a0 = 0256plusmn0008plusmn0007plusmn0018 and a2 = -0031plusmn0015plusmn0015plusmn0009


K+rarrπ0π0eν

Only 1 form factor in this caseNew measurement by NA482 (2006)

(9600 events) Form factors (37K events) consistent with charged Ke4

5004 10)0290019002605872()( extsyststateKBR


ππ scattering in Krarr3π decays

NA482 Kplusmn rarrπplusmnπ0π0 events

Pion scattering effect



1-loop rescattering

2-loop rescattering

2-loop rescattering + pionium

2-loop rescattering not fitting cusp region

Stimulated much theoretical work (Cabibbo Isidori Gasser et al Scimemi et al) NA482



The magnitude of the discontinuity (cusp) is directly related to the (a0-a2) difference in ππ scattering lengths

(a0-a2)mπ = 0268 plusmn 0010 plusmn 0004 plusmn 0013

a2 mπ = 0041 plusmn 0022 plusmn 0014

This new approach potentially very powerful is alternative to the one using Ke4 and the one using ionization of pionium (DIRAC experiment at CERN)

Evidence for pionium formation sensitivity to higher-order effectshellip

NA482


Tests of QM with correlated KK


KLOE interference


The new frontierultra-rare FCNC K decays


The (new) holy grail K ℓℓ(1) Semileptonic main problem of estimating matrix element

avoided (using known Kℓ3)

(2) Short distance physics dominates in loop perturbative SM under control at NLO very sensitive to New Physics

(3) For ℓ = ν no long-distance contributions from γγ

(4) For KL (and ℓ = ν) CP-violating only top loop contributing (very accurate prediction)


K ℓℓExperimental problems

BR 10-11 few (or no) kinematic constraints backgrounds with BR x 107

Dedicated experiments required

KL 0e+e 10-11 (CPVdir 3middot10-12) lt 28 middot10-10

(FNAL KTeV)CPC+CPV eeγγ bkg3 ev (205 bkg)

KL 0μ+μ 10-11 (CPVdir 1middot10-12) lt 38 middot10-10

(FNAL KTeV)CPC+CPV2 ev (087 bkg)

K+ + 8middot10-11 (at 7)147+130

ndash089 middot 10-

10 (BNL E787+E949)

Dedicated expt3 evt (bkg 045)

KL 0 28middot10-11 (at 2)lt 59 middot10-7 (KTeV Dalitz decay)

CPV dirldquoNothing to nothingrdquo


Complex situation 3 contributions

KL 0ℓ+ℓ-

8242120 10)Im(8210)Im(8631510)( ttSSCPVL aaeeKBR

tdtst VV 511Sa measured by KS (sign )

KTeV limits (90 CL) BR(KL 0e+e-) lt 2810-10

BR(KL 0+-) lt 3810-10

bull CP-allowed not predictedderived from KL 0γγ (NA48KTeV)

bull Indirect CP violating not predictedmeasured by KS 0ℓ+ℓ- (NA481)

bull Direct CP violating predicted and proportional to CKM phase


NA481 KS 0ℓ+ℓ-

First measurement 7 eventsBkg 015 +010

-004 (KLee and accid)

BR = (58 +28-23 plusmn08) times10-9


-012 (accid)BR = (28 +15

-12 plusmn02) times10-9

KS 0e+e- KS 0μ+μ-

Blind analysisBackground-free

NA481 preliminary

NA481 preliminary


KL 0ℓ+ℓ-

Isidori et al hep-ph0404127bullKL measurements CP-allowed contribution is small

bullKS measurements indirect CP-violating term dominates

bullSensitivity of BR to CKM phase depends on the (unmeasurable) relative sign of the two CP-violating termsTheoretical predictions constructive interferenceBR(KL 0e+e-)CPV times 1012 asymp 17 (ind) plusmn 9 (interf) + 4 (dir)

BR(KL 0μ+μ-)CPV times 1012 asymp 8 (ind) plusmn 3 (interf) + 2 (dir)


Krarr in the SM

ndash Z(γ) penguin and box diagrams

ndash Top in the loop sensitive to Vtd

ndash Small theoretical uncertainty

W W

s

id

Vis Vid

e

i=uct

W

Z

VisV

idds i

11

20

2410

10)1108(

)(1001)(

AKB

11

2

5

100

10)4082(

)()Im(

1022)(

t

tdtsL xX

VVKB


K

ε εrsquo

Unitarity triangle from K

Required ancillary measurements

VusVud+ VcsVcd+ VtsVtd = λu + λc + λt = 0

Ke3 KL 0

Height

Im(λt )


solid E949 boxdashed E787 box

10301890 10471)(

KBR

K+rarrπ+νν E787-E949 (Brookhaven)

Combined E787E949(3 events observed)

Low-energy K+ stopped in active targetTime reconstruction of πrarrμrarre decayPion range vs energy plot

Experiment no longer taking data


bull Proposal in view of approval based on NA48 detectorbull Decay in flight (75 GeV unseparated K beam)bull Background rejection

ndash K+ tracking in 1 GHzndash PID(pm) by RICHndash High E p0 low ineffndash Missing mass cut

bull Expect 80 SM eventsin 2 years(data-taking 2010)

K+ +

K+rarrπ+νν P-326 (CERN-SPS)


KLrarrπ0νν E391a pilot project (KEK)

Ran in 2004-2005From 1 week data BR lt 21 x 10-7 (90 CL)


KLrarrπ0νν Future project (J-PARC)

J-PARC proton synchrotron in construction at Tokai30 50 GeV 3x1014 ppp - First beam expected in 2008

Re-using KTeV EM calorimeter and improving E391a detectorStep 1 (2010-12) 5 SM events with shared beam lineStep 2 gt100 SM events with dedicated beam line


Conclusions ()The K system as the ldquominimal flavour laboratoryrdquo shaped the SM as we know it (P violation Cabibbo angle CP violation GIM prediction of charm direct CP violation)

As the Phoenix every time it appears to have exhausted its potential as a source of information on Nature it provides something new

Experimental investigations on it never stopped and actually keep providing a vast and diverse wealth of informationNow if only theoreticians were able to fully tame ithellip


Thank-you for your attention


BibliographyCP violation (including MUCH more than K)bull I Bigi A Sanda ndash CP violation ndash Cambridge University Press (2000)bull G Branco et al ndash CP violation ndash Oxford University Press (2000)bull K Kleinknecht ndash CP violation ndash Springer (2003)bull R Sachs ndash The physics of time reversal ndash Chicago University Pressbull Proceedings of the ldquoE Fermirdquo school Varenna ndash SIF and IOP (2006)or if you want to read more about beautiful experimentsbull MS ndash Discrete symmetries and CP violation ndash Oxford University Press (2007)

K mesonsbull R Belusevic ndash Neutral kaons ndash Springer (1999)bull The second DaΦne Physics handbook ndash INFN Frascati Italy (1995)bull KAON 2001 proceedings INFN Frascati Italy (2001)

Direct CP violation in K meson decaysbull B Winstein L Wolfenstein ndash Rev Mod Phys 65 (1993) 1113bull M S I Mannelli ndash Riv Nuovo Cim 26(1) (2003) 1 [hep-ex0312015]


Appendixes


CP-ologybull JP(K) = 0ndash bull JP(π) = 0ndash C(π0) = +1 [π0 γγ and C(γ) = -1]

bull ππ P(ππ) = P(π)2 (-1)ℓ = (-1)ℓ [π0π0 even ℓ] C(π0π0) = +1 C(π+π-) = P(π+π-) = (-1)ℓ

Exchange = CP CP(ππ) = +1bull K ππ

J(ππ) = ℓ(ππ) = 0 P(ππ) = +1 C(ππ) = +1

bull πππ |ℓ-L| le J(πππ) le |ℓ+L| P(πππ) = P(π)3 (-1)ℓ (-1)L = (-1)ℓ+L+1 [π0π0π0 even ℓ P=(-1)L+1]C(π0π0π0) = +1 C(π+π- π0) = (-1)ℓ

bull K πππ J(πππ) = 0 ℓ = L P(πππ) = -1CP(π0π0π0) = -1 CP(π+π-π0) = (-1)ℓ+1 ℓgt0 is kinematically suppressed

ℓL


The Bell-Steinberger relation

SLti

SLLSti

LS

tL

tS

Lti

LSti

S

KKeaaKKeaa

eaea

KeaKea

SLLS

LS

LS

)()(

22

f LSf

fLS KfA

dt

d 2

2

TUnitarity requires

and therefore

A relation linking CP- (and CPT-) violating parameters to all the physical decay amplitudes

f Sff

fS

fLSLLS

f

fLLf

fSS

fKAAKKmi

AA

)(2)(

22


2

22

2

222

0604

mKK

AAAA

LS

LSLS

f

fSf

fLf

fS

fL

Experimentally ΓL laquo ΓS

ΓS(Kℓ3) asymp ΓL(Kℓ3) asymp ΓL(3π) asymp 10minus3 ΓS

SLS KKmi 21

bull If CPT is valid (δ=0) φππ asymp atan(2ΔmΓS) asymp 44deg

bull If T is valid (ε=0) φππ asymp atan(2ΔmΓS) + π2

Experiment φππ = (435 plusmn 1)deg CPT is (largely) OK

)()( 0000

SSS KK

Lee-Wolfenstein relationCP violation is small (KSKL are almost orthogonal)


Outline

bull Express review of K phenomenologybull Neutral K hadronic decays and CP violation bull The measurement of direct CP violationbull More CP violationbull Radiative decaysbull Non CPV physics from Kbull The new frontier ultra-rare FCNC K decays







K0 π+π- K+ μ+ν




BUT




rate


Strangenesshellip







weirdness



11 CCCC

Defining

2)(

2)(

2

1

K

K

One gets 21

211

1 KCCKKCCK

So C(K1) = +1 C(K2) = minus1










τ(KS) = 08910ndash


=K1

=K2





)cos(24

1)]()0([

)cos(24

1)]()0([

2)(00

2)(00

2121

2121

mteeetKtKP

mteeetKtKP

ttt

ttt

Δm=m1-m2






Positrons

Electrons

Start with K0 only




(3) Regeneration






[KS=K1 KL=K2]


Regeneration











6 inch plate

combined

K1 rate



M(K0) = 4977 MeVc2


[ π0 = (uu+dd)2 = π0 ]

K0 ne K0

In terms of quarks











Two-state formalism


)0()( tiet H

ΓΓMM

ΓMH

)(2

)()( ti

ttdt

di

)(2 11

112

Kkkij

kKk

ijKij

mEjHkkHi

mE

jHkkHijHimM



LSLSLS

LSLSLS

im

tKtKi

2

)()(2

ΓM



mm

HH

HH

K

KK HH

2221

1211

0

0

01


0

0

mmm

mmm

K

K


Case of CP symmetry

H11 = H22 = m0 H12 = H21 = δm





Eigenstates

22

11

KKCP

KKCP

21 KKKK LS



Since 00 LJJ

CPCP



K1K2 = 0

CP symmetric case







)0()0()(

2)(

22

1)(

11

222

111

KeKetK

KeKetKtimitiE

timitiE

002

001

2

12

1

KKK

KKK


1212 Re2Re2 Mm


6 eV



CP symmetric case




Brookhaven AD 1963


















(45 plusmn 9)22700



fall 1963









310)4002()(

)(

chargedKBR

KBR

L

L


The new paradigm

K0

K0

K0

K0


CP










Physical states

00

22

00

22

)1()1(

12

1

)1()1(

12

1

KKK

KKK

L

S

00

2122

00

2212

)1()1(12

1

1

1

)1()1(12

1

1

1

KKKKK

KKKKK

LL

L

L

L

L

SS

S

S

S

S

2)(

2)(

SL

LS






M12 ne M21 Γ12 ne Γ21

)2(2

)()(

2

Im)2(Im 112211221212

im

iMM

mi

iM






M11 ne M22 Γ11 ne Γ22

Re(ε) really






34

2

2102

p

p

F

F

FSW

m

m

G

G

m

G

m

G




2

Im)2(Im 1212

mi

iM











KL K2+ ε K1

ππ






KL K2+ ε K1

ππ


K2 (CP=-1) ππ (CP=+1)






This is named



K0 ππ

K0





Decay phase

(direct)




Isospin I=0

Isospin I=2


(CHARGE) BASIS









221

2

)(

)(

21

)(

)(

00

00

000000

S

Li

S

Li

KA

KAe

KA

KAe

)(

0

0

2

2

0

2

0

0

02

)Re(

)Im(

)Re(

)Im(

)Re(

)Re(

2

)Re(

)Im(

iea

a

a

a

a

ai

a

ai

221

)0(

)2(

IKA

IKA

S

S







Questions













p

Target


particle sweeping

Dump

Neutral beam

Collimator

Production

angle

Protonenergy Beam

acceptance

Collimatorbackgroun

d

KL (+KS) beams



KS by regeneration





KL KL + Ar KS








61)Re(612

2

00

)(

)(

)(

)(00

00

2

2

00

L

S

S

L

K

K

K

K







n


d(PSext) d3x d3ph3




Position scale

Momentum

scale



Direct CPV 1996 AD

FNAL E731






The presshellip







KTeV at Fermilab



NA48 at CERN




600

00

10)820045()()(

)()(

KK

KK




4

World average





rsquo why










K decays


(PDG2004)



For kaons


K2ππ




ΔΓ(K3π)Δg(K3π)












K vs B







200

200

200

200

KeKKeK

KeKKeKA

iHtiHt

iHtiHt

T


20

20

20

20

KefKef

KefKefA

iHtCP

iHtCP

iHtCP

iHtCP

CP

200

200

200

200

KeKKeK

KeKKeKA

iHtiHt

iHtiHt

CPT




CPLEAR experiment

(CERN 1990-96)






tf

ft

f

iHtCP

iHtCP

iHtCP

iHtCP

CPLS

LS

e

mte

KefKef

KefKefA

)(2

2)(

20

20

20

20

1

)cos(2)Re(2

π+π

minus

π0π0

π+π minusπ0

π0π0π0

CPLEARAsymmetrie

s


Rate difference


Measure η





Kaon factories




pppp 2

1SLSL KKKKi




[Lipkin (1968)]

EPR correlation


DAΦNE (Frascati)


DAΦNE (Frascati)


MeVc)









p = 127 MeVcλ = 95 cm

KLKS 106 pb-1




KLOE physics




















p

Target

Collimator



Dump

Tagging Separation

Charged beam




Buthellip



rarr Small in SM


2π (εrsquoε)

3π (Ag)


ν


π0

Kplusmn rarr 3π




π1

π2

π3

K


Kinematics



2


2

Matrix element

|M(uv)|2 ~ 1 + gu + hu2 + kv2







KminusK+








10-6

NA482 OKA

10-5

10-4

10-3

10-2

SMSM

SUSYSUSYNewNew

physicsphysics



|Ag|

bull Ag ~ 10minus5


SUSY New Physics

THEORY



C

N



=Ag



54 60 66

1cm

50 100

10 cm

200 250 m





~11012

ppp

K+

Kminus



always in vacuum

focusing beams

BM

z

magnet

vacuum tank

not to scale

K+

K


pipe

0ordm prodangle






ZZ

XXYY

JuraJura

SaleveSaleve

Beam line K+ Up


B+

Bminus






Spectrometer field

K+

Kminus

Reverse each day

Reverse each week


|V| even pion

in beam pipe


KK+ +

KK



No significant

background





-15 -10 -05 0 05 10 u

0

-1

-2

1

2

3

Dalitz plot



EM calorimeter only






2003 result in PLB 634 (2006) 474




2003 result in PLB 638 (2006) 22


excluded


OKA at Protvino





(in preparation)


More CP violation


Indirect

Direct

CP violation

parameters

(2005)


(A) KS decays


CPV in KS decays




000000

000

000 )(

)(

L

S

KA




S+KL

KL




000 000 00

1( )2 ( 2

0

)

( )


tt

NEARf E t



)()()( 00

00

EKNEKN

EKNEKNED

(incoherent

production)



Assuming CPT





N3

20

40

60

00

4 62


No CPV seen yet

























PT() = (-17 23 11) 10-

3

Im = (-53 71 36) 10-3




Im = (-53 71 36) 10-3








ppp

ppp

)0()0(

)0()0(

NN

NNA


Radiative decays








211221 )()(


IB DE

p1 p1

p2p2

q q







)(

)(

S

L

KA

violatingCPKA




KL π+πminus






IB

M1 DE




KL itself





KL ee


BR = (308 020) 10minus7



E1M1 lt 004 (90 CL)



φ




KS ee

No asymmetry for KS

as expected

BR = (471 032) 10-

5

AΦ = (05 43)






IBEE

dEA

)tan( 0


Kplusmn π+π0γ

)730810672()(

)250350353()(

800

800

syststatMeVT

syststatMeVT

INTFrac

DEFrac







KL π+πndashπ0γ















)(

)2030(

3

3

e

ee

K

MeVEKR





bull 6M Ke3 events


ndash R=(0964plusmn0008+0011-0009)












PDG 2004







]21[192 3

52

KmG







Vus measurements





unitarity





KLOE Kl 3

KLOE K2

copy A Antonelli

Vus some more




Ke4 results





K+rarrπ0π0eν










1-loop rescattering

2-loop rescattering











NA482




KLOE interference

















K+ + 8middot10-11 (at 7)147+130

ndash089 middot 10-

10 (BNL E787+E949)






KL 0ℓ+ℓ-




BR(KL 0+-) lt 3810-10





NA481 KS 0ℓ+ℓ-



BR = (58 +28-23 plusmn08) times10-9


-012 (accid)BR = (28 +15


KS 0e+e- KS 0μ+μ-


NA481 preliminary

NA481 preliminary


KL 0ℓ+ℓ-






Krarr in the SM




W W

s

id

Vis Vid

e

i=uct

W

Z

VisV

idds i

11

20

2410

10)1108(

)(1001)(

AKB

11

2

5

100

10)4082(

)()Im(

1022)(

t

tdtsL xX

VVKB


K

ε εrsquo




Ke3 KL 0

Height

Im(λt )



10301890 10471)(

KBR









K+ +




















Appendixes





J(ππ) = ℓ(ππ) = 0 P(ππ) = +1 C(ππ) = +1



ℓL



SLti

SLLSti

LS

tL

tS

Lti

LSti

S

KKeaaKKeaa

eaea

KeaKea

SLLS

LS

LS

)()(

22

f LSf

fLS KfA

dt

d 2

2

TUnitarity requires

and therefore


f Sff

fS

fLSLLS

f

fLLf

fSS

fKAAKKmi

AA

)(2)(

22


2

22

2

222

0604

mKK

AAAA

LS

LSLS

f

fSf

fLf

fS

fL



SLS KKmi 21




)()( 0000

SSS KK








K0 π+π- K+ μ+ν




BUT




rate


Strangenesshellip







weirdness



11 CCCC

Defining

2)(

2)(

2

1

K

K

One gets 21

211

1 KCCKKCCK

So C(K1) = +1 C(K2) = minus1










τ(KS) = 08910ndash


=K1

=K2





)cos(24

1)]()0([

)cos(24

1)]()0([

2)(00

2)(00

2121

2121

mteeetKtKP

mteeetKtKP

ttt

ttt

Δm=m1-m2






Positrons

Electrons

Start with K0 only




(3) Regeneration






[KS=K1 KL=K2]


Regeneration











6 inch plate

combined

K1 rate



M(K0) = 4977 MeVc2


[ π0 = (uu+dd)2 = π0 ]

K0 ne K0

In terms of quarks











Two-state formalism


)0()( tiet H

ΓΓMM

ΓMH

)(2

)()( ti

ttdt

di

)(2 11

112

Kkkij

kKk

ijKij

mEjHkkHi

mE

jHkkHijHimM



LSLSLS

LSLSLS

im

tKtKi

2

)()(2

ΓM



mm

HH

HH

K

KK HH

2221

1211

0

0

01


0

0

mmm

mmm

K

K


Case of CP symmetry

H11 = H22 = m0 H12 = H21 = δm





Eigenstates

22

11

KKCP

KKCP

21 KKKK LS



Since 00 LJJ

CPCP



K1K2 = 0

CP symmetric case







)0()0()(

2)(

22

1)(

11

222

111

KeKetK

KeKetKtimitiE

timitiE

002

001

2

12

1

KKK

KKK


1212 Re2Re2 Mm


6 eV



CP symmetric case




Brookhaven AD 1963


















(45 plusmn 9)22700



fall 1963









310)4002()(

)(

chargedKBR

KBR

L

L


The new paradigm

K0

K0

K0

K0


CP










Physical states

00

22

00

22

)1()1(

12

1

)1()1(

12

1

KKK

KKK

L

S

00

2122

00

2212

)1()1(12

1

1

1

)1()1(12

1

1

1

KKKKK

KKKKK

LL

L

L

L

L

SS

S

S

S

S

2)(

2)(

SL

LS






M12 ne M21 Γ12 ne Γ21

)2(2

)()(

2

Im)2(Im 112211221212

im

iMM

mi

iM






M11 ne M22 Γ11 ne Γ22

Re(ε) really






34

2

2102

p

p

F

F

FSW

m

m

G

G

m

G

m

G




2

Im)2(Im 1212

mi

iM











KL K2+ ε K1

ππ






KL K2+ ε K1

ππ


K2 (CP=-1) ππ (CP=+1)






This is named



K0 ππ

K0





Decay phase

(direct)




Isospin I=0

Isospin I=2


(CHARGE) BASIS









221

2

)(

)(

21

)(

)(

00

00

000000

S

Li

S

Li

KA

KAe

KA

KAe

)(

0

0

2

2

0

2

0

0

02

)Re(

)Im(

)Re(

)Im(

)Re(

)Re(

2

)Re(

)Im(

iea

a

a

a

a

ai

a

ai

221

)0(

)2(

IKA

IKA

S

S







Questions













p

Target


particle sweeping

Dump

Neutral beam

Collimator

Production

angle

Protonenergy Beam

acceptance

Collimatorbackgroun

d

KL (+KS) beams



KS by regeneration





KL KL + Ar KS








61)Re(612

2

00

)(

)(

)(

)(00

00

2

2

00

L

S

S

L

K

K

K

K







n


d(PSext) d3x d3ph3




Position scale

Momentum

scale



Direct CPV 1996 AD

FNAL E731






The presshellip







KTeV at Fermilab



NA48 at CERN




600

00

10)820045()()(

)()(

KK

KK




4

World average





rsquo why










K decays


(PDG2004)



For kaons


K2ππ




ΔΓ(K3π)Δg(K3π)












K vs B







200

200

200

200

KeKKeK

KeKKeKA

iHtiHt

iHtiHt

T


20

20

20

20

KefKef

KefKefA

iHtCP

iHtCP

iHtCP

iHtCP

CP

200

200

200

200

KeKKeK

KeKKeKA

iHtiHt

iHtiHt

CPT




CPLEAR experiment

(CERN 1990-96)






tf

ft

f

iHtCP

iHtCP

iHtCP

iHtCP

CPLS

LS

e

mte

KefKef

KefKefA

)(2

2)(

20

20

20

20

1

)cos(2)Re(2

π+π

minus

π0π0

π+π minusπ0

π0π0π0

CPLEARAsymmetrie

s


Rate difference


Measure η





Kaon factories




pppp 2

1SLSL KKKKi




[Lipkin (1968)]

EPR correlation


DAΦNE (Frascati)


DAΦNE (Frascati)


MeVc)









p = 127 MeVcλ = 95 cm

KLKS 106 pb-1




KLOE physics




















p

Target

Collimator



Dump

Tagging Separation

Charged beam




Buthellip



rarr Small in SM


2π (εrsquoε)

3π (Ag)


ν


π0

Kplusmn rarr 3π




π1

π2

π3

K


Kinematics



2


2

Matrix element

|M(uv)|2 ~ 1 + gu + hu2 + kv2







KminusK+








10-6

NA482 OKA

10-5

10-4

10-3

10-2

SMSM

SUSYSUSYNewNew

physicsphysics



|Ag|

bull Ag ~ 10minus5


SUSY New Physics

THEORY



C

N



=Ag



54 60 66

1cm

50 100

10 cm

200 250 m





~11012

ppp

K+

Kminus



always in vacuum

focusing beams

BM

z

magnet

vacuum tank

not to scale

K+

K


pipe

0ordm prodangle






ZZ

XXYY

JuraJura

SaleveSaleve

Beam line K+ Up


B+

Bminus






Spectrometer field

K+

Kminus

Reverse each day

Reverse each week


|V| even pion

in beam pipe


KK+ +

KK



No significant

background





-15 -10 -05 0 05 10 u

0

-1

-2

1

2

3

Dalitz plot



EM calorimeter only






2003 result in PLB 634 (2006) 474




2003 result in PLB 638 (2006) 22


excluded


OKA at Protvino





(in preparation)


More CP violation


Indirect

Direct

CP violation

parameters

(2005)


(A) KS decays


CPV in KS decays




000000

000

000 )(

)(

L

S

KA




S+KL

KL




000 000 00

1( )2 ( 2

0

)

( )


tt

NEARf E t



)()()( 00

00

EKNEKN

EKNEKNED

(incoherent

production)



Assuming CPT





N3

20

40

60

00

4 62


No CPV seen yet

























PT() = (-17 23 11) 10-

3

Im = (-53 71 36) 10-3




Im = (-53 71 36) 10-3








ppp

ppp

)0()0(

)0()0(

NN

NNA


Radiative decays








211221 )()(


IB DE

p1 p1

p2p2

q q







)(

)(

S

L

KA

violatingCPKA




KL π+πminus






IB

M1 DE




KL itself





KL ee


BR = (308 020) 10minus7



E1M1 lt 004 (90 CL)



φ




KS ee

No asymmetry for KS

as expected

BR = (471 032) 10-

5

AΦ = (05 43)






IBEE

dEA

)tan( 0


Kplusmn π+π0γ

)730810672()(

)250350353()(

800

800

syststatMeVT

syststatMeVT

INTFrac

DEFrac







KL π+πndashπ0γ















)(

)2030(

3

3

e

ee

K

MeVEKR





bull 6M Ke3 events


ndash R=(0964plusmn0008+0011-0009)












PDG 2004







]21[192 3

52

KmG







Vus measurements





unitarity





KLOE Kl 3

KLOE K2

copy A Antonelli

Vus some more




Ke4 results





K+rarrπ0π0eν










1-loop rescattering

2-loop rescattering











NA482




KLOE interference

















K+ + 8middot10-11 (at 7)147+130

ndash089 middot 10-

10 (BNL E787+E949)






KL 0ℓ+ℓ-




BR(KL 0+-) lt 3810-10





NA481 KS 0ℓ+ℓ-



BR = (58 +28-23 plusmn08) times10-9


-012 (accid)BR = (28 +15


KS 0e+e- KS 0μ+μ-


NA481 preliminary

NA481 preliminary


KL 0ℓ+ℓ-






Krarr in the SM




W W

s

id

Vis Vid

e

i=uct

W

Z

VisV

idds i

11

20

2410

10)1108(

)(1001)(

AKB

11

2

5

100

10)4082(

)()Im(

1022)(

t

tdtsL xX

VVKB


K

ε εrsquo




Ke3 KL 0

Height

Im(λt )



10301890 10471)(

KBR









K+ +




















Appendixes





J(ππ) = ℓ(ππ) = 0 P(ππ) = +1 C(ππ) = +1



ℓL



SLti

SLLSti

LS

tL

tS

Lti

LSti

S

KKeaaKKeaa

eaea

KeaKea

SLLS

LS

LS

)()(

22

f LSf

fLS KfA

dt

d 2

2

TUnitarity requires

and therefore


f Sff

fS

fLSLLS

f

fLLf

fSS

fKAAKKmi

AA

)(2)(

22


2

22

2

222

0604

mKK

AAAA

LS

LSLS

f

fSf

fLf

fS

fL



SLS KKmi 21




)()( 0000

SSS KK






K0 π+π- K+ μ+ν




BUT




rate


Strangenesshellip







weirdness



11 CCCC

Defining

2)(

2)(

2

1

K

K

One gets 21

211

1 KCCKKCCK

So C(K1) = +1 C(K2) = minus1










τ(KS) = 08910ndash


=K1

=K2





)cos(24

1)]()0([

)cos(24

1)]()0([

2)(00

2)(00

2121

2121

mteeetKtKP

mteeetKtKP

ttt

ttt

Δm=m1-m2






Positrons

Electrons

Start with K0 only




(3) Regeneration






[KS=K1 KL=K2]


Regeneration











6 inch plate

combined

K1 rate



M(K0) = 4977 MeVc2


[ π0 = (uu+dd)2 = π0 ]

K0 ne K0

In terms of quarks











Two-state formalism


)0()( tiet H

ΓΓMM

ΓMH

)(2

)()( ti

ttdt

di

)(2 11

112

Kkkij

kKk

ijKij

mEjHkkHi

mE

jHkkHijHimM



LSLSLS

LSLSLS

im

tKtKi

2

)()(2

ΓM



mm

HH

HH

K

KK HH

2221

1211

0

0

01


0

0

mmm

mmm

K

K


Case of CP symmetry

H11 = H22 = m0 H12 = H21 = δm





Eigenstates

22

11

KKCP

KKCP

21 KKKK LS



Since 00 LJJ

CPCP



K1K2 = 0

CP symmetric case







)0()0()(

2)(

22

1)(

11

222

111

KeKetK

KeKetKtimitiE

timitiE

002

001

2

12

1

KKK

KKK


1212 Re2Re2 Mm


6 eV



CP symmetric case




Brookhaven AD 1963


















(45 plusmn 9)22700



fall 1963









310)4002()(

)(

chargedKBR

KBR

L

L


The new paradigm

K0

K0

K0

K0


CP










Physical states

00

22

00

22

)1()1(

12

1

)1()1(

12

1

KKK

KKK

L

S

00

2122

00

2212

)1()1(12

1

1

1

)1()1(12

1

1

1

KKKKK

KKKKK

LL

L

L

L

L

SS

S

S

S

S

2)(

2)(

SL

LS






M12 ne M21 Γ12 ne Γ21

)2(2

)()(

2

Im)2(Im 112211221212

im

iMM

mi

iM






M11 ne M22 Γ11 ne Γ22

Re(ε) really






34

2

2102

p

p

F

F

FSW

m

m

G

G

m

G

m

G




2

Im)2(Im 1212

mi

iM











KL K2+ ε K1

ππ






KL K2+ ε K1

ππ


K2 (CP=-1) ππ (CP=+1)






This is named



K0 ππ

K0





Decay phase

(direct)




Isospin I=0

Isospin I=2


(CHARGE) BASIS









221

2

)(

)(

21

)(

)(

00

00

000000

S

Li

S

Li

KA

KAe

KA

KAe

)(

0

0

2

2

0

2

0

0

02

)Re(

)Im(

)Re(

)Im(

)Re(

)Re(

2

)Re(

)Im(

iea

a

a

a

a

ai

a

ai

221

)0(

)2(

IKA

IKA

S

S







Questions













p

Target


particle sweeping

Dump

Neutral beam

Collimator

Production

angle

Protonenergy Beam

acceptance

Collimatorbackgroun

d

KL (+KS) beams



KS by regeneration





KL KL + Ar KS








61)Re(612

2

00

)(

)(

)(

)(00

00

2

2

00

L

S

S

L

K

K

K

K







n


d(PSext) d3x d3ph3




Position scale

Momentum

scale



Direct CPV 1996 AD

FNAL E731






The presshellip







KTeV at Fermilab



NA48 at CERN




600

00

10)820045()()(

)()(

KK

KK




4

World average





rsquo why










K decays


(PDG2004)



For kaons


K2ππ




ΔΓ(K3π)Δg(K3π)












K vs B







200

200

200

200

KeKKeK

KeKKeKA

iHtiHt

iHtiHt

T


20

20

20

20

KefKef

KefKefA

iHtCP

iHtCP

iHtCP

iHtCP

CP

200

200

200

200

KeKKeK

KeKKeKA

iHtiHt

iHtiHt

CPT




CPLEAR experiment

(CERN 1990-96)






tf

ft

f

iHtCP

iHtCP

iHtCP

iHtCP

CPLS

LS

e

mte

KefKef

KefKefA

)(2

2)(

20

20

20

20

1

)cos(2)Re(2

π+π

minus

π0π0

π+π minusπ0

π0π0π0

CPLEARAsymmetrie

s


Rate difference


Measure η





Kaon factories




pppp 2

1SLSL KKKKi




[Lipkin (1968)]

EPR correlation


DAΦNE (Frascati)


DAΦNE (Frascati)


MeVc)









p = 127 MeVcλ = 95 cm

KLKS 106 pb-1




KLOE physics




















p

Target

Collimator



Dump

Tagging Separation

Charged beam




Buthellip



rarr Small in SM


2π (εrsquoε)

3π (Ag)


ν


π0

Kplusmn rarr 3π




π1

π2

π3

K


Kinematics



2


2

Matrix element

|M(uv)|2 ~ 1 + gu + hu2 + kv2







KminusK+








10-6

NA482 OKA

10-5

10-4

10-3

10-2

SMSM

SUSYSUSYNewNew

physicsphysics



|Ag|

bull Ag ~ 10minus5


SUSY New Physics

THEORY



C

N



=Ag



54 60 66

1cm

50 100

10 cm

200 250 m





~11012

ppp

K+

Kminus



always in vacuum

focusing beams

BM

z

magnet

vacuum tank

not to scale

K+

K


pipe

0ordm prodangle






ZZ

XXYY

JuraJura

SaleveSaleve

Beam line K+ Up


B+

Bminus






Spectrometer field

K+

Kminus

Reverse each day

Reverse each week


|V| even pion

in beam pipe


KK+ +

KK



No significant

background





-15 -10 -05 0 05 10 u

0

-1

-2

1

2

3

Dalitz plot



EM calorimeter only






2003 result in PLB 634 (2006) 474




2003 result in PLB 638 (2006) 22


excluded


OKA at Protvino





(in preparation)


More CP violation


Indirect

Direct

CP violation

parameters

(2005)


(A) KS decays


CPV in KS decays




000000

000

000 )(

)(

L

S

KA




S+KL

KL




000 000 00

1( )2 ( 2

0

)

( )


tt

NEARf E t



)()()( 00

00

EKNEKN

EKNEKNED

(incoherent

production)



Assuming CPT





N3

20

40

60

00

4 62


No CPV seen yet

























PT() = (-17 23 11) 10-

3

Im = (-53 71 36) 10-3




Im = (-53 71 36) 10-3








ppp

ppp

)0()0(

)0()0(

NN

NNA


Radiative decays








211221 )()(


IB DE

p1 p1

p2p2

q q







)(

)(

S

L

KA

violatingCPKA




KL π+πminus






IB

M1 DE




KL itself





KL ee


BR = (308 020) 10minus7



E1M1 lt 004 (90 CL)



φ




KS ee

No asymmetry for KS

as expected

BR = (471 032) 10-

5

AΦ = (05 43)






IBEE

dEA

)tan( 0


Kplusmn π+π0γ

)730810672()(

)250350353()(

800

800

syststatMeVT

syststatMeVT

INTFrac

DEFrac







KL π+πndashπ0γ















)(

)2030(

3

3

e

ee

K

MeVEKR





bull 6M Ke3 events


ndash R=(0964plusmn0008+0011-0009)












PDG 2004







]21[192 3

52

KmG







Vus measurements





unitarity





KLOE Kl 3

KLOE K2

copy A Antonelli

Vus some more




Ke4 results





K+rarrπ0π0eν










1-loop rescattering

2-loop rescattering











NA482




KLOE interference

















K+ + 8middot10-11 (at 7)147+130

ndash089 middot 10-

10 (BNL E787+E949)






KL 0ℓ+ℓ-




BR(KL 0+-) lt 3810-10





NA481 KS 0ℓ+ℓ-



BR = (58 +28-23 plusmn08) times10-9


-012 (accid)BR = (28 +15


KS 0e+e- KS 0μ+μ-


NA481 preliminary

NA481 preliminary


KL 0ℓ+ℓ-






Krarr in the SM




W W

s

id

Vis Vid

e

i=uct

W

Z

VisV

idds i

11

20

2410

10)1108(

)(1001)(

AKB

11

2

5

100

10)4082(

)()Im(

1022)(

t

tdtsL xX

VVKB


K

ε εrsquo




Ke3 KL 0

Height

Im(λt )



10301890 10471)(

KBR









K+ +




















Appendixes





J(ππ) = ℓ(ππ) = 0 P(ππ) = +1 C(ππ) = +1



ℓL



SLti

SLLSti

LS

tL

tS

Lti

LSti

S

KKeaaKKeaa

eaea

KeaKea

SLLS

LS

LS

)()(

22

f LSf

fLS KfA

dt

d 2

2

TUnitarity requires

and therefore


f Sff

fS

fLSLLS

f

fLLf

fSS

fKAAKKmi

AA

)(2)(

22


2

22

2

222

0604

mKK

AAAA

LS

LSLS

f

fSf

fLf

fS

fL



SLS KKmi 21




)()( 0000

SSS KK





BUT




rate


Strangenesshellip







weirdness



11 CCCC

Defining

2)(

2)(

2

1

K

K

One gets 21

211

1 KCCKKCCK

So C(K1) = +1 C(K2) = minus1










τ(KS) = 08910ndash


=K1

=K2





)cos(24

1)]()0([

)cos(24

1)]()0([

2)(00

2)(00

2121

2121

mteeetKtKP

mteeetKtKP

ttt

ttt

Δm=m1-m2






Positrons

Electrons

Start with K0 only




(3) Regeneration






[KS=K1 KL=K2]


Regeneration











6 inch plate

combined

K1 rate



M(K0) = 4977 MeVc2


[ π0 = (uu+dd)2 = π0 ]

K0 ne K0

In terms of quarks











Two-state formalism


)0()( tiet H

ΓΓMM

ΓMH

)(2

)()( ti

ttdt

di

)(2 11

112

Kkkij

kKk

ijKij

mEjHkkHi

mE

jHkkHijHimM



LSLSLS

LSLSLS

im

tKtKi

2

)()(2

ΓM



mm

HH

HH

K

KK HH

2221

1211

0

0

01


0

0

mmm

mmm

K

K


Case of CP symmetry

H11 = H22 = m0 H12 = H21 = δm





Eigenstates

22

11

KKCP

KKCP

21 KKKK LS



Since 00 LJJ

CPCP



K1K2 = 0

CP symmetric case







)0()0()(

2)(

22

1)(

11

222

111

KeKetK

KeKetKtimitiE

timitiE

002

001

2

12

1

KKK

KKK


1212 Re2Re2 Mm


6 eV



CP symmetric case




Brookhaven AD 1963


















(45 plusmn 9)22700



fall 1963









310)4002()(

)(

chargedKBR

KBR

L

L


The new paradigm

K0

K0

K0

K0


CP










Physical states

00

22

00

22

)1()1(

12

1

)1()1(

12

1

KKK

KKK

L

S

00

2122

00

2212

)1()1(12

1

1

1

)1()1(12

1

1

1

KKKKK

KKKKK

LL

L

L

L

L

SS

S

S

S

S

2)(

2)(

SL

LS






M12 ne M21 Γ12 ne Γ21

)2(2

)()(

2

Im)2(Im 112211221212

im

iMM

mi

iM






M11 ne M22 Γ11 ne Γ22

Re(ε) really






34

2

2102

p

p

F

F

FSW

m

m

G

G

m

G

m

G




2

Im)2(Im 1212

mi

iM











KL K2+ ε K1

ππ






KL K2+ ε K1

ππ


K2 (CP=-1) ππ (CP=+1)






This is named



K0 ππ

K0





Decay phase

(direct)




Isospin I=0

Isospin I=2


(CHARGE) BASIS









221

2

)(

)(

21

)(

)(

00

00

000000

S

Li

S

Li

KA

KAe

KA

KAe

)(

0

0

2

2

0

2

0

0

02

)Re(

)Im(

)Re(

)Im(

)Re(

)Re(

2

)Re(

)Im(

iea

a

a

a

a

ai

a

ai

221

)0(

)2(

IKA

IKA

S

S







Questions













p

Target


particle sweeping

Dump

Neutral beam

Collimator

Production

angle

Protonenergy Beam

acceptance

Collimatorbackgroun

d

KL (+KS) beams



KS by regeneration





KL KL + Ar KS








61)Re(612

2

00

)(

)(

)(

)(00

00

2

2

00

L

S

S

L

K

K

K

K







n


d(PSext) d3x d3ph3




Position scale

Momentum

scale



Direct CPV 1996 AD

FNAL E731






The presshellip







KTeV at Fermilab



NA48 at CERN




600

00

10)820045()()(

)()(

KK

KK




4

World average





rsquo why










K decays


(PDG2004)



For kaons


K2ππ




ΔΓ(K3π)Δg(K3π)












K vs B







200

200

200

200

KeKKeK

KeKKeKA

iHtiHt

iHtiHt

T


20

20

20

20

KefKef

KefKefA

iHtCP

iHtCP

iHtCP

iHtCP

CP

200

200

200

200

KeKKeK

KeKKeKA

iHtiHt

iHtiHt

CPT




CPLEAR experiment

(CERN 1990-96)






tf

ft

f

iHtCP

iHtCP

iHtCP

iHtCP

CPLS

LS

e

mte

KefKef

KefKefA

)(2

2)(

20

20

20

20

1

)cos(2)Re(2

π+π

minus

π0π0

π+π minusπ0

π0π0π0

CPLEARAsymmetrie

s


Rate difference


Measure η





Kaon factories




pppp 2

1SLSL KKKKi




[Lipkin (1968)]

EPR correlation


DAΦNE (Frascati)


DAΦNE (Frascati)


MeVc)









p = 127 MeVcλ = 95 cm

KLKS 106 pb-1




KLOE physics




















p

Target

Collimator



Dump

Tagging Separation

Charged beam




Buthellip



rarr Small in SM


2π (εrsquoε)

3π (Ag)


ν


π0

Kplusmn rarr 3π




π1

π2

π3

K


Kinematics



2


2

Matrix element

|M(uv)|2 ~ 1 + gu + hu2 + kv2







KminusK+








10-6

NA482 OKA

10-5

10-4

10-3

10-2

SMSM

SUSYSUSYNewNew

physicsphysics



|Ag|

bull Ag ~ 10minus5


SUSY New Physics

THEORY



C

N



=Ag



54 60 66

1cm

50 100

10 cm

200 250 m





~11012

ppp

K+

Kminus



always in vacuum

focusing beams

BM

z

magnet

vacuum tank

not to scale

K+

K


pipe

0ordm prodangle






ZZ

XXYY

JuraJura

SaleveSaleve

Beam line K+ Up


B+

Bminus






Spectrometer field

K+

Kminus

Reverse each day

Reverse each week


|V| even pion

in beam pipe


KK+ +

KK



No significant

background





-15 -10 -05 0 05 10 u

0

-1

-2

1

2

3

Dalitz plot



EM calorimeter only






2003 result in PLB 634 (2006) 474




2003 result in PLB 638 (2006) 22


excluded


OKA at Protvino





(in preparation)


More CP violation


Indirect

Direct

CP violation

parameters

(2005)


(A) KS decays


CPV in KS decays




000000

000

000 )(

)(

L

S

KA




S+KL

KL




000 000 00

1( )2 ( 2

0

)

( )


tt

NEARf E t



)()()( 00

00

EKNEKN

EKNEKNED

(incoherent

production)



Assuming CPT





N3

20

40

60

00

4 62


No CPV seen yet

























PT() = (-17 23 11) 10-

3

Im = (-53 71 36) 10-3




Im = (-53 71 36) 10-3








ppp

ppp

)0()0(

)0()0(

NN

NNA


Radiative decays








211221 )()(


IB DE

p1 p1

p2p2

q q







)(

)(

S

L

KA

violatingCPKA




KL π+πminus






IB

M1 DE




KL itself





KL ee


BR = (308 020) 10minus7



E1M1 lt 004 (90 CL)



φ




KS ee

No asymmetry for KS

as expected

BR = (471 032) 10-

5

AΦ = (05 43)






IBEE

dEA

)tan( 0


Kplusmn π+π0γ

)730810672()(

)250350353()(

800

800

syststatMeVT

syststatMeVT

INTFrac

DEFrac







KL π+πndashπ0γ















)(

)2030(

3

3

e

ee

K

MeVEKR





bull 6M Ke3 events


ndash R=(0964plusmn0008+0011-0009)












PDG 2004







]21[192 3

52

KmG







Vus measurements





unitarity





KLOE Kl 3

KLOE K2

copy A Antonelli

Vus some more




Ke4 results





K+rarrπ0π0eν










1-loop rescattering

2-loop rescattering











NA482




KLOE interference

















K+ + 8middot10-11 (at 7)147+130

ndash089 middot 10-

10 (BNL E787+E949)






KL 0ℓ+ℓ-




BR(KL 0+-) lt 3810-10





NA481 KS 0ℓ+ℓ-



BR = (58 +28-23 plusmn08) times10-9


-012 (accid)BR = (28 +15


KS 0e+e- KS 0μ+μ-


NA481 preliminary

NA481 preliminary


KL 0ℓ+ℓ-






Krarr in the SM




W W

s

id

Vis Vid

e

i=uct

W

Z

VisV

idds i

11

20

2410

10)1108(

)(1001)(

AKB

11

2

5

100

10)4082(

)()Im(

1022)(

t

tdtsL xX

VVKB


K

ε εrsquo




Ke3 KL 0

Height

Im(λt )



10301890 10471)(

KBR









K+ +




















Appendixes





J(ππ) = ℓ(ππ) = 0 P(ππ) = +1 C(ππ) = +1



ℓL



SLti

SLLSti

LS

tL

tS

Lti

LSti

S

KKeaaKKeaa

eaea

KeaKea

SLLS

LS

LS

)()(

22

f LSf

fLS KfA

dt

d 2

2

TUnitarity requires

and therefore


f Sff

fS

fLSLLS

f

fLLf

fSS

fKAAKKmi

AA

)(2)(

22


2

22

2

222

0604

mKK

AAAA

LS

LSLS

f

fSf

fLf

fS

fL



SLS KKmi 21




)()( 0000

SSS KK







weirdness



11 CCCC

Defining

2)(

2)(

2

1

K

K

One gets 21

211

1 KCCKKCCK

So C(K1) = +1 C(K2) = minus1










τ(KS) = 08910ndash


=K1

=K2





)cos(24

1)]()0([

)cos(24

1)]()0([

2)(00

2)(00

2121

2121

mteeetKtKP

mteeetKtKP

ttt

ttt

Δm=m1-m2






Positrons

Electrons

Start with K0 only




(3) Regeneration






[KS=K1 KL=K2]


Regeneration











6 inch plate

combined

K1 rate



M(K0) = 4977 MeVc2


[ π0 = (uu+dd)2 = π0 ]

K0 ne K0

In terms of quarks











Two-state formalism


)0()( tiet H

ΓΓMM

ΓMH

)(2

)()( ti

ttdt

di

)(2 11

112

Kkkij

kKk

ijKij

mEjHkkHi

mE

jHkkHijHimM



LSLSLS

LSLSLS

im

tKtKi

2

)()(2

ΓM



mm

HH

HH

K

KK HH

2221

1211

0

0

01


0

0

mmm

mmm

K

K


Case of CP symmetry

H11 = H22 = m0 H12 = H21 = δm





Eigenstates

22

11

KKCP

KKCP

21 KKKK LS



Since 00 LJJ

CPCP



K1K2 = 0

CP symmetric case







)0()0()(

2)(

22

1)(

11

222

111

KeKetK

KeKetKtimitiE

timitiE

002

001

2

12

1

KKK

KKK


1212 Re2Re2 Mm


6 eV



CP symmetric case




Brookhaven AD 1963


















(45 plusmn 9)22700



fall 1963









310)4002()(

)(

chargedKBR

KBR

L

L


The new paradigm

K0

K0

K0

K0


CP










Physical states

00

22

00

22

)1()1(

12

1

)1()1(

12

1

KKK

KKK

L

S

00

2122

00

2212

)1()1(12

1

1

1

)1()1(12

1

1

1

KKKKK

KKKKK

LL

L

L

L

L

SS

S

S

S

S

2)(

2)(

SL

LS






M12 ne M21 Γ12 ne Γ21

)2(2

)()(

2

Im)2(Im 112211221212

im

iMM

mi

iM






M11 ne M22 Γ11 ne Γ22

Re(ε) really






34

2

2102

p

p

F

F

FSW

m

m

G

G

m

G

m

G




2

Im)2(Im 1212

mi

iM











KL K2+ ε K1

ππ






KL K2+ ε K1

ππ


K2 (CP=-1) ππ (CP=+1)






This is named



K0 ππ

K0





Decay phase

(direct)




Isospin I=0

Isospin I=2


(CHARGE) BASIS









221

2

)(

)(

21

)(

)(

00

00

000000

S

Li

S

Li

KA

KAe

KA

KAe

)(

0

0

2

2

0

2

0

0

02

)Re(

)Im(

)Re(

)Im(

)Re(

)Re(

2

)Re(

)Im(

iea

a

a

a

a

ai

a

ai

221

)0(

)2(

IKA

IKA

S

S







Questions













p

Target


particle sweeping

Dump

Neutral beam

Collimator

Production

angle

Protonenergy Beam

acceptance

Collimatorbackgroun

d

KL (+KS) beams



KS by regeneration





KL KL + Ar KS








61)Re(612

2

00

)(

)(

)(

)(00

00

2

2

00

L

S

S

L

K

K

K

K







n


d(PSext) d3x d3ph3




Position scale

Momentum

scale



Direct CPV 1996 AD

FNAL E731






The presshellip







KTeV at Fermilab



NA48 at CERN




600

00

10)820045()()(

)()(

KK

KK




4

World average





rsquo why










K decays


(PDG2004)



For kaons


K2ππ




ΔΓ(K3π)Δg(K3π)












K vs B







200

200

200

200

KeKKeK

KeKKeKA

iHtiHt

iHtiHt

T


20

20

20

20

KefKef

KefKefA

iHtCP

iHtCP

iHtCP

iHtCP

CP

200

200

200

200

KeKKeK

KeKKeKA

iHtiHt

iHtiHt

CPT




CPLEAR experiment

(CERN 1990-96)






tf

ft

f

iHtCP

iHtCP

iHtCP

iHtCP

CPLS

LS

e

mte

KefKef

KefKefA

)(2

2)(

20

20

20

20

1

)cos(2)Re(2

π+π

minus

π0π0

π+π minusπ0

π0π0π0

CPLEARAsymmetrie

s


Rate difference


Measure η





Kaon factories




pppp 2

1SLSL KKKKi




[Lipkin (1968)]

EPR correlation


DAΦNE (Frascati)


DAΦNE (Frascati)


MeVc)









p = 127 MeVcλ = 95 cm

KLKS 106 pb-1




KLOE physics




















p

Target

Collimator



Dump

Tagging Separation

Charged beam




Buthellip



rarr Small in SM


2π (εrsquoε)

3π (Ag)


ν


π0

Kplusmn rarr 3π




π1

π2

π3

K


Kinematics



2


2

Matrix element

|M(uv)|2 ~ 1 + gu + hu2 + kv2







KminusK+








10-6

NA482 OKA

10-5

10-4

10-3

10-2

SMSM

SUSYSUSYNewNew

physicsphysics



|Ag|

bull Ag ~ 10minus5


SUSY New Physics

THEORY



C

N



=Ag



54 60 66

1cm

50 100

10 cm

200 250 m





~11012

ppp

K+

Kminus



always in vacuum

focusing beams

BM

z

magnet

vacuum tank

not to scale

K+

K


pipe

0ordm prodangle






ZZ

XXYY

JuraJura

SaleveSaleve

Beam line K+ Up


B+

Bminus






Spectrometer field

K+

Kminus

Reverse each day

Reverse each week


|V| even pion

in beam pipe


KK+ +

KK



No significant

background





-15 -10 -05 0 05 10 u

0

-1

-2

1

2

3

Dalitz plot



EM calorimeter only






2003 result in PLB 634 (2006) 474




2003 result in PLB 638 (2006) 22


excluded


OKA at Protvino





(in preparation)


More CP violation


Indirect

Direct

CP violation

parameters

(2005)


(A) KS decays


CPV in KS decays




000000

000

000 )(

)(

L

S

KA




S+KL

KL




000 000 00

1( )2 ( 2

0

)

( )


tt

NEARf E t



)()()( 00

00

EKNEKN

EKNEKNED

(incoherent

production)



Assuming CPT





N3

20

40

60

00

4 62


No CPV seen yet

























PT() = (-17 23 11) 10-

3

Im = (-53 71 36) 10-3




Im = (-53 71 36) 10-3








ppp

ppp

)0()0(

)0()0(

NN

NNA


Radiative decays








211221 )()(


IB DE

p1 p1

p2p2

q q







)(

)(

S

L

KA

violatingCPKA




KL π+πminus






IB

M1 DE




KL itself





KL ee


BR = (308 020) 10minus7



E1M1 lt 004 (90 CL)



φ




KS ee

No asymmetry for KS

as expected

BR = (471 032) 10-

5

AΦ = (05 43)






IBEE

dEA

)tan( 0


Kplusmn π+π0γ

)730810672()(

)250350353()(

800

800

syststatMeVT

syststatMeVT

INTFrac

DEFrac







KL π+πndashπ0γ















)(

)2030(

3

3

e

ee

K

MeVEKR





bull 6M Ke3 events


ndash R=(0964plusmn0008+0011-0009)












PDG 2004







]21[192 3

52

KmG







Vus measurements





unitarity





KLOE Kl 3

KLOE K2

copy A Antonelli

Vus some more




Ke4 results





K+rarrπ0π0eν










1-loop rescattering

2-loop rescattering











NA482




KLOE interference

















K+ + 8middot10-11 (at 7)147+130

ndash089 middot 10-

10 (BNL E787+E949)






KL 0ℓ+ℓ-




BR(KL 0+-) lt 3810-10





NA481 KS 0ℓ+ℓ-



BR = (58 +28-23 plusmn08) times10-9


-012 (accid)BR = (28 +15


KS 0e+e- KS 0μ+μ-


NA481 preliminary

NA481 preliminary


KL 0ℓ+ℓ-






Krarr in the SM




W W

s

id

Vis Vid

e

i=uct

W

Z

VisV

idds i

11

20

2410

10)1108(

)(1001)(

AKB

11

2

5

100

10)4082(

)()Im(

1022)(

t

tdtsL xX

VVKB


K

ε εrsquo




Ke3 KL 0

Height

Im(λt )



10301890 10471)(

KBR









K+ +




















Appendixes





J(ππ) = ℓ(ππ) = 0 P(ππ) = +1 C(ππ) = +1



ℓL



SLti

SLLSti

LS

tL

tS

Lti

LSti

S

KKeaaKKeaa

eaea

KeaKea

SLLS

LS

LS

)()(

22

f LSf

fLS KfA

dt

d 2

2

TUnitarity requires

and therefore


f Sff

fS

fLSLLS

f

fLLf

fSS

fKAAKKmi

AA

)(2)(

22


2

22

2

222

0604

mKK

AAAA

LS

LSLS

f

fSf

fLf

fS

fL



SLS KKmi 21




)()( 0000

SSS KK




11 CCCC

Defining

2)(

2)(

2

1

K

K

One gets 21

211

1 KCCKKCCK

So C(K1) = +1 C(K2) = minus1










τ(KS) = 08910ndash


=K1

=K2





)cos(24

1)]()0([

)cos(24

1)]()0([

2)(00

2)(00

2121

2121

mteeetKtKP

mteeetKtKP

ttt

ttt

Δm=m1-m2






Positrons

Electrons

Start with K0 only




(3) Regeneration






[KS=K1 KL=K2]


Regeneration











6 inch plate

combined

K1 rate



M(K0) = 4977 MeVc2


[ π0 = (uu+dd)2 = π0 ]

K0 ne K0

In terms of quarks











Two-state formalism


)0()( tiet H

ΓΓMM

ΓMH

)(2

)()( ti

ttdt

di

)(2 11

112

Kkkij

kKk

ijKij

mEjHkkHi

mE

jHkkHijHimM



LSLSLS

LSLSLS

im

tKtKi

2

)()(2

ΓM



mm

HH

HH

K

KK HH

2221

1211

0

0

01


0

0

mmm

mmm

K

K


Case of CP symmetry

H11 = H22 = m0 H12 = H21 = δm





Eigenstates

22

11

KKCP

KKCP

21 KKKK LS



Since 00 LJJ

CPCP



K1K2 = 0

CP symmetric case







)0()0()(

2)(

22

1)(

11

222

111

KeKetK

KeKetKtimitiE

timitiE

002

001

2

12

1

KKK

KKK


1212 Re2Re2 Mm


6 eV



CP symmetric case




Brookhaven AD 1963


















(45 plusmn 9)22700



fall 1963









310)4002()(

)(

chargedKBR

KBR

L

L


The new paradigm

K0

K0

K0

K0


CP










Physical states

00

22

00

22

)1()1(

12

1

)1()1(

12

1

KKK

KKK

L

S

00

2122

00

2212

)1()1(12

1

1

1

)1()1(12

1

1

1

KKKKK

KKKKK

LL

L

L

L

L

SS

S

S

S

S

2)(

2)(

SL

LS






M12 ne M21 Γ12 ne Γ21

)2(2

)()(

2

Im)2(Im 112211221212

im

iMM

mi

iM






M11 ne M22 Γ11 ne Γ22

Re(ε) really






34

2

2102

p

p

F

F

FSW

m

m

G

G

m

G

m

G




2

Im)2(Im 1212

mi

iM











KL K2+ ε K1

ππ






KL K2+ ε K1

ππ


K2 (CP=-1) ππ (CP=+1)






This is named



K0 ππ

K0





Decay phase

(direct)




Isospin I=0

Isospin I=2


(CHARGE) BASIS









221

2

)(

)(

21

)(

)(

00

00

000000

S

Li

S

Li

KA

KAe

KA

KAe

)(

0

0

2

2

0

2

0

0

02

)Re(

)Im(

)Re(

)Im(

)Re(

)Re(

2

)Re(

)Im(

iea

a

a

a

a

ai

a

ai

221

)0(

)2(

IKA

IKA

S

S







Questions













p

Target


particle sweeping

Dump

Neutral beam

Collimator

Production

angle

Protonenergy Beam

acceptance

Collimatorbackgroun

d

KL (+KS) beams



KS by regeneration





KL KL + Ar KS








61)Re(612

2

00

)(

)(

)(

)(00

00

2

2

00

L

S

S

L

K

K

K

K







n


d(PSext) d3x d3ph3




Position scale

Momentum

scale



Direct CPV 1996 AD

FNAL E731






The presshellip







KTeV at Fermilab



NA48 at CERN




600

00

10)820045()()(

)()(

KK

KK




4

World average





rsquo why










K decays


(PDG2004)



For kaons


K2ππ




ΔΓ(K3π)Δg(K3π)












K vs B







200

200

200

200

KeKKeK

KeKKeKA

iHtiHt

iHtiHt

T


20

20

20

20

KefKef

KefKefA

iHtCP

iHtCP

iHtCP

iHtCP

CP

200

200

200

200

KeKKeK

KeKKeKA

iHtiHt

iHtiHt

CPT




CPLEAR experiment

(CERN 1990-96)






tf

ft

f

iHtCP

iHtCP

iHtCP

iHtCP

CPLS

LS

e

mte

KefKef

KefKefA

)(2

2)(

20

20

20

20

1

)cos(2)Re(2

π+π

minus

π0π0

π+π minusπ0

π0π0π0

CPLEARAsymmetrie

s


Rate difference


Measure η





Kaon factories




pppp 2

1SLSL KKKKi




[Lipkin (1968)]

EPR correlation


DAΦNE (Frascati)


DAΦNE (Frascati)


MeVc)









p = 127 MeVcλ = 95 cm

KLKS 106 pb-1




KLOE physics




















p

Target

Collimator



Dump

Tagging Separation

Charged beam




Buthellip



rarr Small in SM


2π (εrsquoε)

3π (Ag)


ν


π0

Kplusmn rarr 3π




π1

π2

π3

K


Kinematics



2


2

Matrix element

|M(uv)|2 ~ 1 + gu + hu2 + kv2







KminusK+








10-6

NA482 OKA

10-5

10-4

10-3

10-2

SMSM

SUSYSUSYNewNew

physicsphysics



|Ag|

bull Ag ~ 10minus5


SUSY New Physics

THEORY



C

N



=Ag



54 60 66

1cm

50 100

10 cm

200 250 m





~11012

ppp

K+

Kminus



always in vacuum

focusing beams

BM

z

magnet

vacuum tank

not to scale

K+

K


pipe

0ordm prodangle






ZZ

XXYY

JuraJura

SaleveSaleve

Beam line K+ Up


B+

Bminus






Spectrometer field

K+

Kminus

Reverse each day

Reverse each week


|V| even pion

in beam pipe


KK+ +

KK



No significant

background





-15 -10 -05 0 05 10 u

0

-1

-2

1

2

3

Dalitz plot



EM calorimeter only






2003 result in PLB 634 (2006) 474




2003 result in PLB 638 (2006) 22


excluded


OKA at Protvino





(in preparation)


More CP violation


Indirect

Direct

CP violation

parameters

(2005)


(A) KS decays


CPV in KS decays




000000

000

000 )(

)(

L

S

KA




S+KL

KL




000 000 00

1( )2 ( 2

0

)

( )


tt

NEARf E t



)()()( 00

00

EKNEKN

EKNEKNED

(incoherent

production)



Assuming CPT





N3

20

40

60

00

4 62


No CPV seen yet

























PT() = (-17 23 11) 10-

3

Im = (-53 71 36) 10-3




Im = (-53 71 36) 10-3








ppp

ppp

)0()0(

)0()0(

NN

NNA


Radiative decays








211221 )()(


IB DE

p1 p1

p2p2

q q







)(

)(

S

L

KA

violatingCPKA




KL π+πminus






IB

M1 DE




KL itself





KL ee


BR = (308 020) 10minus7



E1M1 lt 004 (90 CL)



φ




KS ee

No asymmetry for KS

as expected

BR = (471 032) 10-

5

AΦ = (05 43)






IBEE

dEA

)tan( 0


Kplusmn π+π0γ

)730810672()(

)250350353()(

800

800

syststatMeVT

syststatMeVT

INTFrac

DEFrac







KL π+πndashπ0γ















)(

)2030(

3

3

e

ee

K

MeVEKR





bull 6M Ke3 events


ndash R=(0964plusmn0008+0011-0009)












PDG 2004







]21[192 3

52

KmG







Vus measurements





unitarity





KLOE Kl 3

KLOE K2

copy A Antonelli

Vus some more




Ke4 results





K+rarrπ0π0eν










1-loop rescattering

2-loop rescattering











NA482




KLOE interference

















K+ + 8middot10-11 (at 7)147+130

ndash089 middot 10-

10 (BNL E787+E949)






KL 0ℓ+ℓ-




BR(KL 0+-) lt 3810-10





NA481 KS 0ℓ+ℓ-



BR = (58 +28-23 plusmn08) times10-9


-012 (accid)BR = (28 +15


KS 0e+e- KS 0μ+μ-


NA481 preliminary

NA481 preliminary


KL 0ℓ+ℓ-






Krarr in the SM




W W

s

id

Vis Vid

e

i=uct

W

Z

VisV

idds i

11

20

2410

10)1108(

)(1001)(

AKB

11

2

5

100

10)4082(

)()Im(

1022)(

t

tdtsL xX

VVKB


K

ε εrsquo




Ke3 KL 0

Height

Im(λt )



10301890 10471)(

KBR









K+ +




















Appendixes





J(ππ) = ℓ(ππ) = 0 P(ππ) = +1 C(ππ) = +1



ℓL



SLti

SLLSti

LS

tL

tS

Lti

LSti

S

KKeaaKKeaa

eaea

KeaKea

SLLS

LS

LS

)()(

22

f LSf

fLS KfA

dt

d 2

2

TUnitarity requires

and therefore


f Sff

fS

fLSLLS

f

fLLf

fSS

fKAAKKmi

AA

)(2)(

22


2

22

2

222

0604

mKK

AAAA

LS

LSLS

f

fSf

fLf

fS

fL



SLS KKmi 21




)()( 0000

SSS KK








τ(KS) = 08910ndash


=K1

=K2





)cos(24

1)]()0([

)cos(24

1)]()0([

2)(00

2)(00

2121

2121

mteeetKtKP

mteeetKtKP

ttt

ttt

Δm=m1-m2






Positrons

Electrons

Start with K0 only




(3) Regeneration






[KS=K1 KL=K2]


Regeneration











6 inch plate

combined

K1 rate



M(K0) = 4977 MeVc2


[ π0 = (uu+dd)2 = π0 ]

K0 ne K0

In terms of quarks











Two-state formalism


)0()( tiet H

ΓΓMM

ΓMH

)(2

)()( ti

ttdt

di

)(2 11

112

Kkkij

kKk

ijKij

mEjHkkHi

mE

jHkkHijHimM



LSLSLS

LSLSLS

im

tKtKi

2

)()(2

ΓM



mm

HH

HH

K

KK HH

2221

1211

0

0

01


0

0

mmm

mmm

K

K


Case of CP symmetry

H11 = H22 = m0 H12 = H21 = δm





Eigenstates

22

11

KKCP

KKCP

21 KKKK LS



Since 00 LJJ

CPCP



K1K2 = 0

CP symmetric case







)0()0()(

2)(

22

1)(

11

222

111

KeKetK

KeKetKtimitiE

timitiE

002

001

2

12

1

KKK

KKK


1212 Re2Re2 Mm


6 eV



CP symmetric case




Brookhaven AD 1963


















(45 plusmn 9)22700



fall 1963









310)4002()(

)(

chargedKBR

KBR

L

L


The new paradigm

K0

K0

K0

K0


CP










Physical states

00

22

00

22

)1()1(

12

1

)1()1(

12

1

KKK

KKK

L

S

00

2122

00

2212

)1()1(12

1

1

1

)1()1(12

1

1

1

KKKKK

KKKKK

LL

L

L

L

L

SS

S

S

S

S

2)(

2)(

SL

LS






M12 ne M21 Γ12 ne Γ21

)2(2

)()(

2

Im)2(Im 112211221212

im

iMM

mi

iM






M11 ne M22 Γ11 ne Γ22

Re(ε) really






34

2

2102

p

p

F

F

FSW

m

m

G

G

m

G

m

G




2

Im)2(Im 1212

mi

iM











KL K2+ ε K1

ππ






KL K2+ ε K1

ππ


K2 (CP=-1) ππ (CP=+1)






This is named



K0 ππ

K0





Decay phase

(direct)




Isospin I=0

Isospin I=2


(CHARGE) BASIS









221

2

)(

)(

21

)(

)(

00

00

000000

S

Li

S

Li

KA

KAe

KA

KAe

)(

0

0

2

2

0

2

0

0

02

)Re(

)Im(

)Re(

)Im(

)Re(

)Re(

2

)Re(

)Im(

iea

a

a

a

a

ai

a

ai

221

)0(

)2(

IKA

IKA

S

S







Questions













p

Target


particle sweeping

Dump

Neutral beam

Collimator

Production

angle

Protonenergy Beam

acceptance

Collimatorbackgroun

d

KL (+KS) beams



KS by regeneration





KL KL + Ar KS








61)Re(612

2

00

)(

)(

)(

)(00

00

2

2

00

L

S

S

L

K

K

K

K







n


d(PSext) d3x d3ph3




Position scale

Momentum

scale



Direct CPV 1996 AD

FNAL E731






The presshellip







KTeV at Fermilab



NA48 at CERN




600

00

10)820045()()(

)()(

KK

KK




4

World average





rsquo why










K decays


(PDG2004)



For kaons


K2ππ




ΔΓ(K3π)Δg(K3π)












K vs B







200

200

200

200

KeKKeK

KeKKeKA

iHtiHt

iHtiHt

T


20

20

20

20

KefKef

KefKefA

iHtCP

iHtCP

iHtCP

iHtCP

CP

200

200

200

200

KeKKeK

KeKKeKA

iHtiHt

iHtiHt

CPT




CPLEAR experiment

(CERN 1990-96)






tf

ft

f

iHtCP

iHtCP

iHtCP

iHtCP

CPLS

LS

e

mte

KefKef

KefKefA

)(2

2)(

20

20

20

20

1

)cos(2)Re(2

π+π

minus

π0π0

π+π minusπ0

π0π0π0

CPLEARAsymmetrie

s


Rate difference


Measure η





Kaon factories




pppp 2

1SLSL KKKKi




[Lipkin (1968)]

EPR correlation


DAΦNE (Frascati)


DAΦNE (Frascati)


MeVc)









p = 127 MeVcλ = 95 cm

KLKS 106 pb-1




KLOE physics




















p

Target

Collimator



Dump

Tagging Separation

Charged beam




Buthellip



rarr Small in SM


2π (εrsquoε)

3π (Ag)


ν


π0

Kplusmn rarr 3π




π1

π2

π3

K


Kinematics



2


2

Matrix element

|M(uv)|2 ~ 1 + gu + hu2 + kv2







KminusK+








10-6

NA482 OKA

10-5

10-4

10-3

10-2

SMSM

SUSYSUSYNewNew

physicsphysics



|Ag|

bull Ag ~ 10minus5


SUSY New Physics

THEORY



C

N



=Ag



54 60 66

1cm

50 100

10 cm

200 250 m





~11012

ppp

K+

Kminus



always in vacuum

focusing beams

BM

z

magnet

vacuum tank

not to scale

K+

K


pipe

0ordm prodangle






ZZ

XXYY

JuraJura

SaleveSaleve

Beam line K+ Up


B+

Bminus






Spectrometer field

K+

Kminus

Reverse each day

Reverse each week


|V| even pion

in beam pipe


KK+ +

KK



No significant

background





-15 -10 -05 0 05 10 u

0

-1

-2

1

2

3

Dalitz plot



EM calorimeter only






2003 result in PLB 634 (2006) 474




2003 result in PLB 638 (2006) 22


excluded


OKA at Protvino





(in preparation)


More CP violation


Indirect

Direct

CP violation

parameters

(2005)


(A) KS decays


CPV in KS decays




000000

000

000 )(

)(

L

S

KA




S+KL

KL




000 000 00

1( )2 ( 2

0

)

( )


tt

NEARf E t



)()()( 00

00

EKNEKN

EKNEKNED

(incoherent

production)



Assuming CPT





N3

20

40

60

00

4 62


No CPV seen yet

























PT() = (-17 23 11) 10-

3

Im = (-53 71 36) 10-3




Im = (-53 71 36) 10-3








ppp

ppp

)0()0(

)0()0(

NN

NNA


Radiative decays








211221 )()(


IB DE

p1 p1

p2p2

q q







)(

)(

S

L

KA

violatingCPKA




KL π+πminus






IB

M1 DE




KL itself





KL ee


BR = (308 020) 10minus7



E1M1 lt 004 (90 CL)



φ




KS ee

No asymmetry for KS

as expected

BR = (471 032) 10-

5

AΦ = (05 43)






IBEE

dEA

)tan( 0


Kplusmn π+π0γ

)730810672()(

)250350353()(

800

800

syststatMeVT

syststatMeVT

INTFrac

DEFrac







KL π+πndashπ0γ















)(

)2030(

3

3

e

ee

K

MeVEKR





bull 6M Ke3 events


ndash R=(0964plusmn0008+0011-0009)












PDG 2004







]21[192 3

52

KmG







Vus measurements





unitarity





KLOE Kl 3

KLOE K2

copy A Antonelli

Vus some more




Ke4 results





K+rarrπ0π0eν










1-loop rescattering

2-loop rescattering











NA482




KLOE interference

















K+ + 8middot10-11 (at 7)147+130

ndash089 middot 10-

10 (BNL E787+E949)






KL 0ℓ+ℓ-




BR(KL 0+-) lt 3810-10





NA481 KS 0ℓ+ℓ-



BR = (58 +28-23 plusmn08) times10-9


-012 (accid)BR = (28 +15


KS 0e+e- KS 0μ+μ-


NA481 preliminary

NA481 preliminary


KL 0ℓ+ℓ-






Krarr in the SM




W W

s

id

Vis Vid

e

i=uct

W

Z

VisV

idds i

11

20

2410

10)1108(

)(1001)(

AKB

11

2

5

100

10)4082(

)()Im(

1022)(

t

tdtsL xX

VVKB


K

ε εrsquo




Ke3 KL 0

Height

Im(λt )



10301890 10471)(

KBR









K+ +




















Appendixes





J(ππ) = ℓ(ππ) = 0 P(ππ) = +1 C(ππ) = +1



ℓL



SLti

SLLSti

LS

tL

tS

Lti

LSti

S

KKeaaKKeaa

eaea

KeaKea

SLLS

LS

LS

)()(

22

f LSf

fLS KfA

dt

d 2

2

TUnitarity requires

and therefore


f Sff

fS

fLSLLS

f

fLLf

fSS

fKAAKKmi

AA

)(2)(

22


2

22

2

222

0604

mKK

AAAA

LS

LSLS

f

fSf

fLf

fS

fL



SLS KKmi 21




)()( 0000

SSS KK




)cos(24

1)]()0([

)cos(24

1)]()0([

2)(00

2)(00

2121

2121

mteeetKtKP

mteeetKtKP

ttt

ttt

Δm=m1-m2






Positrons

Electrons

Start with K0 only




(3) Regeneration






[KS=K1 KL=K2]


Regeneration











6 inch plate

combined

K1 rate



M(K0) = 4977 MeVc2


[ π0 = (uu+dd)2 = π0 ]

K0 ne K0

In terms of quarks











Two-state formalism


)0()( tiet H

ΓΓMM

ΓMH

)(2

)()( ti

ttdt

di

)(2 11

112

Kkkij

kKk

ijKij

mEjHkkHi

mE

jHkkHijHimM



LSLSLS

LSLSLS

im

tKtKi

2

)()(2

ΓM



mm

HH

HH

K

KK HH

2221

1211

0

0

01


0

0

mmm

mmm

K

K


Case of CP symmetry

H11 = H22 = m0 H12 = H21 = δm





Eigenstates

22

11

KKCP

KKCP

21 KKKK LS



Since 00 LJJ

CPCP



K1K2 = 0

CP symmetric case







)0()0()(

2)(

22

1)(

11

222

111

KeKetK

KeKetKtimitiE

timitiE

002

001

2

12

1

KKK

KKK


1212 Re2Re2 Mm


6 eV



CP symmetric case




Brookhaven AD 1963


















(45 plusmn 9)22700



fall 1963









310)4002()(

)(

chargedKBR

KBR

L

L


The new paradigm

K0

K0

K0

K0


CP










Physical states

00

22

00

22

)1()1(

12

1

)1()1(

12

1

KKK

KKK

L

S

00

2122

00

2212

)1()1(12

1

1

1

)1()1(12

1

1

1

KKKKK

KKKKK

LL

L

L

L

L

SS

S

S

S

S

2)(

2)(

SL

LS






M12 ne M21 Γ12 ne Γ21

)2(2

)()(

2

Im)2(Im 112211221212

im

iMM

mi

iM






M11 ne M22 Γ11 ne Γ22

Re(ε) really






34

2

2102

p

p

F

F

FSW

m

m

G

G

m

G

m

G




2

Im)2(Im 1212

mi

iM











KL K2+ ε K1

ππ






KL K2+ ε K1

ππ


K2 (CP=-1) ππ (CP=+1)






This is named



K0 ππ

K0





Decay phase

(direct)




Isospin I=0

Isospin I=2


(CHARGE) BASIS









221

2

)(

)(

21

)(

)(

00

00

000000

S

Li

S

Li

KA

KAe

KA

KAe

)(

0

0

2

2

0

2

0

0

02

)Re(

)Im(

)Re(

)Im(

)Re(

)Re(

2

)Re(

)Im(

iea

a

a

a

a

ai

a

ai

221

)0(

)2(

IKA

IKA

S

S







Questions













p

Target


particle sweeping

Dump

Neutral beam

Collimator

Production

angle

Protonenergy Beam

acceptance

Collimatorbackgroun

d

KL (+KS) beams



KS by regeneration





KL KL + Ar KS








61)Re(612

2

00

)(

)(

)(

)(00

00

2

2

00

L

S

S

L

K

K

K

K







n


d(PSext) d3x d3ph3




Position scale

Momentum

scale



Direct CPV 1996 AD

FNAL E731






The presshellip







KTeV at Fermilab



NA48 at CERN




600

00

10)820045()()(

)()(

KK

KK




4

World average





rsquo why










K decays


(PDG2004)



For kaons


K2ππ




ΔΓ(K3π)Δg(K3π)












K vs B







200

200

200

200

KeKKeK

KeKKeKA

iHtiHt

iHtiHt

T


20

20

20

20

KefKef

KefKefA

iHtCP

iHtCP

iHtCP

iHtCP

CP

200

200

200

200

KeKKeK

KeKKeKA

iHtiHt

iHtiHt

CPT




CPLEAR experiment

(CERN 1990-96)






tf

ft

f

iHtCP

iHtCP

iHtCP

iHtCP

CPLS

LS

e

mte

KefKef

KefKefA

)(2

2)(

20

20

20

20

1

)cos(2)Re(2

π+π

minus

π0π0

π+π minusπ0

π0π0π0

CPLEARAsymmetrie

s


Rate difference


Measure η





Kaon factories




pppp 2

1SLSL KKKKi




[Lipkin (1968)]

EPR correlation


DAΦNE (Frascati)


DAΦNE (Frascati)


MeVc)









p = 127 MeVcλ = 95 cm

KLKS 106 pb-1




KLOE physics




















p

Target

Collimator



Dump

Tagging Separation

Charged beam




Buthellip



rarr Small in SM


2π (εrsquoε)

3π (Ag)


ν


π0

Kplusmn rarr 3π




π1

π2

π3

K


Kinematics



2


2

Matrix element

|M(uv)|2 ~ 1 + gu + hu2 + kv2







KminusK+








10-6

NA482 OKA

10-5

10-4

10-3

10-2

SMSM

SUSYSUSYNewNew

physicsphysics



|Ag|

bull Ag ~ 10minus5


SUSY New Physics

THEORY



C

N



=Ag



54 60 66

1cm

50 100

10 cm

200 250 m





~11012

ppp

K+

Kminus



always in vacuum

focusing beams

BM

z

magnet

vacuum tank

not to scale

K+

K


pipe

0ordm prodangle






ZZ

XXYY

JuraJura

SaleveSaleve

Beam line K+ Up


B+

Bminus






Spectrometer field

K+

Kminus

Reverse each day

Reverse each week


|V| even pion

in beam pipe


KK+ +

KK



No significant

background





-15 -10 -05 0 05 10 u

0

-1

-2

1

2

3

Dalitz plot



EM calorimeter only






2003 result in PLB 634 (2006) 474




2003 result in PLB 638 (2006) 22


excluded


OKA at Protvino





(in preparation)


More CP violation


Indirect

Direct

CP violation

parameters

(2005)


(A) KS decays


CPV in KS decays




000000

000

000 )(

)(

L

S

KA




S+KL

KL




000 000 00

1( )2 ( 2

0

)

( )


tt

NEARf E t



)()()( 00

00

EKNEKN

EKNEKNED

(incoherent

production)



Assuming CPT





N3

20

40

60

00

4 62


No CPV seen yet

























PT() = (-17 23 11) 10-

3

Im = (-53 71 36) 10-3




Im = (-53 71 36) 10-3








ppp

ppp

)0()0(

)0()0(

NN

NNA


Radiative decays








211221 )()(


IB DE

p1 p1

p2p2

q q







)(

)(

S

L

KA

violatingCPKA




KL π+πminus






IB

M1 DE




KL itself





KL ee


BR = (308 020) 10minus7



E1M1 lt 004 (90 CL)



φ




KS ee

No asymmetry for KS

as expected

BR = (471 032) 10-

5

AΦ = (05 43)






IBEE

dEA

)tan( 0


Kplusmn π+π0γ

)730810672()(

)250350353()(

800

800

syststatMeVT

syststatMeVT

INTFrac

DEFrac







KL π+πndashπ0γ















)(

)2030(

3

3

e

ee

K

MeVEKR





bull 6M Ke3 events


ndash R=(0964plusmn0008+0011-0009)












PDG 2004







]21[192 3

52

KmG







Vus measurements





unitarity





KLOE Kl 3

KLOE K2

copy A Antonelli

Vus some more




Ke4 results





K+rarrπ0π0eν










1-loop rescattering

2-loop rescattering











NA482




KLOE interference

















K+ + 8middot10-11 (at 7)147+130

ndash089 middot 10-

10 (BNL E787+E949)






KL 0ℓ+ℓ-




BR(KL 0+-) lt 3810-10





NA481 KS 0ℓ+ℓ-



BR = (58 +28-23 plusmn08) times10-9


-012 (accid)BR = (28 +15


KS 0e+e- KS 0μ+μ-


NA481 preliminary

NA481 preliminary


KL 0ℓ+ℓ-






Krarr in the SM




W W

s

id

Vis Vid

e

i=uct

W

Z

VisV

idds i

11

20

2410

10)1108(

)(1001)(

AKB

11

2

5

100

10)4082(

)()Im(

1022)(

t

tdtsL xX

VVKB


K

ε εrsquo




Ke3 KL 0

Height

Im(λt )



10301890 10471)(

KBR









K+ +




















Appendixes





J(ππ) = ℓ(ππ) = 0 P(ππ) = +1 C(ππ) = +1



ℓL



SLti

SLLSti

LS

tL

tS

Lti

LSti

S

KKeaaKKeaa

eaea

KeaKea

SLLS

LS

LS

)()(

22

f LSf

fLS KfA

dt

d 2

2

TUnitarity requires

and therefore


f Sff

fS

fLSLLS

f

fLLf

fSS

fKAAKKmi

AA

)(2)(

22


2

22

2

222

0604

mKK

AAAA

LS

LSLS

f

fSf

fLf

fS

fL



SLS KKmi 21




)()( 0000

SSS KK





Positrons

Electrons

Start with K0 only




(3) Regeneration






[KS=K1 KL=K2]


Regeneration











6 inch plate

combined

K1 rate



M(K0) = 4977 MeVc2


[ π0 = (uu+dd)2 = π0 ]

K0 ne K0

In terms of quarks











Two-state formalism


)0()( tiet H

ΓΓMM

ΓMH

)(2

)()( ti

ttdt

di

)(2 11

112

Kkkij

kKk

ijKij

mEjHkkHi

mE

jHkkHijHimM



LSLSLS

LSLSLS

im

tKtKi

2

)()(2

ΓM



mm

HH

HH

K

KK HH

2221

1211

0

0

01


0

0

mmm

mmm

K

K


Case of CP symmetry

H11 = H22 = m0 H12 = H21 = δm





Eigenstates

22

11

KKCP

KKCP

21 KKKK LS



Since 00 LJJ

CPCP



K1K2 = 0

CP symmetric case







)0()0()(

2)(

22

1)(

11

222

111

KeKetK

KeKetKtimitiE

timitiE

002

001

2

12

1

KKK

KKK


1212 Re2Re2 Mm


6 eV



CP symmetric case




Brookhaven AD 1963


















(45 plusmn 9)22700



fall 1963









310)4002()(

)(

chargedKBR

KBR

L

L


The new paradigm

K0

K0

K0

K0


CP










Physical states

00

22

00

22

)1()1(

12

1

)1()1(

12

1

KKK

KKK

L

S

00

2122

00

2212

)1()1(12

1

1

1

)1()1(12

1

1

1

KKKKK

KKKKK

LL

L

L

L

L

SS

S

S

S

S

2)(

2)(

SL

LS






M12 ne M21 Γ12 ne Γ21

)2(2

)()(

2

Im)2(Im 112211221212

im

iMM

mi

iM






M11 ne M22 Γ11 ne Γ22

Re(ε) really






34

2

2102

p

p

F

F

FSW

m

m

G

G

m

G

m

G




2

Im)2(Im 1212

mi

iM











KL K2+ ε K1

ππ






KL K2+ ε K1

ππ


K2 (CP=-1) ππ (CP=+1)






This is named



K0 ππ

K0





Decay phase

(direct)




Isospin I=0

Isospin I=2


(CHARGE) BASIS









221

2

)(

)(

21

)(

)(

00

00

000000

S

Li

S

Li

KA

KAe

KA

KAe

)(

0

0

2

2

0

2

0

0

02

)Re(

)Im(

)Re(

)Im(

)Re(

)Re(

2

)Re(

)Im(

iea

a

a

a

a

ai

a

ai

221

)0(

)2(

IKA

IKA

S

S







Questions













p

Target


particle sweeping

Dump

Neutral beam

Collimator

Production

angle

Protonenergy Beam

acceptance

Collimatorbackgroun

d

KL (+KS) beams



KS by regeneration





KL KL + Ar KS








61)Re(612

2

00

)(

)(

)(

)(00

00

2

2

00

L

S

S

L

K

K

K

K







n


d(PSext) d3x d3ph3




Position scale

Momentum

scale



Direct CPV 1996 AD

FNAL E731






The presshellip







KTeV at Fermilab



NA48 at CERN




600

00

10)820045()()(

)()(

KK

KK




4

World average





rsquo why










K decays


(PDG2004)



For kaons


K2ππ




ΔΓ(K3π)Δg(K3π)












K vs B







200

200

200

200

KeKKeK

KeKKeKA

iHtiHt

iHtiHt

T


20

20

20

20

KefKef

KefKefA

iHtCP

iHtCP

iHtCP

iHtCP

CP

200

200

200

200

KeKKeK

KeKKeKA

iHtiHt

iHtiHt

CPT




CPLEAR experiment

(CERN 1990-96)






tf

ft

f

iHtCP

iHtCP

iHtCP

iHtCP

CPLS

LS

e

mte

KefKef

KefKefA

)(2

2)(

20

20

20

20

1

)cos(2)Re(2

π+π

minus

π0π0

π+π minusπ0

π0π0π0

CPLEARAsymmetrie

s


Rate difference


Measure η





Kaon factories




pppp 2

1SLSL KKKKi




[Lipkin (1968)]

EPR correlation


DAΦNE (Frascati)


DAΦNE (Frascati)


MeVc)









p = 127 MeVcλ = 95 cm

KLKS 106 pb-1




KLOE physics




















p

Target

Collimator



Dump

Tagging Separation

Charged beam




Buthellip



rarr Small in SM


2π (εrsquoε)

3π (Ag)


ν


π0

Kplusmn rarr 3π




π1

π2

π3

K


Kinematics



2


2

Matrix element

|M(uv)|2 ~ 1 + gu + hu2 + kv2







KminusK+








10-6

NA482 OKA

10-5

10-4

10-3

10-2

SMSM

SUSYSUSYNewNew

physicsphysics



|Ag|

bull Ag ~ 10minus5


SUSY New Physics

THEORY



C

N



=Ag



54 60 66

1cm

50 100

10 cm

200 250 m





~11012

ppp

K+

Kminus



always in vacuum

focusing beams

BM

z

magnet

vacuum tank

not to scale

K+

K


pipe

0ordm prodangle






ZZ

XXYY

JuraJura

SaleveSaleve

Beam line K+ Up


B+

Bminus






Spectrometer field

K+

Kminus

Reverse each day

Reverse each week


|V| even pion

in beam pipe


KK+ +

KK



No significant

background





-15 -10 -05 0 05 10 u

0

-1

-2

1

2

3

Dalitz plot



EM calorimeter only






2003 result in PLB 634 (2006) 474




2003 result in PLB 638 (2006) 22


excluded


OKA at Protvino





(in preparation)


More CP violation


Indirect

Direct

CP violation

parameters

(2005)


(A) KS decays


CPV in KS decays




000000

000

000 )(

)(

L

S

KA




S+KL

KL




000 000 00

1( )2 ( 2

0

)

( )


tt

NEARf E t



)()()( 00

00

EKNEKN

EKNEKNED

(incoherent

production)



Assuming CPT





N3

20

40

60

00

4 62


No CPV seen yet

























PT() = (-17 23 11) 10-

3

Im = (-53 71 36) 10-3




Im = (-53 71 36) 10-3








ppp

ppp

)0()0(

)0()0(

NN

NNA


Radiative decays








211221 )()(


IB DE

p1 p1

p2p2

q q







)(

)(

S

L

KA

violatingCPKA




KL π+πminus






IB

M1 DE




KL itself





KL ee


BR = (308 020) 10minus7



E1M1 lt 004 (90 CL)



φ




KS ee

No asymmetry for KS

as expected

BR = (471 032) 10-

5

AΦ = (05 43)






IBEE

dEA

)tan( 0


Kplusmn π+π0γ

)730810672()(

)250350353()(

800

800

syststatMeVT

syststatMeVT

INTFrac

DEFrac







KL π+πndashπ0γ















)(

)2030(

3

3

e

ee

K

MeVEKR





bull 6M Ke3 events


ndash R=(0964plusmn0008+0011-0009)












PDG 2004







]21[192 3

52

KmG







Vus measurements





unitarity





KLOE Kl 3

KLOE K2

copy A Antonelli

Vus some more




Ke4 results





K+rarrπ0π0eν










1-loop rescattering

2-loop rescattering











NA482




KLOE interference

















K+ + 8middot10-11 (at 7)147+130

ndash089 middot 10-

10 (BNL E787+E949)






KL 0ℓ+ℓ-




BR(KL 0+-) lt 3810-10





NA481 KS 0ℓ+ℓ-



BR = (58 +28-23 plusmn08) times10-9


-012 (accid)BR = (28 +15


KS 0e+e- KS 0μ+μ-


NA481 preliminary

NA481 preliminary


KL 0ℓ+ℓ-






Krarr in the SM




W W

s

id

Vis Vid

e

i=uct

W

Z

VisV

idds i

11

20

2410

10)1108(

)(1001)(

AKB

11

2

5

100

10)4082(

)()Im(

1022)(

t

tdtsL xX

VVKB


K

ε εrsquo




Ke3 KL 0

Height

Im(λt )



10301890 10471)(

KBR









K+ +




















Appendixes





J(ππ) = ℓ(ππ) = 0 P(ππ) = +1 C(ππ) = +1



ℓL



SLti

SLLSti

LS

tL

tS

Lti

LSti

S

KKeaaKKeaa

eaea

KeaKea

SLLS

LS

LS

)()(

22

f LSf

fLS KfA

dt

d 2

2

TUnitarity requires

and therefore


f Sff

fS

fLSLLS

f

fLLf

fSS

fKAAKKmi

AA

)(2)(

22


2

22

2

222

0604

mKK

AAAA

LS

LSLS

f

fSf

fLf

fS

fL



SLS KKmi 21




)()( 0000

SSS KK



(3) Regeneration






[KS=K1 KL=K2]


Regeneration











6 inch plate

combined

K1 rate



M(K0) = 4977 MeVc2


[ π0 = (uu+dd)2 = π0 ]

K0 ne K0

In terms of quarks











Two-state formalism


)0()( tiet H

ΓΓMM

ΓMH

)(2

)()( ti

ttdt

di

)(2 11

112

Kkkij

kKk

ijKij

mEjHkkHi

mE

jHkkHijHimM



LSLSLS

LSLSLS

im

tKtKi

2

)()(2

ΓM



mm

HH

HH

K

KK HH

2221

1211

0

0

01


0

0

mmm

mmm

K

K


Case of CP symmetry

H11 = H22 = m0 H12 = H21 = δm





Eigenstates

22

11

KKCP

KKCP

21 KKKK LS



Since 00 LJJ

CPCP



K1K2 = 0

CP symmetric case







)0()0()(

2)(

22

1)(

11

222

111

KeKetK

KeKetKtimitiE

timitiE

002

001

2

12

1

KKK

KKK


1212 Re2Re2 Mm


6 eV



CP symmetric case




Brookhaven AD 1963


















(45 plusmn 9)22700



fall 1963









310)4002()(

)(

chargedKBR

KBR

L

L


The new paradigm

K0

K0

K0

K0


CP










Physical states

00

22

00

22

)1()1(

12

1

)1()1(

12

1

KKK

KKK

L

S

00

2122

00

2212

)1()1(12

1

1

1

)1()1(12

1

1

1

KKKKK

KKKKK

LL

L

L

L

L

SS

S

S

S

S

2)(

2)(

SL

LS






M12 ne M21 Γ12 ne Γ21

)2(2

)()(

2

Im)2(Im 112211221212

im

iMM

mi

iM






M11 ne M22 Γ11 ne Γ22

Re(ε) really






34

2

2102

p

p

F

F

FSW

m

m

G

G

m

G

m

G




2

Im)2(Im 1212

mi

iM











KL K2+ ε K1

ππ






KL K2+ ε K1

ππ


K2 (CP=-1) ππ (CP=+1)






This is named



K0 ππ

K0





Decay phase

(direct)




Isospin I=0

Isospin I=2


(CHARGE) BASIS









221

2

)(

)(

21

)(

)(

00

00

000000

S

Li

S

Li

KA

KAe

KA

KAe

)(

0

0

2

2

0

2

0

0

02

)Re(

)Im(

)Re(

)Im(

)Re(

)Re(

2

)Re(

)Im(

iea

a

a

a

a

ai

a

ai

221

)0(

)2(

IKA

IKA

S

S







Questions













p

Target


particle sweeping

Dump

Neutral beam

Collimator

Production

angle

Protonenergy Beam

acceptance

Collimatorbackgroun

d

KL (+KS) beams



KS by regeneration





KL KL + Ar KS








61)Re(612

2

00

)(

)(

)(

)(00

00

2

2

00

L

S

S

L

K

K

K

K







n


d(PSext) d3x d3ph3




Position scale

Momentum

scale



Direct CPV 1996 AD

FNAL E731






The presshellip







KTeV at Fermilab



NA48 at CERN




600

00

10)820045()()(

)()(

KK

KK




4

World average





rsquo why










K decays


(PDG2004)



For kaons


K2ππ




ΔΓ(K3π)Δg(K3π)












K vs B







200

200

200

200

KeKKeK

KeKKeKA

iHtiHt

iHtiHt

T


20

20

20

20

KefKef

KefKefA

iHtCP

iHtCP

iHtCP

iHtCP

CP

200

200

200

200

KeKKeK

KeKKeKA

iHtiHt

iHtiHt

CPT




CPLEAR experiment

(CERN 1990-96)






tf

ft

f

iHtCP

iHtCP

iHtCP

iHtCP

CPLS

LS

e

mte

KefKef

KefKefA

)(2

2)(

20

20

20

20

1

)cos(2)Re(2

π+π

minus

π0π0

π+π minusπ0

π0π0π0

CPLEARAsymmetrie

s


Rate difference


Measure η





Kaon factories




pppp 2

1SLSL KKKKi




[Lipkin (1968)]

EPR correlation


DAΦNE (Frascati)


DAΦNE (Frascati)


MeVc)









p = 127 MeVcλ = 95 cm

KLKS 106 pb-1




KLOE physics




















p

Target

Collimator



Dump

Tagging Separation

Charged beam




Buthellip



rarr Small in SM


2π (εrsquoε)

3π (Ag)


ν


π0

Kplusmn rarr 3π




π1

π2

π3

K


Kinematics



2


2

Matrix element

|M(uv)|2 ~ 1 + gu + hu2 + kv2







KminusK+








10-6

NA482 OKA

10-5

10-4

10-3

10-2

SMSM

SUSYSUSYNewNew

physicsphysics



|Ag|

bull Ag ~ 10minus5


SUSY New Physics

THEORY



C

N



=Ag



54 60 66

1cm

50 100

10 cm

200 250 m





~11012

ppp

K+

Kminus



always in vacuum

focusing beams

BM

z

magnet

vacuum tank

not to scale

K+

K


pipe

0ordm prodangle






ZZ

XXYY

JuraJura

SaleveSaleve

Beam line K+ Up


B+

Bminus






Spectrometer field

K+

Kminus

Reverse each day

Reverse each week


|V| even pion

in beam pipe


KK+ +

KK



No significant

background





-15 -10 -05 0 05 10 u

0

-1

-2

1

2

3

Dalitz plot



EM calorimeter only






2003 result in PLB 634 (2006) 474




2003 result in PLB 638 (2006) 22


excluded


OKA at Protvino





(in preparation)


More CP violation


Indirect

Direct

CP violation

parameters

(2005)


(A) KS decays


CPV in KS decays




000000

000

000 )(

)(

L

S

KA




S+KL

KL




000 000 00

1( )2 ( 2

0

)

( )


tt

NEARf E t



)()()( 00

00

EKNEKN

EKNEKNED

(incoherent

production)



Assuming CPT





N3

20

40

60

00

4 62


No CPV seen yet

























PT() = (-17 23 11) 10-

3

Im = (-53 71 36) 10-3




Im = (-53 71 36) 10-3








ppp

ppp

)0()0(

)0()0(

NN

NNA


Radiative decays








211221 )()(


IB DE

p1 p1

p2p2

q q







)(

)(

S

L

KA

violatingCPKA




KL π+πminus






IB

M1 DE




KL itself





KL ee


BR = (308 020) 10minus7



E1M1 lt 004 (90 CL)



φ




KS ee

No asymmetry for KS

as expected

BR = (471 032) 10-

5

AΦ = (05 43)






IBEE

dEA

)tan( 0


Kplusmn π+π0γ

)730810672()(

)250350353()(

800

800

syststatMeVT

syststatMeVT

INTFrac

DEFrac







KL π+πndashπ0γ















)(

)2030(

3

3

e

ee

K

MeVEKR





bull 6M Ke3 events


ndash R=(0964plusmn0008+0011-0009)












PDG 2004







]21[192 3

52

KmG







Vus measurements





unitarity





KLOE Kl 3

KLOE K2

copy A Antonelli

Vus some more




Ke4 results





K+rarrπ0π0eν










1-loop rescattering

2-loop rescattering











NA482




KLOE interference

















K+ + 8middot10-11 (at 7)147+130

ndash089 middot 10-

10 (BNL E787+E949)






KL 0ℓ+ℓ-




BR(KL 0+-) lt 3810-10





NA481 KS 0ℓ+ℓ-



BR = (58 +28-23 plusmn08) times10-9


-012 (accid)BR = (28 +15


KS 0e+e- KS 0μ+μ-


NA481 preliminary

NA481 preliminary


KL 0ℓ+ℓ-






Krarr in the SM




W W

s

id

Vis Vid

e

i=uct

W

Z

VisV

idds i

11

20

2410

10)1108(

)(1001)(

AKB

11

2

5

100

10)4082(

)()Im(

1022)(

t

tdtsL xX

VVKB


K

ε εrsquo




Ke3 KL 0

Height

Im(λt )



10301890 10471)(

KBR









K+ +




















Appendixes





J(ππ) = ℓ(ππ) = 0 P(ππ) = +1 C(ππ) = +1



ℓL



SLti

SLLSti

LS

tL

tS

Lti

LSti

S

KKeaaKKeaa

eaea

KeaKea

SLLS

LS

LS

)()(

22

f LSf

fLS KfA

dt

d 2

2

TUnitarity requires

and therefore


f Sff

fS

fLSLLS

f

fLLf

fSS

fKAAKKmi

AA

)(2)(

22


2

22

2

222

0604

mKK

AAAA

LS

LSLS

f

fSf

fLf

fS

fL



SLS KKmi 21




)()( 0000

SSS KK



[KS=K1 KL=K2]


Regeneration











6 inch plate

combined

K1 rate



M(K0) = 4977 MeVc2


[ π0 = (uu+dd)2 = π0 ]

K0 ne K0

In terms of quarks











Two-state formalism


)0()( tiet H

ΓΓMM

ΓMH

)(2

)()( ti

ttdt

di

)(2 11

112

Kkkij

kKk

ijKij

mEjHkkHi

mE

jHkkHijHimM



LSLSLS

LSLSLS

im

tKtKi

2

)()(2

ΓM



mm

HH

HH

K

KK HH

2221

1211

0

0

01


0

0

mmm

mmm

K

K


Case of CP symmetry

H11 = H22 = m0 H12 = H21 = δm





Eigenstates

22

11

KKCP

KKCP

21 KKKK LS



Since 00 LJJ

CPCP



K1K2 = 0

CP symmetric case







)0()0()(

2)(

22

1)(

11

222

111

KeKetK

KeKetKtimitiE

timitiE

002

001

2

12

1

KKK

KKK


1212 Re2Re2 Mm


6 eV



CP symmetric case




Brookhaven AD 1963


















(45 plusmn 9)22700



fall 1963









310)4002()(

)(

chargedKBR

KBR

L

L


The new paradigm

K0

K0

K0

K0


CP










Physical states

00

22

00

22

)1()1(

12

1

)1()1(

12

1

KKK

KKK

L

S

00

2122

00

2212

)1()1(12

1

1

1

)1()1(12

1

1

1

KKKKK

KKKKK

LL

L

L

L

L

SS

S

S

S

S

2)(

2)(

SL

LS






M12 ne M21 Γ12 ne Γ21

)2(2

)()(

2

Im)2(Im 112211221212

im

iMM

mi

iM






M11 ne M22 Γ11 ne Γ22

Re(ε) really






34

2

2102

p

p

F

F

FSW

m

m

G

G

m

G

m

G




2

Im)2(Im 1212

mi

iM











KL K2+ ε K1

ππ






KL K2+ ε K1

ππ


K2 (CP=-1) ππ (CP=+1)






This is named



K0 ππ

K0





Decay phase

(direct)




Isospin I=0

Isospin I=2


(CHARGE) BASIS









221

2

)(

)(

21

)(

)(

00

00

000000

S

Li

S

Li

KA

KAe

KA

KAe

)(

0

0

2

2

0

2

0

0

02

)Re(

)Im(

)Re(

)Im(

)Re(

)Re(

2

)Re(

)Im(

iea

a

a

a

a

ai

a

ai

221

)0(

)2(

IKA

IKA

S

S







Questions













p

Target


particle sweeping

Dump

Neutral beam

Collimator

Production

angle

Protonenergy Beam

acceptance

Collimatorbackgroun

d

KL (+KS) beams



KS by regeneration





KL KL + Ar KS








61)Re(612

2

00

)(

)(

)(

)(00

00

2

2

00

L

S

S

L

K

K

K

K







n


d(PSext) d3x d3ph3




Position scale

Momentum

scale



Direct CPV 1996 AD

FNAL E731






The presshellip







KTeV at Fermilab



NA48 at CERN




600

00

10)820045()()(

)()(

KK

KK




4

World average





rsquo why










K decays


(PDG2004)



For kaons


K2ππ




ΔΓ(K3π)Δg(K3π)












K vs B







200

200

200

200

KeKKeK

KeKKeKA

iHtiHt

iHtiHt

T


20

20

20

20

KefKef

KefKefA

iHtCP

iHtCP

iHtCP

iHtCP

CP

200

200

200

200

KeKKeK

KeKKeKA

iHtiHt

iHtiHt

CPT




CPLEAR experiment

(CERN 1990-96)






tf

ft

f

iHtCP

iHtCP

iHtCP

iHtCP

CPLS

LS

e

mte

KefKef

KefKefA

)(2

2)(

20

20

20

20

1

)cos(2)Re(2

π+π

minus

π0π0

π+π minusπ0

π0π0π0

CPLEARAsymmetrie

s


Rate difference


Measure η





Kaon factories




pppp 2

1SLSL KKKKi




[Lipkin (1968)]

EPR correlation


DAΦNE (Frascati)


DAΦNE (Frascati)


MeVc)









p = 127 MeVcλ = 95 cm

KLKS 106 pb-1




KLOE physics




















p

Target

Collimator



Dump

Tagging Separation

Charged beam




Buthellip



rarr Small in SM


2π (εrsquoε)

3π (Ag)


ν


π0

Kplusmn rarr 3π




π1

π2

π3

K


Kinematics



2


2

Matrix element

|M(uv)|2 ~ 1 + gu + hu2 + kv2







KminusK+








10-6

NA482 OKA

10-5

10-4

10-3

10-2

SMSM

SUSYSUSYNewNew

physicsphysics



|Ag|

bull Ag ~ 10minus5


SUSY New Physics

THEORY



C

N



=Ag



54 60 66

1cm

50 100

10 cm

200 250 m





~11012

ppp

K+

Kminus



always in vacuum

focusing beams

BM

z

magnet

vacuum tank

not to scale

K+

K


pipe

0ordm prodangle






ZZ

XXYY

JuraJura

SaleveSaleve

Beam line K+ Up


B+

Bminus






Spectrometer field

K+

Kminus

Reverse each day

Reverse each week


|V| even pion

in beam pipe


KK+ +

KK



No significant

background





-15 -10 -05 0 05 10 u

0

-1

-2

1

2

3

Dalitz plot



EM calorimeter only






2003 result in PLB 634 (2006) 474




2003 result in PLB 638 (2006) 22


excluded


OKA at Protvino





(in preparation)


More CP violation


Indirect

Direct

CP violation

parameters

(2005)


(A) KS decays


CPV in KS decays




000000

000

000 )(

)(

L

S

KA




S+KL

KL




000 000 00

1( )2 ( 2

0

)

( )


tt

NEARf E t



)()()( 00

00

EKNEKN

EKNEKNED

(incoherent

production)



Assuming CPT





N3

20

40

60

00

4 62


No CPV seen yet

























PT() = (-17 23 11) 10-

3

Im = (-53 71 36) 10-3




Im = (-53 71 36) 10-3








ppp

ppp

)0()0(

)0()0(

NN

NNA


Radiative decays








211221 )()(


IB DE

p1 p1

p2p2

q q







)(

)(

S

L

KA

violatingCPKA




KL π+πminus






IB

M1 DE




KL itself





KL ee


BR = (308 020) 10minus7



E1M1 lt 004 (90 CL)



φ




KS ee

No asymmetry for KS

as expected

BR = (471 032) 10-

5

AΦ = (05 43)






IBEE

dEA

)tan( 0


Kplusmn π+π0γ

)730810672()(

)250350353()(

800

800

syststatMeVT

syststatMeVT

INTFrac

DEFrac







KL π+πndashπ0γ















)(

)2030(

3

3

e

ee

K

MeVEKR





bull 6M Ke3 events


ndash R=(0964plusmn0008+0011-0009)












PDG 2004







]21[192 3

52

KmG







Vus measurements





unitarity





KLOE Kl 3

KLOE K2

copy A Antonelli

Vus some more




Ke4 results





K+rarrπ0π0eν










1-loop rescattering

2-loop rescattering











NA482




KLOE interference

















K+ + 8middot10-11 (at 7)147+130

ndash089 middot 10-

10 (BNL E787+E949)






KL 0ℓ+ℓ-




BR(KL 0+-) lt 3810-10





NA481 KS 0ℓ+ℓ-



BR = (58 +28-23 plusmn08) times10-9


-012 (accid)BR = (28 +15


KS 0e+e- KS 0μ+μ-


NA481 preliminary

NA481 preliminary


KL 0ℓ+ℓ-






Krarr in the SM




W W

s

id

Vis Vid

e

i=uct

W

Z

VisV

idds i

11

20

2410

10)1108(

)(1001)(

AKB

11

2

5

100

10)4082(

)()Im(

1022)(

t

tdtsL xX

VVKB


K

ε εrsquo




Ke3 KL 0

Height

Im(λt )



10301890 10471)(

KBR









K+ +




















Appendixes





J(ππ) = ℓ(ππ) = 0 P(ππ) = +1 C(ππ) = +1



ℓL



SLti

SLLSti

LS

tL

tS

Lti

LSti

S

KKeaaKKeaa

eaea

KeaKea

SLLS

LS

LS

)()(

22

f LSf

fLS KfA

dt

d 2

2

TUnitarity requires

and therefore


f Sff

fS

fLSLLS

f

fLLf

fSS

fKAAKKmi

AA

)(2)(

22


2

22

2

222

0604

mKK

AAAA

LS

LSLS

f

fSf

fLf

fS

fL



SLS KKmi 21




)()( 0000

SSS KK








6 inch plate

combined

K1 rate



M(K0) = 4977 MeVc2


[ π0 = (uu+dd)2 = π0 ]

K0 ne K0

In terms of quarks











Two-state formalism


)0()( tiet H

ΓΓMM

ΓMH

)(2

)()( ti

ttdt

di

)(2 11

112

Kkkij

kKk

ijKij

mEjHkkHi

mE

jHkkHijHimM



LSLSLS

LSLSLS

im

tKtKi

2

)()(2

ΓM



mm

HH

HH

K

KK HH

2221

1211

0

0

01


0

0

mmm

mmm

K

K


Case of CP symmetry

H11 = H22 = m0 H12 = H21 = δm





Eigenstates

22

11

KKCP

KKCP

21 KKKK LS



Since 00 LJJ

CPCP



K1K2 = 0

CP symmetric case







)0()0()(

2)(

22

1)(

11

222

111

KeKetK

KeKetKtimitiE

timitiE

002

001

2

12

1

KKK

KKK


1212 Re2Re2 Mm


6 eV



CP symmetric case




Brookhaven AD 1963


















(45 plusmn 9)22700



fall 1963









310)4002()(

)(

chargedKBR

KBR

L

L


The new paradigm

K0

K0

K0

K0


CP










Physical states

00

22

00

22

)1()1(

12

1

)1()1(

12

1

KKK

KKK

L

S

00

2122

00

2212

)1()1(12

1

1

1

)1()1(12

1

1

1

KKKKK

KKKKK

LL

L

L

L

L

SS

S

S

S

S

2)(

2)(

SL

LS






M12 ne M21 Γ12 ne Γ21

)2(2

)()(

2

Im)2(Im 112211221212

im

iMM

mi

iM






M11 ne M22 Γ11 ne Γ22

Re(ε) really






34

2

2102

p

p

F

F

FSW

m

m

G

G

m

G

m

G




2

Im)2(Im 1212

mi

iM











KL K2+ ε K1

ππ






KL K2+ ε K1

ππ


K2 (CP=-1) ππ (CP=+1)






This is named



K0 ππ

K0





Decay phase

(direct)




Isospin I=0

Isospin I=2


(CHARGE) BASIS









221

2

)(

)(

21

)(

)(

00

00

000000

S

Li

S

Li

KA

KAe

KA

KAe

)(

0

0

2

2

0

2

0

0

02

)Re(

)Im(

)Re(

)Im(

)Re(

)Re(

2

)Re(

)Im(

iea

a

a

a

a

ai

a

ai

221

)0(

)2(

IKA

IKA

S

S







Questions













p

Target


particle sweeping

Dump

Neutral beam

Collimator

Production

angle

Protonenergy Beam

acceptance

Collimatorbackgroun

d

KL (+KS) beams



KS by regeneration





KL KL + Ar KS








61)Re(612

2

00

)(

)(

)(

)(00

00

2

2

00

L

S

S

L

K

K

K

K







n


d(PSext) d3x d3ph3




Position scale

Momentum

scale



Direct CPV 1996 AD

FNAL E731






The presshellip







KTeV at Fermilab



NA48 at CERN




600

00

10)820045()()(

)()(

KK

KK




4

World average





rsquo why










K decays


(PDG2004)



For kaons


K2ππ




ΔΓ(K3π)Δg(K3π)












K vs B







200

200

200

200

KeKKeK

KeKKeKA

iHtiHt

iHtiHt

T


20

20

20

20

KefKef

KefKefA

iHtCP

iHtCP

iHtCP

iHtCP

CP

200

200

200

200

KeKKeK

KeKKeKA

iHtiHt

iHtiHt

CPT




CPLEAR experiment

(CERN 1990-96)






tf

ft

f

iHtCP

iHtCP

iHtCP

iHtCP

CPLS

LS

e

mte

KefKef

KefKefA

)(2

2)(

20

20

20

20

1

)cos(2)Re(2

π+π

minus

π0π0

π+π minusπ0

π0π0π0

CPLEARAsymmetrie

s


Rate difference


Measure η





Kaon factories




pppp 2

1SLSL KKKKi




[Lipkin (1968)]

EPR correlation


DAΦNE (Frascati)


DAΦNE (Frascati)


MeVc)









p = 127 MeVcλ = 95 cm

KLKS 106 pb-1




KLOE physics




















p

Target

Collimator



Dump

Tagging Separation

Charged beam




Buthellip



rarr Small in SM


2π (εrsquoε)

3π (Ag)


ν


π0

Kplusmn rarr 3π




π1

π2

π3

K


Kinematics



2


2

Matrix element

|M(uv)|2 ~ 1 + gu + hu2 + kv2







KminusK+








10-6

NA482 OKA

10-5

10-4

10-3

10-2

SMSM

SUSYSUSYNewNew

physicsphysics



|Ag|

bull Ag ~ 10minus5


SUSY New Physics

THEORY



C

N



=Ag



54 60 66

1cm

50 100

10 cm

200 250 m





~11012

ppp

K+

Kminus



always in vacuum

focusing beams

BM

z

magnet

vacuum tank

not to scale

K+

K


pipe

0ordm prodangle






ZZ

XXYY

JuraJura

SaleveSaleve

Beam line K+ Up


B+

Bminus






Spectrometer field

K+

Kminus

Reverse each day

Reverse each week


|V| even pion

in beam pipe


KK+ +

KK



No significant

background





-15 -10 -05 0 05 10 u

0

-1

-2

1

2

3

Dalitz plot



EM calorimeter only






2003 result in PLB 634 (2006) 474




2003 result in PLB 638 (2006) 22


excluded


OKA at Protvino





(in preparation)


More CP violation


Indirect

Direct

CP violation

parameters

(2005)


(A) KS decays


CPV in KS decays




000000

000

000 )(

)(

L

S

KA




S+KL

KL




000 000 00

1( )2 ( 2

0

)

( )


tt

NEARf E t



)()()( 00

00

EKNEKN

EKNEKNED

(incoherent

production)



Assuming CPT





N3

20

40

60

00

4 62


No CPV seen yet

























PT() = (-17 23 11) 10-

3

Im = (-53 71 36) 10-3




Im = (-53 71 36) 10-3








ppp

ppp

)0()0(

)0()0(

NN

NNA


Radiative decays








211221 )()(


IB DE

p1 p1

p2p2

q q







)(

)(

S

L

KA

violatingCPKA




KL π+πminus






IB

M1 DE




KL itself





KL ee


BR = (308 020) 10minus7



E1M1 lt 004 (90 CL)



φ




KS ee

No asymmetry for KS

as expected

BR = (471 032) 10-

5

AΦ = (05 43)






IBEE

dEA

)tan( 0


Kplusmn π+π0γ

)730810672()(

)250350353()(

800

800

syststatMeVT

syststatMeVT

INTFrac

DEFrac







KL π+πndashπ0γ















)(

)2030(

3

3

e

ee

K

MeVEKR





bull 6M Ke3 events


ndash R=(0964plusmn0008+0011-0009)












PDG 2004







]21[192 3

52

KmG







Vus measurements





unitarity





KLOE Kl 3

KLOE K2

copy A Antonelli

Vus some more




Ke4 results





K+rarrπ0π0eν










1-loop rescattering

2-loop rescattering











NA482




KLOE interference

















K+ + 8middot10-11 (at 7)147+130

ndash089 middot 10-

10 (BNL E787+E949)






KL 0ℓ+ℓ-




BR(KL 0+-) lt 3810-10





NA481 KS 0ℓ+ℓ-



BR = (58 +28-23 plusmn08) times10-9


-012 (accid)BR = (28 +15


KS 0e+e- KS 0μ+μ-


NA481 preliminary

NA481 preliminary


KL 0ℓ+ℓ-






Krarr in the SM




W W

s

id

Vis Vid

e

i=uct

W

Z

VisV

idds i

11

20

2410

10)1108(

)(1001)(

AKB

11

2

5

100

10)4082(

)()Im(

1022)(

t

tdtsL xX

VVKB


K

ε εrsquo




Ke3 KL 0

Height

Im(λt )



10301890 10471)(

KBR









K+ +




















Appendixes





J(ππ) = ℓ(ππ) = 0 P(ππ) = +1 C(ππ) = +1



ℓL



SLti

SLLSti

LS

tL

tS

Lti

LSti

S

KKeaaKKeaa

eaea

KeaKea

SLLS

LS

LS

)()(

22

f LSf

fLS KfA

dt

d 2

2

TUnitarity requires

and therefore


f Sff

fS

fLSLLS

f

fLLf

fSS

fKAAKKmi

AA

)(2)(

22


2

22

2

222

0604

mKK

AAAA

LS

LSLS

f

fSf

fLf

fS

fL



SLS KKmi 21




)()( 0000

SSS KK



M(K0) = 4977 MeVc2


[ π0 = (uu+dd)2 = π0 ]

K0 ne K0

In terms of quarks











Two-state formalism


)0()( tiet H

ΓΓMM

ΓMH

)(2

)()( ti

ttdt

di

)(2 11

112

Kkkij

kKk

ijKij

mEjHkkHi

mE

jHkkHijHimM



LSLSLS

LSLSLS

im

tKtKi

2

)()(2

ΓM



mm

HH

HH

K

KK HH

2221

1211

0

0

01


0

0

mmm

mmm

K

K


Case of CP symmetry

H11 = H22 = m0 H12 = H21 = δm





Eigenstates

22

11

KKCP

KKCP

21 KKKK LS



Since 00 LJJ

CPCP



K1K2 = 0

CP symmetric case







)0()0()(

2)(

22

1)(

11

222

111

KeKetK

KeKetKtimitiE

timitiE

002

001

2

12

1

KKK

KKK


1212 Re2Re2 Mm


6 eV



CP symmetric case




Brookhaven AD 1963


















(45 plusmn 9)22700



fall 1963









310)4002()(

)(

chargedKBR

KBR

L

L


The new paradigm

K0

K0

K0

K0


CP










Physical states

00

22

00

22

)1()1(

12

1

)1()1(

12

1

KKK

KKK

L

S

00

2122

00

2212

)1()1(12

1

1

1

)1()1(12

1

1

1

KKKKK

KKKKK

LL

L

L

L

L

SS

S

S

S

S

2)(

2)(

SL

LS






M12 ne M21 Γ12 ne Γ21

)2(2

)()(

2

Im)2(Im 112211221212

im

iMM

mi

iM






M11 ne M22 Γ11 ne Γ22

Re(ε) really






34

2

2102

p

p

F

F

FSW

m

m

G

G

m

G

m

G




2

Im)2(Im 1212

mi

iM











KL K2+ ε K1

ππ






KL K2+ ε K1

ππ


K2 (CP=-1) ππ (CP=+1)






This is named



K0 ππ

K0





Decay phase

(direct)




Isospin I=0

Isospin I=2


(CHARGE) BASIS









221

2

)(

)(

21

)(

)(

00

00

000000

S

Li

S

Li

KA

KAe

KA

KAe

)(

0

0

2

2

0

2

0

0

02

)Re(

)Im(

)Re(

)Im(

)Re(

)Re(

2

)Re(

)Im(

iea

a

a

a

a

ai

a

ai

221

)0(

)2(

IKA

IKA

S

S







Questions













p

Target


particle sweeping

Dump

Neutral beam

Collimator

Production

angle

Protonenergy Beam

acceptance

Collimatorbackgroun

d

KL (+KS) beams



KS by regeneration





KL KL + Ar KS








61)Re(612

2

00

)(

)(

)(

)(00

00

2

2

00

L

S

S

L

K

K

K

K







n


d(PSext) d3x d3ph3




Position scale

Momentum

scale



Direct CPV 1996 AD

FNAL E731






The presshellip







KTeV at Fermilab



NA48 at CERN




600

00

10)820045()()(

)()(

KK

KK




4

World average





rsquo why










K decays


(PDG2004)



For kaons


K2ππ




ΔΓ(K3π)Δg(K3π)












K vs B







200

200

200

200

KeKKeK

KeKKeKA

iHtiHt

iHtiHt

T


20

20

20

20

KefKef

KefKefA

iHtCP

iHtCP

iHtCP

iHtCP

CP

200

200

200

200

KeKKeK

KeKKeKA

iHtiHt

iHtiHt

CPT




CPLEAR experiment

(CERN 1990-96)






tf

ft

f

iHtCP

iHtCP

iHtCP

iHtCP

CPLS

LS

e

mte

KefKef

KefKefA

)(2

2)(

20

20

20

20

1

)cos(2)Re(2

π+π

minus

π0π0

π+π minusπ0

π0π0π0

CPLEARAsymmetrie

s


Rate difference


Measure η





Kaon factories




pppp 2

1SLSL KKKKi




[Lipkin (1968)]

EPR correlation


DAΦNE (Frascati)


DAΦNE (Frascati)


MeVc)









p = 127 MeVcλ = 95 cm

KLKS 106 pb-1




KLOE physics




















p

Target

Collimator



Dump

Tagging Separation

Charged beam




Buthellip



rarr Small in SM


2π (εrsquoε)

3π (Ag)


ν


π0

Kplusmn rarr 3π




π1

π2

π3

K


Kinematics



2


2

Matrix element

|M(uv)|2 ~ 1 + gu + hu2 + kv2







KminusK+








10-6

NA482 OKA

10-5

10-4

10-3

10-2

SMSM

SUSYSUSYNewNew

physicsphysics



|Ag|

bull Ag ~ 10minus5


SUSY New Physics

THEORY



C

N



=Ag



54 60 66

1cm

50 100

10 cm

200 250 m





~11012

ppp

K+

Kminus



always in vacuum

focusing beams

BM

z

magnet

vacuum tank

not to scale

K+

K


pipe

0ordm prodangle






ZZ

XXYY

JuraJura

SaleveSaleve

Beam line K+ Up


B+

Bminus






Spectrometer field

K+

Kminus

Reverse each day

Reverse each week


|V| even pion

in beam pipe


KK+ +

KK



No significant

background





-15 -10 -05 0 05 10 u

0

-1

-2

1

2

3

Dalitz plot



EM calorimeter only






2003 result in PLB 634 (2006) 474




2003 result in PLB 638 (2006) 22


excluded


OKA at Protvino





(in preparation)


More CP violation


Indirect

Direct

CP violation

parameters

(2005)


(A) KS decays


CPV in KS decays




000000

000

000 )(

)(

L

S

KA




S+KL

KL




000 000 00

1( )2 ( 2

0

)

( )


tt

NEARf E t



)()()( 00

00

EKNEKN

EKNEKNED

(incoherent

production)



Assuming CPT





N3

20

40

60

00

4 62


No CPV seen yet

























PT() = (-17 23 11) 10-

3

Im = (-53 71 36) 10-3




Im = (-53 71 36) 10-3








ppp

ppp

)0()0(

)0()0(

NN

NNA


Radiative decays








211221 )()(


IB DE

p1 p1

p2p2

q q







)(

)(

S

L

KA

violatingCPKA




KL π+πminus






IB

M1 DE




KL itself





KL ee


BR = (308 020) 10minus7



E1M1 lt 004 (90 CL)



φ




KS ee

No asymmetry for KS

as expected

BR = (471 032) 10-

5

AΦ = (05 43)






IBEE

dEA

)tan( 0


Kplusmn π+π0γ

)730810672()(

)250350353()(

800

800

syststatMeVT

syststatMeVT

INTFrac

DEFrac







KL π+πndashπ0γ















)(

)2030(

3

3

e

ee

K

MeVEKR





bull 6M Ke3 events


ndash R=(0964plusmn0008+0011-0009)












PDG 2004







]21[192 3

52

KmG







Vus measurements





unitarity





KLOE Kl 3

KLOE K2

copy A Antonelli

Vus some more




Ke4 results





K+rarrπ0π0eν










1-loop rescattering

2-loop rescattering











NA482




KLOE interference

















K+ + 8middot10-11 (at 7)147+130

ndash089 middot 10-

10 (BNL E787+E949)






KL 0ℓ+ℓ-




BR(KL 0+-) lt 3810-10





NA481 KS 0ℓ+ℓ-



BR = (58 +28-23 plusmn08) times10-9


-012 (accid)BR = (28 +15


KS 0e+e- KS 0μ+μ-


NA481 preliminary

NA481 preliminary


KL 0ℓ+ℓ-






Krarr in the SM




W W

s

id

Vis Vid

e

i=uct

W

Z

VisV

idds i

11

20

2410

10)1108(

)(1001)(

AKB

11

2

5

100

10)4082(

)()Im(

1022)(

t

tdtsL xX

VVKB


K

ε εrsquo




Ke3 KL 0

Height

Im(λt )



10301890 10471)(

KBR









K+ +




















Appendixes





J(ππ) = ℓ(ππ) = 0 P(ππ) = +1 C(ππ) = +1



ℓL



SLti

SLLSti

LS

tL

tS

Lti

LSti

S

KKeaaKKeaa

eaea

KeaKea

SLLS

LS

LS

)()(

22

f LSf

fLS KfA

dt

d 2

2

TUnitarity requires

and therefore


f Sff

fS

fLSLLS

f

fLLf

fSS

fKAAKKmi

AA

)(2)(

22


2

22

2

222

0604

mKK

AAAA

LS

LSLS

f

fSf

fLf

fS

fL



SLS KKmi 21




)()( 0000

SSS KK








Two-state formalism


)0()( tiet H

ΓΓMM

ΓMH

)(2

)()( ti

ttdt

di

)(2 11

112

Kkkij

kKk

ijKij

mEjHkkHi

mE

jHkkHijHimM



LSLSLS

LSLSLS

im

tKtKi

2

)()(2

ΓM



mm

HH

HH

K

KK HH

2221

1211

0

0

01


0

0

mmm

mmm

K

K


Case of CP symmetry

H11 = H22 = m0 H12 = H21 = δm





Eigenstates

22

11

KKCP

KKCP

21 KKKK LS



Since 00 LJJ

CPCP



K1K2 = 0

CP symmetric case







)0()0()(

2)(

22

1)(

11

222

111

KeKetK

KeKetKtimitiE

timitiE

002

001

2

12

1

KKK

KKK


1212 Re2Re2 Mm


6 eV



CP symmetric case




Brookhaven AD 1963


















(45 plusmn 9)22700



fall 1963









310)4002()(

)(

chargedKBR

KBR

L

L


The new paradigm

K0

K0

K0

K0


CP










Physical states

00

22

00

22

)1()1(

12

1

)1()1(

12

1

KKK

KKK

L

S

00

2122

00

2212

)1()1(12

1

1

1

)1()1(12

1

1

1

KKKKK

KKKKK

LL

L

L

L

L

SS

S

S

S

S

2)(

2)(

SL

LS






M12 ne M21 Γ12 ne Γ21

)2(2

)()(

2

Im)2(Im 112211221212

im

iMM

mi

iM






M11 ne M22 Γ11 ne Γ22

Re(ε) really






34

2

2102

p

p

F

F

FSW

m

m

G

G

m

G

m

G




2

Im)2(Im 1212

mi

iM











KL K2+ ε K1

ππ






KL K2+ ε K1

ππ


K2 (CP=-1) ππ (CP=+1)






This is named



K0 ππ

K0





Decay phase

(direct)




Isospin I=0

Isospin I=2


(CHARGE) BASIS









221

2

)(

)(

21

)(

)(

00

00

000000

S

Li

S

Li

KA

KAe

KA

KAe

)(

0

0

2

2

0

2

0

0

02

)Re(

)Im(

)Re(

)Im(

)Re(

)Re(

2

)Re(

)Im(

iea

a

a

a

a

ai

a

ai

221

)0(

)2(

IKA

IKA

S

S







Questions













p

Target


particle sweeping

Dump

Neutral beam

Collimator

Production

angle

Protonenergy Beam

acceptance

Collimatorbackgroun

d

KL (+KS) beams



KS by regeneration





KL KL + Ar KS








61)Re(612

2

00

)(

)(

)(

)(00

00

2

2

00

L

S

S

L

K

K

K

K







n


d(PSext) d3x d3ph3




Position scale

Momentum

scale



Direct CPV 1996 AD

FNAL E731






The presshellip







KTeV at Fermilab



NA48 at CERN




600

00

10)820045()()(

)()(

KK

KK




4

World average





rsquo why










K decays


(PDG2004)



For kaons


K2ππ




ΔΓ(K3π)Δg(K3π)












K vs B







200

200

200

200

KeKKeK

KeKKeKA

iHtiHt

iHtiHt

T


20

20

20

20

KefKef

KefKefA

iHtCP

iHtCP

iHtCP

iHtCP

CP

200

200

200

200

KeKKeK

KeKKeKA

iHtiHt

iHtiHt

CPT




CPLEAR experiment

(CERN 1990-96)






tf

ft

f

iHtCP

iHtCP

iHtCP

iHtCP

CPLS

LS

e

mte

KefKef

KefKefA

)(2

2)(

20

20

20

20

1

)cos(2)Re(2

π+π

minus

π0π0

π+π minusπ0

π0π0π0

CPLEARAsymmetrie

s


Rate difference


Measure η





Kaon factories




pppp 2

1SLSL KKKKi




[Lipkin (1968)]

EPR correlation


DAΦNE (Frascati)


DAΦNE (Frascati)


MeVc)









p = 127 MeVcλ = 95 cm

KLKS 106 pb-1




KLOE physics




















p

Target

Collimator



Dump

Tagging Separation

Charged beam




Buthellip



rarr Small in SM


2π (εrsquoε)

3π (Ag)


ν


π0

Kplusmn rarr 3π




π1

π2

π3

K


Kinematics



2


2

Matrix element

|M(uv)|2 ~ 1 + gu + hu2 + kv2







KminusK+








10-6

NA482 OKA

10-5

10-4

10-3

10-2

SMSM

SUSYSUSYNewNew

physicsphysics



|Ag|

bull Ag ~ 10minus5


SUSY New Physics

THEORY



C

N



=Ag



54 60 66

1cm

50 100

10 cm

200 250 m





~11012

ppp

K+

Kminus



always in vacuum

focusing beams

BM

z

magnet

vacuum tank

not to scale

K+

K


pipe

0ordm prodangle






ZZ

XXYY

JuraJura

SaleveSaleve

Beam line K+ Up


B+

Bminus






Spectrometer field

K+

Kminus

Reverse each day

Reverse each week


|V| even pion

in beam pipe


KK+ +

KK



No significant

background





-15 -10 -05 0 05 10 u

0

-1

-2

1

2

3

Dalitz plot



EM calorimeter only






2003 result in PLB 634 (2006) 474




2003 result in PLB 638 (2006) 22


excluded


OKA at Protvino





(in preparation)


More CP violation


Indirect

Direct

CP violation

parameters

(2005)


(A) KS decays


CPV in KS decays




000000

000

000 )(

)(

L

S

KA




S+KL

KL




000 000 00

1( )2 ( 2

0

)

( )


tt

NEARf E t



)()()( 00

00

EKNEKN

EKNEKNED

(incoherent

production)



Assuming CPT





N3

20

40

60

00

4 62


No CPV seen yet

























PT() = (-17 23 11) 10-

3

Im = (-53 71 36) 10-3




Im = (-53 71 36) 10-3








ppp

ppp

)0()0(

)0()0(

NN

NNA


Radiative decays








211221 )()(


IB DE

p1 p1

p2p2

q q







)(

)(

S

L

KA

violatingCPKA




KL π+πminus






IB

M1 DE




KL itself





KL ee


BR = (308 020) 10minus7



E1M1 lt 004 (90 CL)



φ




KS ee

No asymmetry for KS

as expected

BR = (471 032) 10-

5

AΦ = (05 43)






IBEE

dEA

)tan( 0


Kplusmn π+π0γ

)730810672()(

)250350353()(

800

800

syststatMeVT

syststatMeVT

INTFrac

DEFrac







KL π+πndashπ0γ















)(

)2030(

3

3

e

ee

K

MeVEKR





bull 6M Ke3 events


ndash R=(0964plusmn0008+0011-0009)












PDG 2004







]21[192 3

52

KmG







Vus measurements





unitarity





KLOE Kl 3

KLOE K2

copy A Antonelli

Vus some more




Ke4 results





K+rarrπ0π0eν










1-loop rescattering

2-loop rescattering











NA482




KLOE interference

















K+ + 8middot10-11 (at 7)147+130

ndash089 middot 10-

10 (BNL E787+E949)






KL 0ℓ+ℓ-




BR(KL 0+-) lt 3810-10





NA481 KS 0ℓ+ℓ-



BR = (58 +28-23 plusmn08) times10-9


-012 (accid)BR = (28 +15


KS 0e+e- KS 0μ+μ-


NA481 preliminary

NA481 preliminary


KL 0ℓ+ℓ-






Krarr in the SM




W W

s

id

Vis Vid

e

i=uct

W

Z

VisV

idds i

11

20

2410

10)1108(

)(1001)(

AKB

11

2

5

100

10)4082(

)()Im(

1022)(

t

tdtsL xX

VVKB


K

ε εrsquo




Ke3 KL 0

Height

Im(λt )



10301890 10471)(

KBR









K+ +




















Appendixes





J(ππ) = ℓ(ππ) = 0 P(ππ) = +1 C(ππ) = +1



ℓL



SLti

SLLSti

LS

tL

tS

Lti

LSti

S

KKeaaKKeaa

eaea

KeaKea

SLLS

LS

LS

)()(

22

f LSf

fLS KfA

dt

d 2

2

TUnitarity requires

and therefore


f Sff

fS

fLSLLS

f

fLLf

fSS

fKAAKKmi

AA

)(2)(

22


2

22

2

222

0604

mKK

AAAA

LS

LSLS

f

fSf

fLf

fS

fL



SLS KKmi 21




)()( 0000

SSS KK



Two-state formalism


)0()( tiet H

ΓΓMM

ΓMH

)(2

)()( ti

ttdt

di

)(2 11

112

Kkkij

kKk

ijKij

mEjHkkHi

mE

jHkkHijHimM



LSLSLS

LSLSLS

im

tKtKi

2

)()(2

ΓM



mm

HH

HH

K

KK HH

2221

1211

0

0

01


0

0

mmm

mmm

K

K


Case of CP symmetry

H11 = H22 = m0 H12 = H21 = δm





Eigenstates

22

11

KKCP

KKCP

21 KKKK LS



Since 00 LJJ

CPCP



K1K2 = 0

CP symmetric case







)0()0()(

2)(

22

1)(

11

222

111

KeKetK

KeKetKtimitiE

timitiE

002

001

2

12

1

KKK

KKK


1212 Re2Re2 Mm


6 eV



CP symmetric case




Brookhaven AD 1963


















(45 plusmn 9)22700



fall 1963









310)4002()(

)(

chargedKBR

KBR

L

L


The new paradigm

K0

K0

K0

K0


CP










Physical states

00

22

00

22

)1()1(

12

1

)1()1(

12

1

KKK

KKK

L

S

00

2122

00

2212

)1()1(12

1

1

1

)1()1(12

1

1

1

KKKKK

KKKKK

LL

L

L

L

L

SS

S

S

S

S

2)(

2)(

SL

LS






M12 ne M21 Γ12 ne Γ21

)2(2

)()(

2

Im)2(Im 112211221212

im

iMM

mi

iM






M11 ne M22 Γ11 ne Γ22

Re(ε) really






34

2

2102

p

p

F

F

FSW

m

m

G

G

m

G

m

G




2

Im)2(Im 1212

mi

iM











KL K2+ ε K1

ππ






KL K2+ ε K1

ππ


K2 (CP=-1) ππ (CP=+1)






This is named



K0 ππ

K0





Decay phase

(direct)




Isospin I=0

Isospin I=2


(CHARGE) BASIS









221

2

)(

)(

21

)(

)(

00

00

000000

S

Li

S

Li

KA

KAe

KA

KAe

)(

0

0

2

2

0

2

0

0

02

)Re(

)Im(

)Re(

)Im(

)Re(

)Re(

2

)Re(

)Im(

iea

a

a

a

a

ai

a

ai

221

)0(

)2(

IKA

IKA

S

S







Questions













p

Target


particle sweeping

Dump

Neutral beam

Collimator

Production

angle

Protonenergy Beam

acceptance

Collimatorbackgroun

d

KL (+KS) beams



KS by regeneration





KL KL + Ar KS








61)Re(612

2

00

)(

)(

)(

)(00

00

2

2

00

L

S

S

L

K

K

K

K







n


d(PSext) d3x d3ph3




Position scale

Momentum

scale



Direct CPV 1996 AD

FNAL E731






The presshellip







KTeV at Fermilab



NA48 at CERN




600

00

10)820045()()(

)()(

KK

KK




4

World average





rsquo why










K decays


(PDG2004)



For kaons


K2ππ




ΔΓ(K3π)Δg(K3π)












K vs B







200

200

200

200

KeKKeK

KeKKeKA

iHtiHt

iHtiHt

T


20

20

20

20

KefKef

KefKefA

iHtCP

iHtCP

iHtCP

iHtCP

CP

200

200

200

200

KeKKeK

KeKKeKA

iHtiHt

iHtiHt

CPT




CPLEAR experiment

(CERN 1990-96)






tf

ft

f

iHtCP

iHtCP

iHtCP

iHtCP

CPLS

LS

e

mte

KefKef

KefKefA

)(2

2)(

20

20

20

20

1

)cos(2)Re(2

π+π

minus

π0π0

π+π minusπ0

π0π0π0

CPLEARAsymmetrie

s


Rate difference


Measure η





Kaon factories




pppp 2

1SLSL KKKKi




[Lipkin (1968)]

EPR correlation


DAΦNE (Frascati)


DAΦNE (Frascati)


MeVc)









p = 127 MeVcλ = 95 cm

KLKS 106 pb-1




KLOE physics




















p

Target

Collimator



Dump

Tagging Separation

Charged beam




Buthellip



rarr Small in SM


2π (εrsquoε)

3π (Ag)


ν


π0

Kplusmn rarr 3π




π1

π2

π3

K


Kinematics



2


2

Matrix element

|M(uv)|2 ~ 1 + gu + hu2 + kv2







KminusK+








10-6

NA482 OKA

10-5

10-4

10-3

10-2

SMSM

SUSYSUSYNewNew

physicsphysics



|Ag|

bull Ag ~ 10minus5


SUSY New Physics

THEORY



C

N



=Ag



54 60 66

1cm

50 100

10 cm

200 250 m





~11012

ppp

K+

Kminus



always in vacuum

focusing beams

BM

z

magnet

vacuum tank

not to scale

K+

K


pipe

0ordm prodangle






ZZ

XXYY

JuraJura

SaleveSaleve

Beam line K+ Up


B+

Bminus






Spectrometer field

K+

Kminus

Reverse each day

Reverse each week


|V| even pion

in beam pipe


KK+ +

KK



No significant

background





-15 -10 -05 0 05 10 u

0

-1

-2

1

2

3

Dalitz plot



EM calorimeter only






2003 result in PLB 634 (2006) 474




2003 result in PLB 638 (2006) 22


excluded


OKA at Protvino





(in preparation)


More CP violation


Indirect

Direct

CP violation

parameters

(2005)


(A) KS decays


CPV in KS decays




000000

000

000 )(

)(

L

S

KA




S+KL

KL




000 000 00

1( )2 ( 2

0

)

( )


tt

NEARf E t



)()()( 00

00

EKNEKN

EKNEKNED

(incoherent

production)



Assuming CPT





N3

20

40

60

00

4 62


No CPV seen yet

























PT() = (-17 23 11) 10-

3

Im = (-53 71 36) 10-3




Im = (-53 71 36) 10-3








ppp

ppp

)0()0(

)0()0(

NN

NNA


Radiative decays








211221 )()(


IB DE

p1 p1

p2p2

q q







)(

)(

S

L

KA

violatingCPKA




KL π+πminus






IB

M1 DE




KL itself





KL ee


BR = (308 020) 10minus7



E1M1 lt 004 (90 CL)



φ




KS ee

No asymmetry for KS

as expected

BR = (471 032) 10-

5

AΦ = (05 43)






IBEE

dEA

)tan( 0


Kplusmn π+π0γ

)730810672()(

)250350353()(

800

800

syststatMeVT

syststatMeVT

INTFrac

DEFrac







KL π+πndashπ0γ















)(

)2030(

3

3

e

ee

K

MeVEKR





bull 6M Ke3 events


ndash R=(0964plusmn0008+0011-0009)












PDG 2004







]21[192 3

52

KmG







Vus measurements





unitarity





KLOE Kl 3

KLOE K2

copy A Antonelli

Vus some more




Ke4 results





K+rarrπ0π0eν










1-loop rescattering

2-loop rescattering











NA482




KLOE interference

















K+ + 8middot10-11 (at 7)147+130

ndash089 middot 10-

10 (BNL E787+E949)






KL 0ℓ+ℓ-




BR(KL 0+-) lt 3810-10





NA481 KS 0ℓ+ℓ-



BR = (58 +28-23 plusmn08) times10-9


-012 (accid)BR = (28 +15


KS 0e+e- KS 0μ+μ-


NA481 preliminary

NA481 preliminary


KL 0ℓ+ℓ-






Krarr in the SM




W W

s

id

Vis Vid

e

i=uct

W

Z

VisV

idds i

11

20

2410

10)1108(

)(1001)(

AKB

11

2

5

100

10)4082(

)()Im(

1022)(

t

tdtsL xX

VVKB


K

ε εrsquo




Ke3 KL 0

Height

Im(λt )



10301890 10471)(

KBR









K+ +




















Appendixes





J(ππ) = ℓ(ππ) = 0 P(ππ) = +1 C(ππ) = +1



ℓL



SLti

SLLSti

LS

tL

tS

Lti

LSti

S

KKeaaKKeaa

eaea

KeaKea

SLLS

LS

LS

)()(

22

f LSf

fLS KfA

dt

d 2

2

TUnitarity requires

and therefore


f Sff

fS

fLSLLS

f

fLLf

fSS

fKAAKKmi

AA

)(2)(

22


2

22

2

222

0604

mKK

AAAA

LS

LSLS

f

fSf

fLf

fS

fL



SLS KKmi 21




)()( 0000

SSS KK



mm

HH

HH

K

KK HH

2221

1211

0

0

01


0

0

mmm

mmm

K

K


Case of CP symmetry

H11 = H22 = m0 H12 = H21 = δm





Eigenstates

22

11

KKCP

KKCP

21 KKKK LS



Since 00 LJJ

CPCP



K1K2 = 0

CP symmetric case







)0()0()(

2)(

22

1)(

11

222

111

KeKetK

KeKetKtimitiE

timitiE

002

001

2

12

1

KKK

KKK


1212 Re2Re2 Mm


6 eV



CP symmetric case




Brookhaven AD 1963


















(45 plusmn 9)22700



fall 1963









310)4002()(

)(

chargedKBR

KBR

L

L


The new paradigm

K0

K0

K0

K0


CP










Physical states

00

22

00

22

)1()1(

12

1

)1()1(

12

1

KKK

KKK

L

S

00

2122

00

2212

)1()1(12

1

1

1

)1()1(12

1

1

1

KKKKK

KKKKK

LL

L

L

L

L

SS

S

S

S

S

2)(

2)(

SL

LS






M12 ne M21 Γ12 ne Γ21

)2(2

)()(

2

Im)2(Im 112211221212

im

iMM

mi

iM






M11 ne M22 Γ11 ne Γ22

Re(ε) really






34

2

2102

p

p

F

F

FSW

m

m

G

G

m

G

m

G




2

Im)2(Im 1212

mi

iM











KL K2+ ε K1

ππ






KL K2+ ε K1

ππ


K2 (CP=-1) ππ (CP=+1)






This is named



K0 ππ

K0





Decay phase

(direct)




Isospin I=0

Isospin I=2


(CHARGE) BASIS









221

2

)(

)(

21

)(

)(

00

00

000000

S

Li

S

Li

KA

KAe

KA

KAe

)(

0

0

2

2

0

2

0

0

02

)Re(

)Im(

)Re(

)Im(

)Re(

)Re(

2

)Re(

)Im(

iea

a

a

a

a

ai

a

ai

221

)0(

)2(

IKA

IKA

S

S







Questions













p

Target


particle sweeping

Dump

Neutral beam

Collimator

Production

angle

Protonenergy Beam

acceptance

Collimatorbackgroun

d

KL (+KS) beams



KS by regeneration





KL KL + Ar KS








61)Re(612

2

00

)(

)(

)(

)(00

00

2

2

00

L

S

S

L

K

K

K

K







n


d(PSext) d3x d3ph3




Position scale

Momentum

scale



Direct CPV 1996 AD

FNAL E731






The presshellip







KTeV at Fermilab



NA48 at CERN




600

00

10)820045()()(

)()(

KK

KK




4

World average





rsquo why










K decays


(PDG2004)



For kaons


K2ππ




ΔΓ(K3π)Δg(K3π)












K vs B







200

200

200

200

KeKKeK

KeKKeKA

iHtiHt

iHtiHt

T


20

20

20

20

KefKef

KefKefA

iHtCP

iHtCP

iHtCP

iHtCP

CP

200

200

200

200

KeKKeK

KeKKeKA

iHtiHt

iHtiHt

CPT




CPLEAR experiment

(CERN 1990-96)






tf

ft

f

iHtCP

iHtCP

iHtCP

iHtCP

CPLS

LS

e

mte

KefKef

KefKefA

)(2

2)(

20

20

20

20

1

)cos(2)Re(2

π+π

minus

π0π0

π+π minusπ0

π0π0π0

CPLEARAsymmetrie

s


Rate difference


Measure η





Kaon factories




pppp 2

1SLSL KKKKi




[Lipkin (1968)]

EPR correlation


DAΦNE (Frascati)


DAΦNE (Frascati)


MeVc)









p = 127 MeVcλ = 95 cm

KLKS 106 pb-1




KLOE physics




















p

Target

Collimator



Dump

Tagging Separation

Charged beam




Buthellip



rarr Small in SM


2π (εrsquoε)

3π (Ag)


ν


π0

Kplusmn rarr 3π




π1

π2

π3

K


Kinematics



2


2

Matrix element

|M(uv)|2 ~ 1 + gu + hu2 + kv2







KminusK+








10-6

NA482 OKA

10-5

10-4

10-3

10-2

SMSM

SUSYSUSYNewNew

physicsphysics



|Ag|

bull Ag ~ 10minus5


SUSY New Physics

THEORY



C

N



=Ag



54 60 66

1cm

50 100

10 cm

200 250 m





~11012

ppp

K+

Kminus



always in vacuum

focusing beams

BM

z

magnet

vacuum tank

not to scale

K+

K


pipe

0ordm prodangle






ZZ

XXYY

JuraJura

SaleveSaleve

Beam line K+ Up


B+

Bminus






Spectrometer field

K+

Kminus

Reverse each day

Reverse each week


|V| even pion

in beam pipe


KK+ +

KK



No significant

background





-15 -10 -05 0 05 10 u

0

-1

-2

1

2

3

Dalitz plot



EM calorimeter only






2003 result in PLB 634 (2006) 474




2003 result in PLB 638 (2006) 22


excluded


OKA at Protvino





(in preparation)


More CP violation


Indirect

Direct

CP violation

parameters

(2005)


(A) KS decays


CPV in KS decays




000000

000

000 )(

)(

L

S

KA




S+KL

KL




000 000 00

1( )2 ( 2

0

)

( )


tt

NEARf E t



)()()( 00

00

EKNEKN

EKNEKNED

(incoherent

production)



Assuming CPT





N3

20

40

60

00

4 62


No CPV seen yet

























PT() = (-17 23 11) 10-

3

Im = (-53 71 36) 10-3




Im = (-53 71 36) 10-3








ppp

ppp

)0()0(

)0()0(

NN

NNA


Radiative decays








211221 )()(


IB DE

p1 p1

p2p2

q q







)(

)(

S

L

KA

violatingCPKA




KL π+πminus






IB

M1 DE




KL itself





KL ee


BR = (308 020) 10minus7



E1M1 lt 004 (90 CL)



φ




KS ee

No asymmetry for KS

as expected

BR = (471 032) 10-

5

AΦ = (05 43)






IBEE

dEA

)tan( 0


Kplusmn π+π0γ

)730810672()(

)250350353()(

800

800

syststatMeVT

syststatMeVT

INTFrac

DEFrac







KL π+πndashπ0γ















)(

)2030(

3

3

e

ee

K

MeVEKR





bull 6M Ke3 events


ndash R=(0964plusmn0008+0011-0009)












PDG 2004







]21[192 3

52

KmG







Vus measurements





unitarity





KLOE Kl 3

KLOE K2

copy A Antonelli

Vus some more




Ke4 results





K+rarrπ0π0eν










1-loop rescattering

2-loop rescattering











NA482




KLOE interference

















K+ + 8middot10-11 (at 7)147+130

ndash089 middot 10-

10 (BNL E787+E949)






KL 0ℓ+ℓ-




BR(KL 0+-) lt 3810-10





NA481 KS 0ℓ+ℓ-



BR = (58 +28-23 plusmn08) times10-9


-012 (accid)BR = (28 +15


KS 0e+e- KS 0μ+μ-


NA481 preliminary

NA481 preliminary


KL 0ℓ+ℓ-






Krarr in the SM




W W

s

id

Vis Vid

e

i=uct

W

Z

VisV

idds i

11

20

2410

10)1108(

)(1001)(

AKB

11

2

5

100

10)4082(

)()Im(

1022)(

t

tdtsL xX

VVKB


K

ε εrsquo




Ke3 KL 0

Height

Im(λt )



10301890 10471)(

KBR









K+ +




















Appendixes





J(ππ) = ℓ(ππ) = 0 P(ππ) = +1 C(ππ) = +1



ℓL



SLti

SLLSti

LS

tL

tS

Lti

LSti

S

KKeaaKKeaa

eaea

KeaKea

SLLS

LS

LS

)()(

22

f LSf

fLS KfA

dt

d 2

2

TUnitarity requires

and therefore


f Sff

fS

fLSLLS

f

fLLf

fSS

fKAAKKmi

AA

)(2)(

22


2

22

2

222

0604

mKK

AAAA

LS

LSLS

f

fSf

fLf

fS

fL



SLS KKmi 21




)()( 0000

SSS KK



Eigenstates

22

11

KKCP

KKCP

21 KKKK LS



Since 00 LJJ

CPCP



K1K2 = 0

CP symmetric case







)0()0()(

2)(

22

1)(

11

222

111

KeKetK

KeKetKtimitiE

timitiE

002

001

2

12

1

KKK

KKK


1212 Re2Re2 Mm


6 eV



CP symmetric case




Brookhaven AD 1963


















(45 plusmn 9)22700



fall 1963









310)4002()(

)(

chargedKBR

KBR

L

L


The new paradigm

K0

K0

K0

K0


CP










Physical states

00

22

00

22

)1()1(

12

1

)1()1(

12

1

KKK

KKK

L

S

00

2122

00

2212

)1()1(12

1

1

1

)1()1(12

1

1

1

KKKKK

KKKKK

LL

L

L

L

L

SS

S

S

S

S

2)(

2)(

SL

LS






M12 ne M21 Γ12 ne Γ21

)2(2

)()(

2

Im)2(Im 112211221212

im

iMM

mi

iM






M11 ne M22 Γ11 ne Γ22

Re(ε) really






34

2

2102

p

p

F

F

FSW

m

m

G

G

m

G

m

G




2

Im)2(Im 1212

mi

iM











KL K2+ ε K1

ππ






KL K2+ ε K1

ππ


K2 (CP=-1) ππ (CP=+1)






This is named



K0 ππ

K0





Decay phase

(direct)




Isospin I=0

Isospin I=2


(CHARGE) BASIS









221

2

)(

)(

21

)(

)(

00

00

000000

S

Li

S

Li

KA

KAe

KA

KAe

)(

0

0

2

2

0

2

0

0

02

)Re(

)Im(

)Re(

)Im(

)Re(

)Re(

2

)Re(

)Im(

iea

a

a

a

a

ai

a

ai

221

)0(

)2(

IKA

IKA

S

S







Questions













p

Target


particle sweeping

Dump

Neutral beam

Collimator

Production

angle

Protonenergy Beam

acceptance

Collimatorbackgroun

d

KL (+KS) beams



KS by regeneration





KL KL + Ar KS








61)Re(612

2

00

)(

)(

)(

)(00

00

2

2

00

L

S

S

L

K

K

K

K







n


d(PSext) d3x d3ph3




Position scale

Momentum

scale



Direct CPV 1996 AD

FNAL E731






The presshellip







KTeV at Fermilab



NA48 at CERN




600

00

10)820045()()(

)()(

KK

KK




4

World average





rsquo why










K decays


(PDG2004)



For kaons


K2ππ




ΔΓ(K3π)Δg(K3π)












K vs B







200

200

200

200

KeKKeK

KeKKeKA

iHtiHt

iHtiHt

T


20

20

20

20

KefKef

KefKefA

iHtCP

iHtCP

iHtCP

iHtCP

CP

200

200

200

200

KeKKeK

KeKKeKA

iHtiHt

iHtiHt

CPT




CPLEAR experiment

(CERN 1990-96)






tf

ft

f

iHtCP

iHtCP

iHtCP

iHtCP

CPLS

LS

e

mte

KefKef

KefKefA

)(2

2)(

20

20

20

20

1

)cos(2)Re(2

π+π

minus

π0π0

π+π minusπ0

π0π0π0

CPLEARAsymmetrie

s


Rate difference


Measure η





Kaon factories




pppp 2

1SLSL KKKKi




[Lipkin (1968)]

EPR correlation


DAΦNE (Frascati)


DAΦNE (Frascati)


MeVc)









p = 127 MeVcλ = 95 cm

KLKS 106 pb-1




KLOE physics




















p

Target

Collimator



Dump

Tagging Separation

Charged beam




Buthellip



rarr Small in SM


2π (εrsquoε)

3π (Ag)


ν


π0

Kplusmn rarr 3π




π1

π2

π3

K


Kinematics



2


2

Matrix element

|M(uv)|2 ~ 1 + gu + hu2 + kv2







KminusK+








10-6

NA482 OKA

10-5

10-4

10-3

10-2

SMSM

SUSYSUSYNewNew

physicsphysics



|Ag|

bull Ag ~ 10minus5


SUSY New Physics

THEORY



C

N



=Ag



54 60 66

1cm

50 100

10 cm

200 250 m





~11012

ppp

K+

Kminus



always in vacuum

focusing beams

BM

z

magnet

vacuum tank

not to scale

K+

K


pipe

0ordm prodangle






ZZ

XXYY

JuraJura

SaleveSaleve

Beam line K+ Up


B+

Bminus






Spectrometer field

K+

Kminus

Reverse each day

Reverse each week


|V| even pion

in beam pipe


KK+ +

KK



No significant

background





-15 -10 -05 0 05 10 u

0

-1

-2

1

2

3

Dalitz plot



EM calorimeter only






2003 result in PLB 634 (2006) 474




2003 result in PLB 638 (2006) 22


excluded


OKA at Protvino





(in preparation)


More CP violation


Indirect

Direct

CP violation

parameters

(2005)


(A) KS decays


CPV in KS decays




000000

000

000 )(

)(

L

S

KA




S+KL

KL




000 000 00

1( )2 ( 2

0

)

( )


tt

NEARf E t



)()()( 00

00

EKNEKN

EKNEKNED

(incoherent

production)



Assuming CPT





N3

20

40

60

00

4 62


No CPV seen yet

























PT() = (-17 23 11) 10-

3

Im = (-53 71 36) 10-3




Im = (-53 71 36) 10-3








ppp

ppp

)0()0(

)0()0(

NN

NNA


Radiative decays








211221 )()(


IB DE

p1 p1

p2p2

q q







)(

)(

S

L

KA

violatingCPKA




KL π+πminus






IB

M1 DE




KL itself





KL ee


BR = (308 020) 10minus7



E1M1 lt 004 (90 CL)



φ




KS ee

No asymmetry for KS

as expected

BR = (471 032) 10-

5

AΦ = (05 43)






IBEE

dEA

)tan( 0


Kplusmn π+π0γ

)730810672()(

)250350353()(

800

800

syststatMeVT

syststatMeVT

INTFrac

DEFrac







KL π+πndashπ0γ















)(

)2030(

3

3

e

ee

K

MeVEKR





bull 6M Ke3 events


ndash R=(0964plusmn0008+0011-0009)












PDG 2004







]21[192 3

52

KmG







Vus measurements





unitarity





KLOE Kl 3

KLOE K2

copy A Antonelli

Vus some more




Ke4 results





K+rarrπ0π0eν










1-loop rescattering

2-loop rescattering











NA482




KLOE interference

















K+ + 8middot10-11 (at 7)147+130

ndash089 middot 10-

10 (BNL E787+E949)






KL 0ℓ+ℓ-




BR(KL 0+-) lt 3810-10





NA481 KS 0ℓ+ℓ-



BR = (58 +28-23 plusmn08) times10-9


-012 (accid)BR = (28 +15


KS 0e+e- KS 0μ+μ-


NA481 preliminary

NA481 preliminary


KL 0ℓ+ℓ-






Krarr in the SM




W W

s

id

Vis Vid

e

i=uct

W

Z

VisV

idds i

11

20

2410

10)1108(

)(1001)(

AKB

11

2

5

100

10)4082(

)()Im(

1022)(

t

tdtsL xX

VVKB


K

ε εrsquo




Ke3 KL 0

Height

Im(λt )



10301890 10471)(

KBR









K+ +




















Appendixes





J(ππ) = ℓ(ππ) = 0 P(ππ) = +1 C(ππ) = +1



ℓL



SLti

SLLSti

LS

tL

tS

Lti

LSti

S

KKeaaKKeaa

eaea

KeaKea

SLLS

LS

LS

)()(

22

f LSf

fLS KfA

dt

d 2

2

TUnitarity requires

and therefore


f Sff

fS

fLSLLS

f

fLLf

fSS

fKAAKKmi

AA

)(2)(

22


2

22

2

222

0604

mKK

AAAA

LS

LSLS

f

fSf

fLf

fS

fL



SLS KKmi 21




)()( 0000

SSS KK







)0()0()(

2)(

22

1)(

11

222

111

KeKetK

KeKetKtimitiE

timitiE

002

001

2

12

1

KKK

KKK


1212 Re2Re2 Mm


6 eV



CP symmetric case




Brookhaven AD 1963


















(45 plusmn 9)22700



fall 1963









310)4002()(

)(

chargedKBR

KBR

L

L


The new paradigm

K0

K0

K0

K0


CP










Physical states

00

22

00

22

)1()1(

12

1

)1()1(

12

1

KKK

KKK

L

S

00

2122

00

2212

)1()1(12

1

1

1

)1()1(12

1

1

1

KKKKK

KKKKK

LL

L

L

L

L

SS

S

S

S

S

2)(

2)(

SL

LS






M12 ne M21 Γ12 ne Γ21

)2(2

)()(

2

Im)2(Im 112211221212

im

iMM

mi

iM






M11 ne M22 Γ11 ne Γ22

Re(ε) really






34

2

2102

p

p

F

F

FSW

m

m

G

G

m

G

m

G




2

Im)2(Im 1212

mi

iM











KL K2+ ε K1

ππ






KL K2+ ε K1

ππ


K2 (CP=-1) ππ (CP=+1)






This is named



K0 ππ

K0





Decay phase

(direct)




Isospin I=0

Isospin I=2


(CHARGE) BASIS









221

2

)(

)(

21

)(

)(

00

00

000000

S

Li

S

Li

KA

KAe

KA

KAe

)(

0

0

2

2

0

2

0

0

02

)Re(

)Im(

)Re(

)Im(

)Re(

)Re(

2

)Re(

)Im(

iea

a

a

a

a

ai

a

ai

221

)0(

)2(

IKA

IKA

S

S







Questions













p

Target


particle sweeping

Dump

Neutral beam

Collimator

Production

angle

Protonenergy Beam

acceptance

Collimatorbackgroun

d

KL (+KS) beams



KS by regeneration





KL KL + Ar KS








61)Re(612

2

00

)(

)(

)(

)(00

00

2

2

00

L

S

S

L

K

K

K

K







n


d(PSext) d3x d3ph3




Position scale

Momentum

scale



Direct CPV 1996 AD

FNAL E731






The presshellip







KTeV at Fermilab



NA48 at CERN




600

00

10)820045()()(

)()(

KK

KK




4

World average





rsquo why










K decays


(PDG2004)



For kaons


K2ππ




ΔΓ(K3π)Δg(K3π)












K vs B







200

200

200

200

KeKKeK

KeKKeKA

iHtiHt

iHtiHt

T


20

20

20

20

KefKef

KefKefA

iHtCP

iHtCP

iHtCP

iHtCP

CP

200

200

200

200

KeKKeK

KeKKeKA

iHtiHt

iHtiHt

CPT




CPLEAR experiment

(CERN 1990-96)






tf

ft

f

iHtCP

iHtCP

iHtCP

iHtCP

CPLS

LS

e

mte

KefKef

KefKefA

)(2

2)(

20

20

20

20

1

)cos(2)Re(2

π+π

minus

π0π0

π+π minusπ0

π0π0π0

CPLEARAsymmetrie

s


Rate difference


Measure η





Kaon factories




pppp 2

1SLSL KKKKi




[Lipkin (1968)]

EPR correlation


DAΦNE (Frascati)


DAΦNE (Frascati)


MeVc)









p = 127 MeVcλ = 95 cm

KLKS 106 pb-1




KLOE physics




















p

Target

Collimator



Dump

Tagging Separation

Charged beam




Buthellip



rarr Small in SM


2π (εrsquoε)

3π (Ag)


ν


π0

Kplusmn rarr 3π




π1

π2

π3

K


Kinematics



2


2

Matrix element

|M(uv)|2 ~ 1 + gu + hu2 + kv2







KminusK+








10-6

NA482 OKA

10-5

10-4

10-3

10-2

SMSM

SUSYSUSYNewNew

physicsphysics



|Ag|

bull Ag ~ 10minus5


SUSY New Physics

THEORY



C

N



=Ag



54 60 66

1cm

50 100

10 cm

200 250 m





~11012

ppp

K+

Kminus



always in vacuum

focusing beams

BM

z

magnet

vacuum tank

not to scale

K+

K


pipe

0ordm prodangle






ZZ

XXYY

JuraJura

SaleveSaleve

Beam line K+ Up


B+

Bminus






Spectrometer field

K+

Kminus

Reverse each day

Reverse each week


|V| even pion

in beam pipe


KK+ +

KK



No significant

background





-15 -10 -05 0 05 10 u

0

-1

-2

1

2

3

Dalitz plot



EM calorimeter only






2003 result in PLB 634 (2006) 474




2003 result in PLB 638 (2006) 22


excluded


OKA at Protvino





(in preparation)


More CP violation


Indirect

Direct

CP violation

parameters

(2005)


(A) KS decays


CPV in KS decays




000000

000

000 )(

)(

L

S

KA




S+KL

KL




000 000 00

1( )2 ( 2

0

)

( )


tt

NEARf E t



)()()( 00

00

EKNEKN

EKNEKNED

(incoherent

production)



Assuming CPT





N3

20

40

60

00

4 62


No CPV seen yet

























PT() = (-17 23 11) 10-

3

Im = (-53 71 36) 10-3




Im = (-53 71 36) 10-3








ppp

ppp

)0()0(

)0()0(

NN

NNA


Radiative decays








211221 )()(


IB DE

p1 p1

p2p2

q q







)(

)(

S

L

KA

violatingCPKA




KL π+πminus






IB

M1 DE




KL itself





KL ee


BR = (308 020) 10minus7



E1M1 lt 004 (90 CL)



φ




KS ee

No asymmetry for KS

as expected

BR = (471 032) 10-

5

AΦ = (05 43)






IBEE

dEA

)tan( 0


Kplusmn π+π0γ

)730810672()(

)250350353()(

800

800

syststatMeVT

syststatMeVT

INTFrac

DEFrac







KL π+πndashπ0γ















)(

)2030(

3

3

e

ee

K

MeVEKR





bull 6M Ke3 events


ndash R=(0964plusmn0008+0011-0009)












PDG 2004







]21[192 3

52

KmG







Vus measurements





unitarity





KLOE Kl 3

KLOE K2

copy A Antonelli

Vus some more




Ke4 results





K+rarrπ0π0eν










1-loop rescattering

2-loop rescattering











NA482




KLOE interference

















K+ + 8middot10-11 (at 7)147+130

ndash089 middot 10-

10 (BNL E787+E949)






KL 0ℓ+ℓ-




BR(KL 0+-) lt 3810-10





NA481 KS 0ℓ+ℓ-



BR = (58 +28-23 plusmn08) times10-9


-012 (accid)BR = (28 +15


KS 0e+e- KS 0μ+μ-


NA481 preliminary

NA481 preliminary


KL 0ℓ+ℓ-






Krarr in the SM




W W

s

id

Vis Vid

e

i=uct

W

Z

VisV

idds i

11

20

2410

10)1108(

)(1001)(

AKB

11

2

5

100

10)4082(

)()Im(

1022)(

t

tdtsL xX

VVKB


K

ε εrsquo




Ke3 KL 0

Height

Im(λt )



10301890 10471)(

KBR









K+ +




















Appendixes





J(ππ) = ℓ(ππ) = 0 P(ππ) = +1 C(ππ) = +1



ℓL



SLti

SLLSti

LS

tL

tS

Lti

LSti

S

KKeaaKKeaa

eaea

KeaKea

SLLS

LS

LS

)()(

22

f LSf

fLS KfA

dt

d 2

2

TUnitarity requires

and therefore


f Sff

fS

fLSLLS

f

fLLf

fSS

fKAAKKmi

AA

)(2)(

22


2

22

2

222

0604

mKK

AAAA

LS

LSLS

f

fSf

fLf

fS

fL



SLS KKmi 21




)()( 0000

SSS KK





Brookhaven AD 1963


















(45 plusmn 9)22700



fall 1963









310)4002()(

)(

chargedKBR

KBR

L

L


The new paradigm

K0

K0

K0

K0


CP










Physical states

00

22

00

22

)1()1(

12

1

)1()1(

12

1

KKK

KKK

L

S

00

2122

00

2212

)1()1(12

1

1

1

)1()1(12

1

1

1

KKKKK

KKKKK

LL

L

L

L

L

SS

S

S

S

S

2)(

2)(

SL

LS






M12 ne M21 Γ12 ne Γ21

)2(2

)()(

2

Im)2(Im 112211221212

im

iMM

mi

iM






M11 ne M22 Γ11 ne Γ22

Re(ε) really






34

2

2102

p

p

F

F

FSW

m

m

G

G

m

G

m

G




2

Im)2(Im 1212

mi

iM











KL K2+ ε K1

ππ






KL K2+ ε K1

ππ


K2 (CP=-1) ππ (CP=+1)






This is named



K0 ππ

K0





Decay phase

(direct)




Isospin I=0

Isospin I=2


(CHARGE) BASIS









221

2

)(

)(

21

)(

)(

00

00

000000

S

Li

S

Li

KA

KAe

KA

KAe

)(

0

0

2

2

0

2

0

0

02

)Re(

)Im(

)Re(

)Im(

)Re(

)Re(

2

)Re(

)Im(

iea

a

a

a

a

ai

a

ai

221

)0(

)2(

IKA

IKA

S

S







Questions













p

Target


particle sweeping

Dump

Neutral beam

Collimator

Production

angle

Protonenergy Beam

acceptance

Collimatorbackgroun

d

KL (+KS) beams



KS by regeneration





KL KL + Ar KS








61)Re(612

2

00

)(

)(

)(

)(00

00

2

2

00

L

S

S

L

K

K

K

K







n


d(PSext) d3x d3ph3




Position scale

Momentum

scale



Direct CPV 1996 AD

FNAL E731






The presshellip







KTeV at Fermilab



NA48 at CERN




600

00

10)820045()()(

)()(

KK

KK




4

World average





rsquo why










K decays


(PDG2004)



For kaons


K2ππ




ΔΓ(K3π)Δg(K3π)












K vs B







200

200

200

200

KeKKeK

KeKKeKA

iHtiHt

iHtiHt

T


20

20

20

20

KefKef

KefKefA

iHtCP

iHtCP

iHtCP

iHtCP

CP

200

200

200

200

KeKKeK

KeKKeKA

iHtiHt

iHtiHt

CPT




CPLEAR experiment

(CERN 1990-96)






tf

ft

f

iHtCP

iHtCP

iHtCP

iHtCP

CPLS

LS

e

mte

KefKef

KefKefA

)(2

2)(

20

20

20

20

1

)cos(2)Re(2

π+π

minus

π0π0

π+π minusπ0

π0π0π0

CPLEARAsymmetrie

s


Rate difference


Measure η





Kaon factories




pppp 2

1SLSL KKKKi




[Lipkin (1968)]

EPR correlation


DAΦNE (Frascati)


DAΦNE (Frascati)


MeVc)









p = 127 MeVcλ = 95 cm

KLKS 106 pb-1




KLOE physics




















p

Target

Collimator



Dump

Tagging Separation

Charged beam




Buthellip



rarr Small in SM


2π (εrsquoε)

3π (Ag)


ν


π0

Kplusmn rarr 3π




π1

π2

π3

K


Kinematics



2


2

Matrix element

|M(uv)|2 ~ 1 + gu + hu2 + kv2







KminusK+








10-6

NA482 OKA

10-5

10-4

10-3

10-2

SMSM

SUSYSUSYNewNew

physicsphysics



|Ag|

bull Ag ~ 10minus5


SUSY New Physics

THEORY



C

N



=Ag



54 60 66

1cm

50 100

10 cm

200 250 m





~11012

ppp

K+

Kminus



always in vacuum

focusing beams

BM

z

magnet

vacuum tank

not to scale

K+

K


pipe

0ordm prodangle






ZZ

XXYY

JuraJura

SaleveSaleve

Beam line K+ Up


B+

Bminus






Spectrometer field

K+

Kminus

Reverse each day

Reverse each week


|V| even pion

in beam pipe


KK+ +

KK



No significant

background





-15 -10 -05 0 05 10 u

0

-1

-2

1

2

3

Dalitz plot



EM calorimeter only






2003 result in PLB 634 (2006) 474




2003 result in PLB 638 (2006) 22


excluded


OKA at Protvino





(in preparation)


More CP violation


Indirect

Direct

CP violation

parameters

(2005)


(A) KS decays


CPV in KS decays




000000

000

000 )(

)(

L

S

KA




S+KL

KL




000 000 00

1( )2 ( 2

0

)

( )


tt

NEARf E t



)()()( 00

00

EKNEKN

EKNEKNED

(incoherent

production)



Assuming CPT





N3

20

40

60

00

4 62


No CPV seen yet

























PT() = (-17 23 11) 10-

3

Im = (-53 71 36) 10-3




Im = (-53 71 36) 10-3








ppp

ppp

)0()0(

)0()0(

NN

NNA


Radiative decays








211221 )()(


IB DE

p1 p1

p2p2

q q







)(

)(

S

L

KA

violatingCPKA




KL π+πminus






IB

M1 DE




KL itself





KL ee


BR = (308 020) 10minus7



E1M1 lt 004 (90 CL)



φ




KS ee

No asymmetry for KS

as expected

BR = (471 032) 10-

5

AΦ = (05 43)






IBEE

dEA

)tan( 0


Kplusmn π+π0γ

)730810672()(

)250350353()(

800

800

syststatMeVT

syststatMeVT

INTFrac

DEFrac







KL π+πndashπ0γ















)(

)2030(

3

3

e

ee

K

MeVEKR





bull 6M Ke3 events


ndash R=(0964plusmn0008+0011-0009)












PDG 2004







]21[192 3

52

KmG







Vus measurements





unitarity





KLOE Kl 3

KLOE K2

copy A Antonelli

Vus some more




Ke4 results





K+rarrπ0π0eν










1-loop rescattering

2-loop rescattering











NA482




KLOE interference

















K+ + 8middot10-11 (at 7)147+130

ndash089 middot 10-

10 (BNL E787+E949)






KL 0ℓ+ℓ-




BR(KL 0+-) lt 3810-10





NA481 KS 0ℓ+ℓ-



BR = (58 +28-23 plusmn08) times10-9


-012 (accid)BR = (28 +15


KS 0e+e- KS 0μ+μ-


NA481 preliminary

NA481 preliminary


KL 0ℓ+ℓ-






Krarr in the SM




W W

s

id

Vis Vid

e

i=uct

W

Z

VisV

idds i

11

20

2410

10)1108(

)(1001)(

AKB

11

2

5

100

10)4082(

)()Im(

1022)(

t

tdtsL xX

VVKB


K

ε εrsquo




Ke3 KL 0

Height

Im(λt )



10301890 10471)(

KBR









K+ +




















Appendixes





J(ππ) = ℓ(ππ) = 0 P(ππ) = +1 C(ππ) = +1



ℓL



SLti

SLLSti

LS

tL

tS

Lti

LSti

S

KKeaaKKeaa

eaea

KeaKea

SLLS

LS

LS

)()(

22

f LSf

fLS KfA

dt

d 2

2

TUnitarity requires

and therefore


f Sff

fS

fLSLLS

f

fLLf

fSS

fKAAKKmi

AA

)(2)(

22


2

22

2

222

0604

mKK

AAAA

LS

LSLS

f

fSf

fLf

fS

fL



SLS KKmi 21




)()( 0000

SSS KK



Brookhaven AD 1963


















(45 plusmn 9)22700



fall 1963









310)4002()(

)(

chargedKBR

KBR

L

L


The new paradigm

K0

K0

K0

K0


CP










Physical states

00

22

00

22

)1()1(

12

1

)1()1(

12

1

KKK

KKK

L

S

00

2122

00

2212

)1()1(12

1

1

1

)1()1(12

1

1

1

KKKKK

KKKKK

LL

L

L

L

L

SS

S

S

S

S

2)(

2)(

SL

LS






M12 ne M21 Γ12 ne Γ21

)2(2

)()(

2

Im)2(Im 112211221212

im

iMM

mi

iM






M11 ne M22 Γ11 ne Γ22

Re(ε) really






34

2

2102

p

p

F

F

FSW

m

m

G

G

m

G

m

G




2

Im)2(Im 1212

mi

iM











KL K2+ ε K1

ππ






KL K2+ ε K1

ππ


K2 (CP=-1) ππ (CP=+1)






This is named



K0 ππ

K0





Decay phase

(direct)




Isospin I=0

Isospin I=2


(CHARGE) BASIS









221

2

)(

)(

21

)(

)(

00

00

000000

S

Li

S

Li

KA

KAe

KA

KAe

)(

0

0

2

2

0

2

0

0

02

)Re(

)Im(

)Re(

)Im(

)Re(

)Re(

2

)Re(

)Im(

iea

a

a

a

a

ai

a

ai

221

)0(

)2(

IKA

IKA

S

S







Questions













p

Target


particle sweeping

Dump

Neutral beam

Collimator

Production

angle

Protonenergy Beam

acceptance

Collimatorbackgroun

d

KL (+KS) beams



KS by regeneration





KL KL + Ar KS








61)Re(612

2

00

)(

)(

)(

)(00

00

2

2

00

L

S

S

L

K

K

K

K







n


d(PSext) d3x d3ph3




Position scale

Momentum

scale



Direct CPV 1996 AD

FNAL E731






The presshellip







KTeV at Fermilab



NA48 at CERN




600

00

10)820045()()(

)()(

KK

KK




4

World average





rsquo why










K decays


(PDG2004)



For kaons


K2ππ




ΔΓ(K3π)Δg(K3π)












K vs B







200

200

200

200

KeKKeK

KeKKeKA

iHtiHt

iHtiHt

T


20

20

20

20

KefKef

KefKefA

iHtCP

iHtCP

iHtCP

iHtCP

CP

200

200

200

200

KeKKeK

KeKKeKA

iHtiHt

iHtiHt

CPT




CPLEAR experiment

(CERN 1990-96)






tf

ft

f

iHtCP

iHtCP

iHtCP

iHtCP

CPLS

LS

e

mte

KefKef

KefKefA

)(2

2)(

20

20

20

20

1

)cos(2)Re(2

π+π

minus

π0π0

π+π minusπ0

π0π0π0

CPLEARAsymmetrie

s


Rate difference


Measure η





Kaon factories




pppp 2

1SLSL KKKKi




[Lipkin (1968)]

EPR correlation


DAΦNE (Frascati)


DAΦNE (Frascati)


MeVc)









p = 127 MeVcλ = 95 cm

KLKS 106 pb-1




KLOE physics




















p

Target

Collimator



Dump

Tagging Separation

Charged beam




Buthellip



rarr Small in SM


2π (εrsquoε)

3π (Ag)


ν


π0

Kplusmn rarr 3π




π1

π2

π3

K


Kinematics



2


2

Matrix element

|M(uv)|2 ~ 1 + gu + hu2 + kv2







KminusK+








10-6

NA482 OKA

10-5

10-4

10-3

10-2

SMSM

SUSYSUSYNewNew

physicsphysics



|Ag|

bull Ag ~ 10minus5


SUSY New Physics

THEORY



C

N



=Ag



54 60 66

1cm

50 100

10 cm

200 250 m





~11012

ppp

K+

Kminus



always in vacuum

focusing beams

BM

z

magnet

vacuum tank

not to scale

K+

K


pipe

0ordm prodangle






ZZ

XXYY

JuraJura

SaleveSaleve

Beam line K+ Up


B+

Bminus






Spectrometer field

K+

Kminus

Reverse each day

Reverse each week


|V| even pion

in beam pipe


KK+ +

KK



No significant

background





-15 -10 -05 0 05 10 u

0

-1

-2

1

2

3

Dalitz plot



EM calorimeter only






2003 result in PLB 634 (2006) 474




2003 result in PLB 638 (2006) 22


excluded


OKA at Protvino





(in preparation)


More CP violation


Indirect

Direct

CP violation

parameters

(2005)


(A) KS decays


CPV in KS decays




000000

000

000 )(

)(

L

S

KA




S+KL

KL




000 000 00

1( )2 ( 2

0

)

( )


tt

NEARf E t



)()()( 00

00

EKNEKN

EKNEKNED

(incoherent

production)



Assuming CPT





N3

20

40

60

00

4 62


No CPV seen yet

























PT() = (-17 23 11) 10-

3

Im = (-53 71 36) 10-3




Im = (-53 71 36) 10-3








ppp

ppp

)0()0(

)0()0(

NN

NNA


Radiative decays








211221 )()(


IB DE

p1 p1

p2p2

q q







)(

)(

S

L

KA

violatingCPKA




KL π+πminus






IB

M1 DE




KL itself





KL ee


BR = (308 020) 10minus7



E1M1 lt 004 (90 CL)



φ




KS ee

No asymmetry for KS

as expected

BR = (471 032) 10-

5

AΦ = (05 43)






IBEE

dEA

)tan( 0


Kplusmn π+π0γ

)730810672()(

)250350353()(

800

800

syststatMeVT

syststatMeVT

INTFrac

DEFrac







KL π+πndashπ0γ















)(

)2030(

3

3

e

ee

K

MeVEKR





bull 6M Ke3 events


ndash R=(0964plusmn0008+0011-0009)












PDG 2004







]21[192 3

52

KmG







Vus measurements





unitarity





KLOE Kl 3

KLOE K2

copy A Antonelli

Vus some more




Ke4 results





K+rarrπ0π0eν










1-loop rescattering

2-loop rescattering











NA482




KLOE interference

















K+ + 8middot10-11 (at 7)147+130

ndash089 middot 10-

10 (BNL E787+E949)






KL 0ℓ+ℓ-




BR(KL 0+-) lt 3810-10





NA481 KS 0ℓ+ℓ-



BR = (58 +28-23 plusmn08) times10-9


-012 (accid)BR = (28 +15


KS 0e+e- KS 0μ+μ-


NA481 preliminary

NA481 preliminary


KL 0ℓ+ℓ-






Krarr in the SM




W W

s

id

Vis Vid

e

i=uct

W

Z

VisV

idds i

11

20

2410

10)1108(

)(1001)(

AKB

11

2

5

100

10)4082(

)()Im(

1022)(

t

tdtsL xX

VVKB


K

ε εrsquo




Ke3 KL 0

Height

Im(λt )



10301890 10471)(

KBR









K+ +




















Appendixes





J(ππ) = ℓ(ππ) = 0 P(ππ) = +1 C(ππ) = +1



ℓL



SLti

SLLSti

LS

tL

tS

Lti

LSti

S

KKeaaKKeaa

eaea

KeaKea

SLLS

LS

LS

)()(

22

f LSf

fLS KfA

dt

d 2

2

TUnitarity requires

and therefore


f Sff

fS

fLSLLS

f

fLLf

fSS

fKAAKKmi

AA

)(2)(

22


2

22

2

222

0604

mKK

AAAA

LS

LSLS

f

fSf

fLf

fS

fL



SLS KKmi 21




)()( 0000

SSS KK















(45 plusmn 9)22700



fall 1963









310)4002()(

)(

chargedKBR

KBR

L

L


The new paradigm

K0

K0

K0

K0


CP










Physical states

00

22

00

22

)1()1(

12

1

)1()1(

12

1

KKK

KKK

L

S

00

2122

00

2212

)1()1(12

1

1

1

)1()1(12

1

1

1

KKKKK

KKKKK

LL

L

L

L

L

SS

S

S

S

S

2)(

2)(

SL

LS






M12 ne M21 Γ12 ne Γ21

)2(2

)()(

2

Im)2(Im 112211221212

im

iMM

mi

iM






M11 ne M22 Γ11 ne Γ22

Re(ε) really






34

2

2102

p

p

F

F

FSW

m

m

G

G

m

G

m

G




2

Im)2(Im 1212

mi

iM











KL K2+ ε K1

ππ






KL K2+ ε K1

ππ


K2 (CP=-1) ππ (CP=+1)






This is named



K0 ππ

K0





Decay phase

(direct)




Isospin I=0

Isospin I=2


(CHARGE) BASIS









221

2

)(

)(

21

)(

)(

00

00

000000

S

Li

S

Li

KA

KAe

KA

KAe

)(

0

0

2

2

0

2

0

0

02

)Re(

)Im(

)Re(

)Im(

)Re(

)Re(

2

)Re(

)Im(

iea

a

a

a

a

ai

a

ai

221

)0(

)2(

IKA

IKA

S

S







Questions













p

Target


particle sweeping

Dump

Neutral beam

Collimator

Production

angle

Protonenergy Beam

acceptance

Collimatorbackgroun

d

KL (+KS) beams



KS by regeneration





KL KL + Ar KS








61)Re(612

2

00

)(

)(

)(

)(00

00

2

2

00

L

S

S

L

K

K

K

K







n


d(PSext) d3x d3ph3




Position scale

Momentum

scale



Direct CPV 1996 AD

FNAL E731






The presshellip







KTeV at Fermilab



NA48 at CERN




600

00

10)820045()()(

)()(

KK

KK




4

World average





rsquo why










K decays


(PDG2004)



For kaons


K2ππ




ΔΓ(K3π)Δg(K3π)












K vs B







200

200

200

200

KeKKeK

KeKKeKA

iHtiHt

iHtiHt

T


20

20

20

20

KefKef

KefKefA

iHtCP

iHtCP

iHtCP

iHtCP

CP

200

200

200

200

KeKKeK

KeKKeKA

iHtiHt

iHtiHt

CPT




CPLEAR experiment

(CERN 1990-96)






tf

ft

f

iHtCP

iHtCP

iHtCP

iHtCP

CPLS

LS

e

mte

KefKef

KefKefA

)(2

2)(

20

20

20

20

1

)cos(2)Re(2

π+π

minus

π0π0

π+π minusπ0

π0π0π0

CPLEARAsymmetrie

s


Rate difference


Measure η





Kaon factories




pppp 2

1SLSL KKKKi




[Lipkin (1968)]

EPR correlation


DAΦNE (Frascati)


DAΦNE (Frascati)


MeVc)









p = 127 MeVcλ = 95 cm

KLKS 106 pb-1




KLOE physics




















p

Target

Collimator



Dump

Tagging Separation

Charged beam




Buthellip



rarr Small in SM


2π (εrsquoε)

3π (Ag)


ν


π0

Kplusmn rarr 3π




π1

π2

π3

K


Kinematics



2


2

Matrix element

|M(uv)|2 ~ 1 + gu + hu2 + kv2







KminusK+








10-6

NA482 OKA

10-5

10-4

10-3

10-2

SMSM

SUSYSUSYNewNew

physicsphysics



|Ag|

bull Ag ~ 10minus5


SUSY New Physics

THEORY



C

N



=Ag



54 60 66

1cm

50 100

10 cm

200 250 m





~11012

ppp

K+

Kminus



always in vacuum

focusing beams

BM

z

magnet

vacuum tank

not to scale

K+

K


pipe

0ordm prodangle






ZZ

XXYY

JuraJura

SaleveSaleve

Beam line K+ Up


B+

Bminus






Spectrometer field

K+

Kminus

Reverse each day

Reverse each week


|V| even pion

in beam pipe


KK+ +

KK



No significant

background





-15 -10 -05 0 05 10 u

0

-1

-2

1

2

3

Dalitz plot



EM calorimeter only






2003 result in PLB 634 (2006) 474




2003 result in PLB 638 (2006) 22


excluded


OKA at Protvino





(in preparation)


More CP violation


Indirect

Direct

CP violation

parameters

(2005)


(A) KS decays


CPV in KS decays




000000

000

000 )(

)(

L

S

KA




S+KL

KL




000 000 00

1( )2 ( 2

0

)

( )


tt

NEARf E t



)()()( 00

00

EKNEKN

EKNEKNED

(incoherent

production)



Assuming CPT





N3

20

40

60

00

4 62


No CPV seen yet

























PT() = (-17 23 11) 10-

3

Im = (-53 71 36) 10-3




Im = (-53 71 36) 10-3








ppp

ppp

)0()0(

)0()0(

NN

NNA


Radiative decays








211221 )()(


IB DE

p1 p1

p2p2

q q







)(

)(

S

L

KA

violatingCPKA




KL π+πminus






IB

M1 DE




KL itself





KL ee


BR = (308 020) 10minus7



E1M1 lt 004 (90 CL)



φ




KS ee

No asymmetry for KS

as expected

BR = (471 032) 10-

5

AΦ = (05 43)






IBEE

dEA

)tan( 0


Kplusmn π+π0γ

)730810672()(

)250350353()(

800

800

syststatMeVT

syststatMeVT

INTFrac

DEFrac







KL π+πndashπ0γ















)(

)2030(

3

3

e

ee

K

MeVEKR





bull 6M Ke3 events


ndash R=(0964plusmn0008+0011-0009)












PDG 2004







]21[192 3

52

KmG







Vus measurements





unitarity





KLOE Kl 3

KLOE K2

copy A Antonelli

Vus some more




Ke4 results





K+rarrπ0π0eν










1-loop rescattering

2-loop rescattering











NA482




KLOE interference

















K+ + 8middot10-11 (at 7)147+130

ndash089 middot 10-

10 (BNL E787+E949)






KL 0ℓ+ℓ-




BR(KL 0+-) lt 3810-10





NA481 KS 0ℓ+ℓ-



BR = (58 +28-23 plusmn08) times10-9


-012 (accid)BR = (28 +15


KS 0e+e- KS 0μ+μ-


NA481 preliminary

NA481 preliminary


KL 0ℓ+ℓ-






Krarr in the SM




W W

s

id

Vis Vid

e

i=uct

W

Z

VisV

idds i

11

20

2410

10)1108(

)(1001)(

AKB

11

2

5

100

10)4082(

)()Im(

1022)(

t

tdtsL xX

VVKB


K

ε εrsquo




Ke3 KL 0

Height

Im(λt )



10301890 10471)(

KBR









K+ +




















Appendixes





J(ππ) = ℓ(ππ) = 0 P(ππ) = +1 C(ππ) = +1



ℓL



SLti

SLLSti

LS

tL

tS

Lti

LSti

S

KKeaaKKeaa

eaea

KeaKea

SLLS

LS

LS

)()(

22

f LSf

fLS KfA

dt

d 2

2

TUnitarity requires

and therefore


f Sff

fS

fLSLLS

f

fLLf

fSS

fKAAKKmi

AA

)(2)(

22


2

22

2

222

0604

mKK

AAAA

LS

LSLS

f

fSf

fLf

fS

fL



SLS KKmi 21




)()( 0000

SSS KK



(45 plusmn 9)22700



fall 1963









310)4002()(

)(

chargedKBR

KBR

L

L


The new paradigm

K0

K0

K0

K0


CP










Physical states

00

22

00

22

)1()1(

12

1

)1()1(

12

1

KKK

KKK

L

S

00

2122

00

2212

)1()1(12

1

1

1

)1()1(12

1

1

1

KKKKK

KKKKK

LL

L

L

L

L

SS

S

S

S

S

2)(

2)(

SL

LS






M12 ne M21 Γ12 ne Γ21

)2(2

)()(

2

Im)2(Im 112211221212

im

iMM

mi

iM






M11 ne M22 Γ11 ne Γ22

Re(ε) really






34

2

2102

p

p

F

F

FSW

m

m

G

G

m

G

m

G




2

Im)2(Im 1212

mi

iM











KL K2+ ε K1

ππ






KL K2+ ε K1

ππ


K2 (CP=-1) ππ (CP=+1)






This is named



K0 ππ

K0





Decay phase

(direct)




Isospin I=0

Isospin I=2


(CHARGE) BASIS









221

2

)(

)(

21

)(

)(

00

00

000000

S

Li

S

Li

KA

KAe

KA

KAe

)(

0

0

2

2

0

2

0

0

02

)Re(

)Im(

)Re(

)Im(

)Re(

)Re(

2

)Re(

)Im(

iea

a

a

a

a

ai

a

ai

221

)0(

)2(

IKA

IKA

S

S







Questions













p

Target


particle sweeping

Dump

Neutral beam

Collimator

Production

angle

Protonenergy Beam

acceptance

Collimatorbackgroun

d

KL (+KS) beams



KS by regeneration





KL KL + Ar KS








61)Re(612

2

00

)(

)(

)(

)(00

00

2

2

00

L

S

S

L

K

K

K

K







n


d(PSext) d3x d3ph3




Position scale

Momentum

scale



Direct CPV 1996 AD

FNAL E731






The presshellip







KTeV at Fermilab



NA48 at CERN




600

00

10)820045()()(

)()(

KK

KK




4

World average





rsquo why










K decays


(PDG2004)



For kaons


K2ππ




ΔΓ(K3π)Δg(K3π)












K vs B







200

200

200

200

KeKKeK

KeKKeKA

iHtiHt

iHtiHt

T


20

20

20

20

KefKef

KefKefA

iHtCP

iHtCP

iHtCP

iHtCP

CP

200

200

200

200

KeKKeK

KeKKeKA

iHtiHt

iHtiHt

CPT




CPLEAR experiment

(CERN 1990-96)






tf

ft

f

iHtCP

iHtCP

iHtCP

iHtCP

CPLS

LS

e

mte

KefKef

KefKefA

)(2

2)(

20

20

20

20

1

)cos(2)Re(2

π+π

minus

π0π0

π+π minusπ0

π0π0π0

CPLEARAsymmetrie

s


Rate difference


Measure η





Kaon factories




pppp 2

1SLSL KKKKi




[Lipkin (1968)]

EPR correlation


DAΦNE (Frascati)


DAΦNE (Frascati)


MeVc)









p = 127 MeVcλ = 95 cm

KLKS 106 pb-1




KLOE physics




















p

Target

Collimator



Dump

Tagging Separation

Charged beam




Buthellip



rarr Small in SM


2π (εrsquoε)

3π (Ag)


ν


π0

Kplusmn rarr 3π




π1

π2

π3

K


Kinematics



2


2

Matrix element

|M(uv)|2 ~ 1 + gu + hu2 + kv2







KminusK+








10-6

NA482 OKA

10-5

10-4

10-3

10-2

SMSM

SUSYSUSYNewNew

physicsphysics



|Ag|

bull Ag ~ 10minus5


SUSY New Physics

THEORY



C

N



=Ag



54 60 66

1cm

50 100

10 cm

200 250 m





~11012

ppp

K+

Kminus



always in vacuum

focusing beams

BM

z

magnet

vacuum tank

not to scale

K+

K


pipe

0ordm prodangle






ZZ

XXYY

JuraJura

SaleveSaleve

Beam line K+ Up


B+

Bminus






Spectrometer field

K+

Kminus

Reverse each day

Reverse each week


|V| even pion

in beam pipe


KK+ +

KK



No significant

background





-15 -10 -05 0 05 10 u

0

-1

-2

1

2

3

Dalitz plot



EM calorimeter only






2003 result in PLB 634 (2006) 474




2003 result in PLB 638 (2006) 22


excluded


OKA at Protvino





(in preparation)


More CP violation


Indirect

Direct

CP violation

parameters

(2005)


(A) KS decays


CPV in KS decays




000000

000

000 )(

)(

L

S

KA




S+KL

KL




000 000 00

1( )2 ( 2

0

)

( )


tt

NEARf E t



)()()( 00

00

EKNEKN

EKNEKNED

(incoherent

production)



Assuming CPT





N3

20

40

60

00

4 62


No CPV seen yet

























PT() = (-17 23 11) 10-

3

Im = (-53 71 36) 10-3




Im = (-53 71 36) 10-3








ppp

ppp

)0()0(

)0()0(

NN

NNA


Radiative decays








211221 )()(


IB DE

p1 p1

p2p2

q q







)(

)(

S

L

KA

violatingCPKA




KL π+πminus






IB

M1 DE




KL itself





KL ee


BR = (308 020) 10minus7



E1M1 lt 004 (90 CL)



φ




KS ee

No asymmetry for KS

as expected

BR = (471 032) 10-

5

AΦ = (05 43)






IBEE

dEA

)tan( 0


Kplusmn π+π0γ

)730810672()(

)250350353()(

800

800

syststatMeVT

syststatMeVT

INTFrac

DEFrac







KL π+πndashπ0γ















)(

)2030(

3

3

e

ee

K

MeVEKR





bull 6M Ke3 events


ndash R=(0964plusmn0008+0011-0009)












PDG 2004







]21[192 3

52

KmG







Vus measurements





unitarity





KLOE Kl 3

KLOE K2

copy A Antonelli

Vus some more




Ke4 results





K+rarrπ0π0eν










1-loop rescattering

2-loop rescattering











NA482




KLOE interference

















K+ + 8middot10-11 (at 7)147+130

ndash089 middot 10-

10 (BNL E787+E949)






KL 0ℓ+ℓ-




BR(KL 0+-) lt 3810-10





NA481 KS 0ℓ+ℓ-



BR = (58 +28-23 plusmn08) times10-9


-012 (accid)BR = (28 +15


KS 0e+e- KS 0μ+μ-


NA481 preliminary

NA481 preliminary


KL 0ℓ+ℓ-






Krarr in the SM




W W

s

id

Vis Vid

e

i=uct

W

Z

VisV

idds i

11

20

2410

10)1108(

)(1001)(

AKB

11

2

5

100

10)4082(

)()Im(

1022)(

t

tdtsL xX

VVKB


K

ε εrsquo




Ke3 KL 0

Height

Im(λt )



10301890 10471)(

KBR









K+ +




















Appendixes





J(ππ) = ℓ(ππ) = 0 P(ππ) = +1 C(ππ) = +1



ℓL



SLti

SLLSti

LS

tL

tS

Lti

LSti

S

KKeaaKKeaa

eaea

KeaKea

SLLS

LS

LS

)()(

22

f LSf

fLS KfA

dt

d 2

2

TUnitarity requires

and therefore


f Sff

fS

fLSLLS

f

fLLf

fSS

fKAAKKmi

AA

)(2)(

22


2

22

2

222

0604

mKK

AAAA

LS

LSLS

f

fSf

fLf

fS

fL



SLS KKmi 21




)()( 0000

SSS KK









310)4002()(

)(

chargedKBR

KBR

L

L


The new paradigm

K0

K0

K0

K0


CP










Physical states

00

22

00

22

)1()1(

12

1

)1()1(

12

1

KKK

KKK

L

S

00

2122

00

2212

)1()1(12

1

1

1

)1()1(12

1

1

1

KKKKK

KKKKK

LL

L

L

L

L

SS

S

S

S

S

2)(

2)(

SL

LS






M12 ne M21 Γ12 ne Γ21

)2(2

)()(

2

Im)2(Im 112211221212

im

iMM

mi

iM






M11 ne M22 Γ11 ne Γ22

Re(ε) really






34

2

2102

p

p

F

F

FSW

m

m

G

G

m

G

m

G




2

Im)2(Im 1212

mi

iM











KL K2+ ε K1

ππ






KL K2+ ε K1

ππ


K2 (CP=-1) ππ (CP=+1)






This is named



K0 ππ

K0





Decay phase

(direct)




Isospin I=0

Isospin I=2


(CHARGE) BASIS









221

2

)(

)(

21

)(

)(

00

00

000000

S

Li

S

Li

KA

KAe

KA

KAe

)(

0

0

2

2

0

2

0

0

02

)Re(

)Im(

)Re(

)Im(

)Re(

)Re(

2

)Re(

)Im(

iea

a

a

a

a

ai

a

ai

221

)0(

)2(

IKA

IKA

S

S







Questions













p

Target


particle sweeping

Dump

Neutral beam

Collimator

Production

angle

Protonenergy Beam

acceptance

Collimatorbackgroun

d

KL (+KS) beams



KS by regeneration





KL KL + Ar KS








61)Re(612

2

00

)(

)(

)(

)(00

00

2

2

00

L

S

S

L

K

K

K

K







n


d(PSext) d3x d3ph3




Position scale

Momentum

scale



Direct CPV 1996 AD

FNAL E731






The presshellip







KTeV at Fermilab



NA48 at CERN




600

00

10)820045()()(

)()(

KK

KK




4

World average





rsquo why










K decays


(PDG2004)



For kaons


K2ππ




ΔΓ(K3π)Δg(K3π)












K vs B







200

200

200

200

KeKKeK

KeKKeKA

iHtiHt

iHtiHt

T


20

20

20

20

KefKef

KefKefA

iHtCP

iHtCP

iHtCP

iHtCP

CP

200

200

200

200

KeKKeK

KeKKeKA

iHtiHt

iHtiHt

CPT




CPLEAR experiment

(CERN 1990-96)






tf

ft

f

iHtCP

iHtCP

iHtCP

iHtCP

CPLS

LS

e

mte

KefKef

KefKefA

)(2

2)(

20

20

20

20

1

)cos(2)Re(2

π+π

minus

π0π0

π+π minusπ0

π0π0π0

CPLEARAsymmetrie

s


Rate difference


Measure η





Kaon factories




pppp 2

1SLSL KKKKi




[Lipkin (1968)]

EPR correlation


DAΦNE (Frascati)


DAΦNE (Frascati)


MeVc)









p = 127 MeVcλ = 95 cm

KLKS 106 pb-1




KLOE physics




















p

Target

Collimator



Dump

Tagging Separation

Charged beam




Buthellip



rarr Small in SM


2π (εrsquoε)

3π (Ag)


ν


π0

Kplusmn rarr 3π




π1

π2

π3

K


Kinematics



2


2

Matrix element

|M(uv)|2 ~ 1 + gu + hu2 + kv2







KminusK+








10-6

NA482 OKA

10-5

10-4

10-3

10-2

SMSM

SUSYSUSYNewNew

physicsphysics



|Ag|

bull Ag ~ 10minus5


SUSY New Physics

THEORY



C

N



=Ag



54 60 66

1cm

50 100

10 cm

200 250 m





~11012

ppp

K+

Kminus



always in vacuum

focusing beams

BM

z

magnet

vacuum tank

not to scale

K+

K


pipe

0ordm prodangle






ZZ

XXYY

JuraJura

SaleveSaleve

Beam line K+ Up


B+

Bminus






Spectrometer field

K+

Kminus

Reverse each day

Reverse each week


|V| even pion

in beam pipe


KK+ +

KK



No significant

background





-15 -10 -05 0 05 10 u

0

-1

-2

1

2

3

Dalitz plot



EM calorimeter only






2003 result in PLB 634 (2006) 474




2003 result in PLB 638 (2006) 22


excluded


OKA at Protvino





(in preparation)


More CP violation


Indirect

Direct

CP violation

parameters

(2005)


(A) KS decays


CPV in KS decays




000000

000

000 )(

)(

L

S

KA




S+KL

KL




000 000 00

1( )2 ( 2

0

)

( )


tt

NEARf E t



)()()( 00

00

EKNEKN

EKNEKNED

(incoherent

production)



Assuming CPT





N3

20

40

60

00

4 62


No CPV seen yet

























PT() = (-17 23 11) 10-

3

Im = (-53 71 36) 10-3




Im = (-53 71 36) 10-3








ppp

ppp

)0()0(

)0()0(

NN

NNA


Radiative decays








211221 )()(


IB DE

p1 p1

p2p2

q q







)(

)(

S

L

KA

violatingCPKA




KL π+πminus






IB

M1 DE




KL itself





KL ee


BR = (308 020) 10minus7



E1M1 lt 004 (90 CL)



φ




KS ee

No asymmetry for KS

as expected

BR = (471 032) 10-

5

AΦ = (05 43)






IBEE

dEA

)tan( 0


Kplusmn π+π0γ

)730810672()(

)250350353()(

800

800

syststatMeVT

syststatMeVT

INTFrac

DEFrac







KL π+πndashπ0γ















)(

)2030(

3

3

e

ee

K

MeVEKR





bull 6M Ke3 events


ndash R=(0964plusmn0008+0011-0009)












PDG 2004







]21[192 3

52

KmG







Vus measurements





unitarity





KLOE Kl 3

KLOE K2

copy A Antonelli

Vus some more




Ke4 results





K+rarrπ0π0eν










1-loop rescattering

2-loop rescattering











NA482




KLOE interference

















K+ + 8middot10-11 (at 7)147+130

ndash089 middot 10-

10 (BNL E787+E949)






KL 0ℓ+ℓ-




BR(KL 0+-) lt 3810-10





NA481 KS 0ℓ+ℓ-



BR = (58 +28-23 plusmn08) times10-9


-012 (accid)BR = (28 +15


KS 0e+e- KS 0μ+μ-


NA481 preliminary

NA481 preliminary


KL 0ℓ+ℓ-






Krarr in the SM




W W

s

id

Vis Vid

e

i=uct

W

Z

VisV

idds i

11

20

2410

10)1108(

)(1001)(

AKB

11

2

5

100

10)4082(

)()Im(

1022)(

t

tdtsL xX

VVKB


K

ε εrsquo




Ke3 KL 0

Height

Im(λt )



10301890 10471)(

KBR









K+ +




















Appendixes





J(ππ) = ℓ(ππ) = 0 P(ππ) = +1 C(ππ) = +1



ℓL



SLti

SLLSti

LS

tL

tS

Lti

LSti

S

KKeaaKKeaa

eaea

KeaKea

SLLS

LS

LS

)()(

22

f LSf

fLS KfA

dt

d 2

2

TUnitarity requires

and therefore


f Sff

fS

fLSLLS

f

fLLf

fSS

fKAAKKmi

AA

)(2)(

22


2

22

2

222

0604

mKK

AAAA

LS

LSLS

f

fSf

fLf

fS

fL



SLS KKmi 21




)()( 0000

SSS KK



The new paradigm

K0

K0

K0

K0


CP










Physical states

00

22

00

22

)1()1(

12

1

)1()1(

12

1

KKK

KKK

L

S

00

2122

00

2212

)1()1(12

1

1

1

)1()1(12

1

1

1

KKKKK

KKKKK

LL

L

L

L

L

SS

S

S

S

S

2)(

2)(

SL

LS






M12 ne M21 Γ12 ne Γ21

)2(2

)()(

2

Im)2(Im 112211221212

im

iMM

mi

iM






M11 ne M22 Γ11 ne Γ22

Re(ε) really






34

2

2102

p

p

F

F

FSW

m

m

G

G

m

G

m

G




2

Im)2(Im 1212

mi

iM











KL K2+ ε K1

ππ






KL K2+ ε K1

ππ


K2 (CP=-1) ππ (CP=+1)






This is named



K0 ππ

K0





Decay phase

(direct)




Isospin I=0

Isospin I=2


(CHARGE) BASIS









221

2

)(

)(

21

)(

)(

00

00

000000

S

Li

S

Li

KA

KAe

KA

KAe

)(

0

0

2

2

0

2

0

0

02

)Re(

)Im(

)Re(

)Im(

)Re(

)Re(

2

)Re(

)Im(

iea

a

a

a

a

ai

a

ai

221

)0(

)2(

IKA

IKA

S

S







Questions













p

Target


particle sweeping

Dump

Neutral beam

Collimator

Production

angle

Protonenergy Beam

acceptance

Collimatorbackgroun

d

KL (+KS) beams



KS by regeneration





KL KL + Ar KS








61)Re(612

2

00

)(

)(

)(

)(00

00

2

2

00

L

S

S

L

K

K

K

K







n


d(PSext) d3x d3ph3




Position scale

Momentum

scale



Direct CPV 1996 AD

FNAL E731






The presshellip







KTeV at Fermilab



NA48 at CERN




600

00

10)820045()()(

)()(

KK

KK




4

World average





rsquo why










K decays


(PDG2004)



For kaons


K2ππ




ΔΓ(K3π)Δg(K3π)












K vs B







200

200

200

200

KeKKeK

KeKKeKA

iHtiHt

iHtiHt

T


20

20

20

20

KefKef

KefKefA

iHtCP

iHtCP

iHtCP

iHtCP

CP

200

200

200

200

KeKKeK

KeKKeKA

iHtiHt

iHtiHt

CPT




CPLEAR experiment

(CERN 1990-96)






tf

ft

f

iHtCP

iHtCP

iHtCP

iHtCP

CPLS

LS

e

mte

KefKef

KefKefA

)(2

2)(

20

20

20

20

1

)cos(2)Re(2

π+π

minus

π0π0

π+π minusπ0

π0π0π0

CPLEARAsymmetrie

s


Rate difference


Measure η





Kaon factories




pppp 2

1SLSL KKKKi




[Lipkin (1968)]

EPR correlation


DAΦNE (Frascati)


DAΦNE (Frascati)


MeVc)









p = 127 MeVcλ = 95 cm

KLKS 106 pb-1




KLOE physics




















p

Target

Collimator



Dump

Tagging Separation

Charged beam




Buthellip



rarr Small in SM


2π (εrsquoε)

3π (Ag)


ν


π0

Kplusmn rarr 3π




π1

π2

π3

K


Kinematics



2


2

Matrix element

|M(uv)|2 ~ 1 + gu + hu2 + kv2







KminusK+








10-6

NA482 OKA

10-5

10-4

10-3

10-2

SMSM

SUSYSUSYNewNew

physicsphysics



|Ag|

bull Ag ~ 10minus5


SUSY New Physics

THEORY



C

N



=Ag



54 60 66

1cm

50 100

10 cm

200 250 m





~11012

ppp

K+

Kminus



always in vacuum

focusing beams

BM

z

magnet

vacuum tank

not to scale

K+

K


pipe

0ordm prodangle






ZZ

XXYY

JuraJura

SaleveSaleve

Beam line K+ Up


B+

Bminus






Spectrometer field

K+

Kminus

Reverse each day

Reverse each week


|V| even pion

in beam pipe


KK+ +

KK



No significant

background





-15 -10 -05 0 05 10 u

0

-1

-2

1

2

3

Dalitz plot



EM calorimeter only






2003 result in PLB 634 (2006) 474




2003 result in PLB 638 (2006) 22


excluded


OKA at Protvino





(in preparation)


More CP violation


Indirect

Direct

CP violation

parameters

(2005)


(A) KS decays


CPV in KS decays




000000

000

000 )(

)(

L

S

KA




S+KL

KL




000 000 00

1( )2 ( 2

0

)

( )


tt

NEARf E t



)()()( 00

00

EKNEKN

EKNEKNED

(incoherent

production)



Assuming CPT





N3

20

40

60

00

4 62


No CPV seen yet

























PT() = (-17 23 11) 10-

3

Im = (-53 71 36) 10-3




Im = (-53 71 36) 10-3








ppp

ppp

)0()0(

)0()0(

NN

NNA


Radiative decays








211221 )()(


IB DE

p1 p1

p2p2

q q







)(

)(

S

L

KA

violatingCPKA




KL π+πminus






IB

M1 DE




KL itself





KL ee


BR = (308 020) 10minus7



E1M1 lt 004 (90 CL)



φ




KS ee

No asymmetry for KS

as expected

BR = (471 032) 10-

5

AΦ = (05 43)






IBEE

dEA

)tan( 0


Kplusmn π+π0γ

)730810672()(

)250350353()(

800

800

syststatMeVT

syststatMeVT

INTFrac

DEFrac







KL π+πndashπ0γ















)(

)2030(

3

3

e

ee

K

MeVEKR





bull 6M Ke3 events


ndash R=(0964plusmn0008+0011-0009)












PDG 2004







]21[192 3

52

KmG







Vus measurements





unitarity





KLOE Kl 3

KLOE K2

copy A Antonelli

Vus some more




Ke4 results





K+rarrπ0π0eν










1-loop rescattering

2-loop rescattering











NA482




KLOE interference

















K+ + 8middot10-11 (at 7)147+130

ndash089 middot 10-

10 (BNL E787+E949)






KL 0ℓ+ℓ-




BR(KL 0+-) lt 3810-10





NA481 KS 0ℓ+ℓ-



BR = (58 +28-23 plusmn08) times10-9


-012 (accid)BR = (28 +15


KS 0e+e- KS 0μ+μ-


NA481 preliminary

NA481 preliminary


KL 0ℓ+ℓ-






Krarr in the SM




W W

s

id

Vis Vid

e

i=uct

W

Z

VisV

idds i

11

20

2410

10)1108(

)(1001)(

AKB

11

2

5

100

10)4082(

)()Im(

1022)(

t

tdtsL xX

VVKB


K

ε εrsquo




Ke3 KL 0

Height

Im(λt )



10301890 10471)(

KBR









K+ +




















Appendixes





J(ππ) = ℓ(ππ) = 0 P(ππ) = +1 C(ππ) = +1



ℓL



SLti

SLLSti

LS

tL

tS

Lti

LSti

S

KKeaaKKeaa

eaea

KeaKea

SLLS

LS

LS

)()(

22

f LSf

fLS KfA

dt

d 2

2

TUnitarity requires

and therefore


f Sff

fS

fLSLLS

f

fLLf

fSS

fKAAKKmi

AA

)(2)(

22


2

22

2

222

0604

mKK

AAAA

LS

LSLS

f

fSf

fLf

fS

fL



SLS KKmi 21




)()( 0000

SSS KK








Physical states

00

22

00

22

)1()1(

12

1

)1()1(

12

1

KKK

KKK

L

S

00

2122

00

2212

)1()1(12

1

1

1

)1()1(12

1

1

1

KKKKK

KKKKK

LL

L

L

L

L

SS

S

S

S

S

2)(

2)(

SL

LS






M12 ne M21 Γ12 ne Γ21

)2(2

)()(

2

Im)2(Im 112211221212

im

iMM

mi

iM






M11 ne M22 Γ11 ne Γ22

Re(ε) really






34

2

2102

p

p

F

F

FSW

m

m

G

G

m

G

m

G




2

Im)2(Im 1212

mi

iM











KL K2+ ε K1

ππ






KL K2+ ε K1

ππ


K2 (CP=-1) ππ (CP=+1)






This is named



K0 ππ

K0





Decay phase

(direct)




Isospin I=0

Isospin I=2


(CHARGE) BASIS









221

2

)(

)(

21

)(

)(

00

00

000000

S

Li

S

Li

KA

KAe

KA

KAe

)(

0

0

2

2

0

2

0

0

02

)Re(

)Im(

)Re(

)Im(

)Re(

)Re(

2

)Re(

)Im(

iea

a

a

a

a

ai

a

ai

221

)0(

)2(

IKA

IKA

S

S







Questions













p

Target


particle sweeping

Dump

Neutral beam

Collimator

Production

angle

Protonenergy Beam

acceptance

Collimatorbackgroun

d

KL (+KS) beams



KS by regeneration





KL KL + Ar KS








61)Re(612

2

00

)(

)(

)(

)(00

00

2

2

00

L

S

S

L

K

K

K

K







n


d(PSext) d3x d3ph3




Position scale

Momentum

scale



Direct CPV 1996 AD

FNAL E731






The presshellip







KTeV at Fermilab



NA48 at CERN




600

00

10)820045()()(

)()(

KK

KK




4

World average





rsquo why










K decays


(PDG2004)



For kaons


K2ππ




ΔΓ(K3π)Δg(K3π)












K vs B







200

200

200

200

KeKKeK

KeKKeKA

iHtiHt

iHtiHt

T


20

20

20

20

KefKef

KefKefA

iHtCP

iHtCP

iHtCP

iHtCP

CP

200

200

200

200

KeKKeK

KeKKeKA

iHtiHt

iHtiHt

CPT




CPLEAR experiment

(CERN 1990-96)






tf

ft

f

iHtCP

iHtCP

iHtCP

iHtCP

CPLS

LS

e

mte

KefKef

KefKefA

)(2

2)(

20

20

20

20

1

)cos(2)Re(2

π+π

minus

π0π0

π+π minusπ0

π0π0π0

CPLEARAsymmetrie

s


Rate difference


Measure η





Kaon factories




pppp 2

1SLSL KKKKi




[Lipkin (1968)]

EPR correlation


DAΦNE (Frascati)


DAΦNE (Frascati)


MeVc)









p = 127 MeVcλ = 95 cm

KLKS 106 pb-1




KLOE physics




















p

Target

Collimator



Dump

Tagging Separation

Charged beam




Buthellip



rarr Small in SM


2π (εrsquoε)

3π (Ag)


ν


π0

Kplusmn rarr 3π




π1

π2

π3

K


Kinematics



2


2

Matrix element

|M(uv)|2 ~ 1 + gu + hu2 + kv2







KminusK+








10-6

NA482 OKA

10-5

10-4

10-3

10-2

SMSM

SUSYSUSYNewNew

physicsphysics



|Ag|

bull Ag ~ 10minus5


SUSY New Physics

THEORY



C

N



=Ag



54 60 66

1cm

50 100

10 cm

200 250 m





~11012

ppp

K+

Kminus



always in vacuum

focusing beams

BM

z

magnet

vacuum tank

not to scale

K+

K


pipe

0ordm prodangle






ZZ

XXYY

JuraJura

SaleveSaleve

Beam line K+ Up


B+

Bminus






Spectrometer field

K+

Kminus

Reverse each day

Reverse each week


|V| even pion

in beam pipe


KK+ +

KK



No significant

background





-15 -10 -05 0 05 10 u

0

-1

-2

1

2

3

Dalitz plot



EM calorimeter only






2003 result in PLB 634 (2006) 474




2003 result in PLB 638 (2006) 22


excluded


OKA at Protvino





(in preparation)


More CP violation


Indirect

Direct

CP violation

parameters

(2005)


(A) KS decays


CPV in KS decays




000000

000

000 )(

)(

L

S

KA




S+KL

KL




000 000 00

1( )2 ( 2

0

)

( )


tt

NEARf E t



)()()( 00

00

EKNEKN

EKNEKNED

(incoherent

production)



Assuming CPT





N3

20

40

60

00

4 62


No CPV seen yet

























PT() = (-17 23 11) 10-

3

Im = (-53 71 36) 10-3




Im = (-53 71 36) 10-3








ppp

ppp

)0()0(

)0()0(

NN

NNA


Radiative decays








211221 )()(


IB DE

p1 p1

p2p2

q q







)(

)(

S

L

KA

violatingCPKA




KL π+πminus






IB

M1 DE




KL itself





KL ee


BR = (308 020) 10minus7



E1M1 lt 004 (90 CL)



φ




KS ee

No asymmetry for KS

as expected

BR = (471 032) 10-

5

AΦ = (05 43)






IBEE

dEA

)tan( 0


Kplusmn π+π0γ

)730810672()(

)250350353()(

800

800

syststatMeVT

syststatMeVT

INTFrac

DEFrac







KL π+πndashπ0γ















)(

)2030(

3

3

e

ee

K

MeVEKR





bull 6M Ke3 events


ndash R=(0964plusmn0008+0011-0009)












PDG 2004







]21[192 3

52

KmG







Vus measurements





unitarity





KLOE Kl 3

KLOE K2

copy A Antonelli

Vus some more




Ke4 results





K+rarrπ0π0eν










1-loop rescattering

2-loop rescattering











NA482




KLOE interference

















K+ + 8middot10-11 (at 7)147+130

ndash089 middot 10-

10 (BNL E787+E949)






KL 0ℓ+ℓ-




BR(KL 0+-) lt 3810-10





NA481 KS 0ℓ+ℓ-



BR = (58 +28-23 plusmn08) times10-9


-012 (accid)BR = (28 +15


KS 0e+e- KS 0μ+μ-


NA481 preliminary

NA481 preliminary


KL 0ℓ+ℓ-






Krarr in the SM




W W

s

id

Vis Vid

e

i=uct

W

Z

VisV

idds i

11

20

2410

10)1108(

)(1001)(

AKB

11

2

5

100

10)4082(

)()Im(

1022)(

t

tdtsL xX

VVKB


K

ε εrsquo




Ke3 KL 0

Height

Im(λt )



10301890 10471)(

KBR









K+ +




















Appendixes





J(ππ) = ℓ(ππ) = 0 P(ππ) = +1 C(ππ) = +1



ℓL



SLti

SLLSti

LS

tL

tS

Lti

LSti

S

KKeaaKKeaa

eaea

KeaKea

SLLS

LS

LS

)()(

22

f LSf

fLS KfA

dt

d 2

2

TUnitarity requires

and therefore


f Sff

fS

fLSLLS

f

fLLf

fSS

fKAAKKmi

AA

)(2)(

22


2

22

2

222

0604

mKK

AAAA

LS

LSLS

f

fSf

fLf

fS

fL



SLS KKmi 21




)()( 0000

SSS KK



Physical states

00

22

00

22

)1()1(

12

1

)1()1(

12

1

KKK

KKK

L

S

00

2122

00

2212

)1()1(12

1

1

1

)1()1(12

1

1

1

KKKKK

KKKKK

LL

L

L

L

L

SS

S

S

S

S

2)(

2)(

SL

LS






M12 ne M21 Γ12 ne Γ21

)2(2

)()(

2

Im)2(Im 112211221212

im

iMM

mi

iM






M11 ne M22 Γ11 ne Γ22

Re(ε) really






34

2

2102

p

p

F

F

FSW

m

m

G

G

m

G

m

G




2

Im)2(Im 1212

mi

iM











KL K2+ ε K1

ππ






KL K2+ ε K1

ππ


K2 (CP=-1) ππ (CP=+1)






This is named



K0 ππ

K0





Decay phase

(direct)




Isospin I=0

Isospin I=2


(CHARGE) BASIS









221

2

)(

)(

21

)(

)(

00

00

000000

S

Li

S

Li

KA

KAe

KA

KAe

)(

0

0

2

2

0

2

0

0

02

)Re(

)Im(

)Re(

)Im(

)Re(

)Re(

2

)Re(

)Im(

iea

a

a

a

a

ai

a

ai

221

)0(

)2(

IKA

IKA

S

S







Questions













p

Target


particle sweeping

Dump

Neutral beam

Collimator

Production

angle

Protonenergy Beam

acceptance

Collimatorbackgroun

d

KL (+KS) beams



KS by regeneration





KL KL + Ar KS








61)Re(612

2

00

)(

)(

)(

)(00

00

2

2

00

L

S

S

L

K

K

K

K







n


d(PSext) d3x d3ph3




Position scale

Momentum

scale



Direct CPV 1996 AD

FNAL E731






The presshellip







KTeV at Fermilab



NA48 at CERN




600

00

10)820045()()(

)()(

KK

KK




4

World average





rsquo why










K decays


(PDG2004)



For kaons


K2ππ




ΔΓ(K3π)Δg(K3π)












K vs B







200

200

200

200

KeKKeK

KeKKeKA

iHtiHt

iHtiHt

T


20

20

20

20

KefKef

KefKefA

iHtCP

iHtCP

iHtCP

iHtCP

CP

200

200

200

200

KeKKeK

KeKKeKA

iHtiHt

iHtiHt

CPT




CPLEAR experiment

(CERN 1990-96)






tf

ft

f

iHtCP

iHtCP

iHtCP

iHtCP

CPLS

LS

e

mte

KefKef

KefKefA

)(2

2)(

20

20

20

20

1

)cos(2)Re(2

π+π

minus

π0π0

π+π minusπ0

π0π0π0

CPLEARAsymmetrie

s


Rate difference


Measure η





Kaon factories




pppp 2

1SLSL KKKKi




[Lipkin (1968)]

EPR correlation


DAΦNE (Frascati)


DAΦNE (Frascati)


MeVc)









p = 127 MeVcλ = 95 cm

KLKS 106 pb-1




KLOE physics




















p

Target

Collimator



Dump

Tagging Separation

Charged beam




Buthellip



rarr Small in SM


2π (εrsquoε)

3π (Ag)


ν


π0

Kplusmn rarr 3π




π1

π2

π3

K


Kinematics



2


2

Matrix element

|M(uv)|2 ~ 1 + gu + hu2 + kv2







KminusK+








10-6

NA482 OKA

10-5

10-4

10-3

10-2

SMSM

SUSYSUSYNewNew

physicsphysics



|Ag|

bull Ag ~ 10minus5


SUSY New Physics

THEORY



C

N



=Ag



54 60 66

1cm

50 100

10 cm

200 250 m





~11012

ppp

K+

Kminus



always in vacuum

focusing beams

BM

z

magnet

vacuum tank

not to scale

K+

K


pipe

0ordm prodangle






ZZ

XXYY

JuraJura

SaleveSaleve

Beam line K+ Up


B+

Bminus






Spectrometer field

K+

Kminus

Reverse each day

Reverse each week


|V| even pion

in beam pipe


KK+ +

KK



No significant

background





-15 -10 -05 0 05 10 u

0

-1

-2

1

2

3

Dalitz plot



EM calorimeter only






2003 result in PLB 634 (2006) 474




2003 result in PLB 638 (2006) 22


excluded


OKA at Protvino





(in preparation)


More CP violation


Indirect

Direct

CP violation

parameters

(2005)


(A) KS decays


CPV in KS decays




000000

000

000 )(

)(

L

S

KA




S+KL

KL




000 000 00

1( )2 ( 2

0

)

( )


tt

NEARf E t



)()()( 00

00

EKNEKN

EKNEKNED

(incoherent

production)



Assuming CPT





N3

20

40

60

00

4 62


No CPV seen yet

























PT() = (-17 23 11) 10-

3

Im = (-53 71 36) 10-3




Im = (-53 71 36) 10-3








ppp

ppp

)0()0(

)0()0(

NN

NNA


Radiative decays








211221 )()(


IB DE

p1 p1

p2p2

q q







)(

)(

S

L

KA

violatingCPKA




KL π+πminus






IB

M1 DE




KL itself





KL ee


BR = (308 020) 10minus7



E1M1 lt 004 (90 CL)



φ




KS ee

No asymmetry for KS

as expected

BR = (471 032) 10-

5

AΦ = (05 43)






IBEE

dEA

)tan( 0


Kplusmn π+π0γ

)730810672()(

)250350353()(

800

800

syststatMeVT

syststatMeVT

INTFrac

DEFrac







KL π+πndashπ0γ















)(

)2030(

3

3

e

ee

K

MeVEKR





bull 6M Ke3 events


ndash R=(0964plusmn0008+0011-0009)












PDG 2004







]21[192 3

52

KmG







Vus measurements





unitarity





KLOE Kl 3

KLOE K2

copy A Antonelli

Vus some more




Ke4 results





K+rarrπ0π0eν










1-loop rescattering

2-loop rescattering











NA482




KLOE interference

















K+ + 8middot10-11 (at 7)147+130

ndash089 middot 10-

10 (BNL E787+E949)






KL 0ℓ+ℓ-




BR(KL 0+-) lt 3810-10





NA481 KS 0ℓ+ℓ-



BR = (58 +28-23 plusmn08) times10-9


-012 (accid)BR = (28 +15


KS 0e+e- KS 0μ+μ-


NA481 preliminary

NA481 preliminary


KL 0ℓ+ℓ-






Krarr in the SM




W W

s

id

Vis Vid

e

i=uct

W

Z

VisV

idds i

11

20

2410

10)1108(

)(1001)(

AKB

11

2

5

100

10)4082(

)()Im(

1022)(

t

tdtsL xX

VVKB


K

ε εrsquo




Ke3 KL 0

Height

Im(λt )



10301890 10471)(

KBR









K+ +




















Appendixes





J(ππ) = ℓ(ππ) = 0 P(ππ) = +1 C(ππ) = +1



ℓL



SLti

SLLSti

LS

tL

tS

Lti

LSti

S

KKeaaKKeaa

eaea

KeaKea

SLLS

LS

LS

)()(

22

f LSf

fLS KfA

dt

d 2

2

TUnitarity requires

and therefore


f Sff

fS

fLSLLS

f

fLLf

fSS

fKAAKKmi

AA

)(2)(

22


2

22

2

222

0604

mKK

AAAA

LS

LSLS

f

fSf

fLf

fS

fL



SLS KKmi 21




)()( 0000

SSS KK




M12 ne M21 Γ12 ne Γ21

)2(2

)()(

2

Im)2(Im 112211221212

im

iMM

mi

iM






M11 ne M22 Γ11 ne Γ22

Re(ε) really






34

2

2102

p

p

F

F

FSW

m

m

G

G

m

G

m

G




2

Im)2(Im 1212

mi

iM











KL K2+ ε K1

ππ






KL K2+ ε K1

ππ


K2 (CP=-1) ππ (CP=+1)






This is named



K0 ππ

K0





Decay phase

(direct)




Isospin I=0

Isospin I=2


(CHARGE) BASIS









221

2

)(

)(

21

)(

)(

00

00

000000

S

Li

S

Li

KA

KAe

KA

KAe

)(

0

0

2

2

0

2

0

0

02

)Re(

)Im(

)Re(

)Im(

)Re(

)Re(

2

)Re(

)Im(

iea

a

a

a

a

ai

a

ai

221

)0(

)2(

IKA

IKA

S

S







Questions













p

Target


particle sweeping

Dump

Neutral beam

Collimator

Production

angle

Protonenergy Beam

acceptance

Collimatorbackgroun

d

KL (+KS) beams



KS by regeneration





KL KL + Ar KS








61)Re(612

2

00

)(

)(

)(

)(00

00

2

2

00

L

S

S

L

K

K

K

K







n


d(PSext) d3x d3ph3




Position scale

Momentum

scale



Direct CPV 1996 AD

FNAL E731






The presshellip







KTeV at Fermilab



NA48 at CERN




600

00

10)820045()()(

)()(

KK

KK




4

World average





rsquo why










K decays


(PDG2004)



For kaons


K2ππ




ΔΓ(K3π)Δg(K3π)












K vs B







200

200

200

200

KeKKeK

KeKKeKA

iHtiHt

iHtiHt

T


20

20

20

20

KefKef

KefKefA

iHtCP

iHtCP

iHtCP

iHtCP

CP

200

200

200

200

KeKKeK

KeKKeKA

iHtiHt

iHtiHt

CPT




CPLEAR experiment

(CERN 1990-96)






tf

ft

f

iHtCP

iHtCP

iHtCP

iHtCP

CPLS

LS

e

mte

KefKef

KefKefA

)(2

2)(

20

20

20

20

1

)cos(2)Re(2

π+π

minus

π0π0

π+π minusπ0

π0π0π0

CPLEARAsymmetrie

s


Rate difference


Measure η





Kaon factories




pppp 2

1SLSL KKKKi




[Lipkin (1968)]

EPR correlation


DAΦNE (Frascati)


DAΦNE (Frascati)


MeVc)









p = 127 MeVcλ = 95 cm

KLKS 106 pb-1




KLOE physics




















p

Target

Collimator



Dump

Tagging Separation

Charged beam




Buthellip



rarr Small in SM


2π (εrsquoε)

3π (Ag)


ν


π0

Kplusmn rarr 3π




π1

π2

π3

K


Kinematics



2


2

Matrix element

|M(uv)|2 ~ 1 + gu + hu2 + kv2







KminusK+








10-6

NA482 OKA

10-5

10-4

10-3

10-2

SMSM

SUSYSUSYNewNew

physicsphysics



|Ag|

bull Ag ~ 10minus5


SUSY New Physics

THEORY



C

N



=Ag



54 60 66

1cm

50 100

10 cm

200 250 m





~11012

ppp

K+

Kminus



always in vacuum

focusing beams

BM

z

magnet

vacuum tank

not to scale

K+

K


pipe

0ordm prodangle






ZZ

XXYY

JuraJura

SaleveSaleve

Beam line K+ Up


B+

Bminus






Spectrometer field

K+

Kminus

Reverse each day

Reverse each week


|V| even pion

in beam pipe


KK+ +

KK



No significant

background





-15 -10 -05 0 05 10 u

0

-1

-2

1

2

3

Dalitz plot



EM calorimeter only






2003 result in PLB 634 (2006) 474




2003 result in PLB 638 (2006) 22


excluded


OKA at Protvino





(in preparation)


More CP violation


Indirect

Direct

CP violation

parameters

(2005)


(A) KS decays


CPV in KS decays




000000

000

000 )(

)(

L

S

KA




S+KL

KL




000 000 00

1( )2 ( 2

0

)

( )


tt

NEARf E t



)()()( 00

00

EKNEKN

EKNEKNED

(incoherent

production)



Assuming CPT





N3

20

40

60

00

4 62


No CPV seen yet

























PT() = (-17 23 11) 10-

3

Im = (-53 71 36) 10-3




Im = (-53 71 36) 10-3








ppp

ppp

)0()0(

)0()0(

NN

NNA


Radiative decays








211221 )()(


IB DE

p1 p1

p2p2

q q







)(

)(

S

L

KA

violatingCPKA




KL π+πminus






IB

M1 DE




KL itself





KL ee


BR = (308 020) 10minus7



E1M1 lt 004 (90 CL)



φ




KS ee

No asymmetry for KS

as expected

BR = (471 032) 10-

5

AΦ = (05 43)






IBEE

dEA

)tan( 0


Kplusmn π+π0γ

)730810672()(

)250350353()(

800

800

syststatMeVT

syststatMeVT

INTFrac

DEFrac







KL π+πndashπ0γ















)(

)2030(

3

3

e

ee

K

MeVEKR





bull 6M Ke3 events


ndash R=(0964plusmn0008+0011-0009)












PDG 2004







]21[192 3

52

KmG







Vus measurements





unitarity





KLOE Kl 3

KLOE K2

copy A Antonelli

Vus some more




Ke4 results





K+rarrπ0π0eν










1-loop rescattering

2-loop rescattering











NA482




KLOE interference

















K+ + 8middot10-11 (at 7)147+130

ndash089 middot 10-

10 (BNL E787+E949)






KL 0ℓ+ℓ-




BR(KL 0+-) lt 3810-10





NA481 KS 0ℓ+ℓ-



BR = (58 +28-23 plusmn08) times10-9


-012 (accid)BR = (28 +15


KS 0e+e- KS 0μ+μ-


NA481 preliminary

NA481 preliminary


KL 0ℓ+ℓ-






Krarr in the SM




W W

s

id

Vis Vid

e

i=uct

W

Z

VisV

idds i

11

20

2410

10)1108(

)(1001)(

AKB

11

2

5

100

10)4082(

)()Im(

1022)(

t

tdtsL xX

VVKB


K

ε εrsquo




Ke3 KL 0

Height

Im(λt )



10301890 10471)(

KBR









K+ +




















Appendixes





J(ππ) = ℓ(ππ) = 0 P(ππ) = +1 C(ππ) = +1



ℓL



SLti

SLLSti

LS

tL

tS

Lti

LSti

S

KKeaaKKeaa

eaea

KeaKea

SLLS

LS

LS

)()(

22

f LSf

fLS KfA

dt

d 2

2

TUnitarity requires

and therefore


f Sff

fS

fLSLLS

f

fLLf

fSS

fKAAKKmi

AA

)(2)(

22


2

22

2

222

0604

mKK

AAAA

LS

LSLS

f

fSf

fLf

fS

fL



SLS KKmi 21




)()( 0000

SSS KK






34

2

2102

p

p

F

F

FSW

m

m

G

G

m

G

m

G




2

Im)2(Im 1212

mi

iM











KL K2+ ε K1

ππ






KL K2+ ε K1

ππ


K2 (CP=-1) ππ (CP=+1)






This is named



K0 ππ

K0





Decay phase

(direct)




Isospin I=0

Isospin I=2


(CHARGE) BASIS









221

2

)(

)(

21

)(

)(

00

00

000000

S

Li

S

Li

KA

KAe

KA

KAe

)(

0

0

2

2

0

2

0

0

02

)Re(

)Im(

)Re(

)Im(

)Re(

)Re(

2

)Re(

)Im(

iea

a

a

a

a

ai

a

ai

221

)0(

)2(

IKA

IKA

S

S







Questions













p

Target


particle sweeping

Dump

Neutral beam

Collimator

Production

angle

Protonenergy Beam

acceptance

Collimatorbackgroun

d

KL (+KS) beams



KS by regeneration





KL KL + Ar KS








61)Re(612

2

00

)(

)(

)(

)(00

00

2

2

00

L

S

S

L

K

K

K

K







n


d(PSext) d3x d3ph3




Position scale

Momentum

scale



Direct CPV 1996 AD

FNAL E731






The presshellip







KTeV at Fermilab



NA48 at CERN




600

00

10)820045()()(

)()(

KK

KK




4

World average





rsquo why










K decays


(PDG2004)



For kaons


K2ππ




ΔΓ(K3π)Δg(K3π)












K vs B







200

200

200

200

KeKKeK

KeKKeKA

iHtiHt

iHtiHt

T


20

20

20

20

KefKef

KefKefA

iHtCP

iHtCP

iHtCP

iHtCP

CP

200

200

200

200

KeKKeK

KeKKeKA

iHtiHt

iHtiHt

CPT




CPLEAR experiment

(CERN 1990-96)






tf

ft

f

iHtCP

iHtCP

iHtCP

iHtCP

CPLS

LS

e

mte

KefKef

KefKefA

)(2

2)(

20

20

20

20

1

)cos(2)Re(2

π+π

minus

π0π0

π+π minusπ0

π0π0π0

CPLEARAsymmetrie

s


Rate difference


Measure η





Kaon factories




pppp 2

1SLSL KKKKi




[Lipkin (1968)]

EPR correlation


DAΦNE (Frascati)


DAΦNE (Frascati)


MeVc)









p = 127 MeVcλ = 95 cm

KLKS 106 pb-1




KLOE physics




















p

Target

Collimator



Dump

Tagging Separation

Charged beam




Buthellip



rarr Small in SM


2π (εrsquoε)

3π (Ag)


ν


π0

Kplusmn rarr 3π




π1

π2

π3

K


Kinematics



2


2

Matrix element

|M(uv)|2 ~ 1 + gu + hu2 + kv2







KminusK+








10-6

NA482 OKA

10-5

10-4

10-3

10-2

SMSM

SUSYSUSYNewNew

physicsphysics



|Ag|

bull Ag ~ 10minus5


SUSY New Physics

THEORY



C

N



=Ag



54 60 66

1cm

50 100

10 cm

200 250 m





~11012

ppp

K+

Kminus



always in vacuum

focusing beams

BM

z

magnet

vacuum tank

not to scale

K+

K


pipe

0ordm prodangle






ZZ

XXYY

JuraJura

SaleveSaleve

Beam line K+ Up


B+

Bminus






Spectrometer field

K+

Kminus

Reverse each day

Reverse each week


|V| even pion

in beam pipe


KK+ +

KK



No significant

background





-15 -10 -05 0 05 10 u

0

-1

-2

1

2

3

Dalitz plot



EM calorimeter only






2003 result in PLB 634 (2006) 474




2003 result in PLB 638 (2006) 22


excluded


OKA at Protvino





(in preparation)


More CP violation


Indirect

Direct

CP violation

parameters

(2005)


(A) KS decays


CPV in KS decays




000000

000

000 )(

)(

L

S

KA




S+KL

KL




000 000 00

1( )2 ( 2

0

)

( )


tt

NEARf E t



)()()( 00

00

EKNEKN

EKNEKNED

(incoherent

production)



Assuming CPT





N3

20

40

60

00

4 62


No CPV seen yet

























PT() = (-17 23 11) 10-

3

Im = (-53 71 36) 10-3




Im = (-53 71 36) 10-3








ppp

ppp

)0()0(

)0()0(

NN

NNA


Radiative decays








211221 )()(


IB DE

p1 p1

p2p2

q q







)(

)(

S

L

KA

violatingCPKA




KL π+πminus






IB

M1 DE




KL itself





KL ee


BR = (308 020) 10minus7



E1M1 lt 004 (90 CL)



φ




KS ee

No asymmetry for KS

as expected

BR = (471 032) 10-

5

AΦ = (05 43)






IBEE

dEA

)tan( 0


Kplusmn π+π0γ

)730810672()(

)250350353()(

800

800

syststatMeVT

syststatMeVT

INTFrac

DEFrac







KL π+πndashπ0γ















)(

)2030(

3

3

e

ee

K

MeVEKR





bull 6M Ke3 events


ndash R=(0964plusmn0008+0011-0009)












PDG 2004







]21[192 3

52

KmG







Vus measurements





unitarity





KLOE Kl 3

KLOE K2

copy A Antonelli

Vus some more




Ke4 results





K+rarrπ0π0eν










1-loop rescattering

2-loop rescattering











NA482




KLOE interference

















K+ + 8middot10-11 (at 7)147+130

ndash089 middot 10-

10 (BNL E787+E949)






KL 0ℓ+ℓ-




BR(KL 0+-) lt 3810-10





NA481 KS 0ℓ+ℓ-



BR = (58 +28-23 plusmn08) times10-9


-012 (accid)BR = (28 +15


KS 0e+e- KS 0μ+μ-


NA481 preliminary

NA481 preliminary


KL 0ℓ+ℓ-






Krarr in the SM




W W

s

id

Vis Vid

e

i=uct

W

Z

VisV

idds i

11

20

2410

10)1108(

)(1001)(

AKB

11

2

5

100

10)4082(

)()Im(

1022)(

t

tdtsL xX

VVKB


K

ε εrsquo




Ke3 KL 0

Height

Im(λt )



10301890 10471)(

KBR









K+ +




















Appendixes





J(ππ) = ℓ(ππ) = 0 P(ππ) = +1 C(ππ) = +1



ℓL



SLti

SLLSti

LS

tL

tS

Lti

LSti

S

KKeaaKKeaa

eaea

KeaKea

SLLS

LS

LS

)()(

22

f LSf

fLS KfA

dt

d 2

2

TUnitarity requires

and therefore


f Sff

fS

fLSLLS

f

fLLf

fSS

fKAAKKmi

AA

)(2)(

22


2

22

2

222

0604

mKK

AAAA

LS

LSLS

f

fSf

fLf

fS

fL



SLS KKmi 21




)()( 0000

SSS KK




34

2

2102

p

p

F

F

FSW

m

m

G

G

m

G

m

G




2

Im)2(Im 1212

mi

iM











KL K2+ ε K1

ππ






KL K2+ ε K1

ππ


K2 (CP=-1) ππ (CP=+1)






This is named



K0 ππ

K0





Decay phase

(direct)




Isospin I=0

Isospin I=2


(CHARGE) BASIS









221

2

)(

)(

21

)(

)(

00

00

000000

S

Li

S

Li

KA

KAe

KA

KAe

)(

0

0

2

2

0

2

0

0

02

)Re(

)Im(

)Re(

)Im(

)Re(

)Re(

2

)Re(

)Im(

iea

a

a

a

a

ai

a

ai

221

)0(

)2(

IKA

IKA

S

S







Questions













p

Target


particle sweeping

Dump

Neutral beam

Collimator

Production

angle

Protonenergy Beam

acceptance

Collimatorbackgroun

d

KL (+KS) beams



KS by regeneration





KL KL + Ar KS








61)Re(612

2

00

)(

)(

)(

)(00

00

2

2

00

L

S

S

L

K

K

K

K







n


d(PSext) d3x d3ph3




Position scale

Momentum

scale



Direct CPV 1996 AD

FNAL E731






The presshellip







KTeV at Fermilab



NA48 at CERN




600

00

10)820045()()(

)()(

KK

KK




4

World average





rsquo why










K decays


(PDG2004)



For kaons


K2ππ




ΔΓ(K3π)Δg(K3π)












K vs B







200

200

200

200

KeKKeK

KeKKeKA

iHtiHt

iHtiHt

T


20

20

20

20

KefKef

KefKefA

iHtCP

iHtCP

iHtCP

iHtCP

CP

200

200

200

200

KeKKeK

KeKKeKA

iHtiHt

iHtiHt

CPT




CPLEAR experiment

(CERN 1990-96)






tf

ft

f

iHtCP

iHtCP

iHtCP

iHtCP

CPLS

LS

e

mte

KefKef

KefKefA

)(2

2)(

20

20

20

20

1

)cos(2)Re(2

π+π

minus

π0π0

π+π minusπ0

π0π0π0

CPLEARAsymmetrie

s


Rate difference


Measure η





Kaon factories




pppp 2

1SLSL KKKKi




[Lipkin (1968)]

EPR correlation


DAΦNE (Frascati)


DAΦNE (Frascati)


MeVc)









p = 127 MeVcλ = 95 cm

KLKS 106 pb-1




KLOE physics




















p

Target

Collimator



Dump

Tagging Separation

Charged beam




Buthellip



rarr Small in SM


2π (εrsquoε)

3π (Ag)


ν


π0

Kplusmn rarr 3π




π1

π2

π3

K


Kinematics



2


2

Matrix element

|M(uv)|2 ~ 1 + gu + hu2 + kv2







KminusK+








10-6

NA482 OKA

10-5

10-4

10-3

10-2

SMSM

SUSYSUSYNewNew

physicsphysics



|Ag|

bull Ag ~ 10minus5


SUSY New Physics

THEORY



C

N



=Ag



54 60 66

1cm

50 100

10 cm

200 250 m





~11012

ppp

K+

Kminus



always in vacuum

focusing beams

BM

z

magnet

vacuum tank

not to scale

K+

K


pipe

0ordm prodangle






ZZ

XXYY

JuraJura

SaleveSaleve

Beam line K+ Up


B+

Bminus






Spectrometer field

K+

Kminus

Reverse each day

Reverse each week


|V| even pion

in beam pipe


KK+ +

KK



No significant

background





-15 -10 -05 0 05 10 u

0

-1

-2

1

2

3

Dalitz plot



EM calorimeter only






2003 result in PLB 634 (2006) 474




2003 result in PLB 638 (2006) 22


excluded


OKA at Protvino





(in preparation)


More CP violation


Indirect

Direct

CP violation

parameters

(2005)


(A) KS decays


CPV in KS decays




000000

000

000 )(

)(

L

S

KA




S+KL

KL




000 000 00

1( )2 ( 2

0

)

( )


tt

NEARf E t



)()()( 00

00

EKNEKN

EKNEKNED

(incoherent

production)



Assuming CPT





N3

20

40

60

00

4 62


No CPV seen yet

























PT() = (-17 23 11) 10-

3

Im = (-53 71 36) 10-3




Im = (-53 71 36) 10-3








ppp

ppp

)0()0(

)0()0(

NN

NNA


Radiative decays








211221 )()(


IB DE

p1 p1

p2p2

q q







)(

)(

S

L

KA

violatingCPKA




KL π+πminus






IB

M1 DE




KL itself





KL ee


BR = (308 020) 10minus7



E1M1 lt 004 (90 CL)



φ




KS ee

No asymmetry for KS

as expected

BR = (471 032) 10-

5

AΦ = (05 43)






IBEE

dEA

)tan( 0


Kplusmn π+π0γ

)730810672()(

)250350353()(

800

800

syststatMeVT

syststatMeVT

INTFrac

DEFrac







KL π+πndashπ0γ















)(

)2030(

3

3

e

ee

K

MeVEKR





bull 6M Ke3 events


ndash R=(0964plusmn0008+0011-0009)












PDG 2004







]21[192 3

52

KmG







Vus measurements





unitarity





KLOE Kl 3

KLOE K2

copy A Antonelli

Vus some more




Ke4 results





K+rarrπ0π0eν










1-loop rescattering

2-loop rescattering











NA482




KLOE interference

















K+ + 8middot10-11 (at 7)147+130

ndash089 middot 10-

10 (BNL E787+E949)






KL 0ℓ+ℓ-




BR(KL 0+-) lt 3810-10





NA481 KS 0ℓ+ℓ-



BR = (58 +28-23 plusmn08) times10-9


-012 (accid)BR = (28 +15


KS 0e+e- KS 0μ+μ-


NA481 preliminary

NA481 preliminary


KL 0ℓ+ℓ-






Krarr in the SM




W W

s

id

Vis Vid

e

i=uct

W

Z

VisV

idds i

11

20

2410

10)1108(

)(1001)(

AKB

11

2

5

100

10)4082(

)()Im(

1022)(

t

tdtsL xX

VVKB


K

ε εrsquo




Ke3 KL 0

Height

Im(λt )



10301890 10471)(

KBR









K+ +




















Appendixes





J(ππ) = ℓ(ππ) = 0 P(ππ) = +1 C(ππ) = +1



ℓL



SLti

SLLSti

LS

tL

tS

Lti

LSti

S

KKeaaKKeaa

eaea

KeaKea

SLLS

LS

LS

)()(

22

f LSf

fLS KfA

dt

d 2

2

TUnitarity requires

and therefore


f Sff

fS

fLSLLS

f

fLLf

fSS

fKAAKKmi

AA

)(2)(

22


2

22

2

222

0604

mKK

AAAA

LS

LSLS

f

fSf

fLf

fS

fL



SLS KKmi 21




)()( 0000

SSS KK












KL K2+ ε K1

ππ






KL K2+ ε K1

ππ


K2 (CP=-1) ππ (CP=+1)






This is named



K0 ππ

K0





Decay phase

(direct)




Isospin I=0

Isospin I=2


(CHARGE) BASIS









221

2

)(

)(

21

)(

)(

00

00

000000

S

Li

S

Li

KA

KAe

KA

KAe

)(

0

0

2

2

0

2

0

0

02

)Re(

)Im(

)Re(

)Im(

)Re(

)Re(

2

)Re(

)Im(

iea

a

a

a

a

ai

a

ai

221

)0(

)2(

IKA

IKA

S

S







Questions













p

Target


particle sweeping

Dump

Neutral beam

Collimator

Production

angle

Protonenergy Beam

acceptance

Collimatorbackgroun

d

KL (+KS) beams



KS by regeneration





KL KL + Ar KS








61)Re(612

2

00

)(

)(

)(

)(00

00

2

2

00

L

S

S

L

K

K

K

K







n


d(PSext) d3x d3ph3




Position scale

Momentum

scale



Direct CPV 1996 AD

FNAL E731






The presshellip







KTeV at Fermilab



NA48 at CERN




600

00

10)820045()()(

)()(

KK

KK




4

World average





rsquo why










K decays


(PDG2004)



For kaons


K2ππ




ΔΓ(K3π)Δg(K3π)












K vs B







200

200

200

200

KeKKeK

KeKKeKA

iHtiHt

iHtiHt

T


20

20

20

20

KefKef

KefKefA

iHtCP

iHtCP

iHtCP

iHtCP

CP

200

200

200

200

KeKKeK

KeKKeKA

iHtiHt

iHtiHt

CPT




CPLEAR experiment

(CERN 1990-96)






tf

ft

f

iHtCP

iHtCP

iHtCP

iHtCP

CPLS

LS

e

mte

KefKef

KefKefA

)(2

2)(

20

20

20

20

1

)cos(2)Re(2

π+π

minus

π0π0

π+π minusπ0

π0π0π0

CPLEARAsymmetrie

s


Rate difference


Measure η





Kaon factories




pppp 2

1SLSL KKKKi




[Lipkin (1968)]

EPR correlation


DAΦNE (Frascati)


DAΦNE (Frascati)


MeVc)









p = 127 MeVcλ = 95 cm

KLKS 106 pb-1




KLOE physics




















p

Target

Collimator



Dump

Tagging Separation

Charged beam




Buthellip



rarr Small in SM


2π (εrsquoε)

3π (Ag)


ν


π0

Kplusmn rarr 3π




π1

π2

π3

K


Kinematics



2


2

Matrix element

|M(uv)|2 ~ 1 + gu + hu2 + kv2







KminusK+








10-6

NA482 OKA

10-5

10-4

10-3

10-2

SMSM

SUSYSUSYNewNew

physicsphysics



|Ag|

bull Ag ~ 10minus5


SUSY New Physics

THEORY



C

N



=Ag



54 60 66

1cm

50 100

10 cm

200 250 m





~11012

ppp

K+

Kminus



always in vacuum

focusing beams

BM

z

magnet

vacuum tank

not to scale

K+

K


pipe

0ordm prodangle






ZZ

XXYY

JuraJura

SaleveSaleve

Beam line K+ Up


B+

Bminus






Spectrometer field

K+

Kminus

Reverse each day

Reverse each week


|V| even pion

in beam pipe


KK+ +

KK



No significant

background





-15 -10 -05 0 05 10 u

0

-1

-2

1

2

3

Dalitz plot



EM calorimeter only






2003 result in PLB 634 (2006) 474




2003 result in PLB 638 (2006) 22


excluded


OKA at Protvino





(in preparation)


More CP violation


Indirect

Direct

CP violation

parameters

(2005)


(A) KS decays


CPV in KS decays




000000

000

000 )(

)(

L

S

KA




S+KL

KL




000 000 00

1( )2 ( 2

0

)

( )


tt

NEARf E t



)()()( 00

00

EKNEKN

EKNEKNED

(incoherent

production)



Assuming CPT





N3

20

40

60

00

4 62


No CPV seen yet

























PT() = (-17 23 11) 10-

3

Im = (-53 71 36) 10-3




Im = (-53 71 36) 10-3








ppp

ppp

)0()0(

)0()0(

NN

NNA


Radiative decays








211221 )()(


IB DE

p1 p1

p2p2

q q







)(

)(

S

L

KA

violatingCPKA




KL π+πminus






IB

M1 DE




KL itself





KL ee


BR = (308 020) 10minus7



E1M1 lt 004 (90 CL)



φ




KS ee

No asymmetry for KS

as expected

BR = (471 032) 10-

5

AΦ = (05 43)






IBEE

dEA

)tan( 0


Kplusmn π+π0γ

)730810672()(

)250350353()(

800

800

syststatMeVT

syststatMeVT

INTFrac

DEFrac







KL π+πndashπ0γ















)(

)2030(

3

3

e

ee

K

MeVEKR





bull 6M Ke3 events


ndash R=(0964plusmn0008+0011-0009)












PDG 2004







]21[192 3

52

KmG







Vus measurements





unitarity





KLOE Kl 3

KLOE K2

copy A Antonelli

Vus some more




Ke4 results





K+rarrπ0π0eν










1-loop rescattering

2-loop rescattering











NA482




KLOE interference

















K+ + 8middot10-11 (at 7)147+130

ndash089 middot 10-

10 (BNL E787+E949)






KL 0ℓ+ℓ-




BR(KL 0+-) lt 3810-10





NA481 KS 0ℓ+ℓ-



BR = (58 +28-23 plusmn08) times10-9


-012 (accid)BR = (28 +15


KS 0e+e- KS 0μ+μ-


NA481 preliminary

NA481 preliminary


KL 0ℓ+ℓ-






Krarr in the SM




W W

s

id

Vis Vid

e

i=uct

W

Z

VisV

idds i

11

20

2410

10)1108(

)(1001)(

AKB

11

2

5

100

10)4082(

)()Im(

1022)(

t

tdtsL xX

VVKB


K

ε εrsquo




Ke3 KL 0

Height

Im(λt )



10301890 10471)(

KBR









K+ +




















Appendixes





J(ππ) = ℓ(ππ) = 0 P(ππ) = +1 C(ππ) = +1



ℓL



SLti

SLLSti

LS

tL

tS

Lti

LSti

S

KKeaaKKeaa

eaea

KeaKea

SLLS

LS

LS

)()(

22

f LSf

fLS KfA

dt

d 2

2

TUnitarity requires

and therefore


f Sff

fS

fLSLLS

f

fLLf

fSS

fKAAKKmi

AA

)(2)(

22


2

22

2

222

0604

mKK

AAAA

LS

LSLS

f

fSf

fLf

fS

fL



SLS KKmi 21




)()( 0000

SSS KK







KL K2+ ε K1

ππ






KL K2+ ε K1

ππ


K2 (CP=-1) ππ (CP=+1)






This is named



K0 ππ

K0





Decay phase

(direct)




Isospin I=0

Isospin I=2


(CHARGE) BASIS









221

2

)(

)(

21

)(

)(

00

00

000000

S

Li

S

Li

KA

KAe

KA

KAe

)(

0

0

2

2

0

2

0

0

02

)Re(

)Im(

)Re(

)Im(

)Re(

)Re(

2

)Re(

)Im(

iea

a

a

a

a

ai

a

ai

221

)0(

)2(

IKA

IKA

S

S







Questions













p

Target


particle sweeping

Dump

Neutral beam

Collimator

Production

angle

Protonenergy Beam

acceptance

Collimatorbackgroun

d

KL (+KS) beams



KS by regeneration





KL KL + Ar KS








61)Re(612

2

00

)(

)(

)(

)(00

00

2

2

00

L

S

S

L

K

K

K

K







n


d(PSext) d3x d3ph3




Position scale

Momentum

scale



Direct CPV 1996 AD

FNAL E731






The presshellip







KTeV at Fermilab



NA48 at CERN




600

00

10)820045()()(

)()(

KK

KK




4

World average





rsquo why










K decays


(PDG2004)



For kaons


K2ππ




ΔΓ(K3π)Δg(K3π)












K vs B







200

200

200

200

KeKKeK

KeKKeKA

iHtiHt

iHtiHt

T


20

20

20

20

KefKef

KefKefA

iHtCP

iHtCP

iHtCP

iHtCP

CP

200

200

200

200

KeKKeK

KeKKeKA

iHtiHt

iHtiHt

CPT




CPLEAR experiment

(CERN 1990-96)






tf

ft

f

iHtCP

iHtCP

iHtCP

iHtCP

CPLS

LS

e

mte

KefKef

KefKefA

)(2

2)(

20

20

20

20

1

)cos(2)Re(2

π+π

minus

π0π0

π+π minusπ0

π0π0π0

CPLEARAsymmetrie

s


Rate difference


Measure η





Kaon factories




pppp 2

1SLSL KKKKi




[Lipkin (1968)]

EPR correlation


DAΦNE (Frascati)


DAΦNE (Frascati)


MeVc)









p = 127 MeVcλ = 95 cm

KLKS 106 pb-1




KLOE physics




















p

Target

Collimator



Dump

Tagging Separation

Charged beam




Buthellip



rarr Small in SM


2π (εrsquoε)

3π (Ag)


ν


π0

Kplusmn rarr 3π




π1

π2

π3

K


Kinematics



2


2

Matrix element

|M(uv)|2 ~ 1 + gu + hu2 + kv2







KminusK+








10-6

NA482 OKA

10-5

10-4

10-3

10-2

SMSM

SUSYSUSYNewNew

physicsphysics



|Ag|

bull Ag ~ 10minus5


SUSY New Physics

THEORY



C

N



=Ag



54 60 66

1cm

50 100

10 cm

200 250 m





~11012

ppp

K+

Kminus



always in vacuum

focusing beams

BM

z

magnet

vacuum tank

not to scale

K+

K


pipe

0ordm prodangle






ZZ

XXYY

JuraJura

SaleveSaleve

Beam line K+ Up


B+

Bminus






Spectrometer field

K+

Kminus

Reverse each day

Reverse each week


|V| even pion

in beam pipe


KK+ +

KK



No significant

background





-15 -10 -05 0 05 10 u

0

-1

-2

1

2

3

Dalitz plot



EM calorimeter only






2003 result in PLB 634 (2006) 474




2003 result in PLB 638 (2006) 22


excluded


OKA at Protvino





(in preparation)


More CP violation


Indirect

Direct

CP violation

parameters

(2005)


(A) KS decays


CPV in KS decays




000000

000

000 )(

)(

L

S

KA




S+KL

KL




000 000 00

1( )2 ( 2

0

)

( )


tt

NEARf E t



)()()( 00

00

EKNEKN

EKNEKNED

(incoherent

production)



Assuming CPT





N3

20

40

60

00

4 62


No CPV seen yet

























PT() = (-17 23 11) 10-

3

Im = (-53 71 36) 10-3




Im = (-53 71 36) 10-3








ppp

ppp

)0()0(

)0()0(

NN

NNA


Radiative decays








211221 )()(


IB DE

p1 p1

p2p2

q q







)(

)(

S

L

KA

violatingCPKA




KL π+πminus






IB

M1 DE




KL itself





KL ee


BR = (308 020) 10minus7



E1M1 lt 004 (90 CL)



φ




KS ee

No asymmetry for KS

as expected

BR = (471 032) 10-

5

AΦ = (05 43)






IBEE

dEA

)tan( 0


Kplusmn π+π0γ

)730810672()(

)250350353()(

800

800

syststatMeVT

syststatMeVT

INTFrac

DEFrac







KL π+πndashπ0γ















)(

)2030(

3

3

e

ee

K

MeVEKR





bull 6M Ke3 events


ndash R=(0964plusmn0008+0011-0009)












PDG 2004







]21[192 3

52

KmG







Vus measurements





unitarity





KLOE Kl 3

KLOE K2

copy A Antonelli

Vus some more




Ke4 results





K+rarrπ0π0eν










1-loop rescattering

2-loop rescattering











NA482




KLOE interference

















K+ + 8middot10-11 (at 7)147+130

ndash089 middot 10-

10 (BNL E787+E949)






KL 0ℓ+ℓ-




BR(KL 0+-) lt 3810-10





NA481 KS 0ℓ+ℓ-



BR = (58 +28-23 plusmn08) times10-9


-012 (accid)BR = (28 +15


KS 0e+e- KS 0μ+μ-


NA481 preliminary

NA481 preliminary


KL 0ℓ+ℓ-






Krarr in the SM




W W

s

id

Vis Vid

e

i=uct

W

Z

VisV

idds i

11

20

2410

10)1108(

)(1001)(

AKB

11

2

5

100

10)4082(

)()Im(

1022)(

t

tdtsL xX

VVKB


K

ε εrsquo




Ke3 KL 0

Height

Im(λt )



10301890 10471)(

KBR









K+ +




















Appendixes





J(ππ) = ℓ(ππ) = 0 P(ππ) = +1 C(ππ) = +1



ℓL



SLti

SLLSti

LS

tL

tS

Lti

LSti

S

KKeaaKKeaa

eaea

KeaKea

SLLS

LS

LS

)()(

22

f LSf

fLS KfA

dt

d 2

2

TUnitarity requires

and therefore


f Sff

fS

fLSLLS

f

fLLf

fSS

fKAAKKmi

AA

)(2)(

22


2

22

2

222

0604

mKK

AAAA

LS

LSLS

f

fSf

fLf

fS

fL



SLS KKmi 21




)()( 0000

SSS KK






KL K2+ ε K1

ππ


K2 (CP=-1) ππ (CP=+1)






This is named



K0 ππ

K0





Decay phase

(direct)




Isospin I=0

Isospin I=2


(CHARGE) BASIS









221

2

)(

)(

21

)(

)(

00

00

000000

S

Li

S

Li

KA

KAe

KA

KAe

)(

0

0

2

2

0

2

0

0

02

)Re(

)Im(

)Re(

)Im(

)Re(

)Re(

2

)Re(

)Im(

iea

a

a

a

a

ai

a

ai

221

)0(

)2(

IKA

IKA

S

S







Questions













p

Target


particle sweeping

Dump

Neutral beam

Collimator

Production

angle

Protonenergy Beam

acceptance

Collimatorbackgroun

d

KL (+KS) beams



KS by regeneration





KL KL + Ar KS








61)Re(612

2

00

)(

)(

)(

)(00

00

2

2

00

L

S

S

L

K

K

K

K







n


d(PSext) d3x d3ph3




Position scale

Momentum

scale



Direct CPV 1996 AD

FNAL E731






The presshellip







KTeV at Fermilab



NA48 at CERN




600

00

10)820045()()(

)()(

KK

KK




4

World average





rsquo why










K decays


(PDG2004)



For kaons


K2ππ




ΔΓ(K3π)Δg(K3π)












K vs B







200

200

200

200

KeKKeK

KeKKeKA

iHtiHt

iHtiHt

T


20

20

20

20

KefKef

KefKefA

iHtCP

iHtCP

iHtCP

iHtCP

CP

200

200

200

200

KeKKeK

KeKKeKA

iHtiHt

iHtiHt

CPT




CPLEAR experiment

(CERN 1990-96)






tf

ft

f

iHtCP

iHtCP

iHtCP

iHtCP

CPLS

LS

e

mte

KefKef

KefKefA

)(2

2)(

20

20

20

20

1

)cos(2)Re(2

π+π

minus

π0π0

π+π minusπ0

π0π0π0

CPLEARAsymmetrie

s


Rate difference


Measure η





Kaon factories




pppp 2

1SLSL KKKKi




[Lipkin (1968)]

EPR correlation


DAΦNE (Frascati)


DAΦNE (Frascati)


MeVc)









p = 127 MeVcλ = 95 cm

KLKS 106 pb-1




KLOE physics




















p

Target

Collimator



Dump

Tagging Separation

Charged beam




Buthellip



rarr Small in SM


2π (εrsquoε)

3π (Ag)


ν


π0

Kplusmn rarr 3π




π1

π2

π3

K


Kinematics



2


2

Matrix element

|M(uv)|2 ~ 1 + gu + hu2 + kv2







KminusK+








10-6

NA482 OKA

10-5

10-4

10-3

10-2

SMSM

SUSYSUSYNewNew

physicsphysics



|Ag|

bull Ag ~ 10minus5


SUSY New Physics

THEORY



C

N



=Ag



54 60 66

1cm

50 100

10 cm

200 250 m





~11012

ppp

K+

Kminus



always in vacuum

focusing beams

BM

z

magnet

vacuum tank

not to scale

K+

K


pipe

0ordm prodangle






ZZ

XXYY

JuraJura

SaleveSaleve

Beam line K+ Up


B+

Bminus






Spectrometer field

K+

Kminus

Reverse each day

Reverse each week


|V| even pion

in beam pipe


KK+ +

KK



No significant

background





-15 -10 -05 0 05 10 u

0

-1

-2

1

2

3

Dalitz plot



EM calorimeter only






2003 result in PLB 634 (2006) 474




2003 result in PLB 638 (2006) 22


excluded


OKA at Protvino





(in preparation)


More CP violation


Indirect

Direct

CP violation

parameters

(2005)


(A) KS decays


CPV in KS decays




000000

000

000 )(

)(

L

S

KA




S+KL

KL




000 000 00

1( )2 ( 2

0

)

( )


tt

NEARf E t



)()()( 00

00

EKNEKN

EKNEKNED

(incoherent

production)



Assuming CPT





N3

20

40

60

00

4 62


No CPV seen yet

























PT() = (-17 23 11) 10-

3

Im = (-53 71 36) 10-3




Im = (-53 71 36) 10-3








ppp

ppp

)0()0(

)0()0(

NN

NNA


Radiative decays








211221 )()(


IB DE

p1 p1

p2p2

q q







)(

)(

S

L

KA

violatingCPKA




KL π+πminus






IB

M1 DE




KL itself





KL ee


BR = (308 020) 10minus7



E1M1 lt 004 (90 CL)



φ




KS ee

No asymmetry for KS

as expected

BR = (471 032) 10-

5

AΦ = (05 43)






IBEE

dEA

)tan( 0


Kplusmn π+π0γ

)730810672()(

)250350353()(

800

800

syststatMeVT

syststatMeVT

INTFrac

DEFrac







KL π+πndashπ0γ















)(

)2030(

3

3

e

ee

K

MeVEKR





bull 6M Ke3 events


ndash R=(0964plusmn0008+0011-0009)












PDG 2004







]21[192 3

52

KmG







Vus measurements





unitarity





KLOE Kl 3

KLOE K2

copy A Antonelli

Vus some more




Ke4 results





K+rarrπ0π0eν










1-loop rescattering

2-loop rescattering











NA482




KLOE interference

















K+ + 8middot10-11 (at 7)147+130

ndash089 middot 10-

10 (BNL E787+E949)






KL 0ℓ+ℓ-




BR(KL 0+-) lt 3810-10





NA481 KS 0ℓ+ℓ-



BR = (58 +28-23 plusmn08) times10-9


-012 (accid)BR = (28 +15


KS 0e+e- KS 0μ+μ-


NA481 preliminary

NA481 preliminary


KL 0ℓ+ℓ-






Krarr in the SM




W W

s

id

Vis Vid

e

i=uct

W

Z

VisV

idds i

11

20

2410

10)1108(

)(1001)(

AKB

11

2

5

100

10)4082(

)()Im(

1022)(

t

tdtsL xX

VVKB


K

ε εrsquo




Ke3 KL 0

Height

Im(λt )



10301890 10471)(

KBR









K+ +




















Appendixes





J(ππ) = ℓ(ππ) = 0 P(ππ) = +1 C(ππ) = +1



ℓL



SLti

SLLSti

LS

tL

tS

Lti

LSti

S

KKeaaKKeaa

eaea

KeaKea

SLLS

LS

LS

)()(

22

f LSf

fLS KfA

dt

d 2

2

TUnitarity requires

and therefore


f Sff

fS

fLSLLS

f

fLLf

fSS

fKAAKKmi

AA

)(2)(

22


2

22

2

222

0604

mKK

AAAA

LS

LSLS

f

fSf

fLf

fS

fL



SLS KKmi 21




)()( 0000

SSS KK



This is named



K0 ππ

K0





Decay phase

(direct)




Isospin I=0

Isospin I=2


(CHARGE) BASIS









221

2

)(

)(

21

)(

)(

00

00

000000

S

Li

S

Li

KA

KAe

KA

KAe

)(

0

0

2

2

0

2

0

0

02

)Re(

)Im(

)Re(

)Im(

)Re(

)Re(

2

)Re(

)Im(

iea

a

a

a

a

ai

a

ai

221

)0(

)2(

IKA

IKA

S

S







Questions













p

Target


particle sweeping

Dump

Neutral beam

Collimator

Production

angle

Protonenergy Beam

acceptance

Collimatorbackgroun

d

KL (+KS) beams



KS by regeneration





KL KL + Ar KS








61)Re(612

2

00

)(

)(

)(

)(00

00

2

2

00

L

S

S

L

K

K

K

K







n


d(PSext) d3x d3ph3




Position scale

Momentum

scale



Direct CPV 1996 AD

FNAL E731






The presshellip







KTeV at Fermilab



NA48 at CERN




600

00

10)820045()()(

)()(

KK

KK




4

World average





rsquo why










K decays


(PDG2004)



For kaons


K2ππ




ΔΓ(K3π)Δg(K3π)












K vs B







200

200

200

200

KeKKeK

KeKKeKA

iHtiHt

iHtiHt

T


20

20

20

20

KefKef

KefKefA

iHtCP

iHtCP

iHtCP

iHtCP

CP

200

200

200

200

KeKKeK

KeKKeKA

iHtiHt

iHtiHt

CPT




CPLEAR experiment

(CERN 1990-96)






tf

ft

f

iHtCP

iHtCP

iHtCP

iHtCP

CPLS

LS

e

mte

KefKef

KefKefA

)(2

2)(

20

20

20

20

1

)cos(2)Re(2

π+π

minus

π0π0

π+π minusπ0

π0π0π0

CPLEARAsymmetrie

s


Rate difference


Measure η





Kaon factories




pppp 2

1SLSL KKKKi




[Lipkin (1968)]

EPR correlation


DAΦNE (Frascati)


DAΦNE (Frascati)


MeVc)









p = 127 MeVcλ = 95 cm

KLKS 106 pb-1




KLOE physics




















p

Target

Collimator



Dump

Tagging Separation

Charged beam




Buthellip



rarr Small in SM


2π (εrsquoε)

3π (Ag)


ν


π0

Kplusmn rarr 3π




π1

π2

π3

K


Kinematics



2


2

Matrix element

|M(uv)|2 ~ 1 + gu + hu2 + kv2







KminusK+








10-6

NA482 OKA

10-5

10-4

10-3

10-2

SMSM

SUSYSUSYNewNew

physicsphysics



|Ag|

bull Ag ~ 10minus5


SUSY New Physics

THEORY



C

N



=Ag



54 60 66

1cm

50 100

10 cm

200 250 m





~11012

ppp

K+

Kminus



always in vacuum

focusing beams

BM

z

magnet

vacuum tank

not to scale

K+

K


pipe

0ordm prodangle






ZZ

XXYY

JuraJura

SaleveSaleve

Beam line K+ Up


B+

Bminus






Spectrometer field

K+

Kminus

Reverse each day

Reverse each week


|V| even pion

in beam pipe


KK+ +

KK



No significant

background





-15 -10 -05 0 05 10 u

0

-1

-2

1

2

3

Dalitz plot



EM calorimeter only






2003 result in PLB 634 (2006) 474




2003 result in PLB 638 (2006) 22


excluded


OKA at Protvino





(in preparation)


More CP violation


Indirect

Direct

CP violation

parameters

(2005)


(A) KS decays


CPV in KS decays




000000

000

000 )(

)(

L

S

KA




S+KL

KL




000 000 00

1( )2 ( 2

0

)

( )


tt

NEARf E t



)()()( 00

00

EKNEKN

EKNEKNED

(incoherent

production)



Assuming CPT





N3

20

40

60

00

4 62


No CPV seen yet

























PT() = (-17 23 11) 10-

3

Im = (-53 71 36) 10-3




Im = (-53 71 36) 10-3








ppp

ppp

)0()0(

)0()0(

NN

NNA


Radiative decays








211221 )()(


IB DE

p1 p1

p2p2

q q







)(

)(

S

L

KA

violatingCPKA




KL π+πminus






IB

M1 DE




KL itself





KL ee


BR = (308 020) 10minus7



E1M1 lt 004 (90 CL)



φ




KS ee

No asymmetry for KS

as expected

BR = (471 032) 10-

5

AΦ = (05 43)






IBEE

dEA

)tan( 0


Kplusmn π+π0γ

)730810672()(

)250350353()(

800

800

syststatMeVT

syststatMeVT

INTFrac

DEFrac







KL π+πndashπ0γ















)(

)2030(

3

3

e

ee

K

MeVEKR





bull 6M Ke3 events


ndash R=(0964plusmn0008+0011-0009)












PDG 2004







]21[192 3

52

KmG







Vus measurements





unitarity





KLOE Kl 3

KLOE K2

copy A Antonelli

Vus some more




Ke4 results





K+rarrπ0π0eν










1-loop rescattering

2-loop rescattering











NA482




KLOE interference

















K+ + 8middot10-11 (at 7)147+130

ndash089 middot 10-

10 (BNL E787+E949)






KL 0ℓ+ℓ-




BR(KL 0+-) lt 3810-10





NA481 KS 0ℓ+ℓ-



BR = (58 +28-23 plusmn08) times10-9


-012 (accid)BR = (28 +15


KS 0e+e- KS 0μ+μ-


NA481 preliminary

NA481 preliminary


KL 0ℓ+ℓ-






Krarr in the SM




W W

s

id

Vis Vid

e

i=uct

W

Z

VisV

idds i

11

20

2410

10)1108(

)(1001)(

AKB

11

2

5

100

10)4082(

)()Im(

1022)(

t

tdtsL xX

VVKB


K

ε εrsquo




Ke3 KL 0

Height

Im(λt )



10301890 10471)(

KBR









K+ +




















Appendixes





J(ππ) = ℓ(ππ) = 0 P(ππ) = +1 C(ππ) = +1



ℓL



SLti

SLLSti

LS

tL

tS

Lti

LSti

S

KKeaaKKeaa

eaea

KeaKea

SLLS

LS

LS

)()(

22

f LSf

fLS KfA

dt

d 2

2

TUnitarity requires

and therefore


f Sff

fS

fLSLLS

f

fLLf

fSS

fKAAKKmi

AA

)(2)(

22


2

22

2

222

0604

mKK

AAAA

LS

LSLS

f

fSf

fLf

fS

fL



SLS KKmi 21




)()( 0000

SSS KK





Isospin I=0

Isospin I=2


(CHARGE) BASIS









221

2

)(

)(

21

)(

)(

00

00

000000

S

Li

S

Li

KA

KAe

KA

KAe

)(

0

0

2

2

0

2

0

0

02

)Re(

)Im(

)Re(

)Im(

)Re(

)Re(

2

)Re(

)Im(

iea

a

a

a

a

ai

a

ai

221

)0(

)2(

IKA

IKA

S

S







Questions













p

Target


particle sweeping

Dump

Neutral beam

Collimator

Production

angle

Protonenergy Beam

acceptance

Collimatorbackgroun

d

KL (+KS) beams



KS by regeneration





KL KL + Ar KS








61)Re(612

2

00

)(

)(

)(

)(00

00

2

2

00

L

S

S

L

K

K

K

K







n


d(PSext) d3x d3ph3




Position scale

Momentum

scale



Direct CPV 1996 AD

FNAL E731






The presshellip







KTeV at Fermilab



NA48 at CERN




600

00

10)820045()()(

)()(

KK

KK




4

World average





rsquo why










K decays


(PDG2004)



For kaons


K2ππ




ΔΓ(K3π)Δg(K3π)












K vs B







200

200

200

200

KeKKeK

KeKKeKA

iHtiHt

iHtiHt

T


20

20

20

20

KefKef

KefKefA

iHtCP

iHtCP

iHtCP

iHtCP

CP

200

200

200

200

KeKKeK

KeKKeKA

iHtiHt

iHtiHt

CPT




CPLEAR experiment

(CERN 1990-96)






tf

ft

f

iHtCP

iHtCP

iHtCP

iHtCP

CPLS

LS

e

mte

KefKef

KefKefA

)(2

2)(

20

20

20

20

1

)cos(2)Re(2

π+π

minus

π0π0

π+π minusπ0

π0π0π0

CPLEARAsymmetrie

s


Rate difference


Measure η





Kaon factories




pppp 2

1SLSL KKKKi




[Lipkin (1968)]

EPR correlation


DAΦNE (Frascati)


DAΦNE (Frascati)


MeVc)









p = 127 MeVcλ = 95 cm

KLKS 106 pb-1




KLOE physics




















p

Target

Collimator



Dump

Tagging Separation

Charged beam




Buthellip



rarr Small in SM


2π (εrsquoε)

3π (Ag)


ν


π0

Kplusmn rarr 3π




π1

π2

π3

K


Kinematics



2


2

Matrix element

|M(uv)|2 ~ 1 + gu + hu2 + kv2







KminusK+








10-6

NA482 OKA

10-5

10-4

10-3

10-2

SMSM

SUSYSUSYNewNew

physicsphysics



|Ag|

bull Ag ~ 10minus5


SUSY New Physics

THEORY



C

N



=Ag



54 60 66

1cm

50 100

10 cm

200 250 m





~11012

ppp

K+

Kminus



always in vacuum

focusing beams

BM

z

magnet

vacuum tank

not to scale

K+

K


pipe

0ordm prodangle






ZZ

XXYY

JuraJura

SaleveSaleve

Beam line K+ Up


B+

Bminus






Spectrometer field

K+

Kminus

Reverse each day

Reverse each week


|V| even pion

in beam pipe


KK+ +

KK



No significant

background





-15 -10 -05 0 05 10 u

0

-1

-2

1

2

3

Dalitz plot



EM calorimeter only






2003 result in PLB 634 (2006) 474




2003 result in PLB 638 (2006) 22


excluded


OKA at Protvino





(in preparation)


More CP violation


Indirect

Direct

CP violation

parameters

(2005)


(A) KS decays


CPV in KS decays




000000

000

000 )(

)(

L

S

KA




S+KL

KL




000 000 00

1( )2 ( 2

0

)

( )


tt

NEARf E t



)()()( 00

00

EKNEKN

EKNEKNED

(incoherent

production)



Assuming CPT





N3

20

40

60

00

4 62


No CPV seen yet

























PT() = (-17 23 11) 10-

3

Im = (-53 71 36) 10-3




Im = (-53 71 36) 10-3








ppp

ppp

)0()0(

)0()0(

NN

NNA


Radiative decays








211221 )()(


IB DE

p1 p1

p2p2

q q







)(

)(

S

L

KA

violatingCPKA




KL π+πminus






IB

M1 DE




KL itself





KL ee


BR = (308 020) 10minus7



E1M1 lt 004 (90 CL)



φ




KS ee

No asymmetry for KS

as expected

BR = (471 032) 10-

5

AΦ = (05 43)






IBEE

dEA

)tan( 0


Kplusmn π+π0γ

)730810672()(

)250350353()(

800

800

syststatMeVT

syststatMeVT

INTFrac

DEFrac







KL π+πndashπ0γ















)(

)2030(

3

3

e

ee

K

MeVEKR





bull 6M Ke3 events


ndash R=(0964plusmn0008+0011-0009)












PDG 2004







]21[192 3

52

KmG







Vus measurements





unitarity





KLOE Kl 3

KLOE K2

copy A Antonelli

Vus some more




Ke4 results





K+rarrπ0π0eν










1-loop rescattering

2-loop rescattering











NA482




KLOE interference

















K+ + 8middot10-11 (at 7)147+130

ndash089 middot 10-

10 (BNL E787+E949)






KL 0ℓ+ℓ-




BR(KL 0+-) lt 3810-10





NA481 KS 0ℓ+ℓ-



BR = (58 +28-23 plusmn08) times10-9


-012 (accid)BR = (28 +15


KS 0e+e- KS 0μ+μ-


NA481 preliminary

NA481 preliminary


KL 0ℓ+ℓ-






Krarr in the SM




W W

s

id

Vis Vid

e

i=uct

W

Z

VisV

idds i

11

20

2410

10)1108(

)(1001)(

AKB

11

2

5

100

10)4082(

)()Im(

1022)(

t

tdtsL xX

VVKB


K

ε εrsquo




Ke3 KL 0

Height

Im(λt )



10301890 10471)(

KBR









K+ +




















Appendixes





J(ππ) = ℓ(ππ) = 0 P(ππ) = +1 C(ππ) = +1



ℓL



SLti

SLLSti

LS

tL

tS

Lti

LSti

S

KKeaaKKeaa

eaea

KeaKea

SLLS

LS

LS

)()(

22

f LSf

fLS KfA

dt

d 2

2

TUnitarity requires

and therefore


f Sff

fS

fLSLLS

f

fLLf

fSS

fKAAKKmi

AA

)(2)(

22


2

22

2

222

0604

mKK

AAAA

LS

LSLS

f

fSf

fLf

fS

fL



SLS KKmi 21




)()( 0000

SSS KK




221

2

)(

)(

21

)(

)(

00

00

000000

S

Li

S

Li

KA

KAe

KA

KAe

)(

0

0

2

2

0

2

0

0

02

)Re(

)Im(

)Re(

)Im(

)Re(

)Re(

2

)Re(

)Im(

iea

a

a

a

a

ai

a

ai

221

)0(

)2(

IKA

IKA

S

S







Questions













p

Target


particle sweeping

Dump

Neutral beam

Collimator

Production

angle

Protonenergy Beam

acceptance

Collimatorbackgroun

d

KL (+KS) beams



KS by regeneration





KL KL + Ar KS








61)Re(612

2

00

)(

)(

)(

)(00

00

2

2

00

L

S

S

L

K

K

K

K







n


d(PSext) d3x d3ph3




Position scale

Momentum

scale



Direct CPV 1996 AD

FNAL E731






The presshellip







KTeV at Fermilab



NA48 at CERN




600

00

10)820045()()(

)()(

KK

KK




4

World average





rsquo why










K decays


(PDG2004)



For kaons


K2ππ




ΔΓ(K3π)Δg(K3π)












K vs B







200

200

200

200

KeKKeK

KeKKeKA

iHtiHt

iHtiHt

T


20

20

20

20

KefKef

KefKefA

iHtCP

iHtCP

iHtCP

iHtCP

CP

200

200

200

200

KeKKeK

KeKKeKA

iHtiHt

iHtiHt

CPT




CPLEAR experiment

(CERN 1990-96)






tf

ft

f

iHtCP

iHtCP

iHtCP

iHtCP

CPLS

LS

e

mte

KefKef

KefKefA

)(2

2)(

20

20

20

20

1

)cos(2)Re(2

π+π

minus

π0π0

π+π minusπ0

π0π0π0

CPLEARAsymmetrie

s


Rate difference


Measure η





Kaon factories




pppp 2

1SLSL KKKKi




[Lipkin (1968)]

EPR correlation


DAΦNE (Frascati)


DAΦNE (Frascati)


MeVc)









p = 127 MeVcλ = 95 cm

KLKS 106 pb-1




KLOE physics




















p

Target

Collimator



Dump

Tagging Separation

Charged beam




Buthellip



rarr Small in SM


2π (εrsquoε)

3π (Ag)


ν


π0

Kplusmn rarr 3π




π1

π2

π3

K


Kinematics



2


2

Matrix element

|M(uv)|2 ~ 1 + gu + hu2 + kv2







KminusK+








10-6

NA482 OKA

10-5

10-4

10-3

10-2

SMSM

SUSYSUSYNewNew

physicsphysics



|Ag|

bull Ag ~ 10minus5


SUSY New Physics

THEORY



C

N



=Ag



54 60 66

1cm

50 100

10 cm

200 250 m





~11012

ppp

K+

Kminus



always in vacuum

focusing beams

BM

z

magnet

vacuum tank

not to scale

K+

K


pipe

0ordm prodangle






ZZ

XXYY

JuraJura

SaleveSaleve

Beam line K+ Up


B+

Bminus






Spectrometer field

K+

Kminus

Reverse each day

Reverse each week


|V| even pion

in beam pipe


KK+ +

KK



No significant

background





-15 -10 -05 0 05 10 u

0

-1

-2

1

2

3

Dalitz plot



EM calorimeter only






2003 result in PLB 634 (2006) 474




2003 result in PLB 638 (2006) 22


excluded


OKA at Protvino





(in preparation)


More CP violation


Indirect

Direct

CP violation

parameters

(2005)


(A) KS decays


CPV in KS decays




000000

000

000 )(

)(

L

S

KA




S+KL

KL




000 000 00

1( )2 ( 2

0

)

( )


tt

NEARf E t



)()()( 00

00

EKNEKN

EKNEKNED

(incoherent

production)



Assuming CPT





N3

20

40

60

00

4 62


No CPV seen yet

























PT() = (-17 23 11) 10-

3

Im = (-53 71 36) 10-3




Im = (-53 71 36) 10-3








ppp

ppp

)0()0(

)0()0(

NN

NNA


Radiative decays








211221 )()(


IB DE

p1 p1

p2p2

q q







)(

)(

S

L

KA

violatingCPKA




KL π+πminus






IB

M1 DE




KL itself





KL ee


BR = (308 020) 10minus7



E1M1 lt 004 (90 CL)



φ




KS ee

No asymmetry for KS

as expected

BR = (471 032) 10-

5

AΦ = (05 43)






IBEE

dEA

)tan( 0


Kplusmn π+π0γ

)730810672()(

)250350353()(

800

800

syststatMeVT

syststatMeVT

INTFrac

DEFrac







KL π+πndashπ0γ















)(

)2030(

3

3

e

ee

K

MeVEKR





bull 6M Ke3 events


ndash R=(0964plusmn0008+0011-0009)












PDG 2004







]21[192 3

52

KmG







Vus measurements





unitarity





KLOE Kl 3

KLOE K2

copy A Antonelli

Vus some more




Ke4 results





K+rarrπ0π0eν










1-loop rescattering

2-loop rescattering











NA482




KLOE interference

















K+ + 8middot10-11 (at 7)147+130

ndash089 middot 10-

10 (BNL E787+E949)






KL 0ℓ+ℓ-




BR(KL 0+-) lt 3810-10





NA481 KS 0ℓ+ℓ-



BR = (58 +28-23 plusmn08) times10-9


-012 (accid)BR = (28 +15


KS 0e+e- KS 0μ+μ-


NA481 preliminary

NA481 preliminary


KL 0ℓ+ℓ-






Krarr in the SM




W W

s

id

Vis Vid

e

i=uct

W

Z

VisV

idds i

11

20

2410

10)1108(

)(1001)(

AKB

11

2

5

100

10)4082(

)()Im(

1022)(

t

tdtsL xX

VVKB


K

ε εrsquo




Ke3 KL 0

Height

Im(λt )



10301890 10471)(

KBR









K+ +




















Appendixes





J(ππ) = ℓ(ππ) = 0 P(ππ) = +1 C(ππ) = +1



ℓL



SLti

SLLSti

LS

tL

tS

Lti

LSti

S

KKeaaKKeaa

eaea

KeaKea

SLLS

LS

LS

)()(

22

f LSf

fLS KfA

dt

d 2

2

TUnitarity requires

and therefore


f Sff

fS

fLSLLS

f

fLLf

fSS

fKAAKKmi

AA

)(2)(

22


2

22

2

222

0604

mKK

AAAA

LS

LSLS

f

fSf

fLf

fS

fL



SLS KKmi 21




)()( 0000

SSS KK






Questions













p

Target


particle sweeping

Dump

Neutral beam

Collimator

Production

angle

Protonenergy Beam

acceptance

Collimatorbackgroun

d

KL (+KS) beams



KS by regeneration





KL KL + Ar KS








61)Re(612

2

00

)(

)(

)(

)(00

00

2

2

00

L

S

S

L

K

K

K

K







n


d(PSext) d3x d3ph3




Position scale

Momentum

scale



Direct CPV 1996 AD

FNAL E731






The presshellip







KTeV at Fermilab



NA48 at CERN




600

00

10)820045()()(

)()(

KK

KK




4

World average





rsquo why










K decays


(PDG2004)



For kaons


K2ππ




ΔΓ(K3π)Δg(K3π)












K vs B







200

200

200

200

KeKKeK

KeKKeKA

iHtiHt

iHtiHt

T


20

20

20

20

KefKef

KefKefA

iHtCP

iHtCP

iHtCP

iHtCP

CP

200

200

200

200

KeKKeK

KeKKeKA

iHtiHt

iHtiHt

CPT




CPLEAR experiment

(CERN 1990-96)






tf

ft

f

iHtCP

iHtCP

iHtCP

iHtCP

CPLS

LS

e

mte

KefKef

KefKefA

)(2

2)(

20

20

20

20

1

)cos(2)Re(2

π+π

minus

π0π0

π+π minusπ0

π0π0π0

CPLEARAsymmetrie

s


Rate difference


Measure η





Kaon factories




pppp 2

1SLSL KKKKi




[Lipkin (1968)]

EPR correlation


DAΦNE (Frascati)


DAΦNE (Frascati)


MeVc)









p = 127 MeVcλ = 95 cm

KLKS 106 pb-1




KLOE physics




















p

Target

Collimator



Dump

Tagging Separation

Charged beam




Buthellip



rarr Small in SM


2π (εrsquoε)

3π (Ag)


ν


π0

Kplusmn rarr 3π




π1

π2

π3

K


Kinematics



2


2

Matrix element

|M(uv)|2 ~ 1 + gu + hu2 + kv2







KminusK+








10-6

NA482 OKA

10-5

10-4

10-3

10-2

SMSM

SUSYSUSYNewNew

physicsphysics



|Ag|

bull Ag ~ 10minus5


SUSY New Physics

THEORY



C

N



=Ag



54 60 66

1cm

50 100

10 cm

200 250 m





~11012

ppp

K+

Kminus



always in vacuum

focusing beams

BM

z

magnet

vacuum tank

not to scale

K+

K


pipe

0ordm prodangle






ZZ

XXYY

JuraJura

SaleveSaleve

Beam line K+ Up


B+

Bminus






Spectrometer field

K+

Kminus

Reverse each day

Reverse each week


|V| even pion

in beam pipe


KK+ +

KK



No significant

background





-15 -10 -05 0 05 10 u

0

-1

-2

1

2

3

Dalitz plot



EM calorimeter only






2003 result in PLB 634 (2006) 474




2003 result in PLB 638 (2006) 22


excluded


OKA at Protvino





(in preparation)


More CP violation


Indirect

Direct

CP violation

parameters

(2005)


(A) KS decays


CPV in KS decays




000000

000

000 )(

)(

L

S

KA




S+KL

KL




000 000 00

1( )2 ( 2

0

)

( )


tt

NEARf E t



)()()( 00

00

EKNEKN

EKNEKNED

(incoherent

production)



Assuming CPT





N3

20

40

60

00

4 62


No CPV seen yet

























PT() = (-17 23 11) 10-

3

Im = (-53 71 36) 10-3




Im = (-53 71 36) 10-3








ppp

ppp

)0()0(

)0()0(

NN

NNA


Radiative decays








211221 )()(


IB DE

p1 p1

p2p2

q q







)(

)(

S

L

KA

violatingCPKA




KL π+πminus






IB

M1 DE




KL itself





KL ee


BR = (308 020) 10minus7



E1M1 lt 004 (90 CL)



φ




KS ee

No asymmetry for KS

as expected

BR = (471 032) 10-

5

AΦ = (05 43)






IBEE

dEA

)tan( 0


Kplusmn π+π0γ

)730810672()(

)250350353()(

800

800

syststatMeVT

syststatMeVT

INTFrac

DEFrac







KL π+πndashπ0γ















)(

)2030(

3

3

e

ee

K

MeVEKR





bull 6M Ke3 events


ndash R=(0964plusmn0008+0011-0009)












PDG 2004







]21[192 3

52

KmG







Vus measurements





unitarity





KLOE Kl 3

KLOE K2

copy A Antonelli

Vus some more




Ke4 results





K+rarrπ0π0eν










1-loop rescattering

2-loop rescattering











NA482




KLOE interference

















K+ + 8middot10-11 (at 7)147+130

ndash089 middot 10-

10 (BNL E787+E949)






KL 0ℓ+ℓ-




BR(KL 0+-) lt 3810-10





NA481 KS 0ℓ+ℓ-



BR = (58 +28-23 plusmn08) times10-9


-012 (accid)BR = (28 +15


KS 0e+e- KS 0μ+μ-


NA481 preliminary

NA481 preliminary


KL 0ℓ+ℓ-






Krarr in the SM




W W

s

id

Vis Vid

e

i=uct

W

Z

VisV

idds i

11

20

2410

10)1108(

)(1001)(

AKB

11

2

5

100

10)4082(

)()Im(

1022)(

t

tdtsL xX

VVKB


K

ε εrsquo




Ke3 KL 0

Height

Im(λt )



10301890 10471)(

KBR









K+ +




















Appendixes





J(ππ) = ℓ(ππ) = 0 P(ππ) = +1 C(ππ) = +1



ℓL



SLti

SLLSti

LS

tL

tS

Lti

LSti

S

KKeaaKKeaa

eaea

KeaKea

SLLS

LS

LS

)()(

22

f LSf

fLS KfA

dt

d 2

2

TUnitarity requires

and therefore


f Sff

fS

fLSLLS

f

fLLf

fSS

fKAAKKmi

AA

)(2)(

22


2

22

2

222

0604

mKK

AAAA

LS

LSLS

f

fSf

fLf

fS

fL



SLS KKmi 21




)()( 0000

SSS KK












p

Target


particle sweeping

Dump

Neutral beam

Collimator

Production

angle

Protonenergy Beam

acceptance

Collimatorbackgroun

d

KL (+KS) beams



KS by regeneration





KL KL + Ar KS








61)Re(612

2

00

)(

)(

)(

)(00

00

2

2

00

L

S

S

L

K

K

K

K







n


d(PSext) d3x d3ph3




Position scale

Momentum

scale



Direct CPV 1996 AD

FNAL E731






The presshellip







KTeV at Fermilab



NA48 at CERN




600

00

10)820045()()(

)()(

KK

KK




4

World average





rsquo why










K decays


(PDG2004)



For kaons


K2ππ




ΔΓ(K3π)Δg(K3π)












K vs B







200

200

200

200

KeKKeK

KeKKeKA

iHtiHt

iHtiHt

T


20

20

20

20

KefKef

KefKefA

iHtCP

iHtCP

iHtCP

iHtCP

CP

200

200

200

200

KeKKeK

KeKKeKA

iHtiHt

iHtiHt

CPT




CPLEAR experiment

(CERN 1990-96)






tf

ft

f

iHtCP

iHtCP

iHtCP

iHtCP

CPLS

LS

e

mte

KefKef

KefKefA

)(2

2)(

20

20

20

20

1

)cos(2)Re(2

π+π

minus

π0π0

π+π minusπ0

π0π0π0

CPLEARAsymmetrie

s


Rate difference


Measure η





Kaon factories




pppp 2

1SLSL KKKKi




[Lipkin (1968)]

EPR correlation


DAΦNE (Frascati)


DAΦNE (Frascati)


MeVc)









p = 127 MeVcλ = 95 cm

KLKS 106 pb-1




KLOE physics




















p

Target

Collimator



Dump

Tagging Separation

Charged beam




Buthellip



rarr Small in SM


2π (εrsquoε)

3π (Ag)


ν


π0

Kplusmn rarr 3π




π1

π2

π3

K


Kinematics



2


2

Matrix element

|M(uv)|2 ~ 1 + gu + hu2 + kv2







KminusK+








10-6

NA482 OKA

10-5

10-4

10-3

10-2

SMSM

SUSYSUSYNewNew

physicsphysics



|Ag|

bull Ag ~ 10minus5


SUSY New Physics

THEORY



C

N



=Ag



54 60 66

1cm

50 100

10 cm

200 250 m





~11012

ppp

K+

Kminus



always in vacuum

focusing beams

BM

z

magnet

vacuum tank

not to scale

K+

K


pipe

0ordm prodangle






ZZ

XXYY

JuraJura

SaleveSaleve

Beam line K+ Up


B+

Bminus






Spectrometer field

K+

Kminus

Reverse each day

Reverse each week


|V| even pion

in beam pipe


KK+ +

KK



No significant

background





-15 -10 -05 0 05 10 u

0

-1

-2

1

2

3

Dalitz plot



EM calorimeter only






2003 result in PLB 634 (2006) 474




2003 result in PLB 638 (2006) 22


excluded


OKA at Protvino





(in preparation)


More CP violation


Indirect

Direct

CP violation

parameters

(2005)


(A) KS decays


CPV in KS decays




000000

000

000 )(

)(

L

S

KA




S+KL

KL




000 000 00

1( )2 ( 2

0

)

( )


tt

NEARf E t



)()()( 00

00

EKNEKN

EKNEKNED

(incoherent

production)



Assuming CPT





N3

20

40

60

00

4 62


No CPV seen yet

























PT() = (-17 23 11) 10-

3

Im = (-53 71 36) 10-3




Im = (-53 71 36) 10-3








ppp

ppp

)0()0(

)0()0(

NN

NNA


Radiative decays








211221 )()(


IB DE

p1 p1

p2p2

q q







)(

)(

S

L

KA

violatingCPKA




KL π+πminus






IB

M1 DE




KL itself





KL ee


BR = (308 020) 10minus7



E1M1 lt 004 (90 CL)



φ




KS ee

No asymmetry for KS

as expected

BR = (471 032) 10-

5

AΦ = (05 43)






IBEE

dEA

)tan( 0


Kplusmn π+π0γ

)730810672()(

)250350353()(

800

800

syststatMeVT

syststatMeVT

INTFrac

DEFrac







KL π+πndashπ0γ















)(

)2030(

3

3

e

ee

K

MeVEKR





bull 6M Ke3 events


ndash R=(0964plusmn0008+0011-0009)












PDG 2004







]21[192 3

52

KmG







Vus measurements





unitarity





KLOE Kl 3

KLOE K2

copy A Antonelli

Vus some more




Ke4 results





K+rarrπ0π0eν










1-loop rescattering

2-loop rescattering











NA482




KLOE interference

















K+ + 8middot10-11 (at 7)147+130

ndash089 middot 10-

10 (BNL E787+E949)






KL 0ℓ+ℓ-




BR(KL 0+-) lt 3810-10





NA481 KS 0ℓ+ℓ-



BR = (58 +28-23 plusmn08) times10-9


-012 (accid)BR = (28 +15


KS 0e+e- KS 0μ+μ-


NA481 preliminary

NA481 preliminary


KL 0ℓ+ℓ-






Krarr in the SM




W W

s

id

Vis Vid

e

i=uct

W

Z

VisV

idds i

11

20

2410

10)1108(

)(1001)(

AKB

11

2

5

100

10)4082(

)()Im(

1022)(

t

tdtsL xX

VVKB


K

ε εrsquo




Ke3 KL 0

Height

Im(λt )



10301890 10471)(

KBR









K+ +




















Appendixes





J(ππ) = ℓ(ππ) = 0 P(ππ) = +1 C(ππ) = +1



ℓL



SLti

SLLSti

LS

tL

tS

Lti

LSti

S

KKeaaKKeaa

eaea

KeaKea

SLLS

LS

LS

)()(

22

f LSf

fLS KfA

dt

d 2

2

TUnitarity requires

and therefore


f Sff

fS

fLSLLS

f

fLLf

fSS

fKAAKKmi

AA

)(2)(

22


2

22

2

222

0604

mKK

AAAA

LS

LSLS

f

fSf

fLf

fS

fL



SLS KKmi 21




)()( 0000

SSS KK



p

Target


particle sweeping

Dump

Neutral beam

Collimator

Production

angle

Protonenergy Beam

acceptance

Collimatorbackgroun

d

KL (+KS) beams



KS by regeneration





KL KL + Ar KS








61)Re(612

2

00

)(

)(

)(

)(00

00

2

2

00

L

S

S

L

K

K

K

K







n


d(PSext) d3x d3ph3




Position scale

Momentum

scale



Direct CPV 1996 AD

FNAL E731






The presshellip







KTeV at Fermilab



NA48 at CERN




600

00

10)820045()()(

)()(

KK

KK




4

World average





rsquo why










K decays


(PDG2004)



For kaons


K2ππ




ΔΓ(K3π)Δg(K3π)












K vs B







200

200

200

200

KeKKeK

KeKKeKA

iHtiHt

iHtiHt

T


20

20

20

20

KefKef

KefKefA

iHtCP

iHtCP

iHtCP

iHtCP

CP

200

200

200

200

KeKKeK

KeKKeKA

iHtiHt

iHtiHt

CPT




CPLEAR experiment

(CERN 1990-96)






tf

ft

f

iHtCP

iHtCP

iHtCP

iHtCP

CPLS

LS

e

mte

KefKef

KefKefA

)(2

2)(

20

20

20

20

1

)cos(2)Re(2

π+π

minus

π0π0

π+π minusπ0

π0π0π0

CPLEARAsymmetrie

s


Rate difference


Measure η





Kaon factories




pppp 2

1SLSL KKKKi




[Lipkin (1968)]

EPR correlation


DAΦNE (Frascati)


DAΦNE (Frascati)


MeVc)









p = 127 MeVcλ = 95 cm

KLKS 106 pb-1




KLOE physics




















p

Target

Collimator



Dump

Tagging Separation

Charged beam




Buthellip



rarr Small in SM


2π (εrsquoε)

3π (Ag)


ν


π0

Kplusmn rarr 3π




π1

π2

π3

K


Kinematics



2


2

Matrix element

|M(uv)|2 ~ 1 + gu + hu2 + kv2







KminusK+








10-6

NA482 OKA

10-5

10-4

10-3

10-2

SMSM

SUSYSUSYNewNew

physicsphysics



|Ag|

bull Ag ~ 10minus5


SUSY New Physics

THEORY



C

N



=Ag



54 60 66

1cm

50 100

10 cm

200 250 m





~11012

ppp

K+

Kminus



always in vacuum

focusing beams

BM

z

magnet

vacuum tank

not to scale

K+

K


pipe

0ordm prodangle






ZZ

XXYY

JuraJura

SaleveSaleve

Beam line K+ Up


B+

Bminus






Spectrometer field

K+

Kminus

Reverse each day

Reverse each week


|V| even pion

in beam pipe


KK+ +

KK



No significant

background





-15 -10 -05 0 05 10 u

0

-1

-2

1

2

3

Dalitz plot



EM calorimeter only






2003 result in PLB 634 (2006) 474




2003 result in PLB 638 (2006) 22


excluded


OKA at Protvino





(in preparation)


More CP violation


Indirect

Direct

CP violation

parameters

(2005)


(A) KS decays


CPV in KS decays




000000

000

000 )(

)(

L

S

KA




S+KL

KL




000 000 00

1( )2 ( 2

0

)

( )


tt

NEARf E t



)()()( 00

00

EKNEKN

EKNEKNED

(incoherent

production)



Assuming CPT





N3

20

40

60

00

4 62


No CPV seen yet

























PT() = (-17 23 11) 10-

3

Im = (-53 71 36) 10-3




Im = (-53 71 36) 10-3








ppp

ppp

)0()0(

)0()0(

NN

NNA


Radiative decays








211221 )()(


IB DE

p1 p1

p2p2

q q







)(

)(

S

L

KA

violatingCPKA




KL π+πminus






IB

M1 DE




KL itself





KL ee


BR = (308 020) 10minus7



E1M1 lt 004 (90 CL)



φ




KS ee

No asymmetry for KS

as expected

BR = (471 032) 10-

5

AΦ = (05 43)






IBEE

dEA

)tan( 0


Kplusmn π+π0γ

)730810672()(

)250350353()(

800

800

syststatMeVT

syststatMeVT

INTFrac

DEFrac







KL π+πndashπ0γ















)(

)2030(

3

3

e

ee

K

MeVEKR





bull 6M Ke3 events


ndash R=(0964plusmn0008+0011-0009)












PDG 2004







]21[192 3

52

KmG







Vus measurements





unitarity





KLOE Kl 3

KLOE K2

copy A Antonelli

Vus some more




Ke4 results





K+rarrπ0π0eν










1-loop rescattering

2-loop rescattering











NA482




KLOE interference

















K+ + 8middot10-11 (at 7)147+130

ndash089 middot 10-

10 (BNL E787+E949)






KL 0ℓ+ℓ-




BR(KL 0+-) lt 3810-10





NA481 KS 0ℓ+ℓ-



BR = (58 +28-23 plusmn08) times10-9


-012 (accid)BR = (28 +15


KS 0e+e- KS 0μ+μ-


NA481 preliminary

NA481 preliminary


KL 0ℓ+ℓ-






Krarr in the SM




W W

s

id

Vis Vid

e

i=uct

W

Z

VisV

idds i

11

20

2410

10)1108(

)(1001)(

AKB

11

2

5

100

10)4082(

)()Im(

1022)(

t

tdtsL xX

VVKB


K

ε εrsquo




Ke3 KL 0

Height

Im(λt )



10301890 10471)(

KBR









K+ +




















Appendixes





J(ππ) = ℓ(ππ) = 0 P(ππ) = +1 C(ππ) = +1



ℓL



SLti

SLLSti

LS

tL

tS

Lti

LSti

S

KKeaaKKeaa

eaea

KeaKea

SLLS

LS

LS

)()(

22

f LSf

fLS KfA

dt

d 2

2

TUnitarity requires

and therefore


f Sff

fS

fLSLLS

f

fLLf

fSS

fKAAKKmi

AA

)(2)(

22


2

22

2

222

0604

mKK

AAAA

LS

LSLS

f

fSf

fLf

fS

fL



SLS KKmi 21




)()( 0000

SSS KK



KS by regeneration





KL KL + Ar KS








61)Re(612

2

00

)(

)(

)(

)(00

00

2

2

00

L

S

S

L

K

K

K

K







n


d(PSext) d3x d3ph3




Position scale

Momentum

scale



Direct CPV 1996 AD

FNAL E731






The presshellip







KTeV at Fermilab



NA48 at CERN




600

00

10)820045()()(

)()(

KK

KK




4

World average





rsquo why










K decays


(PDG2004)



For kaons


K2ππ




ΔΓ(K3π)Δg(K3π)












K vs B







200

200

200

200

KeKKeK

KeKKeKA

iHtiHt

iHtiHt

T


20

20

20

20

KefKef

KefKefA

iHtCP

iHtCP

iHtCP

iHtCP

CP

200

200

200

200

KeKKeK

KeKKeKA

iHtiHt

iHtiHt

CPT




CPLEAR experiment

(CERN 1990-96)






tf

ft

f

iHtCP

iHtCP

iHtCP

iHtCP

CPLS

LS

e

mte

KefKef

KefKefA

)(2

2)(

20

20

20

20

1

)cos(2)Re(2

π+π

minus

π0π0

π+π minusπ0

π0π0π0

CPLEARAsymmetrie

s


Rate difference


Measure η





Kaon factories




pppp 2

1SLSL KKKKi




[Lipkin (1968)]

EPR correlation


DAΦNE (Frascati)


DAΦNE (Frascati)


MeVc)









p = 127 MeVcλ = 95 cm

KLKS 106 pb-1




KLOE physics




















p

Target

Collimator



Dump

Tagging Separation

Charged beam




Buthellip



rarr Small in SM


2π (εrsquoε)

3π (Ag)


ν


π0

Kplusmn rarr 3π




π1

π2

π3

K


Kinematics



2


2

Matrix element

|M(uv)|2 ~ 1 + gu + hu2 + kv2







KminusK+








10-6

NA482 OKA

10-5

10-4

10-3

10-2

SMSM

SUSYSUSYNewNew

physicsphysics



|Ag|

bull Ag ~ 10minus5


SUSY New Physics

THEORY



C

N



=Ag



54 60 66

1cm

50 100

10 cm

200 250 m





~11012

ppp

K+

Kminus



always in vacuum

focusing beams

BM

z

magnet

vacuum tank

not to scale

K+

K


pipe

0ordm prodangle






ZZ

XXYY

JuraJura

SaleveSaleve

Beam line K+ Up


B+

Bminus






Spectrometer field

K+

Kminus

Reverse each day

Reverse each week


|V| even pion

in beam pipe


KK+ +

KK



No significant

background





-15 -10 -05 0 05 10 u

0

-1

-2

1

2

3

Dalitz plot



EM calorimeter only






2003 result in PLB 634 (2006) 474




2003 result in PLB 638 (2006) 22


excluded


OKA at Protvino





(in preparation)


More CP violation


Indirect

Direct

CP violation

parameters

(2005)


(A) KS decays


CPV in KS decays




000000

000

000 )(

)(

L

S

KA




S+KL

KL




000 000 00

1( )2 ( 2

0

)

( )


tt

NEARf E t



)()()( 00

00

EKNEKN

EKNEKNED

(incoherent

production)



Assuming CPT





N3

20

40

60

00

4 62


No CPV seen yet

























PT() = (-17 23 11) 10-

3

Im = (-53 71 36) 10-3




Im = (-53 71 36) 10-3








ppp

ppp

)0()0(

)0()0(

NN

NNA


Radiative decays








211221 )()(


IB DE

p1 p1

p2p2

q q







)(

)(

S

L

KA

violatingCPKA




KL π+πminus






IB

M1 DE




KL itself





KL ee


BR = (308 020) 10minus7



E1M1 lt 004 (90 CL)



φ




KS ee

No asymmetry for KS

as expected

BR = (471 032) 10-

5

AΦ = (05 43)






IBEE

dEA

)tan( 0


Kplusmn π+π0γ

)730810672()(

)250350353()(

800

800

syststatMeVT

syststatMeVT

INTFrac

DEFrac







KL π+πndashπ0γ















)(

)2030(

3

3

e

ee

K

MeVEKR





bull 6M Ke3 events


ndash R=(0964plusmn0008+0011-0009)












PDG 2004







]21[192 3

52

KmG







Vus measurements





unitarity





KLOE Kl 3

KLOE K2

copy A Antonelli

Vus some more




Ke4 results





K+rarrπ0π0eν










1-loop rescattering

2-loop rescattering











NA482




KLOE interference

















K+ + 8middot10-11 (at 7)147+130

ndash089 middot 10-

10 (BNL E787+E949)






KL 0ℓ+ℓ-




BR(KL 0+-) lt 3810-10





NA481 KS 0ℓ+ℓ-



BR = (58 +28-23 plusmn08) times10-9


-012 (accid)BR = (28 +15


KS 0e+e- KS 0μ+μ-


NA481 preliminary

NA481 preliminary


KL 0ℓ+ℓ-






Krarr in the SM




W W

s

id

Vis Vid

e

i=uct

W

Z

VisV

idds i

11

20

2410

10)1108(

)(1001)(

AKB

11

2

5

100

10)4082(

)()Im(

1022)(

t

tdtsL xX

VVKB


K

ε εrsquo




Ke3 KL 0

Height

Im(λt )



10301890 10471)(

KBR









K+ +




















Appendixes





J(ππ) = ℓ(ππ) = 0 P(ππ) = +1 C(ππ) = +1



ℓL



SLti

SLLSti

LS

tL

tS

Lti

LSti

S

KKeaaKKeaa

eaea

KeaKea

SLLS

LS

LS

)()(

22

f LSf

fLS KfA

dt

d 2

2

TUnitarity requires

and therefore


f Sff

fS

fLSLLS

f

fLLf

fSS

fKAAKKmi

AA

)(2)(

22


2

22

2

222

0604

mKK

AAAA

LS

LSLS

f

fSf

fLf

fS

fL



SLS KKmi 21




)()( 0000

SSS KK









61)Re(612

2

00

)(

)(

)(

)(00

00

2

2

00

L

S

S

L

K

K

K

K







n


d(PSext) d3x d3ph3




Position scale

Momentum

scale



Direct CPV 1996 AD

FNAL E731






The presshellip







KTeV at Fermilab



NA48 at CERN




600

00

10)820045()()(

)()(

KK

KK




4

World average





rsquo why










K decays


(PDG2004)



For kaons


K2ππ




ΔΓ(K3π)Δg(K3π)












K vs B







200

200

200

200

KeKKeK

KeKKeKA

iHtiHt

iHtiHt

T


20

20

20

20

KefKef

KefKefA

iHtCP

iHtCP

iHtCP

iHtCP

CP

200

200

200

200

KeKKeK

KeKKeKA

iHtiHt

iHtiHt

CPT




CPLEAR experiment

(CERN 1990-96)






tf

ft

f

iHtCP

iHtCP

iHtCP

iHtCP

CPLS

LS

e

mte

KefKef

KefKefA

)(2

2)(

20

20

20

20

1

)cos(2)Re(2

π+π

minus

π0π0

π+π minusπ0

π0π0π0

CPLEARAsymmetrie

s


Rate difference


Measure η





Kaon factories




pppp 2

1SLSL KKKKi




[Lipkin (1968)]

EPR correlation


DAΦNE (Frascati)


DAΦNE (Frascati)


MeVc)









p = 127 MeVcλ = 95 cm

KLKS 106 pb-1




KLOE physics




















p

Target

Collimator



Dump

Tagging Separation

Charged beam




Buthellip



rarr Small in SM


2π (εrsquoε)

3π (Ag)


ν


π0

Kplusmn rarr 3π




π1

π2

π3

K


Kinematics



2


2

Matrix element

|M(uv)|2 ~ 1 + gu + hu2 + kv2







KminusK+








10-6

NA482 OKA

10-5

10-4

10-3

10-2

SMSM

SUSYSUSYNewNew

physicsphysics



|Ag|

bull Ag ~ 10minus5


SUSY New Physics

THEORY



C

N



=Ag



54 60 66

1cm

50 100

10 cm

200 250 m





~11012

ppp

K+

Kminus



always in vacuum

focusing beams

BM

z

magnet

vacuum tank

not to scale

K+

K


pipe

0ordm prodangle






ZZ

XXYY

JuraJura

SaleveSaleve

Beam line K+ Up


B+

Bminus






Spectrometer field

K+

Kminus

Reverse each day

Reverse each week


|V| even pion

in beam pipe


KK+ +

KK



No significant

background





-15 -10 -05 0 05 10 u

0

-1

-2

1

2

3

Dalitz plot



EM calorimeter only






2003 result in PLB 634 (2006) 474




2003 result in PLB 638 (2006) 22


excluded


OKA at Protvino





(in preparation)


More CP violation


Indirect

Direct

CP violation

parameters

(2005)


(A) KS decays


CPV in KS decays




000000

000

000 )(

)(

L

S

KA




S+KL

KL




000 000 00

1( )2 ( 2

0

)

( )


tt

NEARf E t



)()()( 00

00

EKNEKN

EKNEKNED

(incoherent

production)



Assuming CPT





N3

20

40

60

00

4 62


No CPV seen yet

























PT() = (-17 23 11) 10-

3

Im = (-53 71 36) 10-3




Im = (-53 71 36) 10-3








ppp

ppp

)0()0(

)0()0(

NN

NNA


Radiative decays








211221 )()(


IB DE

p1 p1

p2p2

q q







)(

)(

S

L

KA

violatingCPKA




KL π+πminus






IB

M1 DE




KL itself





KL ee


BR = (308 020) 10minus7



E1M1 lt 004 (90 CL)



φ




KS ee

No asymmetry for KS

as expected

BR = (471 032) 10-

5

AΦ = (05 43)






IBEE

dEA

)tan( 0


Kplusmn π+π0γ

)730810672()(

)250350353()(

800

800

syststatMeVT

syststatMeVT

INTFrac

DEFrac







KL π+πndashπ0γ















)(

)2030(

3

3

e

ee

K

MeVEKR





bull 6M Ke3 events


ndash R=(0964plusmn0008+0011-0009)












PDG 2004







]21[192 3

52

KmG







Vus measurements





unitarity





KLOE Kl 3

KLOE K2

copy A Antonelli

Vus some more




Ke4 results





K+rarrπ0π0eν










1-loop rescattering

2-loop rescattering











NA482




KLOE interference

















K+ + 8middot10-11 (at 7)147+130

ndash089 middot 10-

10 (BNL E787+E949)






KL 0ℓ+ℓ-




BR(KL 0+-) lt 3810-10





NA481 KS 0ℓ+ℓ-



BR = (58 +28-23 plusmn08) times10-9


-012 (accid)BR = (28 +15


KS 0e+e- KS 0μ+μ-


NA481 preliminary

NA481 preliminary


KL 0ℓ+ℓ-






Krarr in the SM




W W

s

id

Vis Vid

e

i=uct

W

Z

VisV

idds i

11

20

2410

10)1108(

)(1001)(

AKB

11

2

5

100

10)4082(

)()Im(

1022)(

t

tdtsL xX

VVKB


K

ε εrsquo




Ke3 KL 0

Height

Im(λt )



10301890 10471)(

KBR









K+ +




















Appendixes





J(ππ) = ℓ(ππ) = 0 P(ππ) = +1 C(ππ) = +1



ℓL



SLti

SLLSti

LS

tL

tS

Lti

LSti

S

KKeaaKKeaa

eaea

KeaKea

SLLS

LS

LS

)()(

22

f LSf

fLS KfA

dt

d 2

2

TUnitarity requires

and therefore


f Sff

fS

fLSLLS

f

fLLf

fSS

fKAAKKmi

AA

)(2)(

22


2

22

2

222

0604

mKK

AAAA

LS

LSLS

f

fSf

fLf

fS

fL



SLS KKmi 21




)()( 0000

SSS KK








n


d(PSext) d3x d3ph3




Position scale

Momentum

scale



Direct CPV 1996 AD

FNAL E731






The presshellip







KTeV at Fermilab



NA48 at CERN




600

00

10)820045()()(

)()(

KK

KK




4

World average





rsquo why










K decays


(PDG2004)



For kaons


K2ππ




ΔΓ(K3π)Δg(K3π)












K vs B







200

200

200

200

KeKKeK

KeKKeKA

iHtiHt

iHtiHt

T


20

20

20

20

KefKef

KefKefA

iHtCP

iHtCP

iHtCP

iHtCP

CP

200

200

200

200

KeKKeK

KeKKeKA

iHtiHt

iHtiHt

CPT




CPLEAR experiment

(CERN 1990-96)






tf

ft

f

iHtCP

iHtCP

iHtCP

iHtCP

CPLS

LS

e

mte

KefKef

KefKefA

)(2

2)(

20

20

20

20

1

)cos(2)Re(2

π+π

minus

π0π0

π+π minusπ0

π0π0π0

CPLEARAsymmetrie

s


Rate difference


Measure η





Kaon factories




pppp 2

1SLSL KKKKi




[Lipkin (1968)]

EPR correlation


DAΦNE (Frascati)


DAΦNE (Frascati)


MeVc)









p = 127 MeVcλ = 95 cm

KLKS 106 pb-1




KLOE physics




















p

Target

Collimator



Dump

Tagging Separation

Charged beam




Buthellip



rarr Small in SM


2π (εrsquoε)

3π (Ag)


ν


π0

Kplusmn rarr 3π




π1

π2

π3

K


Kinematics



2


2

Matrix element

|M(uv)|2 ~ 1 + gu + hu2 + kv2







KminusK+








10-6

NA482 OKA

10-5

10-4

10-3

10-2

SMSM

SUSYSUSYNewNew

physicsphysics



|Ag|

bull Ag ~ 10minus5


SUSY New Physics

THEORY



C

N



=Ag



54 60 66

1cm

50 100

10 cm

200 250 m





~11012

ppp

K+

Kminus



always in vacuum

focusing beams

BM

z

magnet

vacuum tank

not to scale

K+

K


pipe

0ordm prodangle






ZZ

XXYY

JuraJura

SaleveSaleve

Beam line K+ Up


B+

Bminus






Spectrometer field

K+

Kminus

Reverse each day

Reverse each week


|V| even pion

in beam pipe


KK+ +

KK



No significant

background





-15 -10 -05 0 05 10 u

0

-1

-2

1

2

3

Dalitz plot



EM calorimeter only






2003 result in PLB 634 (2006) 474




2003 result in PLB 638 (2006) 22


excluded


OKA at Protvino





(in preparation)


More CP violation


Indirect

Direct

CP violation

parameters

(2005)


(A) KS decays


CPV in KS decays




000000

000

000 )(

)(

L

S

KA




S+KL

KL




000 000 00

1( )2 ( 2

0

)

( )


tt

NEARf E t



)()()( 00

00

EKNEKN

EKNEKNED

(incoherent

production)



Assuming CPT





N3

20

40

60

00

4 62


No CPV seen yet

























PT() = (-17 23 11) 10-

3

Im = (-53 71 36) 10-3




Im = (-53 71 36) 10-3








ppp

ppp

)0()0(

)0()0(

NN

NNA


Radiative decays








211221 )()(


IB DE

p1 p1

p2p2

q q







)(

)(

S

L

KA

violatingCPKA




KL π+πminus






IB

M1 DE




KL itself





KL ee


BR = (308 020) 10minus7



E1M1 lt 004 (90 CL)



φ




KS ee

No asymmetry for KS

as expected

BR = (471 032) 10-

5

AΦ = (05 43)






IBEE

dEA

)tan( 0


Kplusmn π+π0γ

)730810672()(

)250350353()(

800

800

syststatMeVT

syststatMeVT

INTFrac

DEFrac







KL π+πndashπ0γ















)(

)2030(

3

3

e

ee

K

MeVEKR





bull 6M Ke3 events


ndash R=(0964plusmn0008+0011-0009)












PDG 2004







]21[192 3

52

KmG







Vus measurements





unitarity





KLOE Kl 3

KLOE K2

copy A Antonelli

Vus some more




Ke4 results





K+rarrπ0π0eν










1-loop rescattering

2-loop rescattering











NA482




KLOE interference

















K+ + 8middot10-11 (at 7)147+130

ndash089 middot 10-

10 (BNL E787+E949)






KL 0ℓ+ℓ-




BR(KL 0+-) lt 3810-10





NA481 KS 0ℓ+ℓ-



BR = (58 +28-23 plusmn08) times10-9


-012 (accid)BR = (28 +15


KS 0e+e- KS 0μ+μ-


NA481 preliminary

NA481 preliminary


KL 0ℓ+ℓ-






Krarr in the SM




W W

s

id

Vis Vid

e

i=uct

W

Z

VisV

idds i

11

20

2410

10)1108(

)(1001)(

AKB

11

2

5

100

10)4082(

)()Im(

1022)(

t

tdtsL xX

VVKB


K

ε εrsquo




Ke3 KL 0

Height

Im(λt )



10301890 10471)(

KBR









K+ +




















Appendixes





J(ππ) = ℓ(ππ) = 0 P(ππ) = +1 C(ππ) = +1



ℓL



SLti

SLLSti

LS

tL

tS

Lti

LSti

S

KKeaaKKeaa

eaea

KeaKea

SLLS

LS

LS

)()(

22

f LSf

fLS KfA

dt

d 2

2

TUnitarity requires

and therefore


f Sff

fS

fLSLLS

f

fLLf

fSS

fKAAKKmi

AA

)(2)(

22


2

22

2

222

0604

mKK

AAAA

LS

LSLS

f

fSf

fLf

fS

fL



SLS KKmi 21




)()( 0000

SSS KK



Direct CPV 1996 AD

FNAL E731






The presshellip







KTeV at Fermilab



NA48 at CERN




600

00

10)820045()()(

)()(

KK

KK




4

World average





rsquo why










K decays


(PDG2004)



For kaons


K2ππ




ΔΓ(K3π)Δg(K3π)












K vs B







200

200

200

200

KeKKeK

KeKKeKA

iHtiHt

iHtiHt

T


20

20

20

20

KefKef

KefKefA

iHtCP

iHtCP

iHtCP

iHtCP

CP

200

200

200

200

KeKKeK

KeKKeKA

iHtiHt

iHtiHt

CPT




CPLEAR experiment

(CERN 1990-96)






tf

ft

f

iHtCP

iHtCP

iHtCP

iHtCP

CPLS

LS

e

mte

KefKef

KefKefA

)(2

2)(

20

20

20

20

1

)cos(2)Re(2

π+π

minus

π0π0

π+π minusπ0

π0π0π0

CPLEARAsymmetrie

s


Rate difference


Measure η





Kaon factories




pppp 2

1SLSL KKKKi




[Lipkin (1968)]

EPR correlation


DAΦNE (Frascati)


DAΦNE (Frascati)


MeVc)









p = 127 MeVcλ = 95 cm

KLKS 106 pb-1




KLOE physics




















p

Target

Collimator



Dump

Tagging Separation

Charged beam




Buthellip



rarr Small in SM


2π (εrsquoε)

3π (Ag)


ν


π0

Kplusmn rarr 3π




π1

π2

π3

K


Kinematics



2


2

Matrix element

|M(uv)|2 ~ 1 + gu + hu2 + kv2







KminusK+








10-6

NA482 OKA

10-5

10-4

10-3

10-2

SMSM

SUSYSUSYNewNew

physicsphysics



|Ag|

bull Ag ~ 10minus5


SUSY New Physics

THEORY



C

N



=Ag



54 60 66

1cm

50 100

10 cm

200 250 m





~11012

ppp

K+

Kminus



always in vacuum

focusing beams

BM

z

magnet

vacuum tank

not to scale

K+

K


pipe

0ordm prodangle






ZZ

XXYY

JuraJura

SaleveSaleve

Beam line K+ Up


B+

Bminus






Spectrometer field

K+

Kminus

Reverse each day

Reverse each week


|V| even pion

in beam pipe


KK+ +

KK



No significant

background





-15 -10 -05 0 05 10 u

0

-1

-2

1

2

3

Dalitz plot



EM calorimeter only






2003 result in PLB 634 (2006) 474




2003 result in PLB 638 (2006) 22


excluded


OKA at Protvino





(in preparation)


More CP violation


Indirect

Direct

CP violation

parameters

(2005)


(A) KS decays


CPV in KS decays




000000

000

000 )(

)(

L

S

KA




S+KL

KL




000 000 00

1( )2 ( 2

0

)

( )


tt

NEARf E t



)()()( 00

00

EKNEKN

EKNEKNED

(incoherent

production)



Assuming CPT





N3

20

40

60

00

4 62


No CPV seen yet

























PT() = (-17 23 11) 10-

3

Im = (-53 71 36) 10-3




Im = (-53 71 36) 10-3








ppp

ppp

)0()0(

)0()0(

NN

NNA


Radiative decays








211221 )()(


IB DE

p1 p1

p2p2

q q







)(

)(

S

L

KA

violatingCPKA




KL π+πminus






IB

M1 DE




KL itself





KL ee


BR = (308 020) 10minus7



E1M1 lt 004 (90 CL)



φ




KS ee

No asymmetry for KS

as expected

BR = (471 032) 10-

5

AΦ = (05 43)






IBEE

dEA

)tan( 0


Kplusmn π+π0γ

)730810672()(

)250350353()(

800

800

syststatMeVT

syststatMeVT

INTFrac

DEFrac







KL π+πndashπ0γ















)(

)2030(

3

3

e

ee

K

MeVEKR





bull 6M Ke3 events


ndash R=(0964plusmn0008+0011-0009)












PDG 2004







]21[192 3

52

KmG







Vus measurements





unitarity





KLOE Kl 3

KLOE K2

copy A Antonelli

Vus some more




Ke4 results





K+rarrπ0π0eν










1-loop rescattering

2-loop rescattering











NA482




KLOE interference

















K+ + 8middot10-11 (at 7)147+130

ndash089 middot 10-

10 (BNL E787+E949)






KL 0ℓ+ℓ-




BR(KL 0+-) lt 3810-10





NA481 KS 0ℓ+ℓ-



BR = (58 +28-23 plusmn08) times10-9


-012 (accid)BR = (28 +15


KS 0e+e- KS 0μ+μ-


NA481 preliminary

NA481 preliminary


KL 0ℓ+ℓ-






Krarr in the SM




W W

s

id

Vis Vid

e

i=uct

W

Z

VisV

idds i

11

20

2410

10)1108(

)(1001)(

AKB

11

2

5

100

10)4082(

)()Im(

1022)(

t

tdtsL xX

VVKB


K

ε εrsquo




Ke3 KL 0

Height

Im(λt )



10301890 10471)(

KBR









K+ +




















Appendixes





J(ππ) = ℓ(ππ) = 0 P(ππ) = +1 C(ππ) = +1



ℓL



SLti

SLLSti

LS

tL

tS

Lti

LSti

S

KKeaaKKeaa

eaea

KeaKea

SLLS

LS

LS

)()(

22

f LSf

fLS KfA

dt

d 2

2

TUnitarity requires

and therefore


f Sff

fS

fLSLLS

f

fLLf

fSS

fKAAKKmi

AA

)(2)(

22


2

22

2

222

0604

mKK

AAAA

LS

LSLS

f

fSf

fLf

fS

fL



SLS KKmi 21




)()( 0000

SSS KK



The presshellip







KTeV at Fermilab



NA48 at CERN




600

00

10)820045()()(

)()(

KK

KK




4

World average





rsquo why










K decays


(PDG2004)



For kaons


K2ππ




ΔΓ(K3π)Δg(K3π)












K vs B







200

200

200

200

KeKKeK

KeKKeKA

iHtiHt

iHtiHt

T


20

20

20

20

KefKef

KefKefA

iHtCP

iHtCP

iHtCP

iHtCP

CP

200

200

200

200

KeKKeK

KeKKeKA

iHtiHt

iHtiHt

CPT




CPLEAR experiment

(CERN 1990-96)






tf

ft

f

iHtCP

iHtCP

iHtCP

iHtCP

CPLS

LS

e

mte

KefKef

KefKefA

)(2

2)(

20

20

20

20

1

)cos(2)Re(2

π+π

minus

π0π0

π+π minusπ0

π0π0π0

CPLEARAsymmetrie

s


Rate difference


Measure η





Kaon factories




pppp 2

1SLSL KKKKi




[Lipkin (1968)]

EPR correlation


DAΦNE (Frascati)


DAΦNE (Frascati)


MeVc)









p = 127 MeVcλ = 95 cm

KLKS 106 pb-1




KLOE physics




















p

Target

Collimator



Dump

Tagging Separation

Charged beam




Buthellip



rarr Small in SM


2π (εrsquoε)

3π (Ag)


ν


π0

Kplusmn rarr 3π




π1

π2

π3

K


Kinematics



2


2

Matrix element

|M(uv)|2 ~ 1 + gu + hu2 + kv2







KminusK+








10-6

NA482 OKA

10-5

10-4

10-3

10-2

SMSM

SUSYSUSYNewNew

physicsphysics



|Ag|

bull Ag ~ 10minus5


SUSY New Physics

THEORY



C

N



=Ag



54 60 66

1cm

50 100

10 cm

200 250 m





~11012

ppp

K+

Kminus



always in vacuum

focusing beams

BM

z

magnet

vacuum tank

not to scale

K+

K


pipe

0ordm prodangle






ZZ

XXYY

JuraJura

SaleveSaleve

Beam line K+ Up


B+

Bminus






Spectrometer field

K+

Kminus

Reverse each day

Reverse each week


|V| even pion

in beam pipe


KK+ +

KK



No significant

background





-15 -10 -05 0 05 10 u

0

-1

-2

1

2

3

Dalitz plot



EM calorimeter only






2003 result in PLB 634 (2006) 474




2003 result in PLB 638 (2006) 22


excluded


OKA at Protvino





(in preparation)


More CP violation


Indirect

Direct

CP violation

parameters

(2005)


(A) KS decays


CPV in KS decays




000000

000

000 )(

)(

L

S

KA




S+KL

KL




000 000 00

1( )2 ( 2

0

)

( )


tt

NEARf E t



)()()( 00

00

EKNEKN

EKNEKNED

(incoherent

production)



Assuming CPT





N3

20

40

60

00

4 62


No CPV seen yet

























PT() = (-17 23 11) 10-

3

Im = (-53 71 36) 10-3




Im = (-53 71 36) 10-3








ppp

ppp

)0()0(

)0()0(

NN

NNA


Radiative decays








211221 )()(


IB DE

p1 p1

p2p2

q q







)(

)(

S

L

KA

violatingCPKA




KL π+πminus






IB

M1 DE




KL itself





KL ee


BR = (308 020) 10minus7



E1M1 lt 004 (90 CL)



φ




KS ee

No asymmetry for KS

as expected

BR = (471 032) 10-

5

AΦ = (05 43)






IBEE

dEA

)tan( 0


Kplusmn π+π0γ

)730810672()(

)250350353()(

800

800

syststatMeVT

syststatMeVT

INTFrac

DEFrac







KL π+πndashπ0γ















)(

)2030(

3

3

e

ee

K

MeVEKR





bull 6M Ke3 events


ndash R=(0964plusmn0008+0011-0009)












PDG 2004







]21[192 3

52

KmG







Vus measurements





unitarity





KLOE Kl 3

KLOE K2

copy A Antonelli

Vus some more




Ke4 results





K+rarrπ0π0eν










1-loop rescattering

2-loop rescattering











NA482




KLOE interference

















K+ + 8middot10-11 (at 7)147+130

ndash089 middot 10-

10 (BNL E787+E949)






KL 0ℓ+ℓ-




BR(KL 0+-) lt 3810-10





NA481 KS 0ℓ+ℓ-



BR = (58 +28-23 plusmn08) times10-9


-012 (accid)BR = (28 +15


KS 0e+e- KS 0μ+μ-


NA481 preliminary

NA481 preliminary


KL 0ℓ+ℓ-






Krarr in the SM




W W

s

id

Vis Vid

e

i=uct

W

Z

VisV

idds i

11

20

2410

10)1108(

)(1001)(

AKB

11

2

5

100

10)4082(

)()Im(

1022)(

t

tdtsL xX

VVKB


K

ε εrsquo




Ke3 KL 0

Height

Im(λt )



10301890 10471)(

KBR









K+ +




















Appendixes





J(ππ) = ℓ(ππ) = 0 P(ππ) = +1 C(ππ) = +1



ℓL



SLti

SLLSti

LS

tL

tS

Lti

LSti

S

KKeaaKKeaa

eaea

KeaKea

SLLS

LS

LS

)()(

22

f LSf

fLS KfA

dt

d 2

2

TUnitarity requires

and therefore


f Sff

fS

fLSLLS

f

fLLf

fSS

fKAAKKmi

AA

)(2)(

22


2

22

2

222

0604

mKK

AAAA

LS

LSLS

f

fSf

fLf

fS

fL



SLS KKmi 21




)()( 0000

SSS KK








KTeV at Fermilab



NA48 at CERN




600

00

10)820045()()(

)()(

KK

KK




4

World average





rsquo why










K decays


(PDG2004)



For kaons


K2ππ




ΔΓ(K3π)Δg(K3π)












K vs B







200

200

200

200

KeKKeK

KeKKeKA

iHtiHt

iHtiHt

T


20

20

20

20

KefKef

KefKefA

iHtCP

iHtCP

iHtCP

iHtCP

CP

200

200

200

200

KeKKeK

KeKKeKA

iHtiHt

iHtiHt

CPT




CPLEAR experiment

(CERN 1990-96)






tf

ft

f

iHtCP

iHtCP

iHtCP

iHtCP

CPLS

LS

e

mte

KefKef

KefKefA

)(2

2)(

20

20

20

20

1

)cos(2)Re(2

π+π

minus

π0π0

π+π minusπ0

π0π0π0

CPLEARAsymmetrie

s


Rate difference


Measure η





Kaon factories




pppp 2

1SLSL KKKKi




[Lipkin (1968)]

EPR correlation


DAΦNE (Frascati)


DAΦNE (Frascati)


MeVc)









p = 127 MeVcλ = 95 cm

KLKS 106 pb-1




KLOE physics




















p

Target

Collimator



Dump

Tagging Separation

Charged beam




Buthellip



rarr Small in SM


2π (εrsquoε)

3π (Ag)


ν


π0

Kplusmn rarr 3π




π1

π2

π3

K


Kinematics



2


2

Matrix element

|M(uv)|2 ~ 1 + gu + hu2 + kv2







KminusK+








10-6

NA482 OKA

10-5

10-4

10-3

10-2

SMSM

SUSYSUSYNewNew

physicsphysics



|Ag|

bull Ag ~ 10minus5


SUSY New Physics

THEORY



C

N



=Ag



54 60 66

1cm

50 100

10 cm

200 250 m





~11012

ppp

K+

Kminus



always in vacuum

focusing beams

BM

z

magnet

vacuum tank

not to scale

K+

K


pipe

0ordm prodangle






ZZ

XXYY

JuraJura

SaleveSaleve

Beam line K+ Up


B+

Bminus






Spectrometer field

K+

Kminus

Reverse each day

Reverse each week


|V| even pion

in beam pipe


KK+ +

KK



No significant

background





-15 -10 -05 0 05 10 u

0

-1

-2

1

2

3

Dalitz plot



EM calorimeter only






2003 result in PLB 634 (2006) 474




2003 result in PLB 638 (2006) 22


excluded


OKA at Protvino





(in preparation)


More CP violation


Indirect

Direct

CP violation

parameters

(2005)


(A) KS decays


CPV in KS decays




000000

000

000 )(

)(

L

S

KA




S+KL

KL




000 000 00

1( )2 ( 2

0

)

( )


tt

NEARf E t



)()()( 00

00

EKNEKN

EKNEKNED

(incoherent

production)



Assuming CPT





N3

20

40

60

00

4 62


No CPV seen yet

























PT() = (-17 23 11) 10-

3

Im = (-53 71 36) 10-3




Im = (-53 71 36) 10-3








ppp

ppp

)0()0(

)0()0(

NN

NNA


Radiative decays








211221 )()(


IB DE

p1 p1

p2p2

q q







)(

)(

S

L

KA

violatingCPKA




KL π+πminus






IB

M1 DE




KL itself





KL ee


BR = (308 020) 10minus7



E1M1 lt 004 (90 CL)



φ




KS ee

No asymmetry for KS

as expected

BR = (471 032) 10-

5

AΦ = (05 43)






IBEE

dEA

)tan( 0


Kplusmn π+π0γ

)730810672()(

)250350353()(

800

800

syststatMeVT

syststatMeVT

INTFrac

DEFrac







KL π+πndashπ0γ















)(

)2030(

3

3

e

ee

K

MeVEKR





bull 6M Ke3 events


ndash R=(0964plusmn0008+0011-0009)












PDG 2004







]21[192 3

52

KmG







Vus measurements





unitarity





KLOE Kl 3

KLOE K2

copy A Antonelli

Vus some more




Ke4 results





K+rarrπ0π0eν










1-loop rescattering

2-loop rescattering











NA482




KLOE interference

















K+ + 8middot10-11 (at 7)147+130

ndash089 middot 10-

10 (BNL E787+E949)






KL 0ℓ+ℓ-




BR(KL 0+-) lt 3810-10





NA481 KS 0ℓ+ℓ-



BR = (58 +28-23 plusmn08) times10-9


-012 (accid)BR = (28 +15


KS 0e+e- KS 0μ+μ-


NA481 preliminary

NA481 preliminary


KL 0ℓ+ℓ-






Krarr in the SM




W W

s

id

Vis Vid

e

i=uct

W

Z

VisV

idds i

11

20

2410

10)1108(

)(1001)(

AKB

11

2

5

100

10)4082(

)()Im(

1022)(

t

tdtsL xX

VVKB


K

ε εrsquo




Ke3 KL 0

Height

Im(λt )



10301890 10471)(

KBR









K+ +




















Appendixes





J(ππ) = ℓ(ππ) = 0 P(ππ) = +1 C(ππ) = +1



ℓL



SLti

SLLSti

LS

tL

tS

Lti

LSti

S

KKeaaKKeaa

eaea

KeaKea

SLLS

LS

LS

)()(

22

f LSf

fLS KfA

dt

d 2

2

TUnitarity requires

and therefore


f Sff

fS

fLSLLS

f

fLLf

fSS

fKAAKKmi

AA

)(2)(

22


2

22

2

222

0604

mKK

AAAA

LS

LSLS

f

fSf

fLf

fS

fL



SLS KKmi 21




)()( 0000

SSS KK



KTeV at Fermilab



NA48 at CERN




600

00

10)820045()()(

)()(

KK

KK




4

World average





rsquo why










K decays


(PDG2004)



For kaons


K2ππ




ΔΓ(K3π)Δg(K3π)












K vs B







200

200

200

200

KeKKeK

KeKKeKA

iHtiHt

iHtiHt

T


20

20

20

20

KefKef

KefKefA

iHtCP

iHtCP

iHtCP

iHtCP

CP

200

200

200

200

KeKKeK

KeKKeKA

iHtiHt

iHtiHt

CPT




CPLEAR experiment

(CERN 1990-96)






tf

ft

f

iHtCP

iHtCP

iHtCP

iHtCP

CPLS

LS

e

mte

KefKef

KefKefA

)(2

2)(

20

20

20

20

1

)cos(2)Re(2

π+π

minus

π0π0

π+π minusπ0

π0π0π0

CPLEARAsymmetrie

s


Rate difference


Measure η





Kaon factories




pppp 2

1SLSL KKKKi




[Lipkin (1968)]

EPR correlation


DAΦNE (Frascati)


DAΦNE (Frascati)


MeVc)









p = 127 MeVcλ = 95 cm

KLKS 106 pb-1




KLOE physics




















p

Target

Collimator



Dump

Tagging Separation

Charged beam




Buthellip



rarr Small in SM


2π (εrsquoε)

3π (Ag)


ν


π0

Kplusmn rarr 3π




π1

π2

π3

K


Kinematics



2


2

Matrix element

|M(uv)|2 ~ 1 + gu + hu2 + kv2







KminusK+








10-6

NA482 OKA

10-5

10-4

10-3

10-2

SMSM

SUSYSUSYNewNew

physicsphysics



|Ag|

bull Ag ~ 10minus5


SUSY New Physics

THEORY



C

N



=Ag



54 60 66

1cm

50 100

10 cm

200 250 m





~11012

ppp

K+

Kminus



always in vacuum

focusing beams

BM

z

magnet

vacuum tank

not to scale

K+

K


pipe

0ordm prodangle






ZZ

XXYY

JuraJura

SaleveSaleve

Beam line K+ Up


B+

Bminus






Spectrometer field

K+

Kminus

Reverse each day

Reverse each week


|V| even pion

in beam pipe


KK+ +

KK



No significant

background





-15 -10 -05 0 05 10 u

0

-1

-2

1

2

3

Dalitz plot



EM calorimeter only






2003 result in PLB 634 (2006) 474




2003 result in PLB 638 (2006) 22


excluded


OKA at Protvino





(in preparation)


More CP violation


Indirect

Direct

CP violation

parameters

(2005)


(A) KS decays


CPV in KS decays




000000

000

000 )(

)(

L

S

KA




S+KL

KL




000 000 00

1( )2 ( 2

0

)

( )


tt

NEARf E t



)()()( 00

00

EKNEKN

EKNEKNED

(incoherent

production)



Assuming CPT





N3

20

40

60

00

4 62


No CPV seen yet

























PT() = (-17 23 11) 10-

3

Im = (-53 71 36) 10-3




Im = (-53 71 36) 10-3








ppp

ppp

)0()0(

)0()0(

NN

NNA


Radiative decays








211221 )()(


IB DE

p1 p1

p2p2

q q







)(

)(

S

L

KA

violatingCPKA




KL π+πminus






IB

M1 DE




KL itself





KL ee


BR = (308 020) 10minus7



E1M1 lt 004 (90 CL)



φ




KS ee

No asymmetry for KS

as expected

BR = (471 032) 10-

5

AΦ = (05 43)






IBEE

dEA

)tan( 0


Kplusmn π+π0γ

)730810672()(

)250350353()(

800

800

syststatMeVT

syststatMeVT

INTFrac

DEFrac







KL π+πndashπ0γ















)(

)2030(

3

3

e

ee

K

MeVEKR





bull 6M Ke3 events


ndash R=(0964plusmn0008+0011-0009)












PDG 2004







]21[192 3

52

KmG







Vus measurements





unitarity





KLOE Kl 3

KLOE K2

copy A Antonelli

Vus some more




Ke4 results





K+rarrπ0π0eν










1-loop rescattering

2-loop rescattering











NA482




KLOE interference

















K+ + 8middot10-11 (at 7)147+130

ndash089 middot 10-

10 (BNL E787+E949)






KL 0ℓ+ℓ-




BR(KL 0+-) lt 3810-10





NA481 KS 0ℓ+ℓ-



BR = (58 +28-23 plusmn08) times10-9


-012 (accid)BR = (28 +15


KS 0e+e- KS 0μ+μ-


NA481 preliminary

NA481 preliminary


KL 0ℓ+ℓ-






Krarr in the SM




W W

s

id

Vis Vid

e

i=uct

W

Z

VisV

idds i

11

20

2410

10)1108(

)(1001)(

AKB

11

2

5

100

10)4082(

)()Im(

1022)(

t

tdtsL xX

VVKB


K

ε εrsquo




Ke3 KL 0

Height

Im(λt )



10301890 10471)(

KBR









K+ +




















Appendixes





J(ππ) = ℓ(ππ) = 0 P(ππ) = +1 C(ππ) = +1



ℓL



SLti

SLLSti

LS

tL

tS

Lti

LSti

S

KKeaaKKeaa

eaea

KeaKea

SLLS

LS

LS

)()(

22

f LSf

fLS KfA

dt

d 2

2

TUnitarity requires

and therefore


f Sff

fS

fLSLLS

f

fLLf

fSS

fKAAKKmi

AA

)(2)(

22


2

22

2

222

0604

mKK

AAAA

LS

LSLS

f

fSf

fLf

fS

fL



SLS KKmi 21




)()( 0000

SSS KK



NA48 at CERN




600

00

10)820045()()(

)()(

KK

KK




4

World average





rsquo why










K decays


(PDG2004)



For kaons


K2ππ




ΔΓ(K3π)Δg(K3π)












K vs B







200

200

200

200

KeKKeK

KeKKeKA

iHtiHt

iHtiHt

T


20

20

20

20

KefKef

KefKefA

iHtCP

iHtCP

iHtCP

iHtCP

CP

200

200

200

200

KeKKeK

KeKKeKA

iHtiHt

iHtiHt

CPT




CPLEAR experiment

(CERN 1990-96)






tf

ft

f

iHtCP

iHtCP

iHtCP

iHtCP

CPLS

LS

e

mte

KefKef

KefKefA

)(2

2)(

20

20

20

20

1

)cos(2)Re(2

π+π

minus

π0π0

π+π minusπ0

π0π0π0

CPLEARAsymmetrie

s


Rate difference


Measure η





Kaon factories




pppp 2

1SLSL KKKKi




[Lipkin (1968)]

EPR correlation


DAΦNE (Frascati)


DAΦNE (Frascati)


MeVc)









p = 127 MeVcλ = 95 cm

KLKS 106 pb-1




KLOE physics




















p

Target

Collimator



Dump

Tagging Separation

Charged beam




Buthellip



rarr Small in SM


2π (εrsquoε)

3π (Ag)


ν


π0

Kplusmn rarr 3π




π1

π2

π3

K


Kinematics



2


2

Matrix element

|M(uv)|2 ~ 1 + gu + hu2 + kv2







KminusK+








10-6

NA482 OKA

10-5

10-4

10-3

10-2

SMSM

SUSYSUSYNewNew

physicsphysics



|Ag|

bull Ag ~ 10minus5


SUSY New Physics

THEORY



C

N



=Ag



54 60 66

1cm

50 100

10 cm

200 250 m





~11012

ppp

K+

Kminus



always in vacuum

focusing beams

BM

z

magnet

vacuum tank

not to scale

K+

K


pipe

0ordm prodangle






ZZ

XXYY

JuraJura

SaleveSaleve

Beam line K+ Up


B+

Bminus






Spectrometer field

K+

Kminus

Reverse each day

Reverse each week


|V| even pion

in beam pipe


KK+ +

KK



No significant

background





-15 -10 -05 0 05 10 u

0

-1

-2

1

2

3

Dalitz plot



EM calorimeter only






2003 result in PLB 634 (2006) 474




2003 result in PLB 638 (2006) 22


excluded


OKA at Protvino





(in preparation)


More CP violation


Indirect

Direct

CP violation

parameters

(2005)


(A) KS decays


CPV in KS decays




000000

000

000 )(

)(

L

S

KA




S+KL

KL




000 000 00

1( )2 ( 2

0

)

( )


tt

NEARf E t



)()()( 00

00

EKNEKN

EKNEKNED

(incoherent

production)



Assuming CPT





N3

20

40

60

00

4 62


No CPV seen yet

























PT() = (-17 23 11) 10-

3

Im = (-53 71 36) 10-3




Im = (-53 71 36) 10-3








ppp

ppp

)0()0(

)0()0(

NN

NNA


Radiative decays








211221 )()(


IB DE

p1 p1

p2p2

q q







)(

)(

S

L

KA

violatingCPKA




KL π+πminus






IB

M1 DE




KL itself





KL ee


BR = (308 020) 10minus7



E1M1 lt 004 (90 CL)



φ




KS ee

No asymmetry for KS

as expected

BR = (471 032) 10-

5

AΦ = (05 43)






IBEE

dEA

)tan( 0


Kplusmn π+π0γ

)730810672()(

)250350353()(

800

800

syststatMeVT

syststatMeVT

INTFrac

DEFrac







KL π+πndashπ0γ















)(

)2030(

3

3

e

ee

K

MeVEKR





bull 6M Ke3 events


ndash R=(0964plusmn0008+0011-0009)












PDG 2004







]21[192 3

52

KmG







Vus measurements





unitarity





KLOE Kl 3

KLOE K2

copy A Antonelli

Vus some more




Ke4 results





K+rarrπ0π0eν










1-loop rescattering

2-loop rescattering











NA482




KLOE interference

















K+ + 8middot10-11 (at 7)147+130

ndash089 middot 10-

10 (BNL E787+E949)






KL 0ℓ+ℓ-




BR(KL 0+-) lt 3810-10





NA481 KS 0ℓ+ℓ-



BR = (58 +28-23 plusmn08) times10-9


-012 (accid)BR = (28 +15


KS 0e+e- KS 0μ+μ-


NA481 preliminary

NA481 preliminary


KL 0ℓ+ℓ-






Krarr in the SM




W W

s

id

Vis Vid

e

i=uct

W

Z

VisV

idds i

11

20

2410

10)1108(

)(1001)(

AKB

11

2

5

100

10)4082(

)()Im(

1022)(

t

tdtsL xX

VVKB


K

ε εrsquo




Ke3 KL 0

Height

Im(λt )



10301890 10471)(

KBR









K+ +




















Appendixes





J(ππ) = ℓ(ππ) = 0 P(ππ) = +1 C(ππ) = +1



ℓL



SLti

SLLSti

LS

tL

tS

Lti

LSti

S

KKeaaKKeaa

eaea

KeaKea

SLLS

LS

LS

)()(

22

f LSf

fLS KfA

dt

d 2

2

TUnitarity requires

and therefore


f Sff

fS

fLSLLS

f

fLLf

fSS

fKAAKKmi

AA

)(2)(

22


2

22

2

222

0604

mKK

AAAA

LS

LSLS

f

fSf

fLf

fS

fL



SLS KKmi 21




)()( 0000

SSS KK




600

00

10)820045()()(

)()(

KK

KK




4

World average





rsquo why










K decays


(PDG2004)



For kaons


K2ππ




ΔΓ(K3π)Δg(K3π)












K vs B







200

200

200

200

KeKKeK

KeKKeKA

iHtiHt

iHtiHt

T


20

20

20

20

KefKef

KefKefA

iHtCP

iHtCP

iHtCP

iHtCP

CP

200

200

200

200

KeKKeK

KeKKeKA

iHtiHt

iHtiHt

CPT




CPLEAR experiment

(CERN 1990-96)






tf

ft

f

iHtCP

iHtCP

iHtCP

iHtCP

CPLS

LS

e

mte

KefKef

KefKefA

)(2

2)(

20

20

20

20

1

)cos(2)Re(2

π+π

minus

π0π0

π+π minusπ0

π0π0π0

CPLEARAsymmetrie

s


Rate difference


Measure η





Kaon factories




pppp 2

1SLSL KKKKi




[Lipkin (1968)]

EPR correlation


DAΦNE (Frascati)


DAΦNE (Frascati)


MeVc)









p = 127 MeVcλ = 95 cm

KLKS 106 pb-1




KLOE physics




















p

Target

Collimator



Dump

Tagging Separation

Charged beam




Buthellip



rarr Small in SM


2π (εrsquoε)

3π (Ag)


ν


π0

Kplusmn rarr 3π




π1

π2

π3

K


Kinematics



2


2

Matrix element

|M(uv)|2 ~ 1 + gu + hu2 + kv2







KminusK+








10-6

NA482 OKA

10-5

10-4

10-3

10-2

SMSM

SUSYSUSYNewNew

physicsphysics



|Ag|

bull Ag ~ 10minus5


SUSY New Physics

THEORY



C

N



=Ag



54 60 66

1cm

50 100

10 cm

200 250 m





~11012

ppp

K+

Kminus



always in vacuum

focusing beams

BM

z

magnet

vacuum tank

not to scale

K+

K


pipe

0ordm prodangle






ZZ

XXYY

JuraJura

SaleveSaleve

Beam line K+ Up


B+

Bminus






Spectrometer field

K+

Kminus

Reverse each day

Reverse each week


|V| even pion

in beam pipe


KK+ +

KK



No significant

background





-15 -10 -05 0 05 10 u

0

-1

-2

1

2

3

Dalitz plot



EM calorimeter only






2003 result in PLB 634 (2006) 474




2003 result in PLB 638 (2006) 22


excluded


OKA at Protvino





(in preparation)


More CP violation


Indirect

Direct

CP violation

parameters

(2005)


(A) KS decays


CPV in KS decays




000000

000

000 )(

)(

L

S

KA




S+KL

KL




000 000 00

1( )2 ( 2

0

)

( )


tt

NEARf E t



)()()( 00

00

EKNEKN

EKNEKNED

(incoherent

production)



Assuming CPT





N3

20

40

60

00

4 62


No CPV seen yet

























PT() = (-17 23 11) 10-

3

Im = (-53 71 36) 10-3




Im = (-53 71 36) 10-3








ppp

ppp

)0()0(

)0()0(

NN

NNA


Radiative decays








211221 )()(


IB DE

p1 p1

p2p2

q q







)(

)(

S

L

KA

violatingCPKA




KL π+πminus






IB

M1 DE




KL itself





KL ee


BR = (308 020) 10minus7



E1M1 lt 004 (90 CL)



φ




KS ee

No asymmetry for KS

as expected

BR = (471 032) 10-

5

AΦ = (05 43)






IBEE

dEA

)tan( 0


Kplusmn π+π0γ

)730810672()(

)250350353()(

800

800

syststatMeVT

syststatMeVT

INTFrac

DEFrac







KL π+πndashπ0γ















)(

)2030(

3

3

e

ee

K

MeVEKR





bull 6M Ke3 events


ndash R=(0964plusmn0008+0011-0009)












PDG 2004







]21[192 3

52

KmG







Vus measurements





unitarity





KLOE Kl 3

KLOE K2

copy A Antonelli

Vus some more




Ke4 results





K+rarrπ0π0eν










1-loop rescattering

2-loop rescattering











NA482




KLOE interference

















K+ + 8middot10-11 (at 7)147+130

ndash089 middot 10-

10 (BNL E787+E949)






KL 0ℓ+ℓ-




BR(KL 0+-) lt 3810-10





NA481 KS 0ℓ+ℓ-



BR = (58 +28-23 plusmn08) times10-9


-012 (accid)BR = (28 +15


KS 0e+e- KS 0μ+μ-


NA481 preliminary

NA481 preliminary


KL 0ℓ+ℓ-






Krarr in the SM




W W

s

id

Vis Vid

e

i=uct

W

Z

VisV

idds i

11

20

2410

10)1108(

)(1001)(

AKB

11

2

5

100

10)4082(

)()Im(

1022)(

t

tdtsL xX

VVKB


K

ε εrsquo




Ke3 KL 0

Height

Im(λt )



10301890 10471)(

KBR









K+ +




















Appendixes





J(ππ) = ℓ(ππ) = 0 P(ππ) = +1 C(ππ) = +1



ℓL



SLti

SLLSti

LS

tL

tS

Lti

LSti

S

KKeaaKKeaa

eaea

KeaKea

SLLS

LS

LS

)()(

22

f LSf

fLS KfA

dt

d 2

2

TUnitarity requires

and therefore


f Sff

fS

fLSLLS

f

fLLf

fSS

fKAAKKmi

AA

)(2)(

22


2

22

2

222

0604

mKK

AAAA

LS

LSLS

f

fSf

fLf

fS

fL



SLS KKmi 21




)()( 0000

SSS KK





rsquo why










K decays


(PDG2004)



For kaons


K2ππ




ΔΓ(K3π)Δg(K3π)












K vs B







200

200

200

200

KeKKeK

KeKKeKA

iHtiHt

iHtiHt

T


20

20

20

20

KefKef

KefKefA

iHtCP

iHtCP

iHtCP

iHtCP

CP

200

200

200

200

KeKKeK

KeKKeKA

iHtiHt

iHtiHt

CPT




CPLEAR experiment

(CERN 1990-96)






tf

ft

f

iHtCP

iHtCP

iHtCP

iHtCP

CPLS

LS

e

mte

KefKef

KefKefA

)(2

2)(

20

20

20

20

1

)cos(2)Re(2

π+π

minus

π0π0

π+π minusπ0

π0π0π0

CPLEARAsymmetrie

s


Rate difference


Measure η





Kaon factories




pppp 2

1SLSL KKKKi




[Lipkin (1968)]

EPR correlation


DAΦNE (Frascati)


DAΦNE (Frascati)


MeVc)









p = 127 MeVcλ = 95 cm

KLKS 106 pb-1




KLOE physics




















p

Target

Collimator



Dump

Tagging Separation

Charged beam




Buthellip



rarr Small in SM


2π (εrsquoε)

3π (Ag)


ν


π0

Kplusmn rarr 3π




π1

π2

π3

K


Kinematics



2


2

Matrix element

|M(uv)|2 ~ 1 + gu + hu2 + kv2







KminusK+








10-6

NA482 OKA

10-5

10-4

10-3

10-2

SMSM

SUSYSUSYNewNew

physicsphysics



|Ag|

bull Ag ~ 10minus5


SUSY New Physics

THEORY



C

N



=Ag



54 60 66

1cm

50 100

10 cm

200 250 m





~11012

ppp

K+

Kminus



always in vacuum

focusing beams

BM

z

magnet

vacuum tank

not to scale

K+

K


pipe

0ordm prodangle






ZZ

XXYY

JuraJura

SaleveSaleve

Beam line K+ Up


B+

Bminus






Spectrometer field

K+

Kminus

Reverse each day

Reverse each week


|V| even pion

in beam pipe


KK+ +

KK



No significant

background





-15 -10 -05 0 05 10 u

0

-1

-2

1

2

3

Dalitz plot



EM calorimeter only






2003 result in PLB 634 (2006) 474




2003 result in PLB 638 (2006) 22


excluded


OKA at Protvino





(in preparation)


More CP violation


Indirect

Direct

CP violation

parameters

(2005)


(A) KS decays


CPV in KS decays




000000

000

000 )(

)(

L

S

KA




S+KL

KL




000 000 00

1( )2 ( 2

0

)

( )


tt

NEARf E t



)()()( 00

00

EKNEKN

EKNEKNED

(incoherent

production)



Assuming CPT





N3

20

40

60

00

4 62


No CPV seen yet

























PT() = (-17 23 11) 10-

3

Im = (-53 71 36) 10-3




Im = (-53 71 36) 10-3








ppp

ppp

)0()0(

)0()0(

NN

NNA


Radiative decays








211221 )()(


IB DE

p1 p1

p2p2

q q







)(

)(

S

L

KA

violatingCPKA




KL π+πminus






IB

M1 DE




KL itself





KL ee


BR = (308 020) 10minus7



E1M1 lt 004 (90 CL)



φ




KS ee

No asymmetry for KS

as expected

BR = (471 032) 10-

5

AΦ = (05 43)






IBEE

dEA

)tan( 0


Kplusmn π+π0γ

)730810672()(

)250350353()(

800

800

syststatMeVT

syststatMeVT

INTFrac

DEFrac







KL π+πndashπ0γ















)(

)2030(

3

3

e

ee

K

MeVEKR





bull 6M Ke3 events


ndash R=(0964plusmn0008+0011-0009)












PDG 2004







]21[192 3

52

KmG







Vus measurements





unitarity





KLOE Kl 3

KLOE K2

copy A Antonelli

Vus some more




Ke4 results





K+rarrπ0π0eν










1-loop rescattering

2-loop rescattering











NA482




KLOE interference

















K+ + 8middot10-11 (at 7)147+130

ndash089 middot 10-

10 (BNL E787+E949)






KL 0ℓ+ℓ-




BR(KL 0+-) lt 3810-10





NA481 KS 0ℓ+ℓ-



BR = (58 +28-23 plusmn08) times10-9


-012 (accid)BR = (28 +15


KS 0e+e- KS 0μ+μ-


NA481 preliminary

NA481 preliminary


KL 0ℓ+ℓ-






Krarr in the SM




W W

s

id

Vis Vid

e

i=uct

W

Z

VisV

idds i

11

20

2410

10)1108(

)(1001)(

AKB

11

2

5

100

10)4082(

)()Im(

1022)(

t

tdtsL xX

VVKB


K

ε εrsquo




Ke3 KL 0

Height

Im(λt )



10301890 10471)(

KBR









K+ +




















Appendixes





J(ππ) = ℓ(ππ) = 0 P(ππ) = +1 C(ππ) = +1



ℓL



SLti

SLLSti

LS

tL

tS

Lti

LSti

S

KKeaaKKeaa

eaea

KeaKea

SLLS

LS

LS

)()(

22

f LSf

fLS KfA

dt

d 2

2

TUnitarity requires

and therefore


f Sff

fS

fLSLLS

f

fLLf

fSS

fKAAKKmi

AA

)(2)(

22


2

22

2

222

0604

mKK

AAAA

LS

LSLS

f

fSf

fLf

fS

fL



SLS KKmi 21




)()( 0000

SSS KK





K decays


(PDG2004)



For kaons


K2ππ




ΔΓ(K3π)Δg(K3π)












K vs B







200

200

200

200

KeKKeK

KeKKeKA

iHtiHt

iHtiHt

T


20

20

20

20

KefKef

KefKefA

iHtCP

iHtCP

iHtCP

iHtCP

CP

200

200

200

200

KeKKeK

KeKKeKA

iHtiHt

iHtiHt

CPT




CPLEAR experiment

(CERN 1990-96)






tf

ft

f

iHtCP

iHtCP

iHtCP

iHtCP

CPLS

LS

e

mte

KefKef

KefKefA

)(2

2)(

20

20

20

20

1

)cos(2)Re(2

π+π

minus

π0π0

π+π minusπ0

π0π0π0

CPLEARAsymmetrie

s


Rate difference


Measure η





Kaon factories




pppp 2

1SLSL KKKKi




[Lipkin (1968)]

EPR correlation


DAΦNE (Frascati)


DAΦNE (Frascati)


MeVc)









p = 127 MeVcλ = 95 cm

KLKS 106 pb-1




KLOE physics




















p

Target

Collimator



Dump

Tagging Separation

Charged beam




Buthellip



rarr Small in SM


2π (εrsquoε)

3π (Ag)


ν


π0

Kplusmn rarr 3π




π1

π2

π3

K


Kinematics



2


2

Matrix element

|M(uv)|2 ~ 1 + gu + hu2 + kv2







KminusK+








10-6

NA482 OKA

10-5

10-4

10-3

10-2

SMSM

SUSYSUSYNewNew

physicsphysics



|Ag|

bull Ag ~ 10minus5


SUSY New Physics

THEORY



C

N



=Ag



54 60 66

1cm

50 100

10 cm

200 250 m





~11012

ppp

K+

Kminus



always in vacuum

focusing beams

BM

z

magnet

vacuum tank

not to scale

K+

K


pipe

0ordm prodangle






ZZ

XXYY

JuraJura

SaleveSaleve

Beam line K+ Up


B+

Bminus






Spectrometer field

K+

Kminus

Reverse each day

Reverse each week


|V| even pion

in beam pipe


KK+ +

KK



No significant

background





-15 -10 -05 0 05 10 u

0

-1

-2

1

2

3

Dalitz plot



EM calorimeter only






2003 result in PLB 634 (2006) 474




2003 result in PLB 638 (2006) 22


excluded


OKA at Protvino





(in preparation)


More CP violation


Indirect

Direct

CP violation

parameters

(2005)


(A) KS decays


CPV in KS decays




000000

000

000 )(

)(

L

S

KA




S+KL

KL




000 000 00

1( )2 ( 2

0

)

( )


tt

NEARf E t



)()()( 00

00

EKNEKN

EKNEKNED

(incoherent

production)



Assuming CPT





N3

20

40

60

00

4 62


No CPV seen yet

























PT() = (-17 23 11) 10-

3

Im = (-53 71 36) 10-3




Im = (-53 71 36) 10-3








ppp

ppp

)0()0(

)0()0(

NN

NNA


Radiative decays








211221 )()(


IB DE

p1 p1

p2p2

q q







)(

)(

S

L

KA

violatingCPKA




KL π+πminus






IB

M1 DE




KL itself





KL ee


BR = (308 020) 10minus7



E1M1 lt 004 (90 CL)



φ




KS ee

No asymmetry for KS

as expected

BR = (471 032) 10-

5

AΦ = (05 43)






IBEE

dEA

)tan( 0


Kplusmn π+π0γ

)730810672()(

)250350353()(

800

800

syststatMeVT

syststatMeVT

INTFrac

DEFrac







KL π+πndashπ0γ















)(

)2030(

3

3

e

ee

K

MeVEKR





bull 6M Ke3 events


ndash R=(0964plusmn0008+0011-0009)












PDG 2004







]21[192 3

52

KmG







Vus measurements





unitarity





KLOE Kl 3

KLOE K2

copy A Antonelli

Vus some more




Ke4 results





K+rarrπ0π0eν










1-loop rescattering

2-loop rescattering











NA482




KLOE interference

















K+ + 8middot10-11 (at 7)147+130

ndash089 middot 10-

10 (BNL E787+E949)






KL 0ℓ+ℓ-




BR(KL 0+-) lt 3810-10





NA481 KS 0ℓ+ℓ-



BR = (58 +28-23 plusmn08) times10-9


-012 (accid)BR = (28 +15


KS 0e+e- KS 0μ+μ-


NA481 preliminary

NA481 preliminary


KL 0ℓ+ℓ-






Krarr in the SM




W W

s

id

Vis Vid

e

i=uct

W

Z

VisV

idds i

11

20

2410

10)1108(

)(1001)(

AKB

11

2

5

100

10)4082(

)()Im(

1022)(

t

tdtsL xX

VVKB


K

ε εrsquo




Ke3 KL 0

Height

Im(λt )



10301890 10471)(

KBR









K+ +




















Appendixes





J(ππ) = ℓ(ππ) = 0 P(ππ) = +1 C(ππ) = +1



ℓL



SLti

SLLSti

LS

tL

tS

Lti

LSti

S

KKeaaKKeaa

eaea

KeaKea

SLLS

LS

LS

)()(

22

f LSf

fLS KfA

dt

d 2

2

TUnitarity requires

and therefore


f Sff

fS

fLSLLS

f

fLLf

fSS

fKAAKKmi

AA

)(2)(

22


2

22

2

222

0604

mKK

AAAA

LS

LSLS

f

fSf

fLf

fS

fL



SLS KKmi 21




)()( 0000

SSS KK



K decays


(PDG2004)



For kaons


K2ππ




ΔΓ(K3π)Δg(K3π)












K vs B







200

200

200

200

KeKKeK

KeKKeKA

iHtiHt

iHtiHt

T


20

20

20

20

KefKef

KefKefA

iHtCP

iHtCP

iHtCP

iHtCP

CP

200

200

200

200

KeKKeK

KeKKeKA

iHtiHt

iHtiHt

CPT




CPLEAR experiment

(CERN 1990-96)






tf

ft

f

iHtCP

iHtCP

iHtCP

iHtCP

CPLS

LS

e

mte

KefKef

KefKefA

)(2

2)(

20

20

20

20

1

)cos(2)Re(2

π+π

minus

π0π0

π+π minusπ0

π0π0π0

CPLEARAsymmetrie

s


Rate difference


Measure η





Kaon factories




pppp 2

1SLSL KKKKi




[Lipkin (1968)]

EPR correlation


DAΦNE (Frascati)


DAΦNE (Frascati)


MeVc)









p = 127 MeVcλ = 95 cm

KLKS 106 pb-1




KLOE physics




















p

Target

Collimator



Dump

Tagging Separation

Charged beam




Buthellip



rarr Small in SM


2π (εrsquoε)

3π (Ag)


ν


π0

Kplusmn rarr 3π




π1

π2

π3

K


Kinematics



2


2

Matrix element

|M(uv)|2 ~ 1 + gu + hu2 + kv2







KminusK+








10-6

NA482 OKA

10-5

10-4

10-3

10-2

SMSM

SUSYSUSYNewNew

physicsphysics



|Ag|

bull Ag ~ 10minus5


SUSY New Physics

THEORY



C

N



=Ag



54 60 66

1cm

50 100

10 cm

200 250 m





~11012

ppp

K+

Kminus



always in vacuum

focusing beams

BM

z

magnet

vacuum tank

not to scale

K+

K


pipe

0ordm prodangle






ZZ

XXYY

JuraJura

SaleveSaleve

Beam line K+ Up


B+

Bminus






Spectrometer field

K+

Kminus

Reverse each day

Reverse each week


|V| even pion

in beam pipe


KK+ +

KK



No significant

background





-15 -10 -05 0 05 10 u

0

-1

-2

1

2

3

Dalitz plot



EM calorimeter only






2003 result in PLB 634 (2006) 474




2003 result in PLB 638 (2006) 22


excluded


OKA at Protvino





(in preparation)


More CP violation


Indirect

Direct

CP violation

parameters

(2005)


(A) KS decays


CPV in KS decays




000000

000

000 )(

)(

L

S

KA




S+KL

KL




000 000 00

1( )2 ( 2

0

)

( )


tt

NEARf E t



)()()( 00

00

EKNEKN

EKNEKNED

(incoherent

production)



Assuming CPT





N3

20

40

60

00

4 62


No CPV seen yet

























PT() = (-17 23 11) 10-

3

Im = (-53 71 36) 10-3




Im = (-53 71 36) 10-3








ppp

ppp

)0()0(

)0()0(

NN

NNA


Radiative decays








211221 )()(


IB DE

p1 p1

p2p2

q q







)(

)(

S

L

KA

violatingCPKA




KL π+πminus






IB

M1 DE




KL itself





KL ee


BR = (308 020) 10minus7



E1M1 lt 004 (90 CL)



φ




KS ee

No asymmetry for KS

as expected

BR = (471 032) 10-

5

AΦ = (05 43)






IBEE

dEA

)tan( 0


Kplusmn π+π0γ

)730810672()(

)250350353()(

800

800

syststatMeVT

syststatMeVT

INTFrac

DEFrac







KL π+πndashπ0γ















)(

)2030(

3

3

e

ee

K

MeVEKR





bull 6M Ke3 events


ndash R=(0964plusmn0008+0011-0009)












PDG 2004







]21[192 3

52

KmG







Vus measurements





unitarity





KLOE Kl 3

KLOE K2

copy A Antonelli

Vus some more




Ke4 results





K+rarrπ0π0eν










1-loop rescattering

2-loop rescattering











NA482




KLOE interference

















K+ + 8middot10-11 (at 7)147+130

ndash089 middot 10-

10 (BNL E787+E949)






KL 0ℓ+ℓ-




BR(KL 0+-) lt 3810-10





NA481 KS 0ℓ+ℓ-



BR = (58 +28-23 plusmn08) times10-9


-012 (accid)BR = (28 +15


KS 0e+e- KS 0μ+μ-


NA481 preliminary

NA481 preliminary


KL 0ℓ+ℓ-






Krarr in the SM




W W

s

id

Vis Vid

e

i=uct

W

Z

VisV

idds i

11

20

2410

10)1108(

)(1001)(

AKB

11

2

5

100

10)4082(

)()Im(

1022)(

t

tdtsL xX

VVKB


K

ε εrsquo




Ke3 KL 0

Height

Im(λt )



10301890 10471)(

KBR









K+ +




















Appendixes





J(ππ) = ℓ(ππ) = 0 P(ππ) = +1 C(ππ) = +1



ℓL



SLti

SLLSti

LS

tL

tS

Lti

LSti

S

KKeaaKKeaa

eaea

KeaKea

SLLS

LS

LS

)()(

22

f LSf

fLS KfA

dt

d 2

2

TUnitarity requires

and therefore


f Sff

fS

fLSLLS

f

fLLf

fSS

fKAAKKmi

AA

)(2)(

22


2

22

2

222

0604

mKK

AAAA

LS

LSLS

f

fSf

fLf

fS

fL



SLS KKmi 21




)()( 0000

SSS KK




For kaons


K2ππ




ΔΓ(K3π)Δg(K3π)












K vs B







200

200

200

200

KeKKeK

KeKKeKA

iHtiHt

iHtiHt

T


20

20

20

20

KefKef

KefKefA

iHtCP

iHtCP

iHtCP

iHtCP

CP

200

200

200

200

KeKKeK

KeKKeKA

iHtiHt

iHtiHt

CPT




CPLEAR experiment

(CERN 1990-96)






tf

ft

f

iHtCP

iHtCP

iHtCP

iHtCP

CPLS

LS

e

mte

KefKef

KefKefA

)(2

2)(

20

20

20

20

1

)cos(2)Re(2

π+π

minus

π0π0

π+π minusπ0

π0π0π0

CPLEARAsymmetrie

s


Rate difference


Measure η





Kaon factories




pppp 2

1SLSL KKKKi




[Lipkin (1968)]

EPR correlation


DAΦNE (Frascati)


DAΦNE (Frascati)


MeVc)









p = 127 MeVcλ = 95 cm

KLKS 106 pb-1




KLOE physics




















p

Target

Collimator



Dump

Tagging Separation

Charged beam




Buthellip



rarr Small in SM


2π (εrsquoε)

3π (Ag)


ν


π0

Kplusmn rarr 3π




π1

π2

π3

K


Kinematics



2


2

Matrix element

|M(uv)|2 ~ 1 + gu + hu2 + kv2







KminusK+








10-6

NA482 OKA

10-5

10-4

10-3

10-2

SMSM

SUSYSUSYNewNew

physicsphysics



|Ag|

bull Ag ~ 10minus5


SUSY New Physics

THEORY



C

N



=Ag



54 60 66

1cm

50 100

10 cm

200 250 m





~11012

ppp

K+

Kminus



always in vacuum

focusing beams

BM

z

magnet

vacuum tank

not to scale

K+

K


pipe

0ordm prodangle






ZZ

XXYY

JuraJura

SaleveSaleve

Beam line K+ Up


B+

Bminus






Spectrometer field

K+

Kminus

Reverse each day

Reverse each week


|V| even pion

in beam pipe


KK+ +

KK



No significant

background





-15 -10 -05 0 05 10 u

0

-1

-2

1

2

3

Dalitz plot



EM calorimeter only






2003 result in PLB 634 (2006) 474




2003 result in PLB 638 (2006) 22


excluded


OKA at Protvino





(in preparation)


More CP violation


Indirect

Direct

CP violation

parameters

(2005)


(A) KS decays


CPV in KS decays




000000

000

000 )(

)(

L

S

KA




S+KL

KL




000 000 00

1( )2 ( 2

0

)

( )


tt

NEARf E t



)()()( 00

00

EKNEKN

EKNEKNED

(incoherent

production)



Assuming CPT





N3

20

40

60

00

4 62


No CPV seen yet

























PT() = (-17 23 11) 10-

3

Im = (-53 71 36) 10-3




Im = (-53 71 36) 10-3








ppp

ppp

)0()0(

)0()0(

NN

NNA


Radiative decays








211221 )()(


IB DE

p1 p1

p2p2

q q







)(

)(

S

L

KA

violatingCPKA




KL π+πminus






IB

M1 DE




KL itself





KL ee


BR = (308 020) 10minus7



E1M1 lt 004 (90 CL)



φ




KS ee

No asymmetry for KS

as expected

BR = (471 032) 10-

5

AΦ = (05 43)






IBEE

dEA

)tan( 0


Kplusmn π+π0γ

)730810672()(

)250350353()(

800

800

syststatMeVT

syststatMeVT

INTFrac

DEFrac







KL π+πndashπ0γ















)(

)2030(

3

3

e

ee

K

MeVEKR





bull 6M Ke3 events


ndash R=(0964plusmn0008+0011-0009)












PDG 2004







]21[192 3

52

KmG







Vus measurements





unitarity





KLOE Kl 3

KLOE K2

copy A Antonelli

Vus some more




Ke4 results





K+rarrπ0π0eν










1-loop rescattering

2-loop rescattering











NA482




KLOE interference

















K+ + 8middot10-11 (at 7)147+130

ndash089 middot 10-

10 (BNL E787+E949)






KL 0ℓ+ℓ-




BR(KL 0+-) lt 3810-10





NA481 KS 0ℓ+ℓ-



BR = (58 +28-23 plusmn08) times10-9


-012 (accid)BR = (28 +15


KS 0e+e- KS 0μ+μ-


NA481 preliminary

NA481 preliminary


KL 0ℓ+ℓ-






Krarr in the SM




W W

s

id

Vis Vid

e

i=uct

W

Z

VisV

idds i

11

20

2410

10)1108(

)(1001)(

AKB

11

2

5

100

10)4082(

)()Im(

1022)(

t

tdtsL xX

VVKB


K

ε εrsquo




Ke3 KL 0

Height

Im(λt )



10301890 10471)(

KBR









K+ +




















Appendixes





J(ππ) = ℓ(ππ) = 0 P(ππ) = +1 C(ππ) = +1



ℓL



SLti

SLLSti

LS

tL

tS

Lti

LSti

S

KKeaaKKeaa

eaea

KeaKea

SLLS

LS

LS

)()(

22

f LSf

fLS KfA

dt

d 2

2

TUnitarity requires

and therefore


f Sff

fS

fLSLLS

f

fLLf

fSS

fKAAKKmi

AA

)(2)(

22


2

22

2

222

0604

mKK

AAAA

LS

LSLS

f

fSf

fLf

fS

fL



SLS KKmi 21




)()( 0000

SSS KK











K vs B







200

200

200

200

KeKKeK

KeKKeKA

iHtiHt

iHtiHt

T


20

20

20

20

KefKef

KefKefA

iHtCP

iHtCP

iHtCP

iHtCP

CP

200

200

200

200

KeKKeK

KeKKeKA

iHtiHt

iHtiHt

CPT




CPLEAR experiment

(CERN 1990-96)






tf

ft

f

iHtCP

iHtCP

iHtCP

iHtCP

CPLS

LS

e

mte

KefKef

KefKefA

)(2

2)(

20

20

20

20

1

)cos(2)Re(2

π+π

minus

π0π0

π+π minusπ0

π0π0π0

CPLEARAsymmetrie

s


Rate difference


Measure η





Kaon factories




pppp 2

1SLSL KKKKi




[Lipkin (1968)]

EPR correlation


DAΦNE (Frascati)


DAΦNE (Frascati)


MeVc)









p = 127 MeVcλ = 95 cm

KLKS 106 pb-1




KLOE physics




















p

Target

Collimator



Dump

Tagging Separation

Charged beam




Buthellip



rarr Small in SM


2π (εrsquoε)

3π (Ag)


ν


π0

Kplusmn rarr 3π




π1

π2

π3

K


Kinematics



2


2

Matrix element

|M(uv)|2 ~ 1 + gu + hu2 + kv2







KminusK+








10-6

NA482 OKA

10-5

10-4

10-3

10-2

SMSM

SUSYSUSYNewNew

physicsphysics



|Ag|

bull Ag ~ 10minus5


SUSY New Physics

THEORY



C

N



=Ag



54 60 66

1cm

50 100

10 cm

200 250 m





~11012

ppp

K+

Kminus



always in vacuum

focusing beams

BM

z

magnet

vacuum tank

not to scale

K+

K


pipe

0ordm prodangle






ZZ

XXYY

JuraJura

SaleveSaleve

Beam line K+ Up


B+

Bminus






Spectrometer field

K+

Kminus

Reverse each day

Reverse each week


|V| even pion

in beam pipe


KK+ +

KK



No significant

background





-15 -10 -05 0 05 10 u

0

-1

-2

1

2

3

Dalitz plot



EM calorimeter only






2003 result in PLB 634 (2006) 474




2003 result in PLB 638 (2006) 22


excluded


OKA at Protvino





(in preparation)


More CP violation


Indirect

Direct

CP violation

parameters

(2005)


(A) KS decays


CPV in KS decays




000000

000

000 )(

)(

L

S

KA




S+KL

KL




000 000 00

1( )2 ( 2

0

)

( )


tt

NEARf E t



)()()( 00

00

EKNEKN

EKNEKNED

(incoherent

production)



Assuming CPT





N3

20

40

60

00

4 62


No CPV seen yet

























PT() = (-17 23 11) 10-

3

Im = (-53 71 36) 10-3




Im = (-53 71 36) 10-3








ppp

ppp

)0()0(

)0()0(

NN

NNA


Radiative decays








211221 )()(


IB DE

p1 p1

p2p2

q q







)(

)(

S

L

KA

violatingCPKA




KL π+πminus






IB

M1 DE




KL itself





KL ee


BR = (308 020) 10minus7



E1M1 lt 004 (90 CL)



φ




KS ee

No asymmetry for KS

as expected

BR = (471 032) 10-

5

AΦ = (05 43)






IBEE

dEA

)tan( 0


Kplusmn π+π0γ

)730810672()(

)250350353()(

800

800

syststatMeVT

syststatMeVT

INTFrac

DEFrac







KL π+πndashπ0γ















)(

)2030(

3

3

e

ee

K

MeVEKR





bull 6M Ke3 events


ndash R=(0964plusmn0008+0011-0009)












PDG 2004







]21[192 3

52

KmG







Vus measurements





unitarity





KLOE Kl 3

KLOE K2

copy A Antonelli

Vus some more




Ke4 results





K+rarrπ0π0eν










1-loop rescattering

2-loop rescattering











NA482




KLOE interference

















K+ + 8middot10-11 (at 7)147+130

ndash089 middot 10-

10 (BNL E787+E949)






KL 0ℓ+ℓ-




BR(KL 0+-) lt 3810-10





NA481 KS 0ℓ+ℓ-



BR = (58 +28-23 plusmn08) times10-9


-012 (accid)BR = (28 +15


KS 0e+e- KS 0μ+μ-


NA481 preliminary

NA481 preliminary


KL 0ℓ+ℓ-






Krarr in the SM




W W

s

id

Vis Vid

e

i=uct

W

Z

VisV

idds i

11

20

2410

10)1108(

)(1001)(

AKB

11

2

5

100

10)4082(

)()Im(

1022)(

t

tdtsL xX

VVKB


K

ε εrsquo




Ke3 KL 0

Height

Im(λt )



10301890 10471)(

KBR









K+ +




















Appendixes





J(ππ) = ℓ(ππ) = 0 P(ππ) = +1 C(ππ) = +1



ℓL



SLti

SLLSti

LS

tL

tS

Lti

LSti

S

KKeaaKKeaa

eaea

KeaKea

SLLS

LS

LS

)()(

22

f LSf

fLS KfA

dt

d 2

2

TUnitarity requires

and therefore


f Sff

fS

fLSLLS

f

fLLf

fSS

fKAAKKmi

AA

)(2)(

22


2

22

2

222

0604

mKK

AAAA

LS

LSLS

f

fSf

fLf

fS

fL



SLS KKmi 21




)()( 0000

SSS KK








200

200

200

200

KeKKeK

KeKKeKA

iHtiHt

iHtiHt

T


20

20

20

20

KefKef

KefKefA

iHtCP

iHtCP

iHtCP

iHtCP

CP

200

200

200

200

KeKKeK

KeKKeKA

iHtiHt

iHtiHt

CPT




CPLEAR experiment

(CERN 1990-96)






tf

ft

f

iHtCP

iHtCP

iHtCP

iHtCP

CPLS

LS

e

mte

KefKef

KefKefA

)(2

2)(

20

20

20

20

1

)cos(2)Re(2

π+π

minus

π0π0

π+π minusπ0

π0π0π0

CPLEARAsymmetrie

s


Rate difference


Measure η





Kaon factories




pppp 2

1SLSL KKKKi




[Lipkin (1968)]

EPR correlation


DAΦNE (Frascati)


DAΦNE (Frascati)


MeVc)









p = 127 MeVcλ = 95 cm

KLKS 106 pb-1




KLOE physics




















p

Target

Collimator



Dump

Tagging Separation

Charged beam




Buthellip



rarr Small in SM


2π (εrsquoε)

3π (Ag)


ν


π0

Kplusmn rarr 3π




π1

π2

π3

K


Kinematics



2


2

Matrix element

|M(uv)|2 ~ 1 + gu + hu2 + kv2







KminusK+








10-6

NA482 OKA

10-5

10-4

10-3

10-2

SMSM

SUSYSUSYNewNew

physicsphysics



|Ag|

bull Ag ~ 10minus5


SUSY New Physics

THEORY



C

N



=Ag



54 60 66

1cm

50 100

10 cm

200 250 m





~11012

ppp

K+

Kminus



always in vacuum

focusing beams

BM

z

magnet

vacuum tank

not to scale

K+

K


pipe

0ordm prodangle






ZZ

XXYY

JuraJura

SaleveSaleve

Beam line K+ Up


B+

Bminus






Spectrometer field

K+

Kminus

Reverse each day

Reverse each week


|V| even pion

in beam pipe


KK+ +

KK



No significant

background





-15 -10 -05 0 05 10 u

0

-1

-2

1

2

3

Dalitz plot



EM calorimeter only






2003 result in PLB 634 (2006) 474




2003 result in PLB 638 (2006) 22


excluded


OKA at Protvino





(in preparation)


More CP violation


Indirect

Direct

CP violation

parameters

(2005)


(A) KS decays


CPV in KS decays




000000

000

000 )(

)(

L

S

KA




S+KL

KL




000 000 00

1( )2 ( 2

0

)

( )


tt

NEARf E t



)()()( 00

00

EKNEKN

EKNEKNED

(incoherent

production)



Assuming CPT





N3

20

40

60

00

4 62


No CPV seen yet

























PT() = (-17 23 11) 10-

3

Im = (-53 71 36) 10-3




Im = (-53 71 36) 10-3








ppp

ppp

)0()0(

)0()0(

NN

NNA


Radiative decays








211221 )()(


IB DE

p1 p1

p2p2

q q







)(

)(

S

L

KA

violatingCPKA




KL π+πminus






IB

M1 DE




KL itself





KL ee


BR = (308 020) 10minus7



E1M1 lt 004 (90 CL)



φ




KS ee

No asymmetry for KS

as expected

BR = (471 032) 10-

5

AΦ = (05 43)






IBEE

dEA

)tan( 0


Kplusmn π+π0γ

)730810672()(

)250350353()(

800

800

syststatMeVT

syststatMeVT

INTFrac

DEFrac







KL π+πndashπ0γ















)(

)2030(

3

3

e

ee

K

MeVEKR





bull 6M Ke3 events


ndash R=(0964plusmn0008+0011-0009)












PDG 2004







]21[192 3

52

KmG







Vus measurements





unitarity





KLOE Kl 3

KLOE K2

copy A Antonelli

Vus some more




Ke4 results





K+rarrπ0π0eν










1-loop rescattering

2-loop rescattering











NA482




KLOE interference

















K+ + 8middot10-11 (at 7)147+130

ndash089 middot 10-

10 (BNL E787+E949)






KL 0ℓ+ℓ-




BR(KL 0+-) lt 3810-10





NA481 KS 0ℓ+ℓ-



BR = (58 +28-23 plusmn08) times10-9


-012 (accid)BR = (28 +15


KS 0e+e- KS 0μ+μ-


NA481 preliminary

NA481 preliminary


KL 0ℓ+ℓ-






Krarr in the SM




W W

s

id

Vis Vid

e

i=uct

W

Z

VisV

idds i

11

20

2410

10)1108(

)(1001)(

AKB

11

2

5

100

10)4082(

)()Im(

1022)(

t

tdtsL xX

VVKB


K

ε εrsquo




Ke3 KL 0

Height

Im(λt )



10301890 10471)(

KBR









K+ +




















Appendixes





J(ππ) = ℓ(ππ) = 0 P(ππ) = +1 C(ππ) = +1



ℓL



SLti

SLLSti

LS

tL

tS

Lti

LSti

S

KKeaaKKeaa

eaea

KeaKea

SLLS

LS

LS

)()(

22

f LSf

fLS KfA

dt

d 2

2

TUnitarity requires

and therefore


f Sff

fS

fLSLLS

f

fLLf

fSS

fKAAKKmi

AA

)(2)(

22


2

22

2

222

0604

mKK

AAAA

LS

LSLS

f

fSf

fLf

fS

fL



SLS KKmi 21




)()( 0000

SSS KK





200

200

200

200

KeKKeK

KeKKeKA

iHtiHt

iHtiHt

T


20

20

20

20

KefKef

KefKefA

iHtCP

iHtCP

iHtCP

iHtCP

CP

200

200

200

200

KeKKeK

KeKKeKA

iHtiHt

iHtiHt

CPT




CPLEAR experiment

(CERN 1990-96)






tf

ft

f

iHtCP

iHtCP

iHtCP

iHtCP

CPLS

LS

e

mte

KefKef

KefKefA

)(2

2)(

20

20

20

20

1

)cos(2)Re(2

π+π

minus

π0π0

π+π minusπ0

π0π0π0

CPLEARAsymmetrie

s


Rate difference


Measure η





Kaon factories




pppp 2

1SLSL KKKKi




[Lipkin (1968)]

EPR correlation


DAΦNE (Frascati)


DAΦNE (Frascati)


MeVc)









p = 127 MeVcλ = 95 cm

KLKS 106 pb-1




KLOE physics




















p

Target

Collimator



Dump

Tagging Separation

Charged beam




Buthellip



rarr Small in SM


2π (εrsquoε)

3π (Ag)


ν


π0

Kplusmn rarr 3π




π1

π2

π3

K


Kinematics



2


2

Matrix element

|M(uv)|2 ~ 1 + gu + hu2 + kv2







KminusK+








10-6

NA482 OKA

10-5

10-4

10-3

10-2

SMSM

SUSYSUSYNewNew

physicsphysics



|Ag|

bull Ag ~ 10minus5


SUSY New Physics

THEORY



C

N



=Ag



54 60 66

1cm

50 100

10 cm

200 250 m





~11012

ppp

K+

Kminus



always in vacuum

focusing beams

BM

z

magnet

vacuum tank

not to scale

K+

K


pipe

0ordm prodangle






ZZ

XXYY

JuraJura

SaleveSaleve

Beam line K+ Up


B+

Bminus






Spectrometer field

K+

Kminus

Reverse each day

Reverse each week


|V| even pion

in beam pipe


KK+ +

KK



No significant

background





-15 -10 -05 0 05 10 u

0

-1

-2

1

2

3

Dalitz plot



EM calorimeter only






2003 result in PLB 634 (2006) 474




2003 result in PLB 638 (2006) 22


excluded


OKA at Protvino





(in preparation)


More CP violation


Indirect

Direct

CP violation

parameters

(2005)


(A) KS decays


CPV in KS decays




000000

000

000 )(

)(

L

S

KA




S+KL

KL




000 000 00

1( )2 ( 2

0

)

( )


tt

NEARf E t



)()()( 00

00

EKNEKN

EKNEKNED

(incoherent

production)



Assuming CPT





N3

20

40

60

00

4 62


No CPV seen yet

























PT() = (-17 23 11) 10-

3

Im = (-53 71 36) 10-3




Im = (-53 71 36) 10-3








ppp

ppp

)0()0(

)0()0(

NN

NNA


Radiative decays








211221 )()(


IB DE

p1 p1

p2p2

q q







)(

)(

S

L

KA

violatingCPKA




KL π+πminus






IB

M1 DE




KL itself





KL ee


BR = (308 020) 10minus7



E1M1 lt 004 (90 CL)



φ




KS ee

No asymmetry for KS

as expected

BR = (471 032) 10-

5

AΦ = (05 43)






IBEE

dEA

)tan( 0


Kplusmn π+π0γ

)730810672()(

)250350353()(

800

800

syststatMeVT

syststatMeVT

INTFrac

DEFrac







KL π+πndashπ0γ















)(

)2030(

3

3

e

ee

K

MeVEKR





bull 6M Ke3 events


ndash R=(0964plusmn0008+0011-0009)












PDG 2004







]21[192 3

52

KmG







Vus measurements





unitarity





KLOE Kl 3

KLOE K2

copy A Antonelli

Vus some more




Ke4 results





K+rarrπ0π0eν










1-loop rescattering

2-loop rescattering











NA482




KLOE interference

















K+ + 8middot10-11 (at 7)147+130

ndash089 middot 10-

10 (BNL E787+E949)






KL 0ℓ+ℓ-




BR(KL 0+-) lt 3810-10





NA481 KS 0ℓ+ℓ-



BR = (58 +28-23 plusmn08) times10-9


-012 (accid)BR = (28 +15


KS 0e+e- KS 0μ+μ-


NA481 preliminary

NA481 preliminary


KL 0ℓ+ℓ-






Krarr in the SM




W W

s

id

Vis Vid

e

i=uct

W

Z

VisV

idds i

11

20

2410

10)1108(

)(1001)(

AKB

11

2

5

100

10)4082(

)()Im(

1022)(

t

tdtsL xX

VVKB


K

ε εrsquo




Ke3 KL 0

Height

Im(λt )



10301890 10471)(

KBR









K+ +




















Appendixes





J(ππ) = ℓ(ππ) = 0 P(ππ) = +1 C(ππ) = +1



ℓL



SLti

SLLSti

LS

tL

tS

Lti

LSti

S

KKeaaKKeaa

eaea

KeaKea

SLLS

LS

LS

)()(

22

f LSf

fLS KfA

dt

d 2

2

TUnitarity requires

and therefore


f Sff

fS

fLSLLS

f

fLLf

fSS

fKAAKKmi

AA

)(2)(

22


2

22

2

222

0604

mKK

AAAA

LS

LSLS

f

fSf

fLf

fS

fL



SLS KKmi 21




)()( 0000

SSS KK



CPLEAR experiment

(CERN 1990-96)






tf

ft

f

iHtCP

iHtCP

iHtCP

iHtCP

CPLS

LS

e

mte

KefKef

KefKefA

)(2

2)(

20

20

20

20

1

)cos(2)Re(2

π+π

minus

π0π0

π+π minusπ0

π0π0π0

CPLEARAsymmetrie

s


Rate difference


Measure η





Kaon factories




pppp 2

1SLSL KKKKi




[Lipkin (1968)]

EPR correlation


DAΦNE (Frascati)


DAΦNE (Frascati)


MeVc)









p = 127 MeVcλ = 95 cm

KLKS 106 pb-1




KLOE physics




















p

Target

Collimator



Dump

Tagging Separation

Charged beam




Buthellip



rarr Small in SM


2π (εrsquoε)

3π (Ag)


ν


π0

Kplusmn rarr 3π




π1

π2

π3

K


Kinematics



2


2

Matrix element

|M(uv)|2 ~ 1 + gu + hu2 + kv2







KminusK+








10-6

NA482 OKA

10-5

10-4

10-3

10-2

SMSM

SUSYSUSYNewNew

physicsphysics



|Ag|

bull Ag ~ 10minus5


SUSY New Physics

THEORY



C

N



=Ag



54 60 66

1cm

50 100

10 cm

200 250 m





~11012

ppp

K+

Kminus



always in vacuum

focusing beams

BM

z

magnet

vacuum tank

not to scale

K+

K


pipe

0ordm prodangle






ZZ

XXYY

JuraJura

SaleveSaleve

Beam line K+ Up


B+

Bminus






Spectrometer field

K+

Kminus

Reverse each day

Reverse each week


|V| even pion

in beam pipe


KK+ +

KK



No significant

background





-15 -10 -05 0 05 10 u

0

-1

-2

1

2

3

Dalitz plot



EM calorimeter only






2003 result in PLB 634 (2006) 474




2003 result in PLB 638 (2006) 22


excluded


OKA at Protvino





(in preparation)


More CP violation


Indirect

Direct

CP violation

parameters

(2005)


(A) KS decays


CPV in KS decays




000000

000

000 )(

)(

L

S

KA




S+KL

KL




000 000 00

1( )2 ( 2

0

)

( )


tt

NEARf E t



)()()( 00

00

EKNEKN

EKNEKNED

(incoherent

production)



Assuming CPT





N3

20

40

60

00

4 62


No CPV seen yet

























PT() = (-17 23 11) 10-

3

Im = (-53 71 36) 10-3




Im = (-53 71 36) 10-3








ppp

ppp

)0()0(

)0()0(

NN

NNA


Radiative decays








211221 )()(


IB DE

p1 p1

p2p2

q q







)(

)(

S

L

KA

violatingCPKA




KL π+πminus






IB

M1 DE




KL itself





KL ee


BR = (308 020) 10minus7



E1M1 lt 004 (90 CL)



φ




KS ee

No asymmetry for KS

as expected

BR = (471 032) 10-

5

AΦ = (05 43)






IBEE

dEA

)tan( 0


Kplusmn π+π0γ

)730810672()(

)250350353()(

800

800

syststatMeVT

syststatMeVT

INTFrac

DEFrac







KL π+πndashπ0γ















)(

)2030(

3

3

e

ee

K

MeVEKR





bull 6M Ke3 events


ndash R=(0964plusmn0008+0011-0009)












PDG 2004







]21[192 3

52

KmG







Vus measurements





unitarity





KLOE Kl 3

KLOE K2

copy A Antonelli

Vus some more




Ke4 results





K+rarrπ0π0eν










1-loop rescattering

2-loop rescattering











NA482




KLOE interference

















K+ + 8middot10-11 (at 7)147+130

ndash089 middot 10-

10 (BNL E787+E949)






KL 0ℓ+ℓ-




BR(KL 0+-) lt 3810-10





NA481 KS 0ℓ+ℓ-



BR = (58 +28-23 plusmn08) times10-9


-012 (accid)BR = (28 +15


KS 0e+e- KS 0μ+μ-


NA481 preliminary

NA481 preliminary


KL 0ℓ+ℓ-






Krarr in the SM




W W

s

id

Vis Vid

e

i=uct

W

Z

VisV

idds i

11

20

2410

10)1108(

)(1001)(

AKB

11

2

5

100

10)4082(

)()Im(

1022)(

t

tdtsL xX

VVKB


K

ε εrsquo




Ke3 KL 0

Height

Im(λt )



10301890 10471)(

KBR









K+ +




















Appendixes





J(ππ) = ℓ(ππ) = 0 P(ππ) = +1 C(ππ) = +1



ℓL



SLti

SLLSti

LS

tL

tS

Lti

LSti

S

KKeaaKKeaa

eaea

KeaKea

SLLS

LS

LS

)()(

22

f LSf

fLS KfA

dt

d 2

2

TUnitarity requires

and therefore


f Sff

fS

fLSLLS

f

fLLf

fSS

fKAAKKmi

AA

)(2)(

22


2

22

2

222

0604

mKK

AAAA

LS

LSLS

f

fSf

fLf

fS

fL



SLS KKmi 21




)()( 0000

SSS KK



tf

ft

f

iHtCP

iHtCP

iHtCP

iHtCP

CPLS

LS

e

mte

KefKef

KefKefA

)(2

2)(

20

20

20

20

1

)cos(2)Re(2

π+π

minus

π0π0

π+π minusπ0

π0π0π0

CPLEARAsymmetrie

s


Rate difference


Measure η





Kaon factories




pppp 2

1SLSL KKKKi




[Lipkin (1968)]

EPR correlation


DAΦNE (Frascati)


DAΦNE (Frascati)


MeVc)









p = 127 MeVcλ = 95 cm

KLKS 106 pb-1




KLOE physics




















p

Target

Collimator



Dump

Tagging Separation

Charged beam




Buthellip



rarr Small in SM


2π (εrsquoε)

3π (Ag)


ν


π0

Kplusmn rarr 3π




π1

π2

π3

K


Kinematics



2


2

Matrix element

|M(uv)|2 ~ 1 + gu + hu2 + kv2







KminusK+








10-6

NA482 OKA

10-5

10-4

10-3

10-2

SMSM

SUSYSUSYNewNew

physicsphysics



|Ag|

bull Ag ~ 10minus5


SUSY New Physics

THEORY



C

N



=Ag



54 60 66

1cm

50 100

10 cm

200 250 m





~11012

ppp

K+

Kminus



always in vacuum

focusing beams

BM

z

magnet

vacuum tank

not to scale

K+

K


pipe

0ordm prodangle






ZZ

XXYY

JuraJura

SaleveSaleve

Beam line K+ Up


B+

Bminus






Spectrometer field

K+

Kminus

Reverse each day

Reverse each week


|V| even pion

in beam pipe


KK+ +

KK



No significant

background





-15 -10 -05 0 05 10 u

0

-1

-2

1

2

3

Dalitz plot



EM calorimeter only






2003 result in PLB 634 (2006) 474




2003 result in PLB 638 (2006) 22


excluded


OKA at Protvino





(in preparation)


More CP violation


Indirect

Direct

CP violation

parameters

(2005)


(A) KS decays


CPV in KS decays




000000

000

000 )(

)(

L

S

KA




S+KL

KL




000 000 00

1( )2 ( 2

0

)

( )


tt

NEARf E t



)()()( 00

00

EKNEKN

EKNEKNED

(incoherent

production)



Assuming CPT





N3

20

40

60

00

4 62


No CPV seen yet

























PT() = (-17 23 11) 10-

3

Im = (-53 71 36) 10-3




Im = (-53 71 36) 10-3








ppp

ppp

)0()0(

)0()0(

NN

NNA


Radiative decays








211221 )()(


IB DE

p1 p1

p2p2

q q







)(

)(

S

L

KA

violatingCPKA




KL π+πminus






IB

M1 DE




KL itself





KL ee


BR = (308 020) 10minus7



E1M1 lt 004 (90 CL)



φ




KS ee

No asymmetry for KS

as expected

BR = (471 032) 10-

5

AΦ = (05 43)






IBEE

dEA

)tan( 0


Kplusmn π+π0γ

)730810672()(

)250350353()(

800

800

syststatMeVT

syststatMeVT

INTFrac

DEFrac







KL π+πndashπ0γ















)(

)2030(

3

3

e

ee

K

MeVEKR





bull 6M Ke3 events


ndash R=(0964plusmn0008+0011-0009)












PDG 2004







]21[192 3

52

KmG







Vus measurements





unitarity





KLOE Kl 3

KLOE K2

copy A Antonelli

Vus some more




Ke4 results





K+rarrπ0π0eν










1-loop rescattering

2-loop rescattering











NA482




KLOE interference

















K+ + 8middot10-11 (at 7)147+130

ndash089 middot 10-

10 (BNL E787+E949)






KL 0ℓ+ℓ-




BR(KL 0+-) lt 3810-10





NA481 KS 0ℓ+ℓ-



BR = (58 +28-23 plusmn08) times10-9


-012 (accid)BR = (28 +15


KS 0e+e- KS 0μ+μ-


NA481 preliminary

NA481 preliminary


KL 0ℓ+ℓ-






Krarr in the SM




W W

s

id

Vis Vid

e

i=uct

W

Z

VisV

idds i

11

20

2410

10)1108(

)(1001)(

AKB

11

2

5

100

10)4082(

)()Im(

1022)(

t

tdtsL xX

VVKB


K

ε εrsquo




Ke3 KL 0

Height

Im(λt )



10301890 10471)(

KBR









K+ +




















Appendixes





J(ππ) = ℓ(ππ) = 0 P(ππ) = +1 C(ππ) = +1



ℓL



SLti

SLLSti

LS

tL

tS

Lti

LSti

S

KKeaaKKeaa

eaea

KeaKea

SLLS

LS

LS

)()(

22

f LSf

fLS KfA

dt

d 2

2

TUnitarity requires

and therefore


f Sff

fS

fLSLLS

f

fLLf

fSS

fKAAKKmi

AA

)(2)(

22


2

22

2

222

0604

mKK

AAAA

LS

LSLS

f

fSf

fLf

fS

fL



SLS KKmi 21




)()( 0000

SSS KK






Kaon factories




pppp 2

1SLSL KKKKi




[Lipkin (1968)]

EPR correlation


DAΦNE (Frascati)


DAΦNE (Frascati)


MeVc)









p = 127 MeVcλ = 95 cm

KLKS 106 pb-1




KLOE physics




















p

Target

Collimator



Dump

Tagging Separation

Charged beam




Buthellip



rarr Small in SM


2π (εrsquoε)

3π (Ag)


ν


π0

Kplusmn rarr 3π




π1

π2

π3

K


Kinematics



2


2

Matrix element

|M(uv)|2 ~ 1 + gu + hu2 + kv2







KminusK+








10-6

NA482 OKA

10-5

10-4

10-3

10-2

SMSM

SUSYSUSYNewNew

physicsphysics



|Ag|

bull Ag ~ 10minus5


SUSY New Physics

THEORY



C

N



=Ag



54 60 66

1cm

50 100

10 cm

200 250 m





~11012

ppp

K+

Kminus



always in vacuum

focusing beams

BM

z

magnet

vacuum tank

not to scale

K+

K


pipe

0ordm prodangle






ZZ

XXYY

JuraJura

SaleveSaleve

Beam line K+ Up


B+

Bminus






Spectrometer field

K+

Kminus

Reverse each day

Reverse each week


|V| even pion

in beam pipe


KK+ +

KK



No significant

background





-15 -10 -05 0 05 10 u

0

-1

-2

1

2

3

Dalitz plot



EM calorimeter only






2003 result in PLB 634 (2006) 474




2003 result in PLB 638 (2006) 22


excluded


OKA at Protvino





(in preparation)


More CP violation


Indirect

Direct

CP violation

parameters

(2005)


(A) KS decays


CPV in KS decays




000000

000

000 )(

)(

L

S

KA




S+KL

KL




000 000 00

1( )2 ( 2

0

)

( )


tt

NEARf E t



)()()( 00

00

EKNEKN

EKNEKNED

(incoherent

production)



Assuming CPT





N3

20

40

60

00

4 62


No CPV seen yet

























PT() = (-17 23 11) 10-

3

Im = (-53 71 36) 10-3




Im = (-53 71 36) 10-3








ppp

ppp

)0()0(

)0()0(

NN

NNA


Radiative decays








211221 )()(


IB DE

p1 p1

p2p2

q q







)(

)(

S

L

KA

violatingCPKA




KL π+πminus






IB

M1 DE




KL itself





KL ee


BR = (308 020) 10minus7



E1M1 lt 004 (90 CL)



φ




KS ee

No asymmetry for KS

as expected

BR = (471 032) 10-

5

AΦ = (05 43)






IBEE

dEA

)tan( 0


Kplusmn π+π0γ

)730810672()(

)250350353()(

800

800

syststatMeVT

syststatMeVT

INTFrac

DEFrac







KL π+πndashπ0γ















)(

)2030(

3

3

e

ee

K

MeVEKR





bull 6M Ke3 events


ndash R=(0964plusmn0008+0011-0009)












PDG 2004







]21[192 3

52

KmG







Vus measurements





unitarity





KLOE Kl 3

KLOE K2

copy A Antonelli

Vus some more




Ke4 results





K+rarrπ0π0eν










1-loop rescattering

2-loop rescattering











NA482




KLOE interference

















K+ + 8middot10-11 (at 7)147+130

ndash089 middot 10-

10 (BNL E787+E949)






KL 0ℓ+ℓ-




BR(KL 0+-) lt 3810-10





NA481 KS 0ℓ+ℓ-



BR = (58 +28-23 plusmn08) times10-9


-012 (accid)BR = (28 +15


KS 0e+e- KS 0μ+μ-


NA481 preliminary

NA481 preliminary


KL 0ℓ+ℓ-






Krarr in the SM




W W

s

id

Vis Vid

e

i=uct

W

Z

VisV

idds i

11

20

2410

10)1108(

)(1001)(

AKB

11

2

5

100

10)4082(

)()Im(

1022)(

t

tdtsL xX

VVKB


K

ε εrsquo




Ke3 KL 0

Height

Im(λt )



10301890 10471)(

KBR









K+ +




















Appendixes





J(ππ) = ℓ(ππ) = 0 P(ππ) = +1 C(ππ) = +1



ℓL



SLti

SLLSti

LS

tL

tS

Lti

LSti

S

KKeaaKKeaa

eaea

KeaKea

SLLS

LS

LS

)()(

22

f LSf

fLS KfA

dt

d 2

2

TUnitarity requires

and therefore


f Sff

fS

fLSLLS

f

fLLf

fSS

fKAAKKmi

AA

)(2)(

22


2

22

2

222

0604

mKK

AAAA

LS

LSLS

f

fSf

fLf

fS

fL



SLS KKmi 21




)()( 0000

SSS KK



Kaon factories




pppp 2

1SLSL KKKKi




[Lipkin (1968)]

EPR correlation


DAΦNE (Frascati)


DAΦNE (Frascati)


MeVc)









p = 127 MeVcλ = 95 cm

KLKS 106 pb-1




KLOE physics




















p

Target

Collimator



Dump

Tagging Separation

Charged beam




Buthellip



rarr Small in SM


2π (εrsquoε)

3π (Ag)


ν


π0

Kplusmn rarr 3π




π1

π2

π3

K


Kinematics



2


2

Matrix element

|M(uv)|2 ~ 1 + gu + hu2 + kv2







KminusK+








10-6

NA482 OKA

10-5

10-4

10-3

10-2

SMSM

SUSYSUSYNewNew

physicsphysics



|Ag|

bull Ag ~ 10minus5


SUSY New Physics

THEORY



C

N



=Ag



54 60 66

1cm

50 100

10 cm

200 250 m





~11012

ppp

K+

Kminus



always in vacuum

focusing beams

BM

z

magnet

vacuum tank

not to scale

K+

K


pipe

0ordm prodangle






ZZ

XXYY

JuraJura

SaleveSaleve

Beam line K+ Up


B+

Bminus






Spectrometer field

K+

Kminus

Reverse each day

Reverse each week


|V| even pion

in beam pipe


KK+ +

KK



No significant

background





-15 -10 -05 0 05 10 u

0

-1

-2

1

2

3

Dalitz plot



EM calorimeter only






2003 result in PLB 634 (2006) 474




2003 result in PLB 638 (2006) 22


excluded


OKA at Protvino





(in preparation)


More CP violation


Indirect

Direct

CP violation

parameters

(2005)


(A) KS decays


CPV in KS decays




000000

000

000 )(

)(

L

S

KA




S+KL

KL




000 000 00

1( )2 ( 2

0

)

( )


tt

NEARf E t



)()()( 00

00

EKNEKN

EKNEKNED

(incoherent

production)



Assuming CPT





N3

20

40

60

00

4 62


No CPV seen yet

























PT() = (-17 23 11) 10-

3

Im = (-53 71 36) 10-3




Im = (-53 71 36) 10-3








ppp

ppp

)0()0(

)0()0(

NN

NNA


Radiative decays








211221 )()(


IB DE

p1 p1

p2p2

q q







)(

)(

S

L

KA

violatingCPKA




KL π+πminus






IB

M1 DE




KL itself





KL ee


BR = (308 020) 10minus7



E1M1 lt 004 (90 CL)



φ




KS ee

No asymmetry for KS

as expected

BR = (471 032) 10-

5

AΦ = (05 43)






IBEE

dEA

)tan( 0


Kplusmn π+π0γ

)730810672()(

)250350353()(

800

800

syststatMeVT

syststatMeVT

INTFrac

DEFrac







KL π+πndashπ0γ















)(

)2030(

3

3

e

ee

K

MeVEKR





bull 6M Ke3 events


ndash R=(0964plusmn0008+0011-0009)












PDG 2004







]21[192 3

52

KmG







Vus measurements





unitarity





KLOE Kl 3

KLOE K2

copy A Antonelli

Vus some more




Ke4 results





K+rarrπ0π0eν










1-loop rescattering

2-loop rescattering











NA482




KLOE interference

















K+ + 8middot10-11 (at 7)147+130

ndash089 middot 10-

10 (BNL E787+E949)






KL 0ℓ+ℓ-




BR(KL 0+-) lt 3810-10





NA481 KS 0ℓ+ℓ-



BR = (58 +28-23 plusmn08) times10-9


-012 (accid)BR = (28 +15


KS 0e+e- KS 0μ+μ-


NA481 preliminary

NA481 preliminary


KL 0ℓ+ℓ-






Krarr in the SM




W W

s

id

Vis Vid

e

i=uct

W

Z

VisV

idds i

11

20

2410

10)1108(

)(1001)(

AKB

11

2

5

100

10)4082(

)()Im(

1022)(

t

tdtsL xX

VVKB


K

ε εrsquo




Ke3 KL 0

Height

Im(λt )



10301890 10471)(

KBR









K+ +




















Appendixes





J(ππ) = ℓ(ππ) = 0 P(ππ) = +1 C(ππ) = +1



ℓL



SLti

SLLSti

LS

tL

tS

Lti

LSti

S

KKeaaKKeaa

eaea

KeaKea

SLLS

LS

LS

)()(

22

f LSf

fLS KfA

dt

d 2

2

TUnitarity requires

and therefore


f Sff

fS

fLSLLS

f

fLLf

fSS

fKAAKKmi

AA

)(2)(

22


2

22

2

222

0604

mKK

AAAA

LS

LSLS

f

fSf

fLf

fS

fL



SLS KKmi 21




)()( 0000

SSS KK



DAΦNE (Frascati)


DAΦNE (Frascati)


MeVc)









p = 127 MeVcλ = 95 cm

KLKS 106 pb-1




KLOE physics




















p

Target

Collimator



Dump

Tagging Separation

Charged beam




Buthellip



rarr Small in SM


2π (εrsquoε)

3π (Ag)


ν


π0

Kplusmn rarr 3π




π1

π2

π3

K


Kinematics



2


2

Matrix element

|M(uv)|2 ~ 1 + gu + hu2 + kv2







KminusK+








10-6

NA482 OKA

10-5

10-4

10-3

10-2

SMSM

SUSYSUSYNewNew

physicsphysics



|Ag|

bull Ag ~ 10minus5


SUSY New Physics

THEORY



C

N



=Ag



54 60 66

1cm

50 100

10 cm

200 250 m





~11012

ppp

K+

Kminus



always in vacuum

focusing beams

BM

z

magnet

vacuum tank

not to scale

K+

K


pipe

0ordm prodangle






ZZ

XXYY

JuraJura

SaleveSaleve

Beam line K+ Up


B+

Bminus






Spectrometer field

K+

Kminus

Reverse each day

Reverse each week


|V| even pion

in beam pipe


KK+ +

KK



No significant

background





-15 -10 -05 0 05 10 u

0

-1

-2

1

2

3

Dalitz plot



EM calorimeter only






2003 result in PLB 634 (2006) 474




2003 result in PLB 638 (2006) 22


excluded


OKA at Protvino





(in preparation)


More CP violation


Indirect

Direct

CP violation

parameters

(2005)


(A) KS decays


CPV in KS decays




000000

000

000 )(

)(

L

S

KA




S+KL

KL




000 000 00

1( )2 ( 2

0

)

( )


tt

NEARf E t



)()()( 00

00

EKNEKN

EKNEKNED

(incoherent

production)



Assuming CPT





N3

20

40

60

00

4 62


No CPV seen yet

























PT() = (-17 23 11) 10-

3

Im = (-53 71 36) 10-3




Im = (-53 71 36) 10-3








ppp

ppp

)0()0(

)0()0(

NN

NNA


Radiative decays








211221 )()(


IB DE

p1 p1

p2p2

q q







)(

)(

S

L

KA

violatingCPKA




KL π+πminus






IB

M1 DE




KL itself





KL ee


BR = (308 020) 10minus7



E1M1 lt 004 (90 CL)



φ




KS ee

No asymmetry for KS

as expected

BR = (471 032) 10-

5

AΦ = (05 43)






IBEE

dEA

)tan( 0


Kplusmn π+π0γ

)730810672()(

)250350353()(

800

800

syststatMeVT

syststatMeVT

INTFrac

DEFrac







KL π+πndashπ0γ















)(

)2030(

3

3

e

ee

K

MeVEKR





bull 6M Ke3 events


ndash R=(0964plusmn0008+0011-0009)












PDG 2004







]21[192 3

52

KmG







Vus measurements





unitarity





KLOE Kl 3

KLOE K2

copy A Antonelli

Vus some more




Ke4 results





K+rarrπ0π0eν










1-loop rescattering

2-loop rescattering











NA482




KLOE interference

















K+ + 8middot10-11 (at 7)147+130

ndash089 middot 10-

10 (BNL E787+E949)






KL 0ℓ+ℓ-




BR(KL 0+-) lt 3810-10





NA481 KS 0ℓ+ℓ-



BR = (58 +28-23 plusmn08) times10-9


-012 (accid)BR = (28 +15


KS 0e+e- KS 0μ+μ-


NA481 preliminary

NA481 preliminary


KL 0ℓ+ℓ-






Krarr in the SM




W W

s

id

Vis Vid

e

i=uct

W

Z

VisV

idds i

11

20

2410

10)1108(

)(1001)(

AKB

11

2

5

100

10)4082(

)()Im(

1022)(

t

tdtsL xX

VVKB


K

ε εrsquo




Ke3 KL 0

Height

Im(λt )



10301890 10471)(

KBR









K+ +




















Appendixes





J(ππ) = ℓ(ππ) = 0 P(ππ) = +1 C(ππ) = +1



ℓL



SLti

SLLSti

LS

tL

tS

Lti

LSti

S

KKeaaKKeaa

eaea

KeaKea

SLLS

LS

LS

)()(

22

f LSf

fLS KfA

dt

d 2

2

TUnitarity requires

and therefore


f Sff

fS

fLSLLS

f

fLLf

fSS

fKAAKKmi

AA

)(2)(

22


2

22

2

222

0604

mKK

AAAA

LS

LSLS

f

fSf

fLf

fS

fL



SLS KKmi 21




)()( 0000

SSS KK



DAΦNE (Frascati)


MeVc)









p = 127 MeVcλ = 95 cm

KLKS 106 pb-1




KLOE physics




















p

Target

Collimator



Dump

Tagging Separation

Charged beam




Buthellip



rarr Small in SM


2π (εrsquoε)

3π (Ag)


ν


π0

Kplusmn rarr 3π




π1

π2

π3

K


Kinematics



2


2

Matrix element

|M(uv)|2 ~ 1 + gu + hu2 + kv2







KminusK+








10-6

NA482 OKA

10-5

10-4

10-3

10-2

SMSM

SUSYSUSYNewNew

physicsphysics



|Ag|

bull Ag ~ 10minus5


SUSY New Physics

THEORY



C

N



=Ag



54 60 66

1cm

50 100

10 cm

200 250 m





~11012

ppp

K+

Kminus



always in vacuum

focusing beams

BM

z

magnet

vacuum tank

not to scale

K+

K


pipe

0ordm prodangle






ZZ

XXYY

JuraJura

SaleveSaleve

Beam line K+ Up


B+

Bminus






Spectrometer field

K+

Kminus

Reverse each day

Reverse each week


|V| even pion

in beam pipe


KK+ +

KK



No significant

background





-15 -10 -05 0 05 10 u

0

-1

-2

1

2

3

Dalitz plot



EM calorimeter only






2003 result in PLB 634 (2006) 474




2003 result in PLB 638 (2006) 22


excluded


OKA at Protvino





(in preparation)


More CP violation


Indirect

Direct

CP violation

parameters

(2005)


(A) KS decays


CPV in KS decays




000000

000

000 )(

)(

L

S

KA




S+KL

KL




000 000 00

1( )2 ( 2

0

)

( )


tt

NEARf E t



)()()( 00

00

EKNEKN

EKNEKNED

(incoherent

production)



Assuming CPT





N3

20

40

60

00

4 62


No CPV seen yet

























PT() = (-17 23 11) 10-

3

Im = (-53 71 36) 10-3




Im = (-53 71 36) 10-3








ppp

ppp

)0()0(

)0()0(

NN

NNA


Radiative decays








211221 )()(


IB DE

p1 p1

p2p2

q q







)(

)(

S

L

KA

violatingCPKA




KL π+πminus






IB

M1 DE




KL itself





KL ee


BR = (308 020) 10minus7



E1M1 lt 004 (90 CL)



φ




KS ee

No asymmetry for KS

as expected

BR = (471 032) 10-

5

AΦ = (05 43)






IBEE

dEA

)tan( 0


Kplusmn π+π0γ

)730810672()(

)250350353()(

800

800

syststatMeVT

syststatMeVT

INTFrac

DEFrac







KL π+πndashπ0γ















)(

)2030(

3

3

e

ee

K

MeVEKR





bull 6M Ke3 events


ndash R=(0964plusmn0008+0011-0009)












PDG 2004







]21[192 3

52

KmG







Vus measurements





unitarity





KLOE Kl 3

KLOE K2

copy A Antonelli

Vus some more




Ke4 results





K+rarrπ0π0eν










1-loop rescattering

2-loop rescattering











NA482




KLOE interference

















K+ + 8middot10-11 (at 7)147+130

ndash089 middot 10-

10 (BNL E787+E949)






KL 0ℓ+ℓ-




BR(KL 0+-) lt 3810-10





NA481 KS 0ℓ+ℓ-



BR = (58 +28-23 plusmn08) times10-9


-012 (accid)BR = (28 +15


KS 0e+e- KS 0μ+μ-


NA481 preliminary

NA481 preliminary


KL 0ℓ+ℓ-






Krarr in the SM




W W

s

id

Vis Vid

e

i=uct

W

Z

VisV

idds i

11

20

2410

10)1108(

)(1001)(

AKB

11

2

5

100

10)4082(

)()Im(

1022)(

t

tdtsL xX

VVKB


K

ε εrsquo




Ke3 KL 0

Height

Im(λt )



10301890 10471)(

KBR









K+ +




















Appendixes





J(ππ) = ℓ(ππ) = 0 P(ππ) = +1 C(ππ) = +1



ℓL



SLti

SLLSti

LS

tL

tS

Lti

LSti

S

KKeaaKKeaa

eaea

KeaKea

SLLS

LS

LS

)()(

22

f LSf

fLS KfA

dt

d 2

2

TUnitarity requires

and therefore


f Sff

fS

fLSLLS

f

fLLf

fSS

fKAAKKmi

AA

)(2)(

22


2

22

2

222

0604

mKK

AAAA

LS

LSLS

f

fSf

fLf

fS

fL



SLS KKmi 21




)()( 0000

SSS KK







p = 127 MeVcλ = 95 cm

KLKS 106 pb-1




KLOE physics




















p

Target

Collimator



Dump

Tagging Separation

Charged beam




Buthellip



rarr Small in SM


2π (εrsquoε)

3π (Ag)


ν


π0

Kplusmn rarr 3π




π1

π2

π3

K


Kinematics



2


2

Matrix element

|M(uv)|2 ~ 1 + gu + hu2 + kv2







KminusK+








10-6

NA482 OKA

10-5

10-4

10-3

10-2

SMSM

SUSYSUSYNewNew

physicsphysics



|Ag|

bull Ag ~ 10minus5


SUSY New Physics

THEORY



C

N



=Ag



54 60 66

1cm

50 100

10 cm

200 250 m





~11012

ppp

K+

Kminus



always in vacuum

focusing beams

BM

z

magnet

vacuum tank

not to scale

K+

K


pipe

0ordm prodangle






ZZ

XXYY

JuraJura

SaleveSaleve

Beam line K+ Up


B+

Bminus






Spectrometer field

K+

Kminus

Reverse each day

Reverse each week


|V| even pion

in beam pipe


KK+ +

KK



No significant

background





-15 -10 -05 0 05 10 u

0

-1

-2

1

2

3

Dalitz plot



EM calorimeter only






2003 result in PLB 634 (2006) 474




2003 result in PLB 638 (2006) 22


excluded


OKA at Protvino





(in preparation)


More CP violation


Indirect

Direct

CP violation

parameters

(2005)


(A) KS decays


CPV in KS decays




000000

000

000 )(

)(

L

S

KA




S+KL

KL




000 000 00

1( )2 ( 2

0

)

( )


tt

NEARf E t



)()()( 00

00

EKNEKN

EKNEKNED

(incoherent

production)



Assuming CPT





N3

20

40

60

00

4 62


No CPV seen yet

























PT() = (-17 23 11) 10-

3

Im = (-53 71 36) 10-3




Im = (-53 71 36) 10-3








ppp

ppp

)0()0(

)0()0(

NN

NNA


Radiative decays








211221 )()(


IB DE

p1 p1

p2p2

q q







)(

)(

S

L

KA

violatingCPKA




KL π+πminus






IB

M1 DE




KL itself





KL ee


BR = (308 020) 10minus7



E1M1 lt 004 (90 CL)



φ




KS ee

No asymmetry for KS

as expected

BR = (471 032) 10-

5

AΦ = (05 43)






IBEE

dEA

)tan( 0


Kplusmn π+π0γ

)730810672()(

)250350353()(

800

800

syststatMeVT

syststatMeVT

INTFrac

DEFrac







KL π+πndashπ0γ















)(

)2030(

3

3

e

ee

K

MeVEKR





bull 6M Ke3 events


ndash R=(0964plusmn0008+0011-0009)












PDG 2004







]21[192 3

52

KmG







Vus measurements





unitarity





KLOE Kl 3

KLOE K2

copy A Antonelli

Vus some more




Ke4 results





K+rarrπ0π0eν










1-loop rescattering

2-loop rescattering











NA482




KLOE interference

















K+ + 8middot10-11 (at 7)147+130

ndash089 middot 10-

10 (BNL E787+E949)






KL 0ℓ+ℓ-




BR(KL 0+-) lt 3810-10





NA481 KS 0ℓ+ℓ-



BR = (58 +28-23 plusmn08) times10-9


-012 (accid)BR = (28 +15


KS 0e+e- KS 0μ+μ-


NA481 preliminary

NA481 preliminary


KL 0ℓ+ℓ-






Krarr in the SM




W W

s

id

Vis Vid

e

i=uct

W

Z

VisV

idds i

11

20

2410

10)1108(

)(1001)(

AKB

11

2

5

100

10)4082(

)()Im(

1022)(

t

tdtsL xX

VVKB


K

ε εrsquo




Ke3 KL 0

Height

Im(λt )



10301890 10471)(

KBR









K+ +




















Appendixes





J(ππ) = ℓ(ππ) = 0 P(ππ) = +1 C(ππ) = +1



ℓL



SLti

SLLSti

LS

tL

tS

Lti

LSti

S

KKeaaKKeaa

eaea

KeaKea

SLLS

LS

LS

)()(

22

f LSf

fLS KfA

dt

d 2

2

TUnitarity requires

and therefore


f Sff

fS

fLSLLS

f

fLLf

fSS

fKAAKKmi

AA

)(2)(

22


2

22

2

222

0604

mKK

AAAA

LS

LSLS

f

fSf

fLf

fS

fL



SLS KKmi 21




)()( 0000

SSS KK



KLOE physics




















p

Target

Collimator



Dump

Tagging Separation

Charged beam




Buthellip



rarr Small in SM


2π (εrsquoε)

3π (Ag)


ν


π0

Kplusmn rarr 3π




π1

π2

π3

K


Kinematics



2


2

Matrix element

|M(uv)|2 ~ 1 + gu + hu2 + kv2







KminusK+








10-6

NA482 OKA

10-5

10-4

10-3

10-2

SMSM

SUSYSUSYNewNew

physicsphysics



|Ag|

bull Ag ~ 10minus5


SUSY New Physics

THEORY



C

N



=Ag



54 60 66

1cm

50 100

10 cm

200 250 m





~11012

ppp

K+

Kminus



always in vacuum

focusing beams

BM

z

magnet

vacuum tank

not to scale

K+

K


pipe

0ordm prodangle






ZZ

XXYY

JuraJura

SaleveSaleve

Beam line K+ Up


B+

Bminus






Spectrometer field

K+

Kminus

Reverse each day

Reverse each week


|V| even pion

in beam pipe


KK+ +

KK



No significant

background





-15 -10 -05 0 05 10 u

0

-1

-2

1

2

3

Dalitz plot



EM calorimeter only






2003 result in PLB 634 (2006) 474




2003 result in PLB 638 (2006) 22


excluded


OKA at Protvino





(in preparation)


More CP violation


Indirect

Direct

CP violation

parameters

(2005)


(A) KS decays


CPV in KS decays




000000

000

000 )(

)(

L

S

KA




S+KL

KL




000 000 00

1( )2 ( 2

0

)

( )


tt

NEARf E t



)()()( 00

00

EKNEKN

EKNEKNED

(incoherent

production)



Assuming CPT





N3

20

40

60

00

4 62


No CPV seen yet

























PT() = (-17 23 11) 10-

3

Im = (-53 71 36) 10-3




Im = (-53 71 36) 10-3








ppp

ppp

)0()0(

)0()0(

NN

NNA


Radiative decays








211221 )()(


IB DE

p1 p1

p2p2

q q







)(

)(

S

L

KA

violatingCPKA




KL π+πminus






IB

M1 DE




KL itself





KL ee


BR = (308 020) 10minus7



E1M1 lt 004 (90 CL)



φ




KS ee

No asymmetry for KS

as expected

BR = (471 032) 10-

5

AΦ = (05 43)






IBEE

dEA

)tan( 0


Kplusmn π+π0γ

)730810672()(

)250350353()(

800

800

syststatMeVT

syststatMeVT

INTFrac

DEFrac







KL π+πndashπ0γ















)(

)2030(

3

3

e

ee

K

MeVEKR





bull 6M Ke3 events


ndash R=(0964plusmn0008+0011-0009)












PDG 2004







]21[192 3

52

KmG







Vus measurements





unitarity





KLOE Kl 3

KLOE K2

copy A Antonelli

Vus some more




Ke4 results





K+rarrπ0π0eν










1-loop rescattering

2-loop rescattering











NA482




KLOE interference

















K+ + 8middot10-11 (at 7)147+130

ndash089 middot 10-

10 (BNL E787+E949)






KL 0ℓ+ℓ-




BR(KL 0+-) lt 3810-10





NA481 KS 0ℓ+ℓ-



BR = (58 +28-23 plusmn08) times10-9


-012 (accid)BR = (28 +15


KS 0e+e- KS 0μ+μ-


NA481 preliminary

NA481 preliminary


KL 0ℓ+ℓ-






Krarr in the SM




W W

s

id

Vis Vid

e

i=uct

W

Z

VisV

idds i

11

20

2410

10)1108(

)(1001)(

AKB

11

2

5

100

10)4082(

)()Im(

1022)(

t

tdtsL xX

VVKB


K

ε εrsquo




Ke3 KL 0

Height

Im(λt )



10301890 10471)(

KBR









K+ +




















Appendixes





J(ππ) = ℓ(ππ) = 0 P(ππ) = +1 C(ππ) = +1



ℓL



SLti

SLLSti

LS

tL

tS

Lti

LSti

S

KKeaaKKeaa

eaea

KeaKea

SLLS

LS

LS

)()(

22

f LSf

fLS KfA

dt

d 2

2

TUnitarity requires

and therefore


f Sff

fS

fLSLLS

f

fLLf

fSS

fKAAKKmi

AA

)(2)(

22


2

22

2

222

0604

mKK

AAAA

LS

LSLS

f

fSf

fLf

fS

fL



SLS KKmi 21




)()( 0000

SSS KK















p

Target

Collimator



Dump

Tagging Separation

Charged beam




Buthellip



rarr Small in SM


2π (εrsquoε)

3π (Ag)


ν


π0

Kplusmn rarr 3π




π1

π2

π3

K


Kinematics



2


2

Matrix element

|M(uv)|2 ~ 1 + gu + hu2 + kv2







KminusK+








10-6

NA482 OKA

10-5

10-4

10-3

10-2

SMSM

SUSYSUSYNewNew

physicsphysics



|Ag|

bull Ag ~ 10minus5


SUSY New Physics

THEORY



C

N



=Ag



54 60 66

1cm

50 100

10 cm

200 250 m





~11012

ppp

K+

Kminus



always in vacuum

focusing beams

BM

z

magnet

vacuum tank

not to scale

K+

K


pipe

0ordm prodangle






ZZ

XXYY

JuraJura

SaleveSaleve

Beam line K+ Up


B+

Bminus






Spectrometer field

K+

Kminus

Reverse each day

Reverse each week


|V| even pion

in beam pipe


KK+ +

KK



No significant

background





-15 -10 -05 0 05 10 u

0

-1

-2

1

2

3

Dalitz plot



EM calorimeter only






2003 result in PLB 634 (2006) 474




2003 result in PLB 638 (2006) 22


excluded


OKA at Protvino





(in preparation)


More CP violation


Indirect

Direct

CP violation

parameters

(2005)


(A) KS decays


CPV in KS decays




000000

000

000 )(

)(

L

S

KA




S+KL

KL




000 000 00

1( )2 ( 2

0

)

( )


tt

NEARf E t



)()()( 00

00

EKNEKN

EKNEKNED

(incoherent

production)



Assuming CPT





N3

20

40

60

00

4 62


No CPV seen yet

























PT() = (-17 23 11) 10-

3

Im = (-53 71 36) 10-3




Im = (-53 71 36) 10-3








ppp

ppp

)0()0(

)0()0(

NN

NNA


Radiative decays








211221 )()(


IB DE

p1 p1

p2p2

q q







)(

)(

S

L

KA

violatingCPKA




KL π+πminus






IB

M1 DE




KL itself





KL ee


BR = (308 020) 10minus7



E1M1 lt 004 (90 CL)



φ




KS ee

No asymmetry for KS

as expected

BR = (471 032) 10-

5

AΦ = (05 43)






IBEE

dEA

)tan( 0


Kplusmn π+π0γ

)730810672()(

)250350353()(

800

800

syststatMeVT

syststatMeVT

INTFrac

DEFrac







KL π+πndashπ0γ















)(

)2030(

3

3

e

ee

K

MeVEKR





bull 6M Ke3 events


ndash R=(0964plusmn0008+0011-0009)












PDG 2004







]21[192 3

52

KmG







Vus measurements





unitarity





KLOE Kl 3

KLOE K2

copy A Antonelli

Vus some more




Ke4 results





K+rarrπ0π0eν










1-loop rescattering

2-loop rescattering











NA482




KLOE interference

















K+ + 8middot10-11 (at 7)147+130

ndash089 middot 10-

10 (BNL E787+E949)






KL 0ℓ+ℓ-




BR(KL 0+-) lt 3810-10





NA481 KS 0ℓ+ℓ-



BR = (58 +28-23 plusmn08) times10-9


-012 (accid)BR = (28 +15


KS 0e+e- KS 0μ+μ-


NA481 preliminary

NA481 preliminary


KL 0ℓ+ℓ-






Krarr in the SM




W W

s

id

Vis Vid

e

i=uct

W

Z

VisV

idds i

11

20

2410

10)1108(

)(1001)(

AKB

11

2

5

100

10)4082(

)()Im(

1022)(

t

tdtsL xX

VVKB


K

ε εrsquo




Ke3 KL 0

Height

Im(λt )



10301890 10471)(

KBR









K+ +




















Appendixes





J(ππ) = ℓ(ππ) = 0 P(ππ) = +1 C(ππ) = +1



ℓL



SLti

SLLSti

LS

tL

tS

Lti

LSti

S

KKeaaKKeaa

eaea

KeaKea

SLLS

LS

LS

)()(

22

f LSf

fLS KfA

dt

d 2

2

TUnitarity requires

and therefore


f Sff

fS

fLSLLS

f

fLLf

fSS

fKAAKKmi

AA

)(2)(

22


2

22

2

222

0604

mKK

AAAA

LS

LSLS

f

fSf

fLf

fS

fL



SLS KKmi 21




)()( 0000

SSS KK













p

Target

Collimator



Dump

Tagging Separation

Charged beam




Buthellip



rarr Small in SM


2π (εrsquoε)

3π (Ag)


ν


π0

Kplusmn rarr 3π




π1

π2

π3

K


Kinematics



2


2

Matrix element

|M(uv)|2 ~ 1 + gu + hu2 + kv2







KminusK+








10-6

NA482 OKA

10-5

10-4

10-3

10-2

SMSM

SUSYSUSYNewNew

physicsphysics



|Ag|

bull Ag ~ 10minus5


SUSY New Physics

THEORY



C

N



=Ag



54 60 66

1cm

50 100

10 cm

200 250 m





~11012

ppp

K+

Kminus



always in vacuum

focusing beams

BM

z

magnet

vacuum tank

not to scale

K+

K


pipe

0ordm prodangle






ZZ

XXYY

JuraJura

SaleveSaleve

Beam line K+ Up


B+

Bminus






Spectrometer field

K+

Kminus

Reverse each day

Reverse each week


|V| even pion

in beam pipe


KK+ +

KK



No significant

background





-15 -10 -05 0 05 10 u

0

-1

-2

1

2

3

Dalitz plot



EM calorimeter only






2003 result in PLB 634 (2006) 474




2003 result in PLB 638 (2006) 22


excluded


OKA at Protvino





(in preparation)


More CP violation


Indirect

Direct

CP violation

parameters

(2005)


(A) KS decays


CPV in KS decays




000000

000

000 )(

)(

L

S

KA




S+KL

KL




000 000 00

1( )2 ( 2

0

)

( )


tt

NEARf E t



)()()( 00

00

EKNEKN

EKNEKNED

(incoherent

production)



Assuming CPT





N3

20

40

60

00

4 62


No CPV seen yet

























PT() = (-17 23 11) 10-

3

Im = (-53 71 36) 10-3




Im = (-53 71 36) 10-3








ppp

ppp

)0()0(

)0()0(

NN

NNA


Radiative decays








211221 )()(


IB DE

p1 p1

p2p2

q q







)(

)(

S

L

KA

violatingCPKA




KL π+πminus






IB

M1 DE




KL itself





KL ee


BR = (308 020) 10minus7



E1M1 lt 004 (90 CL)



φ




KS ee

No asymmetry for KS

as expected

BR = (471 032) 10-

5

AΦ = (05 43)






IBEE

dEA

)tan( 0


Kplusmn π+π0γ

)730810672()(

)250350353()(

800

800

syststatMeVT

syststatMeVT

INTFrac

DEFrac







KL π+πndashπ0γ















)(

)2030(

3

3

e

ee

K

MeVEKR





bull 6M Ke3 events


ndash R=(0964plusmn0008+0011-0009)












PDG 2004







]21[192 3

52

KmG







Vus measurements





unitarity





KLOE Kl 3

KLOE K2

copy A Antonelli

Vus some more




Ke4 results





K+rarrπ0π0eν










1-loop rescattering

2-loop rescattering











NA482




KLOE interference

















K+ + 8middot10-11 (at 7)147+130

ndash089 middot 10-

10 (BNL E787+E949)






KL 0ℓ+ℓ-




BR(KL 0+-) lt 3810-10





NA481 KS 0ℓ+ℓ-



BR = (58 +28-23 plusmn08) times10-9


-012 (accid)BR = (28 +15


KS 0e+e- KS 0μ+μ-


NA481 preliminary

NA481 preliminary


KL 0ℓ+ℓ-






Krarr in the SM




W W

s

id

Vis Vid

e

i=uct

W

Z

VisV

idds i

11

20

2410

10)1108(

)(1001)(

AKB

11

2

5

100

10)4082(

)()Im(

1022)(

t

tdtsL xX

VVKB


K

ε εrsquo




Ke3 KL 0

Height

Im(λt )



10301890 10471)(

KBR









K+ +




















Appendixes





J(ππ) = ℓ(ππ) = 0 P(ππ) = +1 C(ππ) = +1



ℓL



SLti

SLLSti

LS

tL

tS

Lti

LSti

S

KKeaaKKeaa

eaea

KeaKea

SLLS

LS

LS

)()(

22

f LSf

fLS KfA

dt

d 2

2

TUnitarity requires

and therefore


f Sff

fS

fLSLLS

f

fLLf

fSS

fKAAKKmi

AA

)(2)(

22


2

22

2

222

0604

mKK

AAAA

LS

LSLS

f

fSf

fLf

fS

fL



SLS KKmi 21




)()( 0000

SSS KK









p

Target

Collimator



Dump

Tagging Separation

Charged beam




Buthellip



rarr Small in SM


2π (εrsquoε)

3π (Ag)


ν


π0

Kplusmn rarr 3π




π1

π2

π3

K


Kinematics



2


2

Matrix element

|M(uv)|2 ~ 1 + gu + hu2 + kv2







KminusK+








10-6

NA482 OKA

10-5

10-4

10-3

10-2

SMSM

SUSYSUSYNewNew

physicsphysics



|Ag|

bull Ag ~ 10minus5


SUSY New Physics

THEORY



C

N



=Ag



54 60 66

1cm

50 100

10 cm

200 250 m





~11012

ppp

K+

Kminus



always in vacuum

focusing beams

BM

z

magnet

vacuum tank

not to scale

K+

K


pipe

0ordm prodangle






ZZ

XXYY

JuraJura

SaleveSaleve

Beam line K+ Up


B+

Bminus






Spectrometer field

K+

Kminus

Reverse each day

Reverse each week


|V| even pion

in beam pipe


KK+ +

KK



No significant

background





-15 -10 -05 0 05 10 u

0

-1

-2

1

2

3

Dalitz plot



EM calorimeter only






2003 result in PLB 634 (2006) 474




2003 result in PLB 638 (2006) 22


excluded


OKA at Protvino





(in preparation)


More CP violation


Indirect

Direct

CP violation

parameters

(2005)


(A) KS decays


CPV in KS decays




000000

000

000 )(

)(

L

S

KA




S+KL

KL




000 000 00

1( )2 ( 2

0

)

( )


tt

NEARf E t



)()()( 00

00

EKNEKN

EKNEKNED

(incoherent

production)



Assuming CPT





N3

20

40

60

00

4 62


No CPV seen yet

























PT() = (-17 23 11) 10-

3

Im = (-53 71 36) 10-3




Im = (-53 71 36) 10-3








ppp

ppp

)0()0(

)0()0(

NN

NNA


Radiative decays








211221 )()(


IB DE

p1 p1

p2p2

q q







)(

)(

S

L

KA

violatingCPKA




KL π+πminus






IB

M1 DE




KL itself





KL ee


BR = (308 020) 10minus7



E1M1 lt 004 (90 CL)



φ




KS ee

No asymmetry for KS

as expected

BR = (471 032) 10-

5

AΦ = (05 43)






IBEE

dEA

)tan( 0


Kplusmn π+π0γ

)730810672()(

)250350353()(

800

800

syststatMeVT

syststatMeVT

INTFrac

DEFrac







KL π+πndashπ0γ















)(

)2030(

3

3

e

ee

K

MeVEKR





bull 6M Ke3 events


ndash R=(0964plusmn0008+0011-0009)












PDG 2004







]21[192 3

52

KmG







Vus measurements





unitarity





KLOE Kl 3

KLOE K2

copy A Antonelli

Vus some more




Ke4 results





K+rarrπ0π0eν










1-loop rescattering

2-loop rescattering











NA482




KLOE interference

















K+ + 8middot10-11 (at 7)147+130

ndash089 middot 10-

10 (BNL E787+E949)






KL 0ℓ+ℓ-




BR(KL 0+-) lt 3810-10





NA481 KS 0ℓ+ℓ-



BR = (58 +28-23 plusmn08) times10-9


-012 (accid)BR = (28 +15


KS 0e+e- KS 0μ+μ-


NA481 preliminary

NA481 preliminary


KL 0ℓ+ℓ-






Krarr in the SM




W W

s

id

Vis Vid

e

i=uct

W

Z

VisV

idds i

11

20

2410

10)1108(

)(1001)(

AKB

11

2

5

100

10)4082(

)()Im(

1022)(

t

tdtsL xX

VVKB


K

ε εrsquo




Ke3 KL 0

Height

Im(λt )



10301890 10471)(

KBR









K+ +




















Appendixes





J(ππ) = ℓ(ππ) = 0 P(ππ) = +1 C(ππ) = +1



ℓL



SLti

SLLSti

LS

tL

tS

Lti

LSti

S

KKeaaKKeaa

eaea

KeaKea

SLLS

LS

LS

)()(

22

f LSf

fLS KfA

dt

d 2

2

TUnitarity requires

and therefore


f Sff

fS

fLSLLS

f

fLLf

fSS

fKAAKKmi

AA

)(2)(

22


2

22

2

222

0604

mKK

AAAA

LS

LSLS

f

fSf

fLf

fS

fL



SLS KKmi 21




)()( 0000

SSS KK





Buthellip



rarr Small in SM


2π (εrsquoε)

3π (Ag)


ν


π0

Kplusmn rarr 3π




π1

π2

π3

K


Kinematics



2


2

Matrix element

|M(uv)|2 ~ 1 + gu + hu2 + kv2







KminusK+








10-6

NA482 OKA

10-5

10-4

10-3

10-2

SMSM

SUSYSUSYNewNew

physicsphysics



|Ag|

bull Ag ~ 10minus5


SUSY New Physics

THEORY



C

N



=Ag



54 60 66

1cm

50 100

10 cm

200 250 m





~11012

ppp

K+

Kminus



always in vacuum

focusing beams

BM

z

magnet

vacuum tank

not to scale

K+

K


pipe

0ordm prodangle






ZZ

XXYY

JuraJura

SaleveSaleve

Beam line K+ Up


B+

Bminus






Spectrometer field

K+

Kminus

Reverse each day

Reverse each week


|V| even pion

in beam pipe


KK+ +

KK



No significant

background





-15 -10 -05 0 05 10 u

0

-1

-2

1

2

3

Dalitz plot



EM calorimeter only






2003 result in PLB 634 (2006) 474




2003 result in PLB 638 (2006) 22


excluded


OKA at Protvino





(in preparation)


More CP violation


Indirect

Direct

CP violation

parameters

(2005)


(A) KS decays


CPV in KS decays




000000

000

000 )(

)(

L

S

KA




S+KL

KL




000 000 00

1( )2 ( 2

0

)

( )


tt

NEARf E t



)()()( 00

00

EKNEKN

EKNEKNED

(incoherent

production)



Assuming CPT





N3

20

40

60

00

4 62


No CPV seen yet

























PT() = (-17 23 11) 10-

3

Im = (-53 71 36) 10-3




Im = (-53 71 36) 10-3








ppp

ppp

)0()0(

)0()0(

NN

NNA


Radiative decays








211221 )()(


IB DE

p1 p1

p2p2

q q







)(

)(

S

L

KA

violatingCPKA




KL π+πminus






IB

M1 DE




KL itself





KL ee


BR = (308 020) 10minus7



E1M1 lt 004 (90 CL)



φ




KS ee

No asymmetry for KS

as expected

BR = (471 032) 10-

5

AΦ = (05 43)






IBEE

dEA

)tan( 0


Kplusmn π+π0γ

)730810672()(

)250350353()(

800

800

syststatMeVT

syststatMeVT

INTFrac

DEFrac







KL π+πndashπ0γ















)(

)2030(

3

3

e

ee

K

MeVEKR





bull 6M Ke3 events


ndash R=(0964plusmn0008+0011-0009)












PDG 2004







]21[192 3

52

KmG







Vus measurements





unitarity





KLOE Kl 3

KLOE K2

copy A Antonelli

Vus some more




Ke4 results





K+rarrπ0π0eν










1-loop rescattering

2-loop rescattering











NA482




KLOE interference

















K+ + 8middot10-11 (at 7)147+130

ndash089 middot 10-

10 (BNL E787+E949)






KL 0ℓ+ℓ-




BR(KL 0+-) lt 3810-10





NA481 KS 0ℓ+ℓ-



BR = (58 +28-23 plusmn08) times10-9


-012 (accid)BR = (28 +15


KS 0e+e- KS 0μ+μ-


NA481 preliminary

NA481 preliminary


KL 0ℓ+ℓ-






Krarr in the SM




W W

s

id

Vis Vid

e

i=uct

W

Z

VisV

idds i

11

20

2410

10)1108(

)(1001)(

AKB

11

2

5

100

10)4082(

)()Im(

1022)(

t

tdtsL xX

VVKB


K

ε εrsquo




Ke3 KL 0

Height

Im(λt )



10301890 10471)(

KBR









K+ +




















Appendixes





J(ππ) = ℓ(ππ) = 0 P(ππ) = +1 C(ππ) = +1



ℓL



SLti

SLLSti

LS

tL

tS

Lti

LSti

S

KKeaaKKeaa

eaea

KeaKea

SLLS

LS

LS

)()(

22

f LSf

fLS KfA

dt

d 2

2

TUnitarity requires

and therefore


f Sff

fS

fLSLLS

f

fLLf

fSS

fKAAKKmi

AA

)(2)(

22


2

22

2

222

0604

mKK

AAAA

LS

LSLS

f

fSf

fLf

fS

fL



SLS KKmi 21




)()( 0000

SSS KK





π1

π2

π3

K


Kinematics



2


2

Matrix element

|M(uv)|2 ~ 1 + gu + hu2 + kv2







KminusK+








10-6

NA482 OKA

10-5

10-4

10-3

10-2

SMSM

SUSYSUSYNewNew

physicsphysics



|Ag|

bull Ag ~ 10minus5


SUSY New Physics

THEORY



C

N



=Ag



54 60 66

1cm

50 100

10 cm

200 250 m





~11012

ppp

K+

Kminus



always in vacuum

focusing beams

BM

z

magnet

vacuum tank

not to scale

K+

K


pipe

0ordm prodangle






ZZ

XXYY

JuraJura

SaleveSaleve

Beam line K+ Up


B+

Bminus






Spectrometer field

K+

Kminus

Reverse each day

Reverse each week


|V| even pion

in beam pipe


KK+ +

KK



No significant

background





-15 -10 -05 0 05 10 u

0

-1

-2

1

2

3

Dalitz plot



EM calorimeter only






2003 result in PLB 634 (2006) 474




2003 result in PLB 638 (2006) 22


excluded


OKA at Protvino





(in preparation)


More CP violation


Indirect

Direct

CP violation

parameters

(2005)


(A) KS decays


CPV in KS decays




000000

000

000 )(

)(

L

S

KA




S+KL

KL




000 000 00

1( )2 ( 2

0

)

( )


tt

NEARf E t



)()()( 00

00

EKNEKN

EKNEKNED

(incoherent

production)



Assuming CPT





N3

20

40

60

00

4 62


No CPV seen yet

























PT() = (-17 23 11) 10-

3

Im = (-53 71 36) 10-3




Im = (-53 71 36) 10-3








ppp

ppp

)0()0(

)0()0(

NN

NNA


Radiative decays








211221 )()(


IB DE

p1 p1

p2p2

q q







)(

)(

S

L

KA

violatingCPKA




KL π+πminus






IB

M1 DE




KL itself





KL ee


BR = (308 020) 10minus7



E1M1 lt 004 (90 CL)



φ




KS ee

No asymmetry for KS

as expected

BR = (471 032) 10-

5

AΦ = (05 43)






IBEE

dEA

)tan( 0


Kplusmn π+π0γ

)730810672()(

)250350353()(

800

800

syststatMeVT

syststatMeVT

INTFrac

DEFrac







KL π+πndashπ0γ















)(

)2030(

3

3

e

ee

K

MeVEKR





bull 6M Ke3 events


ndash R=(0964plusmn0008+0011-0009)












PDG 2004







]21[192 3

52

KmG







Vus measurements





unitarity





KLOE Kl 3

KLOE K2

copy A Antonelli

Vus some more




Ke4 results





K+rarrπ0π0eν










1-loop rescattering

2-loop rescattering











NA482




KLOE interference

















K+ + 8middot10-11 (at 7)147+130

ndash089 middot 10-

10 (BNL E787+E949)






KL 0ℓ+ℓ-




BR(KL 0+-) lt 3810-10





NA481 KS 0ℓ+ℓ-



BR = (58 +28-23 plusmn08) times10-9


-012 (accid)BR = (28 +15


KS 0e+e- KS 0μ+μ-


NA481 preliminary

NA481 preliminary


KL 0ℓ+ℓ-






Krarr in the SM




W W

s

id

Vis Vid

e

i=uct

W

Z

VisV

idds i

11

20

2410

10)1108(

)(1001)(

AKB

11

2

5

100

10)4082(

)()Im(

1022)(

t

tdtsL xX

VVKB


K

ε εrsquo




Ke3 KL 0

Height

Im(λt )



10301890 10471)(

KBR









K+ +




















Appendixes





J(ππ) = ℓ(ππ) = 0 P(ππ) = +1 C(ππ) = +1



ℓL



SLti

SLLSti

LS

tL

tS

Lti

LSti

S

KKeaaKKeaa

eaea

KeaKea

SLLS

LS

LS

)()(

22

f LSf

fLS KfA

dt

d 2

2

TUnitarity requires

and therefore


f Sff

fS

fLSLLS

f

fLLf

fSS

fKAAKKmi

AA

)(2)(

22


2

22

2

222

0604

mKK

AAAA

LS

LSLS

f

fSf

fLf

fS

fL



SLS KKmi 21




)()( 0000

SSS KK






KminusK+








10-6

NA482 OKA

10-5

10-4

10-3

10-2

SMSM

SUSYSUSYNewNew

physicsphysics



|Ag|

bull Ag ~ 10minus5


SUSY New Physics

THEORY



C

N



=Ag



54 60 66

1cm

50 100

10 cm

200 250 m





~11012

ppp

K+

Kminus



always in vacuum

focusing beams

BM

z

magnet

vacuum tank

not to scale

K+

K


pipe

0ordm prodangle






ZZ

XXYY

JuraJura

SaleveSaleve

Beam line K+ Up


B+

Bminus






Spectrometer field

K+

Kminus

Reverse each day

Reverse each week


|V| even pion

in beam pipe


KK+ +

KK



No significant

background





-15 -10 -05 0 05 10 u

0

-1

-2

1

2

3

Dalitz plot



EM calorimeter only






2003 result in PLB 634 (2006) 474




2003 result in PLB 638 (2006) 22


excluded


OKA at Protvino





(in preparation)


More CP violation


Indirect

Direct

CP violation

parameters

(2005)


(A) KS decays


CPV in KS decays




000000

000

000 )(

)(

L

S

KA




S+KL

KL




000 000 00

1( )2 ( 2

0

)

( )


tt

NEARf E t



)()()( 00

00

EKNEKN

EKNEKNED

(incoherent

production)



Assuming CPT





N3

20

40

60

00

4 62


No CPV seen yet

























PT() = (-17 23 11) 10-

3

Im = (-53 71 36) 10-3




Im = (-53 71 36) 10-3








ppp

ppp

)0()0(

)0()0(

NN

NNA


Radiative decays








211221 )()(


IB DE

p1 p1

p2p2

q q







)(

)(

S

L

KA

violatingCPKA




KL π+πminus






IB

M1 DE




KL itself





KL ee


BR = (308 020) 10minus7



E1M1 lt 004 (90 CL)



φ




KS ee

No asymmetry for KS

as expected

BR = (471 032) 10-

5

AΦ = (05 43)






IBEE

dEA

)tan( 0


Kplusmn π+π0γ

)730810672()(

)250350353()(

800

800

syststatMeVT

syststatMeVT

INTFrac

DEFrac







KL π+πndashπ0γ















)(

)2030(

3

3

e

ee

K

MeVEKR





bull 6M Ke3 events


ndash R=(0964plusmn0008+0011-0009)












PDG 2004







]21[192 3

52

KmG







Vus measurements





unitarity





KLOE Kl 3

KLOE K2

copy A Antonelli

Vus some more




Ke4 results





K+rarrπ0π0eν










1-loop rescattering

2-loop rescattering











NA482




KLOE interference

















K+ + 8middot10-11 (at 7)147+130

ndash089 middot 10-

10 (BNL E787+E949)






KL 0ℓ+ℓ-




BR(KL 0+-) lt 3810-10





NA481 KS 0ℓ+ℓ-



BR = (58 +28-23 plusmn08) times10-9


-012 (accid)BR = (28 +15


KS 0e+e- KS 0μ+μ-


NA481 preliminary

NA481 preliminary


KL 0ℓ+ℓ-






Krarr in the SM




W W

s

id

Vis Vid

e

i=uct

W

Z

VisV

idds i

11

20

2410

10)1108(

)(1001)(

AKB

11

2

5

100

10)4082(

)()Im(

1022)(

t

tdtsL xX

VVKB


K

ε εrsquo




Ke3 KL 0

Height

Im(λt )



10301890 10471)(

KBR









K+ +




















Appendixes





J(ππ) = ℓ(ππ) = 0 P(ππ) = +1 C(ππ) = +1



ℓL



SLti

SLLSti

LS

tL

tS

Lti

LSti

S

KKeaaKKeaa

eaea

KeaKea

SLLS

LS

LS

)()(

22

f LSf

fLS KfA

dt

d 2

2

TUnitarity requires

and therefore


f Sff

fS

fLSLLS

f

fLLf

fSS

fKAAKKmi

AA

)(2)(

22


2

22

2

222

0604

mKK

AAAA

LS

LSLS

f

fSf

fLf

fS

fL



SLS KKmi 21




)()( 0000

SSS KK




10-6

NA482 OKA

10-5

10-4

10-3

10-2

SMSM

SUSYSUSYNewNew

physicsphysics



|Ag|

bull Ag ~ 10minus5


SUSY New Physics

THEORY



C

N



=Ag



54 60 66

1cm

50 100

10 cm

200 250 m





~11012

ppp

K+

Kminus



always in vacuum

focusing beams

BM

z

magnet

vacuum tank

not to scale

K+

K


pipe

0ordm prodangle






ZZ

XXYY

JuraJura

SaleveSaleve

Beam line K+ Up


B+

Bminus






Spectrometer field

K+

Kminus

Reverse each day

Reverse each week


|V| even pion

in beam pipe


KK+ +

KK



No significant

background





-15 -10 -05 0 05 10 u

0

-1

-2

1

2

3

Dalitz plot



EM calorimeter only






2003 result in PLB 634 (2006) 474




2003 result in PLB 638 (2006) 22


excluded


OKA at Protvino





(in preparation)


More CP violation


Indirect

Direct

CP violation

parameters

(2005)


(A) KS decays


CPV in KS decays




000000

000

000 )(

)(

L

S

KA




S+KL

KL




000 000 00

1( )2 ( 2

0

)

( )


tt

NEARf E t



)()()( 00

00

EKNEKN

EKNEKNED

(incoherent

production)



Assuming CPT





N3

20

40

60

00

4 62


No CPV seen yet

























PT() = (-17 23 11) 10-

3

Im = (-53 71 36) 10-3




Im = (-53 71 36) 10-3








ppp

ppp

)0()0(

)0()0(

NN

NNA


Radiative decays








211221 )()(


IB DE

p1 p1

p2p2

q q







)(

)(

S

L

KA

violatingCPKA




KL π+πminus






IB

M1 DE




KL itself





KL ee


BR = (308 020) 10minus7



E1M1 lt 004 (90 CL)



φ




KS ee

No asymmetry for KS

as expected

BR = (471 032) 10-

5

AΦ = (05 43)






IBEE

dEA

)tan( 0


Kplusmn π+π0γ

)730810672()(

)250350353()(

800

800

syststatMeVT

syststatMeVT

INTFrac

DEFrac







KL π+πndashπ0γ















)(

)2030(

3

3

e

ee

K

MeVEKR





bull 6M Ke3 events


ndash R=(0964plusmn0008+0011-0009)












PDG 2004







]21[192 3

52

KmG







Vus measurements





unitarity





KLOE Kl 3

KLOE K2

copy A Antonelli

Vus some more




Ke4 results





K+rarrπ0π0eν










1-loop rescattering

2-loop rescattering











NA482




KLOE interference

















K+ + 8middot10-11 (at 7)147+130

ndash089 middot 10-

10 (BNL E787+E949)






KL 0ℓ+ℓ-




BR(KL 0+-) lt 3810-10





NA481 KS 0ℓ+ℓ-



BR = (58 +28-23 plusmn08) times10-9


-012 (accid)BR = (28 +15


KS 0e+e- KS 0μ+μ-


NA481 preliminary

NA481 preliminary


KL 0ℓ+ℓ-






Krarr in the SM




W W

s

id

Vis Vid

e

i=uct

W

Z

VisV

idds i

11

20

2410

10)1108(

)(1001)(

AKB

11

2

5

100

10)4082(

)()Im(

1022)(

t

tdtsL xX

VVKB


K

ε εrsquo




Ke3 KL 0

Height

Im(λt )



10301890 10471)(

KBR









K+ +




















Appendixes





J(ππ) = ℓ(ππ) = 0 P(ππ) = +1 C(ππ) = +1



ℓL



SLti

SLLSti

LS

tL

tS

Lti

LSti

S

KKeaaKKeaa

eaea

KeaKea

SLLS

LS

LS

)()(

22

f LSf

fLS KfA

dt

d 2

2

TUnitarity requires

and therefore


f Sff

fS

fLSLLS

f

fLLf

fSS

fKAAKKmi

AA

)(2)(

22


2

22

2

222

0604

mKK

AAAA

LS

LSLS

f

fSf

fLf

fS

fL



SLS KKmi 21




)()( 0000

SSS KK




=Ag



54 60 66

1cm

50 100

10 cm

200 250 m





~11012

ppp

K+

Kminus



always in vacuum

focusing beams

BM

z

magnet

vacuum tank

not to scale

K+

K


pipe

0ordm prodangle






ZZ

XXYY

JuraJura

SaleveSaleve

Beam line K+ Up


B+

Bminus






Spectrometer field

K+

Kminus

Reverse each day

Reverse each week


|V| even pion

in beam pipe


KK+ +

KK



No significant

background





-15 -10 -05 0 05 10 u

0

-1

-2

1

2

3

Dalitz plot



EM calorimeter only






2003 result in PLB 634 (2006) 474




2003 result in PLB 638 (2006) 22


excluded


OKA at Protvino





(in preparation)


More CP violation


Indirect

Direct

CP violation

parameters

(2005)


(A) KS decays


CPV in KS decays




000000

000

000 )(

)(

L

S

KA




S+KL

KL




000 000 00

1( )2 ( 2

0

)

( )


tt

NEARf E t



)()()( 00

00

EKNEKN

EKNEKNED

(incoherent

production)



Assuming CPT





N3

20

40

60

00

4 62


No CPV seen yet

























PT() = (-17 23 11) 10-

3

Im = (-53 71 36) 10-3




Im = (-53 71 36) 10-3








ppp

ppp

)0()0(

)0()0(

NN

NNA


Radiative decays








211221 )()(


IB DE

p1 p1

p2p2

q q







)(

)(

S

L

KA

violatingCPKA




KL π+πminus






IB

M1 DE




KL itself





KL ee


BR = (308 020) 10minus7



E1M1 lt 004 (90 CL)



φ




KS ee

No asymmetry for KS

as expected

BR = (471 032) 10-

5

AΦ = (05 43)






IBEE

dEA

)tan( 0


Kplusmn π+π0γ

)730810672()(

)250350353()(

800

800

syststatMeVT

syststatMeVT

INTFrac

DEFrac







KL π+πndashπ0γ















)(

)2030(

3

3

e

ee

K

MeVEKR





bull 6M Ke3 events


ndash R=(0964plusmn0008+0011-0009)












PDG 2004







]21[192 3

52

KmG







Vus measurements





unitarity





KLOE Kl 3

KLOE K2

copy A Antonelli

Vus some more




Ke4 results





K+rarrπ0π0eν










1-loop rescattering

2-loop rescattering











NA482




KLOE interference

















K+ + 8middot10-11 (at 7)147+130

ndash089 middot 10-

10 (BNL E787+E949)






KL 0ℓ+ℓ-




BR(KL 0+-) lt 3810-10





NA481 KS 0ℓ+ℓ-



BR = (58 +28-23 plusmn08) times10-9


-012 (accid)BR = (28 +15


KS 0e+e- KS 0μ+μ-


NA481 preliminary

NA481 preliminary


KL 0ℓ+ℓ-






Krarr in the SM




W W

s

id

Vis Vid

e

i=uct

W

Z

VisV

idds i

11

20

2410

10)1108(

)(1001)(

AKB

11

2

5

100

10)4082(

)()Im(

1022)(

t

tdtsL xX

VVKB


K

ε εrsquo




Ke3 KL 0

Height

Im(λt )



10301890 10471)(

KBR









K+ +




















Appendixes





J(ππ) = ℓ(ππ) = 0 P(ππ) = +1 C(ππ) = +1



ℓL



SLti

SLLSti

LS

tL

tS

Lti

LSti

S

KKeaaKKeaa

eaea

KeaKea

SLLS

LS

LS

)()(

22

f LSf

fLS KfA

dt

d 2

2

TUnitarity requires

and therefore


f Sff

fS

fLSLLS

f

fLLf

fSS

fKAAKKmi

AA

)(2)(

22


2

22

2

222

0604

mKK

AAAA

LS

LSLS

f

fSf

fLf

fS

fL



SLS KKmi 21




)()( 0000

SSS KK




54 60 66

1cm

50 100

10 cm

200 250 m





~11012

ppp

K+

Kminus



always in vacuum

focusing beams

BM

z

magnet

vacuum tank

not to scale

K+

K


pipe

0ordm prodangle






ZZ

XXYY

JuraJura

SaleveSaleve

Beam line K+ Up


B+

Bminus






Spectrometer field

K+

Kminus

Reverse each day

Reverse each week


|V| even pion

in beam pipe


KK+ +

KK



No significant

background





-15 -10 -05 0 05 10 u

0

-1

-2

1

2

3

Dalitz plot



EM calorimeter only






2003 result in PLB 634 (2006) 474




2003 result in PLB 638 (2006) 22


excluded


OKA at Protvino





(in preparation)


More CP violation


Indirect

Direct

CP violation

parameters

(2005)


(A) KS decays


CPV in KS decays




000000

000

000 )(

)(

L

S

KA




S+KL

KL




000 000 00

1( )2 ( 2

0

)

( )


tt

NEARf E t



)()()( 00

00

EKNEKN

EKNEKNED

(incoherent

production)



Assuming CPT





N3

20

40

60

00

4 62


No CPV seen yet

























PT() = (-17 23 11) 10-

3

Im = (-53 71 36) 10-3




Im = (-53 71 36) 10-3








ppp

ppp

)0()0(

)0()0(

NN

NNA


Radiative decays








211221 )()(


IB DE

p1 p1

p2p2

q q







)(

)(

S

L

KA

violatingCPKA




KL π+πminus






IB

M1 DE




KL itself





KL ee


BR = (308 020) 10minus7



E1M1 lt 004 (90 CL)



φ




KS ee

No asymmetry for KS

as expected

BR = (471 032) 10-

5

AΦ = (05 43)






IBEE

dEA

)tan( 0


Kplusmn π+π0γ

)730810672()(

)250350353()(

800

800

syststatMeVT

syststatMeVT

INTFrac

DEFrac







KL π+πndashπ0γ















)(

)2030(

3

3

e

ee

K

MeVEKR





bull 6M Ke3 events


ndash R=(0964plusmn0008+0011-0009)












PDG 2004







]21[192 3

52

KmG







Vus measurements





unitarity





KLOE Kl 3

KLOE K2

copy A Antonelli

Vus some more




Ke4 results





K+rarrπ0π0eν










1-loop rescattering

2-loop rescattering











NA482




KLOE interference

















K+ + 8middot10-11 (at 7)147+130

ndash089 middot 10-

10 (BNL E787+E949)






KL 0ℓ+ℓ-




BR(KL 0+-) lt 3810-10





NA481 KS 0ℓ+ℓ-



BR = (58 +28-23 plusmn08) times10-9


-012 (accid)BR = (28 +15


KS 0e+e- KS 0μ+μ-


NA481 preliminary

NA481 preliminary


KL 0ℓ+ℓ-






Krarr in the SM




W W

s

id

Vis Vid

e

i=uct

W

Z

VisV

idds i

11

20

2410

10)1108(

)(1001)(

AKB

11

2

5

100

10)4082(

)()Im(

1022)(

t

tdtsL xX

VVKB


K

ε εrsquo




Ke3 KL 0

Height

Im(λt )



10301890 10471)(

KBR









K+ +




















Appendixes





J(ππ) = ℓ(ππ) = 0 P(ππ) = +1 C(ππ) = +1



ℓL



SLti

SLLSti

LS

tL

tS

Lti

LSti

S

KKeaaKKeaa

eaea

KeaKea

SLLS

LS

LS

)()(

22

f LSf

fLS KfA

dt

d 2

2

TUnitarity requires

and therefore


f Sff

fS

fLSLLS

f

fLLf

fSS

fKAAKKmi

AA

)(2)(

22


2

22

2

222

0604

mKK

AAAA

LS

LSLS

f

fSf

fLf

fS

fL



SLS KKmi 21




)()( 0000

SSS KK






ZZ

XXYY

JuraJura

SaleveSaleve

Beam line K+ Up


B+

Bminus






Spectrometer field

K+

Kminus

Reverse each day

Reverse each week


|V| even pion

in beam pipe


KK+ +

KK



No significant

background





-15 -10 -05 0 05 10 u

0

-1

-2

1

2

3

Dalitz plot



EM calorimeter only






2003 result in PLB 634 (2006) 474




2003 result in PLB 638 (2006) 22


excluded


OKA at Protvino





(in preparation)


More CP violation


Indirect

Direct

CP violation

parameters

(2005)


(A) KS decays


CPV in KS decays




000000

000

000 )(

)(

L

S

KA




S+KL

KL




000 000 00

1( )2 ( 2

0

)

( )


tt

NEARf E t



)()()( 00

00

EKNEKN

EKNEKNED

(incoherent

production)



Assuming CPT





N3

20

40

60

00

4 62


No CPV seen yet

























PT() = (-17 23 11) 10-

3

Im = (-53 71 36) 10-3




Im = (-53 71 36) 10-3








ppp

ppp

)0()0(

)0()0(

NN

NNA


Radiative decays








211221 )()(


IB DE

p1 p1

p2p2

q q







)(

)(

S

L

KA

violatingCPKA




KL π+πminus






IB

M1 DE




KL itself





KL ee


BR = (308 020) 10minus7



E1M1 lt 004 (90 CL)



φ




KS ee

No asymmetry for KS

as expected

BR = (471 032) 10-

5

AΦ = (05 43)






IBEE

dEA

)tan( 0


Kplusmn π+π0γ

)730810672()(

)250350353()(

800

800

syststatMeVT

syststatMeVT

INTFrac

DEFrac







KL π+πndashπ0γ















)(

)2030(

3

3

e

ee

K

MeVEKR





bull 6M Ke3 events


ndash R=(0964plusmn0008+0011-0009)












PDG 2004







]21[192 3

52

KmG







Vus measurements





unitarity





KLOE Kl 3

KLOE K2

copy A Antonelli

Vus some more




Ke4 results





K+rarrπ0π0eν










1-loop rescattering

2-loop rescattering











NA482




KLOE interference

















K+ + 8middot10-11 (at 7)147+130

ndash089 middot 10-

10 (BNL E787+E949)






KL 0ℓ+ℓ-




BR(KL 0+-) lt 3810-10





NA481 KS 0ℓ+ℓ-



BR = (58 +28-23 plusmn08) times10-9


-012 (accid)BR = (28 +15


KS 0e+e- KS 0μ+μ-


NA481 preliminary

NA481 preliminary


KL 0ℓ+ℓ-






Krarr in the SM




W W

s

id

Vis Vid

e

i=uct

W

Z

VisV

idds i

11

20

2410

10)1108(

)(1001)(

AKB

11

2

5

100

10)4082(

)()Im(

1022)(

t

tdtsL xX

VVKB


K

ε εrsquo




Ke3 KL 0

Height

Im(λt )



10301890 10471)(

KBR









K+ +




















Appendixes





J(ππ) = ℓ(ππ) = 0 P(ππ) = +1 C(ππ) = +1



ℓL



SLti

SLLSti

LS

tL

tS

Lti

LSti

S

KKeaaKKeaa

eaea

KeaKea

SLLS

LS

LS

)()(

22

f LSf

fLS KfA

dt

d 2

2

TUnitarity requires

and therefore


f Sff

fS

fLSLLS

f

fLLf

fSS

fKAAKKmi

AA

)(2)(

22


2

22

2

222

0604

mKK

AAAA

LS

LSLS

f

fSf

fLf

fS

fL



SLS KKmi 21




)()( 0000

SSS KK



|V| even pion

in beam pipe


KK+ +

KK



No significant

background





-15 -10 -05 0 05 10 u

0

-1

-2

1

2

3

Dalitz plot



EM calorimeter only






2003 result in PLB 634 (2006) 474




2003 result in PLB 638 (2006) 22


excluded


OKA at Protvino





(in preparation)


More CP violation


Indirect

Direct

CP violation

parameters

(2005)


(A) KS decays


CPV in KS decays




000000

000

000 )(

)(

L

S

KA




S+KL

KL




000 000 00

1( )2 ( 2

0

)

( )


tt

NEARf E t



)()()( 00

00

EKNEKN

EKNEKNED

(incoherent

production)



Assuming CPT





N3

20

40

60

00

4 62


No CPV seen yet

























PT() = (-17 23 11) 10-

3

Im = (-53 71 36) 10-3




Im = (-53 71 36) 10-3








ppp

ppp

)0()0(

)0()0(

NN

NNA


Radiative decays








211221 )()(


IB DE

p1 p1

p2p2

q q







)(

)(

S

L

KA

violatingCPKA




KL π+πminus






IB

M1 DE




KL itself





KL ee


BR = (308 020) 10minus7



E1M1 lt 004 (90 CL)



φ




KS ee

No asymmetry for KS

as expected

BR = (471 032) 10-

5

AΦ = (05 43)






IBEE

dEA

)tan( 0


Kplusmn π+π0γ

)730810672()(

)250350353()(

800

800

syststatMeVT

syststatMeVT

INTFrac

DEFrac







KL π+πndashπ0γ















)(

)2030(

3

3

e

ee

K

MeVEKR





bull 6M Ke3 events


ndash R=(0964plusmn0008+0011-0009)












PDG 2004







]21[192 3

52

KmG







Vus measurements





unitarity





KLOE Kl 3

KLOE K2

copy A Antonelli

Vus some more




Ke4 results





K+rarrπ0π0eν










1-loop rescattering

2-loop rescattering











NA482




KLOE interference

















K+ + 8middot10-11 (at 7)147+130

ndash089 middot 10-

10 (BNL E787+E949)






KL 0ℓ+ℓ-




BR(KL 0+-) lt 3810-10





NA481 KS 0ℓ+ℓ-



BR = (58 +28-23 plusmn08) times10-9


-012 (accid)BR = (28 +15


KS 0e+e- KS 0μ+μ-


NA481 preliminary

NA481 preliminary


KL 0ℓ+ℓ-






Krarr in the SM




W W

s

id

Vis Vid

e

i=uct

W

Z

VisV

idds i

11

20

2410

10)1108(

)(1001)(

AKB

11

2

5

100

10)4082(

)()Im(

1022)(

t

tdtsL xX

VVKB


K

ε εrsquo




Ke3 KL 0

Height

Im(λt )



10301890 10471)(

KBR









K+ +




















Appendixes





J(ππ) = ℓ(ππ) = 0 P(ππ) = +1 C(ππ) = +1



ℓL



SLti

SLLSti

LS

tL

tS

Lti

LSti

S

KKeaaKKeaa

eaea

KeaKea

SLLS

LS

LS

)()(

22

f LSf

fLS KfA

dt

d 2

2

TUnitarity requires

and therefore


f Sff

fS

fLSLLS

f

fLLf

fSS

fKAAKKmi

AA

)(2)(

22


2

22

2

222

0604

mKK

AAAA

LS

LSLS

f

fSf

fLf

fS

fL



SLS KKmi 21




)()( 0000

SSS KK




-15 -10 -05 0 05 10 u

0

-1

-2

1

2

3

Dalitz plot



EM calorimeter only






2003 result in PLB 634 (2006) 474




2003 result in PLB 638 (2006) 22


excluded


OKA at Protvino





(in preparation)


More CP violation


Indirect

Direct

CP violation

parameters

(2005)


(A) KS decays


CPV in KS decays




000000

000

000 )(

)(

L

S

KA




S+KL

KL




000 000 00

1( )2 ( 2

0

)

( )


tt

NEARf E t



)()()( 00

00

EKNEKN

EKNEKNED

(incoherent

production)



Assuming CPT





N3

20

40

60

00

4 62


No CPV seen yet

























PT() = (-17 23 11) 10-

3

Im = (-53 71 36) 10-3




Im = (-53 71 36) 10-3








ppp

ppp

)0()0(

)0()0(

NN

NNA


Radiative decays








211221 )()(


IB DE

p1 p1

p2p2

q q







)(

)(

S

L

KA

violatingCPKA




KL π+πminus






IB

M1 DE




KL itself





KL ee


BR = (308 020) 10minus7



E1M1 lt 004 (90 CL)



φ




KS ee

No asymmetry for KS

as expected

BR = (471 032) 10-

5

AΦ = (05 43)






IBEE

dEA

)tan( 0


Kplusmn π+π0γ

)730810672()(

)250350353()(

800

800

syststatMeVT

syststatMeVT

INTFrac

DEFrac







KL π+πndashπ0γ















)(

)2030(

3

3

e

ee

K

MeVEKR





bull 6M Ke3 events


ndash R=(0964plusmn0008+0011-0009)












PDG 2004







]21[192 3

52

KmG







Vus measurements





unitarity





KLOE Kl 3

KLOE K2

copy A Antonelli

Vus some more




Ke4 results





K+rarrπ0π0eν










1-loop rescattering

2-loop rescattering











NA482




KLOE interference

















K+ + 8middot10-11 (at 7)147+130

ndash089 middot 10-

10 (BNL E787+E949)






KL 0ℓ+ℓ-




BR(KL 0+-) lt 3810-10





NA481 KS 0ℓ+ℓ-



BR = (58 +28-23 plusmn08) times10-9


-012 (accid)BR = (28 +15


KS 0e+e- KS 0μ+μ-


NA481 preliminary

NA481 preliminary


KL 0ℓ+ℓ-






Krarr in the SM




W W

s

id

Vis Vid

e

i=uct

W

Z

VisV

idds i

11

20

2410

10)1108(

)(1001)(

AKB

11

2

5

100

10)4082(

)()Im(

1022)(

t

tdtsL xX

VVKB


K

ε εrsquo




Ke3 KL 0

Height

Im(λt )



10301890 10471)(

KBR









K+ +




















Appendixes





J(ππ) = ℓ(ππ) = 0 P(ππ) = +1 C(ππ) = +1



ℓL



SLti

SLLSti

LS

tL

tS

Lti

LSti

S

KKeaaKKeaa

eaea

KeaKea

SLLS

LS

LS

)()(

22

f LSf

fLS KfA

dt

d 2

2

TUnitarity requires

and therefore


f Sff

fS

fLSLLS

f

fLLf

fSS

fKAAKKmi

AA

)(2)(

22


2

22

2

222

0604

mKK

AAAA

LS

LSLS

f

fSf

fLf

fS

fL



SLS KKmi 21




)()( 0000

SSS KK







2003 result in PLB 634 (2006) 474




2003 result in PLB 638 (2006) 22


excluded


OKA at Protvino





(in preparation)


More CP violation


Indirect

Direct

CP violation

parameters

(2005)


(A) KS decays


CPV in KS decays




000000

000

000 )(

)(

L

S

KA




S+KL

KL




000 000 00

1( )2 ( 2

0

)

( )


tt

NEARf E t



)()()( 00

00

EKNEKN

EKNEKNED

(incoherent

production)



Assuming CPT





N3

20

40

60

00

4 62


No CPV seen yet

























PT() = (-17 23 11) 10-

3

Im = (-53 71 36) 10-3




Im = (-53 71 36) 10-3








ppp

ppp

)0()0(

)0()0(

NN

NNA


Radiative decays








211221 )()(


IB DE

p1 p1

p2p2

q q







)(

)(

S

L

KA

violatingCPKA




KL π+πminus






IB

M1 DE




KL itself





KL ee


BR = (308 020) 10minus7



E1M1 lt 004 (90 CL)



φ




KS ee

No asymmetry for KS

as expected

BR = (471 032) 10-

5

AΦ = (05 43)






IBEE

dEA

)tan( 0


Kplusmn π+π0γ

)730810672()(

)250350353()(

800

800

syststatMeVT

syststatMeVT

INTFrac

DEFrac







KL π+πndashπ0γ















)(

)2030(

3

3

e

ee

K

MeVEKR





bull 6M Ke3 events


ndash R=(0964plusmn0008+0011-0009)












PDG 2004







]21[192 3

52

KmG







Vus measurements





unitarity





KLOE Kl 3

KLOE K2

copy A Antonelli

Vus some more




Ke4 results





K+rarrπ0π0eν










1-loop rescattering

2-loop rescattering











NA482




KLOE interference

















K+ + 8middot10-11 (at 7)147+130

ndash089 middot 10-

10 (BNL E787+E949)






KL 0ℓ+ℓ-




BR(KL 0+-) lt 3810-10





NA481 KS 0ℓ+ℓ-



BR = (58 +28-23 plusmn08) times10-9


-012 (accid)BR = (28 +15


KS 0e+e- KS 0μ+μ-


NA481 preliminary

NA481 preliminary


KL 0ℓ+ℓ-






Krarr in the SM




W W

s

id

Vis Vid

e

i=uct

W

Z

VisV

idds i

11

20

2410

10)1108(

)(1001)(

AKB

11

2

5

100

10)4082(

)()Im(

1022)(

t

tdtsL xX

VVKB


K

ε εrsquo




Ke3 KL 0

Height

Im(λt )



10301890 10471)(

KBR









K+ +




















Appendixes





J(ππ) = ℓ(ππ) = 0 P(ππ) = +1 C(ππ) = +1



ℓL



SLti

SLLSti

LS

tL

tS

Lti

LSti

S

KKeaaKKeaa

eaea

KeaKea

SLLS

LS

LS

)()(

22

f LSf

fLS KfA

dt

d 2

2

TUnitarity requires

and therefore


f Sff

fS

fLSLLS

f

fLLf

fSS

fKAAKKmi

AA

)(2)(

22


2

22

2

222

0604

mKK

AAAA

LS

LSLS

f

fSf

fLf

fS

fL



SLS KKmi 21




)()( 0000

SSS KK



OKA at Protvino





(in preparation)


More CP violation


Indirect

Direct

CP violation

parameters

(2005)


(A) KS decays


CPV in KS decays




000000

000

000 )(

)(

L

S

KA




S+KL

KL




000 000 00

1( )2 ( 2

0

)

( )


tt

NEARf E t



)()()( 00

00

EKNEKN

EKNEKNED

(incoherent

production)



Assuming CPT





N3

20

40

60

00

4 62


No CPV seen yet

























PT() = (-17 23 11) 10-

3

Im = (-53 71 36) 10-3




Im = (-53 71 36) 10-3








ppp

ppp

)0()0(

)0()0(

NN

NNA


Radiative decays








211221 )()(


IB DE

p1 p1

p2p2

q q







)(

)(

S

L

KA

violatingCPKA




KL π+πminus






IB

M1 DE




KL itself





KL ee


BR = (308 020) 10minus7



E1M1 lt 004 (90 CL)



φ




KS ee

No asymmetry for KS

as expected

BR = (471 032) 10-

5

AΦ = (05 43)






IBEE

dEA

)tan( 0


Kplusmn π+π0γ

)730810672()(

)250350353()(

800

800

syststatMeVT

syststatMeVT

INTFrac

DEFrac







KL π+πndashπ0γ















)(

)2030(

3

3

e

ee

K

MeVEKR





bull 6M Ke3 events


ndash R=(0964plusmn0008+0011-0009)












PDG 2004







]21[192 3

52

KmG







Vus measurements





unitarity





KLOE Kl 3

KLOE K2

copy A Antonelli

Vus some more




Ke4 results





K+rarrπ0π0eν










1-loop rescattering

2-loop rescattering











NA482




KLOE interference

















K+ + 8middot10-11 (at 7)147+130

ndash089 middot 10-

10 (BNL E787+E949)






KL 0ℓ+ℓ-




BR(KL 0+-) lt 3810-10





NA481 KS 0ℓ+ℓ-



BR = (58 +28-23 plusmn08) times10-9


-012 (accid)BR = (28 +15


KS 0e+e- KS 0μ+μ-


NA481 preliminary

NA481 preliminary


KL 0ℓ+ℓ-






Krarr in the SM




W W

s

id

Vis Vid

e

i=uct

W

Z

VisV

idds i

11

20

2410

10)1108(

)(1001)(

AKB

11

2

5

100

10)4082(

)()Im(

1022)(

t

tdtsL xX

VVKB


K

ε εrsquo




Ke3 KL 0

Height

Im(λt )



10301890 10471)(

KBR









K+ +




















Appendixes





J(ππ) = ℓ(ππ) = 0 P(ππ) = +1 C(ππ) = +1



ℓL



SLti

SLLSti

LS

tL

tS

Lti

LSti

S

KKeaaKKeaa

eaea

KeaKea

SLLS

LS

LS

)()(

22

f LSf

fLS KfA

dt

d 2

2

TUnitarity requires

and therefore


f Sff

fS

fLSLLS

f

fLLf

fSS

fKAAKKmi

AA

)(2)(

22


2

22

2

222

0604

mKK

AAAA

LS

LSLS

f

fSf

fLf

fS

fL



SLS KKmi 21




)()( 0000

SSS KK



More CP violation


Indirect

Direct

CP violation

parameters

(2005)


(A) KS decays


CPV in KS decays




000000

000

000 )(

)(

L

S

KA




S+KL

KL




000 000 00

1( )2 ( 2

0

)

( )


tt

NEARf E t



)()()( 00

00

EKNEKN

EKNEKNED

(incoherent

production)



Assuming CPT





N3

20

40

60

00

4 62


No CPV seen yet

























PT() = (-17 23 11) 10-

3

Im = (-53 71 36) 10-3




Im = (-53 71 36) 10-3








ppp

ppp

)0()0(

)0()0(

NN

NNA


Radiative decays








211221 )()(


IB DE

p1 p1

p2p2

q q







)(

)(

S

L

KA

violatingCPKA




KL π+πminus






IB

M1 DE




KL itself





KL ee


BR = (308 020) 10minus7



E1M1 lt 004 (90 CL)



φ




KS ee

No asymmetry for KS

as expected

BR = (471 032) 10-

5

AΦ = (05 43)






IBEE

dEA

)tan( 0


Kplusmn π+π0γ

)730810672()(

)250350353()(

800

800

syststatMeVT

syststatMeVT

INTFrac

DEFrac







KL π+πndashπ0γ















)(

)2030(

3

3

e

ee

K

MeVEKR





bull 6M Ke3 events


ndash R=(0964plusmn0008+0011-0009)












PDG 2004







]21[192 3

52

KmG







Vus measurements





unitarity





KLOE Kl 3

KLOE K2

copy A Antonelli

Vus some more




Ke4 results





K+rarrπ0π0eν










1-loop rescattering

2-loop rescattering











NA482




KLOE interference

















K+ + 8middot10-11 (at 7)147+130

ndash089 middot 10-

10 (BNL E787+E949)






KL 0ℓ+ℓ-




BR(KL 0+-) lt 3810-10





NA481 KS 0ℓ+ℓ-



BR = (58 +28-23 plusmn08) times10-9


-012 (accid)BR = (28 +15


KS 0e+e- KS 0μ+μ-


NA481 preliminary

NA481 preliminary


KL 0ℓ+ℓ-






Krarr in the SM




W W

s

id

Vis Vid

e

i=uct

W

Z

VisV

idds i

11

20

2410

10)1108(

)(1001)(

AKB

11

2

5

100

10)4082(

)()Im(

1022)(

t

tdtsL xX

VVKB


K

ε εrsquo




Ke3 KL 0

Height

Im(λt )



10301890 10471)(

KBR









K+ +




















Appendixes





J(ππ) = ℓ(ππ) = 0 P(ππ) = +1 C(ππ) = +1



ℓL



SLti

SLLSti

LS

tL

tS

Lti

LSti

S

KKeaaKKeaa

eaea

KeaKea

SLLS

LS

LS

)()(

22

f LSf

fLS KfA

dt

d 2

2

TUnitarity requires

and therefore


f Sff

fS

fLSLLS

f

fLLf

fSS

fKAAKKmi

AA

)(2)(

22


2

22

2

222

0604

mKK

AAAA

LS

LSLS

f

fSf

fLf

fS

fL



SLS KKmi 21




)()( 0000

SSS KK



Indirect

Direct

CP violation

parameters

(2005)


(A) KS decays


CPV in KS decays




000000

000

000 )(

)(

L

S

KA




S+KL

KL




000 000 00

1( )2 ( 2

0

)

( )


tt

NEARf E t



)()()( 00

00

EKNEKN

EKNEKNED

(incoherent

production)



Assuming CPT





N3

20

40

60

00

4 62


No CPV seen yet

























PT() = (-17 23 11) 10-

3

Im = (-53 71 36) 10-3




Im = (-53 71 36) 10-3








ppp

ppp

)0()0(

)0()0(

NN

NNA


Radiative decays








211221 )()(


IB DE

p1 p1

p2p2

q q







)(

)(

S

L

KA

violatingCPKA




KL π+πminus






IB

M1 DE




KL itself





KL ee


BR = (308 020) 10minus7



E1M1 lt 004 (90 CL)



φ




KS ee

No asymmetry for KS

as expected

BR = (471 032) 10-

5

AΦ = (05 43)






IBEE

dEA

)tan( 0


Kplusmn π+π0γ

)730810672()(

)250350353()(

800

800

syststatMeVT

syststatMeVT

INTFrac

DEFrac







KL π+πndashπ0γ















)(

)2030(

3

3

e

ee

K

MeVEKR





bull 6M Ke3 events


ndash R=(0964plusmn0008+0011-0009)












PDG 2004







]21[192 3

52

KmG







Vus measurements





unitarity





KLOE Kl 3

KLOE K2

copy A Antonelli

Vus some more




Ke4 results





K+rarrπ0π0eν










1-loop rescattering

2-loop rescattering











NA482




KLOE interference

















K+ + 8middot10-11 (at 7)147+130

ndash089 middot 10-

10 (BNL E787+E949)






KL 0ℓ+ℓ-




BR(KL 0+-) lt 3810-10





NA481 KS 0ℓ+ℓ-



BR = (58 +28-23 plusmn08) times10-9


-012 (accid)BR = (28 +15


KS 0e+e- KS 0μ+μ-


NA481 preliminary

NA481 preliminary


KL 0ℓ+ℓ-






Krarr in the SM




W W

s

id

Vis Vid

e

i=uct

W

Z

VisV

idds i

11

20

2410

10)1108(

)(1001)(

AKB

11

2

5

100

10)4082(

)()Im(

1022)(

t

tdtsL xX

VVKB


K

ε εrsquo




Ke3 KL 0

Height

Im(λt )



10301890 10471)(

KBR









K+ +




















Appendixes





J(ππ) = ℓ(ππ) = 0 P(ππ) = +1 C(ππ) = +1



ℓL



SLti

SLLSti

LS

tL

tS

Lti

LSti

S

KKeaaKKeaa

eaea

KeaKea

SLLS

LS

LS

)()(

22

f LSf

fLS KfA

dt

d 2

2

TUnitarity requires

and therefore


f Sff

fS

fLSLLS

f

fLLf

fSS

fKAAKKmi

AA

)(2)(

22


2

22

2

222

0604

mKK

AAAA

LS

LSLS

f

fSf

fLf

fS

fL



SLS KKmi 21




)()( 0000

SSS KK



(A) KS decays


CPV in KS decays




000000

000

000 )(

)(

L

S

KA




S+KL

KL




000 000 00

1( )2 ( 2

0

)

( )


tt

NEARf E t



)()()( 00

00

EKNEKN

EKNEKNED

(incoherent

production)



Assuming CPT





N3

20

40

60

00

4 62


No CPV seen yet

























PT() = (-17 23 11) 10-

3

Im = (-53 71 36) 10-3




Im = (-53 71 36) 10-3








ppp

ppp

)0()0(

)0()0(

NN

NNA


Radiative decays








211221 )()(


IB DE

p1 p1

p2p2

q q







)(

)(

S

L

KA

violatingCPKA




KL π+πminus






IB

M1 DE




KL itself





KL ee


BR = (308 020) 10minus7



E1M1 lt 004 (90 CL)



φ




KS ee

No asymmetry for KS

as expected

BR = (471 032) 10-

5

AΦ = (05 43)






IBEE

dEA

)tan( 0


Kplusmn π+π0γ

)730810672()(

)250350353()(

800

800

syststatMeVT

syststatMeVT

INTFrac

DEFrac







KL π+πndashπ0γ















)(

)2030(

3

3

e

ee

K

MeVEKR





bull 6M Ke3 events


ndash R=(0964plusmn0008+0011-0009)












PDG 2004







]21[192 3

52

KmG







Vus measurements





unitarity





KLOE Kl 3

KLOE K2

copy A Antonelli

Vus some more




Ke4 results





K+rarrπ0π0eν










1-loop rescattering

2-loop rescattering











NA482




KLOE interference

















K+ + 8middot10-11 (at 7)147+130

ndash089 middot 10-

10 (BNL E787+E949)






KL 0ℓ+ℓ-




BR(KL 0+-) lt 3810-10





NA481 KS 0ℓ+ℓ-



BR = (58 +28-23 plusmn08) times10-9


-012 (accid)BR = (28 +15


KS 0e+e- KS 0μ+μ-


NA481 preliminary

NA481 preliminary


KL 0ℓ+ℓ-






Krarr in the SM




W W

s

id

Vis Vid

e

i=uct

W

Z

VisV

idds i

11

20

2410

10)1108(

)(1001)(

AKB

11

2

5

100

10)4082(

)()Im(

1022)(

t

tdtsL xX

VVKB


K

ε εrsquo




Ke3 KL 0

Height

Im(λt )



10301890 10471)(

KBR









K+ +




















Appendixes





J(ππ) = ℓ(ππ) = 0 P(ππ) = +1 C(ππ) = +1



ℓL



SLti

SLLSti

LS

tL

tS

Lti

LSti

S

KKeaaKKeaa

eaea

KeaKea

SLLS

LS

LS

)()(

22

f LSf

fLS KfA

dt

d 2

2

TUnitarity requires

and therefore


f Sff

fS

fLSLLS

f

fLLf

fSS

fKAAKKmi

AA

)(2)(

22


2

22

2

222

0604

mKK

AAAA

LS

LSLS

f

fSf

fLf

fS

fL



SLS KKmi 21




)()( 0000

SSS KK



CPV in KS decays




000000

000

000 )(

)(

L

S

KA




S+KL

KL




000 000 00

1( )2 ( 2

0

)

( )


tt

NEARf E t



)()()( 00

00

EKNEKN

EKNEKNED

(incoherent

production)



Assuming CPT





N3

20

40

60

00

4 62


No CPV seen yet

























PT() = (-17 23 11) 10-

3

Im = (-53 71 36) 10-3




Im = (-53 71 36) 10-3








ppp

ppp

)0()0(

)0()0(

NN

NNA


Radiative decays








211221 )()(


IB DE

p1 p1

p2p2

q q







)(

)(

S

L

KA

violatingCPKA




KL π+πminus






IB

M1 DE




KL itself





KL ee


BR = (308 020) 10minus7



E1M1 lt 004 (90 CL)



φ




KS ee

No asymmetry for KS

as expected

BR = (471 032) 10-

5

AΦ = (05 43)






IBEE

dEA

)tan( 0


Kplusmn π+π0γ

)730810672()(

)250350353()(

800

800

syststatMeVT

syststatMeVT

INTFrac

DEFrac







KL π+πndashπ0γ















)(

)2030(

3

3

e

ee

K

MeVEKR





bull 6M Ke3 events


ndash R=(0964plusmn0008+0011-0009)












PDG 2004







]21[192 3

52

KmG







Vus measurements





unitarity





KLOE Kl 3

KLOE K2

copy A Antonelli

Vus some more




Ke4 results





K+rarrπ0π0eν










1-loop rescattering

2-loop rescattering











NA482




KLOE interference

















K+ + 8middot10-11 (at 7)147+130

ndash089 middot 10-

10 (BNL E787+E949)






KL 0ℓ+ℓ-




BR(KL 0+-) lt 3810-10





NA481 KS 0ℓ+ℓ-



BR = (58 +28-23 plusmn08) times10-9


-012 (accid)BR = (28 +15


KS 0e+e- KS 0μ+μ-


NA481 preliminary

NA481 preliminary


KL 0ℓ+ℓ-






Krarr in the SM




W W

s

id

Vis Vid

e

i=uct

W

Z

VisV

idds i

11

20

2410

10)1108(

)(1001)(

AKB

11

2

5

100

10)4082(

)()Im(

1022)(

t

tdtsL xX

VVKB


K

ε εrsquo




Ke3 KL 0

Height

Im(λt )



10301890 10471)(

KBR









K+ +




















Appendixes





J(ππ) = ℓ(ππ) = 0 P(ππ) = +1 C(ππ) = +1



ℓL



SLti

SLLSti

LS

tL

tS

Lti

LSti

S

KKeaaKKeaa

eaea

KeaKea

SLLS

LS

LS

)()(

22

f LSf

fLS KfA

dt

d 2

2

TUnitarity requires

and therefore


f Sff

fS

fLSLLS

f

fLLf

fSS

fKAAKKmi

AA

)(2)(

22


2

22

2

222

0604

mKK

AAAA

LS

LSLS

f

fSf

fLf

fS

fL



SLS KKmi 21




)()( 0000

SSS KK




S+KL

KL




000 000 00

1( )2 ( 2

0

)

( )


tt

NEARf E t



)()()( 00

00

EKNEKN

EKNEKNED

(incoherent

production)



Assuming CPT





N3

20

40

60

00

4 62


No CPV seen yet

























PT() = (-17 23 11) 10-

3

Im = (-53 71 36) 10-3




Im = (-53 71 36) 10-3








ppp

ppp

)0()0(

)0()0(

NN

NNA


Radiative decays








211221 )()(


IB DE

p1 p1

p2p2

q q







)(

)(

S

L

KA

violatingCPKA




KL π+πminus






IB

M1 DE




KL itself





KL ee


BR = (308 020) 10minus7



E1M1 lt 004 (90 CL)



φ




KS ee

No asymmetry for KS

as expected

BR = (471 032) 10-

5

AΦ = (05 43)






IBEE

dEA

)tan( 0


Kplusmn π+π0γ

)730810672()(

)250350353()(

800

800

syststatMeVT

syststatMeVT

INTFrac

DEFrac







KL π+πndashπ0γ















)(

)2030(

3

3

e

ee

K

MeVEKR





bull 6M Ke3 events


ndash R=(0964plusmn0008+0011-0009)












PDG 2004







]21[192 3

52

KmG







Vus measurements





unitarity





KLOE Kl 3

KLOE K2

copy A Antonelli

Vus some more




Ke4 results





K+rarrπ0π0eν










1-loop rescattering

2-loop rescattering











NA482




KLOE interference

















K+ + 8middot10-11 (at 7)147+130

ndash089 middot 10-

10 (BNL E787+E949)






KL 0ℓ+ℓ-




BR(KL 0+-) lt 3810-10





NA481 KS 0ℓ+ℓ-



BR = (58 +28-23 plusmn08) times10-9


-012 (accid)BR = (28 +15


KS 0e+e- KS 0μ+μ-


NA481 preliminary

NA481 preliminary


KL 0ℓ+ℓ-






Krarr in the SM




W W

s

id

Vis Vid

e

i=uct

W

Z

VisV

idds i

11

20

2410

10)1108(

)(1001)(

AKB

11

2

5

100

10)4082(

)()Im(

1022)(

t

tdtsL xX

VVKB


K

ε εrsquo




Ke3 KL 0

Height

Im(λt )



10301890 10471)(

KBR









K+ +




















Appendixes





J(ππ) = ℓ(ππ) = 0 P(ππ) = +1 C(ππ) = +1



ℓL



SLti

SLLSti

LS

tL

tS

Lti

LSti

S

KKeaaKKeaa

eaea

KeaKea

SLLS

LS

LS

)()(

22

f LSf

fLS KfA

dt

d 2

2

TUnitarity requires

and therefore


f Sff

fS

fLSLLS

f

fLLf

fSS

fKAAKKmi

AA

)(2)(

22


2

22

2

222

0604

mKK

AAAA

LS

LSLS

f

fSf

fLf

fS

fL



SLS KKmi 21




)()( 0000

SSS KK





N3

20

40

60

00

4 62


No CPV seen yet

























PT() = (-17 23 11) 10-

3

Im = (-53 71 36) 10-3




Im = (-53 71 36) 10-3








ppp

ppp

)0()0(

)0()0(

NN

NNA


Radiative decays








211221 )()(


IB DE

p1 p1

p2p2

q q







)(

)(

S

L

KA

violatingCPKA




KL π+πminus






IB

M1 DE




KL itself





KL ee


BR = (308 020) 10minus7



E1M1 lt 004 (90 CL)



φ




KS ee

No asymmetry for KS

as expected

BR = (471 032) 10-

5

AΦ = (05 43)






IBEE

dEA

)tan( 0


Kplusmn π+π0γ

)730810672()(

)250350353()(

800

800

syststatMeVT

syststatMeVT

INTFrac

DEFrac







KL π+πndashπ0γ















)(

)2030(

3

3

e

ee

K

MeVEKR





bull 6M Ke3 events


ndash R=(0964plusmn0008+0011-0009)












PDG 2004







]21[192 3

52

KmG







Vus measurements





unitarity





KLOE Kl 3

KLOE K2

copy A Antonelli

Vus some more




Ke4 results





K+rarrπ0π0eν










1-loop rescattering

2-loop rescattering











NA482




KLOE interference

















K+ + 8middot10-11 (at 7)147+130

ndash089 middot 10-

10 (BNL E787+E949)






KL 0ℓ+ℓ-




BR(KL 0+-) lt 3810-10





NA481 KS 0ℓ+ℓ-



BR = (58 +28-23 plusmn08) times10-9


-012 (accid)BR = (28 +15


KS 0e+e- KS 0μ+μ-


NA481 preliminary

NA481 preliminary


KL 0ℓ+ℓ-






Krarr in the SM




W W

s

id

Vis Vid

e

i=uct

W

Z

VisV

idds i

11

20

2410

10)1108(

)(1001)(

AKB

11

2

5

100

10)4082(

)()Im(

1022)(

t

tdtsL xX

VVKB


K

ε εrsquo




Ke3 KL 0

Height

Im(λt )



10301890 10471)(

KBR









K+ +




















Appendixes





J(ππ) = ℓ(ππ) = 0 P(ππ) = +1 C(ππ) = +1



ℓL



SLti

SLLSti

LS

tL

tS

Lti

LSti

S

KKeaaKKeaa

eaea

KeaKea

SLLS

LS

LS

)()(

22

f LSf

fLS KfA

dt

d 2

2

TUnitarity requires

and therefore


f Sff

fS

fLSLLS

f

fLLf

fSS

fKAAKKmi

AA

)(2)(

22


2

22

2

222

0604

mKK

AAAA

LS

LSLS

f

fSf

fLf

fS

fL



SLS KKmi 21




)()( 0000

SSS KK
























PT() = (-17 23 11) 10-

3

Im = (-53 71 36) 10-3




Im = (-53 71 36) 10-3








ppp

ppp

)0()0(

)0()0(

NN

NNA


Radiative decays








211221 )()(


IB DE

p1 p1

p2p2

q q







)(

)(

S

L

KA

violatingCPKA




KL π+πminus






IB

M1 DE




KL itself





KL ee


BR = (308 020) 10minus7



E1M1 lt 004 (90 CL)



φ




KS ee

No asymmetry for KS

as expected

BR = (471 032) 10-

5

AΦ = (05 43)






IBEE

dEA

)tan( 0


Kplusmn π+π0γ

)730810672()(

)250350353()(

800

800

syststatMeVT

syststatMeVT

INTFrac

DEFrac







KL π+πndashπ0γ















)(

)2030(

3

3

e

ee

K

MeVEKR





bull 6M Ke3 events


ndash R=(0964plusmn0008+0011-0009)












PDG 2004







]21[192 3

52

KmG







Vus measurements





unitarity





KLOE Kl 3

KLOE K2

copy A Antonelli

Vus some more




Ke4 results





K+rarrπ0π0eν










1-loop rescattering

2-loop rescattering











NA482




KLOE interference

















K+ + 8middot10-11 (at 7)147+130

ndash089 middot 10-

10 (BNL E787+E949)






KL 0ℓ+ℓ-




BR(KL 0+-) lt 3810-10





NA481 KS 0ℓ+ℓ-



BR = (58 +28-23 plusmn08) times10-9


-012 (accid)BR = (28 +15


KS 0e+e- KS 0μ+μ-


NA481 preliminary

NA481 preliminary


KL 0ℓ+ℓ-






Krarr in the SM




W W

s

id

Vis Vid

e

i=uct

W

Z

VisV

idds i

11

20

2410

10)1108(

)(1001)(

AKB

11

2

5

100

10)4082(

)()Im(

1022)(

t

tdtsL xX

VVKB


K

ε εrsquo




Ke3 KL 0

Height

Im(λt )



10301890 10471)(

KBR









K+ +




















Appendixes





J(ππ) = ℓ(ππ) = 0 P(ππ) = +1 C(ππ) = +1



ℓL



SLti

SLLSti

LS

tL

tS

Lti

LSti

S

KKeaaKKeaa

eaea

KeaKea

SLLS

LS

LS

)()(

22

f LSf

fLS KfA

dt

d 2

2

TUnitarity requires

and therefore


f Sff

fS

fLSLLS

f

fLLf

fSS

fKAAKKmi

AA

)(2)(

22


2

22

2

222

0604

mKK

AAAA

LS

LSLS

f

fSf

fLf

fS

fL



SLS KKmi 21




)()( 0000

SSS KK






















PT() = (-17 23 11) 10-

3

Im = (-53 71 36) 10-3




Im = (-53 71 36) 10-3








ppp

ppp

)0()0(

)0()0(

NN

NNA


Radiative decays








211221 )()(


IB DE

p1 p1

p2p2

q q







)(

)(

S

L

KA

violatingCPKA




KL π+πminus






IB

M1 DE




KL itself





KL ee


BR = (308 020) 10minus7



E1M1 lt 004 (90 CL)



φ




KS ee

No asymmetry for KS

as expected

BR = (471 032) 10-

5

AΦ = (05 43)






IBEE

dEA

)tan( 0


Kplusmn π+π0γ

)730810672()(

)250350353()(

800

800

syststatMeVT

syststatMeVT

INTFrac

DEFrac







KL π+πndashπ0γ















)(

)2030(

3

3

e

ee

K

MeVEKR





bull 6M Ke3 events


ndash R=(0964plusmn0008+0011-0009)












PDG 2004







]21[192 3

52

KmG







Vus measurements





unitarity





KLOE Kl 3

KLOE K2

copy A Antonelli

Vus some more




Ke4 results





K+rarrπ0π0eν










1-loop rescattering

2-loop rescattering











NA482




KLOE interference

















K+ + 8middot10-11 (at 7)147+130

ndash089 middot 10-

10 (BNL E787+E949)






KL 0ℓ+ℓ-




BR(KL 0+-) lt 3810-10





NA481 KS 0ℓ+ℓ-



BR = (58 +28-23 plusmn08) times10-9


-012 (accid)BR = (28 +15


KS 0e+e- KS 0μ+μ-


NA481 preliminary

NA481 preliminary


KL 0ℓ+ℓ-






Krarr in the SM




W W

s

id

Vis Vid

e

i=uct

W

Z

VisV

idds i

11

20

2410

10)1108(

)(1001)(

AKB

11

2

5

100

10)4082(

)()Im(

1022)(

t

tdtsL xX

VVKB


K

ε εrsquo




Ke3 KL 0

Height

Im(λt )



10301890 10471)(

KBR









K+ +




















Appendixes





J(ππ) = ℓ(ππ) = 0 P(ππ) = +1 C(ππ) = +1



ℓL



SLti

SLLSti

LS

tL

tS

Lti

LSti

S

KKeaaKKeaa

eaea

KeaKea

SLLS

LS

LS

)()(

22

f LSf

fLS KfA

dt

d 2

2

TUnitarity requires

and therefore


f Sff

fS

fLSLLS

f

fLLf

fSS

fKAAKKmi

AA

)(2)(

22


2

22

2

222

0604

mKK

AAAA

LS

LSLS

f

fSf

fLf

fS

fL



SLS KKmi 21




)()( 0000

SSS KK














PT() = (-17 23 11) 10-

3

Im = (-53 71 36) 10-3




Im = (-53 71 36) 10-3








ppp

ppp

)0()0(

)0()0(

NN

NNA


Radiative decays








211221 )()(


IB DE

p1 p1

p2p2

q q







)(

)(

S

L

KA

violatingCPKA




KL π+πminus






IB

M1 DE




KL itself





KL ee


BR = (308 020) 10minus7



E1M1 lt 004 (90 CL)



φ




KS ee

No asymmetry for KS

as expected

BR = (471 032) 10-

5

AΦ = (05 43)






IBEE

dEA

)tan( 0


Kplusmn π+π0γ

)730810672()(

)250350353()(

800

800

syststatMeVT

syststatMeVT

INTFrac

DEFrac







KL π+πndashπ0γ















)(

)2030(

3

3

e

ee

K

MeVEKR





bull 6M Ke3 events


ndash R=(0964plusmn0008+0011-0009)












PDG 2004







]21[192 3

52

KmG







Vus measurements





unitarity





KLOE Kl 3

KLOE K2

copy A Antonelli

Vus some more




Ke4 results





K+rarrπ0π0eν










1-loop rescattering

2-loop rescattering











NA482




KLOE interference

















K+ + 8middot10-11 (at 7)147+130

ndash089 middot 10-

10 (BNL E787+E949)






KL 0ℓ+ℓ-




BR(KL 0+-) lt 3810-10





NA481 KS 0ℓ+ℓ-



BR = (58 +28-23 plusmn08) times10-9


-012 (accid)BR = (28 +15


KS 0e+e- KS 0μ+μ-


NA481 preliminary

NA481 preliminary


KL 0ℓ+ℓ-






Krarr in the SM




W W

s

id

Vis Vid

e

i=uct

W

Z

VisV

idds i

11

20

2410

10)1108(

)(1001)(

AKB

11

2

5

100

10)4082(

)()Im(

1022)(

t

tdtsL xX

VVKB


K

ε εrsquo




Ke3 KL 0

Height

Im(λt )



10301890 10471)(

KBR









K+ +




















Appendixes





J(ππ) = ℓ(ππ) = 0 P(ππ) = +1 C(ππ) = +1



ℓL



SLti

SLLSti

LS

tL

tS

Lti

LSti

S

KKeaaKKeaa

eaea

KeaKea

SLLS

LS

LS

)()(

22

f LSf

fLS KfA

dt

d 2

2

TUnitarity requires

and therefore


f Sff

fS

fLSLLS

f

fLLf

fSS

fKAAKKmi

AA

)(2)(

22


2

22

2

222

0604

mKK

AAAA

LS

LSLS

f

fSf

fLf

fS

fL



SLS KKmi 21




)()( 0000

SSS KK












PT() = (-17 23 11) 10-

3

Im = (-53 71 36) 10-3




Im = (-53 71 36) 10-3








ppp

ppp

)0()0(

)0()0(

NN

NNA


Radiative decays








211221 )()(


IB DE

p1 p1

p2p2

q q







)(

)(

S

L

KA

violatingCPKA




KL π+πminus






IB

M1 DE




KL itself





KL ee


BR = (308 020) 10minus7



E1M1 lt 004 (90 CL)



φ




KS ee

No asymmetry for KS

as expected

BR = (471 032) 10-

5

AΦ = (05 43)






IBEE

dEA

)tan( 0


Kplusmn π+π0γ

)730810672()(

)250350353()(

800

800

syststatMeVT

syststatMeVT

INTFrac

DEFrac







KL π+πndashπ0γ















)(

)2030(

3

3

e

ee

K

MeVEKR





bull 6M Ke3 events


ndash R=(0964plusmn0008+0011-0009)












PDG 2004







]21[192 3

52

KmG







Vus measurements





unitarity





KLOE Kl 3

KLOE K2

copy A Antonelli

Vus some more




Ke4 results





K+rarrπ0π0eν










1-loop rescattering

2-loop rescattering











NA482




KLOE interference

















K+ + 8middot10-11 (at 7)147+130

ndash089 middot 10-

10 (BNL E787+E949)






KL 0ℓ+ℓ-




BR(KL 0+-) lt 3810-10





NA481 KS 0ℓ+ℓ-



BR = (58 +28-23 plusmn08) times10-9


-012 (accid)BR = (28 +15


KS 0e+e- KS 0μ+μ-


NA481 preliminary

NA481 preliminary


KL 0ℓ+ℓ-






Krarr in the SM




W W

s

id

Vis Vid

e

i=uct

W

Z

VisV

idds i

11

20

2410

10)1108(

)(1001)(

AKB

11

2

5

100

10)4082(

)()Im(

1022)(

t

tdtsL xX

VVKB


K

ε εrsquo




Ke3 KL 0

Height

Im(λt )



10301890 10471)(

KBR









K+ +




















Appendixes





J(ππ) = ℓ(ππ) = 0 P(ππ) = +1 C(ππ) = +1



ℓL



SLti

SLLSti

LS

tL

tS

Lti

LSti

S

KKeaaKKeaa

eaea

KeaKea

SLLS

LS

LS

)()(

22

f LSf

fLS KfA

dt

d 2

2

TUnitarity requires

and therefore


f Sff

fS

fLSLLS

f

fLLf

fSS

fKAAKKmi

AA

)(2)(

22


2

22

2

222

0604

mKK

AAAA

LS

LSLS

f

fSf

fLf

fS

fL



SLS KKmi 21




)()( 0000

SSS KK





PT() = (-17 23 11) 10-

3

Im = (-53 71 36) 10-3




Im = (-53 71 36) 10-3








ppp

ppp

)0()0(

)0()0(

NN

NNA


Radiative decays








211221 )()(


IB DE

p1 p1

p2p2

q q







)(

)(

S

L

KA

violatingCPKA




KL π+πminus






IB

M1 DE




KL itself





KL ee


BR = (308 020) 10minus7



E1M1 lt 004 (90 CL)



φ




KS ee

No asymmetry for KS

as expected

BR = (471 032) 10-

5

AΦ = (05 43)






IBEE

dEA

)tan( 0


Kplusmn π+π0γ

)730810672()(

)250350353()(

800

800

syststatMeVT

syststatMeVT

INTFrac

DEFrac







KL π+πndashπ0γ















)(

)2030(

3

3

e

ee

K

MeVEKR





bull 6M Ke3 events


ndash R=(0964plusmn0008+0011-0009)












PDG 2004







]21[192 3

52

KmG







Vus measurements





unitarity





KLOE Kl 3

KLOE K2

copy A Antonelli

Vus some more




Ke4 results





K+rarrπ0π0eν










1-loop rescattering

2-loop rescattering











NA482




KLOE interference

















K+ + 8middot10-11 (at 7)147+130

ndash089 middot 10-

10 (BNL E787+E949)






KL 0ℓ+ℓ-




BR(KL 0+-) lt 3810-10





NA481 KS 0ℓ+ℓ-



BR = (58 +28-23 plusmn08) times10-9


-012 (accid)BR = (28 +15


KS 0e+e- KS 0μ+μ-


NA481 preliminary

NA481 preliminary


KL 0ℓ+ℓ-






Krarr in the SM




W W

s

id

Vis Vid

e

i=uct

W

Z

VisV

idds i

11

20

2410

10)1108(

)(1001)(

AKB

11

2

5

100

10)4082(

)()Im(

1022)(

t

tdtsL xX

VVKB


K

ε εrsquo




Ke3 KL 0

Height

Im(λt )



10301890 10471)(

KBR









K+ +




















Appendixes





J(ππ) = ℓ(ππ) = 0 P(ππ) = +1 C(ππ) = +1



ℓL



SLti

SLLSti

LS

tL

tS

Lti

LSti

S

KKeaaKKeaa

eaea

KeaKea

SLLS

LS

LS

)()(

22

f LSf

fLS KfA

dt

d 2

2

TUnitarity requires

and therefore


f Sff

fS

fLSLLS

f

fLLf

fSS

fKAAKKmi

AA

)(2)(

22


2

22

2

222

0604

mKK

AAAA

LS

LSLS

f

fSf

fLf

fS

fL



SLS KKmi 21




)()( 0000

SSS KK









ppp

ppp

)0()0(

)0()0(

NN

NNA


Radiative decays








211221 )()(


IB DE

p1 p1

p2p2

q q







)(

)(

S

L

KA

violatingCPKA




KL π+πminus






IB

M1 DE




KL itself





KL ee


BR = (308 020) 10minus7



E1M1 lt 004 (90 CL)



φ




KS ee

No asymmetry for KS

as expected

BR = (471 032) 10-

5

AΦ = (05 43)






IBEE

dEA

)tan( 0


Kplusmn π+π0γ

)730810672()(

)250350353()(

800

800

syststatMeVT

syststatMeVT

INTFrac

DEFrac







KL π+πndashπ0γ















)(

)2030(

3

3

e

ee

K

MeVEKR





bull 6M Ke3 events


ndash R=(0964plusmn0008+0011-0009)












PDG 2004







]21[192 3

52

KmG







Vus measurements





unitarity





KLOE Kl 3

KLOE K2

copy A Antonelli

Vus some more




Ke4 results





K+rarrπ0π0eν










1-loop rescattering

2-loop rescattering











NA482




KLOE interference

















K+ + 8middot10-11 (at 7)147+130

ndash089 middot 10-

10 (BNL E787+E949)






KL 0ℓ+ℓ-




BR(KL 0+-) lt 3810-10





NA481 KS 0ℓ+ℓ-



BR = (58 +28-23 plusmn08) times10-9


-012 (accid)BR = (28 +15


KS 0e+e- KS 0μ+μ-


NA481 preliminary

NA481 preliminary


KL 0ℓ+ℓ-






Krarr in the SM




W W

s

id

Vis Vid

e

i=uct

W

Z

VisV

idds i

11

20

2410

10)1108(

)(1001)(

AKB

11

2

5

100

10)4082(

)()Im(

1022)(

t

tdtsL xX

VVKB


K

ε εrsquo




Ke3 KL 0

Height

Im(λt )



10301890 10471)(

KBR









K+ +




















Appendixes





J(ππ) = ℓ(ππ) = 0 P(ππ) = +1 C(ππ) = +1



ℓL



SLti

SLLSti

LS

tL

tS

Lti

LSti

S

KKeaaKKeaa

eaea

KeaKea

SLLS

LS

LS

)()(

22

f LSf

fLS KfA

dt

d 2

2

TUnitarity requires

and therefore


f Sff

fS

fLSLLS

f

fLLf

fSS

fKAAKKmi

AA

)(2)(

22


2

22

2

222

0604

mKK

AAAA

LS

LSLS

f

fSf

fLf

fS

fL



SLS KKmi 21




)()( 0000

SSS KK



Radiative decays








211221 )()(


IB DE

p1 p1

p2p2

q q







)(

)(

S

L

KA

violatingCPKA




KL π+πminus






IB

M1 DE




KL itself





KL ee


BR = (308 020) 10minus7



E1M1 lt 004 (90 CL)



φ




KS ee

No asymmetry for KS

as expected

BR = (471 032) 10-

5

AΦ = (05 43)






IBEE

dEA

)tan( 0


Kplusmn π+π0γ

)730810672()(

)250350353()(

800

800

syststatMeVT

syststatMeVT

INTFrac

DEFrac







KL π+πndashπ0γ















)(

)2030(

3

3

e

ee

K

MeVEKR





bull 6M Ke3 events


ndash R=(0964plusmn0008+0011-0009)












PDG 2004







]21[192 3

52

KmG







Vus measurements





unitarity





KLOE Kl 3

KLOE K2

copy A Antonelli

Vus some more




Ke4 results





K+rarrπ0π0eν










1-loop rescattering

2-loop rescattering











NA482




KLOE interference

















K+ + 8middot10-11 (at 7)147+130

ndash089 middot 10-

10 (BNL E787+E949)






KL 0ℓ+ℓ-




BR(KL 0+-) lt 3810-10





NA481 KS 0ℓ+ℓ-



BR = (58 +28-23 plusmn08) times10-9


-012 (accid)BR = (28 +15


KS 0e+e- KS 0μ+μ-


NA481 preliminary

NA481 preliminary


KL 0ℓ+ℓ-






Krarr in the SM




W W

s

id

Vis Vid

e

i=uct

W

Z

VisV

idds i

11

20

2410

10)1108(

)(1001)(

AKB

11

2

5

100

10)4082(

)()Im(

1022)(

t

tdtsL xX

VVKB


K

ε εrsquo




Ke3 KL 0

Height

Im(λt )



10301890 10471)(

KBR









K+ +




















Appendixes





J(ππ) = ℓ(ππ) = 0 P(ππ) = +1 C(ππ) = +1



ℓL



SLti

SLLSti

LS

tL

tS

Lti

LSti

S

KKeaaKKeaa

eaea

KeaKea

SLLS

LS

LS

)()(

22

f LSf

fLS KfA

dt

d 2

2

TUnitarity requires

and therefore


f Sff

fS

fLSLLS

f

fLLf

fSS

fKAAKKmi

AA

)(2)(

22


2

22

2

222

0604

mKK

AAAA

LS

LSLS

f

fSf

fLf

fS

fL



SLS KKmi 21




)()( 0000

SSS KK









211221 )()(


IB DE

p1 p1

p2p2

q q







)(

)(

S

L

KA

violatingCPKA




KL π+πminus






IB

M1 DE




KL itself





KL ee


BR = (308 020) 10minus7



E1M1 lt 004 (90 CL)



φ




KS ee

No asymmetry for KS

as expected

BR = (471 032) 10-

5

AΦ = (05 43)






IBEE

dEA

)tan( 0


Kplusmn π+π0γ

)730810672()(

)250350353()(

800

800

syststatMeVT

syststatMeVT

INTFrac

DEFrac







KL π+πndashπ0γ















)(

)2030(

3

3

e

ee

K

MeVEKR





bull 6M Ke3 events


ndash R=(0964plusmn0008+0011-0009)












PDG 2004







]21[192 3

52

KmG







Vus measurements





unitarity





KLOE Kl 3

KLOE K2

copy A Antonelli

Vus some more




Ke4 results





K+rarrπ0π0eν










1-loop rescattering

2-loop rescattering











NA482




KLOE interference

















K+ + 8middot10-11 (at 7)147+130

ndash089 middot 10-

10 (BNL E787+E949)






KL 0ℓ+ℓ-




BR(KL 0+-) lt 3810-10





NA481 KS 0ℓ+ℓ-



BR = (58 +28-23 plusmn08) times10-9


-012 (accid)BR = (28 +15


KS 0e+e- KS 0μ+μ-


NA481 preliminary

NA481 preliminary


KL 0ℓ+ℓ-






Krarr in the SM




W W

s

id

Vis Vid

e

i=uct

W

Z

VisV

idds i

11

20

2410

10)1108(

)(1001)(

AKB

11

2

5

100

10)4082(

)()Im(

1022)(

t

tdtsL xX

VVKB


K

ε εrsquo




Ke3 KL 0

Height

Im(λt )



10301890 10471)(

KBR









K+ +




















Appendixes





J(ππ) = ℓ(ππ) = 0 P(ππ) = +1 C(ππ) = +1



ℓL



SLti

SLLSti

LS

tL

tS

Lti

LSti

S

KKeaaKKeaa

eaea

KeaKea

SLLS

LS

LS

)()(

22

f LSf

fLS KfA

dt

d 2

2

TUnitarity requires

and therefore


f Sff

fS

fLSLLS

f

fLLf

fSS

fKAAKKmi

AA

)(2)(

22


2

22

2

222

0604

mKK

AAAA

LS

LSLS

f

fSf

fLf

fS

fL



SLS KKmi 21




)()( 0000

SSS KK








)(

)(

S

L

KA

violatingCPKA




KL π+πminus






IB

M1 DE




KL itself





KL ee


BR = (308 020) 10minus7



E1M1 lt 004 (90 CL)



φ




KS ee

No asymmetry for KS

as expected

BR = (471 032) 10-

5

AΦ = (05 43)






IBEE

dEA

)tan( 0


Kplusmn π+π0γ

)730810672()(

)250350353()(

800

800

syststatMeVT

syststatMeVT

INTFrac

DEFrac







KL π+πndashπ0γ















)(

)2030(

3

3

e

ee

K

MeVEKR





bull 6M Ke3 events


ndash R=(0964plusmn0008+0011-0009)












PDG 2004







]21[192 3

52

KmG







Vus measurements





unitarity





KLOE Kl 3

KLOE K2

copy A Antonelli

Vus some more




Ke4 results





K+rarrπ0π0eν










1-loop rescattering

2-loop rescattering











NA482




KLOE interference

















K+ + 8middot10-11 (at 7)147+130

ndash089 middot 10-

10 (BNL E787+E949)






KL 0ℓ+ℓ-




BR(KL 0+-) lt 3810-10





NA481 KS 0ℓ+ℓ-



BR = (58 +28-23 plusmn08) times10-9


-012 (accid)BR = (28 +15


KS 0e+e- KS 0μ+μ-


NA481 preliminary

NA481 preliminary


KL 0ℓ+ℓ-






Krarr in the SM




W W

s

id

Vis Vid

e

i=uct

W

Z

VisV

idds i

11

20

2410

10)1108(

)(1001)(

AKB

11

2

5

100

10)4082(

)()Im(

1022)(

t

tdtsL xX

VVKB


K

ε εrsquo




Ke3 KL 0

Height

Im(λt )



10301890 10471)(

KBR









K+ +




















Appendixes





J(ππ) = ℓ(ππ) = 0 P(ππ) = +1 C(ππ) = +1



ℓL



SLti

SLLSti

LS

tL

tS

Lti

LSti

S

KKeaaKKeaa

eaea

KeaKea

SLLS

LS

LS

)()(

22

f LSf

fLS KfA

dt

d 2

2

TUnitarity requires

and therefore


f Sff

fS

fLSLLS

f

fLLf

fSS

fKAAKKmi

AA

)(2)(

22


2

22

2

222

0604

mKK

AAAA

LS

LSLS

f

fSf

fLf

fS

fL



SLS KKmi 21




)()( 0000

SSS KK



KL π+πminus






IB

M1 DE




KL itself





KL ee


BR = (308 020) 10minus7



E1M1 lt 004 (90 CL)



φ




KS ee

No asymmetry for KS

as expected

BR = (471 032) 10-

5

AΦ = (05 43)






IBEE

dEA

)tan( 0


Kplusmn π+π0γ

)730810672()(

)250350353()(

800

800

syststatMeVT

syststatMeVT

INTFrac

DEFrac







KL π+πndashπ0γ















)(

)2030(

3

3

e

ee

K

MeVEKR





bull 6M Ke3 events


ndash R=(0964plusmn0008+0011-0009)












PDG 2004







]21[192 3

52

KmG







Vus measurements





unitarity





KLOE Kl 3

KLOE K2

copy A Antonelli

Vus some more




Ke4 results





K+rarrπ0π0eν










1-loop rescattering

2-loop rescattering











NA482




KLOE interference

















K+ + 8middot10-11 (at 7)147+130

ndash089 middot 10-

10 (BNL E787+E949)






KL 0ℓ+ℓ-




BR(KL 0+-) lt 3810-10





NA481 KS 0ℓ+ℓ-



BR = (58 +28-23 plusmn08) times10-9


-012 (accid)BR = (28 +15


KS 0e+e- KS 0μ+μ-


NA481 preliminary

NA481 preliminary


KL 0ℓ+ℓ-






Krarr in the SM




W W

s

id

Vis Vid

e

i=uct

W

Z

VisV

idds i

11

20

2410

10)1108(

)(1001)(

AKB

11

2

5

100

10)4082(

)()Im(

1022)(

t

tdtsL xX

VVKB


K

ε εrsquo




Ke3 KL 0

Height

Im(λt )



10301890 10471)(

KBR









K+ +




















Appendixes





J(ππ) = ℓ(ππ) = 0 P(ππ) = +1 C(ππ) = +1



ℓL



SLti

SLLSti

LS

tL

tS

Lti

LSti

S

KKeaaKKeaa

eaea

KeaKea

SLLS

LS

LS

)()(

22

f LSf

fLS KfA

dt

d 2

2

TUnitarity requires

and therefore


f Sff

fS

fLSLLS

f

fLLf

fSS

fKAAKKmi

AA

)(2)(

22


2

22

2

222

0604

mKK

AAAA

LS

LSLS

f

fSf

fLf

fS

fL



SLS KKmi 21




)()( 0000

SSS KK





KL itself





KL ee


BR = (308 020) 10minus7



E1M1 lt 004 (90 CL)



φ




KS ee

No asymmetry for KS

as expected

BR = (471 032) 10-

5

AΦ = (05 43)






IBEE

dEA

)tan( 0


Kplusmn π+π0γ

)730810672()(

)250350353()(

800

800

syststatMeVT

syststatMeVT

INTFrac

DEFrac







KL π+πndashπ0γ















)(

)2030(

3

3

e

ee

K

MeVEKR





bull 6M Ke3 events


ndash R=(0964plusmn0008+0011-0009)












PDG 2004







]21[192 3

52

KmG







Vus measurements





unitarity





KLOE Kl 3

KLOE K2

copy A Antonelli

Vus some more




Ke4 results





K+rarrπ0π0eν










1-loop rescattering

2-loop rescattering











NA482




KLOE interference

















K+ + 8middot10-11 (at 7)147+130

ndash089 middot 10-

10 (BNL E787+E949)






KL 0ℓ+ℓ-




BR(KL 0+-) lt 3810-10





NA481 KS 0ℓ+ℓ-



BR = (58 +28-23 plusmn08) times10-9


-012 (accid)BR = (28 +15


KS 0e+e- KS 0μ+μ-


NA481 preliminary

NA481 preliminary


KL 0ℓ+ℓ-






Krarr in the SM




W W

s

id

Vis Vid

e

i=uct

W

Z

VisV

idds i

11

20

2410

10)1108(

)(1001)(

AKB

11

2

5

100

10)4082(

)()Im(

1022)(

t

tdtsL xX

VVKB


K

ε εrsquo




Ke3 KL 0

Height

Im(λt )



10301890 10471)(

KBR









K+ +




















Appendixes





J(ππ) = ℓ(ππ) = 0 P(ππ) = +1 C(ππ) = +1



ℓL



SLti

SLLSti

LS

tL

tS

Lti

LSti

S

KKeaaKKeaa

eaea

KeaKea

SLLS

LS

LS

)()(

22

f LSf

fLS KfA

dt

d 2

2

TUnitarity requires

and therefore


f Sff

fS

fLSLLS

f

fLLf

fSS

fKAAKKmi

AA

)(2)(

22


2

22

2

222

0604

mKK

AAAA

LS

LSLS

f

fSf

fLf

fS

fL



SLS KKmi 21




)()( 0000

SSS KK



KL ee


BR = (308 020) 10minus7



E1M1 lt 004 (90 CL)



φ




KS ee

No asymmetry for KS

as expected

BR = (471 032) 10-

5

AΦ = (05 43)






IBEE

dEA

)tan( 0


Kplusmn π+π0γ

)730810672()(

)250350353()(

800

800

syststatMeVT

syststatMeVT

INTFrac

DEFrac







KL π+πndashπ0γ















)(

)2030(

3

3

e

ee

K

MeVEKR





bull 6M Ke3 events


ndash R=(0964plusmn0008+0011-0009)












PDG 2004







]21[192 3

52

KmG







Vus measurements





unitarity





KLOE Kl 3

KLOE K2

copy A Antonelli

Vus some more




Ke4 results





K+rarrπ0π0eν










1-loop rescattering

2-loop rescattering











NA482




KLOE interference

















K+ + 8middot10-11 (at 7)147+130

ndash089 middot 10-

10 (BNL E787+E949)






KL 0ℓ+ℓ-




BR(KL 0+-) lt 3810-10





NA481 KS 0ℓ+ℓ-



BR = (58 +28-23 plusmn08) times10-9


-012 (accid)BR = (28 +15


KS 0e+e- KS 0μ+μ-


NA481 preliminary

NA481 preliminary


KL 0ℓ+ℓ-






Krarr in the SM




W W

s

id

Vis Vid

e

i=uct

W

Z

VisV

idds i

11

20

2410

10)1108(

)(1001)(

AKB

11

2

5

100

10)4082(

)()Im(

1022)(

t

tdtsL xX

VVKB


K

ε εrsquo




Ke3 KL 0

Height

Im(λt )



10301890 10471)(

KBR









K+ +




















Appendixes





J(ππ) = ℓ(ππ) = 0 P(ππ) = +1 C(ππ) = +1



ℓL



SLti

SLLSti

LS

tL

tS

Lti

LSti

S

KKeaaKKeaa

eaea

KeaKea

SLLS

LS

LS

)()(

22

f LSf

fLS KfA

dt

d 2

2

TUnitarity requires

and therefore


f Sff

fS

fLSLLS

f

fLLf

fSS

fKAAKKmi

AA

)(2)(

22


2

22

2

222

0604

mKK

AAAA

LS

LSLS

f

fSf

fLf

fS

fL



SLS KKmi 21




)()( 0000

SSS KK




φ




KS ee

No asymmetry for KS

as expected

BR = (471 032) 10-

5

AΦ = (05 43)






IBEE

dEA

)tan( 0


Kplusmn π+π0γ

)730810672()(

)250350353()(

800

800

syststatMeVT

syststatMeVT

INTFrac

DEFrac







KL π+πndashπ0γ















)(

)2030(

3

3

e

ee

K

MeVEKR





bull 6M Ke3 events


ndash R=(0964plusmn0008+0011-0009)












PDG 2004







]21[192 3

52

KmG







Vus measurements





unitarity





KLOE Kl 3

KLOE K2

copy A Antonelli

Vus some more




Ke4 results





K+rarrπ0π0eν










1-loop rescattering

2-loop rescattering











NA482




KLOE interference

















K+ + 8middot10-11 (at 7)147+130

ndash089 middot 10-

10 (BNL E787+E949)






KL 0ℓ+ℓ-




BR(KL 0+-) lt 3810-10





NA481 KS 0ℓ+ℓ-



BR = (58 +28-23 plusmn08) times10-9


-012 (accid)BR = (28 +15


KS 0e+e- KS 0μ+μ-


NA481 preliminary

NA481 preliminary


KL 0ℓ+ℓ-






Krarr in the SM




W W

s

id

Vis Vid

e

i=uct

W

Z

VisV

idds i

11

20

2410

10)1108(

)(1001)(

AKB

11

2

5

100

10)4082(

)()Im(

1022)(

t

tdtsL xX

VVKB


K

ε εrsquo




Ke3 KL 0

Height

Im(λt )



10301890 10471)(

KBR









K+ +




















Appendixes





J(ππ) = ℓ(ππ) = 0 P(ππ) = +1 C(ππ) = +1



ℓL



SLti

SLLSti

LS

tL

tS

Lti

LSti

S

KKeaaKKeaa

eaea

KeaKea

SLLS

LS

LS

)()(

22

f LSf

fLS KfA

dt

d 2

2

TUnitarity requires

and therefore


f Sff

fS

fLSLLS

f

fLLf

fSS

fKAAKKmi

AA

)(2)(

22


2

22

2

222

0604

mKK

AAAA

LS

LSLS

f

fSf

fLf

fS

fL



SLS KKmi 21




)()( 0000

SSS KK



KS ee

No asymmetry for KS

as expected

BR = (471 032) 10-

5

AΦ = (05 43)






IBEE

dEA

)tan( 0


Kplusmn π+π0γ

)730810672()(

)250350353()(

800

800

syststatMeVT

syststatMeVT

INTFrac

DEFrac







KL π+πndashπ0γ















)(

)2030(

3

3

e

ee

K

MeVEKR





bull 6M Ke3 events


ndash R=(0964plusmn0008+0011-0009)












PDG 2004







]21[192 3

52

KmG







Vus measurements





unitarity





KLOE Kl 3

KLOE K2

copy A Antonelli

Vus some more




Ke4 results





K+rarrπ0π0eν










1-loop rescattering

2-loop rescattering











NA482




KLOE interference

















K+ + 8middot10-11 (at 7)147+130

ndash089 middot 10-

10 (BNL E787+E949)






KL 0ℓ+ℓ-




BR(KL 0+-) lt 3810-10





NA481 KS 0ℓ+ℓ-



BR = (58 +28-23 plusmn08) times10-9


-012 (accid)BR = (28 +15


KS 0e+e- KS 0μ+μ-


NA481 preliminary

NA481 preliminary


KL 0ℓ+ℓ-






Krarr in the SM




W W

s

id

Vis Vid

e

i=uct

W

Z

VisV

idds i

11

20

2410

10)1108(

)(1001)(

AKB

11

2

5

100

10)4082(

)()Im(

1022)(

t

tdtsL xX

VVKB


K

ε εrsquo




Ke3 KL 0

Height

Im(λt )



10301890 10471)(

KBR









K+ +




















Appendixes





J(ππ) = ℓ(ππ) = 0 P(ππ) = +1 C(ππ) = +1



ℓL



SLti

SLLSti

LS

tL

tS

Lti

LSti

S

KKeaaKKeaa

eaea

KeaKea

SLLS

LS

LS

)()(

22

f LSf

fLS KfA

dt

d 2

2

TUnitarity requires

and therefore


f Sff

fS

fLSLLS

f

fLLf

fSS

fKAAKKmi

AA

)(2)(

22


2

22

2

222

0604

mKK

AAAA

LS

LSLS

f

fSf

fLf

fS

fL



SLS KKmi 21




)()( 0000

SSS KK






IBEE

dEA

)tan( 0


Kplusmn π+π0γ

)730810672()(

)250350353()(

800

800

syststatMeVT

syststatMeVT

INTFrac

DEFrac







KL π+πndashπ0γ















)(

)2030(

3

3

e

ee

K

MeVEKR





bull 6M Ke3 events


ndash R=(0964plusmn0008+0011-0009)












PDG 2004







]21[192 3

52

KmG







Vus measurements





unitarity





KLOE Kl 3

KLOE K2

copy A Antonelli

Vus some more




Ke4 results





K+rarrπ0π0eν










1-loop rescattering

2-loop rescattering











NA482




KLOE interference

















K+ + 8middot10-11 (at 7)147+130

ndash089 middot 10-

10 (BNL E787+E949)






KL 0ℓ+ℓ-




BR(KL 0+-) lt 3810-10





NA481 KS 0ℓ+ℓ-



BR = (58 +28-23 plusmn08) times10-9


-012 (accid)BR = (28 +15


KS 0e+e- KS 0μ+μ-


NA481 preliminary

NA481 preliminary


KL 0ℓ+ℓ-






Krarr in the SM




W W

s

id

Vis Vid

e

i=uct

W

Z

VisV

idds i

11

20

2410

10)1108(

)(1001)(

AKB

11

2

5

100

10)4082(

)()Im(

1022)(

t

tdtsL xX

VVKB


K

ε εrsquo




Ke3 KL 0

Height

Im(λt )



10301890 10471)(

KBR









K+ +




















Appendixes





J(ππ) = ℓ(ππ) = 0 P(ππ) = +1 C(ππ) = +1



ℓL



SLti

SLLSti

LS

tL

tS

Lti

LSti

S

KKeaaKKeaa

eaea

KeaKea

SLLS

LS

LS

)()(

22

f LSf

fLS KfA

dt

d 2

2

TUnitarity requires

and therefore


f Sff

fS

fLSLLS

f

fLLf

fSS

fKAAKKmi

AA

)(2)(

22


2

22

2

222

0604

mKK

AAAA

LS

LSLS

f

fSf

fLf

fS

fL



SLS KKmi 21




)()( 0000

SSS KK



Kplusmn π+π0γ

)730810672()(

)250350353()(

800

800

syststatMeVT

syststatMeVT

INTFrac

DEFrac







KL π+πndashπ0γ















)(

)2030(

3

3

e

ee

K

MeVEKR





bull 6M Ke3 events


ndash R=(0964plusmn0008+0011-0009)












PDG 2004







]21[192 3

52

KmG







Vus measurements





unitarity





KLOE Kl 3

KLOE K2

copy A Antonelli

Vus some more




Ke4 results





K+rarrπ0π0eν










1-loop rescattering

2-loop rescattering











NA482




KLOE interference

















K+ + 8middot10-11 (at 7)147+130

ndash089 middot 10-

10 (BNL E787+E949)






KL 0ℓ+ℓ-




BR(KL 0+-) lt 3810-10





NA481 KS 0ℓ+ℓ-



BR = (58 +28-23 plusmn08) times10-9


-012 (accid)BR = (28 +15


KS 0e+e- KS 0μ+μ-


NA481 preliminary

NA481 preliminary


KL 0ℓ+ℓ-






Krarr in the SM




W W

s

id

Vis Vid

e

i=uct

W

Z

VisV

idds i

11

20

2410

10)1108(

)(1001)(

AKB

11

2

5

100

10)4082(

)()Im(

1022)(

t

tdtsL xX

VVKB


K

ε εrsquo




Ke3 KL 0

Height

Im(λt )



10301890 10471)(

KBR









K+ +




















Appendixes





J(ππ) = ℓ(ππ) = 0 P(ππ) = +1 C(ππ) = +1



ℓL



SLti

SLLSti

LS

tL

tS

Lti

LSti

S

KKeaaKKeaa

eaea

KeaKea

SLLS

LS

LS

)()(

22

f LSf

fLS KfA

dt

d 2

2

TUnitarity requires

and therefore


f Sff

fS

fLSLLS

f

fLLf

fSS

fKAAKKmi

AA

)(2)(

22


2

22

2

222

0604

mKK

AAAA

LS

LSLS

f

fSf

fLf

fS

fL



SLS KKmi 21




)()( 0000

SSS KK






KL π+πndashπ0γ















)(

)2030(

3

3

e

ee

K

MeVEKR





bull 6M Ke3 events


ndash R=(0964plusmn0008+0011-0009)












PDG 2004







]21[192 3

52

KmG







Vus measurements





unitarity





KLOE Kl 3

KLOE K2

copy A Antonelli

Vus some more




Ke4 results





K+rarrπ0π0eν










1-loop rescattering

2-loop rescattering











NA482




KLOE interference

















K+ + 8middot10-11 (at 7)147+130

ndash089 middot 10-

10 (BNL E787+E949)






KL 0ℓ+ℓ-




BR(KL 0+-) lt 3810-10





NA481 KS 0ℓ+ℓ-



BR = (58 +28-23 plusmn08) times10-9


-012 (accid)BR = (28 +15


KS 0e+e- KS 0μ+μ-


NA481 preliminary

NA481 preliminary


KL 0ℓ+ℓ-






Krarr in the SM




W W

s

id

Vis Vid

e

i=uct

W

Z

VisV

idds i

11

20

2410

10)1108(

)(1001)(

AKB

11

2

5

100

10)4082(

)()Im(

1022)(

t

tdtsL xX

VVKB


K

ε εrsquo




Ke3 KL 0

Height

Im(λt )



10301890 10471)(

KBR









K+ +




















Appendixes





J(ππ) = ℓ(ππ) = 0 P(ππ) = +1 C(ππ) = +1



ℓL



SLti

SLLSti

LS

tL

tS

Lti

LSti

S

KKeaaKKeaa

eaea

KeaKea

SLLS

LS

LS

)()(

22

f LSf

fLS KfA

dt

d 2

2

TUnitarity requires

and therefore


f Sff

fS

fLSLLS

f

fLLf

fSS

fKAAKKmi

AA

)(2)(

22


2

22

2

222

0604

mKK

AAAA

LS

LSLS

f

fSf

fLf

fS

fL



SLS KKmi 21




)()( 0000

SSS KK



KL π+πndashπ0γ















)(

)2030(

3

3

e

ee

K

MeVEKR





bull 6M Ke3 events


ndash R=(0964plusmn0008+0011-0009)












PDG 2004







]21[192 3

52

KmG







Vus measurements





unitarity





KLOE Kl 3

KLOE K2

copy A Antonelli

Vus some more




Ke4 results





K+rarrπ0π0eν










1-loop rescattering

2-loop rescattering











NA482




KLOE interference

















K+ + 8middot10-11 (at 7)147+130

ndash089 middot 10-

10 (BNL E787+E949)






KL 0ℓ+ℓ-




BR(KL 0+-) lt 3810-10





NA481 KS 0ℓ+ℓ-



BR = (58 +28-23 plusmn08) times10-9


-012 (accid)BR = (28 +15


KS 0e+e- KS 0μ+μ-


NA481 preliminary

NA481 preliminary


KL 0ℓ+ℓ-






Krarr in the SM




W W

s

id

Vis Vid

e

i=uct

W

Z

VisV

idds i

11

20

2410

10)1108(

)(1001)(

AKB

11

2

5

100

10)4082(

)()Im(

1022)(

t

tdtsL xX

VVKB


K

ε εrsquo




Ke3 KL 0

Height

Im(λt )



10301890 10471)(

KBR









K+ +




















Appendixes





J(ππ) = ℓ(ππ) = 0 P(ππ) = +1 C(ππ) = +1



ℓL



SLti

SLLSti

LS

tL

tS

Lti

LSti

S

KKeaaKKeaa

eaea

KeaKea

SLLS

LS

LS

)()(

22

f LSf

fLS KfA

dt

d 2

2

TUnitarity requires

and therefore


f Sff

fS

fLSLLS

f

fLLf

fSS

fKAAKKmi

AA

)(2)(

22


2

22

2

222

0604

mKK

AAAA

LS

LSLS

f

fSf

fLf

fS

fL



SLS KKmi 21




)()( 0000

SSS KK










)(

)2030(

3

3

e

ee

K

MeVEKR





bull 6M Ke3 events


ndash R=(0964plusmn0008+0011-0009)












PDG 2004







]21[192 3

52

KmG







Vus measurements





unitarity





KLOE Kl 3

KLOE K2

copy A Antonelli

Vus some more




Ke4 results





K+rarrπ0π0eν










1-loop rescattering

2-loop rescattering











NA482




KLOE interference

















K+ + 8middot10-11 (at 7)147+130

ndash089 middot 10-

10 (BNL E787+E949)






KL 0ℓ+ℓ-




BR(KL 0+-) lt 3810-10





NA481 KS 0ℓ+ℓ-



BR = (58 +28-23 plusmn08) times10-9


-012 (accid)BR = (28 +15


KS 0e+e- KS 0μ+μ-


NA481 preliminary

NA481 preliminary


KL 0ℓ+ℓ-






Krarr in the SM




W W

s

id

Vis Vid

e

i=uct

W

Z

VisV

idds i

11

20

2410

10)1108(

)(1001)(

AKB

11

2

5

100

10)4082(

)()Im(

1022)(

t

tdtsL xX

VVKB


K

ε εrsquo




Ke3 KL 0

Height

Im(λt )



10301890 10471)(

KBR









K+ +




















Appendixes





J(ππ) = ℓ(ππ) = 0 P(ππ) = +1 C(ππ) = +1



ℓL



SLti

SLLSti

LS

tL

tS

Lti

LSti

S

KKeaaKKeaa

eaea

KeaKea

SLLS

LS

LS

)()(

22

f LSf

fLS KfA

dt

d 2

2

TUnitarity requires

and therefore


f Sff

fS

fLSLLS

f

fLLf

fSS

fKAAKKmi

AA

)(2)(

22


2

22

2

222

0604

mKK

AAAA

LS

LSLS

f

fSf

fLf

fS

fL



SLS KKmi 21




)()( 0000

SSS KK





bull 6M Ke3 events


ndash R=(0964plusmn0008+0011-0009)












PDG 2004







]21[192 3

52

KmG







Vus measurements





unitarity





KLOE Kl 3

KLOE K2

copy A Antonelli

Vus some more




Ke4 results





K+rarrπ0π0eν










1-loop rescattering

2-loop rescattering











NA482




KLOE interference

















K+ + 8middot10-11 (at 7)147+130

ndash089 middot 10-

10 (BNL E787+E949)






KL 0ℓ+ℓ-




BR(KL 0+-) lt 3810-10





NA481 KS 0ℓ+ℓ-



BR = (58 +28-23 plusmn08) times10-9


-012 (accid)BR = (28 +15


KS 0e+e- KS 0μ+μ-


NA481 preliminary

NA481 preliminary


KL 0ℓ+ℓ-






Krarr in the SM




W W

s

id

Vis Vid

e

i=uct

W

Z

VisV

idds i

11

20

2410

10)1108(

)(1001)(

AKB

11

2

5

100

10)4082(

)()Im(

1022)(

t

tdtsL xX

VVKB


K

ε εrsquo




Ke3 KL 0

Height

Im(λt )



10301890 10471)(

KBR









K+ +




















Appendixes





J(ππ) = ℓ(ππ) = 0 P(ππ) = +1 C(ππ) = +1



ℓL



SLti

SLLSti

LS

tL

tS

Lti

LSti

S

KKeaaKKeaa

eaea

KeaKea

SLLS

LS

LS

)()(

22

f LSf

fLS KfA

dt

d 2

2

TUnitarity requires

and therefore


f Sff

fS

fLSLLS

f

fLLf

fSS

fKAAKKmi

AA

)(2)(

22


2

22

2

222

0604

mKK

AAAA

LS

LSLS

f

fSf

fLf

fS

fL



SLS KKmi 21




)()( 0000

SSS KK











PDG 2004







]21[192 3

52

KmG







Vus measurements





unitarity





KLOE Kl 3

KLOE K2

copy A Antonelli

Vus some more




Ke4 results





K+rarrπ0π0eν










1-loop rescattering

2-loop rescattering











NA482




KLOE interference

















K+ + 8middot10-11 (at 7)147+130

ndash089 middot 10-

10 (BNL E787+E949)






KL 0ℓ+ℓ-




BR(KL 0+-) lt 3810-10





NA481 KS 0ℓ+ℓ-



BR = (58 +28-23 plusmn08) times10-9


-012 (accid)BR = (28 +15


KS 0e+e- KS 0μ+μ-


NA481 preliminary

NA481 preliminary


KL 0ℓ+ℓ-






Krarr in the SM




W W

s

id

Vis Vid

e

i=uct

W

Z

VisV

idds i

11

20

2410

10)1108(

)(1001)(

AKB

11

2

5

100

10)4082(

)()Im(

1022)(

t

tdtsL xX

VVKB


K

ε εrsquo




Ke3 KL 0

Height

Im(λt )



10301890 10471)(

KBR









K+ +




















Appendixes





J(ππ) = ℓ(ππ) = 0 P(ππ) = +1 C(ππ) = +1



ℓL



SLti

SLLSti

LS

tL

tS

Lti

LSti

S

KKeaaKKeaa

eaea

KeaKea

SLLS

LS

LS

)()(

22

f LSf

fLS KfA

dt

d 2

2

TUnitarity requires

and therefore


f Sff

fS

fLSLLS

f

fLLf

fSS

fKAAKKmi

AA

)(2)(

22


2

22

2

222

0604

mKK

AAAA

LS

LSLS

f

fSf

fLf

fS

fL



SLS KKmi 21




)()( 0000

SSS KK









PDG 2004







]21[192 3

52

KmG







Vus measurements





unitarity





KLOE Kl 3

KLOE K2

copy A Antonelli

Vus some more




Ke4 results





K+rarrπ0π0eν










1-loop rescattering

2-loop rescattering











NA482




KLOE interference

















K+ + 8middot10-11 (at 7)147+130

ndash089 middot 10-

10 (BNL E787+E949)






KL 0ℓ+ℓ-




BR(KL 0+-) lt 3810-10





NA481 KS 0ℓ+ℓ-



BR = (58 +28-23 plusmn08) times10-9


-012 (accid)BR = (28 +15


KS 0e+e- KS 0μ+μ-


NA481 preliminary

NA481 preliminary


KL 0ℓ+ℓ-






Krarr in the SM




W W

s

id

Vis Vid

e

i=uct

W

Z

VisV

idds i

11

20

2410

10)1108(

)(1001)(

AKB

11

2

5

100

10)4082(

)()Im(

1022)(

t

tdtsL xX

VVKB


K

ε εrsquo




Ke3 KL 0

Height

Im(λt )



10301890 10471)(

KBR









K+ +




















Appendixes





J(ππ) = ℓ(ππ) = 0 P(ππ) = +1 C(ππ) = +1



ℓL



SLti

SLLSti

LS

tL

tS

Lti

LSti

S

KKeaaKKeaa

eaea

KeaKea

SLLS

LS

LS

)()(

22

f LSf

fLS KfA

dt

d 2

2

TUnitarity requires

and therefore


f Sff

fS

fLSLLS

f

fLLf

fSS

fKAAKKmi

AA

)(2)(

22


2

22

2

222

0604

mKK

AAAA

LS

LSLS

f

fSf

fLf

fS

fL



SLS KKmi 21




)()( 0000

SSS KK





]21[192 3

52

KmG







Vus measurements





unitarity





KLOE Kl 3

KLOE K2

copy A Antonelli

Vus some more




Ke4 results





K+rarrπ0π0eν










1-loop rescattering

2-loop rescattering











NA482




KLOE interference

















K+ + 8middot10-11 (at 7)147+130

ndash089 middot 10-

10 (BNL E787+E949)






KL 0ℓ+ℓ-




BR(KL 0+-) lt 3810-10





NA481 KS 0ℓ+ℓ-



BR = (58 +28-23 plusmn08) times10-9


-012 (accid)BR = (28 +15


KS 0e+e- KS 0μ+μ-


NA481 preliminary

NA481 preliminary


KL 0ℓ+ℓ-






Krarr in the SM




W W

s

id

Vis Vid

e

i=uct

W

Z

VisV

idds i

11

20

2410

10)1108(

)(1001)(

AKB

11

2

5

100

10)4082(

)()Im(

1022)(

t

tdtsL xX

VVKB


K

ε εrsquo




Ke3 KL 0

Height

Im(λt )



10301890 10471)(

KBR









K+ +




















Appendixes





J(ππ) = ℓ(ππ) = 0 P(ππ) = +1 C(ππ) = +1



ℓL



SLti

SLLSti

LS

tL

tS

Lti

LSti

S

KKeaaKKeaa

eaea

KeaKea

SLLS

LS

LS

)()(

22

f LSf

fLS KfA

dt

d 2

2

TUnitarity requires

and therefore


f Sff

fS

fLSLLS

f

fLLf

fSS

fKAAKKmi

AA

)(2)(

22


2

22

2

222

0604

mKK

AAAA

LS

LSLS

f

fSf

fLf

fS

fL



SLS KKmi 21




)()( 0000

SSS KK



Vus measurements





unitarity





KLOE Kl 3

KLOE K2

copy A Antonelli

Vus some more




Ke4 results





K+rarrπ0π0eν










1-loop rescattering

2-loop rescattering











NA482




KLOE interference

















K+ + 8middot10-11 (at 7)147+130

ndash089 middot 10-

10 (BNL E787+E949)






KL 0ℓ+ℓ-




BR(KL 0+-) lt 3810-10





NA481 KS 0ℓ+ℓ-



BR = (58 +28-23 plusmn08) times10-9


-012 (accid)BR = (28 +15


KS 0e+e- KS 0μ+μ-


NA481 preliminary

NA481 preliminary


KL 0ℓ+ℓ-






Krarr in the SM




W W

s

id

Vis Vid

e

i=uct

W

Z

VisV

idds i

11

20

2410

10)1108(

)(1001)(

AKB

11

2

5

100

10)4082(

)()Im(

1022)(

t

tdtsL xX

VVKB


K

ε εrsquo




Ke3 KL 0

Height

Im(λt )



10301890 10471)(

KBR









K+ +




















Appendixes





J(ππ) = ℓ(ππ) = 0 P(ππ) = +1 C(ππ) = +1



ℓL



SLti

SLLSti

LS

tL

tS

Lti

LSti

S

KKeaaKKeaa

eaea

KeaKea

SLLS

LS

LS

)()(

22

f LSf

fLS KfA

dt

d 2

2

TUnitarity requires

and therefore


f Sff

fS

fLSLLS

f

fLLf

fSS

fKAAKKmi

AA

)(2)(

22


2

22

2

222

0604

mKK

AAAA

LS

LSLS

f

fSf

fLf

fS

fL



SLS KKmi 21




)()( 0000

SSS KK



unitarity





KLOE Kl 3

KLOE K2

copy A Antonelli

Vus some more




Ke4 results





K+rarrπ0π0eν










1-loop rescattering

2-loop rescattering











NA482




KLOE interference

















K+ + 8middot10-11 (at 7)147+130

ndash089 middot 10-

10 (BNL E787+E949)






KL 0ℓ+ℓ-




BR(KL 0+-) lt 3810-10





NA481 KS 0ℓ+ℓ-



BR = (58 +28-23 plusmn08) times10-9


-012 (accid)BR = (28 +15


KS 0e+e- KS 0μ+μ-


NA481 preliminary

NA481 preliminary


KL 0ℓ+ℓ-






Krarr in the SM




W W

s

id

Vis Vid

e

i=uct

W

Z

VisV

idds i

11

20

2410

10)1108(

)(1001)(

AKB

11

2

5

100

10)4082(

)()Im(

1022)(

t

tdtsL xX

VVKB


K

ε εrsquo




Ke3 KL 0

Height

Im(λt )



10301890 10471)(

KBR









K+ +




















Appendixes





J(ππ) = ℓ(ππ) = 0 P(ππ) = +1 C(ππ) = +1



ℓL



SLti

SLLSti

LS

tL

tS

Lti

LSti

S

KKeaaKKeaa

eaea

KeaKea

SLLS

LS

LS

)()(

22

f LSf

fLS KfA

dt

d 2

2

TUnitarity requires

and therefore


f Sff

fS

fLSLLS

f

fLLf

fSS

fKAAKKmi

AA

)(2)(

22


2

22

2

222

0604

mKK

AAAA

LS

LSLS

f

fSf

fLf

fS

fL



SLS KKmi 21




)()( 0000

SSS KK





Ke4 results





K+rarrπ0π0eν










1-loop rescattering

2-loop rescattering











NA482




KLOE interference

















K+ + 8middot10-11 (at 7)147+130

ndash089 middot 10-

10 (BNL E787+E949)






KL 0ℓ+ℓ-




BR(KL 0+-) lt 3810-10





NA481 KS 0ℓ+ℓ-



BR = (58 +28-23 plusmn08) times10-9


-012 (accid)BR = (28 +15


KS 0e+e- KS 0μ+μ-


NA481 preliminary

NA481 preliminary


KL 0ℓ+ℓ-






Krarr in the SM




W W

s

id

Vis Vid

e

i=uct

W

Z

VisV

idds i

11

20

2410

10)1108(

)(1001)(

AKB

11

2

5

100

10)4082(

)()Im(

1022)(

t

tdtsL xX

VVKB


K

ε εrsquo




Ke3 KL 0

Height

Im(λt )



10301890 10471)(

KBR









K+ +




















Appendixes





J(ππ) = ℓ(ππ) = 0 P(ππ) = +1 C(ππ) = +1



ℓL



SLti

SLLSti

LS

tL

tS

Lti

LSti

S

KKeaaKKeaa

eaea

KeaKea

SLLS

LS

LS

)()(

22

f LSf

fLS KfA

dt

d 2

2

TUnitarity requires

and therefore


f Sff

fS

fLSLLS

f

fLLf

fSS

fKAAKKmi

AA

)(2)(

22


2

22

2

222

0604

mKK

AAAA

LS

LSLS

f

fSf

fLf

fS

fL



SLS KKmi 21




)()( 0000

SSS KK



Ke4 results





K+rarrπ0π0eν










1-loop rescattering

2-loop rescattering











NA482




KLOE interference

















K+ + 8middot10-11 (at 7)147+130

ndash089 middot 10-

10 (BNL E787+E949)






KL 0ℓ+ℓ-




BR(KL 0+-) lt 3810-10





NA481 KS 0ℓ+ℓ-



BR = (58 +28-23 plusmn08) times10-9


-012 (accid)BR = (28 +15


KS 0e+e- KS 0μ+μ-


NA481 preliminary

NA481 preliminary


KL 0ℓ+ℓ-






Krarr in the SM




W W

s

id

Vis Vid

e

i=uct

W

Z

VisV

idds i

11

20

2410

10)1108(

)(1001)(

AKB

11

2

5

100

10)4082(

)()Im(

1022)(

t

tdtsL xX

VVKB


K

ε εrsquo




Ke3 KL 0

Height

Im(λt )



10301890 10471)(

KBR









K+ +




















Appendixes





J(ππ) = ℓ(ππ) = 0 P(ππ) = +1 C(ππ) = +1



ℓL



SLti

SLLSti

LS

tL

tS

Lti

LSti

S

KKeaaKKeaa

eaea

KeaKea

SLLS

LS

LS

)()(

22

f LSf

fLS KfA

dt

d 2

2

TUnitarity requires

and therefore


f Sff

fS

fLSLLS

f

fLLf

fSS

fKAAKKmi

AA

)(2)(

22


2

22

2

222

0604

mKK

AAAA

LS

LSLS

f

fSf

fLf

fS

fL



SLS KKmi 21




)()( 0000

SSS KK



K+rarrπ0π0eν










1-loop rescattering

2-loop rescattering











NA482




KLOE interference

















K+ + 8middot10-11 (at 7)147+130

ndash089 middot 10-

10 (BNL E787+E949)






KL 0ℓ+ℓ-




BR(KL 0+-) lt 3810-10





NA481 KS 0ℓ+ℓ-



BR = (58 +28-23 plusmn08) times10-9


-012 (accid)BR = (28 +15


KS 0e+e- KS 0μ+μ-


NA481 preliminary

NA481 preliminary


KL 0ℓ+ℓ-






Krarr in the SM




W W

s

id

Vis Vid

e

i=uct

W

Z

VisV

idds i

11

20

2410

10)1108(

)(1001)(

AKB

11

2

5

100

10)4082(

)()Im(

1022)(

t

tdtsL xX

VVKB


K

ε εrsquo




Ke3 KL 0

Height

Im(λt )



10301890 10471)(

KBR









K+ +




















Appendixes





J(ππ) = ℓ(ππ) = 0 P(ππ) = +1 C(ππ) = +1



ℓL



SLti

SLLSti

LS

tL

tS

Lti

LSti

S

KKeaaKKeaa

eaea

KeaKea

SLLS

LS

LS

)()(

22

f LSf

fLS KfA

dt

d 2

2

TUnitarity requires

and therefore


f Sff

fS

fLSLLS

f

fLLf

fSS

fKAAKKmi

AA

)(2)(

22


2

22

2

222

0604

mKK

AAAA

LS

LSLS

f

fSf

fLf

fS

fL



SLS KKmi 21




)()( 0000

SSS KK








1-loop rescattering

2-loop rescattering











NA482




KLOE interference

















K+ + 8middot10-11 (at 7)147+130

ndash089 middot 10-

10 (BNL E787+E949)






KL 0ℓ+ℓ-




BR(KL 0+-) lt 3810-10





NA481 KS 0ℓ+ℓ-



BR = (58 +28-23 plusmn08) times10-9


-012 (accid)BR = (28 +15


KS 0e+e- KS 0μ+μ-


NA481 preliminary

NA481 preliminary


KL 0ℓ+ℓ-






Krarr in the SM




W W

s

id

Vis Vid

e

i=uct

W

Z

VisV

idds i

11

20

2410

10)1108(

)(1001)(

AKB

11

2

5

100

10)4082(

)()Im(

1022)(

t

tdtsL xX

VVKB


K

ε εrsquo




Ke3 KL 0

Height

Im(λt )



10301890 10471)(

KBR









K+ +




















Appendixes





J(ππ) = ℓ(ππ) = 0 P(ππ) = +1 C(ππ) = +1



ℓL



SLti

SLLSti

LS

tL

tS

Lti

LSti

S

KKeaaKKeaa

eaea

KeaKea

SLLS

LS

LS

)()(

22

f LSf

fLS KfA

dt

d 2

2

TUnitarity requires

and therefore


f Sff

fS

fLSLLS

f

fLLf

fSS

fKAAKKmi

AA

)(2)(

22


2

22

2

222

0604

mKK

AAAA

LS

LSLS

f

fSf

fLf

fS

fL



SLS KKmi 21




)()( 0000

SSS KK




1-loop rescattering

2-loop rescattering











NA482




KLOE interference

















K+ + 8middot10-11 (at 7)147+130

ndash089 middot 10-

10 (BNL E787+E949)






KL 0ℓ+ℓ-




BR(KL 0+-) lt 3810-10





NA481 KS 0ℓ+ℓ-



BR = (58 +28-23 plusmn08) times10-9


-012 (accid)BR = (28 +15


KS 0e+e- KS 0μ+μ-


NA481 preliminary

NA481 preliminary


KL 0ℓ+ℓ-






Krarr in the SM




W W

s

id

Vis Vid

e

i=uct

W

Z

VisV

idds i

11

20

2410

10)1108(

)(1001)(

AKB

11

2

5

100

10)4082(

)()Im(

1022)(

t

tdtsL xX

VVKB


K

ε εrsquo




Ke3 KL 0

Height

Im(λt )



10301890 10471)(

KBR









K+ +




















Appendixes





J(ππ) = ℓ(ππ) = 0 P(ππ) = +1 C(ππ) = +1



ℓL



SLti

SLLSti

LS

tL

tS

Lti

LSti

S

KKeaaKKeaa

eaea

KeaKea

SLLS

LS

LS

)()(

22

f LSf

fLS KfA

dt

d 2

2

TUnitarity requires

and therefore


f Sff

fS

fLSLLS

f

fLLf

fSS

fKAAKKmi

AA

)(2)(

22


2

22

2

222

0604

mKK

AAAA

LS

LSLS

f

fSf

fLf

fS

fL



SLS KKmi 21




)()( 0000

SSS KK









NA482




KLOE interference

















K+ + 8middot10-11 (at 7)147+130

ndash089 middot 10-

10 (BNL E787+E949)






KL 0ℓ+ℓ-




BR(KL 0+-) lt 3810-10





NA481 KS 0ℓ+ℓ-



BR = (58 +28-23 plusmn08) times10-9


-012 (accid)BR = (28 +15


KS 0e+e- KS 0μ+μ-


NA481 preliminary

NA481 preliminary


KL 0ℓ+ℓ-






Krarr in the SM




W W

s

id

Vis Vid

e

i=uct

W

Z

VisV

idds i

11

20

2410

10)1108(

)(1001)(

AKB

11

2

5

100

10)4082(

)()Im(

1022)(

t

tdtsL xX

VVKB


K

ε εrsquo




Ke3 KL 0

Height

Im(λt )



10301890 10471)(

KBR









K+ +




















Appendixes





J(ππ) = ℓ(ππ) = 0 P(ππ) = +1 C(ππ) = +1



ℓL



SLti

SLLSti

LS

tL

tS

Lti

LSti

S

KKeaaKKeaa

eaea

KeaKea

SLLS

LS

LS

)()(

22

f LSf

fLS KfA

dt

d 2

2

TUnitarity requires

and therefore


f Sff

fS

fLSLLS

f

fLLf

fSS

fKAAKKmi

AA

)(2)(

22


2

22

2

222

0604

mKK

AAAA

LS

LSLS

f

fSf

fLf

fS

fL



SLS KKmi 21




)()( 0000

SSS KK





KLOE interference

















K+ + 8middot10-11 (at 7)147+130

ndash089 middot 10-

10 (BNL E787+E949)






KL 0ℓ+ℓ-




BR(KL 0+-) lt 3810-10





NA481 KS 0ℓ+ℓ-



BR = (58 +28-23 plusmn08) times10-9


-012 (accid)BR = (28 +15


KS 0e+e- KS 0μ+μ-


NA481 preliminary

NA481 preliminary


KL 0ℓ+ℓ-






Krarr in the SM




W W

s

id

Vis Vid

e

i=uct

W

Z

VisV

idds i

11

20

2410

10)1108(

)(1001)(

AKB

11

2

5

100

10)4082(

)()Im(

1022)(

t

tdtsL xX

VVKB


K

ε εrsquo




Ke3 KL 0

Height

Im(λt )



10301890 10471)(

KBR









K+ +




















Appendixes





J(ππ) = ℓ(ππ) = 0 P(ππ) = +1 C(ππ) = +1



ℓL



SLti

SLLSti

LS

tL

tS

Lti

LSti

S

KKeaaKKeaa

eaea

KeaKea

SLLS

LS

LS

)()(

22

f LSf

fLS KfA

dt

d 2

2

TUnitarity requires

and therefore


f Sff

fS

fLSLLS

f

fLLf

fSS

fKAAKKmi

AA

)(2)(

22


2

22

2

222

0604

mKK

AAAA

LS

LSLS

f

fSf

fLf

fS

fL



SLS KKmi 21




)()( 0000

SSS KK



KLOE interference

















K+ + 8middot10-11 (at 7)147+130

ndash089 middot 10-

10 (BNL E787+E949)






KL 0ℓ+ℓ-




BR(KL 0+-) lt 3810-10





NA481 KS 0ℓ+ℓ-



BR = (58 +28-23 plusmn08) times10-9


-012 (accid)BR = (28 +15


KS 0e+e- KS 0μ+μ-


NA481 preliminary

NA481 preliminary


KL 0ℓ+ℓ-






Krarr in the SM




W W

s

id

Vis Vid

e

i=uct

W

Z

VisV

idds i

11

20

2410

10)1108(

)(1001)(

AKB

11

2

5

100

10)4082(

)()Im(

1022)(

t

tdtsL xX

VVKB


K

ε εrsquo




Ke3 KL 0

Height

Im(λt )



10301890 10471)(

KBR









K+ +




















Appendixes





J(ππ) = ℓ(ππ) = 0 P(ππ) = +1 C(ππ) = +1



ℓL



SLti

SLLSti

LS

tL

tS

Lti

LSti

S

KKeaaKKeaa

eaea

KeaKea

SLLS

LS

LS

)()(

22

f LSf

fLS KfA

dt

d 2

2

TUnitarity requires

and therefore


f Sff

fS

fLSLLS

f

fLLf

fSS

fKAAKKmi

AA

)(2)(

22


2

22

2

222

0604

mKK

AAAA

LS

LSLS

f

fSf

fLf

fS

fL



SLS KKmi 21




)()( 0000

SSS KK


















K+ + 8middot10-11 (at 7)147+130

ndash089 middot 10-

10 (BNL E787+E949)






KL 0ℓ+ℓ-




BR(KL 0+-) lt 3810-10





NA481 KS 0ℓ+ℓ-



BR = (58 +28-23 plusmn08) times10-9


-012 (accid)BR = (28 +15


KS 0e+e- KS 0μ+μ-


NA481 preliminary

NA481 preliminary


KL 0ℓ+ℓ-






Krarr in the SM




W W

s

id

Vis Vid

e

i=uct

W

Z

VisV

idds i

11

20

2410

10)1108(

)(1001)(

AKB

11

2

5

100

10)4082(

)()Im(

1022)(

t

tdtsL xX

VVKB


K

ε εrsquo




Ke3 KL 0

Height

Im(λt )



10301890 10471)(

KBR









K+ +




















Appendixes





J(ππ) = ℓ(ππ) = 0 P(ππ) = +1 C(ππ) = +1



ℓL



SLti

SLLSti

LS

tL

tS

Lti

LSti

S

KKeaaKKeaa

eaea

KeaKea

SLLS

LS

LS

)()(

22

f LSf

fLS KfA

dt

d 2

2

TUnitarity requires

and therefore


f Sff

fS

fLSLLS

f

fLLf

fSS

fKAAKKmi

AA

)(2)(

22


2

22

2

222

0604

mKK

AAAA

LS

LSLS

f

fSf

fLf

fS

fL



SLS KKmi 21




)()( 0000

SSS KK
















K+ + 8middot10-11 (at 7)147+130

ndash089 middot 10-

10 (BNL E787+E949)






KL 0ℓ+ℓ-




BR(KL 0+-) lt 3810-10





NA481 KS 0ℓ+ℓ-



BR = (58 +28-23 plusmn08) times10-9


-012 (accid)BR = (28 +15


KS 0e+e- KS 0μ+μ-


NA481 preliminary

NA481 preliminary


KL 0ℓ+ℓ-






Krarr in the SM




W W

s

id

Vis Vid

e

i=uct

W

Z

VisV

idds i

11

20

2410

10)1108(

)(1001)(

AKB

11

2

5

100

10)4082(

)()Im(

1022)(

t

tdtsL xX

VVKB


K

ε εrsquo




Ke3 KL 0

Height

Im(λt )



10301890 10471)(

KBR









K+ +




















Appendixes





J(ππ) = ℓ(ππ) = 0 P(ππ) = +1 C(ππ) = +1



ℓL



SLti

SLLSti

LS

tL

tS

Lti

LSti

S

KKeaaKKeaa

eaea

KeaKea

SLLS

LS

LS

)()(

22

f LSf

fLS KfA

dt

d 2

2

TUnitarity requires

and therefore


f Sff

fS

fLSLLS

f

fLLf

fSS

fKAAKKmi

AA

)(2)(

22


2

22

2

222

0604

mKK

AAAA

LS

LSLS

f

fSf

fLf

fS

fL



SLS KKmi 21




)()( 0000

SSS KK










K+ + 8middot10-11 (at 7)147+130

ndash089 middot 10-

10 (BNL E787+E949)






KL 0ℓ+ℓ-




BR(KL 0+-) lt 3810-10





NA481 KS 0ℓ+ℓ-



BR = (58 +28-23 plusmn08) times10-9


-012 (accid)BR = (28 +15


KS 0e+e- KS 0μ+μ-


NA481 preliminary

NA481 preliminary


KL 0ℓ+ℓ-






Krarr in the SM




W W

s

id

Vis Vid

e

i=uct

W

Z

VisV

idds i

11

20

2410

10)1108(

)(1001)(

AKB

11

2

5

100

10)4082(

)()Im(

1022)(

t

tdtsL xX

VVKB


K

ε εrsquo




Ke3 KL 0

Height

Im(λt )



10301890 10471)(

KBR









K+ +




















Appendixes





J(ππ) = ℓ(ππ) = 0 P(ππ) = +1 C(ππ) = +1



ℓL



SLti

SLLSti

LS

tL

tS

Lti

LSti

S

KKeaaKKeaa

eaea

KeaKea

SLLS

LS

LS

)()(

22

f LSf

fLS KfA

dt

d 2

2

TUnitarity requires

and therefore


f Sff

fS

fLSLLS

f

fLLf

fSS

fKAAKKmi

AA

)(2)(

22


2

22

2

222

0604

mKK

AAAA

LS

LSLS

f

fSf

fLf

fS

fL



SLS KKmi 21




)()( 0000

SSS KK




KL 0ℓ+ℓ-




BR(KL 0+-) lt 3810-10





NA481 KS 0ℓ+ℓ-



BR = (58 +28-23 plusmn08) times10-9


-012 (accid)BR = (28 +15


KS 0e+e- KS 0μ+μ-


NA481 preliminary

NA481 preliminary


KL 0ℓ+ℓ-






Krarr in the SM




W W

s

id

Vis Vid

e

i=uct

W

Z

VisV

idds i

11

20

2410

10)1108(

)(1001)(

AKB

11

2

5

100

10)4082(

)()Im(

1022)(

t

tdtsL xX

VVKB


K

ε εrsquo




Ke3 KL 0

Height

Im(λt )



10301890 10471)(

KBR









K+ +




















Appendixes





J(ππ) = ℓ(ππ) = 0 P(ππ) = +1 C(ππ) = +1



ℓL



SLti

SLLSti

LS

tL

tS

Lti

LSti

S

KKeaaKKeaa

eaea

KeaKea

SLLS

LS

LS

)()(

22

f LSf

fLS KfA

dt

d 2

2

TUnitarity requires

and therefore


f Sff

fS

fLSLLS

f

fLLf

fSS

fKAAKKmi

AA

)(2)(

22


2

22

2

222

0604

mKK

AAAA

LS

LSLS

f

fSf

fLf

fS

fL



SLS KKmi 21




)()( 0000

SSS KK



NA481 KS 0ℓ+ℓ-



BR = (58 +28-23 plusmn08) times10-9


-012 (accid)BR = (28 +15


KS 0e+e- KS 0μ+μ-


NA481 preliminary

NA481 preliminary


KL 0ℓ+ℓ-






Krarr in the SM




W W

s

id

Vis Vid

e

i=uct

W

Z

VisV

idds i

11

20

2410

10)1108(

)(1001)(

AKB

11

2

5

100

10)4082(

)()Im(

1022)(

t

tdtsL xX

VVKB


K

ε εrsquo




Ke3 KL 0

Height

Im(λt )



10301890 10471)(

KBR









K+ +




















Appendixes





J(ππ) = ℓ(ππ) = 0 P(ππ) = +1 C(ππ) = +1



ℓL



SLti

SLLSti

LS

tL

tS

Lti

LSti

S

KKeaaKKeaa

eaea

KeaKea

SLLS

LS

LS

)()(

22

f LSf

fLS KfA

dt

d 2

2

TUnitarity requires

and therefore


f Sff

fS

fLSLLS

f

fLLf

fSS

fKAAKKmi

AA

)(2)(

22


2

22

2

222

0604

mKK

AAAA

LS

LSLS

f

fSf

fLf

fS

fL



SLS KKmi 21




)()( 0000

SSS KK



KL 0ℓ+ℓ-






Krarr in the SM




W W

s

id

Vis Vid

e

i=uct

W

Z

VisV

idds i

11

20

2410

10)1108(

)(1001)(

AKB

11

2

5

100

10)4082(

)()Im(

1022)(

t

tdtsL xX

VVKB


K

ε εrsquo




Ke3 KL 0

Height

Im(λt )



10301890 10471)(

KBR









K+ +




















Appendixes





J(ππ) = ℓ(ππ) = 0 P(ππ) = +1 C(ππ) = +1



ℓL



SLti

SLLSti

LS

tL

tS

Lti

LSti

S

KKeaaKKeaa

eaea

KeaKea

SLLS

LS

LS

)()(

22

f LSf

fLS KfA

dt

d 2

2

TUnitarity requires

and therefore


f Sff

fS

fLSLLS

f

fLLf

fSS

fKAAKKmi

AA

)(2)(

22


2

22

2

222

0604

mKK

AAAA

LS

LSLS

f

fSf

fLf

fS

fL



SLS KKmi 21




)()( 0000

SSS KK



Krarr in the SM




W W

s

id

Vis Vid

e

i=uct

W

Z

VisV

idds i

11

20

2410

10)1108(

)(1001)(

AKB

11

2

5

100

10)4082(

)()Im(

1022)(

t

tdtsL xX

VVKB


K

ε εrsquo




Ke3 KL 0

Height

Im(λt )



10301890 10471)(

KBR









K+ +




















Appendixes





J(ππ) = ℓ(ππ) = 0 P(ππ) = +1 C(ππ) = +1



ℓL



SLti

SLLSti

LS

tL

tS

Lti

LSti

S

KKeaaKKeaa

eaea

KeaKea

SLLS

LS

LS

)()(

22

f LSf

fLS KfA

dt

d 2

2

TUnitarity requires

and therefore


f Sff

fS

fLSLLS

f

fLLf

fSS

fKAAKKmi

AA

)(2)(

22


2

22

2

222

0604

mKK

AAAA

LS

LSLS

f

fSf

fLf

fS

fL



SLS KKmi 21




)()( 0000

SSS KK



K

ε εrsquo




Ke3 KL 0

Height

Im(λt )



10301890 10471)(

KBR









K+ +




















Appendixes





J(ππ) = ℓ(ππ) = 0 P(ππ) = +1 C(ππ) = +1



ℓL



SLti

SLLSti

LS

tL

tS

Lti

LSti

S

KKeaaKKeaa

eaea

KeaKea

SLLS

LS

LS

)()(

22

f LSf

fLS KfA

dt

d 2

2

TUnitarity requires

and therefore


f Sff

fS

fLSLLS

f

fLLf

fSS

fKAAKKmi

AA

)(2)(

22


2

22

2

222

0604

mKK

AAAA

LS

LSLS

f

fSf

fLf

fS

fL



SLS KKmi 21




)()( 0000

SSS KK




10301890 10471)(

KBR









K+ +




















Appendixes





J(ππ) = ℓ(ππ) = 0 P(ππ) = +1 C(ππ) = +1



ℓL



SLti

SLLSti

LS

tL

tS

Lti

LSti

S

KKeaaKKeaa

eaea

KeaKea

SLLS

LS

LS

)()(

22

f LSf

fLS KfA

dt

d 2

2

TUnitarity requires

and therefore


f Sff

fS

fLSLLS

f

fLLf

fSS

fKAAKKmi

AA

)(2)(

22


2

22

2

222

0604

mKK

AAAA

LS

LSLS

f

fSf

fLf

fS

fL



SLS KKmi 21




)()( 0000

SSS KK






K+ +




















Appendixes





J(ππ) = ℓ(ππ) = 0 P(ππ) = +1 C(ππ) = +1



ℓL



SLti

SLLSti

LS

tL

tS

Lti

LSti

S

KKeaaKKeaa

eaea

KeaKea

SLLS

LS

LS

)()(

22

f LSf

fLS KfA

dt

d 2

2

TUnitarity requires

and therefore


f Sff

fS

fLSLLS

f

fLLf

fSS

fKAAKKmi

AA

)(2)(

22


2

22

2

222

0604

mKK

AAAA

LS

LSLS

f

fSf

fLf

fS

fL



SLS KKmi 21




)()( 0000

SSS KK




















Appendixes





J(ππ) = ℓ(ππ) = 0 P(ππ) = +1 C(ππ) = +1



ℓL



SLti

SLLSti

LS

tL

tS

Lti

LSti

S

KKeaaKKeaa

eaea

KeaKea

SLLS

LS

LS

)()(

22

f LSf

fLS KfA

dt

d 2

2

TUnitarity requires

and therefore


f Sff

fS

fLSLLS

f

fLLf

fSS

fKAAKKmi

AA

)(2)(

22


2

22

2

222

0604

mKK

AAAA

LS

LSLS

f

fSf

fLf

fS

fL



SLS KKmi 21




)()( 0000

SSS KK

















Appendixes





J(ππ) = ℓ(ππ) = 0 P(ππ) = +1 C(ππ) = +1



ℓL



SLti

SLLSti

LS

tL

tS

Lti

LSti

S

KKeaaKKeaa

eaea

KeaKea

SLLS

LS

LS

)()(

22

f LSf

fLS KfA

dt

d 2

2

TUnitarity requires

and therefore


f Sff

fS

fLSLLS

f

fLLf

fSS

fKAAKKmi

AA

)(2)(

22


2

22

2

222

0604

mKK

AAAA

LS

LSLS

f

fSf

fLf

fS

fL



SLS KKmi 21




)()( 0000

SSS KK













Appendixes





J(ππ) = ℓ(ππ) = 0 P(ππ) = +1 C(ππ) = +1



ℓL



SLti

SLLSti

LS

tL

tS

Lti

LSti

S

KKeaaKKeaa

eaea

KeaKea

SLLS

LS

LS

)()(

22

f LSf

fLS KfA

dt

d 2

2

TUnitarity requires

and therefore


f Sff

fS

fLSLLS

f

fLLf

fSS

fKAAKKmi

AA

)(2)(

22


2

22

2

222

0604

mKK

AAAA

LS

LSLS

f

fSf

fLf

fS

fL



SLS KKmi 21




)()( 0000

SSS KK









Appendixes





J(ππ) = ℓ(ππ) = 0 P(ππ) = +1 C(ππ) = +1



ℓL



SLti

SLLSti

LS

tL

tS

Lti

LSti

S

KKeaaKKeaa

eaea

KeaKea

SLLS

LS

LS

)()(

22

f LSf

fLS KfA

dt

d 2

2

TUnitarity requires

and therefore


f Sff

fS

fLSLLS

f

fLLf

fSS

fKAAKKmi

AA

)(2)(

22


2

22

2

222

0604

mKK

AAAA

LS

LSLS

f

fSf

fLf

fS

fL



SLS KKmi 21




)()( 0000

SSS KK







Appendixes





J(ππ) = ℓ(ππ) = 0 P(ππ) = +1 C(ππ) = +1



ℓL



SLti

SLLSti

LS

tL

tS

Lti

LSti

S

KKeaaKKeaa

eaea

KeaKea

SLLS

LS

LS

)()(

22

f LSf

fLS KfA

dt

d 2

2

TUnitarity requires

and therefore


f Sff

fS

fLSLLS

f

fLLf

fSS

fKAAKKmi

AA

)(2)(

22


2

22

2

222

0604

mKK

AAAA

LS

LSLS

f

fSf

fLf

fS

fL



SLS KKmi 21




)()( 0000

SSS KK



Appendixes





J(ππ) = ℓ(ππ) = 0 P(ππ) = +1 C(ππ) = +1



ℓL



SLti

SLLSti

LS

tL

tS

Lti

LSti

S

KKeaaKKeaa

eaea

KeaKea

SLLS

LS

LS

)()(

22

f LSf

fLS KfA

dt

d 2

2

TUnitarity requires

and therefore


f Sff

fS

fLSLLS

f

fLLf

fSS

fKAAKKmi

AA

)(2)(

22


2

22

2

222

0604

mKK

AAAA

LS

LSLS

f

fSf

fLf

fS

fL



SLS KKmi 21




)()( 0000

SSS KK






J(ππ) = ℓ(ππ) = 0 P(ππ) = +1 C(ππ) = +1



ℓL



SLti

SLLSti

LS

tL

tS

Lti

LSti

S

KKeaaKKeaa

eaea

KeaKea

SLLS

LS

LS

)()(

22

f LSf

fLS KfA

dt

d 2

2

TUnitarity requires

and therefore


f Sff

fS

fLSLLS

f

fLLf

fSS

fKAAKKmi

AA

)(2)(

22


2

22

2

222

0604

mKK

AAAA

LS

LSLS

f

fSf

fLf

fS

fL



SLS KKmi 21




)()( 0000

SSS KK




SLti

SLLSti

LS

tL

tS

Lti

LSti

S

KKeaaKKeaa

eaea

KeaKea

SLLS

LS

LS

)()(

22

f LSf

fLS KfA

dt

d 2

2

TUnitarity requires

and therefore


f Sff

fS

fLSLLS

f

fLLf

fSS

fKAAKKmi

AA

)(2)(

22


2

22

2

222

0604

mKK

AAAA

LS

LSLS

f

fSf

fLf

fS

fL



SLS KKmi 21




)()( 0000

SSS KK



2

22

2

222

0604

mKK

AAAA

LS

LSLS

f

fSf

fLf

fS

fL



SLS KKmi 21




)()( 0000

SSS KK


Documents

Zuoz, 18.7.2006 M.S. SozziK physics Kaon physics M. S. Sozzi University of Pisa PSI Summer School Zuoz, July 17-22, 2006