Introduction: general formalism of oscillations Nice review: hep-ph/0712.3367 (Dec 2007): “Topics in Hadronic B decays”, J.Virto QM perturbation theory

Introduction: general formalism of oscillations

Nice review: hep-ph/0712.3367 (Dec 2007): “Topics in Hadronic B decays”, J.Virto

QM perturbation theory

Effective Hamiltonian

General formalism of oscillations

not Hermitian!

Dispersive off-shell part

Absorptive on-shell part

CPT!

CPT!

by def.

by def.

General formalism of oscillationsDiagonalize!

Eigenvalues

Eigenvectors

But CPV if !

PDG notation: r = p/q

CP = ei

arbitrary!

PDG notation: L,H↔1,2

CP!

CP!

General formalism of oscillationsCP!

CP!

For D0 CPV is expected to be very small (see later).

Sometimes by def. m < 0. But we define:

D1 – (almost) CP even, D2 – CP odd (thus m ~ x > 0 is possible)

If CPV=0 we may choose arbitrary phase =0 in :

002

001

2

12

1

DDD

DDD

CP = ei

(like K1, K2)

cbsd ,,

bsd ,,c

u

uContributes only to М12 (х) Contributes both to М12 and to

Г12(y), very difficult to estimate

Can contain New Physics in loops! (Interesting: down-quarks in C=2 loops)

Known resonances dominate, no NP

Long distance effects obscure possible short-distance NP in x. Sign of NP could be either or (better) observation of

large CPV.yx

Box and long distances

cbsd ,,

bsd ,,c

u

u

)(sincos 2222212 dsCCDDD mmfMM

CC

CC

sds

sdd

cossin'

sincos '

GIM mechanism

'sc

d

s

'd

C

Take d’, s’ basis instead of d, s :

usc '

DfDf

Due to different masses in propagators → not

exact 0, but small

b contribution is suppressed in comp. with d,s by → negligible.

In the absence of 3rd generation CPV≈0.

Box diagram(s)

2 3

2 2 4

3 2

1 / 2

1 / 2

1 1

ud

td

us

cd cs cb

ts

b

tb

uV V A

V V V V A O

V V A AV

V i

i

Box diagramsc

u

u

c

d, s, b

d, s, b

W+ W-D0 D0

c

u

u

c

d, s, b d, s, b

W+

W-

D0 D0

Vcj*

Vuj

Vcj*Vuj

Vci* Vui

Vui

Vci*

)(sincos 2222212 bsCCDDD mmfMM

SM: xbox≤10-5, negligible CPV

2 3

2 2 4

3 2

1 / 2

1 / 2

1 1

ud

td

us

cd cs cb

ts

b

tb

uV V A

V V V V A O

V V A AV

V i

i

Boxes for K,D,B,Bs

c

u

u

c

d, s, b

d, s, bW+ W-D0 D0

c

u

u

c

d, s, b d, s, bW+

W-

D0 D0

Vcj*

Vuj

Vcj*Vuj

Vci* Vui

Vui

Vci*

u, c, t

d

s

s

d

u, c, tW+ W-K0 K0

d

s

s

d

u, c, t u, c, tW+

W-

K0 K0

Vid

VjdVis*

Vid Vis*

VjdVjs*Vjs*

d

b

b

d

u, c, t

u, c, tW+ W-B0 B0

d

b

b

d

u, c, t u, c, tW+

W-

B0 B0

Vid

Vjd

Vjb*

Vib*

Vid Vib*

VjdVjb*

s

b

b

s

u, c, t

u, c, tW+ W-B0

s B0s

s

b

b

s

u, c, t u, c, tW+

W-

B0s B0

s

Vis

Vjs

Vjb*

Vib*

Vis Vib*

VjsVjb*

c dominates, sin2C

s dominates, sin2C

t dominates, |VtdV*

tb|2

t dominates, |VtsV*

tb|2

K0 D0

B0 B0s

Recent paper with the largest x,y A.F.Falk et el., hep-ph/0110317, 0402204

Long distance contribution

SU(3) breaking in D0 decays – only due to phase space differences

within SU(3) multiplets (e.g., decay to 4 allowed, to 4К – not)

x ≤ y ~ 10-2

Δ – y■ – x

● – x beyond SM

Old predictionsH.Nelson, hep-ex/9909021

Comparison of K,D,B,Bs

c dominates, sin2C

s dominates, sin2C

t dominates, |VtdV*

tb|2

t dominates, |VtsV*

tb|2

K0 D0

B0 B0s

Boxes

Box:long dist.≈ 80%:20%

S,L are determined by available decays (long dist.)

Long dist. dominateBox:long dist.≈ 80%:20%

S,L are determined by available decays (long dist.)

Long dist. dominate

Box dominates

It contributes through VCKM to 12 as well, 12/M12≈0.05, y≤1%.

CPV is important

Box dominates

12/M12≈0.05, both higher than for B0, y~10%.

CPV is important

Spring 2006, CDF, D0:

x y 1/Г, psec

K0 1/ГS=89.53±0.05

1/ГL=51140±210

(3.24±0.04)E-3

B0 0.776±0.008 SM: ~0.2%

1.530±0.009 0.0026±0.0059

SM:

B0s

1/ГL=1.21±0.09

1/ГH=

1/Г= 1.40±0.05

SM:

D0 SM:

~10-3… ≤0.01

SM:

~ 0.01

0.4101±0.0015 ≈ 0

11|| p

qr

4.03.03.24

06.007.016.0

11.012.066.1

Comparison of K,D,B,Bs

Time evolution of D systemEvolution of eigenvectors according to effective Hamiltonian is simple:

)0(

22)0()(

__0020 Dtim

iDetD

timi

for simplicity, r=p=q=1, CPV=0t=0

2

1

2

1

)(22

)( 00200 tDDtiyxi

tiyxei

tDDtimi

zezz

eee z

zzzzz

2/2/

Now experimental part …

Lepton charge tags D0 flavor!

PDG’ 2006

Semileptonic D0 decays

Probability to have Wrong Sign (WS) lepton = prob. of oscillation =

Time integrated ratio of WS and RS, RM

visually unobservabledeviation from pure exponential

~ Bs0

probab. X0 → X0 or X0 → X0 after time t(no assumption x,y<<1)

Examples of oscillations

c

c

hadron(s)(4s)

B (bu, bd)

B (bu, bd)=0.42

(bb) 1.1 nb (~800·106 bb pairs)

→ numerous measurements of CPV in B system

(cc) 1.3 nb (~900·106 cc- pairs)+ light qq production (uds)

Perfect for charm physics

continuum production BB pair production

Main experiments: two B-factories

Additional help from: charm-factories, Tevatron

hadron(s)

~1 km in diameter

Mt. Tsukuba

KEKBBelle

Continuous injection, peak luminosity: L = 16.5 nb-1 s-1

n.b.: dN/dt = L

Integrated luminosity: Ldt > 700 fb-1

Ldt

20072000

700 fb-1

3.5 GeV e +

8 GeV e

-

Belle

http://kekb.jp/

Belle detector

3(4) layerSi det.

Central Drift Chamber

AerogelCherenkov(n=1.015- 1.030)

1.5T SC solenoid

e-

8 GeV

e+

3.5 GeV

EM calorimeterCsI (16X0)

and KL

Counter(14/15 layersRPC+Fe)

tracking (pt)/pt= 0.2% √(pt2+2.5)

PID (K±) ~ 85% (±→K±) 10% for p < 3.5 GeV/c

detector

Collected at PEP-II at SLAC on- and off- the (4S) resonance NIM A479, 1 (2002)

Dataset: 384 fb-1

s [GeV]

e+e- → (3770) → D0D0, D+D- (coherent 1-- state);

analogous to e+e- → BB @ (4S);symmetric; also higher energy, above DD* or Ds

+Ds-

threshold; ~572 pb-1 of data available at (3770), 2.0x106 D0D0, 1.6x106 D+D-

charm-factory;also upgraded BES at BEPCII

CLEO-c detector at CESR

Had. ID

e- ID

tracking

Cleo-c, hep-ex/0606016

e

Back to semileptonic D0 decays, latest analyses

General method: study D0’s produced from D*+

eeKDDDXDee (*)00** , ,

1. + provides a tag of initial D0 flavor

2. Phase space in D*+ decay is very small

chances to have random background pion there are also small

2a) background is significantly suppressed.

Why?

What to measure: compare signs of + and lepton and

find RM = #wrong sign (WS) / #right sign (RS)

2b) Loss of statistics is acceptable since about 50% of D0 come from D*+ (it has more polarization states, B(D*+ →D0+)≈2/3).

Interesting difference: initial D0 flavor at production is tagged twice:

by sign of s± from D*± and by flavor of the second D meson in the event which

is fully reconstructed in the opposite hemisphere. Efficiency of full reconstruction is ~10%, but sensitivity is about the same.

NWS = 3ev., expected background = 2.85 ev.

eeKDDDDXDee (*)00*__

* , ,

e

Semileptonic D0 decays

Belle (PRD72, 071101 (2005), 253 fb-1):

RM<1.0·10-3 @ 90% CL

NRS = (229.45 ± 0.69) ·103 ev.

Recent BaBar analysis (hep-ex/0705.0704, 344fb-1)

-1.3·10-3<RM<1.2·10-3 @ 90% CL

Another approaches

RM ~ x2, y2.

Are there any effects linearly dependent on x or y?

)0(2

)0()(__

0020 Diyxti

DKetDftimi

Straitforward way: measure y=/2 directly

By measuring difference between Г1 and Г one can find yCP which coincides with y if CP is conserved.

First order in y!

CP can be checked by comparing D & D in К+К-, +-:

A=(D-D)/(D+D)

К+К- and +- can come only from CP-even D1.

К+К- and +- verticies should be distributed according to Г1.

In flavor specific decay, e.g. D0→K-+, both D1 and D2 contribute equally if CP is conserved

te

CPV case:

Here Belle finds evidence of oscillations …

PDG’2006 average yCP=(0.90±0.42)%

Previous results on yCP from К+К- and +-

Problem: Br(D0→+-)/Br(K-+) = 3.6%Br(D0→K+K-)/Br(K-+) = 10.1 %

The same trick with D*+ is used 0** , DDXDee

t = ldec/ = ldec MD/PD,

ldec error translates into t~/2

yCP from D0→ K+K-, +- at Belle

D from cc-bar continuum are hard.

pCMS(D*+)>2.5 GeV:improves error on t, reduces backgrounds, removes D*’s from B→D*X.

Belle D*+ …

Events from D*+ and D0 signal boxes (|q|<0.8 MeV, |MD|<2.3) are used in lifetime measurements

and D0 signals (540 fb-1)

КК К

Time distributions of selected candidates

Where left tail comes from?

Time resolution function

Background from sidebands

Binned LH Fit

Correction for non-one-Gaussian shape

of errors

Fit parameter, correction for MC/data

diff.

i/

yCP from K+K-, +-

Resolution function

= 408.7±0.6 fs

Lifetime in different run periods is about the same

Good agreement with PDG = 410.1±1.5 fs

Check K-+ lifetime from fit:

Distribution of errors

error from vertex fit

Results

K+K-/+-

and K-+ratio

difference of lifetimesvisually observable

evidence for D0 mixing(yCP=0 @ 6*10-4)

3.2 from zero

2/ndf=1.084 (ndf=289)

+

PRL 98, 211803 (2007), 540fb-1

yCP =K/KK – 1

= (1.31 ±0.32 ±0.25)%

A=(D-D)/(D+D)=0.01±0.30 ±0.15 %

CPV check:

yCP from K+K-, +-

D0 K+- from BaBar

From Jonathon Coleman presentation at

19 July 2007

Manchester, England

Interference of

a) Double Cabibbo Suppressed (DCS) and

b) Cabibbo Favored (CF) decay with mixing

(PRL 98,211802 (2007))

EPS HEP 07, 19 July 2007Manchester, England

Jonathon ColemanD0 Mixing at BaBar

We use two decay modes:

1. Reference Cabibbo-favored (CF), “right-sign” (RS) decay

2. “Wrong-sign” (WS) decay

Two amplitudes contribute: a) Doubly Cabibbo-suppressed (DCS) decay

Rate without b): tan4 C ~ 0.3%

b) Mixing followed by CF decayRate without a): 10-4 or less, but interference with DCS can

enhance

Interference term linear in x, y!

BABAR D0K Mixing Analysis



Time-dependent decay rate

Use time dependence to separate DCS and mixing contributions (approximate; for x, y ¿ 1)

DCS decay Interference between DCS and mixing Mixing

Compare with semileptonic decay

with only mixing amplitude:

and with DCS alone: RD



Time-dependent decay rate

x2+y2=x’2+y’2

K is a strong uknown (see later) phase between CF and DCS

This phase may differ between decay modes.

And may vary over phase space for multi-body decays.

DCS decay Interference between DCS and mixing Mixing

What is y’ ?

It is some linear cobination of x,y:



D0 K±Ŧ Analysis Method

Identify the D0 charge conjugation state at prod. & decay using vertices fit to

Determines mK, m, proper-time t and error t

Vertices fit with beamspot constraint is importantImproves the decay-time error

resolution

Improves the m resolution

Right-sign (RS) decay

Beam spot: x ~ 7 m,

y ~ 100 m

D0 decay vertex

D0 productionvertex



RS & WS mK, m distributions

All fits are over the full range shown in the plots1.81 GeV/c2 < mK< 1.92 GeV/c2 and 0.14 GeV/c2 < m < 0.16 GeV/c2

Define a signal region1.843 GeV/c2 < mK< 1.883 GeV/c2 and 0.1445 GeV/c2 < m < 0.1465 GeV/c2



RS & WS mK, m projections

cou

nts

/0.1

MeV

/c2

cou

nts

/1 M

eV/c

2

1,229,000 RS candidates

Signal:background ~ 100:1

64,000WS candidates

Signal:background ~ 1:1

RS mK

WS mK

RS m

WS m



Fitting strategy

Fitting is performed in stages to reduce demand on computing resourcesAll stages are unbinned, extended maximum-likelihood fits.

1. RS & WS mK, m fit. Yields PDF shape parameters mK, m categories.

2. RS lifetime fit. mK, m category shape parameters held constant.Yields D0 lifetime D and proper-time resolution parameters.Constrained by the large statistics of the RS sample.

3. WS lifetime fit.Yields parameters describing the WS time dependence.

Small correlation between fitted parameters in the different stages justifies the staged approach.

The WS fit is performed under three different assumptions.Mixing and CP violation (CPV); mixing but no CPV; and no mixing or CPV.

Monte Carlo (MC) simulations are not used directly in the data fits.MC simulations used only to motivate the fit PDFs WS mis-reconstructed D0 category studied in swapped K↔data.



Right-sign mK, m fit

Shown are the fits to right-sign data for mK (left) and m (right).

The mis-reconstructed D0 category is not included in the RS fit.

This background is too small to be reliably determined.

1,141,500 ± 1,200 RS signal events



Wrong-sign mK, m fit

The mK, m fit determines the WS b.r. RWS = NWS/NRS

BABAR (384 fb-1): RWS = (0.353 ± 0.008 ± 0.004)% (PRL 98,211802 (2007))

BELLE (400 fb-1): RWS = (0.377 ± 0.008 ± 0.005)% (PRL 96, 151801 (2006))

4,030 ± 90 WS signal events

Check

(time integrated, DCS enhanced by CF with mixing)



RSproper decay-time fit

The parameters fitted areD0 lifetime D

Resolution parametersIncluding a 3.6 fsec offset

Signal, background category yields

Consistency checkFitted D = (410.3 ± 0.6) fsec

(statistical error only)

(PDG 2006: 410.1 ± 1.5 fsec)

RS fit projection in the signal region1.843 GeV/c2 < m < 1.883 GeV/c2

0.1445 GeV/c2 < m < 0.1465 GeV/c2



No-mixing WSdecay time fit

The parameters fitted areWS category yields

WS combinatoric shape parameter

As can be seen in the residual plot, there are large residuals.Residuals = data − fit

WS no-mixing fit projection in signal region1.843 GeV/c2 < m < 1.883 GeV/c2

0.1445 GeV/c2 < m < 0.1465 GeV/c2



Mixing WSdecay time fit

The fit is significantly improved by allowing for mixing.dotted line --- no-mixing fit.

solid line --- mixing fit.

DCS Interference Mixing



RWS vs. decay-time slices

If mixing is present, it should be evident in an RWS rate that increases with decay-time.

Perform the RWS fit in five time bins with similar RS statistics.Cross-over occurs at

t ~ 0.5 psec Simiar to residuals

plot.

Dashed line: standard RWS fit (2=24).Solid, red line: independent RWS fits to each time bin (2 = 1.5).

No-mixing fit

RWS fits



Mixing fit likelihood contours

Contours in y’, x’2 computed from −2 ln LBest-fit point is in the

non-physical region x’2 < 0

1 contour extends into physical region

Correlation: −0.95

Contours include systematic errors

The no-mixing point is at the 3.9 contour

Best fit , ’Best fit x 2

≥0 + :No mixing(0,0)

1 – CL =3.17 x 10-1 (1)4.55 x 10-2 (2)2.70 x 10-3 (3)6.33 x 10-5 (4)5.73 x 10-7 (5)

RD: (3.03 0.16 0.10) x 10-3

x’2: (-0.22 0.30 0.21) x 10-3

y’: (9.7 4.4 3.1) x 10-3

Contours at 1intervals



Fits allowing for CP violation

Fit D0 and D0 decay-time dependence separately.

x'2+ = (−0.24 ± 0.43 ± 0.30) x 10-3

y'+ = (9.8 ± 6.4 ± 4.5) x 10-3

x'2- = (−0.20 ± 0.41 ± 0.29) x 10-3

y'- = (9.6 ± 6.1 ± 4.3) x 10-3

D0 D0

No evidence seen for CP violation



List of systematics, validations

Systematics: variations in Functional forms of PDFsFit parametersEvent selection

Computed using full difference with original value

Results are expressed in units of the statistical error

Validations and cross-checksAlternate fit (RWS in time bins)Fit RS data for mixing

x’2 = (−0.01±0.01)x10-3

y’ = (0.26±0.24)x10-3

Fit generic MC for mixingx’2 = (−0.02±0.18)x10-3

y’ = (2.2±3.0)x10-3

Fit toy MCs generated with various values of mixing

Reproduces generated valuesValidation of proper

frequentist coverage in contour construction

Uses 100,000 MC toy simulations

Systematic source

RD y’ x’2

PDF: 0.59 0.45 0.40

Selection criteria:

0.24 0.55 0.57

Quadrature total:

0.63 0.71 0.70



Comparison with BELLE D0 K result PRL 96,151801, 400 fb-1

Results consistent within 2

BABAR 2

BABAR3

BABAR 1 stat. only

BELLE 2(no-mix excl. at 2)

No mixingexcluded > 4

1

23

4

x'2

y'

RD: (3.30 ) x 10-3

x’2: (-0.01±0.20) x 10-3

y’ : (5.5 ) x 10-3

May 2007 HFAG Averages +2.8-3.7

+0.14-0.12

Time dependent Dalitz analysis of D0→ KS +- at Belle

PRL 99,131803 (2007), 540 fb-1

Time dependent Dalitz analysis of D0→ KS +-

different decays identified through (m+2 VS m-

2) plot

CF: D0 → K*-+

DCS: D0 → K*+-

CP: D0 → 0 KS

their relative phases determined (unlike D0 → K+-);

m±2 = m2(KS±)

if CP conserved and : 210

2

1)0( DDD

),(2

)()(),(

2

)()(

)()()()(

)( )( 2

1)(

22212221

210210

2211

mmtete

mmtete

teteDK

teteDK

teDKteDKtK

SS

SSS

AA

222

1

and decay as D or anti-D

propagate …

Dalitz plot can change in time!

Selection is similar to K, Nsig=(534.4±0.8)x103, purity 95%

Time dependent Dalitz analysis of D0→ KS +-

K*(892)+

K*X(1400)+

K*(892)-

Amplitudes and phases in agreement with previous measurement (for 3)PRD73, 112009 (2006)

sum over 18 resonances!

NRr iNR

ir eammBeamm

),(),( 2222A

t

t [fs]

= 409.9±0.9 fs PDG=410.1±1.5 fs

comb.bkg.

Time evolution of D0→ KS +-

Number of decays VS time

Lifetime agrees with PDG

Dalitz plot VS time

most sensitivemeas. of x (2.4)

Cleo, PRD72, 012001 (2005)x = 1.8 ± 3.4 ± 0.6%y = -1.4 ± 2.5 ± 0.9 %

PRD72, 071101 (2005), 253 fb-1

D0 → K(*) l PRL96, 151801 (2006), 400 fb-1

D0 → K+ -

2-d 68% C.L. region

B. Golob, Belle Lepton Photon ‘07, Daegu

)%24.033.0()%29.080.0(

14.010.016.013.0

yx

2-d 68% C.L. region

D0 → K+K-/+-

PRL 98, 211803 (2007), 540fb-1

D0→ KS +-: results

12/1

2/1/ pq

CPV in decay: 1/ Df

DfAA ff

CPV in mixing, if :

0ArgArg0

0

Df

Df

p

q

A

A

p

q

f

fCPV in interf. mix./decay:

D0→ KS +-: CPV search

include |q/p| and as additional free param.

95%C.L.

rad 0.09) (-0.24 31.028.0

002,1 DqDpD

09.010.0

0.290.30 0.86 |q/p|

First attempt to measure strong phase K in D0 K+- using

quantum correlations of D0-D0 pairs produced from (3770) by

Cleo-c

hep-ex/0712.0498 , 281 pb-1

Strong phase K in D0 K+-

CLEO-c:

D0 D0 are in a JPC = 1- - state

D mesons can not be simultaneously in the same CP state (e.g. D1-D1 – Bose particles + antisymmetry) and can not decay to CP eigenstates with the same eigenvalue.

Such quantum correlations result in

)()( ) and ( 20

10

20

10 fDPfDPfDfDP

ee * (3770) D0D0

where is the probability of f2 with the condition that f1 is chosen.

E.g. if f1 = CP even state = S+ , f2 = e- X:


All three probabilities are accessible experimentally.

1. - by counting events Ndbl with reconstructed f1 and f2 (efficiencies are known)

2. - by counting events Nsng with reconstructed f1 and regardless of f2 (or vice versa).

))((or )( 20

10 fDPfDP

) and ( 20

10 fDfDP

) average(

)(

) average(

)|( 21second21 XeDP

XeDP

XeDP

SDXeDP

NN

N

sngsng

dbl

)(

)|(

)()(

),(

2

12

21

21

fP

ffP

fPfP

ffP

)|( 12 ffP

Now, if f1 = CP even state = S+ , f2 = K- +:


yyD

D

XeD

D

D

XeD

XeDP

XeDP

11

1

)(

) average(

) average(

) average(

)(

)(

) average(

)(

2

2

22

) average(

)(

) average(

)|( 21second21 XeDP

XeDP

XeDP

SDXeDP

NN

N

sngsng

dbl

...)cos(1

11

) (

)(

1

1

) (

)(

)(

)(

)(

)(

2

avr

2

avr

avr

2

2

avr

2

MDD

iD

RyRR

eRy

KD

KD

y

KD

D

D

KD

KDP

KDP


Consider different pairs of f1, f2 (K, S+, S-, eX).

Formulas with and without correlations differ!

)( 2,10 fDP

) and

(

2sec

1

fD

fDP frst

sensitivity to various parameters, e.g. cos

Hadronic Single Tags Identify the final state with

E Ebeam-ED,

Cut on E, fit MBC distribution to signal and background shapes.

Efficiencies from (uncorrelated) DD Monte Carlo simulations.

Peaking backgrounds for:– K from K/ particle ID

swap.– Modes with K0

S from non-resonant MBC for K0

S0 (CP-)

MBC for (CP+)

MBC for K (f)

Note log scale DATA

(GeV)

2 2| |BC beam DM E p

Data clearly favors quantumcorrelations showing constructive and destructive interference and no effect as predicted

K-+ vs K-+

K-+ vs K+-

CP+ vs CP+

CP- vs CP-

K vs CP+

K vs CP-

CP+ vs CP-

Quantum correlations are visible!


Not enough statistics to compete with Belle / BaBar results on x, y, y’, but:

First measurement

cos()=1.03±0.19 ±0.08 or 0.93 ±0.32 ±0.04

(depending on external measurements used in fit)

Main contribution

from K/S±

Summary1. First evidence of D0 mixing in several modes:

a) K+K-, +-

b) DCS+CF with mixing K+-

c) Dalitz plot evolution in K0S+-

2. First information on strong phase K from CLEO-c (more data will be added, x2-3).

3. Theory:

The SM box is tiny. D0 mixing is the only down-quark-mediated transition with F=2. In principle ideal room for New Physics to show up (extended Higgs, 4th generation, SUSY, leptoquarks).

But big long distance effects, hard to calculate since mc~hadronic scale, obscure possible short-distance NP in x.

Estimates: xbox≤10-5, xlong dist.≤O(10-3).

Since in data x,y ~0.5% - interpretation is difficult (NP or not NP?)

4. The only clear sign - large CPV (immune to hadronic uncertainties)

Documents

Introduction: general formalism of oscillations Nice review: hep-ph/0712.3367 (Dec 2007): “Topics in Hadronic B decays”, J.Virto QM perturbation theory