Recent Results from FOCUS

Sandra Malvezzi - Recent results from FOCUS

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Sandra MalvezziI.N.F.N. Milano

Recent Results from FOCUS

SLAC16 March 2004

FOCUS Collaboration


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A new charm physics eraThe high statistics and excellent quality of data allow for unprecedented sensitivity & sophisticated studies

• Investigation of decay dynamics both in the hadronic and semileptonic sector Phases and Quantum Mechanics interference FSI role & CP studies• Lifetime measurements @ better than 1% non-spectator processes

• Mixing and rare & forbidden decays possible window on physics beyond SM

What can we learn for the future (charm and beauty @ higher statistics )?


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Over 1 million reconstructed!!

Successor to E687. Designed to study charm particles produced by ~200 GeV photons using a fixed target spectrometer with upgraded Vertexing, Cerenkov, E+M Calorimetry, and Muon id capabilities. Includes groups from USA, Italy, Brazil, Mexico, Korea

1 million charm particles reconstructed into DK , K2 , K3

FOCUS Spectrometer


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• Lifetime • Mixing • Rare & forbidden decays • Semileptonic • Hadronic decays (Dalitz plot)• Multi-body channels (4,5,6 bodies!) • Charm Baryons• D* spectroscopy

FOCUS role

]not covered here


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Charm lifetimes

FOCUS (*) produced new lifetimes results with precision better than the previous world average (○), PDG 2002

0

0

( ) 2.54 0.02( )

( ) 1.22 0.01( )

s

DD

DD

0 1 1( ) ( ) ( )15 3c cD


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Rare & forbidden decays8 rare & SM forbidden decays

( ,,

)sD D h

h K

improvement over previousresults by a factor of 1.7 -14

Phys.Lett. B572 (2003) 21


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Mixing

I play in the enemy’s territory! Preliminary FOCUS semimuonic mixing

0.131%mixr @95%


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the unexpected

• i.e. the analysis complications

• i.e the lessons for the future– Higher charm statistics– Beauty accurate studies

...the semileptonic sector


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New results on D K

Our K spectrum lookslike 100% K*(892)

This has been known for about20 years

...but a funny thing happened when we tried to measure the form factor ratios by fitting the angular distributions


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Decay is very accessible to theoryAssuming the K spectrum contains nothing but K*, the decay rateis straight-foreward


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An unexpected asymmetry in the K* decay A 4-body decay requires 5 kinematics variables: 3 angles and 2 masses

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WM q t

KM

Vdd 2cos1

forward-backwardasymmetry incos below the K*pole but almost noneabove the pole

V

Sounds like QM interference


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Try an interfering spin-0 amplitude2

2 2

0

(1 cos )sin2 2

(1 cos ) sin( )2 2

sin (cos )2

il V

il V

iδl V

B

B

e H

M t m e H

AeB H

will produce 3 interference terms

iAe

(plus mass terms)

02 2

0 0

mB

m m im

iAe We simply add a constant amplitude in the place where the K* couples to an m=0 W+ with amplitude 0H

Phys.Lett.B535,43,2002


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Studies of the acoplanarity-averaged interference2 2

0*8cos sin Re( )V KViA e B H

Extract this interference term by weighting data by all averaged terms in the decay intensity for pure are constant or 2cos V

cos V

We begin with the mass dependence: *Re( )i

Ke B

A constant 45ºphase worksgreat.......but the solution is notunique.

KM

*0D K


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-6000

-4000

-2000

0

2000

4000

0.8 0.82 0.84 0.86 0.88 0.9 0.92 0.94 0.96 0.98 1

FOCUS fitLASS Scaled fitKappaKappa

.. other options would work as well.Asymmetry expected directly from LASS s-wave K phase shift analysis.

And Kappa with no fsi phase shift and with a 100 degree phase shift.

cos V

term

Km

cos v weighted M(K), GeV/c2


15


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FOCUS D+K*0+semileptonic BRs

*0( ) 0.602 0.01( ) 0.021( )( )

D K stat sysD K

Our number is 1.59standard deviation below CLEO and 2.1 standard deviation above E691

All values consistent with their average value with a CL of 19%


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...and form factors

The vector and axial form factors are generally parametrized by a pole dominance form

22 2

(0)( )1

ii

A

AA qq M

22 2

(0)( )1 V

VV qq M

2.5

2.1A

V

MM

2/GeV c2/GeV c

Nominal spectroscopicpole masses

v 1(0) (0)r V A 2 2 1(0) (0)r A A

3 3 1(0) (0)r A A

D+d

d

uus

5

02

2 2 2,0, 1,2,3

( , , )cos cos

( ) ( ), ( ))

tK V

t

d f H H Hdm dq d d d

H q g A q V q


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Form Factor Ratios v 2

1.45 0.23 0.07 1.00 0.15 0.03791( ) 1.90 0.11 0.09 0.71 0.08 0.09791( ) 1.84 0.11 0.09 0.75 0.08 0.09

687 1.74 0.27 0.28 0.78 0.18 0.11653 2.0

1.504 0.057 0.039 0.875 0.049 0.06

0 0 3

4

. 3

Group r rFOCUS

BEATRICEE eE

EE

0.16 0.82 0.22 0.11691 2.0 0.6 0.3 0.0 0.5 0.2E

Our analysis is the first to include the effects on the acceptance due to changes in the angular distribution brought about the s-wave interference

0.330 0.022 0.015A 1GeV

0.68 0.07 0.05 rad

Phys.Lett.B 544(2002) 89

Form factor lattice calculation Damir Becirevic (ICHEP02) RV = 1.55 0.11which is remarkably close to the FOCUS result.


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sD sD sD

Baseline cuts

a) 2682 evtsb) 4695 evts

Baseline, out-of-material.isolation cuts

c) 793 evtsd) 2192 evts

Phys.Lett.B 541 (2002), 243


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( ) 0.54 0.033( ) 0.048( )( )

s

s

D stat sysD

sD

Group electron muonFOCUS 0.540.0330.048

CLEO2 0.540.050.04

E687 0.580.170.07ARGUS 0.570.150.15

CLEO 0.490.100.12

All values consistent with an average of 0.54 0.04

FOCUS BRs


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New measurement of the Ds+ ff

• According to flavor SU(3) symmetry the form factor ratios rv and r2 describing D+K0 should be close to Ds

+ since the only difference is a spectator quark d replaced with a s

• Lattice gauge calculations: max diff= 10%

• Experiment: – rv OK

– r2 inconsistent (3.3.

hep-ex/0401001


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Comparing data and model

Data: histogram:Model:dotsccbar background:dashed


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S-wave interference in

K*

dataccbar mc

even

ts

cos V

even

ts

cos V

090

00

045

0m - G 0m + G0m

even

ts

co

s V

data NO evidence for s-wave interference in Ds


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v 2

791 2.27 0.35 0.22 1.570 0.250 0.1900.9 0.6 0.3 1.400 0.500 0.300

653 2.3 1.0 0.4 2.

1.549 0.250 0.145 0.713 0.202 0

100 0.550 0.

.26

0

6

2 0

Group r r

ECLE

FOC

O

US

E

form factor results

1. Most precise measurement to date2. very consistent with D+K03. very consistent with theoretical expectation


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....the lesson “The advantages of high-statistics for the interpretation

of Heavy-Flavour hadronic-decay dynamics will vanish without a strategy for controlling

strong effects among particles involved in weak-decay processes ”

If unexpected complications arise in the semileptonic sector what happens in the three-body

hadronic decay dynamics study?


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Complication for Dalitz plot analysis

had to face the problem of dealing with light scalar particles populating charm meson

hadronic decays, such as D, D

Require understanding of light-quark hadronic physics including the riddle of and (i.e, and states produced close to threshold),

whose existence and nature is still controversial


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A bridge of language, knowledge and measurements between the two worlds

of Light Mesons and Heavy Flavoursis necessary

• S-matrix and its representations• Two-body unitarity • Analyticity • Limits of the Breit-Wigner approximation etc..


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Analysis techniques CAN and MUST be improved now in view of extensive application in high-statistics experiments (Cleo-c, Babar, Belle, BTeV, LHC-b etc...) for precision studies of CP and reliable New Physics measurements

Pioneering work performed by

hep-ex/0312040 to appear in PLB 585 (2004) 200


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An instructive example from FOCUS

Milano group

D

analogy with operatively: complete Dalitz plot analysis (time-dependent) to deal with

all interference with other () intermediate channels

B

crucial for determination of the angle of the SM unitarity triangle


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For a well-defined wave with specific isospin and spin (IJ)characterized by narrow and well-isolated resonances, we knowhow.

How can we formulate the problem?D r

| 1 2

3

The problem is to write the propagator for the resonance r

rr3

1

2


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•the propagator is of the simple Breit-Wigner type

1 3 13 2 212

1(cos )J J r

D r Jr r r

A F F p p Pm m im

traditionalisobar modelj

j jj

Aia e M

Spin 0

Spin 1

Spin 2 )1cos3()(2

)2(

1

1322

13

13

ppP

ppP

P

J

J

J

21

21

)339(

)1(

1

4422

22

pRpRF

pRF

F

•the decay amplitude is

•the decay matrix element


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when the specific IJ–wave is characterized by large and heavily overlapping resonances (just as the scalars!), the problem is not that simple.

1( )I iK

where K is the matrix for the scattering of particles 1 and 2.

In this case, it can be demonstrated on very general grounds that the propagator may be written in the context of the K-matrix approach as

Indeed, it is very easy to realize that the propagation is no longer dominated by a single resonance but is the result of a complicated interplay among resonances.

i.e., to write down the propagator we need the scattering matrix

In contrast


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21 0

20 0 0

1 / 2( )

( )(1 )jK A

k kj jA A

g s s s mF I iK f

m s s s s s s

We may summarize by saying that:

The decay amplitude may be written, in general, as a coherent sumof BW terms for waves with well-isolated resonances plus K-matrix terms for waves with overlapping resonances.

00

1 1

( ) i i

m ni i iBW K

i i i ii i m

A D a e a e F a e F

Where the general form of for scalars is K

iF


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•Based on “first principles” of S-matrix scattering theory

The K-matrix formalism E.P.Wigner,Phys. Rev. 70 (1946) 15

S.U. Chung et al.Ann. Physik 4 (1995) 404

1 1K T i 1( )T I iK K

1/ 2 1/ 22S I i T S scattering matrix

= phase space


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•From T

to F

1( )T I iK K

From scattering to production: the P-vector approach

I.J.R. AitchisonNucl. Phys. A189 (1972) 514

1( )F I iK P

known from scattering data

describes coupling of resonances to D


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D

P

1

23 Multi body4 = 5 '

K K

1(1 )iK

K-matrix picture

1( )F I iK P


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K-matrix advantages

• An elegant and direct way of incorporating the two-body unitarity constraint • Proper handling of overlapping and wide resonances• Straightforward inclusion of already known physics

and disadvantages requires translation into T-matrix to get the “physics”


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* p0n,n, ’n, |t|0.2 (GeV/c2)GAMSGAMS

* pn, 0.30|t|1.0 (GeV/c2)GAMSGAMS

* BNLBNL

*p- KKn

CERN-MunichCERN-Munich

::

* Crystal BarrelCrystal Barrel




pp

pp , ,

pp K+K-, KsKs, K+s

np -, KsK-, KsKs-

-p0n, 0|t|1.5 (GeV/c2)E852E852*

At rest, from liquid 2H At rest, from gaseous

At rest, from liquid

At rest, from liquid

2H

2D2H

“K-matrix analysis of the 00++-wave in the mass region below 1900 MeV’’ V.V Anisovich and A.V.Sarantsev Eur.Phys.J.A16 (2003) 229

A description of the scattering ...

A global fit to all the available data has been performed!

goto F amplitude formula


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( ) ( ) 200 0

20 0 0

1 2( )( )(1 )

scatti j scatt A

ij ij scattA A

g g s s s mK s fm s s s s s s

( )ig

is the coupling constant of the bare state to the meson channelscatt

ijf0s describe a smooth part of the K-matrix elements

20 0( 2) ( )(1 )A A As s m s s s suppresses the false kinematical singularity

at s = 0 near the threshold

and

is a 5x5 matrix (i,j=1,2,3,4,5)

'

IJijK

K K1= 2= 3=4 4= 5=

A&S


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A&S K-matrix poles, couplings etc.

4 '

0.65100 0.24844 0.52523 0 0.38878 0.363971.20720 0.91779 0.55427 0 0.38705 0.294481.56122 0.37024 0.23591 0.62605 0.18409 0.189231.21257 0.34501 0.39642 0.97644 0.19746 0.003571.81746 0.15770 0.179

KKPoles g g g g g

0 11 12 13 14 15

0

15 0.90100 0.00931 0.20689

3.30564 0.26681 0.16583 0.19840 0.32808 0.31193

1.0 0.2

scatt scatt scatt scatt scatt scatt

A A

s f f f f f

s s


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A&S T-matrix poles and couplings

4 '13.1 96.5 80.9 98.6 102.1

116.8 100.2 61.9 140

( , / 2)(1.019, 0.038) 0.415 0.580 0.1482 0.484 0.401(1.306, 0.167) 0.406 0.105 0.8912 0.142

KKi i i i i

i i i i

m g g g g ge e e e ee e e e

.0 133.0

97.8 97.4 91.1 115.5 152.4

151.5 149.6 123.3 170.6

0.225(1.470, 0.960) 0.758 0.844 1.681 0.431 0.175(1.489, 0.058) 0.246 0.134 0.4867 0.100 0

i

i i i i i

i i i i

ee e e e ee e e e

133.9

.6 126.7 101.1

.115(1.749, 0.165) 0.536 0.072 0.160 0.313

i

i i i i i

ee e e e e

A&S fit does not need a as measured in the isobar fit


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FOCUS D s +

++- analysis

Observe:

•f0(980)

•f2(1270)

•f0(1500) Sideband

Signal

Yield Ds+ = 1475 50

S/N Ds+ = 3.41


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First fits to charm Dalitz plots in the K-matrix approach!

C.L fit 3 %

sD

Low mass projection High mass projection

+

+20 +

(S - wave)π 87.04 ± 5.60 ± 4.17 0(fixed) f (1275)π 9.74 4.49 2.63 168.0 18.7 2.5ρ (1450)π 6.56 ± 3.43 ± 3.31 234.9 ± 19.5 ± 13.3

decay channel phase (deg)fit fractions (%)

r

j

2iδ 2 2r r 12 13

r 2iδ 2 2j j 12 13j

a e A dm dmf =

a e A dm dm


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sD

•No significant direct three-body-decay component

•No significant (770) contribution

sD

Marginal role of annihilation in charm hadronic decays

But need more data!


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f2(1270)f0(980)

f0(980)

f2(1270)S0(1475)

Isobar approach results: an effective description

C.L. Fit 7.2%

+2

+0

+00

NR 24.85 ± 3.99 ± 5.67 246.8 ± 4.7 ± 4.8 0.516 ± 0.040 ± 0.055f (1275)π 9.58 ± 1.22 ±1.20 141.7 ± 6.8 ± 6.6 0.321 ± 0.021 ± 0.021f (980)π 93.23 ± 2.39 ± 2.55 0(fixed) 1(fixed)

S (1475)π 17.18 ± 2.94 ± 3.00 248.9 ± 3.5 ± 5.7 0.429 ± 0.039 ± 0.041ρ (1 +450)π 4.56 ± 0.79 ± 0.89 191.0 ±13.8 ±17.6 0.221 ± 0.020 ± 0.023

decay channel amplitude coefficientphase (deg)fit fractions (%)

Non-resonant absorbs parametrization problem.....no robust conclusion on annihilation possible

goto Dalitz picture

preliminary


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m = 1473.0 8.8 MeV/c= 109.5 16.3 MeV/c

if f0(1500) PDG m = 1507 5 MeV/c = 109 7 MeV/c

instability

S0(1475)

“Effective resonance”

more complicate interplay between S-wave resonancesand underlying non-resonant S-wave component

then0f (980) = (104.20 ± 3.30)%

NR = (43.53 ± 4.88)%fit fractions preliminary


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Yield DYield D++ = 1527 = 1527 5151

S/N DS/N D++ = 3.64 = 3.64

FOCUS D+ ++- analysis

Sideband Signal


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2lowm

2highm

D

C.L fit 7.7 %

K-matrix fit results

Low mass projection High mass projection

18 11.7

+

+2

0 +

(S - wave)π 56.00 ± 3.24 ± 2.08 0(fixed) f (1275)π 11.74 1.90 0.23 -47.5 .7ρ (770)π 30.82 ± 3.14 ± 2.29 -139.4 ± 16.5 ± 9.9

decay channel phase (deg)fit fractions (%)

No new ingredient (resonance) required not present in the scattering!


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With

Without

C.L. ~ 7.5%

Isobar analysis of D+ ++would instead require a new scalar meson:

C.L. ~ 10-6

m = 442.6± 27.0 MeV/c = 340.4 ± 65.5 MeV/c preliminary


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A.D. Polosa: “ Hadronic pollution in B”?

J.A. Oller: “On the resonant and non-resonant contributions to B”

CKM03 in B


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• We can view the decay as consisting of an initial production of the five virtual states , KK,

’and 4which then scatter via the physical T-matrix into the final state.

The Q-vector contains the production amplitude of each virtual channel in the decay

1 1 1 1( ) ( )F I iK P I iK KK P TK P TQ

The Q-vector approach


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Q-vector for Ds

The two peaks of the ratios correspond to the two dips of the normalizing modulus, while the two peaks due to the K-matrix singularities, visible in the normalization plot, cancel out in the ratios.

Ratios of the moduli of the Q-vector amplitudes

The normalizing modulus


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Q-vector for D+

Ratios of the moduli of the Q-vector amplitudes

The normalizing modulus


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The resulting picture • The S-wave decay amplitude primarily arises from a ss contribution.• For the D+ the ss contribution competes with a dd contribution.• Rather than coupling to an S-wave dipion, the dd piece prefers to

couple to a vector state like (770), that alone accounts for about 30 % of the D+ decay.

• This interpretation also bears on the role of the annihilation diagram in the Ds

+ decay:– the S-wave annihilation contribution is negligible over much of

the dipion mass spectrum. It might be interesting to search for annihilation contributions in higher spin channels, such as 0(1450) and f2(1270)


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ConclusionsCharm physics is revealing itself a rich source of new results

•FOCUS is playing a crucial role in understanding the charm phenomenology, both in the semileptonic and hadronic sector.

•The measurements of the D+ K*0 form factors required the introduction of an S-wave contribution interfering with K*0 •The presence of scalar resonances in D-meson decaysrequired a revision of the Dalitz plot parametrization


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• A self-consistent description of S-wave isoscalar scatteringin the energy range of interest is given in the K-matrix approach by the global fit to data of A&S

• The K-matrix approach has been applied to charm decaysfor the first time.

not at all obvious!

Conclusions cont’d

•The results are extremaly encouraging since the same parametrization of two-body resonances coming from light-quark experiments works for charm decays too


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• For a two-body decay

CP violation on the Dalitz plot

AAtottot = g1M1ei1 + g2M2ei2

CP conjugate

AAtottot = g1M1ei1 + g2M2ei2** **

ii = strong phase

CP asymmetry:

aaCPCP==2Im(2Im(gg2 2 gg11**) sin() sin(11--22)M)M11MM22

|g|g11||22MM1122+|g+|g22||22MM22

22+2Re(+2Re(gg2 2 gg11**)cos()cos(11--22)M)M11MM22

|Atot|2- |Atot|2

|Atot|2+ |Atot|2==

2 different amplitudes strong phase-shift


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Dalitz plot = FULL OBSERVATION FULL OBSERVATION of the decay

COEFFICIENTS and PHASES for each amplitude

Measured phase: =+CP conserving CP violating

CP conjugate =

=-=-

E831

aCP=0.006±0.011±0.005Measure of direct CP violation:asymmetrys in decay rates of DDKKK K

CP violation & Dalitz analysis


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Ds , D+ KK

Ds+ K+ K+ D+ K+ K+

DsD

2Km

2KKm 2

KKm

2Km

KKm


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+ -2K K

m

- +2K π

m

K+ Kprojection K projection

Yield D+ = 7106 92

S/N D+ = 8.62

Decay Fraction and phases

K*(892) = 20.7 1.0 % (0 fixed)

(1020) = 27.8 0.7 % (243.1 5.2)°

K*(1410) = 10.7 1.9 % (-47.4 4.9)°

K* (1430) = 66.5 6.0 % (61.8 3.8)°

f0(1370) = 7.0 1.1 % (60.0 5.3) °

a0(980) = 27.0 4.8 % (145.6 4.3)°

f2(1270) = 0.8 0.2 % (11.6 7.0) °

(1680) = 1.6 0.4 % (-74.3 7.5) °

Preliminary


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phi(1020) K*(1430) a0(980) K1(1410) f2(1270) f0(1370) phi(1680)

K*(1430)phi(1020) a0(980) K1(1410) f2(1270) f0(1370) phi(1680)

Coefficients: D±,, DD++,, DD--

Phases: DD±±,, DD++,, DD--

Preliminary!

No evidence of CPV

K-matrix approach to improve the quality of the analysis


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....ultimately• FOCUS has performed pioneering work in the charm sector

NOWit is your go!

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Recent Results from FOCUS