1

Study of CP Violation in BStudy of CP Violation in B00 ++––00//KKSS Decays Decays

Jinwei Wu Harvard University

Aug 21st, 2006

CP violation Extraction of α from B ρ decay Extraction of β from B KS decay Conclusion

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Direct CP AsymmetryDirect CP Asymmetry

2 2

2 20 Direct

ffCP

ff

A AA

A ACPV

• Sources of direct CP asymmetries:

Interference between two decay amplitudes (Ai) with different strong (i) and weak phases (i)

2

1 2

1

1 2

122sin sin,

1/ cos cosCPA R R

1

2

ARA

2A

1 1A A

1 2A A A

1 2A A A

2A

1 1A A

1 2A A A 1 2A A A

2A2A

no CPV

CPV

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Time-dependent CP AsymmetryTime-dependent CP Asymmetry

B0

fCPno oscillationB0

oscillation

1 cos2

Di m tA e

22 sin

2M Di im tA ie e

B0 fCPno oscillation

B0oscillation

1 cos2

Di m tA e

22 sin

2M Di im tA ie e

0

0

( )

( )

phys CP

phys CP

B t f

B t f

CPV

2 20 0

2 20 0

2

2 2

12Im sin cos1 1

CP

CP CPf

CP CP

f H B t f H B tA t

f H B t f H B t

m t m t

* * 012 12

0

12 12

2

2

CP

CP

iM f H Bi f H BM

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Mixing induced CPV in Charmless B DecayMixing induced CPV in Charmless B Decay

• Decay-amplitude weak-phase structure for b → uud :

** * * iud ub u

u u c t cu

itd t tbub d tdb tV V V VA T P P P P T P R TV Re eV V V P

eff

+i2

-i

e e

iu tCP

u t

R T R PA eA R T R P

qp

• Time dependent asymmetry probes eff:

0 0

0 0

2eff

( )

1 sin 2 sin cos

phys CP phys CP

phys CP phys CP

B t f B t fa t

B t f B t f

C m t C m t

3

ub udV V

3

tb tdV V

5

/

( , , ) (1 )4

1 sin cos

t

tag CP

tag d d

ef t Q Q Q A

Q S Q S m t C Q C m t

Quasi-two-body approximation, ignore interference effect 6 observables through a time-dependent fit:

Quasi-two-body AnalysisQuasi-two-body Analysis

*arg , TTA A rT

ACP Direct CPV

C Direct CPVC DilutionS Mixing-induced CPVS Strong phase difference

2

2sin 2 cos

1T

T

rS

r

2

2cos 2 sin

1T

T

rS

r

2

2

11

T

T

rC

r

free

0CPA 0C Penguin scenario

R. Aleksan et al, 1990

Measure CP violation, but not necessarily phase

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Snyder-Quinn MethodSnyder-Quinn Method

Idea: Extract and the strong phases using the interference between B0 +0 amplitudes

+

+–

00

+0 amplitude parameterization:

The f+, ,0 are relativistic Breit-Wigner form factors

/223 3

22*3 3 3 3

2 22 23 3 3 3

( , )4

Im1 2 sin cos

t

tag

tag d tag d

ef t Q A A

A A A AQ m t Q m t

A A A A

A3 = f+A+ + fA+ + f0A00

A3 = f+A+ + fA+ + f0A00

m(

0 )

2 (G

eV2 )

m(+0)2 (GeV2)

Quinn, SnyderPRD 48, 2139, (1993)

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The Square Dalitz Plot The Square Dalitz Plot

Toy MC

det|J|min

1max min

1 cosm m

mm m

11 cos cos

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Fit Projection PlotsFit Projection Plots

ρ(770) dominate

Strong signal with 347M BBbar

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Extract physics parametersExtract physics parameters

Time-dependent Dalitz plot approach should supersede the previous quasi-two-body analysis, with interference among resonances taken into account.

Q2B, LP2003 Dalitz Plot Analysis

Aρ Direct CPV –0.114 ± 0.062 ± 0.027 –0.142 ± 0.041 ± 0.015

C Direct CPV 0.35 ± 0.14 ± 0.05 0.154 ± 0.090 ± 0.037

C Dilution 0.20 ± 0.14 ± 0.05 0.377 ± 0.091 ± 0.021

S Mixing-induced CPV –0.13 ± 0.18 ± 0.04 0.01 ± 0.12 ± 0.03

S Strong phase difference 0.33 ± 0.18 ± 0.03 0.06 ± 0.13 ± 0.03

* Using a Q2B approach and 144fb-1 data, BELLE measured:

0.16 0.10, 0.25 0.17, 0.38 0.18, 0.28 0.24, 0.33 0.18CPA C C S S

hep-ex/0608002

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Probing Direct CP ViolationProbing Direct CP Violation

2 2

2 2 1

0.03 0.07 0.03

A A A C A CA

C A CA A

2 2

2 2

0.150.16

1

0.38 0.07

A A A C A CA

C A CA A3.0

Define physically more intuitive quantities:

B0

ρ+ B0+

ρ

=?

B0

+

ρ B0

ρ+

=? Large Direct CPV not expected…

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Road to Road to

What is the strong phase between B0ρ+ and B0ρ+?

What is ?

Dalitz plot specific measurements:

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Measuring sin2Measuring sin2ββ with Charmless B decay with Charmless B decay

BR~ 10-3

BR~ 10-5

B0J/K0

B0K0

sin2=0.69±0.03

Both decays dominated by single weak phase

b s

, ,u c t, ,g Z

tb tsV V

Penguin:

s

dd

s

Tree:

b

dd

W cbV

csV

0K

c /J

s0K

New Physics? 3

c

High virtual mass scales involved: believed to be sensitive to New Physics

decays are tree and penguin diagrams, with equal dominant weak phases

decays are pure “internal” and “flavor-singlet” penguin diagrams

b ccs

b sss

?[charmonium]sin2 [ -penguin]sin2 s

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Sources of Standard Model PollutionSources of Standard Model Pollution

There are many modes that dominantly decay via bs(qq)…but not all modes were created equal

uusd

b

d

B0

K0

b

d

sddd 0,0,’(?),f0(?)…

K0B0

0,0,’(?),f0(?)…

This is ok; still givessin2 in SM.

CKM and color suppressed..but will lead to slight deviation.

c,t

There are various estimates for the deviation from sin2β due to SM pollution…most of them expect a larger value!

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sin2sin2ββ from from BB00 KKSS Final State Final State

o quite a few CP events in this decay including 0KS and f0KS

o also a higher (f?) resonance ~1500 MeV

o there is a possible tree diagram which contaminates the sin2 measurement

o time-dependent CP has been measured for f0Ks and 0Ks

Last summer, Belle presented a (time and tag independent) Dalitz Plot analysis of this mode…this approach will be important in the future!

BR ( 10–6) HFAG

B0 →ππK0 (inclusive) 44.8 ± 2.6

B0 →f0K0 5.9 ± 0.8

B0 →ρ0K0 5.6 ± 1.1

B0 →π–K*+ 9.8 ± 1.1

B0 →π–K*(1430)+ 46.6 ± 6.6

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BB00 KKSS Final State Final State

o A Dalitz plot with rich structures, apart from CP eigenstates, there are also flavor eigenstates.

o K*(890)π, K*0(1430)π are important for testing QCD factorization and other schemes.

o Can look for direct CP violation and test SU(3) symmetry in the B → PV decays

o Interference with flavor eigenstates can help lift the degeneracy in the sin2β measurement

K*(890)

K*(1430)

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BB00 ff00 KKSS

ML

fit : 0

0

00

0.32 0.230.95 0.10

0.24 0.31 0.15S

S

f K

f K

S

C

Systematic errors dominated by

Fit bias & interference with other modes

0tagB

0tagB

Asymmetry

0 0 60BR( (980) ) ~ 6.0 10SB f K

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BB00 ρρ0 0 KKSS

Complicationso high level of bkgo ρ is broado Interference with

ππ s-wave at both high mass and low mass

BaBar:S=0.17±0.52±0.26C=0.64±0.41±0.25

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Analysis of BAnalysis of B00 KKSS Dalitz Plot Dalitz Plot

f0

f???

Strong signal with 347M BBbar

Similar analysis technique, need to handle additional flavor eigenstates

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ConclusionConclusion

Extraction of α from B ρπo The isospin analysis appears hopeless for the near futureo There is hope for the Dalitz plot analysis although it’s technically

difficult.o Extract α with no ambiguities. Especially useful when combined

with other experiments or other measurements of α.o Latest result in hep-ex/0608002

Pioneered time-dependent Dalitz plot analysis for B decays. Framework setup to study other three-body B decays.o Already tested on B0→K+–0

o Close to finish CP measurement of B0→K0+–, where CP violation in s-penguin decay and direct CP violation will be tested

o Foresee preliminary results in September.