1

CP Violation and Final State Interactions in Hadronic Charmless B Decays Hai-Yang Cheng 鄭海揚

Academia Sinica

CPV in kaon system

DCPV in BK, ,

FSIs

November 16, 2004, NTHU

2

Consider neutral K’s decays to pions.

Since mK=497 MeV, m=137 MeV, K0,K0 ,

CP| = |, CP| = -|,

Let CP|K1 = |K1, with K1 = (K0+K0)/2

CP|K2 = -|K2, K2 = (K0-K0)/2

Hence, K1 and K2 , but K2 is not allowed

K1 & K2 have widely different lifetimes, K1=KS, K2=KL due to

phase space effects : L/S 580

Christenson, Cronin, Fitch, Turlay (64) found KL at BNL

First discovery of CP violation !

CP Violation in Kaon System

_

_

_

3

Discovery of CP Violation• Phys. Rev. Lett. 13, 138 (1964)

3102 K

“K 20” → ~ 1/300 !

CP

4

5

3-00

00

00 102.3|| with ,)(

)( ,

)(

)(

S

L

S

L

KA

KA

KA

KA

KL K2+ K1, KS K1+ K2 with ||

KL K1 K2

indirect (mixing) CPV direct CPV (CPV in mass matrix) (CPV in decay amplitude)

Two possible sources of CP violation:

'2 ,' 00

A fit to K data yields

||=(2.2840.014)10-3, Re(’/)=(1.670.26)10-3

with : mixing-induced CPV, ’: direct CPV

6

Direct CP Violation: Re(’/)

CERN & Femilab expt’l didn’t agree until 1999

PDG 2004 Average: Re(’/)=(1.670.23) 10-3

KTEV: Bob Hsiung( 熊怡 )

7

6

00

00

10)6.05.5()()(

)()(

)/'Re(

KK

KKAdir

CP

Direct CPV in kaon decays:

In kaon system, ’<< due to I=1/2 rule

8

CP Violation in Standard Model

tbtstd

cbcscd

ubusud

CKM

L

L

L

CKMLLL

VVV

VVV

VVV

VchW

b

s

d

Vtcug

L

..),,(2

VCKM is the only source of CPV in flavor-changing process in the SM. Only charged current interactions can change flavor

Elements depend on 4 real parameters: 3 angles + 1 CPV phase

iiii

ii

iiCKM

scwith

eescsccss

eesscccsc

ssscc

V

sin ,cos

ccssc

scscc

323213223121

233213232112

31131

First proposed by Kobayashi & Maskawa (73)

CKM= Cabibbo-Kobayashi-Maskawa

小林‧益川

1>>1>>2>>3

9

M. Kobayashi & T. Maskawa, Prog. Theor. Phys. 49, 652 (73):

before charm (J/) discovery by Ting & Richter in 1974

KM pointed out that one needs at least six quarks in order to accommodate CPV in SM with one Higgs doublet

K. Nir( 丹生潔 ) et al. at Nagoya had found evidence for a charm production in cosmic ray data, Prog. Theor. Phys. 46, 652 (73).

10

Some disadvantages for VCKM:

Determination of 2 & 3 is ambiguous

Some elements have comparable real & imaginary parts

cc

sc

'

323122132121

233212132121

31331

ii

ii

i

CKM

esscscesccss

esssccesscss

essccc

V

A new parametrization similar to the one originally due to Maiani (76) was proposed by Chau & Keung (84) 喬玲麗，姜偉宜

CKM= Chau-Keung-Maiani

1>>s1>>s2>>s3

adapted by PDG as a standard parametrizarion

11

mixing CPV direct CPV

Can one observe similar mixing-induced & direct CPV in B systems ?

mtSmtCftBftB

ftBftBtA ffCP

sincos))(())((

))(())(()(

00

00

Cf meaures direct CPV, Sf is related to CPV in interference between mixing & decay amplitude

According to SM, CPV in B decays can be of order 10%!

12

Penguin Diagram

Penguin diagram was first discussed by Shifman, Vainshtein, Zakharov (75) motivated by solving I=1/2 puzzle in kaon decay

I=1/2 puzzle: why 450)(

)(0

0

K

KS

Why does it call penguin diagram ?

13

The Duel of the B FactoriesSLAC

BaBar

KEK

Belle

14

In July 2000, BaBar & Belle announced first hints of CPV in B0 meson system, namely, the golden mode B0 J/KS

SK=0.731 0.056, CK 0

Indirect CPV in KS, 0KS, f0KS, KS were also measured recently

What about direct CPV in B decays ?

sinsin )()(

)()(

fBfB

fBfBACP B f

Need at least two different B f paths with different strong & weak phases

It has been claimed by Bigi,Sanda (81) a large CPV in B0J/KS

with SK 0.65- 0.80

strong phase weak phase

ei(+)

15

22 |||| , AAbeaAbeaA ii

22)()( |||| , AAbeaAbeaA ii

16

Direct CP Violation AK

First confirmed DCPV observed in B decays !

Recall that in K system, ACPdir=5.510-6

2004 summer

17

Direct CPV in B0 -+

Average: ACP(B0-+) = -0.47+0.13-0.14

18

B0 +-

19 Average: ACP(B0+-) = 0.37 0.24

20

Predictions of DCPV in B Decays

Based on quark diagrammatic approach and effective Hamiltonian + factorization, we have studied charmless hadronic B decays

Chau, HYC, Sze( 施華強 ), Tseng( 曾龍 ), Yao( 姚珩 ):

PR, D43, 2176 (91): decay rates PR, D45, 3143 (92): direct CP asymmetries

21

Two popular models in recent years: QCD factorization (QCDF): Beneke, Buchalla, Neubert, Sachrajda (99)

PQCD approach based on kT factorization theorem developed by

Keum ( 琴龍淵 ), Li ( 李湘楠 ), Sanda (01) -- Introduce parton’s transverse mometum to regulate endpoint div. -- Form factors for B light meson are perturbatively calculable -- Large strong phase stemming from annihilation diagrams

)()(1||0||

...)()()(),,(

)()(||

1122

21

21

2

1

2

b

QCDs

MMBII

MIBM

M

mOOBjMjM

yxyxdxdyTd

xxdxTFfBOMM

TI:

TII:

22

23

Direct CP violation (%) in QCDF & PQCD

723 6.5 2437

7.1 0.6 48

517 4.5 211

PQCD QCDF Expt

7.133.13

0

1.02.0

6.118.11

1415

0

1.99.9

0

B

B

KB

QCDF predictions for DCPV disagree with experiment !

though QCDF & pQCD describe BRs of hadronic B decays well

24

“Simple” CP violation from perturbative strong phases:

penguin (BSS) vertex corrections (BBNS) annihilation (pQCD)

“Compound” CP violation from LD rescattering: [Atwood,Soni]

weak

strong

25

Other possible hints at large FSI effects in B physics:

Some decay modes do not receive factorizable contributions

e.g. B K0c with sizable BR, though 0c|c(1-5)c|0=0.

Color-suppressed B0 D0 h0 (h0=0,,0,,’) measured by

Belle, CLEO, BaBar are larger than theoretical expectations.

Br(B0 00) 1.5 10-6 cannot be explained by QCDF or PQCD. and likewise for B000

BRs predicted by QCDF for penguin-dominated BK*,K,K,K* are too small by a factor of 2-3 compared to the data

Longitudinal fraction fL 50% for B K* by Belle & BaBar in sharp contrast to the scaling law:

for factorizable amplitudes in B decays to light vector mesons, rescattering effect or new physics ?

)/1(1 2

bL mOf

26

quark exchange

quark annihilation

meson annihilation

possible FSIs

W exchange

Color suppressed C

At hadron level, FSIs manifest as resonant s-channel & OPE t-channel graphs.

B0D00

27

FSI as rescattering of intermediate two-body states

[HYC, Chua( 蔡俊謙 ), Soni; hep-ph/0409317] FSIs via resonances are assumed to be suppressed in B decays due to the lack of resonances at energies close to B mass.

FSI is assumed to be dominated by rescattering of two-body intermediate states with one particle exchange in t-channel. Its absorptive part is computed via optical theorem:

i

ifTiBMfBMm )()( 2

• Strong coupling is fixed on shell. For intermediate heavy mesons,

apply HQET+ChPT (for soft Goldstone boson)

• Cutoff must be introduced as exchanged particle is off-shell

and final states are hard

Alternative: Regge trajectory [Nardulli,Pham][Falk et al.] [Du et al.] …

28

n

t

mtF

2

22

)(

Dispersive part is obtained from the absorptive amplitude via dispersion relation

''

)'( 1)(

22 ds

ms

sMmmMe

s BB

= mexc + rQCD (r: of order unity)

or r is determined form a 2 fit to the measured rates

r is process dependent

n=1 (monopole behavior), consistent with QCD sum rules

Once cutoff is fixed CPV can be predicted

subject to large uncertainties and will be ignored in the present work

Form factor is introduced to render perturbative calculation meaningful

29

B K B K

0.040.04 10 0.8)(12.1

0.030.02- 10 1.3)(24.1

0.140.02 10 1.0)(11.5

0.020.11- 10 0.8)(18.2

BR

60

60

6000

60

KB

KB

KB

KB

A

0.040.11 07.0 107.9)(

0.040.14 009.0 108.17)(

04.0 103.6)(

0.050.17 04.0 109.13)(

60

60

6000

60

SDSD

SDSD

SDSD

SDSD

AKBBr

AKBBr

AKBBr

AKBBr

SD PQCD

Direct CPV in B0K+- was reported by BaBar & Belle

for F0B(0)=0.25 from covariant LF model [HYC,Chua,Hwang(04)]

30

All rescattering diagrams contribute to penguin topology

fit to rates rD = rD* 0.69

predict direct CPV

31

BR

SD

(10-6)

BR

with FSI

(10-6)

BR

Expt

(10-6)

DCPV

SD

DCPV

with FSI

DCPV

Expt

B 17.8 23.3+4.6-3.7 24.11.3 0.01 0.024+0.00

-0.001 -0.020.03

B0+ 13.9 19.3+5.0-3.1 18.20.8 0.04 -0.14+0.01

-0.03 -0.110.02

B0 9.7 12.5+2.6-1.6 12.10.8 0.08 -0.11+0.02

-0.04 0.040.04

B0 6.3 9.1+2.5-1.6

11.51.0 -0.04 0.031+0.008-0.014 0.020.14

Sign of +K- CP asymmetry is flipped after rescattering

and is in agreement with experiment.

K rates are enhanced by (30-40)% via FSI

Isospin sum rule relation [Atwood,Soni]

can be used to test the presence of EWP

0)(2)()()(2 0000 KKKK

32

B B

0.070.02- 10 0.6)(5.5

0.390.17- 10 0.3)(1.5

0.340.61- 0.240.37 10 0.4)(4.6

BR

60

6000

60

B

B

B

SA

Af=-Cf : direct CP asymmetry; Sf: mixing-induced CP violation

A(+-)=0.58 0.17 by Belle, 0.090.16 by BaBar

0 105 101.5)(

0.100.30 61.0 103.0)(

0.070.23 05.0 106.7)(

560

6000

60

SDSD

SDSD

SDSD

ABBr

ABBr

ABBr

SD PQCD

33

Long-distance contributions to B Long-distance contributions to B

)(

)(

)(

edcbaiAbsPP

baiAbsEE

baiAbsCC

SD

CD

SD

Cutoff scale is fixed by B K via SU(3) symmetry

too large +- ( 910-6) and too small 00 (0.410-6)

A dispersive part unique to but not available to K is needed to suppress +- and enhance 00

D+(+)

D-

(-)

+

-

same topology as vertical W-loop diagram V

34

BR

SD

(10-6)

BR

with FSI

(10-6)

BR

Expt

(10-6)

DCPV

SD

DCPV

with FSI

DCPV

Expt

B0+ 7.6 5.0+1.3-0.9 4.60.4 -0.05 0.64+0.03

-0.08 0.370.24

B000 0.3 1.3+0.3-0.2 1.50.3 0.61 -0.30+0.01

-0.04 0.280.39

B0 5.1 4.8 0.1 5.50.6 510-5 -0.0090.001 -0.020.07

Charming penguin alone doesn’t suffice to explain 00 rate

Sign of direct CP asymmetry is flipped after rescattering !

DCPV in -0 mode is very small even after inclusion of FSI. It provides

a nice way to search for New Physics

SU(3) relation: (+-)=-(+K-) [Deshpande,He]

A(+-) -4.0 A(+K-) can be used to predict DCPV in +-

35

0.56 0.18 31.0 36.0

0 0 23.0 23.0

50852055

8432

i

LDSD

i

LDSD

i

LDSD

i

LDSD

SDSD

i

SD

i

SD

eT

Ve

T

Ee

T

Pe

T

C

T

V

T

Ee

T

Pe

T

C

B

W-exchange can receive LD contributions from FSI

|P/T| is of order 0.30, smaller than some recent claims

Define Teff=T+E+V, Ceff=C-E-V Ceff/Teff=0.71 exp[i72]

BK

C/T is similar to the case

36

BR

SD

(10-6)

BR

with FSI

(10-6)

BR

Expt

(10-6)

DCPV

SD

DCPV

with FSI

DCPV

Expt

B0+ 7.9 8.40.3 10.12.0 -0.01 -0.430.11 -0.480.14

B0+ 18.4 18.8+0.3-0.2 13.92.1 -0.03 -0.240.06 -

0.150.09

B000 0.6 1.3+0.4-0.3 1.91.2 0.01 0.57+0.01

-0.03

B0 12.8 14.0+0.7-0.4 12.02.0 -0.04 0.360.10 0.160.13

B 6.8 7.5+0.6-0.3

9.11.3 0.06 -0.56+0.14-0.15 -0.190.11

B B

DCPV in +- mode is well accounted for

Br(00) 1.310-6, recalling BaBar upper limit, 2.910-6, and Belle

result of (5.11.8)10-6. Discrepancy between them should be clarified.

We use F1B(0)=0.30 [HYC,Chua,Hwang]. If F1

B(0)=0.37 is employed,

the will become too large

﹣

﹣

_

_

37

723 5.6 2437

1.7 6.0 48

517 4.5 211

7.133.13

0

1.02.0

6.118.11

1415

0

1.99.9

0

B

B

KB Expt(%) QCDF PQCD

Summary for DCPV

38

723 64 2437

1.7 1143 48

517 14 211

3

8

0

1.0

2.0

14

15

0

1

3

0

B

B

KB Expt(%) QCDF+FSI PQCD

212 624 915

1030 30 3928 0

1

4

000

B

B

Summary for DCPV

pQCD and FSI approaches for DCPV can be discriminated in 00 and +- modes

39

Short-distance induced transverse polarization in B V1V2 (V: light vector meson) is expected to be suppressed

)/(1/ ),/(1 :law scaling ||22

BVBVL mmOffmmOf

Polarization anomaly in B K*,K* Polarization anomaly in B K*,K*

0.7 0.7 )(

0.080.74 0.200.50 0.090.79 )(

0.96 0.96 )(

0.12 0.12 )(

0.090.47 0.140.49 0.120.46 )(

0.040.25 0.080.30 0.050.22 )(

0.050.52 0.090.52 0.050.52 )(

Average Belle BaBar

*

0*

04.0

16.0

04.0

16.0

*0

0.11

0.08

0.11

0.08

*

*

0*

0*

Kf

Kf

Kf

Kf

Kf

Kf

Kf

L

L

L

L

L

Scaling law obeyed by modes is violated in K* and K* (except 0K*+) decays

40

Anomaly can be accommodated in QCDF via large penguin-induced annihilation by adjusting endpoint divergence [Kagan]

BR is enhanced by a factor of 2 via annihilation, too large ?

Transverse gluon in bsg chromodipole operator transversely polarized [Hou & Nagashima]

Similar behavior for K*, but no polarization anomaly in K* modes ?

41

Get large transverse polarization from B Ds*D* and then convey it to

K* via FSI [Colangelo, De Fazio, Pham]

B B

*sD *

sD

*D

*K*K

D

fT(Ds*D*) 0.51 contributes to A only

f|| 0.41, f 0.08

(*)

sD(*)

sD

Regge analysis of FSI [Ladisa,Laporta,Nardulli,Santorelli]

elastic FSI: Pomeron exchange (see also Chua,Hou,Yang)

inelastic FSI: use Regge trajectory method to evalute charming

penguins

42

B BsD *

sD

*D

*K *KD

very small perpendicular polarization, f 2%, in sharp contrast to f 15% obtained by Colangelo et al.

(*)

sD (*)

sD＋ 0 !

We found large cancellation occurs in B{ Ds*D,DsD*}K* proc

esses. This can be understood as CP & SU(3) symmetry

1.29.6 11.2 2.44.0 )10(

0.040.22 0.010.02 0.05

0.060.27 45.0 0.07

0.040.51 53.0 0.88

expt LDSD SD

3.6

9.3

6

05.0

08.0||

07.0

04.0

BR

f

f

fL

While fT 0.50 is achieved, why is f not so small ?

43

Cancellation in B{VP,PV}K* can be circumvented in

B{SA,AS}K*. For S,A=D**,Ds**, it is found

fL: f||: f= 0.71: 0.06 : 0.22 However, K* rate gets only a small enhancement so that effect of

sizable f will be washed out by intermediate states from V,P

Strong phases in K*

For B+K*0+, fL: f||: f= 0.64: 0.35 : 0.01, fLexpt=0.740.08

fL is indeed suppressed

For B+K*+0, fL: f||: f= 0.62: 0.37 : 0.01, fLexpt=0.96+0.04-0.16

Why is scaling law working here ?

0.220.72 0.262.47 1.12 )(

23.021.2 2.34 0.122.53 )(

Belle BaBar LDSD

0.210.24

24.00.21||

rad

rad

44

Conclusion Conclusion

Color–suppressed modes such as B0 D00,00,00,K00

can be substantially enhanced by LD rescattering.

DCPV in charmless B decays is significantly affected by

FSI rescattering. Correct sign and right magnitude of

DCPV in K-+ and +- are obtained after inclusion of FSI.

Large transverse polarization with fT 0.50 can be

obtained from rescattering of

The anomaly of not so small f remains mysterious

*(*)(*) KDDB s