11

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

Academia Sinica

FSIs

DCPV in BK, ,

Polarization anomaly in BK*

FPCP2004, October 4-9, 2004, Daegu, Korea

2

Why FSI in charmless B decays? Why FSI in charmless B decays? Direct CPV (5.7) in B0K+- was established by BaBar and Belle

Combined BaBar & Belle data 3.6 DCPV in B0-+

For DCPV in B+-, 5.2 effect claimed by Belle, not confirmed

by BaBar

723 6.5 2437

7.1 0.6 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

QCDF predictions seem not consistent with experiment !

FSI may play an essential role as DCPV sin sin

: weak phase, : strong phase

3

“Simple” CP violation from perturbative strong phases:

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

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

weak

strong

4

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

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

5

Regge approach [Donoghue,Golowich,Petrov,Soares]

FSI phase is dominated by inelastic scattering and doesn’t vanish even

in mb limit

QCDF [Beneke,Buchalla,Neubert,Sachrajda]

strong phase is O(s, /mb): systematic cancellation of FSIs in mb

Charming penguin [Ciuchini et al.] [Colangelo et al.] [Isola et al.]

long distance in nature, sources of strong phases, supported by SCET

Quasi elastic scattering model [Chua,Hou,Yang]

Consider MMMM (M: octet meson) rescattering in BPP decays

One-particle-exchange model for LD rescattering

has been applied to charm and B decays [Lu,Zou,..], [Du et al.]

Diagrammatic approach [Chiang et al.] …

Approaches for FSIs in charmless B decays

6

Diagrammatic Approach Diagrammatic Approach

All two-body hadronic decays of heavy mesons can be expressed interms of six distinct quark diagrams [Chau, HYC(86)]

All quark graphs are topological and meant to have all stronginteractions included and hence they are not Feynmangraphs. And SU(3) flavor symmetry is assumed.

7

Global fit to B, K data (BRs & DCPV) based on topological diagrammatic approach yields [Chiang et al.]

naively) 25.0( )]94(exp[)46.0( 43

52

43.0

30.0

eff

eff

iT

C

PPB

]59[exp)05.044.0()(

)(2 0

0

000

iET

EC

DBA

DBA

DB

consistent with that determined from B D decays

8

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

9

FSI as rescattering of intermediate two-body states

[HYC, Chua, 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.] …

10

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

11

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)]

12

All rescattering diagrams contribute to penguin topology

fit to rates rD = rD* 0.69

predict direct CPV

13

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

14

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

15

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

16

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 +-

17

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

18

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

﹣

﹣

_

_

19

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

20

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

21

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

22

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 ?

23

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

24

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 ?

25

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

26

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