11

Final state interactions in hadronic B decays

Hai-Yang Cheng

Academia Sinica

FSIs

BRs & CPV in B decays

Polarization anomaly in BK*

QCD & Hadronic Physics, Beijing, June 16-20, 2005

2

Importance of FSI in charm decays has long been recognized

some nearby resonances exist at energies mD

charm is not very heavy

General folklore for B decays:

FSI plays a minor role due to large energy release in B decays

and the absence of nearby resonances

There are growing hints at some possible soft final-state

rescattering effects in B physics

3

sinsin )()(

)()(

fBfB

fBfBACP B f

One needs at least two different B f paths with distinct weak & strong phases

strong phase weak phase

ei(+)

BaBar Belle Average

B0→K-+ -0.130.03

-0.100.25

-0.110.02

B0→+- -0.470.16

-0.530.30

-0.470.14

B0→+- 0.090.16

0.560.13

0.370.10

600

00

10)6.05.5()()(

)()(

KK

KKACP

first confirmed DCPV (5.7) in B decays (2004)

1. Direct CP violation

_

__

Recall in kaon decays

4

1037

47

211

(%) Expt

0

1314

0

0

B

B

KB

723

7.1

517

pQCD

1.02.0

6.5

0.6

4.5

QCDF

2.131.00.31.28.123.08.21.2

5.111.03.12.07.111.06.11.0

7.85.02.21.15.96.05.21.1

10.3

9.12

4.1

QCDF(S4)

pQCD (Keum, Li, Sanda): A sizable strong phase from penguin-induced annihilation by introducing parton’s transverse momentum

QCD factorization (Beneke, Buchalla, Neubert, Sachrajda):Because of endpoint divergences, QCD/mb power corrections due to annihilation and twist-3 spectator interactions can only be modelled

QCDF (S4 scenario): large annihilation with phase chosen so that a correct sign of A(K-+) is produced (A=1, A= -55 for PP, A=-20 for PV and A=-70 for VP)

Comparison with theory: pQCD & QCDF

1 with )1(ln HA,,

0

,,

HAiHA

BHA e

m

y

dyX

input

5

SD perturbative strong phases:

penguin (BSS) vertex corrections (BBNS)

weak

strong

Nonperturbative LD strong phases induced from power corrections especially from final-state rescattering

annihilation (pQCD)

Need sizable strong phases to explain the observed direct CPV

If intermediate states are CKM more favored than final states, e.g. BDDsK

large phases

large corrections to rate

6

2. Some color-suppressed or factorization-forbidden or penguin-dominated modes cannot be accommodated in the naïve factorization approach

Some decay modes do not receive factorizable contributions

e.g. B Kc0 with sizable BR though c0|c(1-5)c|0=0.

Color-suppressed modes e.g. B0 D0 h0 (h0=0,,0,,’), 00, 00 have the measured rates larger than theoretical expectations.

Penguin-dominated modes such as BK*, K, K, K* predicted by QCDF are consistently lower than experiment by a factor of 2 3

importance of power corrections (inverse powers of mb) e.g. FSI, annihilation, EW penguin, New Physics, …

7

Our goal is to study FSI effect on BRs and CPV (direct & indirect) in B decays (Polarization anomaly in BK* will be briefly mentioned)

LD rescattering can be incorporated in any SD approach but it requires modelling of 1/mb power corrections

We would provide a specific model for FSI to compute strong phases so that we can predict (rather than accommodate) the sign and magnitude of direct CP asymmetries

8

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

One-particle-exchange model for LD rescattering has been applied to charm and B decays [Du et al.][Lu,Zou,..]

Quasi elastic scattering model [Chua,Hou,Yang]

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

Diagrammatic approach [Chiang, Gronau, Rosner et al.] …

Approaches for FSIs in charmless B decays

9

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.

Diagrammatic Approach

(penguin) (vertical W loop)

(tree)

(color-suppressed) (exchange)

(annihilation)

10

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

11

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

relevant for e.g. B0

12

FSI as rescattering of intermediate two-body states

[HYC, Chua, Soni]

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

• Form factor or cutoff must be introduced as exchanged particle is

off-shell and final states are necessarily hard

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

13

Dispersive part is obtained from the absorptive amplitude via dispersion relation

''

)'( )(

0

22 ds

ms

sMmPmMe

s BB

= mexc + rQCD (r: of order unity)

or r is determined by a fit to the measured rates

r is process dependent

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

Once cutoff is fixed direct 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

n

QCD

n

t

m

t

mtF

2

22

)(

LD amp. vanishes in HQ limit

14

Inputs

Form factors:covariant light-front approach: relativistic QM for s-wave to s-wave and p-wave transitions (HYC,Chua,Hwang 2004)

CLF Ball & Zwicky Beneke & Neubert

F0B(0) 0.250.03 0.2580.031 0.280.05

A0B(0) 0.280.03 0.3030.028 0.370.06

SD approach: QCD factorization (default scenario) with A=H=0 in

)1(ln ,

,

0

,HAi

HAB

HA em

y

dyX

double counting problem is circumvented

15

Theoretical uncertainties (SD)

1. variation of CKM parameters

=(6315)

2. quark masses: ms(2 GeV)= 9020 MeV

3. renormalization scale: from =2mb to mb/2

4. heavy-to-light form factors: e.g. FB(0)=0.250.03

5. meson distribution amplitudes

16

Theoretical uncertainties (LD)

1. Model assumption

multi-body contributions

form-factor cutoff:

i). n=1

ii). = mexc + rQCD (15% error assigned for QCD)

rD=2.1, 1.6, 0.73, 0.67, respectively, for D, , K modes

varies for penguin-dominated PV modes dispersive contribution

2. Input parameters

strong couplings of heavy mesons and their SU(3) breaking

g(D*D)=17.90.31.9 (CLEO)

heavy-to-heavy form factors

n

t

mtF

2

22

)(

17

SD SD+LD Expt

K0 5.6+1.9-1.8 8.6+1.2+2.9

-1.2-1.8 8.3+1.2-1.0

K0 2.0+3.5-1.3 5.6+2.9+3.7

-1.2-2.1 5.60.9

0K0 2.8+3.2-1.6 5.2+3.2+2.6

-1.5-1.2 5.11.6

’K0 42.1+45.6-19.4 69.4+51.3+50.4

-21.4-19.2 68.64.2

K0 1.8+1.2-0.9 1.8+1.2+0.1

-0.8-0.0 <2.0

0K0 5.8+5.5-3.1 9.6+5.5+8.4

-2.9-3.0 11.51.0

f0K0 8.1+3.1-2.6 8.1+3.1+?

-2.7-? 11.33.6

Br (10-6)

first error: SD, second error: LD

LD uncertainties are comparable to SD ones & SD errors are affected only slightly by FSIs.

No reliable estimate of LD rescattering effects for f0KS

18

All rescattering diagrams contribute to penguin topology,

dominated by charm intermediate states

fit to rates rD = rD* 0.67

predict direct CPV

B B

19

BR

SD

(10-6)

BR

with FSI

(10-6)

BR

Expt

(10-6)

DCPV

SD

DCPV

with FSI

DCPV

Expt

B 16.6 22.9+4.9-3.1 24.11.3 0.01 0.026+0.00

-0.002 -0.020.03

B0 13.7 19.7+4.6-2.9 18.20.8 0.03 -0.15+0.03

-0.01 -0.110.02

B0 9.3 12.1+2.4-1.5 12.10.8 0.17 -0.09+0.06

-0.04 0.040.04

B0 6.0 9.0+2.3-1.5

11.51.0 -0.04 0.022+0.008-0.012 -0.090.14

For simplicity only LD uncertainties are shown here

FSI yields correct sign and magnitude for A(+K-) !

K anomaly: A(0K-) A(+ K-), while experimentally they differ

by 3.4See Fleischer’s talk]

_

_

_

_

20

BR

SD

(10-6)

BR

with FSI

(10-6)

BR

Expt

(10-6)

DCPV

SD

DCPV

with FSI

DCPV

Expt

B0+ 8.3 8.7+0.4-0.2 10.12.0 -0.01 -0.430.11 -0.47+0.13

-0.14

B0+ 18.0 18.4+0.3-0.2 13.92.1 -0.02 -0.250.06 -0.150.09

B000 0.44 1.1+0.4-0.3 1.80.6 -0.005 0.530.01 --

B0 12.3 13.3+0.7-0.5 12.02.0 -0.04 0.370.10 0.160.13

B 6.9 7.6+0.6-0.4

9.11.3 0.06 -0.580.15 -0.190.11

Sign and magnitude for A(+-) are nicely predicted !

DCPVs are sensitive to FSIs, but BRs are not (rD=1.6)

For 00, 1.40.7 BaBar

Br(10-6)= 5.11.8 Belle

1.6+2.2-1.6 CLEO

Discrepancy between BaBar and Belle should be clarified.

﹣

__

B B B

_

21

BR

SD

(10-6)

BR

with FSI

(10-6)

BR

Expt

(10-6)

DCPV

SD

DCPV

with FSI

DCPV

Expt

BK*0 4.4 9.9+3.6-2.7 9.76+1.16

-1.22 0.01 0.0260.003 -0.14+0.09-0.11

B0+K* 3.8 9.9+3.7-2.8 12.7+1.8

-1.7 0.15 -0.44 -0.250.17

BK* 2.8 5.6+1.8-1.4 ? 0.17 -0.390.01 0.040.29

B0*0 1.3 4.4+1.8-1.4

1.70.8 -0.08 0.066+0.005-0.001 -0.01+0.27

-0.26

B B * B *

_

_

BaBar, hep-ex/0504009 Br(B-0K*-)=(6.92.4)10-6

For 0K*0, Br(10-6)= 3.01.0 BaBar

0.4+1.9-1.7

Belle

_

_

K.F. Chen (CKM2005): BaBar

6.92.4

22

Comparison with other approaches

All known existing models fit the data of BRs and DCPV and then make predictions for mixing (indirect) CPV.

e.g. 1. charming penguin (Ciuchini et al. and many others)

Consider charmless B decay BK with BDDsK

charming penguin is CKM doubly enhanced & gives

dominant LD corrections

S(0K0)=0.770.04

CKM2005

a fit result

23

2. Fit QCDF to data fix unknown power correction

parameters A, H, A, H

Aleksan et al. (hep-ph/0301165)

S4 scenario of Beneke & Neubert (hep-ph/0308092)

Leitner, Guo, Thomas (hep-ph/0411392)

Cottingham et al. (hep-ph/0501040)

24

Mixing-induced CP violation [HYC,Chua,Soni]

It is expected in SM that -fSf sin2 0.726 0.037 with deviation at most O(0.1) in B0 KS, KS, 0KS, ’KS, 0KS, f0KS, K+K-KS, KSKSKS

[London,Soni; Grossman, Gronau, Ligeti, Nir, Rosner, Quinn,…

25

G. Kane (and others): The 2.7-3.7 anomaly seen in b→s penguin modes is the strongest hint of New Physics that has been searched in past many many years…

It is extremely important to examine how much of the deviation is allowed in the SM and estimate the theoretical uncertainties as best as we can.

A current hot topic

26

In general, Sf sin2eff sin(2+W). For bsqq modes,

cuib

ccscb

uusub

aAaeRA

aVVaVVfBA24

**0

)(

Since au is larger than ac, it is possible that S will be subject to significant “tree pollution”. However, au here is color-suppressed.

Penguin contributions to KS and 0KS are suppressed due to cancellation between two penguin terms (a4 & a6)

relative importance of tree contribution

large deviation of S from sin2

mtAmtSftBftB

ftBftBff

cossin))(())((

))(())((

Time-dependent CP asymmetries:

27

SD Expt SD Expt

KS 0.747+0.002-0.039 0.350.20 1.4+0.3

-0.5 417

KS 0.850+0.052-0.055 0.550.31 -7.3+3.5

--2.6 4825

0KS 0.635+0.028-0.067 -- 9.0+2.2

-4.6 --

‘KS 0.737+0.002-0.038 0.430.11 1.80.4 48

KS 0.793+0.017-0.044 -- -6.1+5.1

-2.0 --

0KS 0.787+0.018-0.044 0.340.28 -3.4+2.1

-1.1 814

f0KS 0.749+0.002-0.039 0.390.26 7.70.1 1422

S(KS)>sin2, S(0KS)<sin2

FSI can bring in additional weak phase via K*,K intermediate states (even when tree is absent at SD)

-nfSf Af(%)

(see also Beneke)

28

FSI effect is tiny due to small source (K*,K) amplitudes (Br~10-6) com

pared to Ds*D (Br~10-2,-3). It tends to alleviate the deviation from sin2

For 0KS, S=S-sin2<0 at SD but it becomes positive after including FS

I.

Sf is positive and less than 0.1 in SM, while experimentally Sf is al

ways negative

SD SD+LD Expt SD SD+LD Expt

KS 0.747 0.759+0.009-0.041 0.350.20 1.4 -2.6+1.9

-1.3 417

KS 0.850 0.736+0.033-0.38 0.550.31 -7.3 -13.2+4.4

-3.8 4825

0KS 0.635 0.761+0.102-0.127 -- 9.0 46.6+12.9

-15.8 --

‘KS 0.737 0.734+0.004-0.037 0.430.11 1.8 2.1+0.5

-0.3 48

KS 0.793 0.802+0.025--0.046 -- -6.1 -3.7+4.6

-3.0 --

0KS 0.787 0.770+0.016--0.046 0.340.28 -3.4 3.7+2.7

-2.0 - 814

f0KS 0.749 0.749+0.002-0.039

0.390.26 0.8 0.80.1 -1422

-nfSf Af(%)

29

Effective sin2 in K+K-KS & KSKSKS

For K+K-KS, S= -(2f+-1)sin2eff

(f+: CP-even fraction)

For KSKSKS, S= -sin2eff

theory expt theory expt

K+K-KS 0.830+0.063-0.086 0.60+0.22

-0.20 0.74+1.79-1.18 -

910

KSKSKS 0.749+0.003-0.039 0.260.34 0.75+0.09

-0.13 4121

K+K-KS is subject to large tree pollution from color-allowed tree diagrams

KSKSKS is very clean for testing SM

sin2eff

Af(%)

30

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

)/(1/ ),/(1 ||22

|| BVBVLT mmOffmmOffff

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

K* via FSI

B B

*sD *

sD

*D

*K*K

D

(*)

sD(*)

sD

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

fL(Ds*D*) 0.51 contributes to f only

f|| 0.41, f 0.08

[HYC, Chua, Soni]

Confirmed for B with fL 0.97

but for BK* fL 0.50, f|| 0.25, f 0.25

31

B BsD *

sD

*D

*K *KD

very small perpendicular polarization, f 2%, in sharp contrast to f 15% obtained by Colangelo, De FArzio, Pham

(*)

sD (*)

sD＋ 0 !

Large cancellation occurs in B{Ds*D,DsD*}K* processes. Thi

s can be understood as CP & SU(3) symmetry

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

Cancellation in B{VP,PV}K* can be circumvented inB{SA,AS}K*. For S,A=D**,Ds** f 0.22

It is very easy to explain why fL 0.50 by FSI, but it takes some efforts to understand why f f||

3232

Conclusions

DCPV in charmless B decays is significantly affected by

LD rescattering. Correct sign and right magnitude of

DCPV in K-+ and +- are obtained after including FSI.

For penguin-dominated MKS modes, FSI tends to alleviate

the deviation from sin2.

Large transverse polarization fT 0.50 can be obtained

from final-state rescattering of B Ds*D* K*

33

The subleading amplitudes in QCDF develop end-point singularities

)1()(,)(

210 xxx

x

xdx

in twist-3 nonspectator and in annihilation

An end-point singularity means breakdown of simple collinear factorization Use more conservative kT factorizationInclude parton kT to smear the singularity

)(

),(22

210

BT

TT mkxx

kxkddx

Perturbative QCD approach [Keum, Li, Sanda; Lu, Yang, Ukai]

Collinear vs. kT factorization

34

kT factorization

Sudakov factors Sdescribe the parton distribution in kT

KT accumulates after infinitely many gluon exchangesSimilar to the DGLAP evolution up to kT~Q

Parton-level diagrams

Bound-state distributionamplitude

35

Scales and penguin enhancement

b

)( BmO In PQCD this gluon is off-shell by

Slow parton Fast parton

PQCD QCDF 25.1~ 2

For penguin-dominated modes, the branching ratiosWilson coefficients

36

Recent progress on PQCD• Nonfactorizable contributions are important for color-suppresse

d modes---explained B! D00, (J/ c0,c1,c ) K (*) branching ratios, helicity amplitudes (Keum, Kurimoto et al.; Chen, Li).

• Annihilation lowers longitudinal polarization in B! VV. Also predicted pure-annihilation modes, which cannot be done in FA (Lu et al.).

• Predicted CP asymmetry, isospin breaking of B! K*(Matsumori et al.).

• NLO PQCD enhances C, and resolves B! K puzzle (Li, Mishima, Sanda):

LO NLO Data Acp(K+-) -0.13 -0.11 -0.1090.019 Acp(K+0) -0.09 +0.03 0.040.04 Annihilation generates large strong phase, which explains direct CP asymmetries.

37

Baryonic B decays

3-body baryonic B deacys were found to have larger BRs than 2-body decays

There are extensive studies of baryonic B decays in Taiwan both experimentally and theoretically

B-→ppK- : first evidence of charmless baryonic B decay

B→pp(K,K*,)

→p(,K)

→K

B→pp, , pstringent limits)

B→p: first evidence of b→s penguin in baryonic B decays

Expt.

Theory

Chua, Geng, Hou, Hsiao, Tsai, Yang, HYC,…

Publication after 2001: (hep-ph)

0008079, 0107110, 0108068, 0110263, 0112245, 0112294, 0204185, 0204186, 0208185, 0210275, 0211240, 0302110, 0303079, 0306092, 0307307, 0311035, 0503264

0201015, 0405283

Belle group at NTU

first paper on radiative baryonic B decays

C.Q. Geng, this afternoon

38

Back-up slides

39

Regge approach

In evaluating absorptive part via

replace Feynman-diagram strong scattering amplitude T by Regge

amplitude R(s,t):

i

ifTiBMfBMm )()( 2

)()()( 2/)(cos

)(),(1

02

)(

0

2/)( 0

iBMs

ssfBMm

s

s

t

ettsR

tti

(t): residual function, linear Regge trajectory t)=0+’t,

intercept 0=0.45 for , K*,…, -1.8 for D, D*

suppression of FSI with increasing energy s

suppression of charming penguin relative to the light Regge exchanges

''

)'( 1)(

0

22 ds

ms

sMmmM

s BB

uncertainties: t-dep. of (t), BR sensitive to unknown ’

R(s,t) is valid at large s and t 0

40

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

41

without FSI with FSI expt

C/T 0.20 0.30exp(-i50)

E/T 0(by hand) 0.14exp(-i84)

(C-E)/(T+E) 0.20 0.43exp(-i69) (0.460.05)exp(-i61)

Br(B0→D+-) 3.210-3 3.110-3 (2.760.25)10-3

Br(B0→D00) 0.610-4 (2.7+2.31.310-4 (2.90.2)10-4

Br(B-→D0-) 4.910-3 (5.0+0.2-0.110-3 (4.980.29)10-3

Even if short-distance W-exchange vanishes (i.e. ESD=0), final-state rescattering does contribute to weak annihilation

B0Ds+K- proceeds via W-exchange

(expt) 0.0050.014 vs019.0)(

)(2

0

0

ET

E

DB

KDB s

42

)(

)(

)(

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)

An additional rescattering contribution unique to but not available to K is needed to suppress +- and enhance 00

D+(+)

D-

(-)

+

-

B

B0DD() has the same topology as vertical W-loop diagram V

_

43

BR

SD

(10-6)

BR

with FSI

(10-6)

BR

Expt

(10-6)

DCPV

SD

DCPV

with FSI

DCPV

Expt

B0+ 7.6 4.6+0.9-0.7 4.60.4 -0.05 0.370.10

(input)

0.560.13(Belle)

0.090.16(BaBar)

B000 0.3 1.5+0.3-0.2 1.50.3 0.56 -0.45+0.08

-0.06 0.280.39

B0 5.1 5.30.0 5.50.6 5x10-5 -0.0030.001

-0.020.07

Need to fit to rates and CPV of +- simultaneously

Charming penguin alone doesn’t suffice to explain 00 rate (rD=0.67)

Sign of A(00) can be used to discriminate between different models

W-exchange can receive LD contributions from FSI

Define Teff=T+E+V, Ceff=C-E-V Ceff/Teff=(0.900.02) exp[-i(882)]