11

Resolving B-CP puzzles in QCD factorization

- An overview of charmless hadronic B decays -

Hai-Yang Cheng

Academia Sinica

Based on 3 papers with Chun-Khiang Chua

B-CP puzzles in QCDF

Bu,d decays

B (K,K*,K0*,K2

*)(,’)

May 6, 2010 at NTHU

Day in the life – The Emperor’s Tea : Murayama

3

Direct CP asymmetries

=ACP(K-) – ACP(K-)

K-

K- K*0 K-

ACP(%) -9.8+1.2-1.1 386 14.82.8 -379 195 3711 -134

S 8.5 6.3 5.3 4.1 3.8 3.4 3.3

K*- K- K-

ACP(%) -187 156 5.02.5

-137 43+25-24 116

S 2.6 2.5 2.0 1.9 1.8 1.8CDF: ACP(Bs K+)=0.390.17 (2.3)

4

In heavy quark limit, decay amplitude is factorizable, expressed in terms of form factors and decay constants.

Encounter several difficulties:

Rate deficit puzzle: BFs are too small for penguin-dominated

PP,VP,VV modes and for tree-dominated decays ,

CP puzzle:

CP asymmetries for K-, K*-, K-, are wrong in signs

Polarization puzzle:

fT in penguin-dominated BVV decays is too small

1/mb power corrections !

5

A(B0K-+) ua1+c(a4c+ra6

c)

)(

Imsin2)(

64

1*

*

0

cKccscb

usubFM

FMCP

ara

a

VV

VVr

rKBA

Theory Expt

Br 13.1x10-6 (19.40.6)x10-6

ACP 0.04 -0.098+0.012 -0.011

Im4c 0.013 wrong sign for ACP

penguin annihilation

... ][][ 36464 cLD

ccSD

ccc araaraP

charming penguin, FSI penguin annihilation

1/mb corrections

4c4c

6

1

022

...1

)1(

1)()(

2 2121 yxyxyyxdxdy

N

Cfff

GA MMs

c

FMMB

Fann

has endpoint divergence: XA and XA2 with XA 1

0 dy/y

AiA

h

BA e

m

y

dyX

1ln

1

0

Adjust and to fit BRs and ACP 1.10, -50o

Im(c+

c) -0.039

Beneke, Buchalla, Neubert, Sachrajda

77

New CP puzzles

K-

K- K*0 K-

ACP(%) -9.8+1.2-1.1 386 14.82.8 -379 195 3711 -134

S 8.5 6.3 5.3 4.1 3.8 3.4 3.3

mb 3.3

PA ( 1.9)

K*- K- K-

ACP(%) -187 156 5.02.5 -137 43+25-24 116

S 2.6 2.5 2.0 1.9 1.8 1.8

mb

PA

Penguin annihilation solves CP puzzles for K-,,…, but in the meantime introduces new CP puzzles for K-, K*0, …

Also true in SCET with penguin annihilation replaced by charming penguinAlso true in SCET with penguin annihilation replaced by charming penguin

All “problematic” modes receive contributions from c’=C’+P’EW.

T’ a1, C’ a2, P’EW (-a7+a9), P’cEW (a10+ra8), t’=T+P’cEW

AK puzzle is resolved, provided c’/t’ ~ 1.3-1.4 with a large negative

phase (naively, |c’/t’| 0.9) a large complex C’ or P’EW

AK 0 if c’ is negligible

Large complex C’: Charng, Li, Mishima; Kim, Oh, Yu; Gronau, Rosner; …

Large complex P’EW needs New Physics for new strong & weak phases Yoshikawa; Buras et al.; Baek, London; G. Hou et al.; Soni et al.; Khalil et al.

9

Power corrections have been systematically studied by

Beneke, Neubert: S2, S4

Ciuchini et al., 0801.0341

Duraisamy & Kagan, 0812.3162

Li & Mishima, 0901.1272

The two distinct scenarios can be tested in tree-dominated

modes where PEW<<C. CP puzzles of , & large rates of

, cannot be explained by a large PEW

10

a2 a2[1+Cexp(iC)] C 1.3, C -70o for PP modes

a2(K) 0.51exp(-i58o)

Two possible sources: spectator interactions

LDc

sF

c

aHN

VC

N

ccca )()

4(

43 22

2

211

22

NNLO calculations of V2 & H2 are now available

Real part of a2 comes from H and imaginary part from vertex

a2() 0.33 - 0.09i =0.34 exp(-i15o) for = 250 MeV

a2(K) 0.51exp(-i58o) = 4.9 & -77o

[Bell, Pilipp]

final-state rescattering [C.K. Chua]

Neubert: In the presence of soft FSIs, there is no color suppression of C w.r.t. T

Neubert: In the presence of soft FSIs, there is no color suppression of C w.r.t. T

11

K-

K- K*0 K-

ACP(%) -9.8+1.2-1.1 386 14.82.8 -379 195 3711 -134

S 8.5 6.3 5.3 4.1 3.8 3.4 3.3

mb 3.3

PA

( 1.9)

large complex a2

K*- K- K-

ACP(%) -187 156 5.02.5

-137 43+25-24 116

S 2.6 2.5 2.0 1.9 1.8 1.8

mb

PA

large complex a2

All new CP puzzles are resolved !

12

B- K-

A(B0 K-+) = AK(pu1+4p+3

p)= t’+p’2 A(B- K-0) = AK(pu1+4

p+3p)+AK(pu2+3/23,EW

p)= t’+p’+c’

)()0(

)0( ,

)(

Imsin2/Imsin2)(

34

2

0

0*

*

64

1*

*

0

ccBK

BK

cscb

usubCcKc

cscb

usubFM

CFMFMCP

a

Ff

Ff

VV

VVr

ara

a

VV

VVr

rRrKA

mb penguin ann large complex a2 Expt

ACP(K-)(%) 7.3 -5.5 4.9+5.9-5.8 5.02.5

AK(%) 3.3 1.9 12.3+3.0-4.8 14.82.8

In absence of C’ and P’EW, K- and K- have similar CP violation

= a1, = a2

arg(a2)=-58o

13

Br(B PP)

Large K’ rates are naturally accounted for in QCDF

partial NLO

A=1.10 A= -50o C=1.3 C= -70o

14

B K(*)K’

In q & s flavor basis (q=(uu+dd)/√2, s=ss)

cos sin

sin cos

'

s

q

=39.3

BRs in units of 10-6

Interference between (b) & (c) K’ K

For K*, (b) is governed by a4-ra6, (c) by a4; a4, a6 are negative

and |a4|< |a6|; chiral factor r is of order unity additional sign difference between (b) & (c) for K*(‘)

15

ACP(B PP)(%)

Several SCET predictions are in conflict with experiment

16

B0 K0

A(B- K0-) = AK(4p+3

p) = p’2 A(B0 K00) = AK(-4

p-3p) + AK(pu2+pc3/23,EW

c) = -p’+c’

In absence of C’ and P’EW, K0 and K0 have similar CP violationCP violation of both K0 & K0 is naively expected to be very small

A’K=ACP(K0) – ACP(K0) = 2sinImrC+… - AK

mb penguin ann large complex a2 Expt

ACP(K0)(%) -4.0 0.75 -10.6+6.2-5.7 -110

A’K(%) -4.7 0.57 -11.0+6.1-5.7 --

BaBar: -0.130.130.03, Belle: 0.140.130.06 for ACP(K0)

ACP (K0)= -0.150.04

ACP (K0)=-0.0730.041

An observation of ACP(K0) - (0.10 0.15) power corrections to c’

Toplogical quark diagram approach ACP (K0)= -0.08 -0.12

17

B- K-

Destructive interference penguin amp is comparable to tree

amp more sizable CP asymmetry in K than K’

Although fc=-2 MeV is very small compared to f

q = 107 MeV,

fs = -112 MeV , it is CKM enhanced by VcbVcs

*/(VubVus*)

mb penguin ann large complex a2 (w/o charm)

large complex a2 (with charm)

Expt

ACP(K-)(%) -23.3 12.7 -2.0 -14.5 -379

ACP()(%) -11.4 11.4 -5.0 -5.0 -137

Charm content of plays a crucial role for ACP(K-), but not for ACP() Prediction of ACP(K-) still falls short of data

18

pQCD prediction is very sensitive to mqq, mass of q

ACP(K-) = 0.0562, 0.0588, -0.3064

for mqq= 0.14, 0.18, 0.22 GeV

Two issues: (i) with anomaly:

(ii) stability w.r.t. mqq

Akeroyd,Chen,Geng

Xiao et al. (0807.4265) reply on NLO corrections to get a correct

sign:

ACP(K-)= 0.093 to LO, (-11.7+8.4-11.4)% at NLO

1). If NLO effects flip the sign of ACP, pQCD calculations should be

done consistently to NLO

2). Missing parts of NLO: hard spectator & weak annihilation

222 MeV) 741(|~

4|0

2 qs

qqq GG

fmm

19

mtAmtSftBftB

ftBftBff

cossin))(())((

))(())((00

00

Time-dependent CP asymmetries:

SB PP

QCDF prediction for S() agrees well with data

S(’KS) is theoretically very clean in QCDF & SCET but not so in pQCD

Around 2005, CCS and Beneke got S(’KS) 0.74 in QCDF. Why 0.67 this time ?

20

sin2 extracted from charmonium data is 0.725 circ 2005, and 0.6720.023 today. It is more sensible to consider the difference

Sf = -fSf - sin2

Sf = 2|rf|cos2sincosf with rf=(uAfu)/(cAf

c)

small and could be + or –

SKs positive

21

B VV decays

Branching fractions tree-dominated decays: VV>PV>VP>PP (due to fV > fP) penguin-dominated decays: PP>PV~VV>VP (due to amplitudes

a4+rPa6, a4+r

Va6, a4-rPa6, a4+r

Va6

Polarization puzzle in charmless B→VV decays

2

0 ::1::

bb mmAAA

Why is fT so sizable ~ 0.5 in B→ K*Á decays ?

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

|| BVBVLT mmOffmmOffff

In transversity basis 2/)( ,2/)( ||

AAAAAA

2222 A00 >> A-- >> A++

2323

B→ K*Á

®3=a3+a5, ®4=a4-rÂÁa6, ®3,EW=a9+a7, ¯3= penguin ann

007.0:35.0:1|| |:| |:| ,||0|| ****0*

KKK

h

KXXXBJKJX

h=0 h= - h=0 h= -

Coefficients are helicity dependent !

constructive (destructive) interference in A- (A0) ⇒ fL¼ 0.58

with ¯3=0

NLO corrections alone can lower fL and enhance fT significantly !

Yang, HYC

2424

Although fL is reduced to 60% level, polarization puzzle is not resolved as the predicted rate, BR» 4.3£10-6, is too small compared to the data, » 10£10-6 for B →K*Á

Br & fL are fitted by ½A=0.60, ÁA= -50o

Kagan

f|| ¼ f? » 0.25

(S-P)(S+P)(S-P)(S+P) (S-P)(S+P) penguin annihilation contributes to A-- & A00 with similar amount

25

• =0.78, =-43o for K*, =0.65, =-53o for K*

•Rate for is very small

However, pQCD prediction is larger than QCDF by a factor of 20 !

• Br(B0 K*0K*0)=1.28+0.35-0.300.11 by

BaBar, 0.30.30.1 by Belle

• Br(B0)=0.9+1.5+2.4 -2.6-1.5 is obtained with C=0

soft corrections to a2 are large for PP, moderate for VP and very small for VV

rV<<r

P doesn’t help!

or due to Goldstone nature of the pion ? [Duraisamy, Kagan]

2626

Conclusions

In QCDF one needs two 1/mb power corrections (one to penguin annihilation, one to color-suppressed tree amplitude) to explain decay rates and resolve CP puzzles.

CP asymmetries are the best places to discriminate between different models.

27

<< is expected due to near cancellation of a2. Belle’s result ’ > ’ is the other way around

28

Spare slides

29

Br(B VP)

A(VP)=1.07 A(VP)= -700 A(PV)=0.87

A(PV)= -30o

A(K)=0.70A(K)= -40o

C=0.8 C= -70o

Br(B-)=Br(B-) sin

is an - mixing angle 3.3o

Belle:C.C. Chiang

30

Br(B VP)

A(VP)=1.09 A(VP)= -700 A(PV)=0.87

A(PV)= -30o

A(K)=0.70A(K)= -40o

C=0.8 C= -70o

In heavy quark limit, K* rates are too small by (15 50)%, while K are too small by a factor of 2 3 (K*)>(K*)

QCDF predictions for K*’ too small compared to BaBar but consistent with Belle: Br(K*-’)<2.9, Br(K*0’)<2.6

31

ACP(B VP)(%)

K*0-, -K0 have small ACP as they are pure penguin processesAK*=ACP(K*-) - ACP(K*-)= -2sin Imrc(K*)+…. 0.137A’K*=ACP(K*0)- ACP(K*0)= 2sin Imrc(K*) +… -0.111

)()0(

)0()(

34

2

1

0*

**

*

*

ccB

K

BK

cscb

usubC

a

Ff

Af

VV

VVKr

Data of ACP(K*0) is in better agreement with QCDF than pQCD & SCET. The SCET predictions are ruled out by experiment.

32

SB VP

SB VP

S is negativeand sensitive to soft corrections on a2

Expt’l errors of S are very large

33

• is expected to have larger fT as its tree contribution is small

• b d penguin-dominated modes K*0K*0, K*0K*- are expected to have fL 0.5. Experimentally, fL 0.75-0.80 (why ?)

• For K*-0, recent BaBar measurement gives fL=0.90.2 with 2.5 significance

• QCDF leads to