Resolving B-CP puzzles in QCD factorization

HFCPV-2011, Hangzhou

October 12, 2011

Hai-Yang Cheng

Academia Sinica

22

Direct CP asymmetries

ACP(K-) – ACP(K-

)

Bu/Bd K- K- K*0 K*-

K- f2(1270) K-

ACP(%)

-8.70.8

386

-378 195 -236

-68+20-18

3711 -134

S

10.9 6.3 4.6 3.8 3.8 3.6 3.4 3.3Bu/Bd K*- K-

K- *

ACP(%)

-145

3113

-209 3.72.1

2011

4324 116 4525

S 2.8 2.4 1.8 1.8 1.8 1.8 1.8 1.8

12.42.2

5.6

Belle, (16.43.7)% 4.4 Nature (2008)

Bs K+-

ACP(%)

297

S 4.1

CDF & LHCb

33

Bu/Bd K-

K- K*0 K*-

K-

ACP(%)

-8.70.8

386 -378 195 -236 3711

-134

S

10.9 6.3 4.6 3.8 3.8 3.4 3.3

mb

Bu/Bd K*-

K-

K-

*

ACP(%) -145

3113

-209 3.72.1

2011

4324

116 4525

S 2.8 2.4 1.8 1.8 1.8 1.8 1.8 1.8

mb

Bs K+-

ACP(%)

297

S 4.1

mb

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

See Beneke & Neubert (2003)

44

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 (19.550.54)x10-6

ACP 0.04 -0.0870.008

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 (Im4c 0.013)

Beneke, Buchalla, Neubert, Sachrajda

777

New CP puzzles in QCDF

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

Bu/Bd K-

K- K*0 K*-

K-

ACP(%)

-8.70.8

386 -378 195 -236 3711

-134

S

10.9 6.3 4.6 3.8 3.8 3.4 3.3

mb

PA

Bu/Bd K*-

K-

K-

*

ACP(%) -145

3113

-209 3.72.1 2011

4324

116 4525

S 2.8 2.4 1.8 1.8 1.8 1.8 1.8 1.8

mb

PA

12.42.2

5.6

3.3

( 1.9)

8

All “problematic” modes receive contributions from uC+cPEW

PEW (-a7+a9), PcEW (a10+ra8), u=VubV*us, c=VcbV*cs

AK puzzle can be resolved by having a large complex C

(C/T 0.5e–i55 ) or a large complex PEW or the combination

AK 0 if C, PEW, A are negligible AK puzzle

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

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

o

99

The two distinct scenarios can be tested in tree-dominated modes

where ’cPEW << ’uC. CP puzzles of , & large rates of ,

cannot be explained by a large complex PEW

puzzle: ACP=(4324)%, Br = (1.910.22)10-6

12.42.2

5.6

3.3

( 1.9)

Bu/Bd K- K- K*0 K*- K-

ACP(%) -8.70.8 386 -378 195 -236 3711 -134

S 10.9 6.3 4.6 3.8 3.8 3.4 3.3

mb

PA

large complex a2

Bu/Bd K*- K- K- *

ACP(%) -145 3113 -209 3.72.1 2011 4324 116 4525

S 2.8 2.4 1.8 1.8 1.8 1.8 1.8 1.8

mb

PA

large complex a2

10

a2 a2[1+Cexp(iC)]

C 1.3, C -70o for PP modes a2(K) 0.51exp(-i58o), a2() 0.6exp(-i55o)

C 0.8, C -80o for VP modes a2(K*) 0.39exp(-i51o)

Two possible sources: spectator interactions

LDc

sF

c

aHN

VC

N

ccca )()

4(

43 2

211

22

NNLO calculations of V & H are available

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

a2() 0.194 - 0.099i =0.22 exp(-i27o) for = 400 MeV

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

[Bell, Pilipp]

final-state rescattering [C.K. Chua]

[HYC, Chua]

has same topology as CB- K-’ K-’ K-

11

In SM, BRs of the pure EW-penguin decays

are of order 10-7. If new physics in EW penguins, BRs will be

enhanced by an order of magnitude [Hofer et al., arXiv:1011.6319].

Measurements of their BRs of order 10-6 will be a suggestive of NP

in EW penguins.

00)('0 ,, sB

Test of large complex EW penguin

12

B- K-

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

p)

2 A(B- K-0) = AK(pu1+4p+3

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

)()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 3.72.1

AK(%) 3.3 1.9 12.3+3.0-4.8 12.42.2

In absence of C and PEW, K- and K- have similar CP violation

= a1, = a2

arg(a2)=-58o

1313

B0 K0

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

p)

2 A(B0 K00) = AK(-4p-3

p) + AK(pu2+pc3/23,EWc)

In absence of C and PEW, 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-diagram approach ACP (K0)= -0.08 -0.12

Atwood, Soni

Deshpande, He

Chiang et al.

14

K- K- K*0 K-

ACP(%) -8.70.8 386 -378 195 3711 -134

QCDF -7.4+4.6-5.0 17.0+4.5

-8.8 -11.2+17.4-24.3 3.5+2.7

-2.4 45.4+36.1-30.2 -11+7

-5

pQCD -10+7-8 18+20

-12 -11.7+8.4-10.5

4.6+1.2

71+25-35 --

K*- K- K-

ACP(%) -236 2011 3.72.1 -145 43+25-24 116

QCDF -12.1+12.6-16.0 31.9+22.7

-16.8 4.9+5.9-5.8 -5.0+8.7

-10.8 57.2+33.7-40.4 4.4+5.8

-6.8

pQCD -60+32-19 64+24

-30 -1+3-6 -37+9

-7 63+35-34 --

HYC, Chua (’09)

1515

mtCmtSftBftB

ftBftBtA ffCP

cossin

))(())((

))(())(()(

00

00

Cf (= -Af) meaures direct CPV, Sf is related to CPV in interference between mixing & decay amplitude

In SM, -fSf sin2, Cf 0 for b s penguin-dominated modes

(sin2)SM =0.8670.048 deviates from (sin2)expt by 3.3 Lunghi, Soni

16

2006: sin2eff=0.500.06 from b qqs, sin2=0.690.03 from b ccs

2011: sin2eff=0.640.04 from b qqs, sin2=0.6780.020 from b ccs

17

Mode QCDF pQCD Expt Average

’KS 0.00+0.01-0.01 -0.06+0.50

-0.91 -0.100.08 -0.030.11

-0.080.07

KS 0.12+0.09-0.08 -0.07+0.50

-0.92 -- --

KS 0.12+0.07-0.06 0.06+0.02

-0.03 -0.120.20 0.000.32

-0.100.17

KS 0.022+0.044-0.002 0.020.01 -0.410.26

0.23+0.09-0.19

-0.11+0.16-0.18

KS 0.17+0.06-0.08 0.15+0.03

-0.07 -0.12+0.26-0.29

-0.560.47 -0.220.24

0KS -0.17+0.09-0.18 -0.19+0.10

-0.06 -0.32+0.27-0.31

-0.03+0.23-0.28

-0.13+0.18-0.21

Sf = -fSf – sin2

Except for KS, the predicted Sf tend to be positive, while they are negative experimentally

HYC, Chua (‘09)

1818

B VV decays

Polarization puzzle in charmless B→VV decays

2

0 ::1::

b

QCD

b

QCD

mmAAA

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

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

|| BVBVLT mmOffmmOffff

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

AAAAAA

1818

A00 >> A-- >> A++

19

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

NLO corrections alone can lower fL and enhance fT significantly !

Beneke,Rohere,YangHYC,Yang

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

Kagan (S-P)(S+P)(S-P)(S+P) (S-P)(S+P) penguin annihilation

contributes to A-- & A00 with similar amount

422

0 :ln:ln::

b

QCD

h

b

b

QCD

h

b

b

QCDPAPAPA

m

m

m

m

mAAA

20

Decay BFx10-6 (expt) BFx10-6 (QCDF) fL (expt) fL ( QCDF)

B+ 24.0+1.9-2.0 20.0+4.5

-2.1 0.9500.016 0.960.02

B0 24.2+3.1-3.2 25.5+2.8

-3.0 0.978+0.025-0.022 0.920.02

B0 0 0.73+0.27-0.28 0.9+1.9

-0.5 0.75+0.12-0.15 0.92+0.07

-0.37

B0 a1a1

47.312.2 37.4+18.8-13.7 0.310.24 0.64+0.07

-0.17

B+ K*0 9.21.5 9.2+3.8-5.5 0.480.08 0.48+0.52

-0.41

B+ K*+ 4.61.1 5.5+1.4-2.6 0.780.12 ** 0.67+0.31

-0.32

B0 K*+ 10.32.6 8.9+4.9-5.6 0.380.13 0.53+0.45

-0.32

B0 K*0 3.90.8 4.63.5 0.400.14 0.39+0.60-0.31

B+ K*+ 10.01.1 10.0+11.9-6.2 0.500.05 0.49+0.51

-0.42

B0 K*0 9.80.7 9.5+11.9-6.0 0.4800.030 0.50+0.51

-0.43

B+ K*+ < 7.4 3.0+2.5-1.5 0.410.19 0.67+0.32

-0.39

B0 K*0 2.00.5 2.5+2.5-1.6 0.700.13 0.58+0.43

-0.17

Bs 23.28.4 16.7+11.6-9.0 0.3480.046 0.36+0.23

-0.18 ** BaBar’s old result: fL(B+ K*+)= 0.96+0.06

-0.16

？

212121

Polarization puzzle in B TV

fL(K2*+) = 0.560.11, fL(K2

*0) = 0.450.12,

fL(K2*+) = 0.800.10, fL(K2

*0) = 0.901+0.059-0.069

fL(K2*) = 0.88, 0.72, 0.48 for

TV = -30o, -45o, -60o,fL(K2

*)= 0.68, 0.66, 0.64 for VT = -30o, -45o, -60o

In QCDF, fL is very sensitive to the phase TV for B K2

*, but not so sensitive to A

VT for B K2*

Why is fT/ fL <<1 for B K2* and fT /fL 1 for B K2

* ?

Rates & polarization fractions can be accommodated in QCDF, but no dynamical explanation is offered

HYC, K.C. Yang (’10)

For both B K*, K*K*0, fT /fL 1

BaBar

22

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.