1. Resolving B-CP puzzles in QCD factorization
Hai-Yang Cheng
Academia Sinica
HFCPV-2011, Hangzhou
October 12, 2011

2. Direct CP asymmetries AK  ACP(K-0) – ACP(K-+) Bu/Bd K-+ +- K-
K- f2(1270)
K-0

ACP(%)
-8.70.8
386
-378
195
-236
3711
-134 S
10.9
6.3
4.6
3.8
3.6
3.4
3.3
Bu/Bd
-
0K*-
+
K-0
+K-
00
-+
K*0
ACP(%)
-145
3113
-209
3.72.1
2011
4324
116
4525 S
2.8
2.4
1.8
AK  ACP(K-0) – ACP(K-+)
AK
12.42.2
5.6
Belle, (16.43.7)% 4.4 Nature (2008) Bs
K+-
ACP(%)
297 S
4.1
CDF & LHCb 2

3. In heavy quark limit, decay amplitude is factorizable, expressed in terms of form factors and decay constants.
Bu/Bd
K-+
+-
K-
K*0
K*-+
K-0

ACP(%)
-8.70.8
386
-378
195
-236
3711
-134 S
10.9
6.3
4.6
3.8
3.4
3.3
mb  
Bu/Bd
-
0K*-
+
K-0
+K-
00
-+
K*0
ACP(%)
-145
3113
-209
3.72.1
2011
4324
116
4525 S
2.8
2.4
1.8
mb   Bs
K+-
ACP(%)
297 S
4.1
mb 
See Beneke & Neubert (2003) 3

4. Encounter several difficulties:
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 00, 00
CP puzzle:
CP asymmetries for K-+, K*-+, K-0, +-,… are wrong in signs
Polarization puzzle:
fT in penguin-dominated BVV decays is too small
 1/mb power corrections ! 4

5. penguin annihilation A(B0K-+) ua1+c(a4c+ra6c)
Theory
Expt Br
13.1x10-6
(19.550.54)x10-6
ACP
0.04
-0.0870.008
A(B0K-+) ua1+c(a4c+ra6c)
Im4c   wrong sign for ACP
4c
charming penguin, FSI penguin annihilation
1/mb corrections
penguin annihilation

6. has endpoint divergence: XA and XA2 with XA 10 dy/y
Beneke, Buchalla, Neubert, Sachrajda
Adjust A and A to fit BRs and ACP  A 1.10, A -50o
Im(4c+3c)  (Im4c  0.013)

7. New CP puzzles in QCDF
Bu/Bd
K-+
+-
K-
K*0
K*-+
K-0

ACP(%)
-8.70.8
386
-378
195
-236
3711
-134 S
10.9
6.3
4.6
3.8
3.4
3.3
mb   PA
AK
12.42.2
5.6
 3.3
 ( 1.9)
Bu/Bd
-
0K*-
+
K-0
+K-
00
-+
K*0
ACP(%)
-145
3113
-209
3.72.1
2011
4324
116
4525 S
2.8
2.4
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 penguin 7 7

8. All “problematic” modes receive contributions from uC+cPEW
PEW  (-a7+a9), PcEW  (a10+ra8), 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 o
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;…

9. 00 puzzle: ACP=(4324)%, Br = (1.910.22)10-6
The two distinct scenarios can be tested in tree-dominated modes where ’cPEW << ’uC. CP puzzles of -, 00 & large rates of 00, 00 cannot be explained by a large complex PEW
00 puzzle: ACP=(4324)%, Br = (1.910.22)10-6
Bu/Bd
K-+
+-
K-
K*0
K*-+
K-0

ACP(%)
-8.70.8
386
-378
195
-236
3711
-134 S
10.9
6.3
4.6
3.8
3.4
3.3
mb   PA
large complex a2
AK
12.42.2
5.6
 3.3
 ( 1.9) 
Bu/Bd
-
0K*-
+
K-0
+K-
00
-+
K*0
ACP(%)
-145
3113
-209
3.72.1
2011
4324
116
4525 S
2.8
2.4
1.8
mb   PA
large complex a2 9

10. B- K-’ K-’ K-0 has same topology as C Two possible sources:
a2 a2[1+Cexp(iC)]
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)
[HYC, Chua]
Two possible sources:
spectator interactions
NNLO calculations of V & H are available
Real part of a2 comes from H and imaginary part from vertex
a2()  i =0.22 exp(-i27o) for B = 400 MeV
a2(K)  0.51exp(-i58o)  H = 4.9 & H  -77o
[Bell, Pilipp]
final-state rescattering [C.K. Chua]
B- K-’ K-’ K-0
has same topology as C

11. Test of large complex EW penguin
In SM, BRs of the pure EW-penguin decays
are of order If new physics in EW penguins, BRs will be enhanced by an order of magnitude [Hofer et al., arXiv: ].
Measurements of their BRs of order 10-6 will be a suggestive of NP in EW penguins.

12. B- K-0 A(B0 K-+) = AK(pu1+4p+3p)
2 A(B- K-0) = AK(pu1+4p+3p)+AK(pu2+3/23,EWp)
1= a1, 2= a2
In absence of C and PEW, K-0 and K-+ have similar CP violation
arg(a2)=-58o
mb
penguin ann
large complex a2
Expt
ACP(K-0)(%)
7.3
-5.5
3.72.1
AK(%)
3.3
1.9
12.42.2

13. B0 K00 A(B- K0-) = AK(4p+3p)
2 A(B0 K00) = AK(-4p-3p) + AK(pu2+pc3/23,EWc)
In absence of C and PEW, K0+ and K00 have similar CP violation
CP violation of both K0- & K00 is naively expected to be very small
A’K=ACP(K00) – ACP(K0-) = 2sinImrC+… - AK
mb
penguin ann
large complex a2
Expt
ACP(K00)(%)
-4.0
0.75
-110
A’K(%)
-4.7
0.57 --
BaBar: -0.130.130.03, Belle: 0.140.130.06 for ACP(K00)
Atwood, Soni
 ACP (K00)= -0.150.04
Deshpande, He
 ACP (K00)=-0.0730.041
Toplogical-diagram approach
 ACP (K00)=  -0.12
Chiang et al. 13
An observation of ACP(K00)  - (0.10 0.15)  power corrections to c’

14. K-+ +- K- K*0 K-0  ACP(%) -8.70.8 386 -378 195 3711
-134
QCDF
pQCD --
K*-+
+K-
K-0
-
00
-+
ACP(%)
-236
2011
3.72.1
-145
116
QCDF
pQCD
-1+3-6 --
HYC, Chua (’09)

15. In SM, -fSf  sin2, Cf 0 for b s penguin-dominated modes
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 =0.8670.048 deviates from (sin2)expt by 3.3 
Lunghi, Soni 15

16. 2006: sin2eff=0.500.06 from b qqs, sin2=0.690.03 from b ccs

17. Sf = -fSf – sin2
HYC, Chua (‘09)
Mode
QCDF
pQCD
Expt
Average
’KS
-0.100.08
-0.030.11
-0.080.07
KS --
0KS
-0.120.20
0.000.32
-0.100.17
KS
0.020.01
-0.410.26
KS
-0.560.47
-0.220.24
0KS
Except for 0KS, the predicted Sf tend to be positive, while they are negative experimentally

18. B VV decays A00 >> A-- >> A++
Polarization puzzle in charmless B→VV decays
A00 >> A-- >> A++
In transversity basis
Why is fT so sizable ~ 0.5 in B→ K*Á decays ? 18 18 18

19. NLO corrections alone can lower fL and enhance fT significantly !
Beneke,Rohere,Yang
HYC,Yang
constructive (destructive) interference in A- (A0) ⇒ fL¼ 0.58
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
(S-P)(S+P) penguin annihilation contributes to A-- & A00 with similar amount
(S-P)(S+P)
Kagan

20. ** BaBar’s old result: fL(B+ K*+0)= 0.96+0.06-0.16
Decay
BFx10-6 (expt)
BFx10-6 (QCDF)
fL (expt)
fL ( QCDF)
B+ +0
0.9500.016
0.960.02
B0 +-
0.920.02
B0 00
B0 a1a1
47.312.2
0.310.24
B+ K*0+
9.21.5
0.480.08
B+ K*+0
4.61.1
0.780.12 **
B0 K*+-
10.32.6
0.380.13
B0 K*00
3.90.8
4.63.5
0.400.14
B+ K*+
10.01.1
0.500.05
B0 K*0
9.80.7
0.4800.030
B+ K*+
< 7.4
0.410.19
B0 K*0
2.00.5
0.700.13
Bs 
23.28.4
0.3480.046 ？
** BaBar’s old result: fL(B+ K*+0)=

21. Polarization puzzle in B  TV
For both B K*, K*, K*00, fT /fL  1
fL(K2*+) = 0.560.11, fL(K2*0) = 0.450.12,
fL(K2*+) = 0.800.10, fL(K2*0) =
BaBar
Why is fT/ fL <<1 for B K2* and fT /fL 1 for B K2* ?
In QCDF, fL is very sensitive to the phase ATV for B K2*, but not so sensitive to AVT for B K2*
fL(K2*) = 0.88, 0.72, for ATV = -30o, -45o, -60o,
fL(K2*)= 0.68, 0.66, for AVT = -30o, -45o, -60o
Rates & polarization fractions can be accommodated in QCDF, but no dynamical explanation is offered
HYC, K.C. Yang (’10) 21 21

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.