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

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 -68+20-18 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

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

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

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  0.013  wrong sign for ACP 4c charming penguin, FSI penguin annihilation 1/mb corrections penguin annihilation

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)  -0.039 (Im4c  0.013)

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

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;…

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

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()  0.194 - 0.099i =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

Test of large complex EW penguin 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.

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 4.9+5.9-5.8 3.72.1 AK(%) 3.3 1.9 12.3+3.0-4.8 12.42.2

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 -10.6+6.2-5.7 -110 A’K(%) -4.7 0.57 -11.0+6.1-5.7 -- 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)= -0.08  -0.12 Chiang et al. 13 An observation of ACP(K00)  - (0.10 0.15)  power corrections to c’

K-+ +- K- K*0 K-0  ACP(%) -8.70.8 386 -378 195 3711 -134 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+1.2-1.3 71+25-35 -- K*-+ +K- K-0 - 00 -+ ACP(%) -236 2011 3.72.1 -145 43+25-24 116 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)

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

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

Sf = -fSf – sin2 HYC, Chua (‘09) Mode QCDF pQCD Expt Average ’KS 0.00+0.01-0.01 -0.06+0.50-0.91 -0.100.08 -0.030.11 -0.080.07 KS 0.12+0.09-0.08 -0.07+0.50-0.92 -- 0KS 0.12+0.07-0.06 0.06+0.02-0.03 -0.120.20 0.000.32 -0.100.17 KS 0.022+0.044-0.002 0.020.01 -0.410.26 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 -0.560.47 -0.220.24 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 Except for 0KS, the predicted Sf tend to be positive, while they are negative experimentally

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

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

** 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 24.0+1.9-2.0 20.0+4.5-2.1 0.9500.016 0.960.02 B0 +- 24.2+3.1-3.2 25.5+2.8-3.0 0.978+0.025-0.022 0.920.02 B0 0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 a1a1 47.312.2 37.4+18.8-13.7 0.310.24 0.64+0.07-0.17 B+ K*0+ 9.21.5 9.2+3.8-5.5 0.480.08 0.48+0.52-0.41 B+ K*+0 4.61.1 5.5+1.4-2.6 0.780.12 ** 0.67+0.31-0.32 B0 K*+- 10.32.6 8.9+4.9-5.6 0.380.13 0.53+0.45-0.32 B0 K*00 3.90.8 4.63.5 0.400.14 0.39+0.60-0.31 B+ K*+ 10.01.1 10.0+11.9-6.2 0.500.05 0.49+0.51-0.42 B0 K*0 9.80.7 9.5+11.9-6.0 0.4800.030 0.50+0.51-0.43 B+ K*+ < 7.4 3.0+2.5-1.5 0.410.19 0.67+0.32-0.39 B0 K*0 2.00.5 2.5+2.5-1.6 0.700.13 0.58+0.43-0.17 Bs  23.28.4 16.7+11.6-9.0 0.3480.046 0.36+0.23-0.18 ？ ** BaBar’s old result: fL(B+ K*+0)= 0.96+0.06-0.16

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) = 0.901+0.059-0.069 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, 0.48 for ATV = -30o, -45o, -60o, fL(K2*)= 0.68, 0.66, 0.64 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

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.