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Resolving B-CP puzzles in QCD factorization

Resolving B-CP puzzles in QCD factorization. Hai-Yang Cheng Academia Sinica. HFCPV-2011, Hangzhou October 12, 2011. Direct CP asymmetries. A K  A CP (K -  0 ) – A CP (K -  + ). Belle, (16.4  3.7)% 4.4  Nature (2008). CDF & LHCb. 2.

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Resolving B-CP puzzles in QCD factorization

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  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-+) Belle, (16.43.7)% 4.4 Nature (2008) CDF & LHCb 2

  3. In heavy quark limit, decay amplitude is factorizable, expressed in terms of form factors and decay constants. See Beneke & Neubert (2003) 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 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. 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

  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) -0.039 (Im4c  0.013)

  7. 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 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. 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 9

  10. [HYC, Chua] 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) • 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

  11. 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.

  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

  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 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  ACP (K00)=-0.0730.041 Deshpande, He  ACP (K00)= -0.08  -0.12 Toplogical-diagram approach Chiang et al. 13 An observation of ACP(K00) - (0.10 0.15)  power corrections to c’

  14. HYC, Chua (’09)

  15. 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 2011: sin2eff=0.640.04 from b qqs, sin2=0.6780.020 from b ccs

  17. Sf = -fSf – sin2 HYC, Chua (‘09) Except for 0KS, the predicted Sf tend to be positive, while they are negative experimentally

  18. B VV decays • 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

  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) = 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

  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.

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