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Hadronic B decays involving tensor mesons

Hadronic B decays involving tensor mesons. Hai-Yang Cheng ( 鄭海揚 ) Academia Sinica Properties of tensor mesons QCD factorization Comparison with experiment. in collaboration with Kwei -Chou Yang. 2011 Cross Strait Meeting on Particle Physics and Cosmology.

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Hadronic B decays involving tensor mesons

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  1. Hadronic B decays involving tensor mesons • Hai-Yang Cheng (鄭海揚) • Academia Sinica • Properties of tensor mesons • QCD factorization • Comparison with experiment in collaboration with Kwei-Chou Yang 2011 Cross Strait Meeting on Particle Physics and Cosmology April 5, 2011

  2. Even-parity mesons Scalar mesons (JPC= 0++) > 1 GeV  1 GeV Axial-vector mesons 1P1 3P1 (JPC=1+-) (JPC=1++) 2 2 Kwei-Chou Yang, Nucl. Phys. B776, 187-257 (2007).

  3. Tensor mesons For JP=2+ tensor mesons 3P2 nonet: I=0: f2(1270), f’2(1525), I=1/2: K2*(1430) I=1: a2(1320) close to ideal mixing, f2 5.8o 3 3

  4. B SM (M=P,V): HYC, Chua, Yang in QCD factorization (’06, ’08) C.D. Lu et al. in pQCD (’06, ’07, ’09) Delepine et al. (’08) Z. J. Xiao et al. in pQCD (’08 - ’10) B AM: HYC, Yang in QCDF (’07) C.D. Lu et al. in pQCD (’07) B TM: last enterprise

  5. To study B → TM (M=P,V) decays, we need to know • mixing angles • decay constants • light-cone distribution amplitudes • form factors for B → T transition • vertex corrections, spectator interactions, annihilation for decay amplitudes Aliev & Shifman (’82) HYC, Koike, Yang (’10) Braun & Kivel (’01) W. Wang (’10), Yang (’10), Z.G. Wang (’10) ISGW (’89,’95), CCH (’01) HYC, Yang (’10)

  6. Decay constants • Tensor meson cannot be produced from local V-A current owing • to p=0 • Can be created from local current involving covariant derivatives • with Previous estimates: Aliev & Shifman (’82); Aliev, Azizi, Bashiry (’10) Based on QCD sum rules we obtain (HYC, Koike, Yang, arXiv:1007.3526)

  7. Form factors for B → T • ISGW (Isgur-Scora-Grinstein-Wise) non-relativistic quark model (’89,’95) • Covariant light-front quark model (Chua, Hwang, HYC, ’04) Relativistic effects in B-to-light transitions at q2=0 are important • Large energy effective theory (LEET) (Charles et al. ’99) • pQCD approach (W. Wang, arXiv:1008.5326) • QCD sum rules (K.C. Yang, arXiv:1010.2144; Z.G. Wang, arXiv:1011.3200) 7 7

  8. Light-cone distribution amplitudes (LCDAs) first studied by Braun & Kivel (‘01) twist-2: ∥, twist-3: gv, ga, ht, hstwist-4: g3, h3 Due to even G-parity, these LCDAs are anti-symmetric under the replacement u→1-u in SU(3) limit Ci3/2: Gegenbauer polynomial 8 8

  9. Longitudinal & transverse helicity projectors for tensor mesons: Transverse momentum derivative terms should be included before taking collinear approximation • Helicity projectors for vector mesons:

  10. B→ TM in QCDF Apply QCD factorization to B→TM (Beneke, Buchalla, Neubert, Sachrajda) vertex & penguin spectator int. annihilation 10 10

  11. Data dominated by BaBar, f2K modes are due to Belle Previous studies based on naïve or generalized factorization predict rates typically too small by 1-2 orders of magnitude compared to experiment

  12. Penguin-dominated B TP

  13. B-K2*0- vanishes in naïve factorization, while its BR is measured to be ~ 5.610-6  importance of nonfactorizble effects • Beyond naïve factorization, contributions fT defined from local currents involving covariant derivatives can be produced from nonfactorizable contributions such as vertex, penguin and hard spectator corrections • Penguin annihilation is needed in QCDF to account for rates & CP asymmetries ATP=0.83, ATP = -70o APT=0.75, APT = -30o similar to the parameters for B PP

  14. Penguin-dominated B TP 14

  15. B K2*, K2*’ Interference between (b) & (c) is constructive for K2*’ and destructive for K2*  large rate of K2*’ than K2* C.S. Kim et al. obtained Br(B K2*’)/Br(B K2*) ~ 45, while it is ~ 2 experimentally. This is because the matrix elements do not have correct chiral limit behavior due to anomaly and should be replaced by

  16. Tree-dominated B TP

  17. Penguin-dominated B TV

  18. Rate puzzle in BK2* decays It is naively expected that Experimentally, Br(B K2*)  Br(B K2*). This can be accommodated by having penguin annihilation such that 3(K2*) >> 3(K2*). But why ? What is the dynamical origin ?

  19. Polarization puzzle in charmless B→VV decays A00 >> A-- >> A++ In transversity basis Why is fT so sizable ~ 0.5 in penguin-dominated B K*, K*, K*00decays ? 19 19 19 19

  20. NLO corrections alone can lower fL and enhance fT significantly ! Beneke,Rohere,Yang HYC,Yang constructive (destructive) interference in A- (A0) ⇒fL 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* (S-P)(S+P) penguin annihilation contributes to A-- & A00 with similar amount (S-P)(S+P) Kagan 20

  21. Polarization puzzle in B  K2* 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* ? Why is that fT behaves differently in K2* and K* ? 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 21 21 21

  22. Conclusions • Tensor meson cannot be created from local V-A current, but its decay constant can be defined through non-local current or local current with covariant derivative. • Some decays e.g. B-K2*0- prohibited in naïve factorization receive sizable nonfactorizable corrections • Predictions of QCD factorization in general agree with experiment for B TM (M=P,V), but there remains puzzles to be resolved: rate of K2* and polarization of K2*

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