Theoretical Issues in B PV Decays Matthias Neubert Cornell University May 14, 2005 SLAC-INT Workshop 1
Predictions of QCD factorization Have not done a fit to data since 2001 Have not done an update on QCDF since 2003 (but see work by CKM Fitter group) Instead, look at scenario S4 in B&N, which gave a reasonable description of the data in 2003 [Beneke, Neubert: Nucl. Phys. B 675 (2003) 333] 2
B(B Kπ, ππ, KK) K0 K0 K + K K + K 0 π 0 π 0 π + π π + π 0 K0π0 K + 0 π K + π K 0 π + 0.0 12.5 25.0 Branching Ratio x 10 6 3
B(B Kπ, ππ, KK) K0 K0 K + K K + K 0 π 0 π 0 π + π π + π 0 K0π0 K + 0 π K + π K 0 π + 0.0 12.5 25.0 Branching Ratio x 10 6 4
B(B (η, η )(K ( ), π, ρ)) B(B (K, ρ,ω, φ)(π, K,η, η )) φη φπ 0 φπ + ηk 0 φk 0 ηρ 0 φk + ηπ 0 η π 0 η ρ0 η π + ωπ 0 ωk + ρ 0 π 0 ωπ + ωk0 η K 0 ρ 0 π + ρ + π 0 ηπ + η K + ρ + π ηk + ηρ + ηk 0 η ρ + ηk + K 0 π 0 K + ρ 0 K + π K 0 π + K + π0 K + ρ η K0 η + K 0.0 50.0 100.0 Branching Ratio x 10 6 0.0 25.0 50.0 Branching Ratio x 10 6 K 0 ρ 0 K 0 ρ + 5
B(B (η, η )(K ( ), π, ρ)) B(B (K, ρ,ω, φ)(π, K,η, η )) φη φπ 0 φπ + ηk 0 φk 0 ηρ 0 φk + ηπ 0 η π 0 η ρ0 η π + ωπ 0 ωk + ρ 0 π 0 ωπ + ωk0 η K 0 ρ 0 π + ρ + π 0 ηπ + η K + ρ + π ηk + ηρ + ηk 0 η ρ + ηk + K 0 π 0 K + ρ 0 K + π K 0 π + K + π0 K + ρ η K0 η + K 0.0 50.0 100.0 Branching Ratio x 10 6 0.0 25.0 50.0 Branching Ratio x 10 6 K 0 ρ 0 K 0 ρ + 6
π + π π + K + π + π K + KSKS ρ + ρ 0 K + π π 0 K + K K + +1.0 0.0-1.0 CP Asymmetry in Charmless B Decays 7 π 0 π 0 K + π 0 π + π 0 η π + η K + ηk + ηρ + ηk 0 φk 0 φk + φk + ωπ + ωk + K + ρ 0 K 0 ρ + K + ρ ρ + π 0 K + π ρ 0 π + ηπ + ηk + K 0 π + K + π sll sγ K γ
π + π π + K + π + π K + KSKS ρ + ρ 0 K + π π 0 K + K K + +1.0 0.0-1.0 CP Asymmetry in Charmless B Decays 8 π 0 π 0 K + π 0 π + π 0 η π + η K + ηk + ηρ + ηk 0 φk 0 φk + φk + ωπ + ωk + K + ρ 0 K 0 ρ + K + ρ ρ + π 0 K + π ρ 0 π + ηπ + ηk + K 0 π + K + π sll sγ K γ
Successes of QCD factorization Consistent global description of a vast variety of hadronic and radiative two-body decays, with branching fractions ranging from 10-4 to 10-9 Dynamical explanation of smallness of direct CP asymmetries (syst. cancellation of FSI phases in heavy-quark limit) 9
Successes of QCD factorization Dynamical explanation of huge B η K branching fractions Dynamical explanation of smallness of P V /P P amplitude ratios (B PV and VP) Dynamical explanation of intricate pattern of penguin interference seen in B PP, B PV, B VP modes 10
Anatomy of penguins Clean extraction of penguin amplitudes in B ± π ± K 0, B ± π ± K *0, B ± ρ ± K 0 : Important lessons about interference of different penguin amplitudes (scalar vs. vector penguins) 11
Anatomy of penguins B ± π ± K 0 B ± π ± K *0 Data Theory 12
Anatomy of penguins Tree-to-penguin ratios: 13
Anatomy of penguins Smallness of penguins in PV and VP modes understood in terms of interference of penguin contributions from (V-A)(V±A) operators (P 4 ) and (S-P)(S+P) operators (P 6 ), called a 4 and a 6 in QCD factorization Note that a 4 ~1 whereas a 6 ~1/m b (formally power suppressed, but chirally enhanced ), but both are predicted to have similar size in QCD factorization 14
Anatomy of penguins Interference pattern: B PP: P 4 + P 6 B PV: P 4 + ε P 6 dynamical suppression of P 6 B VP: P 4 - P 6 destructive interference B VV: combination of PV, VP cases Data confirm this pattern, which was predicted by QCD factorization Clear evidence for power corrections to penguin amplitudes (neglected in SCET approach ) 15
Extraction of γ in B πρ decay [Beneke, MN, hep-ph/0308039] B PV modes have smaller penguin contributions than B PP modes Smaller theory uncertainties when γ is extracted from time-dependent rates in B πρ decays Result: γ = (62 ± 8) o B πρ B ππ Old data New data Old data New data 16
Conclusions B PV modes offer important clues about dynamics of penguins Interference of vector and scalar penguins Clear evidence for power corrections (problematic for SCET approach) Can exploit dynamical suppression of penguins in vector modes to extract γ 17