Hadronic charmless B decays B→AP

The two-body hadronic decays of B mesons into pseudoscalar and axial-vector mesons are studied within the framework of QCD factorization. The light cone distribution amplitudes (LCDAs) for ³P₁ and ¹P₁ axial-vector mesons have been evaluated using the QCD sum rule method. Owing to the G-parity, the chiral-even two-parton light cone distribution amplitudes of the ³P₁ (¹P₁) mesons are symmetric (antisymmetric) under the exchange of quark and antiquark momentum fractions in the SU(3) limit. For chiral-odd LCDAs, it is the other way around. The main results are the following: (i) The predicted rates for a₁^±(1260)π^∓, b₁^±(1235)π^∓, b₁⁰(1235)π^-, a₁⁺K^-, and b₁⁺K^- modes are in good agreement with the data. However, the naively expected ratios B(B^-→a₁⁰π^-)/B(B̅ ⁰→a₁⁺π^-)≲1, B(B^-→a₁^-π⁰)/B(B̅ ⁰→a₁^-π⁺)∼1/2, and B(B^-→b₁⁰K^-)/B(B̅ ⁰→b₁⁺K^-)∼1/2 are not borne out by experiment. This should be clarified by the improved measurements of these decays. (ii) Since the B̅ →b₁K decays receive sizable annihilation contributions, their rates are sensitive to the interference between penguin and annihilation terms. The measurement of B(B̅ ⁰→b₁⁺K^-) implies a destructive interference which in turn indicates that the form factors for B→b₁ and B→a₁ transitions are of opposite signs. (iii) Sizable power corrections such as weak annihilation are needed to account for the observed rates of the penguin-dominated modes K₁^-(1270)π⁺ and K₁^-(1400)π⁺. (iv) The decays B→K₁K̅ with K₁=K₁(1270), K₁(1400) are in general quite suppressed, of order 10^-7–10^-8, except for B̅ ⁰→K̅ ₁⁰(1270)K⁰ which can have a branching ratio of order 2.3×10^-6. The decay modes K₁^-K⁺ and K₁⁺K^- are of particular interest as they proceed only through weak annihilation. (v) The mixing-induced parameter S is predicted to be negative in the decays B⁰→a₁^±π^∓, while it is positive experimentally. This may call for a larger unitarity angle γ≳80°. (vi) Branching ratios for the decays B→f₁π, f₁K, h₁π and h₁K with f₁=f₁(1285), f₁(1420) and h₁=h₁(1170), h₁(1380) are generally of order 10^-6 except for the color-suppressed modes f₁π⁰ and h₁π⁰ which are suppressed by 1 to 2 orders of magnitude. Measurements of the ratios B(B^-→h₁(1380)π^-)/B(B^-→h₁(1170)π^-) and B(B̅ →f₁(1420)K̅ )/B(B̅ →f₁(1285)K̅ ) will help determine the mixing angles θ_¹P1 and θ_³P1, respectively.