Hadronic charmless B decays B-> AP

Abstract

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 ${}^3{P}_1$ and ${}^1{P}_1$ 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 ${}^3{P}_1$ (${}^1{P}_1$) mesons are symmetric (antisymmetric) under the exchange of quark and anti-quark momentum fractions in the SU(3) limit. For chiral-odd LCDAs, it is other way around. The main results are the following: (i) The predicted rates for $a_1^{\pm }(1260){\pi }^{\mp }$, $b_1^{\pm }(1235){\pi }^{\mp }$, $b_1^0(1235){\pi }^{-}$, $a_1^{+}{K}^{-}$ and $b_1^{+}{K}^{-}$ modes are in good agreement with the data. However, the naively expected ratios $Br(B^-\to a_1^0π^-)/Br(\ov B^0\to a_1^+π^-)\leq 1$, $Br(B^-\to a_1^-π^0)/Br(\ov B^0\to a_1^-π^+)\sim {1\over 2}$ and $Br(B^-\to b_1^0K^-)/Br(\ov B^0\to b_1^+K^-)\sim {1\over 2}$ are not borne out by experiment. This should be clarified by the improved measurements of these decays. (ii) Since the $\bar{B}\to b_{1}K$ decays receive sizable annihilation contributions, their rates are sensitive to the interference between penguin and annihilation terms. The measurement of $Br({\bar{B}}^0\to b_1^{+}{K}^{-})$ implies a destructive interference which in turn indicates that the form factors for $B\to b_1$ and $B\to a_1$ 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 $K_1^{-}(1270){\pi }^{+}$ and $K_1^{-}(1400){\pi }^{+}$.

38 pages, 1 figure. The experimental limit in Fig.1 is updated

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