Constraints on hard spectator scattering and annihilation corrections in B u,d → PV decays within QCD factorization

摘要

In this paper, we investigate the contributions of hard spectator scattering and annihilation in B → PV decays within the QCD factorization framework. With available experimental data on B → π K ? , ρ K , π ρ ?and? K ? decays, comprehensive χ 2 analyses of the parameters X A , H i , f ( ρ A , H i , f , ? A , H i , f ) are performed, where X A f ( X A i ) and X H are used to parameterize the endpoint divergences of the (non)factorizable annihilation and hard spectator scattering amplitudes, respectively. Based on χ 2 analyses, it is observed that (1) The topology-dependent parameterization scheme is feasible for B → PV decays; (2) At the current accuracy of experimental measurements and theoretical evaluations, X H = X A i is allowed by B → PV decays, but X H ≠ X A f at 68 % C.L.; (3) With the simplification X H = X A i , parameters X A f and X A i should be treated individually. The above-described findings are very similar to those obtained from B → PP decays. Numerically, for B → PV decays, we obtain ( ρ A , H i , ? A , H i [ ° ] ) = ( 2.87 ? 1.95 + 0.66 , ? 145 ? 21 + 14 ) and ( ρ A f , ? A f [ ° ] ) = ( 0.91 ? 0.13 + 0.12 , ? 37 ? 9 + 10 ) at 68 % C.L. With the best-fit values, most of the theoretical results are in good agreement with the experimental data within errors. However, significant corrections to the color-suppressed tree amplitude α 2 related to a large ρ H result in the wrong sign for A CP dir ( B ? → π 0 K ? ? ) compared with the most recent BABAR data, which presents a new obstacle in solving “ ππ ” and “ πK ” puzzles through α 2 . A crosscheck with measurements at Belle (or Belle II) and LHCb, which offer higher precision, is urgently expected to confirm or refute such possible mismatch.