Constraints on hard spectator scattering and annihilation corrections in $B_{u,d}$ $\to$ $PV$ decays within QCD factorization

Abstract

In this paper, we investigate the contributions of hard spectator scattering and annihilation in $B\to PV$ decays within the QCD factorization framework. With available experimental data on $B\to \ddot{I}€K^{\ast }$, $\ddot{I}K$, $\ddot{I}€\ddot{I}$ and $K\ddot{I}•$ decays, comprehensive $\ddot{I}{‡}^2$ analyses of the parameters $X_{A,H}^{i,f}(\ddot{I}{}_{A,H}^{i,f},\ddot{I}{•}_{A,H}^{i,f})$ 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 $\ddot{I}{‡}^2$ analyses, it is observed that (1) The topology-dependent parameterization scheme is feasible for $B\to PV$ decays; (2) At the current accuracy of experimental measurements and theoretical evaluations, $X_H=X_A^i$ is allowed by $B\to PV$ decays, but $X_H\ne X_A^f$ 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 $B\to PP$ decays. Numerically, for $B\to PV$ decays, we obtain $(\ddot{I}{}_{A,H}^i,\ddot{I}{•}_{A,H}^i{[}^{\circ }])=(2.87_{-1.95}^{+0.66},-145_{-21}^{+14})$ and $(\ddot{I}{}_A^f,\ddot{I}{•}_A^f{[}^{\circ }])=(0.91_{-0.13}^{+0.12},-37_{-9}^{+10})$ 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 $\hat{I}{\pm }_2$ related to a large $\ddot{I}{}_H$ result in the wrong sign for $A_{CP}^{dir}(B^{-}\to \ddot{I}{€}^0{K}^{\ast -})$ compared with the most recent BABAR data, which presents a new obstacle in solving "$\ddot{I}€\ddot{I}€$" and "$\ddot{I}€K$" puzzles through $\hat{I}{\pm }_2$. 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.

17 pages, 4 figures; Accepted for publication in PLB