Probing Spectator Scattering and Annihilation Corrections in $B_s$ $\to$ $PV$ Decays

Abstract

Motivated by the recent LHCb measurements on ${\bar{B}}_s$ $\to$ $\ddot{I}{€}^{-}{K}^{\ast +}$ and ${\bar{B}}_s$ $\to$ $K^{\pm }{K}^{\ast \mp }$ decay modes, we revisit the $B_s$ $\to$ $PV$ decays within QCD factorization framework. The effects of hard-spectator scattering and annihilation corrections are studied in detail. After performing a $\ddot{I}{‡}^2$-fit on the end-point parameters $X_A^{i,f}$ ($\ddot{I}{}_A^{i,f}$, $\ddot{I}{•}_A^{i,f}$) and $X_H$ ($\ddot{I}{}_H$, $\ddot{I}{•}_H$) with available data, it is found that although some possible mismatches exist, the universalities of $X_A^{i,f}$ and $X_H$ in $B_s$ and $B_{u,d}$ systems are still allowed within theoretical uncertainties and experimental errors. With the end-point parameters gotten from $B_{u,d}$ $\to$ $PV$ decays, the numerical results and detailed analyses for the observables of ${\bar{B}}_s$ $\to$ $\ddot{I}€K^{\ast }$, $\ddot{I}K$, $\ddot{I}€\ddot{I}$, $\ddot{I}€\ddot{I}•$ and $K\ddot{I}•$ decay modes are presented. In addition, we have identified a few useful observables, especially the ones of ${\bar{B}}_s$ $\to$ $\ddot{I}{€}^0\ddot{I}•$ decay for instance, for probing hard-spectator scattering and annihilation contributions.

version accepted by PRD