Probing Spectator Scattering and Annihilation Corrections in $B_{s}$ $\to$ $PV$ Decays

Abstract

Motivated by the recent LHCb measurements on $\bar{B}_{s}$ $\to$ $\pi^{-}K^{*+}$ and $\bar{B}_{s}$ $\to$ $K^{\pm}K^{*\mp}$ 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 $\chi^2$-fit on the end-point parameters $X_A^{i,f}$ ($\rho_A^{i,f}$, $\phi_A^{i,f}$) and $X_H$ ($\rho_H$, $\phi_H$) 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 $\bar{B}_{s}$ ${\to}$ $\pi K^{\ast}$, $\rho K$, $\pi\rho$, $\pi\phi$ and $K\phi$ decay modes are presented. In addition, we have identified a few useful observables, especially the ones of $\bar{B}_{s}$ $\to$ $\pi^{0}\phi$ decay for instance, for probing hard-spectator scattering and annihilation contributions.