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

Abstract

Motivated by the recent LHCb measurements on $\bar{B}_{s}$ $\to$ $π^{-}K^{*+}$ 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 $χ^2$-fit on the end-point parameters $X_A^{i,f}$ ($ρ_A^{i,f}$, $ϕ_A^{i,f}$) and $X_H$ ($ρ_H$, $ϕ_H$) 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 $\bar{B}_{s}$ ${\to}$ $πK^{\ast}$, $ρK$, $πρ$, $πϕ$ and $Kϕ$ decay modes are presented. In addition, we have identified a few useful observables, especially the ones of $\bar{B}_{s}$ $\to$ $π^{0}ϕ$ decay for instance, for probing hard-spectator scattering and annihilation contributions.