Probing spectator scattering and annihilation corrections inBs→PVdecays

Abstract

Motivated by the recent LHCb measurements on ${\overline{B}}_{s}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{\ensuremath{-}}{K}^{*+}$ and ${\overline{B}}_{s}\ensuremath{\rightarrow}{K}^{\ifmmode\pm\else\textpm\fi{}}{K}^{*\ensuremath{\mp}}$ decay modes, we revisit the ${B}_{s}\ensuremath{\rightarrow}PV$ decays within QCD factorization framework. The effects of hard-spectator scattering and annihilation corrections are studied in detail. After performing a ${\ensuremath{\chi}}^{2}$-fit on the end-point parameters ${X}_{A}^{i,f}({\ensuremath{\rho}}_{A}^{i,f},{\ensuremath{\phi}}_{A}^{i,f})$ and ${X}_{H}({\ensuremath{\rho}}_{H},{\ensuremath{\phi}}_{H})$ 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 obtained from ${B}_{u,d}\ensuremath{\rightarrow}PV$ decays, the numerical results and detailed analyses for the observables of ${\overline{B}}_{s}\ensuremath{\rightarrow}\ensuremath{\pi}{K}^{*}$, $\ensuremath{\rho}K$, $\ensuremath{\pi}\ensuremath{\rho}$, $\ensuremath{\pi}\ensuremath{\phi}$, and $K\ensuremath{\phi}$ decay modes are presented. In addition, we have identified a few useful observables, especially the ones of ${\overline{B}}_{s}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{0}\ensuremath{\phi}$ decay for instance, for probing hard-spectator scattering and annihilation contributions.