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

Abstract

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

arXiv commentversion accepted by PRD

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• Estimates of the isospin-violating ${\Lambda }_b\to {\Sigma }^0\varphi ,{\Sigma }^{0}J/\psi$ decays and the $\Sigma -\Lambda$ mixing
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