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

TL;DR

This paper investigates $B_s$ to $PV$ decays within QCD factorization, focusing on hard-spectator scattering and annihilation effects, fitting parameters to recent LHCb data, and identifying key observables for probing these contributions.

Contribution

It provides a detailed analysis of spectator scattering and annihilation corrections in $B_s$ decays, using a $ ext{chi}^2$ fit to experimental data to constrain theoretical parameters.

Findings

Universalities of end-point parameters are consistent within uncertainties.

Numerical predictions for various decay modes are provided.

Certain observables are identified as probes for scattering and annihilation effects.

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.