$B_{u}$ ${\to}$ ${\psi}M$ decays and $S$-$D$ wave mixing effects

TL;DR

This paper investigates $B_{u}$ decays into various $ ext{psi}$ states and light mesons using perturbative QCD, considering wave mixing effects, and finds that theoretical predictions align with experimental data within current uncertainties.

Contribution

It incorporates $S$-$D$ wave mixing effects into the analysis of $B_{u}$ decays to $ ext{psi}$ states, providing updated branching ratio calculations within the perturbative QCD framework.

Findings

Branching ratios match experimental data within errors.

Large uncertainties prevent constraining $S$-$D$ wave mixing angles.

Theoretical predictions are consistent with observations.

Abstract

The $B_{u}$ ${\to}$ ${\psi}M$ decays are studied with the perturbative QCD approach, where the psion ${\psi}$ $=$ ${\psi}(2S)$, ${\psi}(3770)$, ${\psi}(4040)$ and ${\psi}(4160)$, and the light meson $M$ $=$ ${\pi}$, $K$, ${\rho}$ and $K^{\ast}$. The factorizable and nonfactorizable contributions, and the $S$-$D$ wave mixing effects on the psions are considered in the calculation. With appropriate inputs, the branching ratios for the $B_{u}$ ${\to}$ ${\psi}K$ decays are generally coincident with the experimental data within errors. However, due to the large theoretical and experimental errors, it is impossible for the moment to give a severe constraint on the $S$-$D$ wave mixing angles.