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

Abstract

The $B_{u}$ ${\to}$ $ψM$ decays are studied with the perturbative QCD approach, where the psion $ψ$ $=$ $ψ(2S)$, $ψ(3770)$, $ψ(4040)$ and $ψ(4160)$, and the light meson $M$ $=$ $π$, $K$, $ρ$ 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 $B_{u}$ ${\to}$ $ψK$ 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.