Study of $B_{c}$$\to$$ J/\psi V $ and $B_{c}^{*}$$\to$$\eta_{c}V$ decays within the QCD factorization

TL;DR

This paper analyzes non-leptonic $B_c$ and $B_c^*$ decays into $J/a$ or $b$ and vector mesons using QCD factorization, providing predictions for branching ratios and polarization fractions with next-to-leading order corrections.

Contribution

It introduces a comprehensive QCD factorization approach for these decays, including form factor calculations and NLO transverse contributions, with predictions for observables and suggested ratios for experimental testing.

Findings

NLO QCD corrections increase branching ratios by about 8%.

Longitudinal polarization fractions are around 80-90%.

Proposed ratios are suitable for testing theoretical predictions against data.

Abstract

In this paper, we study the non-leptonic $B_{c}\to J/\psi V$ and $B_{c}^{*}\to\eta_{c}V$~$(V=\rho\,,K^{*})$ weak decays in the framework of QCD factorization. In the evaluation, the form factors are calculated by using the Bauer-Stech-Wirbel model and the light-front quark model, respectively. Besides the longitudinal amplitude, the power-suppressed transverse contributions are also evaluated at next-to-leading order. The predictions for the observables of $B_{c}\to J/\psi V$ and $B_{c}^{*}\to\eta_{c}V$ decays are presented. We find that the NLO QCD contribution presents about $ 8\%$ correction to the branching ratios, and the longitudinal polarization fractions of these decays are at the level of $(80\sim90)\%$. In addition, we suggest direct measurements on some useful ratios, $R_{K^{*}/\rho}^{(\lambda=0)}$ and $\widetilde{R}^{(\lambda=0)}_{K^{*}/\rho}$, which are very suitable for test the consistence between theoretical prediction and data because their theoretical uncertainties can be well-controlled.