Some of semileptonic and nonleptonic decays of $B_c$ meson in a Bethe-Salpeter relativistic quark model

TL;DR

This paper studies semileptonic and nonleptonic $B_c$ meson decays using an improved Bethe-Salpeter model, providing numerical results that align well with experimental data, demonstrating the model's effectiveness.

Contribution

The paper introduces an improved instantaneous Bethe-Salpeter approach to calculate $B_c$ decay widths and branching ratios, comparing favorably with other methods and experimental results.

Findings

Calculated decay widths and branching ratios are consistent with experimental data.

The ratio of specific decay branching ratios agrees with LHCb measurements.

The framework effectively models $B_c$ meson decays in the relativistic quark context.

Abstract

The semileptonic decays $B_c^+\rightarrow P(V) +\ell^++\bar{\nu}_\ell$ and the nonleptonic decays $B_c^+\rightarrow P(V)+L$, where $P(V)$ denotes a pseudoscalar (vector) charmonium or ($\bar{b}s$)-meson, and $L$ denotes a light meson, are studied in the framework of improved instantaneous Bethe-Salpeter (BS) equation and the Mandelstam formula. The numerical results (width and branching ratio of the decays) are presented in tables, and in order to compare conveniently, those obtained by other approaches are also put in the relevant tables. Based on the fact that the ratio $\frac{\mathcal{BR}(B_c^+\rightarrow\psi(2S)\pi^+)}{\mathcal{BR}(B_c^+\rightarrow J/\psi \pi^+)}=0.24^{+0.023}_{-0.040}$ estimated here is in good agreement with the observation by the LHCb $\frac{\mathcal{BR}(B_c^+\rightarrow \psi(2S)\pi^+)}{\mathcal{BR}(B_c^+\rightarrow J/\psi \pi^+)}=0.250\pm0.068(\mathrm{stat})\pm0.014(\mathrm{syst})\pm0.006(\mathcal{B})$, one may conclude that with respect to the decays the present framework works quite well.