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

摘要

The semileptonic decays $B_c^+\rightarrow P(V) +\ell^++\bar{\nu}_\ell$ andthe nonleptonic decays $B_c^+\rightarrow P(V)+L$, where $P(V)$ denotes apseudoscalar (vector) charmonium or ($\bar{b}s$)-meson, and $L$ denotes a lightmeson, are studied in the framework of improved instantaneous Bethe-Salpeter(BS) equation and the Mandelstam formula. The numerical results (width andbranching ratio of the decays) are presented in tables, and in order to compareconveniently, those obtained by other approaches are also put in the relevanttables. Based on the fact that the ratio$\frac{\mathcal{BR}(B_c^+\rightarrow\psi(2S)\pi^+)}{\mathcal{BR}(B_c^+\rightarrowJ/\psi \pi^+)}=0.24^{+0.023}_{-0.040}$ estimated here is in good agreement withthe 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 worksquite well.