Semileptonic $$B_c$$ meson decays to S-wave charmonium states

Abstract

We study the semileptonic decays of $$B_c$$ meson to S-wave charmonium states in the framework of relativistic independent quark model based on an average flavor-independent confining potential U(r) in the scalar–vector harmonic form $$U(r)=\frac{1}{2}(1+\gamma ^0)(ar^2+V_0)$$ , where (a, $$V_0$$ ) are the potential parameters. The form factors for $$B_c^+\rightarrow \eta _c /\psi e^+\nu _e$$ transitions are studied in the physical kinematic range. Our predicted branching ratios (BR) for transitions to ground-state charmonia are found comparatively large $$\sim $$ $$10^{-2}$$ , compared to those for transitions to radially excited 2S and 3S states. Like all other model predictions, our predicted BR are obtained in the hierarchy: BR( $$B_c^+\rightarrow \eta _c /\psi (3S)$$ ) < BR( $$B_c^+\rightarrow \eta _c/ \psi (2S)$$ ) < BR( $$B_c^+\rightarrow \eta _c /\psi (1S)$$ ). The longitudinal ( $$\varGamma _L$$ ) and transverse ( $$\varGamma _T$$ ) polarization for $$B_c \rightarrow \psi (ns)$$ decay modes is predicted in the small and large $$q^2$$ -region as well as in the whole physical region. Our predicted polarization ratios: $$\frac{\varGamma _L}{\varGamma _T} < 1$$ for $$B_c^+\rightarrow J/\psi e^+\nu _e$$ and $$B_c^+\rightarrow \psi (2S)e^+\nu _e$$ which means these transitions take place predominantly in transverse mode, whereas for $$B_c\rightarrow \psi (3S)e\nu _e$$ , $$\varGamma _L$$ is comparable with $$\varGamma _T$$ in the whole physical region. These theoretical predictions could be tested in the LHCb and the forthcoming Super-B experiments.