Eur. Phys. J. Plus (2020) 135: 936
https://doi.org/10.1140/epjp/s13360-020-00898-4

Regular Article

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

¹ Department of Physics, Siksha ‘O’ Anusandhan Deemed to be University, Bhubaneswar, 751030, India
² Department of Physics, North Orissa University, Baripada, 757003, India
³ Department of Physics, Utkal University, Bhubaneswar, 751004, India

^* e-mail: patnaiksonali.29@gmail.com

Received: 12 February 2020
Accepted: 29 October 2020
Published online: 25 November 2020

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.