Analyzing the semileptonic and nonleptonic $B_c \to J/ψ, η_c$ decays

Abstract: This study focuses on the decay of the $B_c$ meson to S-wave charmonia. Starting with lattice inputs on $B_c\to J/\psi$ form factors, we have obtained the $B_c\to\eta_c$ form factors using heavy quark spin symmetry (HQSS) relations between the associated form factors after parametrizing and extracting the possible symmetry breaking corrections. Using the $q^2$ shapes of these form factors, we have computed the branching fractions $\mathcal{B}(B_c^-\to \eta_c\ell^-\bar{\nu})$ (with $\ell =\tau, \mu (e)$) and the decay rate distributions and have predicted the Standard model estimate for the observable $R(\eta_c)=\Gamma(B_c^-\to \eta_c\tau^-\bar{\nu})/\Gamma(B_c^-\to \eta_c\mu^-\bar{\nu}) =0.310 \pm 0.042$. In addition, we have estimated the radial wave functions $\psi_{B_c}^R(0)$, $\psi_{J/\psi}^R(0)$ and $\psi_{\eta_c}^R(0)$ at small quark-antiquark distances from the available information on the form factors from lattice, the lattice inputs on the decay constants $f_{J/\psi}$, $f_{\eta_c}$, $f_{B_c}$ and experimental data on radiative and rare decays of the $J/\psi$ and $\eta_c$ mesons. To do so, we choose the theory framework of non-relativistic QCD (NRQCD) effective theory. Using our results, we have predicted the branching fractions of a few non-leptonic decays of $B_c \to J/\psi$ or $\eta_c$ and other light mesons. We have also updated the numerical estimates of the cross sections $\sigma(e^+e^- \to J/\psi \eta_c, \eta_c\gamma)$ and predicted the branching fractions of $Z$ boson decays to either $J/\psi$ or $\eta_c$ final states or both.