Analyzing the semileptonic and nonleptonic $B_c\to J/\psi ,{\eta }_c$ 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.

Comments: 34 Pages, 17 Tables, 6 Figures