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 $B_c\to J/ψ$ form factors, we have obtained the $B_c\toη_c$ 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 $\mathcal{B}(B_c^-\to η_c\ell^-\barν)$ (with $\ell =τ, μ(e)$) and the decay rate distributions and have predicted the Standard model estimate for the observable $R(η_c)=Γ(B_c^-\to η_cτ^-\barν)/Γ(B_c^-\to η_cμ^-\barν) =0.310 \pm 0.042$. In addition, we have estimated the radial wave functions $ψ_{B_c}^R(0)$, $ψ_{J/ψ}^R(0)$ and $ψ_{η_c}^R(0)$ at small quark-antiquark distances from the available information on the form factors from lattice, the lattice inputs on the decay constants $f_{J/ψ}$, $f_{η_c}$, $f_{B_c}$ and experimental data on radiative and rare decays of the $J/ψ$ and $η_c$ 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 $B_c \to J/ψ$ or $η_c$ and other light mesons. We have also updated the numerical estimates of the cross sections $σ(e^+e^- \to J/ψη_c, η_cγ)$ and predicted the branching fractions of $Z$ boson decays to either $J/ψ$ or $η_c$ final states or both.