This study focuses on the decay of the Bc meson to S-wave charmonia. Starting with lattice inputs on Bc → J/ψ form factors, we have obtained the Bc → ηc 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 q2 shapes of these form factors, we have computed the branching fractions \( \mathcal{B} \) ( \( {B}_c^{-} \) → ηcℓ− \( \overline{\nu} \) ) (with ℓ = τ, μ(e)) and the decay rate distributions and have predicted the Standard model estimate for the observable R(ηc) = Γ( \( {B}_c^{-} \) → ηcτ− \( \overline{\nu} \) )/Γ( \( {B}_c^{-} \) → ηcμ− \( \overline{\nu} \) ) = 0.310 ± 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 Bc J/ψ ηc quark-antiquark distances from the available information on the form factors from lattice, the lattice inputs on the decay constants fJ/ψ, \( {f}_{\eta_c} \) , \( {f}_{B_c} \) and experimental data on radiative and rare decays of the J/ψ and ηc 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 Bc → J/ψ or ηc and other light mesons. We have also updated the numerical estimates of the cross sections σ(e+e− → J/ψηc, ηcγ) and predicted the branching fractions of Z boson decays to either J/ψ or ηc final states or both.
