Correlated study on some $B_{c}\rightarrow \text{ }P$ and $B_{c}\rightarrow\text{ }S$ wave channels in light of new inputs

This study investigates the decay modes of the $B_c$ meson, focusing on semileptonic and nonleptonic decay into S and P wave charmonia. The primary objective is to extract the shape parameter of the $B_{c}$ meson distribution amplitude through a data-driven approach, utilizing the lattice results on $B_{c}\rightarrow\eta_{c},J/\psi$ semileptonic form factors and yielding an estimate of ${\omega_B}_c = 0.998(34)$ for the same. We use the form factors derived from the modified perturbative QCD framework in the analysis. This result and various other inputs on the radiative decays of the P wave charmonia enable us to estimate the $q^2$ shapes of the $B_{c}\rightarrow\chi_{c0},\chi_{c1}$ and $h_{c}$ form factors using pole expansion parametrization. Using these results, we have obtained predictions of LFUV observables $R(\chi_{c0})=0.169(11)$, $R(\chi_{c1})=0.126(2)$ and $R(h_{c})=0.113(3)$. Finally, we have presented predictions for branching ratios of some nonleptonic decay modes of the $B_{c}$ meson into S and P wave charmonia in the same modified perturbative QCD framework.