Precision Study of Semileptonic and Non-Leptonic $B_c$ Decays to ${\eta }_c$ and P Wave Charmonia

We analyse semileptonic and non-leptonic decays of the $B_c$ meson into P wave charmonium states. The analytic expressions for the transition form factors are taken from NRQCD, while their normalisations and shapes are constrained directly using experimental data, without introducing any additional model-dependent inputs. Using radiative decay data of ${\chi }_{c0}$, ${\chi }_{c1}$, and $h_c$, we extract the derivatives of their radial wave functions at the origin and update the $B_c\to ({\chi }_{c0},{\chi }_{c1},h_c)$ form factors. We present predictions for the semileptonic branching fractions, the lepton flavour universality ratios $R({\chi }_{c0})=0.185(3)$, $R({\chi }_{c1})=0.147(26)$, and $R(h_c)=0.068(2)$, as well as selected non-leptonic $B_c$ decays and P-wave charmonium production in $e^{+}{e}^{-}$ annihilation and $Z$-boson decays.