Lepton flavor universality violation in semileptonic tree level weak transitions

The recent deviations of the experimental data on some parameters of the tree-level semileptonic $B$ and $B_c$ mesons decays from the standard model (SM) predictions indicate considerable violations of the lepton flavor universality, and as a result possible new physics (NP) effects. To better understand the possible NP effects it is necessary to study deeply the physical quantities defining these decays from many aspects. The calculations of the physical quantities require the determinations of the hadronic form factors entering the matrix elements of the considered transitions as the main inputs. We calculate the form factors governing the tree-level $B_c\rightarrow J/\psi l \nu$ and $B_c \rightarrow \eta_c l \nu$ transitions within the QCD sum rules method. The obtained form factors are used in the calculations of the branching ratios ($BR$s) of the $B_c \rightarrow J/\psi l \nu$ and $B_c \rightarrow \eta_cl \nu$ transitions as well as $R(J/\psi)$ and $R(\eta_c)$. Our result on $R(J/\psi)$ supports the present tension between the SM theory prediction and the experimental data. Our result on $R(\eta_c)$ can be checked in future experiments.