Covariant Light-Front Approach for $B_c$ Decays into Charmonium: Implications on Form Factors and Branching Ratios

In this work, we investigate the form factors of $B_c$ decays into $J\mathrm{/}\mathrm{\Psi },\psi (2S,3S)$, ${\eta }_c,{\eta }_c(2S,3S),{\chi }_{c0},{\chi }_{c1},h_c$ and $X(3872)$ mesons in the covariant light-front quark model (CLFQM). For the purpose of the branching ratio calculation, the form factors of $B_c\to D^{(\ast )},D_s^{(\ast )}$ transitions are also included. In order to obtain the form factors for the physical transition processes, we need extend these form factors from the space-like region to the time-like region. The $q^2$-dependence for each transition form factor is also plotted. Then, under the factorization method, we calculate the branching ratios of 80 $B_c$ decay channels with a charmonium involved in each mode. Most of our predictions are comparable with the results given by most of other approaches. As to the decays with the radially excited state S-wave charmonia, such as $\psi (2S,3S)$ and ${\eta }_c(2S,3S)$, involved, there are two sets of parameters for their light-front wave functions, corresponding to scenario I (SI) and scenario II (SII), are adopted to calculate the branching ratios. Comparing with the future experimental data, one can discriminate which parameters are more favored.