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

TL;DR

This paper uses the covariant light-front quark model to calculate form factors and branching ratios for various $B_c$ decays into charmonium states, providing predictions that can be tested against future experiments.

Contribution

It extends the covariant light-front quark model to include $B_c$ decays into multiple charmonium states and calculates branching ratios for 80 decay channels, comparing different parameter scenarios.

Findings

Predicted branching ratios are mostly consistent with other approaches.

Two parameter scenarios for radially excited charmonia are analyzed.

Results can help discriminate between different model parameters with future data.

Abstract

In this work, we investigate the form factors of $B_c$ decays into $J/\Psi, \psi(2S,3S)$, $\eta_c, \eta_c(2S,3S), \chi_{c0}, \chi_{c1}, h_c$ and $X(3872)$ mesons in the covariant light-front quark model (CLFQM). For the purpose of the branching ratio calculation, the form factors of $B_c\to D^{(*)}, D^{(*)}_s$ 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.