Analysis of molecular state ${{\eta}_cD^*}$ and ${J/\psi D^*}$ in the effective Lagrangian approach

In this work, we investigate the production and decay of the molecular states $cc\bar c\bar q$ with $J^P=1^+$ using the phenomenological analysis and effective Lagrangian approach. Based on an SU(3) flavor symmetry analysis to identify golden channels, we further explore the dynamics of these processes under the molecular assumptions of ${\eta_c D^*}$ and ${J/\psi D^*}$. Our results indicate that the production branching ratio from $B_c$ meson is sizable, it can reach the order of $10^{-4}$ for the molecular configuration ${{\eta}_cD^*}$, and $10^{-5}$ for molecule ${J/\psi D^*}$. In addition, we find that the decay widths of the two molecular configurations ${{\eta}_cD^*}$ and ${J/\psi D^*}$ are not significant, being at level of $\cal{O}$($\rm {MeV}$).