Doubly-charged scalar in rare decays of $B_c$ meson

In this paper, we study the lepton number violation processes of $B_c$ meson induced by possible doubly-charged scalars. Both the three-body decay channels and the four-body decay channels are considered. For the former, $Br\times\left(\frac{s_\Delta h_{ij}}{M_\Delta^2}\right)^{-2}$ is of the order of $10^{-7}\sim 10^{-9}$, and for the later channels, $Br\times\left(\frac{s_\Delta h_{ij}}{M_\Delta^2}\right)^{-2}$ is of the order of $10^{-12}\sim 10^{-20}$, where $s_\Delta$, $h_{ij}$, $M_\Delta$ are the constants related to the doubly-charged boson.