Radiative Leptonic Decays of $B_c$ Meson

To the leading order, the radiative leptonic decays $B_c \to \gamma \ell \bar \nu$($ \ell=e, \mu$) are studied carefully. In the study, a non-relativistic constituent quark model and the effective Lagrangian for the heavy flavour decays are used. As a result, the branching ratios turn out to be of the orders of ${10}^{-5}$ for $B_c\to \gamma \mu \bar{\nu }$ or for $B_c \to \gamma e \bar \nu $. Based on this study, we point out the decays being accessible experimentally at the future LHC, and the possibility to determine the decay constant $f_{B_c}$ through the radiative decays.