We study the branching ratios of the radiative leptonic $B_c$ decays of $B_c^{+}\to l^{+}{\nu }_l\gamma (l=e,\mu ,\tau )$. In our analysis, the form factors for $B_c\to \gamma$ transitions are calculated directly in the entire physical range of momentum transfer within the light front framework. We find that the decay branching ratios of $B_c^{+}\to e^{+}{\nu }_e\gamma ,$ $B_c^{+}\to {\mu }^{+}{\nu }_{\mu }\gamma$, and $B_c^{+}\to {\tau }^{+}{\nu }_{\tau }\gamma$ are $2.0\times {10}^{-5},$ $2.3\times {10}^{-5}$, and $(8.8\mathrm{}-10.7)\times {10}^{-5}$, compared with $1.3\times {10}^{-9},$ $5.6\times {10}^{-5}$, and $1.4\times {10}^{-2}$ for that of $B_c^{+}\to e^{+}{\nu }_e,$ $B_c^{+}\to {\mu }^{+}{\nu }_{\mu },$ and $B_c^{+}\to {\tau }^{+}{\nu }_{\tau },$ respectively.

• Received 14 December 1998

DOI:https://doi.org/10.1103/PhysRevD.59.114002