On the Decay Mode $B^- \to \mu^- \bar \nu_\mu \gamma$

A QCD relativistic potential model is employed to compute the decay rate and the photon spectrum of the process $B^- \to \mu^- {\bar \nu}_\mu \gamma$. The result ${\cal B}(B^- \to \mu^- {\bar \nu}_\mu \gamma) \simeq 1 \times 10^{-6}$ confirms the enhancement of this decay channel with respect to the purely leptonic mode, and supports the proposal of using this process to access relevant hadronic quantities such as the $B$-meson leptonic decay constant and the CKM matrix element $V_{ub}$.