Radiative leptonicBcdecay in the relativistic independent quark model

Abstract

The radiative leptonic decay ${B}_{c}^{\ensuremath{-}}\ensuremath{\rightarrow}{\ensuremath{\mu}}^{\ensuremath{-}}{\overline{\ensuremath{\nu}}}_{\ensuremath{\mu}}\ensuremath{\gamma}$ is analyzed in its leading order in a relativistic independent quark model based on a confining potential in an equally mixed scalar-vector harmonic form. The branching ratio for this decay in the vanishing lepton mass limit is obtained as $\mathcal{B}r({B}_{c}\ensuremath{\rightarrow}\ensuremath{\mu}{\ensuremath{\nu}}_{\ensuremath{\mu}}\ensuremath{\gamma})=6.83\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}5}$, which includes the contributions of the internal bremsstrahlung and structure-dependent diagrams at the level of the quark constituents. The contributions of the bremsstrahlung and the structure-dependent diagrams, as well as their additive interference parts, are compared and found to be of the same order of magnitude. Finally, the predicted photon energy spectrum is observed here to be almost symmetrical about the peak value of the photon energy at ${\stackrel{\texttildelow{}}{E}}_{\ensuremath{\gamma}}\ensuremath{\simeq}\frac{{M}_{{B}_{c}}}{4}$, which may be quite accessible experimentally at LHC in near future.