Rare FCNC radiative leptonic Bs,d→γl+l− decays in the standard model

Abstract

We revisit rare radiative leptonic decays ${B}_{s,d}\ensuremath{\rightarrow}\ensuremath{\gamma}{e}^{+}{e}^{\ensuremath{-}}$ and ${B}_{s,d}\ensuremath{\rightarrow}\ensuremath{\gamma}{\ensuremath{\mu}}^{+}{\ensuremath{\mu}}^{\ensuremath{-}}$ in the standard model and provide the updated estimates for various differential distributions (the branching ratios, the forward-backward asymmetry, and ${R}_{\ensuremath{\mu}/e}$, the ratio of the differential distribution for muons over electrons in the final state). The new ingredients of this work compared to the existing theoretical analyses are the following: (i) we calculate all ${B}_{d}\ensuremath{\rightarrow}\ensuremath{\gamma}$ and ${B}_{s}\ensuremath{\rightarrow}\ensuremath{\gamma}$ form factors induced by the vector, axial-vector, tensor and pseudotensor quark currents within the relativistic dispersion approach based on the constituent quark picture; (ii) we perform a detailed analysis of the charm-loop contributions to radiative leptonic decays: we obtain constraints imposed by electromagnetic gauge invariance and discuss the existing ambiguities in the charmonia contributions.