Rare FCNC radiative leptonic $B_{s,d}\to \gamma l^+l^-$ decays in the Standard Model

Abstract

We revisit rare radiative leptonic decays $B_{s,d}\to \gamma e^+e^-$ and $B_{s,d}\to \gamma \mu^+\mu^-$ in the Standard Model and provide the updated estimates for various differential distributions (the branching ratios, the forward-backward asymmetry, and $R_{\mu/e}$, 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 $B_d\to\gamma$ and $B_s\to\gamma$ 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 the electromagnetic gauge invariance and discuss the existing ambiguities in the charmonia contributions.