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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 updatedestimates for various differential distributions (the branching ratios, theforward-backward asymmetry, and $R_{\mu/e}$, the ratio of the differentialdistribution for muons over electrons in the final state). The new ingredientsof 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 bythe vector, axial-vector, tensor and pseudotensor quark currents within therelativistic dispersion approach based on the constituent quark picture; (ii)we perform a detailed analysis of the charm-loop contributions to radiativeleptonic decays: we obtain constraints imposed by the electromagnetic gaugeinvariance and discuss the existing ambiguities in the charmonia contributions.

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