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We calculate the differential branching fraction, lepton forward-backwardasymmetry and direct CP asymmetry for $B_{d,s}\to\gamma\ell\bar{\ell}$ decayswith an energetic photon. We employ factorization methods, which result inrigorous next-to-leading order predictions in the strong coupling at leadingpower in the large-energy/heavy-quark expansion, together with estimates ofpower corrections and a resonance parameterization of sub-leading power formfactors in the region of small lepton invariant mass $q^2$. The$B_{d,s}\to\gamma\ell\bar{\ell}$ decay shares features of the charged-currentdecay $B_u \to \gamma\ell\bar\nu_\ell$, and the FCNC decays $B\toK^{(*)}\ell\bar\ell$. As in the former, the leading-power decay rates can beexpressed in terms of the $B$-meson light-cone distribution amplitude andshort-distance factors. However, similar to $B\to K^{(*)}\ell\bar\ell$,four-quark and dipole operators contribute to the$B_{d,s}\to\gamma\ell\bar{\ell}$ decay in an essential way, limiting thecalculation to $q^2\lesssim 6\,$GeV$^2$ below the charmonium resonances in thelepton invariant mass spectrum. A detailed analysis of the main observables andtheoretical uncertainties is presented.

$B_{d,s}\to\gamma\ell\bar{\ell}$ decay with an energetic photon