Rare radiative leptonic decays<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mi>B</mml:mi><mml:mrow><mml:mi>d</mml:mi><mml:mo>,</mml:mo><mml:mi>s</mml:mi></mml:mrow></mml:msub><mml:mo>→</mml:mo><mml:msup><mml:mi>ℓ</mml:mi><mml:mo>+</mml:mo></mml:msup><mml:msup><mml:mi>ℓ</mml:mi><mml:mo>−</mml:mo></mml:msup><mml:mi>γ</mml:mi></mml:math>

Long-distance QCD effects in ${B}_{d,s}\ensuremath{\rightarrow}{\ensuremath{\ell}}^{+}{\ensuremath{\ell}}^{\ensuremath{-}}\ensuremath{\gamma}$ decays are analyzed. We show that the contribution of the light vector-meson resonances related to the virtual photon emission from valence quarks of the $B$-meson, which was not considered in previous analyses, strongly influences the dilepton differential distribution. Taking into account photon emission from the $b$-quark loop, weak annihilation, and Bremsstrahlung from leptons in the final state, we give predictions for dilepton spectrum in ${B}_{d,s}\ensuremath{\rightarrow}{\ensuremath{\ell}}^{+}{\ensuremath{\ell}}^{\ensuremath{-}}\ensuremath{\gamma}$ decays within the Standard Model.

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