We present the first analytic $$ \mathcal{O}\left({\alpha}_s\right) $$ O α s -computation at twist-1,2 of the $$ {\overline{B}}_{u,d,s} $$ B ¯ u , d , s → γ form factors within the framework of sum rules on the light-cone. These form factors describe the charged decay $$ {\overline{B}}_u\to \gamma {\mathrm{\ell}}^{-}\overline{v} $$ B ¯ u → γ ℓ − v ¯ , contribute to the flavour changing neutral currents $$ {\overline{B}}_{d,s}\to \gamma {\mathrm{\ell}}^{+}{\mathrm{\ell}}^{-} $$ B ¯ d , s → γ ℓ + ℓ − and serve as inputs to more complicated processes. We provide a fit in terms of a z-expansion with correlation matrix and extrapolate the form factors to the kinematic endpoint by using the gBB*γ couplings as a constraint. Analytic results are available in terms of multiple polylogarithms in the supplementary material. We give binned predictions for the $$ {\overline{B}}_u\to \gamma {\mathrm{\ell}}^{-}\overline{v} $$ B ¯ u → γ ℓ − v ¯ branching ratio along with the associated correlation matrix. By comparing with three SCET-computations we extract the inverse moment B-meson distribution amplitude parameter λB = 360(110) MeV. The uncertainty thereof could be improved by a more dedicated analysis. In passing, we extend the photon distribution amplitude to include quark mass corrections with a prescription for the magnetic vacuum susceptibility, χq, compatible with the twist-expansion. The values χq = 3.21(15) GeV−2 and χs = 3.79(17) GeV−2 are obtained.

The on-shell matrix elements, or couplings $$ {g}_{H{H}^{\ast}\left({H}_1\right)\upgamma} $$ g H H ∗ H 1 γ , describing the $$ B{(D)}_q^{\ast } $$ B D q ∗ → B(D)qγ and B1q → Bqγ (q = u, d, s) radiative decays, are determined from light-cone sum rules at next-to-leading order for the first time. Two different interpolating operators are used for the vector meson, providing additional robustness to our results. For the D*-meson, where some rates are experimentally known, agreement is found. The couplings are of additional interest as they govern the lowest pole residue in the B(D) → γ form factors which in turn are connected to QED-corrections in leptonic decays B(D) → ℓ$$ \overline{\nu} $$ ν ¯ . Since the couplings and residues are related by the decay constants $$ {f}_{H^{\ast}\left({H}_1\right)} $$ f H ∗ H 1 and $$ {f}_{H^{\ast}\left({H}_1\right)}^T $$ f H ∗ H 1 T , we determine them at next-leading order as a by-product. The quantities $$ \left\{{f}_{H^{\ast}}^T,{f}_{H_1}^T\right\} $$ f H ∗ T f H 1 T have not previously been subjected to a QCD sum rule determination. All results are compared with the existing experimental and theoretical literature.