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A bstract 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 )  q   γ  and  B  1 q   →  B   q   γ  ( 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.

Radiative decays of heavy-light mesons and the $$ {f}_{H,{H}^{\ast },{H}_1}^{(T)} $$ decay constants