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Charged and Neutral $\bar B_{u,d,s} \to γ$ Form Factors from Light Cone Sum Rules at NLO

We present the first analytic ${\cal O}(α_s)$-computation at twist-$1$,$2$ of the $\bar B_{u,d,s} \to γ$ form factors within the framework of sum rules on the light-cone. These form factors describe the charged decay $\bar B_u \to γ\ell^- \barν$, contribute to the flavour changing neutral currents $\bar B_{d,s} \to γ\ell^+ \ell^-$ 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 $g_{BB^*γ}$ couplings as a constraint. Analytic results are available in terms of multiple polylogarithms as ancillary files. We give binned predictions for the $\bar B_u \to γ\ell^- \barν$ branching ratio along with the associated correlation matrix. By comparing with three SCET-computations we extract the inverse moment $B$-meson distribution amplitude parameter $λ_B = 360 (110) \text{MeV}$. 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, $χ_q$, compatible with the twist-expansion. The values $χ_q = 3.21 (15) \text{GeV}^{-2}$ and $χ_s = 3.79 (17) \text{GeV}^{-2}$ are obtained.