Charged and neutral B ¯ u , d , s $$ {\overline{B}}_{u,d,s} $$ → γ form factors from light cone sum rules at NLO

Abstract

Abstract We present the first analytic O α s $$ \mathcal{O}\left({\alpha}_s\right) $$ -computation at twist-1,2 of the B ¯ u , d , s $$ {\overline{B}}_{u,d,s} $$ → γ form factors within the framework of sum rules on the light-cone. These form factors describe the charged decay B ¯ u → γ ℓ − v ¯ $$ {\overline{B}}_u\to \gamma {\mathrm{\ell}}^{-}\overline{v} $$ , contribute to the flavour changing neutral currents B ¯ d , s → γ ℓ + ℓ − $$ {\overline{B}}_{d,s}\to \gamma {\mathrm{\ell}}^{+}{\mathrm{\ell}}^{-} $$ 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 in the supplementary material. We give binned predictions for the B ¯ u → γ ℓ − v ¯ $$ {\overline{B}}_u\to \gamma {\mathrm{\ell}}^{-}\overline{v} $$ branching ratio along with the associated correlation matrix. By comparing with three SCET-computations we extract the inverse moment B-meson distribution amplitude parameter λ B = 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, χ q , compatible with the twist-expansion. The values χ q = 3.21(15) GeV −2 and χ s = 3.79(17) GeV −2 are obtained.

Keywords

• Heavy Quark Physics
• Perturbative QCD