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

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.

Inverse moment of the Bs-meson distribution amplitude from QCD sum rule

We derive a QCD sum rule for the inverse moment of the Bs-meson light-cone distribution amplitude in HQET. Within this method, the SU(3)f l symmetry violation is traced to the strange quark mass and to the difference between strange and nonstrange quark condensate densities. We predict the ratio of inverse moments λBs/λB = 1.19 ± 0.14 which can be used in various applications of these distribution amplitudes to the analyses of Bs-meson decays, provided an accurate value of λB is available from other sources, such as the B → ℓνℓγ decay.