Abstract
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.
B
c
(
B
)→
Dl
tilde nu Form Factors in Light-Cone Sum Rules and the
D
-Meson Distribution Amplitude
