Factorization and dispersion relations for radiative leptonic B decay

Applying the dispersion approach we compute perturbative QCD corrections to the power suppressed soft contribution of B → γ`ν at leading twist. QCD factorization for the B → γ∗ form factors is demonstrated explicitly for the hard-collinear transverse polarized photon at one loop, with the aid of the method of regions. While the oneloop hard function is identical to the matching coefficient of the QCD weak current ū γμ⊥ (1−γ5) b in soft-collinear effective theory, the jet function from integrating out the hard-collinear fluctuations differs from the corresponding one entering the factorization formula of B → γ`ν, due to the appearance of an additional hard-collinear momentum mode. Furthermore, we evaluate the sub-leading power contribution to the B → γ form factors from the three-particle B-meson distribution amplitudes (DAs) at tree level, with the dispersion approach. The soft contribution to the B → γ form factors from the three-particle B-meson DAs is shown to be of the same power compared with the corresponding hard correction, in contrast to the two-particle counterparts. Numerically the next-to-leading-order QCD correction to the soft two-particle contribution in B → γ form factors will induce an approximately (10 ∼ 20)% shift to the tree-level contribution at λB(μ0) = 354 MeV. Albeit of power suppression parametrically, the soft two-particle correction can decrease the leading power predictions for the B → γ form factors by an amount of (10 ∼ 30)% with the same value of λB(μ0). Employing the phenomenological model of the three-particle B-meson DAs inspired by a QCD sum rule analysis, the threeparticle contribution to the B → γ form factors is predicted to be of O(1%), at leading order in αs, with the default theory inputs. Finally, we explore theory constraints on the inverse moment of the leading-twist B-meson DA λB from the recent Belle measurements of the partial branching fractions of B → γ`ν, taking into account the newly computed contributions to the B → γ form factors at subleading power. ar X iv :1 60 6. 03 08 0v 1 [ he pph ] 9 J un 2 01 6