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 -> gamma l nu at leading twist. QCD factorization for the B -> gamma* 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 one-loop hard function is identical to the matching coefficient of the QCD weak current (u) over bar gamma(mu perpendicular to) (1 - gamma(5))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 -> gamma l nu, due to the appearance of an additional hard-collinear momentum mode. Furthermore, we evaluate the sub-leading power contribution to the B -> gamma form factors from the three-particle B-meson distribution amplitudes (DAs) at tree level, with the dispersion approach. The soft contribution to the B -> gamma 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 -> gamma form factors will induce an approximately (10 similar to 20)% shift to the tree-level contribution at lambda(B)(mu(0)) = 354 MeV. Albeit of power suppression parametrically, the soft two-particle correction can decrease the leading power predictions for the B -> gamma form factors by an amount of (10 similar to 30)% with the same value of lambda(B) ([10). Employing the phenomenological model of the three-particle B-meson DAs inspired by a QCD sum rule analysis, the three-particle contribution to the B -> gamma form factors is predicted to be of O(1%), at leading order in alpha(s), with the default theory inputs. Finally, we explore theory constraints on the inverse moment of the leading-twist B-meson DA lambda(B) from the recent Belle measurements of the partial branching fractions of B -> gamma lv, taking into account the newly computed contributions to the B -> gamma form factors at subleading power.