Factorization and Sudakov resummation in leptonic radiative B decay — a reappraisal

Abstract

Abstract The B-meson light-cone distribution amplitude is an important non- perturbative quantity arising in the factorization of the amplitudes for many exclusive decays of B mesons, such as B− → γℓ−$$ \overline{\nu} $$ ν ¯ . We reconsider the renormalization-group (RG) equation satisfied by this function and present its solution at next-to-leading order (NLO) in RG-improved perturbation theory in Laplace space and, for the first time, in momentum space and the so-called diagonal (or dual) space. Since the information needed to describe the B decay processes at leading order in ΛQCD/mb is most directly contained in the distribution amplitude in Laplace space evaluated near the origin, we propose a convenient parameterization of this object in terms of a small set of uncorrelated hadronic parameters. Using recent results on the three-loop anomalous dimension for heavy-light current operators, we derive an expression for the convolution integral appearing in the B− → γℓ−$$ \overline{\nu} $$ ν ¯ factorization formula that is explicitly scale independent, and we evaluate this formula at (approximate) NNLO.