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

A bstract 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 Λ QCD /m b 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.

Abstract licence: CC BY

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