Radiative and semi-leptonic B-meson decay spectra: Sudakov resummation beyond logarithmic accuracy and the pole mass

The inclusive spectra of radiative and semi-leptonic B-meson decays near theendpoint is computed taking into account renormalons in the Sudakov exponent(Dressed Gluon Exponentiation). In this framework we demonstrate thefactorization of decay spectra into hard, jet and soft functions and discussthe universality of the latter two. Going beyond perturbation theory the softfunction, which we identify as the longitudinal momentum distribution in anon-shell b quark, is replaced by the b-quark distribution in the B meson. Thetwo differ by power corrections. We show how the resummation ofrunning-coupling effects can be used to perform consistent separation to poweraccuracy between perturbative and non-perturbative contributions. Inparticular, we prove that the leading infrared renormalon ambiguity in theSudakov exponent cancels against the one associated with the definition of thepole mass. This cancellation allows us to identify the non-perturbativeparameter that controls the shift of the perturbative spectrum in theheavy-quark limit as the mass difference between the meson and the quark.Comment: to appear in JHEP; small changes, some refs. added; 36 pages, 2 ps figure