Inclusive spectra in charmless semileptonic B decays by Dressed Gluon Exponentiation

Abstract

The triple differential spectrum in \bar{B} -> X_u l \barν is computed by Dressed Gluon Exponentiation (DGE). In this framework the on-shell calculation, converted into hadronic variables, can be directly used as an approximation to the meson decay spectrum, without involving a leading-power non-perturbative function. Sudakov resummation for the fully differential \bar{B} -> X_u l \barν width is formulated in moment space, where moments are defined using the ratio between the lightcone momentum components of the partonic jet p^+/p^- and the hard scale is p^-. In these variables the correspondence with the \bar{B} -> X_s γcase is transparent. The Sudakov exponent is known to next-to-next-to-leading logarithmic accuracy. Further constraints are put on its Borel sum using the cancellation of the leading renormalon ambiguity and the absence of the next-to-leading one, which was proven in the large-beta_0 limit and assumed here to be general. Based on the resummed spectrum, matched to the fully differential NLO result, we calculate the event fraction associated with experimental cuts on the hadronic mass (or the small lightcone component) as well as on the lepton energy. Finally, we extract |V_ub| from recent measurements by Belle and analyze the theoretical uncertainty.