Threshold resummed spectra in B ->Xu l nu decays in NLO (III)

Abstract

We resum to next-to-leading order (NLO) the distribution in the light-cone momentum p+ = EX - |pX| and the spectrum in the electron energy, in the semileptonic decays B-> Xu l nu, where EX and pX are the total energy and three-momentum of the final hadron state Xu respectively. By expanding our formulas, we obtain the coefficients of all the infrared logarithms alpha^n L^k at order alpha^2 and at order alpha^3, with the exception of the alpha^3 L coefficient. We explicitly show that the relation between these semileptonic spectra and the hadron mass distribution in the radiative decay B -> Xs gamma is not a purely short distance one. By expanding our result for the p+ distribution and comparing it with the recent O(alpha^2 n_f) computation, we obtain an explicit and non trivial verification of our resummation scheme at the two-loop level. We also discuss the validity of the so-called Brodsky-Lepage-Mackenzie (BLM) scheme in the evaluation of the semileptonic spectra by comparing it with our results, finding that it is a reasonable approximation for the leading terms only. Finally, we show that long-distance phenomena, such as Fermi motion, are expected to have an effect on the electron spectrum smaller than on the hadron mass distribution.

arXiv comment24 pages, no figures. Improved discussion on the BLM scheme

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