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

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

2005-09-24

arxiv.org/abs/hep-ph/0509271v2

Phys.Rev.D74:034006,2006

Physics

High Energy Physics

High Energy Physics - Phenomenology

24 pages, no figures. Improved discussion on the BLM scheme

Scientific paper

10.1103/PhysRevD.74.034006

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.

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