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Article
Report number	hep-ph/0104020 ; CERN-TH-2001-099
Title	Resummed $B \to X_{u}l\nu$ Decay Distributions to Next-to-Leading Order
Author(s)	Aglietti, U (CERN)
Publication	2001
Imprint	2 Apr 2001
Number of pages	19
In:	Nucl. Phys. B 610 (2001) 293-315
DOI	10.1016/S0550-3213(01)00316-9
Subject category	Particle Physics - Phenomenology
Abstract	We perform factorization of the most general distribution in semileptonic B -> X_u decays and we resum the threshold logarithms to next-to-leading-order. From this (triple-differential) distribution, any other distribution is obtained by integration. As an application of our method, we derive simple analytical expressions for a few distributions, resummed to leading approximation. It is shown that the shape function can be directly determined measuring the distribution in m_X^2/E_X^2, not in m_X^2/m_B^2. We compute the resummed hadron energy spectrum, which has a ``Sudakov shoulder'', and we show how the distribution in the singular region is related to the shape function. We also present an improved formula for the photon spectrum in B->X_s gamma which includes soft-gluon resummation and non-leading operators in the effective hamiltonian. We explicitly show that the same non-perturbative function - namely the shape function - controls the non-perturbative effects in all the distributions in the semi-leptonic and in the rare decay.

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