Physics – High Energy Physics – High Energy Physics - Phenomenology
Scientific paper
2001-04-02
Nucl.Phys. B610 (2001) 293-315
Physics
High Energy Physics
High Energy Physics - Phenomenology
LaTex file, 19 pages, 3 postscript figures; minor changes, some typos corrected
Scientific paper
10.1016/S0550-3213(01)00316-9
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 by 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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