Toward a NNLO calculation of the B-->X_s gamma decay rate with a cut on photon energy: I. Two-loop result for the soft function

Details Toward a NNLO calculation of the B-->X_s gamma decay rate with a cut on photon energy: I. Two-loop result for the soft function Toward a NNLO calculation of the B-->X_s gamma decay rate with a cut on photon energy: I. Two-loop result for the soft function

2005-12-15

arxiv.org/abs/hep-ph/0512208v1

Phys.Lett.B633:739-747,2006

Physics

High Energy Physics

High Energy Physics - Phenomenology

13 pages, 2 figures

Scientific paper

10.1016/j.physletb.2006.01.006

A theoretical analysis of the partial inclusive B-->X_s gamma decay rate with a cut E_gamma>E_0 on photon energy must deal with short-distance contributions associated with three different mass scales: the hard scale m_b, an intermediate scale \sqrt{m_b Delta}, and a soft scale Delta, where Delta=m_b-2E_0=1GeV for E_0=1.8GeV. The cut-dependent effects are described in terms of two perturbative objects called the jet function and the soft function, which for a next-to-next-to-leading order analysis of the decay rate are required with two-loop accuracy. The two-loop calculation of the soft function is presented here, while that of the jet function will be described in a subsequent paper. As a by-product, we rederive the two-loop anomalous-dimension kernel of the B-meson shape function.

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