Summing Sudakov logarithms in B -> X_s + gamma in effective field theory

Details Summing Sudakov logarithms in B -> X_s + gamma in effective field theory Summing Sudakov logarithms in B -> X_s + gamma in effective field theory

2000-05-29

arxiv.org/abs/hep-ph/0005275v1

Phys.Rev.D63:014006,2000

Physics

High Energy Physics

High Energy Physics - Phenomenology

23 pages, 11 figures

Scientific paper

10.1103/PhysRevD.63.014006

We construct an effective field theory valid for processes in which highly energetic light-like particles interact with collinear and soft degrees of freedom, using the decay B -> X_s + gamma near the endpoint of the photon spectrum, x = 2 E_gamma / m_b -> 1, as an example. Below the scale mu=m_b both soft and collinear degrees of freedom are included in the effective theory, while below the scale mu=m_b sqrt{x-y}, where 1-y is the lightcone momentum fraction of the b quark in the B meson, we match onto a theory of bilocal operators. We show that at one loop large logarithms cancel in the matching conditions, and that we recover the well known renormalization group equations that sum leading Sudakov logarithms.

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