Sudakov logarithms in B → X s γ in effective field theory

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 → Xsγ near the endpoint of the photon spectrum, x = 2Eγ/mb → 1, as an example. Below the scale μ = mb both soft and collinear degrees of freedom are included in the effective theory, while below the scale μ = mb √ 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. ∗[email protected] †[email protected] ‡[email protected]