Summing Sudakov logarithms in [Formula Presented] 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 (Formula presented) near the end point of the photon spectrum, (Formula presented) as an example. Below the scale (Formula presented) both soft and collinear degrees of freedom are included in the effective theory, while below the scale (Formula presented) where (Formula presented) is the light cone 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.