Leading the non-cancelling IR divergences in massless gauge theories: Abelian case

Abstract

We study the cancellation of both soft and collinear infrared divergences at next-to-leading order correction in a process where a massless electron is scattered off of a static point charge. We show that a self-consistent application of the KLN theorem requires including all initial and final degenerate states, which require including diagrams with an arbitrary number of disconnected photons forming a divergent series. We improve on previous work by rearranging the series in a controlled way and exploit the Monotone Convergence Theorem to prove the uniqueness of our rearranged result. This rearrangement yields a factorization of the infinite contribution from the initial state soft photons, that then cancels in the physically observable cross section.