Factorization in one-loop gauge theory

Abstract

Factorization properties of one-loop gauge theory amplitudes have been used as checks on explicitly computed amplitudes and in the construction of ansätze for higher-point ones. In massless theories, such as QCD at high energies, infrared divergences complicate factorization. Here we prove that factorization in such theories is described by a set of universal functions. In particular, a proof of the universality of one-loop splitting functions as the momenta of two particles become collinear is presented. Factorization in multi-particle channels is also given. The discontinuity functions that appear in the splitting functions may also be used to obtain infrared divergent box integral functions from finite ones.