Factorization in One-Loop Gauge Theory

TL;DR

The paper addresses factorization of one-loop gauge-theory amplitudes in massless theories, where infrared divergences pose challenges. It proves that factorization is governed by universal functions, including universal one-loop splitting functions in the collinear limit, and extends this to multi-particle channels. It further shows that discontinuity functions inherent to the splitting functions allow construction of infrared-divergent box integrals from finite ones. These results provide robust checks for computed amplitudes and aid in building ansätze for higher-point amplitudes in QCD and related theories.

Abstract

Factorization properties of one-loop gauge theory amplitudes have been used as checks on explicitly computed amplitudes and in the construction of ansatze 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.