Fusing Gauge Theory Tree Amplitudes Into Loop Amplitudes

TL;DR

The paper tackles the challenge of efficiently computing one-loop amplitudes for massless gauge theories relevant to perturbative QCD. It identifies a large class of one-loop amplitudes that can be constructed from tree-level amplitudes via unitarity, reducing ambiguities in loop calculations. The authors demonstrate the method with concrete results: one-loop n-gluon amplitudes in N=1 supersymmetric theories with Parke-Taylor helicity configurations and all-helicity configurations for six-gluon scattering in N=4 super-Yang-Mills. They also show how many non-supersymmetric amplitudes can be rearranged to fit the unitarity framework, broadening the method's applicability. This approach promises more efficient, systematic loop amplitude computations for collider phenomenology and theoretical studies.

Abstract

We identify a large class of one-loop amplitudes for massless particles that can be constructed via unitarity from tree amplitudes, without any ambiguities. One-loop amplitudes for massless supersymmetric gauge theories fall into this class; in addition, many non-supersymmetric amplitudes can be rearranged to take advantage of the result. As applications, we construct the one-loop amplitudes for $n$-gluon scattering in $N=1$ supersymmetric theories with the helicity configuration of the Parke-Taylor tree amplitudes, and for six-gluon scattering in $N=4$ super-Yang-Mills theory for all helicity configurations.