Generalized Unitarity and One-Loop Amplitudes in N=4 Super-Yang-Mills

TL;DR

This paper demonstrates how generalized unitarity, specifically quadruple cuts, can efficiently compute one-loop gluon amplitudes in N=4 super-Yang-Mills theory, including complex multi-mass scalar box coefficients.

Contribution

It introduces a method using quadruple cuts in generalized unitarity to directly determine scalar box integral coefficients in N=4 super-Yang-Mills amplitudes.

Findings

Successfully computes coefficients for various scalar box integrals.

Reproduces known coefficients for seven-gluon next-to-MHV amplitudes.

Extends calculations to all multiplicities for certain classes of amplitudes.

Abstract

One-loop amplitudes of gluons in N=4 gauge theory can be written as linear combinations of known scalar box integrals with coefficients that are rational functions. In this paper we show how to use generalized unitarity to basically read off the coefficients. The generalized unitarity cuts we use are quadruple cuts. These can be directly applied to the computation of four-mass scalar integral coefficients, and we explicitly present results in next-to-next-to-MHV amplitudes. For scalar box functions with at least one massless external leg we show that by doing the computation in signature (--++) the coefficients can also be obtained from quadruple cuts, which are not useful in Minkowski signature. As examples, we reproduce the coefficients of some one-, two-, and three-mass scalar box integrals of the seven-gluon next-to-MHV amplitude, and we compute several classes of three-mass and two-mass-hard coefficients of next-to-MHV amplitudes to all multiplicities.