One-Loop Gluon Scattering Amplitudes in Theories with $N < 4$ Supersymmetries

TL;DR

This paper employs unitarity methods to compute one-loop gluon scattering amplitudes in gauge theories with less than four supersymmetries, revealing inherited constraints and providing explicit amplitude expressions.

Contribution

It extends unitarity techniques to N<4 supersymmetric theories, showing box coefficients follow N=4 constraints and calculating explicit one-loop amplitudes.

Findings

Box coefficients in N=1 and N=0 theories follow N=4 constraints.

Triple cuts determine triangle integral coefficients.

Explicit one-loop amplitude for N=1 with specific helicities provided.

Abstract

Generalised unitarity techniques are used to calculate the coefficients of box and triangle integral functions of one-loop gluon scattering amplitudes in gauge theories with $N < 4$ supersymmetries. We show that the box coefficients in N=1 and N=0 theories inherit the same coplanar and collinear constraints as the corresponding N=4 coefficients. We use triple cuts to determine the coefficients of the triangle integral functions and present, as an example, the full expression for the one-loop amplitude $A^{N=1}(1^-,2^-,3^-,4^+,..,n^+)$.