Full Colour for Loop Amplitudes in Yang-Mills Theory

TL;DR

The paper introduces a comprehensive method for incorporating full colour dependence in Yang-Mills loop amplitudes, enhancing the precision of multi-loop calculations and their symmetry properties.

Contribution

It presents a novel technique for maintaining colour structures in loop integrand reductions, applicable to multi-loop Yang-Mills amplitudes, including supersymmetric cases.

Findings

Applied to two-loop five-gluon amplitude with positive helicities.

Connected the method to loop-level Kleiss-Kuijf relations.

Explored implications for symmetry factor cancellations at two loops.

Abstract

We present a general method to account for full colour dependence Yang-Mills amplitudes at loop level. The method fits most naturally into the framework of multi-loop integrand reduction and in a nutshell amounts to consistently retaining the colour structures of the unitarity cuts from which the integrand is gradually constructed. This technique has already been used in the recent calculation of the two-loop five-gluon amplitude in pure Yang-Mills theory with all positive helicities, arXiv:1507.08797. In this note, we give a careful exposition of the method and discuss its connection to loop-level Kleiss-Kuijf relations. We also explore its implications for cancellation of nontrivial symmetry factors at two loops. As an example of its generality, we show how it applies to the three-loop case in supersymmetric Yang-Mills case.