A Complete Two-Loop, Five-Gluon Helicity Amplitude in Yang-Mills Theory

TL;DR

This paper computes the complete two-loop five-gluon scattering amplitude in pure Yang-Mills theory with all positive helicities, utilizing generalized unitarity cuts and BCJ relations to efficiently derive full-colour results.

Contribution

It introduces a method to obtain the full-colour, two-loop five-gluon amplitude using BCJ relations and unitarity cuts, including non-planar contributions from known planar data.

Findings

Derived the full-colour two-loop five-gluon amplitude

Verified infrared divergence behavior matches expectations

Presented results in terms of irreducible numerators and colour factors

Abstract

We compute the integrand of the full-colour, two-loop, five-gluon scattering amplitude in pure Yang-Mills theory with all helicities positive, using generalized unitarity cuts. Tree-level BCJ relations, satisfied by amplitudes appearing in the cuts, allow us to deduce all the necessary non-planar information for the full-colour amplitude from known planar data. We present our result in terms of irreducible numerators, with colour factors derived from the multi-peripheral colour decomposition. Finally, the leading soft divergences are checked to reproduce the expected infrared behaviour.