Double-Virtual NNLO QCD Corrections for Five-Parton Scattering: The Gluon Channel

TL;DR

This paper presents the calculation of two-loop five-gluon scattering amplitudes in QCD, including subleading color contributions, with compact analytic expressions and a public code for practical use.

Contribution

It provides the first complete analytic expressions for two-loop five-gluon amplitudes beyond the leading-color approximation, using finite-field methods and a compact rational basis.

Findings

Analytic two-loop five-gluon amplitudes including subleading color terms.

Compact rational coefficient representation of the amplitudes.

Implementation of a public code for numerical evaluations.

Abstract

We compute the two-loop helicity amplitudes for the scattering of five gluons, including all contributions beyond the leading-color approximation. The analytic expressions are represented as linear combinations of transcendental functions with rational coefficients, which we reconstruct from finite-field samples obtained with the numerical unitarity method. Guided by the requirement of removing unphysical singularities, we find a remarkably compact generating set of rational coefficients, which we are able to display entirely in the manuscript. We implement our results in a public code, which provides efficient and reliable numerical evaluations for phenomenological applications.