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

TL;DR

This work advances NNLO QCD in the gluon sector by computing the full-color, two-loop five-gluon amplitudes, a task previously known only in leading color for this process. The authors represent finite remainders as linear combinations of pentagon-function transcendental bases with carefully constructed rational coefficient functions, obtained via analytic reconstruction from finite-field samples and a basis-change that minimizes unphysical poles. They provide a public C++ library for efficient numerical evaluation of the NNLO hard function, along with extensive ancillary files and validation against independent calculations. The methodology promises improved precision for NNLO and potential N3LO applications in di-jet production, and sets the stage for similar full-color treatments in related multi-leg processes.

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.

Figures (2)

• Figure 1: Representative Feynman diagrams for two-loop five-gluon amplitudes. Solid lines represent closed massless quark loops.
• Figure 2: Example of a simple search tree for intersecting null spaces with a global ($\tilde{r}_i$) and a local minimum ($\tilde{\cal N}_{2,1}/({\cal D}_1^2{\cal D}_2)$).