Analytic helicity amplitudes for two-loop five-gluon scattering: the single-minus case

TL;DR

This work addresses the challenge of computing the leading-color two-loop five-gluon amplitude in pure Yang–Mills with a single negative helicity by reconstructing an analytic finite remainder from finite-field evaluations. The authors combine integrand reduction, integration-by-parts identities, and a basis of pentagon functions, evaluated through six-dimensional generalized unitarity cuts, and reconstruct the full analytic result for the finite part. They present a compact, symmetry-aware representation in terms of weight-two polylogarithms, and provide explicit coefficient structures for the $(d_s-2)$ and $(d_s-2)^2$ components, demonstrating a manageable final form despite a complex master-integral basis. The methodology is helicity-agnostic and broadly applicable to other planar and potentially non-planar amplitudes, offering a path toward analytic expressions at two loops in multi-leg QCD processes.

Abstract

We present a compact analytic expression for the leading colour two-loop five-gluon amplitude in Yang-Mills theory with a single negative helicity and four positive helicities. The analytic result is reconstructed from numerical evaluations over finite fields. The numerical method combines integrand reduction, integration-by-parts identities and Laurent expansion into a basis of pentagon functions to compute the coefficients directly from six-dimensional generalised unitarity cuts.

Figures (2)

• Figure 1: Two-loop five-point master topologies. All external momenta are considered out-going, arrows indicate loop momenta directions.
• Figure 2: All distinct two-loop five-point topologies.