Applications of integrand reduction to two-loop five-point scattering amplitudes in QCD

TL;DR

This work surveys integrand reduction strategies for two-loop, five-point scattering in QCD, focusing on a finite-field based reconstruction of integrands and a transverse decomposition of loop momenta. It presents a concrete parametrisation via irreducible numerators, employs generalized unitarity to determine the integrand, and uses first-order differential equations to obtain master integrals with iterated integrals up to weight four. The authors provide benchmark results for leading-color planar five-parton amplitudes in both Euclidean and physical regions across multiple partonic channels, including comparison to universal IR structures. The study demonstrates substantial progress toward analytic and numerical NNLO predictions for high-multiplicity processes, while acknowledging remaining challenges in fully analytic multi-scale reductions and the need for IBP-driven representations.

Abstract

We review the current state-of-the-art in integrand level reduction for five-point scattering amplitudes at two loops in QCD. We present some benchmark results for the evaluation of the leading colour two-loop five-gluon amplitudes in the physical region as well as the partonic channels for two quarks and three gluons and four quarks and one gluon.