Complete reduction of integrals in two-loop five-light-parton scattering amplitudes

TL;DR

This paper presents a method to reduce complex two-loop five-light-parton scattering integrals to basic master integrals, enabling efficient numerical calculations for advanced QCD predictions at colliders.

Contribution

It introduces a systematic reduction technique and a block-triangular system formulation for multiloop integrals, improving computational efficiency.

Findings

All complex integrals reduced to master integrals

Block-triangular relations facilitate numerical calculations

Method applicable to multiscale integrals in QCD

Abstract

We reduce all the most complicated Feynman integrals in two-loop five-light-parton scattering amplitudes to basic master integrals, while other integrals can be reduced even easier. Our results are expressed as systems of linear relations in the block-triangular form, very efficient for numerical calculations. Our results are crucial for complete next-to-next-to-leading order quantum chromodynamics calculations for three-jet, photon, and/or hadron production at hadron colliders. To determine the block-triangular relations, we develop an efficient and general method, which may provide a practical solution to the bottleneck problem of reducing multiloop multiscale integrals.