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

TL;DR

This work tackles the bottleneck of reducing multiloop multiscale Feynman integrals in two-loop, five-light-parton amplitudes by developing a two-step strategy that yields block-triangular systems relating all integrals to a small set of master integrals. The authors explicitly construct block-triangular relations for four topologies, containing thousands of integrals that reduce to 108 master integrals within ~148 MB of data, enabling rapid numerical evaluation across phase space. Compared with explicit IBP solutions or trimmed IBP methods, this approach offers order-of-magnitude improvements in efficiency and is poised to enable complete NNLO QCD predictions for multi-jet and photon/hadron production at the LHC. The method is general and extensible to other processes, potentially tackling further two-loop multiscale problems such as tt̄+jet or multi-jet production.

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.

Figures (2)

• Figure 1: All 8-propagator families: (a) double-pentagon; (b) hexa-box; (c) penta-box; (d) hexa-triangle.
• Figure 2: Matrix density plot for relations of topology (a). Each row represents a relation and each column represents an integral. Black points represent nonzero elements.