A first look at two-loop five-gluon scattering in QCD

TL;DR

This paper tackles the computation of leading-colour two-loop five-gluon amplitudes in massless QCD, a bottleneck for NNLO predictions of 2→3 processes at the LHC. It combines $d$-dimensional generalized unitarity and integrand reduction with finite-field reconstruction to obtain the integrand for all planar helicity configurations, supported by a momentum-twistor parametrisation to keep rational structure. The authors develop a non-Gröbner-basis integrand basis construction, perform top-down reconstruction, and then evaluate the integrals numerically via sector decomposition with dimension-shifting techniques, achieving agreement with known IR structures and all-plus benchmarks. These results provide the first complete benchmarks for five-point two-loop gluon amplitudes in QCD and lay the groundwork for future IBP reductions to master integrals, advancing NNLO predictions for 2→3 processes at the LHC.

Abstract

We compute the leading colour contributions to five-gluon scattering at two loops in massless QCD. The integrands of all independent helicity amplitudes are evaluated using d-dimensional generalised unitarity cuts and finite field reconstruction techniques. Numerical evaluation of the integral basis is performed with sector decomposition methods to obtain the first benchmark results for all helicity configurations of a 2 to 3 scattering process in QCD.

Figures (3)

• Figure 1: The 18 distinct topologies extractable from (1-loop)${}^2$ cuts.
• Figure 2: 31 distinct topologies extractable from 2-loop cuts.
• Figure 3: The 8 distinct topologies with divergent cuts that must be computed simultaneously with subtopologies