Four-particle scattering amplitudes in QCD at NNLO to higher orders in the dimensional regulator

TL;DR

This paper calculates all helicity amplitudes for four-particle massless QCD scattering at NNLO, providing a foundation for future higher-order precision calculations in particle physics.

Contribution

It presents the complete set of four-particle scattering amplitudes in massless QCD at NNLO, including all configurations of quarks and gluons, with results suitable for N$^3$LO computations.

Findings

Amplitudes expressed as Laurent series in dimensional regulator.

Coefficients given in terms of harmonic polylogarithms.

Results applicable in both dimensional regularisation schemes.

Abstract

We compute all helicity amplitudes for four-particle scattering in massless QCD with $n_f$ fermion flavours to next-to-next-to-leading order (NNLO) in perturbation theory. In particular, we consider all possible configurations of external quarks and gluons. We evaluate the amplitudes in terms of a Laurent series in the dimensional regulator to the order required for future next-to-next-to-next-to-leading order (N$^3$LO) calculations. The coefficients of the Laurent series are given in terms of harmonic polylogarithms that can readily be evaluated numerically. We present our findings in the conventional dimensional regularisation and in the t'Hooft-Veltman schemes.