Three-loop helicity amplitudes for four-quark scattering in massless QCD

TL;DR

This paper presents the calculation of three-loop helicity amplitudes for quark-antiquark scattering in massless QCD, providing explicit results and analyzing their infrared divergence structure.

Contribution

It introduces a novel computation of three-loop helicity amplitudes avoiding evanescent structures and expressing results in harmonic polylogarithms.

Findings

Explicit three-loop helicity amplitudes for all relevant channels.

Infrared divergence structure matches theoretical predictions.

Finite remainders are provided for different quark flavor configurations.

Abstract

We compute the three-loop corrections to the helicity amplitudes for $q\bar{q}\to Q\bar{Q}$ scattering in massless QCD. In the Lorentz decomposition of the scattering amplitude we avoid evanescent Lorentz structures and map the corresponding form factors directly to the physical helicity amplitudes. We reduce the amplitudes to master integrals and express them in terms of harmonic polylogarithms. The renormalised amplitudes exhibit infrared divergences of dipole and quadrupole type, as predicted by previous work on the infrared structure of multileg scattering amplitudes. We derive the finite remainders and present explicit results for all relevant partonic channels, both for equal and different quark flavours.