Three-loop gluon scattering in QCD and the gluon Regge trajectory

TL;DR

This paper calculates three-loop gluon scattering amplitudes in QCD, providing key insights into the gluon Regge trajectory, which is essential for high-precision theoretical predictions in particle physics.

Contribution

It presents the first complete three-loop helicity amplitudes for four-gluon scattering in QCD and derives the gluon Regge trajectory at this order.

Findings

Compact expressions in harmonic polylogarithms

Extraction of the three-loop gluon Regge trajectory

Advancement towards NNLL accuracy in Reggeon exchange studies

Abstract

We compute the three-loop helicity amplitudes for the scattering of four gluons in QCD. We employ projectors in the 't Hooft-Veltman scheme and construct the amplitudes from a minimal set of physical building blocks, which allows us to keep the computational complexity under control. We obtain relatively compact results that can be expressed in terms of harmonic polylogarithms. In addition, we consider the Regge limit of our amplitude and extract the gluon Regge trajectory in full three-loop QCD. This is the last missing ingredient required for studying single-Reggeon exchanges at next-to-next-to-leading logarithmic accuracy.