High-energy limit of $2\to 2$ scattering amplitudes at NNLL

TL;DR

This paper analyzes the high-energy behavior of 2-to-2 scattering amplitudes at NNLL accuracy, revealing the interplay of Regge poles and cuts through four-loop calculations, advancing understanding of gauge theory universality.

Contribution

It provides the first explicit four-loop computation of Regge cuts at NNLL, distinguishing between Regge pole and cut contributions in high-energy scattering amplitudes.

Findings

Regge pole involves gluon Regge trajectory and impact factors.

Regge cut contribution at four loops is nonplanar.

Trajectory singularities match cusp anomalous dimension.

Abstract

The high-energy limit of $2\to 2$ scattering amplitudes offers an excellent setting to explore the universal features of gauge theories. At Leading Logarithmic (LL) accuracy the partonic amplitude is governed by Regge poles in the complex angular momentum plane. Beyond LL, Regge cuts in this plane begin to play an important role. Specifically, the real part of the amplitude at Next-to-Next-to-Leading Logarithmic (NNLL) accuracy presents for the first time both a Regge pole and a Regge cut. Analysing this tower of logarithms and computing it explicitly through four loops we are able to systematically separate between the Regge pole and the Regge cut. The former involves two fundamental parameters, namely the gluon Regge trajectory and impact factors. We explain how to consistently define the impact factors at two loops and the Regge trajectory at three loops. We confirm that the singularities of the trajectory are given by the cusp anomalous dimension. We also show that the Regge-cut contribution at four loop is nonplanar.