The five-gluon amplitude in the high-energy limit

TL;DR

This paper analyzes the high-energy limit of the one-loop five-gluon amplitude in N=4 super Yang-Mills theory, deriving new results for gluon-production vertices at one and two loops using advanced factorization and iterative techniques.

Contribution

It provides the first computation of the two-loop gluon-production vertex including finite terms in the high-energy limit of N=4 SYM theory.

Findings

Computed the one-loop five-gluon amplitude to O(eps^2)

Extracted the one-loop gluon-production vertex at high energy

Performed the first two-loop gluon-production vertex calculation including finite terms

Abstract

We consider the high energy limit of the colour ordered one-loop five-gluon amplitude in the planar maximally supersymmetric N=4 Yang-Mills theory in the multi-Regge kinematics where all of the gluons are strongly ordered in rapidity. We apply the calculation of the one-loop pentagon in D=6-2 eps performed in a companion paper to compute the one-loop five-gluon amplitude through to O(eps^2). Using the factorisation properties of the amplitude in the high-energy limit, we extract the one-loop gluon-production vertex to the same accuracy, and, by exploiting the iterative structure of the gluon-production vertex implied by the BDS ansatz, we perform the first computation of the two-loop gluon-production vertex up to and including finite terms.