The five-gluon amplitude in the high-energy limit

TL;DR

This work computes the colour-stripped one-loop five-gluon amplitude in planar N=4 SYM in multi-Regge kinematics using the one-loop pentagon in $D=6-2\epsilon$ to all orders in $\epsilon$ up to $O(\epsilon^2)$. By exploiting high-energy factorisation, it extracts the one-loop Lipatov (gluon-production) vertex to the same accuracy and, leveraging the BDS iterative structure, achieves the first computation of the two-loop Lipatov vertex including finite terms. The results are presented in both Euclidean MRK and the physical region, with detailed analytic continuations of parity-even and parity-odd components and all relevant master integrals. These vertices are essential building blocks for potential NNLL BFKL kernels and provide a stringent test of Regge factorisation in $\mathcal{N}=4$ SYM.

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.

Figures (1)

• Figure 1: Five-point amplitude in the multi-Regge kinematics. The green blobs indicate the coefficient functions (impact factors) and the vertex describing the emission of gluons along the ladder.