The seven-gluon amplitude in multi-Regge kinematics beyond leading logarithmic accuracy

TL;DR

This paper develops a comprehensive dispersion integral for the multi-Regge limit of the 2->5 amplitude in planar N=4 super Yang-Mills theory, enabling precise calculations beyond leading logarithmic accuracy at multiple loops.

Contribution

It introduces the NLO correction to the BFKL central emission vertex for the seven-gluon amplitude, extending previous six-gluon results and enabling high-loop order computations.

Findings

Explicit seven-gluon amplitude calculations at NLL accuracy up to 5 loops.

Derivation of the NLO BFKL central emission vertex for N=7.

Validation of the dispersion integral approach in multi-Regge kinematics.

Abstract

We present an all-loop dispersion integral, well-defined to arbitrary logarithmic accuracy, describing the multi-Regge limit of the 2->5 amplitude in planar N=4 super Yang-Mills theory. It follows from factorization, dual conformal symmetry and consistency with soft limits, and specifically holds in the region where the energies of all produced particles have been analytically continued. After promoting the known symbol of the 2-loop N-particle MHV amplitude in this region to a function, we specialize to N=7, and extract from it the next-to-leading order (NLO) correction to the BFKL central emission vertex, namely the building block of the dispersion integral that had not yet appeared in the well-studied six-gluon case. As an application of our results, we explicitly compute the seven-gluon amplitude at next-to-leading logarithmic accuracy through 5 loops for the MHV case, and through 3 and 4 loops for the two independent NMHV helicity configurations, respectively.