Iterated amplitudes in the high-energy limit

TL;DR

This paper investigates the high-energy behavior of gluon scattering amplitudes in maximally supersymmetric QCD, revealing an iterative structure that confirms the BDS ansatz in certain kinematic regimes and identifying conditions where deviations may occur.

Contribution

It demonstrates an iterative structure in gluon amplitudes that supports the BDS ansatz in multi-Regge kinematics and explores the limits of its applicability.

Findings

BDS ansatz holds for two- and three-loop amplitudes in specific kinematics.

Iterative structure similar to BDS ansatz found in Regge factorization components.

Deviations from BDS are expected in more general kinematic configurations.

Abstract

We consider the high-energy limits of the colour ordered four-, five- and six-gluon MHV amplitudes of the maximally supersymmetric QCD in the multi-Regge kinematics where all the gluons are strongly ordered in rapidity. We show that various building blocks occurring in the Regge factorisation (the Regge trajectory, the coefficient functions and the Lipatov vertex) satisfy an iterative structure very similar to the Bern-Dixon-Smirnov (BDS) ansatz. This iterative structure, combined with the universality of the building blocks, enables us to show that in the Euclidean region any two- and three-loop amplitude in multi-Regge kinematics is guaranteed to satisfy the BDS ansatz. We also consider slightly more general kinematics where the strong rapidity ordering applies to all the gluons except the two with either the largest or smallest rapidities, and we derive the iterative formula for the associated coefficient function. We show that in this kinematic limit the BDS ansatz is also satisfied. Finally, we argue that only for more general kinematics - e.g. with three gluons having similar rapidities, or where the two central gluons have similar rapidities - can a disagreement with the BDS ansatz arise.