MHV amplitude for 3->3 gluon scattering in Regge limit

TL;DR

This paper computes two-loop corrections to the six-particle MHV amplitude in gluon scattering within the multi-Regge kinematics, extending the BDS formula and providing predictions for all-loop behavior.

Contribution

It introduces an analytic continuation approach to evaluate the remainder function beyond the Regge pole approximation, including real and imaginary parts, and predicts the all-loop real part of the amplitude.

Findings

Two-loop remainder function matches BFKL predictions.

Analytic continuation yields both real and imaginary contributions.

Prediction for the all-loop real part multiplied by the BDS phase.

Abstract

We calculate corrections to the BDS formula for the six-particle planar MHV amplitude for the gluon transition 3->3 in the multi-Regge kinematics for the physical region, in which the Regge pole ansatz is not valid. The remainder function at two loops is obtained by an analytic continuation of the expression derived by Goncharov, Spradlin, Vergu and Volovich to the kinematic region described by the Mandelstam singularity exchange in the crossing channel. It contains both the imaginary and real contributions being in agreement with the BFKL predictions. The real part of the three loop expression is found from a dispersion-like all-loop formula for the remainder function in the multi-Regge kinematics derived by one of the authors. We also make a prediction for the all-loop real part of the remainder function multiplied by the BDS phase, which can be accessible through calculations in the regime of the strong coupling constant.