N=4 supersymmetric Yang Mills scattering amplitudes at high energies: the Regge cut contribution

TL;DR

This paper analyzes the high-energy behavior of six-point MHV scattering amplitudes in N=4 supersymmetric Yang-Mills theory, focusing on the Regge cut contribution and its implications for the BDS formula.

Contribution

It computes the energy spectrum of the BFKL equation in the octet channel and explicitly solves it for arbitrary momentum transfers, revealing the Regge cut's role.

Findings

BFKL equation solved for octet channel at arbitrary momentum transfer

Two-loop corrections to amplitude discontinuities calculated

Regge cut does not affect universal collinear and infrared singularities

Abstract

We further investigate, in the planar limit of N=4 supersymmetric Yang Mills theories,the high energy Regge behavior of six-point MHV scattering amplitudes. In particular, for the new Regge cut contribution found in our previous paper, we compute in the leading logarithmic approximation (LLA) the energy spectrum of the BFKL equation in the color octet channel, and we calculate explicitly the two loop corrections to the discontinuities of the amplitudes for the transitions 2 to 4 and 3 to 3. We find an explicit solution of the BFKL equation for the octet channel for arbitrary momentum transfers and investigate the intercepts of the Regge singularities in this channel. As an important result we find that the universal collinear and infrared singularities of the BDS formula are not affected by this Regge-cut contribution. Any improvement of the BDS formula should reproduce this cut to all orders in the coupling.