Analytic properties of high energy production amplitudes in N=4 SUSY

TL;DR

This paper studies the analytic structure of six-point scattering amplitudes in N=4 supersymmetric Yang-Mills theory at high energies, focusing on phase relations, factorization, and corrections up to two loops.

Contribution

It demonstrates how analyticity, unitarity, and factorization constraints can reproduce known two-loop corrections and explore the exponentiation hypothesis for the remainder function.

Findings

Reproduces the two-loop correction to the 6-point BDS amplitude.

Shows the Moebius invariance of contributions in transverse momentum space.

Supports the exponentiation hypothesis for the remainder function.

Abstract

We investigate analytic properties of the six point planar amplitude in N=4 SUSY at the multi-Regge kinematics for final state particles. For inelastic processes the Steinmann relations play an important role because they give a possibility to fix the phase structure of the Regge pole and Mandelstam cut contributions. These contributions have the Moebius invariant form in the transverse momentum subspace. The analyticity and factorization constraints allow us to reproduce the two-loop correction to the 6-point BDS amplitude in N=4 SUSY obtained earlier in the leading logarithmic approximation with the use of the s-channel unitarity. The exponentiation hypothesis for the remainder function in the multi-Regge kinematics is also investigated. The 6-point amplitude in LLA can be completely reproduced from the BDS ansatz with the use of the analyticity and Regge factorization.