Five legs @ three loops: N=4 sYM amplitude near mass-shell

TL;DR

This paper analyzes a three-loop five-particle scattering amplitude in N=4 super-Yang-Mills theory, revealing new structures and confirming exponentiation of infrared divergences.

Contribution

It provides a detailed three-loop calculation of the amplitude near mass-shell, introducing a concise integral representation and uncovering independent functions for each kinematic structure.

Findings

Confirmed exponentiation of infrared and finite terms.

Identified a function of 't Hooft coupling for each kinematic structure.

Demonstrated universality via the octagon anomalous dimension.

Abstract

We present a three-loop analysis of the scattering amplitude of five nearly massless W-bosons in planar maximally supersymmetric Yang-Mills theory. The basis of the master integrals is established, making use of the unitarity-cut sewing technique in six-dimensional N=(1,1) super-Yang-Mills theory. Its dimensional reduction down to four allows us to generate masses for internal and external states. We descend on the special Coulomb branch of maximally supersymmetric Yang-Mills theory by setting all propagator masses to zero. Employing explicit expressions for all integrals that we calculated in a companion paper, we find a concise representation for this infrared-sensitive observable. We confirm its exponentiation, both for infrared and finite terms. The infrared double logarithm manifests the anticipated universality through the octagon anomalous dimension as its governing coefficient. Unlike our previous two-loop result, this consideration reveals that each of the three independent kinematic structures furnishing the amplitude possesses its own function of 't Hooft coupling.