Towards six W-boson amplitude at two loops

TL;DR

This paper constructs the two-loop planar integrand for six W-boson amplitudes in maximally supersymmetric Yang-Mills theory, revealing it as an uplift of the massless six-gluon amplitude from four to six dimensions.

Contribution

It extends the understanding of massive W-boson amplitudes by explicitly constructing the two-loop integrand using advanced supersymmetric and unitarity techniques, generalizing previous lower-leg results.

Findings

The integrand matches the massless six-gluon amplitude in the limit.

The pattern of uplift from four to six dimensions is confirmed for six-leg amplitudes.

The method demonstrates the applicability of six-dimensional formalism to massive amplitude calculations.

Abstract

We construct the planar integrand of the six-leg amplitude of massive W-bosons on the special Coulomb branch of the maximally supersymmetric Yang-Mills theory to two-loop order. We use the six-dimensional supersymmetric spinor-helicity formalism and the generalized unitarity-cut sewing technique to perform this analysis. The thus-found expression corresponds in the massless limit to the six-gluon maximally helicity-violating amplitude. The upshot of the current consideration is that the former is just an uplift of the latter from four to six dimensions. This repeats the pattern found earlier for four- and five-leg amplitudes of massive W-bosons.