Hepta-Cuts of Two-Loop Scattering Amplitudes

TL;DR

This paper introduces a method for calculating hepta-cuts of two-loop scattering amplitudes using unitarity cuts, polynomial fitting, and integration techniques, applicable to complex gauge theory processes.

Contribution

It presents a novel approach combining unitarity cuts, Gram matrix constraints, and polynomial fitting to efficiently compute two-loop hepta-cuts in gauge theories.

Findings

Successfully computed hepta-cut contributions for gluon-gluon scattering.

Applicable to both planar and non-planar topologies in Yang-Mills theory.

Provides a systematic framework for two-loop amplitude calculations.

Abstract

We present a method for the computation of hepta-cuts of two loop scattering amplitudes. Four dimensional unitarity cuts are used to factorise the integrand onto the product of six tree-level amplitudes evaluated at complex momentum values. Using Gram matrix constraints we derive a general parameterisation of the integrand which can be computed using polynomial fitting techniques. The resulting expression is further reduced to master integrals using conventional integration by parts methods. We consider both planar and non-planar topologies for 2 to 2 scattering processes and apply the method to compute hepta-cut contributions to gluon-gluon scattering in Yang-Mills theory with adjoint fermions and scalars.