Hepta-Cuts of Two-Loop Scattering Amplitudes

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.