Feynman loop numerical integral expansions for 3-loop vertex diagrams

The inclusion of higher order corrections by multi-loop diagrams is required in perturbation methods for precise theoretical calculations of high energy interactions. We address 3-loop vertex Feynman diagrams with massless internal lines, and which may exhibit ultra-violet (UV) singularities. The computational methods target automatic numerical integration and extrapolation to approximate the leading coefficients of the integral expansion with respect to the dimensional regularization parameter. Convergence acceleration is achieved by applying linear extrapolation on the integral expansion. Multivariate integration is performed with the ParInt software package, layered over MPI (Message Passing Interface) to speed up the computations. Integrand transformations result in diminishing the effect of singular behavior in the integrand.