Numerical integration and extrapolation for finite and UV-divergent 3-loop Feynman integrals

Automatic numerical integration attempts to alleviate the detailed application of solution methods to the problem. We use automatic multivariate integration with PARINT combined with numerical extrapolation for classes of 3-loop UV-divergent self-energy diagrams with massive internal lines, and finite or UV-divergent massless vertex diagrams. The extrapolation is performed with respect to the dimensional regularization parameter. It is shown that the PARINT software handles the integrations accurately and efficiently.