Regularization with Numerical Extrapolation for Finite and UV-Divergent Multi-loop Integrals

Understand

We give numerical integration results for Feynman loop diagrams such as those covered by Laporta [1] and by Baikov and Chetyrkin [2], and which may give rise to loop integrals with UV singularities.

• We explore automatic adaptive integration using multivariate techniques from the PARINT package for multivariate integration, as well as iterated in- tegration with programs from the QUADPACK package, and a trapezoidal method based on a double exponential trans- formation.
• PARINT is layered over MPI (Message Passing Interface), and incorporates advanced parallel/distributed techniques including load balancing among processes that may be distributed over a cluster or a network/grid of nodes.
• Results are included for 2-loop vertex and box diagrams and for sets of 2-, 3- and 4-loop self-energy diagrams with or without UV terms.