Adaptive Integration for 3-loop Feynman Diagrams with Massless Propagators

摘要

We apply multivariate adaptive integration to problems arising from self-energy Feynman loop diagrams with massless internal lines. Results are obtained with the PARINT software package, which is layered over MPI (Message Passing Interface) and incorporates advanced parallel computation techniques such as load balancing among processes that may be distributed over a network of nodes. To solve the problems numerically we introduce a parameter ? in a factor of the integrand function. Some problem categories allow setting ?= 0; other cases require an extrapolation as ? → 0. Furthermore we apply extrapolation with respect to the dimensional regularization parameter by setting the dimension n= 4 - 2ε and extrapolating as ε → 0. Timing results with Parlnt show near optimal parallel speedups for the problems at hand.