The Sinc Function Representation and Three-Loop Master Diagrams

Abstract

We test the Sinc function representation, a novel method for numerically evaluating Feynman diagrams, by using it to evaluate the three-loop master diagrams. Analytical results have been obtained for all these diagrams, and we find excellent agreement between our calculations and the exact values. The Sinc function representation converges rapidly, and it is straightforward to obtain accuracies of 1 part in 10^6 for these diagrams and with longer runs we found results better than 1 part in 10^{12}. Finally, this paper extends the Sinc function representation to diagrams containing massless propagators.