The Sinc Function Representation and Three-Loop Master Diagrams

TL;DR

This paper demonstrates a new numerical method, the Sinc function representation, for evaluating complex three-loop Feynman diagrams with high accuracy, including diagrams with massless propagators.

Contribution

It introduces and validates the Sinc function representation as an effective tool for precise numerical evaluation of multi-loop Feynman diagrams, extending to diagrams with massless propagators.

Findings

Achieved high-precision results matching analytical calculations.

Demonstrated rapid convergence of the Sinc function method.

Extended the method to diagrams with massless propagators.

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.