A numerical test of differential equations for one- and two-loop sunrise diagrams using configuration space techniques

TL;DR

This paper employs configuration space methods to derive integral representations for sunrise diagrams, enabling numerical verification of their associated differential equations, thus providing a computational check of recent theoretical developments.

Contribution

The authors introduce a novel numerical approach using configuration space techniques to verify differential equations for sunrise diagrams.

Findings

Numerical validation of differential equations for sunrise diagrams.

Integral representations facilitate computational checks.

Supports recent theoretical formulations.

Abstract

We use configuration space methods to write down one-dimensional integral representations for one- and two-loop sunrise diagrams (also called Bessel moments) which we use to numerically check on the correctness of the second order differential equations for one- and two-loop sunrise diagrams that have recently been discussed in the literature.