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

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.

11 pages, no figures, published version

References in corpus (3)

• Elliptic integral evaluations of Bessel moments
• Elliptic integral evaluation of a Bessel moment by contour integration of a lattice Green function
• Laurent series expansion of sunrise-type diagrams using configuration space techniques

Cited by in corpus (6)

• The two-loop sunrise graph in two space-time dimensions with arbitrary masses in terms of elliptic dilogarithms
• The kite integral to all orders in terms of elliptic polylogarithms
• The two-loop sunrise integral around four space-time dimensions and generalisations of the Clausen and Glaisher functions towards the elliptic case
• An Analytic Approach to Sunset Diagrams in Chiral Perturbation Theory: Theory and Practice
• The sunrise integral and elliptic polylogarithms
• Differential equations for Feynman integrals beyond multiple polylogarithms