Configuration Space Based Recurrence Relations for Sunset-Type Diagrams

TL;DR

This paper introduces a configuration space method to derive recurrence relations for multiloop sunset diagrams with massive propagators, facilitating numerical evaluation and providing explicit asymptotic formulas.

Contribution

It presents a novel configuration space approach to derive recurrence relations for sunset diagrams, enhancing numerical computation and analytical understanding.

Findings

Derived recurrence relations for sunset diagrams

Provided explicit formulas for basis integrals in asymptotic regimes

Method improves numerical evaluation of complex multiloop diagrams

Abstract

We derive recurrence relations for the calculation of multiloop sunset-type diagrams with large powers of massive propagators. The technique is formulated in configuration space and exploits the explicit form of the massive propagator raised to a given power. We write down and evaluate a convenient set of basis integrals. The method is well suited for a numerical evaluation of this class of diagrams. We give explicit analytical formulae for the basis integrals in the asymptotic regime.