Massless sunset diagrams in finite asymmetric volumes

TL;DR

This paper develops methods to compute 2-loop massless sunset diagrams and 1-loop sums in finite asymmetric volumes, aiding the matching of effective chiral Lagrangians across different regularizations.

Contribution

It introduces new techniques for calculating 2-loop sunset diagrams and 1-loop sums in finite volumes, extending previous results and improving precision in lattice regularization.

Findings

Extended dimensional regularization results for 1-loop sums

New method for calculating expansion coefficients of lattice sums

Validated methods for matching chiral Lagrangians

Abstract

This paper discusses the methods and the results used in an accompanying paper describing the matching of effective chiral Lagrangians in dimensional and lattice regularizations. We present methods to compute 2-loop massless sunset diagrams in finite asymmetric volumes in the framework of these regularizations. We also consider 1-loop sums in both regularizations, extending the results of Hasenfratz and Leutwyler for the case of dimensional regularization and we introduce a new method to calculate precisely the expansion coefficients of the 1-loop lattice sums.