Massless sunset diagrams in finite asymmetric volumes

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.