New Series Representations for the Two-Loop Massive Sunset Diagram

TL;DR

The paper introduces new convergent series representations for the two-loop sunset diagram with three different masses, enhancing computational tools for various physical theories.

Contribution

It develops novel analytic continuation techniques for Lauricella series to represent the sunset diagram, covering regions relevant to physics applications.

Findings

New series representations with improved convergence

Applicable to Chiral Perturbation Theory and MSSM

Potential for broader use in analytic continuation

Abstract

We derive new convergent series representations for the two-loop sunset diagram with three different propagator masses m1, m2 and m3 and external momentum p by techniques of analytic continuation on a well-known triple series that corresponds to the Lauricella Fc function. The convergence regions of the new series contain regions of interest to physical problems. These include some ranges of masses and squared external momentum values which make them useful from Chiral Perturbation Theory to some regions of the parameter space of the Minimal Supersymmetric Standard Model. The analytic continuation results presented on the Lauricella series could be used in other settings as well.