Sunset integrals with up to three mass scales in chiral perturbation theory: a comparative study of the Mellin-Barnes representation technique

TL;DR

This paper derives and compares Mellin-Barnes integral representations for sunset integrals with up to three mass scales in chiral perturbation theory, providing exact solutions and analytical continuations for various parameter regions.

Contribution

It introduces a systematic approach to evaluate complex two-loop sunset integrals with multiple mass scales using Mellin-Barnes techniques, including exact solutions and parameter continuation.

Findings

Derived Mellin-Barnes representations for sunset integrals

Obtained exact hypergeometric series solutions

Discussed analytical continuation and applications in chiral perturbation theory

Abstract

Sunset integrals are among the simplest of two-loop integrals that appear in perturbative quantum field theories and possess up to four distinct mass scales. By means of integration by parts identities, they can be written in terms of four distinct master integrals. In this article, we discuss the independent configurations of on-shell and off-shell sunset master integrals with one, two and three mass scales that arise in chiral perturbation theory. We derive Mellin-Barnes integral representations of these integrals and analytically solve them using various methods to obtain exact results in the form of single and double convergent series of the hypergeometric type, for the values of the mass parameters that allow us to do so. We then discuss how to analytically continue the results to other regions of the parameters and conclude by discussing a few applications in chiral perturbation theory.