On evaluation of two-loop self-energy diagram with three propogator

TL;DR

This paper derives explicit small momentum expansions for the two-loop sunset diagram with three different masses, expressing coefficients using dilogarithms and elementary functions, and explores various variable sets for expansion.

Contribution

It provides explicit formulas for the sunset diagram's small momentum expansion with three masses, including coefficients in terms of special functions and multiple variable sets.

Findings

Explicit coefficients in terms of dilogarithms and elementary functions.

Power expansions of the sunset diagram in different variable sets.

Enhanced analytical understanding of the sunset diagram's behavior at small momenta.

Abstract

Small momentum expansion of the "sunset" diagram with three different masses is obtained. Coefficients at powers of $p^2$ are evaluated explicitly in terms of dilogarithms and elementary functions. Also some power expansions of "sunset" diagram in terms of different sets of variables are given.