The two-loop sunrise graph in two space-time dimensions with arbitrary masses in terms of elliptic dilogarithms

TL;DR

This paper expresses the two-loop sunrise integral with arbitrary masses in two dimensions using elliptic dilogarithms, revealing a simple structure similar to the equal mass case with geometrically meaningful arguments.

Contribution

It provides a novel elliptic dilogarithm representation for the two-loop sunrise integral with arbitrary masses in two dimensions, extending previous equal mass results.

Findings

The integral is expressed in terms of elliptic dilogarithms.

The structure remains simple and elegant despite mass variations.

Arguments of the dilogarithms have a geometric interpretation.

Abstract

We present the two-loop sunrise integral with arbitrary non-zero masses in two space-time dimensions in terms of elliptic dilogarithms. We find that the structure of the result is as simple and elegant as in the equal mass case, only the arguments of the elliptic dilogarithms are modified. These arguments have a nice geometric interpretation.