The iterated structure of the all-order result for the two-loop sunrise integral

TL;DR

This paper introduces a method to compute the Laurent expansion of the two-loop sunrise integral with equal masses to any order in epsilon, using a new class of elliptic polylogarithmic functions.

Contribution

It develops a novel approach employing generalized elliptic polylogarithms to evaluate the sunrise integral's epsilon expansion to all orders.

Findings

Successfully computes the Laurent expansion to arbitrary order

Introduces a new class of elliptic polylogarithmic functions

Demonstrates all integrations are feasible within this function class

Abstract

We present a method to compute the Laurent expansion of the two-loop sunrise integral with equal non-zero masses to arbitrary order in the dimensional regularisation $\varepsilon$. This is done by introducing a class of functions (generalisations of multiple polylogarithms to include the elliptic case) and by showing that all integrations can be carried out within this class of functions.