The Elliptic Sunrise

TL;DR

This paper presents a detailed computation of the two-loop sunrise integral with arbitrary masses, expressing the results in terms of elliptic functions and their generalizations, advancing the understanding of complex Feynman integrals.

Contribution

The work provides explicit elliptic function representations of the two-loop sunrise integral in various dimensions, a novel approach in multi-loop Feynman integral calculations.

Findings

Result expressed in elliptic dilogarithms in two dimensions

Inclusion of elliptic generalizations of Clausen and Glaisher functions near four dimensions

Enhanced understanding of elliptic structures in quantum field theory integrals

Abstract

In this talk, we discuss our recent computation of the two-loop sunrise integral with arbitrary non-zero particle masses. In two space-time dimensions, we arrive at a result in terms of elliptic dilogarithms. Near four space-time dimensions, we obtain a result which furthermore involves elliptic generalizations of Clausen and Glaisher functions.