The two-loop sunrise graph with arbitrary masses
Luise Adams, Christian Bogner, Stefan Weinzierl
TL;DR
This paper presents an analytical solution for the two-loop sunrise Feynman graph with arbitrary masses in two dimensions, utilizing elliptic integrals and differential equations to express the result.
Contribution
It provides the first explicit analytical solution involving elliptic integrals for the two-loop sunrise graph with arbitrary masses in two dimensions.
Findings
Solution involves elliptic integrals
Homogeneous differential equation solutions are elliptic periods
Analytical expression for the Feynman integral obtained
Abstract
We discuss the analytical solution of the two-loop sunrise graph with arbitrary non-zero masses in two space-time dimensions. The analytical result is obtained by solving a second-order differential equation. The solution involves elliptic integrals and in particular the solutions of the corresponding homogeneous differential equation are given by periods of an elliptic curve.
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