The two-loop sunrise graph with arbitrary masses

By Luise Adams, Christian Bogner, Stefan Weinzierl. 2013

171 citations recorded by the source corpus.

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.

Subfields: Aerospace Engineering, Applied Mathematics, Astronomy and Astrophysics

View Paper: https://www.semanticscholar.org/paper/9043c9ab9b485bcac1ccc66a9e03ef1d3b4333cc

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In Aerospace Engineering

In Applied Mathematics

In Astronomy and Astrophysics

Citations in the corpus

Feynman integrals and hyperlogarithms (2015, background): “Certainly this class is very rich, for it includes involved objects like elliptic polylogarithms [6, 24, 27] and special values of L-functions of modular forms [43].”
Maximal cuts and differential equations for Feynman integrals. An application to the three-loop massive banana graph (2017, unknown): “05 46”
The elliptic dilogarithm for the sunset graph (2013, methodology): “For geometric reasons, we will use an alternative symmetric representation of the integral formulated using homogeneous coordinates (see [17, 18])”
Differential equations and dispersion relations for Feynman amplitudes. The two-loop massive sunrise and the kite integral (2016, methodology): “…increase in our knowledge of the mathematical structures that appear in multiloop Feynman integrals, thanks to the combined use of various computational techniques, such as to the method of differential equations [1–3], the introduction of a class of special functions (dubbed originally…”