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MP: Fachverband Theoretische und Mathematische Grundlagen der Physik

MP 9: Quantenfeldtheorie II

MP 9.1: Talk

Thursday, March 3, 2016, 13:45–14:05, VMP6 HS B

The two-loop sunrise integral and elliptic polylogarithms — •Luise Adams¹, Christian Bogner², and Stefan Weinzierl¹ — ¹Institut für Physik, Johannes Gutenberg - Universität Mainz — ²Institut für Physik, Humboldt-Universität zu Berlin

In this talk, we present a solution for the two-loop sunrise integral with arbitrary masses around two and four space-time dimensions in terms of a generalised elliptic version of the multiple polylogarithms. Furthermore we investigate the elliptic polylogarithms appearing in higher orders in the dimensional regularisation є of the two-dimensional equal mass solution .

Around two space-time dimensions the solution consists of a sum of three elliptic dilogarithms where the arguments have a nice geometric interpretation as intersection points of the integration region and an elliptic curve associated to the sunrise integral.

Around four space-time dimensions the sunrise integral can be expressed with the є⁰- and є¹-solution around two dimensions, mass derivatives thereof and simpler terms.

Considering higher orders of the two-dimensional equal mass solution we find certain generalisations of the elliptic polylogarithms appearing in the є⁰- and є¹-solutions around two and four space-time dimensions. We show that these higher order-solutions can be found by iterative integration within this class of functions.