Hamburg 2016 – scientific programme
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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.