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AbstractAbstract
[en] 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 ε 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 ε"0- and ε"1-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 ε"0- and ε"1-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.
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Source
DPG-Fruehjahrstagung 2016 (Spring meeting) of the section matter and cosmos (SMuK) together with the divisions gravity and relativity, radiation and medical physics, particle physics, theoretical and mathematical physics, and the working group philosophy of physics; DPG-Fruehjahrstagung 2016 der Sektion Materie und Kosmos (SMuK) gemeinsam mit den Fachverbaenden Gravitation und Relativitaetstheorie, Strahlen- und Medizinphysik, Teilchenphysik, Theoretische und Mathematische Grundlagen der Physik sowie der Arbeitsgruppe Philosophie der Physik; Hamburg (Germany); 29 Feb - 4 Mar 2016; Available from http://www.dpg-verhandlungen.de; Session: MP 9.1 Do 13:45; No further information available; Also available as printed version: Verhandlungen der Deutschen Physikalischen Gesellschaft v. 51(2)
Record Type
Journal Article
Literature Type
Conference
Journal
Verhandlungen der Deutschen Physikalischen Gesellschaft; ISSN 0420-0195;
; CODEN VDPEAZ; (Hamburg 2016 issue); [1 p.]

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