The sunrise integral around two and four space-time dimensions in terms of elliptic polylogarithms

Abstract

In this talk we discuss the solution for the sunrise integral around two and four space-time dimensions in terms of a generalised elliptic version of the multiple polylogarithms. In two space-time dimensions we obtain a sum of three elliptic dilogarithms. The arguments of the elliptic dilogarithms have a nice geometric interpretation. In four space-time dimensions the sunrise integral can be expressed with the ${\epsilon }^0$- and ${\epsilon }^1$-solution around two dimensions, mass derivatives thereof and simpler terms.

5 pages, no figures, proceeding to the conference 'Matter To The Deepest', Sept 14-18, 2015, Ustroń, Poland

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Cited by in corpus (5)

• Loop-by-loop Differential Equations for Dual (Elliptic) Feynman Integrals
• Symmetric $\epsilon$- and $(\epsilon +1/2)$-forms and quadratic constraints in "elliptic" sectors
• Position Space Equations for Banana Feynman Diagrams
• Coordinate space calculation of two- and three-loop sunrise-type diagrams, elliptic functions and truncated Bessel integral identities
• From equations in coordinate space to Picard-Fuchs and back