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 ${ϵ}^0$- and ${ϵ}^1$-solution around two dimensions, mass derivatives thereof and simpler terms.

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