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.