The sunrise integral and elliptic polylogarithms

Abstract

We summarize recent computations with a class of elliptic generalizations of polylogarithms, arising from the massive sunrise integral. For the case of arbitrary masses we obtain results in two and four space-time dimensions. The iterated integral structure of our functions allows us to furthermore compute the equal mass case to arbitrary order.

talk given at Loops and Legs 2016

References in corpus (19)

• Differential Equations for Feynman Graph Amplitudes
• Connection between Feynman integrals having different values of the space-time dimension
• Multiple polylogarithms and mixed Tate motives
• The elliptic dilogarithm for the sunset graph
• Two-loop two-point functions with masses: asymptotic expansions and Taylor series, in any dimension
• Analytic treatment of the two loop equal mass sunrise graph
• The two-loop sunrise graph in two space-time dimensions with arbitrary masses in terms of elliptic dilogarithms
• Analytical and numerical methods for massive two-loop self-energy diagrams
• Differential equations and dispersion relations for Feynman amplitudes. The two-loop massive sunrise and the kite integral
• Elliptic integral evaluations of Bessel moments
• Multiple Elliptic Polylogarithms
• Schouten identities for Feynman graph amplitudes; the Master Integrals for the two-loop massive sunrise graph
• A geometrical angle on Feynman integrals
• Precise numerical evaluation of the two loop sunrise graph Master Integrals in the equal mass case
• Towards all-order Laurent expansion of generalized hypergeometric functions around rational values of parameters
• BOKASUN: a fast and precise numerical program to calculate the Master Integrals of the two-loop sunrise diagrams
• A numerical test of differential equations for one- and two-loop sunrise diagrams using configuration space techniques
• Elliptic integral evaluation of a Bessel moment by contour integration of a lattice Green function
• The two-loop sunrise integral around four space-time dimensions and generalisations of the Clausen and Glaisher functions towards the elliptic case

Cited by in corpus (4)

• Higgs Boson Production at Hadron Colliders at N3LO in QCD
• Elliptic Polylogarithms and Basic Hypergeometric Functions
• Analytic representations of $m_K$, $F_K$, $m_{\eta }$ and $F_{\eta }$ in two loop $SU(3)$ chiral perturbation theory
• Multi-valued Feynman Graphs and Scattering Theory