The two-loop sunrise graph in two space-time dimensions with arbitrary masses in terms of elliptic dilogarithms

Abstract

We present the two-loop sunrise integral with arbitrary non-zero masses in two space-time dimensions in terms of elliptic dilogarithms. We find that the structure of the result is as simple and elegant as in the equal mass case, only the arguments of the elliptic dilogarithms are modified. These arguments have a nice geometric interpretation.

22 pages, version to be published

References in corpus (4)

• Elliptic integral evaluations of Bessel moments
• Towards multiple elliptic polylogarithms
• 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

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• Maximal Cuts in Arbitrary Dimension
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• Cutting the traintracks: Cauchy, Schubert and Calabi-Yau
• Massive kite diagrams with elliptics
• The two-loop sunrise integral around four space-time dimensions and generalisations of the Clausen and Glaisher functions towards the elliptic case
• The sunrise integral and elliptic polylogarithms
• Sunrise integral with two internal masses and pseudo-threshold kinematics in terms of elliptic polylogarithms
• Cuts and coproducts of massive triangle diagrams
• The HiggsTools Handbook: Concepts and observables for deciphering the Nature of the Higgs Sector
• Differential equations for Feynman integrals beyond multiple polylogarithms
• The diagrammatic coaction beyond one loop
• Integral representation for three-loop banana graph