A Feynman integral depending on two elliptic curves

Abstract

We study a two-loop four-point function with one internal mass. This Feynman integral is one of the simplest Feynman integrals depending on two elliptic curves. We transform the associated differential equation into an $\epsilon$-form. We study the entries of the differential equation, and in particular the entries which depend on both elliptic curves.

41 pages, v2: version to be published

References in corpus (15)

• Algorithm FIRE -- Feynman Integral REduction
• The two-loop sunrise graph in two space-time dimensions with arbitrary masses in terms of elliptic dilogarithms
• Two-loop planar master integrals for Higgs$\to 3$ partons with full heavy-quark mass dependence
• Elliptic integral evaluations of Bessel moments
• The kite integral to all orders in terms of elliptic polylogarithms
• Decomposition of Feynman Integrals on the Maximal Cut by Intersection Numbers
• The Two-Loop Master Integrals for $q\bar{q}\to VV$
• Elliptic polylogarithms and Feynman parameter integrals
• Elliptic Functions and Maximal Unitarity
• The elliptic double box and symbology beyond polylogarithms
• Meromorphic modular forms and the three-loop equal-mass banana integral
• On Epsilon Factorized Differential Equations for Elliptic Feynman Integrals
• Traintrack Calabi-Yaus from Twistor Geometry
• Modular transformations of elliptic Feynman integrals
• Massive kite diagrams with elliptics