Cuts and Isogenies

Abstract

We consider the genus-one curves which arise in the cuts of the sunrise and in the elliptic double-box Feynman integrals. We compute and compare invariants of these curves in a number of ways, including Feynman parametrization, lightcone and Baikov (in full and loop-by-loop variants). We find that the same geometry for the genus-one curves arises in all cases, which lends support to the idea that there exists an invariant notion of genus-one geometry, independent on the way it is computed. We further indicate how to interpret some previous results which found that these curves are related by isogenies instead.

arXiv comment24 pages, 2 figures

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• Meromorphic modular forms and the three-loop equal-mass banana integral
• On Epsilon Factorized Differential Equations for Elliptic Feynman Integrals
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• Discontinuities of banana integrals in dispersion relation representation
• The spectrum of Feynman-integral geometries at two loops