Cuts and Isogenies

Understand

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.