Elliptic functions and Maximal Unitarity
Yang Zhang (ETH Zürich)

Scattering amplitudes at loop level can be reduced to a basis of linearly independent Feynman integrals. The integral coefficients are extracted from generalized unitarity cuts which define algebraic varieties. We analyze a class of integrals whose maximal cuts give rise to an elliptic curve. We derive unique projectors for all master integrals in terms of multivariate residues along with Weierstrass' elliptic functions. We also show how to generate the leading-topology part of the integration-by-parts identities analytically from exact meromorphic differential forms on a torus.