On Genera of Curves from High-loop Generalized Unitarity Cuts
Abstract
Generalized unitarity cut of a Feynman diagram generates an algebraic system of polynomial equations. At high-loop levels, these equations may define a complex curve or a (hyper-)surface with complicated topology. We study the curve cases, i.e., a 4-dimensional L-loop diagram with (4L-1) cuts. The topology of a complex curve is classified by its genus. Hence in this paper, we use computational algebraic geometry to calculate the genera of curves from two and three-loop unitarity cuts. The global structure of degenerate on-shell equations under some specific kinematic configurations is also sketched. The genus information can also be used to judge if a unitary cut solution could be rationally parameterized.
Keywords
Cite
@article{arxiv.1302.1023,
title = {On Genera of Curves from High-loop Generalized Unitarity Cuts},
author = {Rijun Huang and Yang Zhang},
journal= {arXiv preprint arXiv:1302.1023},
year = {2015}
}
Comments
more examples added, version accepted for publication on JHEP