On genera of curves from high-loop generalized unitarity cuts

TY - JOUR

T1 - On genera of curves from high-loop generalized unitarity cuts

AU - Huang, Rijun

AU - Zhang, Yang

PY - 2013/4/1

Y1 - 2013/4/1

N2 - 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.

AB - 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.

U2 - 10.1007/jhep04(2013)080

DO - 10.1007/jhep04(2013)080

M3 - Journal article

SN - 1126-6708

VL - 2103

JO - Journal of High Energy Physics (Online)

JF - Journal of High Energy Physics (Online)

IS - 4

M1 - 080

ER -