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Title

Critical points and number of master integrals
Authors

Roman N. Lee
Organization: Budker Institute of Nuclear Physics and Novosibirsk State University
Andrei A. Pomeransky
Organization: Budker Institute of Nuclear Physics and Novosibirsk State University
Journal / Anthology

Journal of High Energy Physics
Year: 2013
Volume: 11
Description

We consider the question about the number of master integrals for a multiloop Feynman diagram. We show that, for a given set of denominators, this number is totally determined by the critical points of the polynomials entering either of the two representations: the parametric representation and the Baikov representation. In particular, for the parametric representation the corresponding polynomial is just the sum of Symanzik polynomials. The relevant topological invariant is the sum of the Milnor numbers of the proper critical points. We present a Mathematica package Mint to automatize the counting of the master integrals for the typical case, when all critical points are isolated.
Subjects

*Mathematics > Calculus and Analysis > Differential Geometry
*Science > Physics
Keywords

Scattering Amplitudes, Differential and Algebraic Geometry