Kinematic singularities of Feynman integrals and principal A-determinants

TL;DR

This paper explores the mathematical structure of Feynman integrals' singularities using A-discriminants and hypergeometric functions, providing rigorous descriptions and new computational methods for Landau varieties.

Contribution

It introduces a rigorous mathematical framework for analyzing Feynman integral singularities via A-discriminants and develops efficient parametrization techniques for Landau varieties.

Findings

Rigorous description of Landau varieties using principal A-determinants

Efficient parametrization of Landau varieties via Horn-Kapranov method

New approach to analyze multivalued Feynman integrals using coamoebas

Abstract

We consider the analytic properties of Feynman integrals from the perspective of general A-discriminants and A-hypergeometric functions introduced by Gelfand,Kapranov and Zelevinsky (GKZ). This enables us, to give a clear and mathematically rigour description of the singular locus, also known as Landau variety, via principal A-determinants. We also comprise a description of the various second type singularities. Moreover, by the Horn-Kapranov-parametrization we give a very efficient way to calculate a parametrization of Landau varieties. We furthermore present a new approach to study the sheet structure of multivalued Feynman integrals by use of coamoebas.