Kinematic singularities of Feynman integrals and principal A-determinants
René Pascal Klausen · Journal of High Energy Physics · 2022
Abstract We consider the analytic properties of Feynman integrals from the perspective of general A-discriminants and $$ \mathcal{A} $$ A -hypergeometric functions introduced by Gelfand, Kapranov and Zelevinsky (GKZ). This enables us, to give a clear and mathematically rigorous 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 the use of coamoebas.