Landau gauge Yang-Mills propagators in the complex momentum plane
Christian S. Fischer, Markus Q. Huber
Abstract
We calculate the dressed gluon and ghost propagators of Landau gauge Yang-Mills theory in the complex momentum plane from their Dyson-Schwinger equations. To this end, we develop techniques for a direct calculation such that no mathematically ill-posed inverse problem needs to be solved. We provide a detailed account of the employed ray technique and discuss a range of tools to monitor the stability of the numerical calculation. Within a truncation employing model Ans\"atze for the three-point vertices and neglecting effects due to four-point functions, we find a singularity in the gluon propagator in the second quadrant of the complex ${p}^{2}$ plane. Although the location of this singularity turns out to be strongly dependent on the model for the three-gluon vertex, it always occurs at complex momenta for the range of models considered.