Landau gauge Yang-Mills propagators in the complex momentum plane

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 Ansätze 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 p2 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.