Landau gauge Yang-Mills propagators in the complex momentum plane

TL;DR

This paper develops a numerical method to compute Landau gauge Yang-Mills propagators in the complex momentum plane directly from Dyson-Schwinger equations, revealing a model-dependent singularity in the gluon propagator.

Contribution

It introduces a direct calculation technique avoiding inverse problems and applies it to find complex-plane singularities in gluon propagators.

Findings

Identified a singularity in the gluon propagator in the complex plane.

Developed a stable numerical method for complex momentum calculations.

Singularity location varies with the three-gluon vertex model.

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 ansaetze 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 occurs always at complex momenta for the range of models considered.