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arXiv · 2007.11505

Landau gauge Yang-Mills propagators in the complex momentum plane

Christian S. Fischer·Markus Q. Huber
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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.

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Christian S. Fischer, Markus Q. Huber. 2020-07-22. Landau gauge Yang-Mills propagators in the complex momentum plane. https://doi.org/10.1103/physrevd.102.094005

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