Lattice data inspired but Minkowski space calculated QCD fundamental propagator

TL;DR

This paper solves the Dyson-Schwinger equation for the quark propagator directly in Minkowski space using lattice-inspired data and transformation techniques, revealing complex mass functions without particle poles.

Contribution

It introduces a novel Minkowski space approach to the Dyson-Schwinger equation incorporating lattice data and transformation methods, providing new insights into quark propagator structure.

Findings

Quark propagator lacks particle-like poles and thresholds.

Mass function becomes complex without branch points.

Solution employs Hilbert and Stieltjes transformations.

Abstract

We study the Dyson-Schwinger equation for the quark propagator in Minkowski space. In order to have analytical behaviour at the timelike axis of momenta under control, we use the Stieltjes and the Hilbert transformation for the interaction kernels and discuss the solution from the perspective of these transformations. In addition, a lattice fit for the gluon propagator and approximation for quark-gluon vertex are employed, and within the model the quark propagator is obtained through the solution of Dyson-Schwinger equation in Minkowski space. The resulting propagators in all studied cases do not show up particle like pole and production thresholds. Instead of, the quark propagator satisfies Hilbert transformation and the associated dynamical mass function becomes complex without a presence of particle like branch point.