On the momentum space structure of the quark propagator

TL;DR

This paper investigates the momentum space structure of the quark propagator in non-perturbative QCD, establishing connections with lattice data and providing insights into the quark mass and related quantities.

Contribution

It introduces a model of the quark propagator with a shared pole structure, linking it to lattice data and deriving asymptotic behaviors and estimations for physical parameters.

Findings

Good agreement with lattice QCD data.

Estimation of the shared pole mass as the constituent quark mass.

Derivation of asymptotic scaling laws for the propagator.

Abstract

The structure of the quark propagator in momentum space is explored taking into account non-perturbative QCD dynamics constraints for the quark spectral densities derived previously. We assume that the scalar and vector component of the quark propagator share a simple pole but not its residuum, together with other structures. Furthermore, a connection between the poles of the quark propagator and the zeros of the quark wave function $Z(p^2)$ is established. Asymptotic scaling laws for the representation of the quark propagator, after removing the shared pole, are also derived. The confrontation of our results with lattice data for the full QCD quark propagator data are in good agreement. Exploring the link with the lattice data and looking at the Bethe-Salpeter vertex and amplitude, in the chiral limit, we are able to provide estimations for these quantities, for $f_\pi$ and for the shared pole mass. The pole mass reproduces the constituent quark mass used in the quark models.