Confinement and dynamical chiral symmetry breaking in a non-perturbative renormalizable quark model

TL;DR

This paper introduces a non-perturbative, renormalizable quark model that captures confinement and chiral symmetry breaking, aligning well with lattice data and reproducing key hadronic features.

Contribution

It presents a novel quark model incorporating confinement and spontaneous chiral symmetry breaking within a renormalizable framework, inspired by the Gribov-Zwanziger approach.

Findings

Quark propagator exhibits confining features with complex conjugate poles.

Model reproduces lattice data for the quark mass function.

Identifies a massless pion in the chiral limit and estimates rho meson properties.

Abstract

Inspired by the construction of the Gribov-Zwanziger action in the Landau gauge, we introduce a quark model exhibiting both confinement and chiral symmetry aspects. An important feature is the incorporation of spontaneous chiral symmetry breaking in a renormalizable fashion. The quark propagator in the condensed vacuum turns out to be of a confining type. Besides a real pole, it exhibits complex conjugate poles. The resulting spectral form is explicitly shown to violate positivity, indicative of its unphysical character. Moreover, the ensuing quark mass function fits well to existing lattice data. To further validate the physical nature of the model, we identify a massless pseudoscalar (i.e. a pion) in the chiral limit and present estimates for the rho meson mass and decay constant.