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Inspired by the construction of the Gribov-Zwanziger action in the Landaugauge, we introduce a quark model exhibiting both confinement and chiralsymmetry aspects. An important feature is the incorporation of spontaneouschiral symmetry breaking in a renormalizable fashion. The quark propagator inthe condensed vacuum turns out to be of a confining type. Besides a real pole,it exhibits complex conjugate poles. The resulting spectral form is explicitlyshown to violate positivity, indicative of its unphysical character. Moreover,the ensuing quark mass function fits well to existing lattice data. To furthervalidate 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 massand decay constant.

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