The Kugo – Ojima confinement criterion and the Infrared Behavior of Landau gauge QCD ∗

Recent investigations of the Dyson–Schwinger equations and Monte– Carlo lattice calculations resulted in a coherent description of the fully dressed gluon, ghost and quark propagators in Landau gauge QCD. In the Dyson–Schwinger approach the infrared behaviour of these propagators is determined analytically. For finite spacelike momenta the gluon, ghost and quark propagators are compared to available corresponding results of lattice Monte–Carlo calculations. For all three propagators an almost quantitative agreement is found. These results for the non-perturbative propagators allow an analytical verification of the Kugo–Ojima confinement criterion. Our numerical analysis clearly reveals positivity violation for the gluon propagator generated by a cut in the complex momentum plane. The non-perturbative strong running coupling resulting from these propagators possesses an infrared fixed point. The quark propagator obtained from quenched and unquenched calculations displays dynamical chiral symmetry breaking with quark masses close to “phenomenological” and lattice values. We confirm that linear extrapolations of the quark propagator for different bare masses to the chiral limit are inaccurate. Based on an invited talk given by R.A. at the Second International Conference “Nuclear and Particle physics with CEBAF at Jefferson Laboratory, Dubrovnik, Croatia, 26 – 31 May, 2003