A Phenomenological Treatment of Chiral Symmetry Restoration and Deconfinement Numerical studies of confinement in the Landau gauge by the larger lattice simulation

A phenomenological expression for the thermodynamic potential of gluons and quarks is constructed which incorporates the features of deconfinement and chiral symmetry restoration known from lattice simulations. The thermodynamic potential is a function of the Polyakov loop and chiral condensate expectation values. The gluonic sector uses a successful model for pure (SU(N_c)) gauge theories in which the Polyakov loop eigenvalues are the fundamental order parameters for deconfinement. The quark sector is given by a Nambu-Jona-Lasinio model in which a constant background (A_0) field couples the chiral condensate to the Polyakov loop. We consider the case of (N_f = 2) in detail. For two massless quarks, we find a second order chiral phase transition. Confinement effects push the transition to higher temperatures, but the entropy associated with the gluonic sector acts in the opposite direction. For light mass quarks, only a rapid crossover occurs. For sufficiently heavy quarks, a first order deconfinement transition emerges. This simplest model has one adjustable parameter, which can be set from the chiral transition temperature for light quarks. It predicts all thermodynamic quantities as well as the behavior of the chiral condensate and the Polyakov loop over a wide range of temperatures. The infrared behaviour of QCD in the Landau gauge is studied in 24^4 and 32^4 lattices by measuring the Kugo-Ojima parameter, gluon propagator, ghost propagator and the QCD running coupling. The Kugo-Ojima parameter c remains about 0.8 instead of the expectation value 1. We observe infrared suppression of the singularity of the gluon propagator and the enhancement of the ghost propagator but the shifts are smaller than those of Dyson-Schwinger approach. The momentum dependence of the running coupling in the infrared region is weak and alpha_s(0) ~= 1