Infrared Features of the Landau Gauge QCD

Abstract

The infrared features of Landau gauge QCD are studied by the lattice simulation of $\beta=6.0, 16^4, 24^4, 32^4$ and $\beta=6.4, 32^4, 48^4$. We adopt two definitions of the gauge field; 1) $U-$linear 2) $\log U$ and measured the gluon propagator and ghost propagator. Infrared singularity of the gluon propagator is less than that of tree level result but the gluon propagator at 0 momentum remains finite. The infrared singularity of ghost propagator is stronger than the tree level. The QCD running coupling measured by using the gluon propagator and the ghost propagator has a maximum $\alpha_s(p)\simeq 1$ at around $p=0.5GeV$ and decreases as $p$ approaches 0. The data are analyzed in use of formula of the principle of minimal sensitivity(PMS), the effective charge method and the contour-improved perturbation method, which suggest necessity of the resummation of perturbation series in the infrared region together with existence of the infrared fixed point. Kugo-Ojima parameter saturates at about -0.8 in contrast to the theoretically expected value -1.