Color Confinement in Lattice Landau Gauge

The problem of color confinement in lattice Landau gauge QCD is briefly reviewed in the light of Kugo-Ojima criterion and Gribov-Zwanziger theory. The infrared properties of the Landau gauge QCD is studied by the measurement of the gluon propagator, ghost propagator, Kugo-Ojima parameter and the running coupling via β = 6.0, 16⁴, 24⁴, 32⁴ and β = 6.4, 32⁴, 48⁴ lattice simulation. The data are analyzed in the principle of minimum sensitivity(PMS) in the \widetilde {MOM} scheme. We observe the running coupling α_s (q) has a maximum about 1 and decreases near q = 0. The Kugo-Ojima parameter, which is expected to be 1 was about 0.8.