Colour Confinement in the Lattice Landau Gauge Qcd Simulation

Two decades ago, Gribov pointed out a possible mechanism of colour confinement in Coulomb gauge or Landau gauge QCD via infrared divergence of the Faddeev-Popov ghost propagator. At nearly the same time, Kugo and Ojima proposed a criterion for the absence of coloured massless asymptoptic states in Landau gauge QCD using the BRST symmetry. We study the confinement signal in the gluon propagator, the ghost propagator and the Kugo-Ojima parameter, and their dependence on the gauge field. Usually, the gauge field on lattice Aμ(x) is defined from the link variable Uμ(x) as Ax,μ = 1 2 (Ux,μ − U † x,μ)|traceless part, which we call U -linear version. A more natural definition is Ux,μ = expAx,μ, A † x,μ = −Ax,μ, which we call logU version. We observe that the Kugo-Ojima parameter u(0) at β = 5.5 is about -0.7 in the logU and about -0.6 in the U -linear version. If the configuration is in the core region, the tensorG μν = tr(λ̄ Dμ 1 −∂D (−Dν)λ )xy divided by N − 1, where N is the number of colours, is expected to approach a function E(U) defined by the optimizing function. They are E(U) = ∑