Numerical Study of the Kugo-ojima Criterion and the Gribov Problem in the Landau Gauge

The Kugo-Ojima color confinement criterion, which is based on the BRST symmetry of the continuum QCD is numerically tested by the lattice Landau gauge simulation. We first discuss the Gribov copy problem and the BRST symmetry on the lattice. The lattice Landau gauge can be formulated with options of the gauge field definition, U(link)-linear type or logU type. The Kugo-Ojima parameter u b which is expected to be −1δ b in the continuum theory is found to be −0.7δ b in the strong coupling region, and the magnitude is a little less in the weak coupling region in logU type simulation. Those values are weakened even further in U -linear type. The horizon function defined by Zwanziger is evaluated in both types of gauge field and compared. The horizon function in the logU version is larger than the other, but in the weak coupling region, the expectation value of the horizon function is suggested to be zero or negative.