Numerical studies of confinement in the lattice Landau gauge

Critical conjectures on confinement in the Landau gauge is numerically test ed in focus to Gribov copy effects. One of the subjects is of the Kugo-Ojim a confinement criterion and the other is of various viewpoints in the Gribo v-Zwanziger theory. We use the smearing gauge as a reference gauge free of Gribov copy, and performed three types of simulations, log U, U-linear and log U in the smearing gauge. It is found that Gribov copy effect on the Kug o-Ojima parameter is small. log U and U-linear simulations yield only globa l scale factor difference in gluon propagator, but nontrivial difference of momentum behaviour in ghost propagator, and about 10% difference in Kugo-O jima parameter. The horizon function defined by Zwanziger is evaluated in t hree types of gauge field and compared. All data show the negative horizon function as expected.