Behavior of Gluons at non-perturbative region and Confinement Mechanism

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Quarks and gluons are two ingredients of QCD,whose prominent character is the confinement. Although they are not physical observables, gluon propagators are a fundamentaal object in QCD as a quantum field theory. Their long distance behavior may reveal a hint of the gluon confinement mechanism. Gribov found that standard gauge fixing conditions are not enough to select a single cofiguration among gauge equivalent ones for non-Abelian gauge theories.We calculate gluon propagators numerically by using Zwanziger's stochastic gauge which guarantees that we are in the Gribov region. Large deviation appears as tau increases ; the gluon seems to become massive at large tau. At intermediate region, the shape of the propgator is convex to the above. If we would interpret the behavior as the sum of maass poles, the spectral function can not be positive definite, i.e., there is an admixture of negative norm states. The effective mass seems to vanish at very large tau, although there error bars are very large. The result can be quantitatively fit by Gribov conjecture, but not quantitatively.