Confinement in the lattice Landau Gauge QCD simulation

Abstract

The running coupling and the Kugo-Ojima parameter of the confinement criterion are measured for the quenched SU(3) β=6.4, 6.45, 56^4 lattice and the unquenched β=5.2, 20^3 x 48 lattice of JLQCD, β=2.1, κ=0.1357, 0.1382, 24^3 x 48 lattice of CP-PACS and β_{imp}=6.76,a m_{u,d}=0.007, 6.83,a m_{u,d}=0.040, 20^3 x 64 lattice of MILC collaboration. The quenched SU(3) 56^4 lattice data suggest presence of infrared fixed point of α_s=2.5(5) and the approach of the ensemble of the 1st copy to the Gribov boundary. The running coupling of q>2GeV can be fitted by the perturbative QCD(pQCD) + c/q^2 correction. We find the Kugo-Ojima parameter u(0)=-0.83(3). The rotational symmetry of the gluon propagator of the unquenched SU(3) is partially recovered, but its magnitude depends on whether the Wilson fermion or the Kogut-Susskind(KS) fermion are coupled to the gauge field. The gluon propagator coupled to KS fermion is more suppressed than that coupled to Wilson fermion. The running coupling inherits the same trend. The unquenched running coupling of the of q>3GeV can be fitted by the pQCD without c/q^2 term. The Kugo-Ojima parameter of unquenched configurations with light fermion masses is consistent with u(0)=-1.0.