A test of the Kugo-Ojima confinement criterion by lattice Landau gauge QCD simulations

The first test of the Kugo-Ojima colour confinement criterion by the lattice Landau gauge QCD simulation is performed. The parameter u which is expected to be -1\delta^a_b in the continuum theory was found to be -0.7\delta^a_b in the strong coupling region. The data is analyzed in connection with the theory of Zwanziger. In the weak coupling region, the expectation value of the horizon function is negative or consistent to 0.Comment: 4 pages, 2 figures, Talk given at International Conference on Quark Nuclear Physics(QNP2000), Adelaide, Australia, 21-25 February 200

Color Confinement in Lattice Landau Gauge

The problem of color confinement in lattice Landau gauge QCD is briefly reviewed in the light of Kugo-Ojima criterion and Gribov-Zwanziger theory. The infrared properties of the Landau gauge QCD is studied by the measurement of the gluon propagator, ghost propagator, Kugo-Ojima parameter and the running coupling via $\beta=6.4,32^4,48^4$ lattice simulation. The data are analyzed in the principle of minimum sensitivity(PMS) in the $\widetilde{MOM}$ scheme. We observe the running coupling $\alpha_s(q)$ has a maximum about 1 and decreases near q=0. The Kugo-Ojima parameter, which is expected to be 1 was about 0.8.Comment: 7 pages, 4 figures, SCGT02 conference proceedings, Dec.10-13 200

Confinement in the lattice Landau Gauge QCD simulation

The running coupling and the Kugo-Ojima parameter of the confinement criterion are measured for the quenched SU(3) \beta=6.4, 6.45, 56^4 lattice and the unquenched \beta=5.2, 20^3 x 48 lattice of JLQCD, \beta=2.1, \kappa=0.1357, 0.1382, 24^3 x 48 lattice of CP-PACS and \beta_{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 \alpha_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.Comment: 3pages, 2 figures. MILC data in Figure 1 and Table 1 are correcte

Roles of the quark field in the infrared lattice Coulomb gauge and Landau gauge QCD

The effective coupling of QCD is measured by using the gauge configurations produced by the MILC collaboration in which the Kogut Susskind (KS) fermion is incorporated and by using that produced by the QCDOC collaboration in which the domain wall fermion (DWF) is incorporated. We fix the gauge to the Landau gauge and to the Coulomb gauge. The infrared effective coupling in the Coulomb gauge agrees with the recent extraction at JLab, but that in the Landau gauge shows infrared suppression. The suppression is expected to be due to the color anti-symmetric ghost propagator which in the unquenched configurations has stronger infrared singularity than the color diagonal ghost propagator. The Coulomb form factor in the infrared depends on the kind of the fermion incorporated in the system and the temperature. The quark has the effect of quenching randomness and the fluctuation of the color anti-symmetric ghost propagator is reduced in the unquenched configuration, and the Kugo-Ojima parameter c is closer to 1 in the unquenched configuration than in the quenched configuration.Comment: 7 pages, 9 figures, Lattice2007 proceedings (use PoS.cls