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Infrared features of the ghost propagator of color diagonal and color antisymmetric ghost propagator of quenched SU(2) and quenched SU(3) are compared with those of unquenched Kogut-Susskind fermion SU(3) lattice Landau gauge.We compare 1) the fluctuation of the ghost propagator, 2) the ghost condensate parameter v of the local composite operator (LCO) approach and 3) the Binder cumulant of color anti-symmetric ghost propagator between quenched and unquenched configurations.The color diagonal SU(3) ghost dressing function of unquenched configurations has weaker singularity than the quenched configurations. In both cases fluctuations become large in q < 0.5GeV.The ghost condensate parameter v in the ghost propagator of the unquenched MILCc configuration samples is 0.002 ∼ 0.04GeV 2 while that of the SU(2) PT samples is consistent with 0.The Binder cumulant defined as Uis the color anti-symmetric ghost propagator measured by the sample average of gauge fixed configurations via parallel tempering method becomes ∼ 4/9 in all the momentum region. The Binder cumulant of the color antisymmetric ghost propagator of quenched SU(2) can be explained by the 3-d gaussian distribution, but that of the unquenched MILCc deviates slightly from that of the 8-dimensional gaussian distribution.The stronger singularity and large fluctuation in the quenched configuration could be the cause of the deviation of the Kugo-Ojima confinement parameter c from 1, and the presence of ordering in the ghost propagator of unquenched configurations makes it closer to 1.

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Quark propagators of the unquenched Kogut-Susskind(KS) fermion obtained from the gauge configurations of the MILC collaboration are measured after Landau gauge fixing and using the Staple+Naik action. Presence of theqq condensates and A 2 condensates in the dynamical mass M (q) and the quark wave function renormalization Z ψ (q 2 ) are investigated. We obtain the correlation of the renormalization factor of the running coupling taken at µ ∼ 6GeV and that of the quark wave function renormalization Z ψ (q 2 ) of the Staple+Naik action. The mass function M (q) is finite at q = 0 and its chiral limit is ∼ 0.38GeV. We compared the results corrected by the scale of the vertex renormalization and the tadpole renormalization with the corresponding values obtained by the Asqtad action without renormalization and observed good agreement.Implication of infrared finite Z2(q) = 1/Z ψ (q 2 ) to the Kugo-Ojima confinement criterion is discussed.

We performed lattice Landau gauge QCD simulation on β = 6.0, 16 4 , 24 4 , 32 4 and β = 6.4, 32 4 , 48 4 and 56 4 by adopting the gauge fixing that minimizes the norm of the gauge field, and measured the running coupling by using the gluon propagator and the ghost propagator. In view of ambiguity in the vertex renormalization factorZ1 in the lattice, we adjust the normalization of the running coupling by the perturbative QCD results near the highest momentum point. It has a maximum αs(q) ≃ 2.1(3) at around q = 0.5 GeV and decreases as q approaches 0, and the Kugo-Ojima parameter reached -0.83(2). The infrared exponent of the ghost propagator at 0.4GeV region is αG = 0.20 but there is an exceptional Gribov copy with αG = 0.27. The features of the exceptional Gribov copy are investigated by measuring four one-dimensional Fourier transform(1-d FT) of the gluon propagator transverse to each lattice axis. We observe, in general, correlation between absolute value of the Kugo-Ojima parameter and the degree of reflection positivity violation in the 1-d FT of the gluon propagator.@The 1-d FT of the exceptional Gribov copy has an axis whose sample-wise gluon propagator manifestly violates reflection positivity, and the average of the Cartan subalgebra components of the Kugo-Ojima parameter along this axis is consistent to -1. The running coupling of the ensemble average shows a suppression at 0 momentum, but when the ghost propagator of the exceptional Gribov copy is adopted, the suppression disappears and the data implies presence of the infrared fixed point αs(0) ∼ 2.5(5) and κ = 0.5 suggested by the Dyson-Schwinger approach in the multiplicative renormalizable scheme. Comparison with the SU(2) QCD and N f = 2 unquenched SU(3) QCD are also made.