No abstract

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.

No abstract

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.

Abstract. The running coupling and the Kugo-Ojima parameter of unquenched lattice Landau gauge are simulated and compared with the continuum theory. Although the running coupling measured by the ghost and gluon dressing function is infrared suppressed, the running coupling has the maximum of α 0 ∼ 2 − 2.5 at around q = 0.5GeV irrespective of the fermion actions (Wilson fermions and Kogut-Susskind(KS) fermions). The Kugo-Ojima parameter c which saturated to about 0.8 in quenched simulations becomes consistent with 1 in the MILC configurations produced with the use of the Asqtad action, after averaging the dependence on polarization directions caused by the asymmetry of the lattice. Presence of 1 + c 1 /q 2 correction factor in the running coupling depends on the lattice size and the sea quark mass. In the large lattice size and small sea quark mass, c 1 is confirmed of the order of a few GeV. The MILC configuration of a = 0.09fm suggests also the presence of dimension-4 condensates with a sign opposite to the dimension-2 condensates. The gluon propagator, the ghost propagator and the running coupling are compared with recent pQCD results including an anomalous dimension of fields up to the four-loop level.

The color diagonal and color antisymmetric ghost propagators slightly above Tc of N f = 2 MILC 24 3 × 12 lattices are measured and compared with zero temperature unquenched N f = 2 + 1 MILCc 20 3 × 64 and MILC f 28 3 × 96 lattices and zero temperature quenched 56 4 β = 6.4 and 6.45 lattices. The expectation value of the color antisymmetric ghost propagator φ c (q) is zero but its Binder cumulant, which is consistent with that of N 2 c − 1 dimensional Gaussian distribution below Tc, decreases above Tc. Although the color diagonal ghost propagator is temperature independent, the l 1 norm of the color antisymmetric ghost propagator is temperature dependent. The expectation value of the ghost condensate observed at zero temperature unquenched configuration is consistent with 0 in T > Tc.We also measure transverse, magnetic and electric gluon propagator and extract gluon screening masses. The running coupling measured from the product of the gluon dressing function and the ghost dressing function are almost temperature independent but the effect of A 2 condensate observed at zero temperature is consistent with 0 in T > Tc.The transverse gluon dressing function at low temperature has a peak in the infrared at low temperature but it becomes flatter at high temperature. The magnetic gluon propagator at high momentum depends on the temperature. These data imply that the magnetic gluon propagator and the color antisymmetric ghost propagator are affected by the presence of dynamical quarks and there are strong non-perturbative effects through the temperature-dependent color anti-symmetric ghost propagator.

Effects of the quark field on the ghost propagator of the lattice Landau gauge are investigated by using the unquenched SU(3) configurations produced by the MILC collaboration and compared with quenched gauge configurations of SU(2) first copy of the overrelaxation gauge fixing, the parallel tempering (PT) gauge fixing and quenched SU(3) 56 4 configurations. We measure the color symmetric and the color antisymmetric ghost propagator and the Binder cumulant of the l 1 norm and the l 2 norm of color antisymmetric ghost propagators and investigate deviation from those of Gaussian distributions. In the first copy samples of quenched SU (2)