Effects of the quark field on the ghost propagator of lattice Landau gauge QCD

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 (i) the fluctuation of the ghost propagator, (ii) the ghost condensate parameter $v$ of the local composite operator (LCO) approach, and (iii) the Binder cumulant of color antisymmetric 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 $q<0.5\text{ }\text{ }\mathrm{GeV}$. The ghost condensate parameter $v$ in the ghost propagator of the unquenched ${\mathrm{MILC}}_{c}$ configuration samples is $\ensuremath{\sim}0.002--0.04\text{ }\text{ }{\mathrm{GeV}}^{2}$ while that of the SU(2) parallel tempering samples is consistent with 0. The Binder cumulant defined as $U(q)=1\ensuremath{-}\frac{1}{3}\frac{⟨{\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\phi}}}^{4}⟩}{(⟨{\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\phi}}}^{2}⟩{)}^{2}}$, where $\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\phi}}(q)$ is the color antisymmetric ghost propagator measured by the sample average of gauge fixed configurations via parallel tempering method, becomes $\ensuremath{\sim}4/9$ in all the momentum region. The Binder cumulant of the color antisymmetric ghost propagator of quenched SU(2) can be explained by the 3D Gaussian distribution, but that of the unquenched ${\mathrm{MILC}}_{c}$ deviates slightly from that of the eight-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.