Unquenched Kogut-Susskind quark propagator in lattice Landau gauge QCD

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 $\mathrm{\text{Staple}}+\mathrm{\text{Naik}}$ action. Presence of the $\overline{q}q$ condensates and $A^2$ condensates in the dynamical mass $M(q)$ and the quark wave function renormalization $Z_{\psi }(q^2)$ are investigated. We obtain the correlation of the renormalization factor of the running coupling taken at $\mu \sim 6\mathrm{GeV}$ and that of the quark wave function renormalization $Z_{\psi }(q^2)$ of the $\mathrm{\text{Staple}}+\mathrm{\text{Naik}}$ action. The mass function $M(q)$ is finite at $q=0$ and its chiral limit is $\sim 0.38\mathrm{GeV}$. 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 $Z_2(q)=1/Z_{\psi }(q^2)$ to the Kugo-Ojima confinement criterion is discussed.