Condensates in Lattice Landau Gauge QCD

The running coupling and the Kugo-Ojima parameter c of unquenched lattice Landau gauge are measured and compared with the continuum theory. We used gauge configurations of JLQCD/CP- PACS with Wilson fermion and those of Columbia University and MILC with Kogut-Susskind fermions. Although there exists dependence on the polarization due to asymmetry of the lattice, it is observed that c is consistent with 1. Presence of infrared fixed point of $\alpha_0\sim 2-2.5$ irrespective of the fermion actions in the continuum and in the chiral limit is suggested. In comparison with pQCD results in $\widetilde{MOM}$ scheme up to the 4-loop level, the MILC data of $\alpha_s$ in the region $1\sim 3$GeV exhibit presence of dimension 2 condensates and dimension 4 condensates with sign opposite to the dimension 2 condensates. We observed that Zwanziger’s horizon condition is satisfied within errors. The dimension 2 condensates is interpreted as the square norm of the gauge field which is related to the Zwanziger's horizon condition and the dimension 4 condensates is interpreted as the quark condensates.