Lattice QCD study for the Quark-Gluon Mixed Condensate (anti-Q sigma G Q)

We study the quark-gluon mixed condensate g<\bar{q} sigma G q>, which is another chiral order parameter, using the SU(3)c lattice QCD with the Kogut-Susskind(KS) fermion at the quenched level. We generate 100 gauge configurations on the 16^4 lattice with \beta = 6.0, and measure the mixed condensate at 16 points in each gauge configuration for each current-quark mass of m_q=21, 36, 52 MeV. From the 1600 data for each m_q, we find the ratio between the mixed condensate and the quark condensate, m_0^2 = g<\bar{q} sigma G q> / <\bar{q}q> \simeq 2.5 GeV^2 at the lattice scale of 1/a \simeq 2 GeV in the chiral limit. The large value of the mixed condensate suggests its importance in the operator product expansions in QCD.