The Determination of the Quark-Gluon Mixed Condensate (anti-Q sigma G Q) from Lattice QCD

Abstract

We study the quark-gluon mixed condensate g<\bar{q} sigma G q>, using the SU(3)c lattice QCD with the Kogut-Susskind fermion at the quenched level. We generate 100 gauge configurations on the 16^4 lattice with β= 6.0, and perform the measurement of the mixed condensate at 16 points in each gauge configuration for each current quark mass of m_q=21, 36, 52 MeV. Using 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. We study also chiral restoration at finite temperature in terms of the mixed condensate, which is another chiral order parameter. We present the lattice QCD results of the mixed condensate at finite temperature.