Vacuum condensates in the global color symmetry model

Abstract

Based on the quark propagator in the instanton dilute liquid approximation, we calculate analytically the quark condensate $<\bar{q}q>$, the mixed quark gluon condensate $g_{s}<\bar{q}G_{\mu\nu}\sigma^{\mu\nu}q>$ and the four quark condensate $<\bar{q} \Gamma q\bar{q} \Gamma q>$ at the mean field level in the framework of global color symmetry model. The numerical calculation shows that the values of these condensates are compatible with the ranges determined by other nonperturbative approaches. Moreover, we find that for nonlocal four quark condensate the previous vacuum saturation assumption is not a good approximation even at the mean field level.