A New Approach to the Calculation of Some Properties of Vacuum and $\pi$ and $\sigma$ Mesons

Abstract

It is shown in a systematic way that the instanton dilute model can be combined with the global colour symmetry model to form a new nonperturbative QCD model. Based on the quark propagator derived in the instanton dilute liquid approximation, the quark condensate $<\bar{q}q>$, the mixed quark gluon condensate $g_{s}<\bar{q}G_{\mu\nu}\sigma^{\mu\nu}q>$, the four quark condensate $<|bar{q}\Gamma q\bar{q}\Gamma q>$ and tensor, pion vacuum susceptibilities have been calculated at the mean field level in the framework of the new nonperturbative QCD model. The numerical results are compatible with the values obtained within other nonperturbative approaches. The calculated masses and decay constants of $\pi$ and $\sigma$ mesons are also close to the experimental values.