Mean field approach to the instanton-induced effects close to the QCD phase transition

It was suggested earlier that the chiral phase transition is driven by a transition from random instanton–anti-instanton liquid to correlated instanton–anti-instanton molecules. So far this phenomenon was studied by numerical simulations, while we develop an alternative semianalytic approach. For two massless quark flavors, both instantons and “molecules” generate specific four-fermion effective interactions. After those are derived, we determine the temperature dependence of the thermodynamic quantities, the quark condensate, and the fraction of molecules using the standard mean field method. Using the Bethe-Salpeter equation, we calculate the [Formula presented]-dependence of mesonic correlation functions. These results shed new light on the problem of modification of hadrons, and they can be tested directly in lattice simulations.