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The relation between the NJL model and QCD with condensed gluons

We try to find the relation between the three-flavor Nambu-Jona-Lasinio model and QCD based on the hypothesis that the gluon momenta are sharply condensed around the QCD scale, μ_g. We find that the effective four- and six-fermion interactions, G_4 and G_6, should be scaled by G_4 proportional to μ_g^(-2) and G_6 proportional to μ_g^(-5) being consistent with the mass dimension counting in the obtained effective Lagrangian. We then study the μ_g dependence on the phase diagram of the chiral phase transition at finite temperature and chemical potential and the location of the critical point. We find that the location of the critical point are sensitively affected by the value of the introduced gluon energy scale.