A renormalizable extension of the NJL-model

Abstract

The Nambu-Jona-Lasinio model is supplemented by the quark interaction generated by the one-gluon exchange. The employed gluon propagator exhibits the correct large momentum behavior of QCD, whereas the Landau-pole at low energies is screened. The emerging constituent quark model is one-loop renormalizable and interpolates between the phenomenologically successful Nambu-Jona-Lasinio model at low energies and perturbative QCD at high momenta. Consequently, the momentum dependence of the quark self-energy at high energy coincides with the prediction from perturbative QCD. The chiral phase transition is studied in dependence on the low energy four quark interaction strength in the Dyson-Schwinger equation approach. The critical exponents of the quark self-energy and the quark condensate are obtained. The latter exponent deviates from the NJL-result. Pion properties are addressed by means of the Bethe-Salpeter equation. The validity of the Gell-Mann-Oakes-Renner relation is verified. Finally, we study the conditions which are necessary to allow for an accurate estimate of observables by the NJL-model as well as the shortcoming of the NJL-model due to its inherent non-renormalizability.