Resonating mean-field theoretical approach to the Nambu-Jona-Lasinio model- art. no. 065203

Using the Nambu-Jona-Lasinio (NJL) model, the dynamical chiral-symmetry bre aking, the light-mesons spectra, and the properties of the mesons have been investigated on the basis of a conventional Hartree-Fock approach. In orde r to show the advantage of the resonating (Res) mean-field theory for a fer mion system with large quantum fluctuations over the usual mean-field theor y, we apply it to the NJL model to describe more precisely such phenomena a ssociated with the pionic excitation. For the sake of simplicity, a state w ith large quantum fluctuations is approximated by the superposition of two Dirac seas, namely nonorthogonal Slater determinants (S-dets) with differen t correlation structures. We consider two cases: in the first case both Dir ac seas an composed of equal "constituent quark masses" while in the second case the constituent quark masses are unequal. We make a direct optimizati on of the Res-mean-field energy functional, i.e., a variation of the Res-me an-field ground-state energy with respect to the Res-mean-field parameters, the "constituent quark masses." Then the Res-mean-held ground and excited states generated with the S-dets explain most of a mass spectrum and associ ated properties of the pion. [S0556-2813(99)05811-2].