Resonating mean-field theoretical approach to the Nambu–Jona-Lasinio model

Abstract

Using the Nambu--Jona-Lasinio (NJL) model, the dynamical chiral-symmetry breaking, the light-mesons spectra, and the properties of the mesons have been investigated on the basis of a conventional Hartree-Fock approach. In order to show the advantage of the resonating (Res) mean-field theory for a fermion system with large quantum fluctuations over the usual mean-field theory, we apply it to the NJL model to describe more precisely such phenomena associated with the pionic excitation. For the sake of simplicity, a state with large quantum fluctuations is approximated by the superposition of two Dirac seas, namely nonorthogonal Slater determinants (S-dets) with different correlation structures. We consider two cases: in the first case both Dirac seas are composed of equal ``constituent quark masses'' while in the second case the constituent quark masses are unequal. We make a direct optimization of the Res-mean-field energy functional, i.e., a variation of the Res-mean-field ground-state energy with respect to the Res-mean-field parameters, the ``constituent quark masses.'' Then the Res-mean-field ground and excited states generated with the S-dets explain most of a mass spectrum and associated properties of the pion.