Resonating mean-field theoretical description of π and σ mesons by the Nambu–Jona-Lasinio model Original Research Article

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 have applied it successfully to the Nambu–Jona-Lasinio model to describe precisely phenomena associated with pionic excitation. We apply it further to describe more accurately phenomena which are associate simultaneously with pionic and sigma-mesonic excitations. A state with large quantum fluctuations is approximated by a superposition of three Dirac seas composed of constituent quark masses, i.e., nonorthogonal Slater determinants (S-dets) with different correlation structures. We make a direct optimization 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 mass spectra and associated properties of pion and sigma meson.