Sea quark effects in non-topological chiral soliton models and the Nambu-Jona-Lasinio approach

Abstract

Abstract The Nambu-Jona-Lasinio model (NJL) in the chiral invariant SU (2)-sector with scalar couplings is solved numerically in the Hartree approximation (zero boson loop) for baryon number B =1. To this end first the polarized vacuum solution ( B =0) is constructed using appropriately parametrized non-dynamic meson fields on the chiral circle. The cut-off Λ is fixed to reproduce the pion decay constant. With this choice a full treatment of the polarized vacuum is shown in second-order gradient expansion to be equivalent to considering kinetic energies of the mesons. Solutions of the NJL model with baryon number B =1 are obtained by adding N c=3 valence quarks to the full polarized vacuum and subjecting them to the same meson fields. If one adds the valence quarks to the kinetic energy of the mesons the usual chiral soliton model with valence quarks (CSM) is obtained. For both, NJL and CSM, the equilibrium radii of the B =1 solution are evaluated and shown to be rather close to each other. The present approach shows no vacuum instabilities. The resulting radii are different from those of the renormalized one-quark-loop model.