Solitonic solutions of the Nambu-Jona-Lasinio model: Selfconsistency and mean-field-quantities

Abstract

We consider a partially bosonized version of the Nambu-Jona-Lasinio model in the SU(2-flavour sector (u and d quarks) with classical scalar and pseudoscalar meson fields (σ and π). The polarization of the Dirac sea (fermion-1-loop effects) is fully included. The theory is regularized by using the Schwinger proper time method. Adjusting the parameters of the model in the vacuum and mesonic sector to the pion mass m π and the pion decay constant f π we are left with the constituent quark mass M as the only free parameter. The theory is solved for a system with baryon number B = 1 for various values of M by using a selfconsistent procedure. For M < M cr ≈ 360 MeV no solitonic solution exists. For M cr < M < 725 MeV one obtains N c = 3 explicit valence quarks, whereas for M > 725 MeV their contribution is contained in the regularized Dirac sea. We calculate important mean-field quantities as the classical energy E, the isoscalar quadratic baryon radius 〈 R 2〉, the isoscalar electric and the pion-nucleon form factor, the axial vector coupling constant g A and the nuclear sigma commutator Σ. Hereby the linear and the non-linear version of the model are compared and the effect of a finite pion mass is studied. It turns out that the physically relevant range of M is slightly above the critical point M cr favouring a clear valence quark picture.