Symmetry energy and neutron star properties in the saturated Nambu-Jona-Lasinio model

In this work, we adopt the Nambu-Jona-Lasinio (NJL) model that ensures the nuclear matter saturation properties to study the density dependence of the symmetry energy. With the interactions constrained by the chiral symmetry, the symmetry energy shows novel characters different from those in conventional mean-field models. First, the negative symmetry energy at high densities that is absent in relativistic mean-field (RMF) models can be obtained in the RMF approximation by introducing a chiral isovector-vector interaction, although it would be ruled out by the neutron star (NS) stability. Second, with the inclusion of the isovector-scalar interaction the symmetry energy exhibits a general softening at high densities even for the large slope parameter of the symmetry energy. The NS properties obtained in the present NJL model can be in accord with the observations. The NS maximum mass obtained with various isovector-scalar couplings and momentum cutoffs is well above the 2M⊙, and the NS radius obtained well meets the limits extracted from recent measurements. In particular, the significant reduction of the canonical NS radius occurs with the moderate decrease of the slope of the symmetry energy.