Exclusion of super-soft symmetry energies and neutron star properties in the saturated Nambu-Jona-Lasinio model

Considering the importance of Lorentz invariance and chiral symmetry, we adopt the saturated Nambu-Jona-Lasinio (NJL) model to study the density dependence of the symmetry energy. The super-soft symmetry energy can be obtained from introducing a chiral isovector-vector interaction in the lagrangian, but should be ruled out by the neutron star (NS) stability in the mean-field approximation. It is found that the isovector-scalar interaction in the NJL model can play an important role in softening of the symmetry energy. We have investigated NS properties. The NS maximum mass obtained with various isovector-scalar couplings and momentum cutoffs is well above the $2M_\odot$, and the NS radius obtained well meets the limits extracted from recent measurements.