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

Abstract

Considering the importance of Lorentz invariance and chiral symmetry, we adopt the Nambu-Jona-Lasinio (NJL) model that ensures the nuclear matter saturation properties to study the density dependence of the symmetry energy. The negative symmetry energy at high densities that is usually dubbed 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⊙, 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, while the effect of the symmetry energy on the NS maximum mass remains insignificant as usual.

Nuclear Potentials Relevant to the Symmetry Energy in Chiral Models

“…The models to be used are the extended NJL model (NJL350) with a momentum cutoff 350 MeV [20,45,49], SLCd that is a density-dependent relativistic model with chiral limit [24,54], the extended linear-σ model in the strong coupling limit (denoted by SCL) [16], and the RMF model FSUGold [51]. The RMF model FSUGold can reproduce the properties of finite nuclei well [51], while it produces the maximum mass of neutron stars below the 2M constraint.…”

“…The progress to describe the properties of finite nuclei and neutron stars is also made with the SCL [16,56]. The NJL model, developed to have the saturation property, is used to constrain the symmetry energy and describe the properties of neutron stars including the glitches of the Vela pulsar [20,49]. In Table 1, we tabulate some properties of saturation, symmetry energy and neutron stars with these four models.…”

“…The extended NJL model includes the additional interaction terms with the scalar-vector, scalar-isovector couplings (G SV , G ρS ) to fit the saturation and density dependence of the symmetry energy. Here, the additional terms are given by [20,45,49]…”

“…where G S is the scalar coupling, and m 0 is the bare nucleon mass which is determined by the Gell-Mann-Oakes-Reinner relation on the hadron level [20].…”

“…This is seemly digressive but, instead, restates the importance of the vacuum. Since the original linear-σ and NJL models fail to fit nuclear matter saturation, a dozen of extended models have been developed to fit nuclear matter saturation and properties of finite nuclei [9][10][11][12][13][14][15][16][17][18][19][20]. In addition, the chiral symmetry can also be manifest by virtue of the vector channel in the hidden local symmetry [21].…”