Physics Letters B 763 (2016) 145–150
Contents lists available at ScienceDirect
Physics Letters B
www.elsevier.com/locate/physletb
Symmetry energy and neutron star properties in the saturated
Nambu–Jona-Lasinio model
Si-Na Wei, Wei-Zhou Jiang
∗
, Rong-Yao Yang, Dong-Rui Zhang
Department of Physics, Southeast University, Nanjing 211189, China
a r t i c l e i n f o a b s t r a c t
Article history:
Received
25 May 2016
Received
in revised form 9 October 2016
Accepted
10 October 2016
Available
online 17 October 2016
Editor:
W. Haxton
Keywords:
Symmetry
energy
Neutron
stars
NJL
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.
© 2016 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license
(http://creativecommons.org/licenses/by/4.0/). Funded by SCOAP
3
.
1. Introduction
The nuclear symmetry energy is important for understanding
the reaction dynamics of heavy-ion collisions, the structures of
neutron- and proton-rich nuclei, and properties of neutron stars
(NS) [1–3]. Though the symmetry energy, which is the energy dif-
ference
per nucleon between pure neutron matter and symmetric
matter, is well constrained at saturation density to date [4–8],
the density dependence of the symmetry energy is still poorly
known especially at supra-normal densities [2,9]. The symmetry
energy predicted by different models is rather diverse at high den-
sities [10–17].
Unfortunately, the symmetry energy extracted from
the data with various isospin diffusion models also suffers from
the large uncertainty which diversifies in super-soft [18], soft [19],
and stiff [20] forms at high densities. We note that new experi-
ments
to probe the high-density symmetry energy are also on the
way [21]. While different high-density behaviors of the symmetry
energy are usually classified by the magnitude of the slope of the
symmetry energy at saturation density, we may raise the question:
Are there new high-density behaviors of the symmetry energy that
can’t be simply elaborated by the slope parameter?
*
Corresponding author.
E-mail
address: wzjiang@seu.edu.cn (W.-Z. Jiang).
On the other hand, the super-soft symmetry energy which
reaches the maximum and then turns to negative values at high
densities can be obtained from some non-relativistic models [12,
13],
while it can not be produced in the relativistic mean field
(RMF) models [14–17]. For instance, the nonlinear RMF mod-
els [15],
the density-dependent RMF models [16,22], and the point
coupling RMF models [23–25] predict similar tendencies of sym-
metry
energy, and no super-soft symmetry energy arises in these
models [17]. Since the success of RMF models in interpreting the
pseudospin symmetry [26–28] and analyzing polarization observ-
ables
in proton–nuclei reactions [29,30] indicates that the relativis-
tic
dynamics that includes the large attractive scalar and repulsive
vector [31–35] is of special importance, we may ask whether the
super-soft symmetry energy is incompatible with the relativistic
covariance, or it is hidden in some special interactions that are not
included in usual RMF models.
To
answer these questions, let’s first recall the prime impor-
tance
of the chiral symmetry in the strong interaction. In fact,
the chiral symmetry has served as a cornerstone to construct the
effective QCD models of the strong interaction [36,37]. In the de-
velopment
of RMF models, the chiral symmetry has also played
an important role in guiding the nonlinear form of the meson
self-interacting terms needed for the appropriate in-medium ef-
fects [38–42].
To explore the novel high-density behaviors of the
http://dx.doi.org/10.1016/j.physletb.2016.10.019
0370-2693/
© 2016 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). Funded by
SCOAP
3
.