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We investigate the properties of isospin-symmetric nuclear matter and neutron stars in a chiral model approach adopting the SU(2) parity doublet formulation. This ansatz explicitly incorporates chiral symmetry restoration with the limit of degenerate masses of the nucleons and their parity partners. Instead of searching for an optimized parameter set we explore the general parameter dependence of nuclear matter and star properties in the model. We are able to get a good description of ground state nuclear matter as well as large values of mass for neutron stars in agreement with observation.
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We investigate the properties of dense matter and neutron stars. In particular we discuss model calculations based on the parity doublet picture of hadronic chiral symmetry. In this ansatz the onset of chiral symmetry restoration is reflected by the degeneracy of baryons and their parity partners. In this approach we also incorporate quarks as degrees of freedom to be able to study hybrid stars.
We study dense nuclear matter and the chiral phase transition in a SU(2) parity doublet model at zero temperature. The model is defined by adding the chiral partner of the nucleon, the N, to the linear sigma model, treating the mass of the N as an unknown free parameter. The parity doublet model gives a reasonable description of the properties of cold nuclear matter, and avoids unphysical behaviour present in the standard SU(2) linear sigma model. If the N is identified as the N(1535), the parity doublet model shows a first order phase transition to a chirally restored phase at large densities, $rho approx 10 rho_0$, defining the transition by the degeneracy of the masses of the nucleon and the N. If the mass of the N is chosen to be 1.2 GeV, then the critical density of the chiral phase transition is lowered to three times normal nuclear matter density, and for physical values of the pion mass, the first order transition turns into a smooth crossover.
Using an extended parity doublet model with the hidden local symmetry, we study the properties of nuclei in the mean field approximation to see if the parity doublet model could reproduce nuclear properties and also to estimate the value of the chiral invariant nucleon mass $m_0$ preferred by nuclear structure. We first determined our model parameters using the inputs from free space and from nuclear matter properties. Then, we study some basic nuclear properties such as the nuclear binding energy with several different choices of the chiral invariant mass. We observe that our results, especially the nuclear binding energy, approach the experimental values as $m_0$ is increased until $m_0=700$ MeV and start to deviate more from the experiments afterwards with $m_0$ larger than $m_0=700$ MeV, which may imply that $m_0=700$ MeV is preferred by some nuclear properties.
We study the chiral condensates in neutron star matter from nuclear to quark matter domain. We describe nuclear matter with a parity doublet model (PDM), quark matter with the Nambu--Jona-Lasino (NJL) model, and a matter at the intermediate density by interpolating nuclear and quark matter equations of state. The model parameters are constrained by nuclear physics and neutron star observations. Various condensates in the interpolated domain are estimated from the chemical potential dependence of the condensates at the boundaries of the interpolation. The use of the PDM with substantial chiral invariant mass ($m_0 gtrsim 500$ MeV, which is favored by the neutron star observations) predicts the mild chiral restoration, and the significant chiral condensate remains to baryon density $n_B sim 2-3n_0$ ($n_0simeq 0.16,{rm fm}^{-3}$: nuclear saturation density), smoothly approaching the NJL predictions for the color-flavor-locked phase at $n_B gtrsim 5n_0$. The same method is applied to estimate diquark condensates, number densities of up-, down- and strange-quarks, and the lepton fraction. In our descriptions the chiral restoration in the interpolated domain proceeds with two conceptually distinct chiral restoration effects; the first is associated with the positive scalar density in a nucleon, relevant in dilute regime, and the other primarily arises from the modification of the quark Dirac sea, which is triggered by the growth of the quark Fermi sea. We discuss several qualitative conjectures to interpolate the microphysics in nuclear and quark matter.
We construct an equation of state (EOS) for neutron stars by interpolating hadronic EOS at low density and quark EOS at high density. A hadronic model based on the parity doublet structure is used for hadronic matter and a quark model of Nambu--Jona-Lasinio type is for quark matter. We assume crossover between hadronic matter and quark matter in the the color-flavor locked phase. The nucleon mass of the parity doublet model has a mass associated with the chiral symmetry breaking, and a chiral invariant mass $m_0$ which is insensitive to the chiral condensate. The value of $m_0$ affects the nuclear EOSs at low density, and has strong correlations with the radii of neutron stars. Using the constraint to the radius obtained by LIGO-Virgo and NICER, we find that $m_0$ is restricted as $600,mathrm{MeV}lesssim m_0 lesssim 900,mathrm{MeV}$.
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