In a parity doublet model, self-consistent minimization keeps the quark fraction at zero up to about 8n0, showing quark onset and chiral restoration need not coincide.
Quark-hadron crossover equations of state for neutron stars: constraining the chiral invariant mass in a parity doublet model
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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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Suppression of dynamical momentum-space shell by chiral symmetry
In a parity doublet model, self-consistent minimization keeps the quark fraction at zero up to about 8n0, showing quark onset and chiral restoration need not coincide.