Constraining the competition between the deconfinement and chiral phase transitions in light of the multimessenger era

TL;DR

This work develops a hybrid-star framework combining a parity doublet hadronic EOS with a (2+1)-flavor NJL quark EOS, linked via a Maxwell construction and regulated by a free vacuum pressure $B$ to control the deconfinement–chiral transition split. The chiral transition is tracked in the quark sector by the chiral susceptibility peak at $\mu_\chi$, while deconfinement is determined by the equality of hadronic and quark pressures at $\mu_{\mathrm{de}}$, yielding a gap $\Delta=\mu_{\mathrm{de}}-\mu_\chi$ that is sensitive to the vector interaction strength $\alpha$ and to $B$. Across parameter scans, stable hybrid stars with quark cores emerge for a range of $m_0$, $\alpha$, and $B$, with a maximum mass around $M_{\max}\sim 2.2\,M_\odot$ when $m_0\approx 600$ MeV and $\alpha$ is large enough to stiffen the quark EOS; tidal deformability and NICER constraints prefer such a configuration, indicating a moderately soft intermediate-density hadronic EOS joined to a stiff high-density quark phase. The results underscore the utility of controlling the deconfinement density via $B$ and of allowing a nonzero split between chiral restoration and deconfinement to reconcile mass and radius observations in the multimessenger era. Overall, the study provides a concrete, testable framework for probing high-density QCD phases inside neutron stars through astrophysical data.

Abstract

We extend the parity doublet model for hadronic matter and study the possible presence of quark matter inside the cores of neutron stars with the Nambu-Jona-Lasinio (NJL) model. Considering the uncertainties of the QCD phase diagram and the location of the critical endpoint, we aim to explore the competition between the chiral phase transition and the deconfinement phase transition systematically, regulated by the vacuum pressure $-B$ in the NJL model. Employing a Maxwell construction, a sharp first-order deconfinement phase transition is implemented combining the parity doublet model for the hadronic phase and the NJL model for the high-energy quark phase. The position of the chiral phase transition is obtained from the NJL model self-consistently. We find stable neutron stars with a quark core within a specific parameter space that satisfies current astronomical observations. The observations suggest a relatively large chiral invariant mass $m_0=600$ MeV in the parity doublet model and a larger split between the chiral and deconfinement phase transitions while assuming the first-order deconfinement phase transition. The maximum mass of the hybrid star that we obtain is $\sim 2.2 M_{\odot}$.

Figures (7)

• Figure 1: Upper penal: Dynamical quark mass $M$ of $u$, $d$ and $s$ quarks versus quark chemical potential $\mu_q$ for modified (2+1)-flavor NJL models with $\alpha=0.0$, $\alpha=0.6$ and $\alpha=0.8$. Lower penal: The corresponding quark number densities $\rho_f$ as functions of $\mu_q$ with the same parameter sets.
• Figure 2: Chiral susceptibility as a function of quark chemical potential at zero temperature for $\alpha=0.00$, $\alpha=0.60$, $\alpha=0.80$ and $\alpha=0.95$, highlighting the chiral phase transition is a crossover. The maximum change of the chiral condensates within NJL models is indicated with black stars at $\mu_q=301.0 \;\text{MeV}$, $\mu_q= 307.6 \;\text{MeV}$, $\mu_q=385.0\;\text{MeV}$, and $\mu_q=318.7\;\text{MeV}$ respectively.
• Figure 3: Pressure as a function of baryon chemical potential for hadronic matter and strange quark matter. The green curves correspond to the results from the present modified NJL model, while red curves present PDM model calculations for hadronic matter with chiral invariant mass for $m_0=500\;\text{MeV}$, $m_0=600\;\text{MeV}$, and $m_0=700\;\text{MeV}$, respectively.
• Figure 4: The position of the chiral phase transition and the deconfinement phase transition, indicated with colored squares and stars respectively, as functions of baryon chemical potential for hybrid EOS adopting $\alpha=0.0$, $B^{1/4}=150 \;\text{MeV}$; $\alpha=0.6$, $B^{1/4}=145\;\text{MeV}$, and $\alpha=0.8$$B^{1/4}=150 \;\text{MeV}$ within NJL model for quark phase and $m_0=500\;\text{MeV}$ or $m_0=600\;\text{MeV}$ within PDM for hadronic phase.
• Figure 5: The split between the chiral phase transition and the deconfinement phase transition($\Delta=\mu_{\rm de}- \mu_{\chi}$) as a function of $\alpha$ for hadronic matter with $\rm PDM600$ and quark matter EOS at $B^{1/4}=130\;\text{MeV}$.