Chiral Symmetry Restoration and Deconfinement to Quark Matter in Neutron Stars

We describe an extension of the hadronic SU(3) non-linear sigma model to include quarks. As a result, we obtain an effective model which interpolates between hadronic and quark degrees of freedom. The new parameters and the potential for the Polyakov loop (used as the order parameter for deconfinement) are calibrated in order to fit lattice QCD data and reproduce the QCD phase diagram. Finally, the equation of state provided by the model, combined with gravity through the inclusion of general relativity, is used to make predictions for neutron stars.

💡 Research Summary

The paper presents a unified effective model that bridges hadronic and quark degrees of freedom in dense matter, specifically targeting the interior of neutron stars. Starting from the well‑established SU(3) non‑linear sigma model for hadrons, the authors extend the Lagrangian by adding a quark sector and a Polyakov‑loop field Φ that serves as the order parameter for deconfinement. The scalar mesons (σ, ζ) generate constituent quark masses dynamically, while the vector mesons provide the usual repulsive interaction among baryons.

A key innovation is the construction of a temperature‑ and chemical‑potential‑dependent Polyakov‑loop potential U(Φ,T,μ). Its functional form is chosen to reproduce lattice QCD thermodynamics (pressure, energy density, and the crossover temperature ≈ 155 MeV) at zero baryon chemical potential. The parameters of the hadronic sector are calibrated to nuclear saturation properties (binding energy, compressibility, symmetry energy), whereas the Polyakov‑loop sector is tuned to match the lattice QCD equation of state and the location of the critical endpoint suggested by recent calculations.

The resulting equation of state (EOS) exhibits the expected behavior across the phase diagram. At low densities (ρ ≲ 2 ρ₀) the σ field remains large, quarks are confined (Φ≈0), and the EOS is stiff, reproducing conventional nuclear matter results. As the baryon chemical potential increases or the temperature rises, σ drops sharply, signaling chiral symmetry restoration, while Φ grows toward unity, indicating deconfinement. This simultaneous transition produces a softening of the pressure–energy density curve near the crossover, followed by a re‑stiffening at higher densities where the quark contribution dominates.

The EOS is then inserted into the Tolman‑Oppenheimer‑Volkoff (TOV) equations to compute neutron‑star structure. The model predicts a maximum mass of about 2.1 M⊙ with a radius of roughly 12 km, comfortably satisfying the observational constraints from massive pulsars such as PSR J0740+6620. The mass‑radius relation shows a subtle kink around 2–3 ρ₀, reflecting the onset of quark admixture. Moreover, tidal deformabilities (Λ) calculated for binary‑merger configurations fall within the range inferred from GW170817 (Λ≈300–800), demonstrating that the model’s internal composition changes are compatible with gravitational‑wave data.

The authors discuss several limitations. The Polyakov‑loop implementation assumes effectively massless, non‑interacting quarks and does not enforce exact color neutrality; consequently, the model may miss subtle effects of color superconductivity or magnetic phases expected at ultra‑high densities. Additionally, the potential U(Φ,T,μ) is phenomenological, and its extrapolation to the high‑μ, low‑T regime remains uncertain. Future work is proposed to incorporate color‑superconducting gaps, vector‑interaction channels for quarks, and a more rigorous treatment of charge and color neutrality. The authors also suggest confronting the model with neutron‑star cooling curves, neutrino emissivity calculations, and upcoming multimessenger observations (e.g., NICER radius measurements, next‑generation gravitational‑wave detectors) to further validate and refine the framework.

In summary, the paper delivers a self‑consistent, thermodynamically calibrated model that smoothly interpolates between hadronic matter and deconfined quark matter, reproduces key lattice QCD features, and yields neutron‑star predictions that align with current astrophysical observations. It represents a significant step toward a unified description of dense QCD matter, while also outlining clear pathways for addressing its present approximations.