A Quarkyonic Quark-Meson Coupling Model for Nuclear and Neutron Matter

TL;DR

This work develops a quarkyonic quark-meson coupling (QQMC) framework that unifies the dual quarkyonic picture with the quark-meson coupling model to describe dense nuclear matter across densities, from presaturation to crossover regions. By employing a relativistic Gaussian quark wavefunction and an infrared regulator, the authors address singular behavior at the quark-saturation density and introduce a Pauli-blocking–driven quarkyonic phase that interacts with meson mean fields in a self-consistent manner. The QQMC model reproduces neutron-star sound speeds inferred from observations and aligns with high-energy heavy-ion collision pressure constraints, with the results strongly depending on the nucleon radius in the Gaussian quark description. While promising, the approach requires further justification of boundary conditions for the post-saturation regime and a deeper QCD-based treatment of the saturation region, with potential extensions to finite temperature and hyperon degrees of freedom. Overall, QQMC provides a practical, quark-based EOS framework bridging baryonic and quark matter regimes and contributing to resolving the hyperon puzzle through quark-level dynamics and medium-modified nucleon structure.

Abstract

We unite the dual quarkyonic model with the quark-meson coupling (QMC) model to construct a novel nuclear model based on the quark degrees of freedom, which can cover a wide range of nuclear density from low density to the crossover region. In the model, the relativistic, gaussian quark wavefunction is used to describe the nucleon structure. We first evaluate the energy density, chemical potential, pressure and sound velocity within the ideal Fermi gas picture. In this case, those physical quantities are discontinuous or divergent at the quark saturation density, where quarkyonic phase emerges. To remove such singular behavior, we next introduce an infrared regulator, and combine the dual quarkyonic model and the QMC model to include the nuclear interaction -- we call it the quarkyonic quark-meson coupling (QQMC) model. We then find that the quark saturation density depends strongly on the nucleon size. For example, when $r_p = 0.6\, (0.8)$ fm, where $r_p$ is the root-mean-square radius of proton, the quark saturation density is about $3.6\,(1.5) \times ρ_0$ in symmetric nuclear matter, where $ρ_0$ is the nuclear saturation density. It is notable that the nuclear interaction is quite important to consider physical quantities quantitatively. In fact, the QQMC model can produce the sound velocity which is consistent with that inferred from the observed data of several neutron stars. Furthermore, pressure in symmetric or pure neutron matter deduced from the experiments of heavy-ion collisions at high energy can be explained by the QQMC model as well. We discuss in detail the formulation for the QQMC model and the physical quantities calculated by the model.

Figures (18)

• Figure 1: Density dependence of $k_{s}$ and $k_{b}$ in the case of $r_p=0.8$ fm.
• Figure 2: Quark and nucleon momentum distributions in symmetric nuclear matter. We take $r_p=0.8$ fm.
• Figure 3: Energy density, chemical potential, pressure or sound velocity as a function of $\rho_N$.
• Figure 4: Density dependence of $k_s$ and $k_b$ in the case of $r_p=0.8$ fm. We take $\nu =1.8$ and $w=0.25$ GeV.
• Figure 5: Energy density, chemical potential, pressure and sound velocity in the case of $\nu =1.8$ and $w=0.25$ GeV.