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

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 $3.6\,(1.5) \times \rho_0$ in symmetric nuclear matter, where $\rho_0$ 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.