An extended NJL model for baryonic matter and quark matter

By considering baryons as clusters of three quarks, we extend the Nambu-Jona-Lasinio (NJL) model to describe baryonic matter, quark matter, and their transitions in a unified manner, where the Dirac sea and spontaneous chiral symmetry breaking are considered. In particular, a density-dependent structural function $\alpha_S$ is introduced to modulate the four(six)-point interaction strengths to reproduce the baryon masses in vacuum and medium. Vector interactions are considered with the exchange of $\omega$ and $\rho$ mesons, where the density-dependent coupling constants are fixed by reproducing nuclear matter properties as well as the $\Lambda$-hyperon potential depth in nuclear medium. As density increases, quarks will emerge as quasi-free particles and coexist with baryons. This phase is interpreted as quarkyonic matter, where quarks are restricted to the lowest energy states in the presence of baryons, i.e., quarks are still confined. Similar to the treatment of $\alpha$ clustering in nuclear medium, a Pauli blocking term is added to baryon masses so that baryons eventually become unbound in the presence of a quark Fermi Sea. Then at large enough densities baryons vanish and a Mott transition takes place, we consider such a transition as deconfinement phase transition. Depending on the strengths of Pauli blocking term and quark-vector meson couplings, both first-order and continues phase transitions are observed for quarkyonic, chiral, and deconfinement phase transitions. The corresponding compact star structures are then investigated and confronted with various astrophysical constraints.