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 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 and mesons, where the density-dependent coupling constants are fixed by reproducing nuclear matter properties as well as the -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 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.