Exploring the first-order phase transition in neutron stars using the parity doublet model and NJL-type quark model

We investigate the possibility and impacts of a first-order phase transition from hadronic matter to quark matter in neutron stars (NSs) using two specific models: the parity doublet model (PDM) for the hadronic phase and the Nambu-Jona-Lasinio (NJL) type model for the quark phase. By combining these models, we construct hybrid equations of state (EOSs) that capture the transition between the two phases. We explore the parameter space of both models to identify the conditions under which a first-order phase transition can occur and study its effects on NS properties. We identify the suitable parameter space and constrain the onset density of the first-order phase transition. For m₀ = 500 MeV -- the chiral invariant mass in PDM, the phase transition occurs between 1.9n₀ and 2.95n₀ and ends between 2.1n₀ and 3.6n₀. Increasing m₀ to 600 MeV shifts the phase transition to higher densities, occurring between 2.9n₀ and 4.1n₀ and ending between 3.4n₀ and 4.6n₀.