Constraining the competition between the deconfinement and chiral phase transitions in light of the multimessenger era

In this paper, we extend the parity doublet model for hadronic matter and study the possible presence of quark matter inside the cores of neutron stars with the modified Nambu–Jona-Lasinio (NJL) model. Considering the uncertainties of the QCD phase diagram and the location of the critical endpoint, we aim to explore the competition between the chiral phase transition and the deconfinement phase transition systematically, regulated by the vacuum pressure [Formula: see text] in the NJL model. Employing a Maxwell construction, a sharp first-order deconfinement phase transition is implemented, combining the parity doublet model (PDM) for the hadronic phase and the NJL model for the high density quark phase. The position of chiral phase transition is obtained from the NJL model self-consistently. We find stable neutron stars with a quark core within a specific parameter space that satisfies current astronomical observations. The observations suggest a relatively large chiral invariant mass [Formula: see text] [Formula: see text]MeV in the PDM and a larger split between the chiral and deconfinement phase transitions while assuming the first-order deconfinement phase transition. The maximum mass of the hybrid star that we obtain is [Formula: see text].