We aim at drawing the hadron-quark phase transition line in the QCD phase diagram by using the two-phase model (TPM) in which the entanglement Polyakov-loop extended Nambu-Jona-Lasinio (EPNJL) model with the vector-type four-quark interaction is used for the quark phase and the relativistic mean field (RMF) model is used for the hadron phase. A reasonable TPM is constructed by using lattice QCD data and neutron star observations as reliable constraints. For the EPNJL model, we determine the strength of vector-type four-quark interaction at zero quark chemical potential from lattice QCD data on quark number density normalized by its Stefan-Boltzmann limit. For the hadron phase, we consider three RMF models: NL3; TM1; and the model proposed by Maruyama, Tatsumi, Endo, and Chiba (MTEC). We find that MTEC is most consistent with the neutron star observations and TM1 is the second best. Assuming that the hadron-quark phase transition occurs in the core of a neutron star, we explore the density dependence of vector-type four-quark interaction. Particularly for the critical baryon chemical potential ${\mu }_{\mathrm{B}}^{\mathrm{c}}$ at zero temperature, we determine a range of ${\mu }_{\mathrm{B}}^{\mathrm{c}}$ for the quark phase to occur in the core of a neutron star. The values of ${\mu }_{\mathrm{B}}^{\mathrm{c}}$ lie in the range $1560\mathrm{MeV}\le {\mu }_{\mathrm{B}}^{\mathrm{c}}\le 1910\mathrm{MeV}$.

• Received 12 May 2016

DOI:https://doi.org/10.1103/PhysRevD.94.014024