  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 vector-type
four-quark interaction is used for the quark phase and the relativistic mean
field (RMF) model is for the hadron phase. 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 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 neutron star, we explore the
density-dependence of vector-type four-quark interaction. Particularly for the
critical baryon chemical potential at zero temperature, we determine a range
for the quark phase to occur in the core of neutron star.

Nuclear Theory