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We aim at drawing the hadron-quark phase transition line in the QCD phasediagram by using the two phase model (TPM) in which the entanglementPolyakov-loop extended Nambu--Jona-Lasinio (EPNJL) model with vector-typefour-quark interaction is used for the quark phase and the relativistic meanfield (RMF) model is for the hadron phase. Reasonable TPM is constructed byusing lattice QCD data and neutron star observations as reliable constraints.For the EPNJL model, we determine the strength of vector-type four-quarkinteraction at zero quark chemical potential from lattice QCD data on quarknumber 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 neutronstar observations and TM1 is the second best. Assuming that the hadron-quarkphase transition occurs in the core of neutron star, we explore thedensity-dependence of vector-type four-quark interaction. Particularly for thecritical baryon chemical potential at zero temperature, we determine a rangefor the quark phase to occur in the core of neutron star.

Determination of hadron-quark phase transition line from lattice QCD and two-solar-mass neutron star observations