Determination of the strength of the vector-type four-quark interaction in the entanglement Polyakov-extended Nambu-Jona-Lasino model

We determine the strength $G_{rm v}$ of the vector-type four-quark interaction in the entanglement Polyakov-extended Nambu-Jona-Lasinio (EPNJL) model from the results of recent lattice QCD simulations with two-flavor Wilson fermions. The quark-number density is normalized by the Stefan-Boltzmann limit for small baryon chemical potential $mu$ and temperature $T$ higher than the pseudo-critical temperature $T_c$ of the deconfinement transition. The strength determined from the normalized quark-number density is $G_{rm v}=0.33 G_{rm s}$ for the strength $G_{rm s}$ of the scalar-type four-quark interaction. We explore the hadron-quark phase transition in the $mu$-$T$ plane, using the two-phase model consisting of the quantum hadrodynamics model for the hadron phase and the EPNJL model for the quark phase. When $G_{rm v}=0.33 G_{rm s}$, the critical baryon chemical potential of the transition at zero $T$ is $mu_c sim 1.6$ GeV that accounts for two solar mass measurements of neutron stars in the framework of the quark-hadron hybrid star model.