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

Abstract

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