Abstract
Lattice QCD has the sign problem at real quark chemical potential. There are some regions with no sign problem; one is the imaginary quark chemical potential region and the others are the real and imaginary isospin chemical potential regions. We show that the Polyakov-loop extended Nambu-Jona-Lasinio (PNJL) model can reproduce LQCD data in the regions. We also determine the model parameters from the data and predict the QCD phase diagram in the real quark chemical potential region.
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