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The first-principle approach to the dense state of QCD matter, i.e. thelattice-QCD simulation at finite baryon density, is not under theoreticalcontrol for the moment. The effective model study based on QCD symmetries is apractical alternative. However the model parameters that are fixed by hadronicproperties in the vacuum may have unknown dependence on the baryon chemicalpotential. We propose a new prescription to constrain the effective modelparameters by the matching condition with the thermal Statistical Model. In thetransitional region where thermal quantities blow up in the Statistical Model,deconfined quarks and gluons should smoothly take over the relevant degrees offreedom from hadrons and resonances. We use the Polyakov-loop coupledNambu--Jona-Lasinio (PNJL) model as an effective description in the quark sideand show how the matching condition is satisfied by a simple ansatz on thePolyakov loop potential. Our results favor a phase diagram with the chiralphase transition located at slightly higher temperature than deconfinementwhich stays close to the chemical freeze-out points.

Effective Model Approach to the Dense State of QCD Matter