Phase diagram of hot and dense QCD constrained by the Statistical Model

We propose a prescription to constrain the chiral effective model approach to the QCD phase diagram using the thermal Statistical Model which is a hadronic description consistent with the heavy-ion experimental data at the chemical freeze-out. In the transition region where thermal quantities of hadrons blow up, deconfined quarks and gluons should smoothly take over the relevant degrees of freedom from color confined hadrons. We use the Polyakov-loop coupled Nambu-Jona-Lasinio (PNJL) model as an effective description in the quark side. We require that the validity regions of these models should have an overlap on the phase diagram, which gives a condition to reduce model uncertainty. Our results favor a phase diagram with the chiral and the deconfinement phase transitions both staying close to the chemical freeze-out points until μB=500-600 MeV, above which the model parameter is not well constrained.