QCD critical end point from a realistic PNJL model

With parameters fixed by critical temperature and equation of state at zero baryon chemical potential, a realistic Polyakov--Nambu--Jona-Lasinio (rPNJL) model predicts a critical end point of chiral phase transition at $(\mu_B^E= 720 {\rm MeV}, T^E=93 {\rm MeV})$. The extracted freeze-out line from heavy ion collisions is close to the chiral phase transition boundary in the rPNJL model, and the kurtosis $\kappa \sigma^2$ of baryon number fluctuations from the rPNJL model along the experimental freeze-out line agrees well with the BES-I measurement. Our analysis shows that the dip structure of measured $\kappa\sigma^2$ is determined by the relationship between the freeze-out line and chiral phase transition line at low baryon density region, and the peak structure can be regarded as a clean signature for the existence of CEP.