The formation of dip and peak structures for the kurtosis of net baryon number fluctuations along the freeze-out line.
We analyze the structure of the kurtosis $\kappa \sigma^2$ of net baryon number fluctuation along the freeze out line and discuss the signature of the existence of the QCD critical end point (CEP) in the NJL model, PNJL model as well as $\mu$PNJL model with different parameter sets. It is found that at zero chemical potential, the main contribution to the baryon number fluctuation comes from gluodynamics, and the temperature dependent $\kappa \sigma^2$ can be used to constrain the model. The peak structure of $\kappa \sigma^2$ along the freeze-out line is solely determined by the existence of the CEP mountain and can be used as a clean signature for the existence of CEP. The formation of the dip structure is sensitive to the relation between the freeze-out line and the phase boundary. The dip structure can be formed if the freeze-out line starts from the temperature above the critical temperature at $\mu=0$ and crosses the foot of the CEP mountain. It is noticed that the extracted freeze-out temperature from beam energy scan measurement at RHIC is indeed higher than the crossover phase boundary, which supports our analysis for the formation of the dip structure. Around the CEP for chiral phase transition there is a negative region of $\kappa \sigma^2$ from the crossover side, the positive $\kappa \sigma^2$ at the dip from measurement indicates that the freeze-out line is away from the negative region
Publisher URL: http://arxiv.org/abs/1801.09215
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