Abstract
Firstly we qualitatively analyze the formation of the dip and peak structures of the kurtosis kappa sigma ^2 of net baryon number fluctuation along imagined freeze-out lines and discuss the signature of the existence of the QCD critical end point (CEP) in the Nambu–Jona-Lasinio (NJL) model, Polyakov-NJL (PNJL) model as well as mu -dependent PNJL(mu PNJL) model with different parameter sets, and then we apply a realistic PNJL model with parameters fixed by lattice data at zero chemical potential, and quantitatively investigate its kappa sigma ^2 along the real freeze-out line extracted from experiments. The important contribution from gluodynamics to the baryon number fluctuations is discussed. 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, and the freeze-out line starts from the back-ridge of the phase boundary is required. To our surprise, the kurtosis kappa sigma ^2 produced from the realistic PNJL model along the experimental freeze-out line agrees with BES-I data well, which indicates that equilibrium result can explain the experimental data. It is worth to point out that the extracted freeze-out temperatures from beam energy scan measurement are indeed higher than the critical temperatures at small chemical potentials, which supports our qualitative analysis.
Highlights
The phase transition and phase structure of Quantum Chromodynamics (QCD) under extreme conditions is the main topic of relativistic heavy ion collisions, and it is highly related to the evolution of the early universe and the equation of state inside the compact stars
Firstly we qualitatively investigate the kurtosis κσ 2 of net baryon number fluctuation and analyze the formation of its dip and peak structures along the imagined freezeout lines in the NJL model, Polyakov-loop improved NJL (PNJL) model as well as μ-dependent Polyakov-loop potential improved NJL (μPNJL) model with different parameter sets, and we apply a realistic PNJL model and quantitatively investigate its κσ 2 along the real freeze-out line extracted from experiments
We find that: (1) at zero chemical potential, the magnitude of κσ 2 is rather small in the NJL model comparing with lattice result, and it can reach around 1.5 in the PNJL and μPNJL models around the critical temperature
Summary
The phase transition and phase structure of Quantum Chromodynamics (QCD) under extreme conditions is the main topic of relativistic heavy ion collisions, and it is highly related to the evolution of the early universe and the equation of state inside the compact stars. 2, we give a brief introduction to the two-flavor NJL model, the Polyakov-loop improved NJL (PNJL) model as well as μ Polyakov-loop improved NJL (μPNJL) model, and qualitatively analyze the formation of the dip and peak structures of the kurtosis κσ 2 of net baryon number fluctuation along imagined freeze-out lines and discuss the signature of the existence of the QCD critical end point (CEP). 4. In order to qualitatively analyze the formation of the dip and peak structure of the kurtosis of the net baryon number distribution κσ 2 along the freeze-out line, as well as to investigate the gluodynamics contribution to κσ 2, we will compare κσ 2 in the framework of NJL model, the Polyakov-loop improved NJL (PNJL) model as well as NJL with μ-dependent Polyakov-loop potential (μPNJL) model.
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