Correlated fluctuations near the QCD critical point

In this article, we introduce a freeze-out scheme for the dynamical models near the QCD critical point through coupling the decoupled classical particles with the order parameter field. With a modified distribution function that satisfies specific static fluctuations, we calculate the correlated fluctuations of net protons on the hydrodynamic freeze-out surface. A comparison with recent STAR data shows that our model calculations could roughly reproduce energy-dependent cumulant $C_4$ and $\kappa {\sigma }^2$ of net protons through tuning the related parameters. However, the calculated $C_2$ and $C_3$ with both Poisson and binomial baselines are always above the experimental data due to the positive contributions from the static critical fluctuations. To qualitatively and quantitatively describe all the related experimental data, the dynamical critical fluctuations and more realistic noncritical fluctuation baselines should be investigated in the near future.

Figure 1

Energy dependence of cumulants $C_1$–$C_4$ for net protons in 0%–5% Au+Au collisions within $0.4<p_T<0.8$ GeV (left panels) and within $0.4<p_T<2$ GeV (right panels). The red stars are the STAR preliminary data [18, 19], dashed blue lines are the Poisson expectations, and black and gray curves with symbols are the results from our model calculations with the Poisson baselines.

Figure 2

The same as Fig. 1, but with binomial baselines.

Figure 3

Energy dependence of cumulants $C_1$–$C_4$ for net protons in 30%–40% $\mathrm{Au}+\mathrm{Au}$ collisions, with Poisson baselines.

Figure 4

The same as Fig. 3, but with binomial baselines.

Figure 5

Energy dependence of cumulant ratios, $S\sigma$ and $\kappa {\sigma }^2$, for net protons in 0%–5% $\mathrm{Au}+\mathrm{Au}$ collisions, with different $p_T$ ranges and different noncritical fluctuation baselines.

Figure 6

The same as Fig. 5, but for 30%–40% centrality bins.

Figure 7

Energy dependence of cumulants $C_1$–$C_4$ for protons, antiprotons, and net protons, with Poisson baselines (left panels) and binomial baselines (right panels).

Figure 8

$p_T$ acceptance dependence of $C_2^{\mathrm{critical}},C_3^{\mathrm{critical}}$, and $C_4^{\mathrm{critical}}$ of net protons.