Correlating the skewness and kurtosis of baryon number distributions

The skewness and the kurtosis of the baryon number distributions are computed within QCD-improved low energy effective models including quantum thermal and density fluctuations. The results are compared with the Beam Energy Scan experiment at RHIC. The theoretical results agree with the experimental measurements up to errors, for the collision energy $\sqrt{s}\ge 19.6\mathrm{GeV}$. For smaller collision energies a discrepancy between theoretical and experimental results develops. This discrepancy partially relates to the lack of precision of the current setup for small collision energies. It is outlined how this deficiency can be overcome.

Figure 1

Flow equation for the effective action $\mathrm{\Gamma }$ in full QCD. The four loops correspond to contributions from gluons, ghosts, quarks, and mesons, respectively.

Figure 2

Skewness $S\sigma$ (red dashed lines) and kurtosis $\kappa {\sigma }^2$ (black solid lines) of the baryon number distributions as functions of the temperature, for different values of chemical potential, i.e. different collision energy, shown in Table 1. The yellow vertical band in each plot shows an estimate of the freeze-out temperature, with its center located at a temperature which produces the measured $S\sigma$ in experiments. All bands have a width of 20 MeV accounting for the systematic errors, for details see the discussion below (11).

Figure 3

Theoretical calculations of $S\sigma$ (left panel) and $\kappa {\sigma }^2$ (right panel) as functions of the collision energy, in comparison with experimental measurements in $\mathrm{Au}+\mathrm{Au}$ collisions at RHIC with centralities 0–5%, 5–10% [4]. The gray regions show error estimates resulting from the determination of freeze-out temperatures, which corresponds to the vertical yellow bands in Fig. 2. The black vertical lines indicate the collision energy, below which the UV-cutoff effect becomes significant.