Centrality dependence of chemical freeze-out parameters from net-proton and net-charge fluctuations using a hadron resonance gas model

We estimate chemical freeze-out parameters in Hadron Resonance Gas (HRG) and Excluded Volume HRG (EVHRG) models by fitting the experimental information of net-proton and net-charge fluctuations measured in Au + Au collisions by the STAR Collaboration at the BNL Relativistic Heavy Ion Collider (RHIC). We observe that chemical freeze-out parameters obtained from lower and higher order fluctuations are almost the same for $\sqrt{s_{\mathit{NN}}}>27$ GeV, but tend to deviate from each other at lower $\sqrt{s_{\mathit{NN}}}$. Moreover, these separations increase with decrease of $\sqrt{s_{\mathit{NN}}}$, and for a fixed $\sqrt{s_{\mathit{NN}}}$ increase towards central collisions. Furthermore, we observe an approximate scaling behavior of $({\mu }_B/T)/{({\mu }_B/T)}_{\mathrm{central}}$ with $\left(N_{\mathrm{part}}\right)/{\left(N_{\mathrm{part}}\right)}_{\mathrm{central}}$ for the parameters estimated from lower order fluctuations for $11.5\le \sqrt{s_{\mathit{NN}}}\le 200$ GeV. Scaling is violated for the parameters estimated from higher order fluctuations for $\sqrt{s_{\mathit{NN}}}=11.5$ and 19.6 GeV. It is observed that the chemical freeze-out parameter, which can describe ${\sigma }^2/M$ of net protons very well in all energies and centralities, cannot describe the $s\sigma$ equally well, and vice versa.

Figure 1

Centrality (in terms of $N_{\mathrm{part}})$ dependence of chemical freeze-out temperatures and baryon chemical potentials for Au + Au collisions at $\sqrt{s_{\mathit{NN}}}=200$, 62.4, 39, 27, 19.6, 11.5, and 7.7 GeV. $\sqrt{s_{\mathit{NN}}}$ varies column wise. Four sets of chemical freeze-out parameters (CFO) have been plotted. For specifications of different sets of parameters see Table 1.

Figure 2

Chemical freeze-out parameters in the $\left(T,{\mu }_B\right)$ plane of the QCD phase diagram. We plot chemical freeze-out parameters for the most central $\left(0–5\%\right)$ as well as for the most peripheral $\left(70–80\%\right)$ collisions for $7.7\le \sqrt{s_{\mathit{NN}}}\le 200$ GeV. We compare our results of CFO1 and CFO2 with chemical freeze-out parameters for $0–5\%$ centralities given by Alba et al. [20] for $11.5\le \sqrt{s_{\mathit{NN}}}\le 200$ GeV. Chemical freeze-out parameters given by Chatterjee et al. [53] have also been plotted.

Figure 3

Variation of ${\mu }_B/T$ with $N_{\mathrm{part}}$ (black points). Blue solid points correspond to the ${\mu }_B/T$ according to Eq. (13).

Figure 4

Scaling behavior of ${\mu }_B/T$ with centrality. On the horizontal axis $N_{\mathrm{part}}$ is normalized with that of the most central collision and similarly in the vertical axis ${\mu }_B/T$ is normalized to that of the most central collision. Therefore, in the horizontal axis, the maximum value, which is equal to 1, corresponds to the most central collision $\left(0–5\%\right)$ and the minimum value corresponds to the most peripheral collision $\left(70–80\%\right)$.

Figure 5

Centrality dependence of ratios of cumulants of net protons and net charge. “nc” and “np” correspond to net protons and net charge respectively. Experimental data of fluctuations measured in Au + Au collisions by the STAR Collaboration are taken from [10, 14]. Blue and black points have been used for net protons and net charge respectively.

Figure 6

Same as Fig. 5 but for parameter sets CFO3 and CFO4.