Energy and centrality dependence of chemical freeze-out thermodynamics parameters

Driven by the Beam Energy Scan (BES) program at the RHIC, researches and discussions on the QCD phase diagram have flourished recently. In order to provide a reference from microscopic transport models, we performed a systematic analysis, using a multiphase transport (AMPT) model for the particle yields and a statistical model (thermus) for the thermal fit, for Au + Au collisions at $\sqrt{s_{\mathrm{NN}}}=7.7–200$ GeV. It is found that at a fixed collision centrality the chemical freeze-out parameter, temperature $T_{\mathrm{ch}}$, increases with collision energy and somehow saturates at certain values of $T_{\mathrm{ch}}$ in collisions near $\sqrt{s_{\mathrm{NN}}}=10$ GeV, indicating the limiting temperature in hadronic interactions; meanwhile the baryon chemical potential ${\mu }_B$ decrease with the collision energy. The saturation temperature is also found to be dependent on partonic interaction. At a given collision energy, it is found that both $T_{\mathrm{ch}}$ and ${\mu }_B$ decrease towards more peripheral collisions in the grand canonical approach. The energy and centrality dependence of other chemical freeze-out parameters, strangeness chemical potential ${\mu }_S$, strangeness undersaturation factor ${\gamma }_S$, and the volume of the fireball $V$ are also presented in this paper. The chemical potential ratio ${\mu }_s/{\mu }_B$ is also compared with lattice QCD calculation. The AMPT default model gives better descriptions on both the particle yields and the chemical freeze-out parameters than those from the AMPT string-melting model.

Figure 1

Chemical freeze-out parameters temperature $T_{\mathrm{ch}}$ versus baryon chemical potential ${\mu }_B$ from Au + Au collisions at $\sqrt{s_{\mathrm{NN}}}=7.7$–200 GeV. The particle yields are from different AMPT models for $t_{\mathrm{hc}}=30$ fm/$c$. The symbols are drawn from the thermus with GCE approach. The results from the D model are shown in plot (a). Plots (b)–(d) are from the SM models with various partonic interaction cross sections. The curves are phenomenological parametrizations to quantity the experimental data from SPS to RHIC energies for the top 0%–5% centrality collisions [15, 16].

Figure 2

Upper panel: Particle yields from the STAR experiment [17, 18, 19] and different AMPT models at $\sqrt{s_{\mathrm{NN}}}=200$ GeV for the top $5\%$ central Au + Au collision. $T_{\mathrm{ch}}$'s are labeled in the legend. Lower panel: Ratios of particle yield difference between the AMPT and the STAR data relative to the STAR data.

Figure 3

Top Panel: Proton-to-$\pi$ ratios from the SM model with ${\sigma }_{pp}=3$ mb at $\sqrt{s_{\mathrm{NN}}}=200$ GeV Au + Au collision. Bottom Panel: Net baryons (including proton, $\Lambda$, $\Xi$, $\Omega ,$ and their antiparticles) over $N_{\text{part}}$ as function as $N_{\text{part}}$ from the SM model with ${\sigma }_{pp}=3$ mb at $\sqrt{s_{\mathrm{NN}}}=39$ GeV Au + Au collision.

Figure 4

Chemical freeze-out temperature $T_{\mathrm{ch}}$ and ${\mu }_B$ as functions of centrality, with the termination time of hadron cascade $t_{\mathrm{hc}}=0.6$ (open symbols) and 30 fm/$c$ (filled symbols) from the D model (circles) and the SM model (triangles) with ${\sigma }_{pp}=3$ mb at $\sqrt{s_{\mathrm{NN}}}=39$ GeV Au + Au collision.

Figure 5

Chemical freeze-out parameters, strangeness chemical potential ${\mu }_S$, strangeness undersaturation factor ${\gamma }_s$, and the volume of the fireball $V$ of chemical freeze-out from the thermus GCE fit as functions as $N_{\text{part}}$. Left panels are the results from the D model; right panels are the results from the SM model for ${\sigma }_{pp}=10$ mb.

Figure 6

Strangeness over baryon chemical potential ratio ${\mu }_S/{\mu }_B$ as a function of the baryon chemical potential ${\mu }_B$. All results are from the top $5\%$ central Au + Au collisions at RHIC energies. In case of the SM mode, filled squares, filled triangles, and filled inverted triangles correspond to partonic cross sections of 3, 6, and 10 mb, respectively. The open squares are fitting results from the SM model with a parton cross section of 3 mb when only the yields of $\pi$, $K$, and $p$ are included. Results from the D model are shown as filled circles. The dashed lines are polynomial fits to the calculations. The three bands are taken from lattice QCD NLO calculations for three different critical temperature values.