Freeze-Out Parameters from Electric Charge and Baryon Number Fluctuations: Is There Consistency?

Recent results for moments of multiplicity distributions of net protons and net-electric charge from the STAR Collaboration are compared to lattice QCD results for higher order fluctuations of baryon number and electric charge by the Wuppertal-Budapest Collaboration, with the purpose of extracting the freeze-out temperature and chemical potential. All lattice simulations are performed for a system of $2+1$ dynamical quark flavors, at the physical mass for light and strange quarks; all results are continuum extrapolated. We show that it is possible to extract an upper value for the freeze-out temperature, as well as precise baryochemical potential values corresponding to the four highest collision energies of the experimental beam energy scan. Consistency between the freeze-out parameters obtained from baryon number and electric charge fluctuations is found. The freeze-out chemical potentials are now in agreement with the statistical hadronization model.

Figure 1

$R_{31}^B$: The colored symbols show finite-$N_t$ lattice QCD results. The continuum extrapolation is represented by black points (from Ref. [11]). The dark-orange band shows the recent experimental measurement by the STAR Collaboration [7]: it was obtained by averaging the 0%–5% and 5%–10% data at the four highest energies ($\sqrt{s}=27$, 39, 62.4, and 200 GeV). The green-shaded area shows the valid temperature range.

Figure 2

Upper panel: $R_{12}^B$ as a function of ${\mu }_B$. The three points correspond to the STAR data for $M_p/{\sigma }_p^2$ at collision energies $\sqrt{s}=39$, 62.4, and 200 GeV and centrality 0%–10%, from Ref. [7] (the $\sqrt{s}=27\mathrm{GeV}$ point is also shown, but the nonmonotonicity of the lattice results at ${\mu }_B\ge 130\mathrm{MeV}$ does not allow a determination of ${\mu }_B$ from it). Lower panel: $R_{12}^Q$ as a function of ${\mu }_B$. The four points correspond to the STAR data for $M_Q/{\sigma }_Q^2$ at $\sqrt{s}=27$, 39, 62.4, and 200 GeV and centrality 0%–10%, from Ref. [8]. In both panels, the colored symbols correspond to the lattice QCD results in the continuum limit, for the range $(140\le T_f\le 150)\mathrm{MeV}$. The arrows show the extracted values for ${\mu }_B$ at freeze-out.

Figure 3

Freeze-out chemical potential ${\mu }_B$ as a function of the collision energy. The red stars show the ${\mu }_B$ obtained by fitting $R_{12}^B$, the blue squares have been obtained by fitting $R_{12}^Q$. The black curve comes from the statistical hadronization model analysis of Refs. [12, 30].

Figure 4

$R_{12}^Q/R_{12}^B$: the colored symbols correspond to continuum-extrapolated lattice QCD simulations at different values of ${\mu }_B$. The dashed lines show the recent experimental measurements by the STAR Collaboration [7, 8] for a 0%–10% centrality and different collision energies. The green-shaded area shows the valid temperature range, $T_f=(144\pm 6)\mathrm{MeV}$.