Systematics of the chemical freeze-out line in the high baryon density regime explored at SIS100

TL;DR

This work investigates how systematic uncertainties affect the extraction of chemical freeze-out parameters at SIS100 energies by combining UrQMD transport with Thermal-FIST HRG-based fits. By varying the hadron set and the underlying equation of state (CMF vs cascade) and including light nuclei, the study shows that the extracted temperature $T$ and baryon chemical potential $\mu_B$ shift in a controlled way, with $T$ rising when deuterons and anti-protons are included and $\mu_B$ rising with a stiffer EoS; baryon densities follow similar trends. Notably, the fits remain of high quality even though the UrQMD evolution is not strictly in equilibrium, underscoring that a good thermal fit does not guarantee equilibration. The results highlight substantial systematic uncertainties that must be accounted for when mapping the chemical freeze-out line to the QCD phase diagram, particularly near the CEP, with typical shifts of $\Delta T$ around $10$ MeV, $\Delta \mu_B$ around $50$ MeV, and potential beam-energy shifts around $0.5$ GeV.

Abstract

The systematic uncertainties of chemical freeze-out fits at SIS100 energies (Au+Au reactions at $\sqrt{s_{NN}}=3-5$ GeV) are studied using UrQMD simulations. Although hadron production in UrQMD does not occur on a sharp chemical freeze-out hyper-surface, the extracted fit quality is shown to be very good. The extracted chemical parameters depend on the selected hadron species as well as the underlying equation of state (EoS) of the matter. Including light nuclei and anti-protons in the fit increases the expected freeze-out temperature, while a stiffer EoS increases the obtained chemical potential. Similarly, the baryon densities extracted by the thermal fits depend on the choice of hadrons as well as the underlying equation of state. These results are important for the upcoming CBM@FAIR physics program and highlight that a degree of caution is advised when one relates the chemical freeze-out curve to features on the QCD phase diagram like the critical endpoint or a possible phase transition

Figures (5)

• Figure 1: Ratios of full acceptance hadron yields of $\pi^+$ (black squares, solid lines), $K^+$ (red circles, solid lines) and $\Bar{p}$ (blue triangles, solid lines) as a function of $\sqrt{s_{NN}}$ from UrQMD simulations with CMF potentials with respect to cascade mode (CAS).
• Figure 2: Fit quality given by $\chi^2/\mathrm{d.o.f.}$ for the different scenarios as a function of $\sqrt{s_{NN}}$. The blue curves show UrQMD calculations in cascade mode (CAS), red curves show UrQMD with CMF potentials. The full squares with solid lines show the fit quality including all hadrons (Set 1), open circles with dotted lines exclude the deuteron (Set 2) and full triangles with dashed lines exclude both, the deuteron and the anti-proton (Set 3).
• Figure 3: Extracted chemical freeze-out curves in the $T-\mu_\mathrm{B}$ plane from UrQMD simulations with CMF potentials (left panel) and UrQMD in cascade mode (right panel). Three scenarios are compared: all hadrons (Set 1, full squares, solid lines), excluding deuterons from the fit (Set 2, open circles, dotted lines) and also excluding anti-protons (Set 3, full triangles, dashed lines). T,$\mu_B$ values obtained from fits to experimental data are shown as grey symbols Cleymans:1998fqBecattini:2000jwCleymans:2005xvAndronic:2005ypHADES:2010wuaLorenz:2014ejaBecattini:2016xctLysenko:2024hqp. The magenta lines correspond to a constant energy per hadron line as a proxy for chemical freeze-out line, both for vanishing net-strangenss and $Q/A=0.4$ conditions. The CEP shown as orange symbol with transition line is taken from Shah:2024img and does not assume strangeness neutrality.
• Figure 4: Extracted chemical freeze-out curves in the $T-n_\mathrm{B}$ plane from UrQMD simulations with CMF potentials (left) and UrQMD in cascade mode (right). Three scenarios are compared: all hadrons (full squares, solid lines), excluding deuterons from the fit (open circles, dotted lines) and also excluding anti-protons (full triangles, dashed lines). Densities have been computed assuming an ideal HRG and the thermal parameters from the fits enforcing vanishing net-strangeness. The orange diamond symbol depicts the location of the CEP shown in figures \ref{['fig:curves_mu']} for comparison, where the net baryon density was calculated assuming $\mu_S=0$ and $\mu_Q=0$.
• Figure 5: Thermal parameters (Temperature left and chemical potential right) from the FIST fits to the different UrQMD simulations as function of beam energy. Blue lines correspond to fits to the cascade mode and red lines to the CMF-potentials.