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

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.

💡 Research Summary

The paper investigates systematic uncertainties in extracting chemical freeze‑out parameters (temperature T and baryon chemical potential μ_B) for Au+Au collisions at SIS100 energies (√sₙₙ = 3–5 GeV). Using the Ultra‑relativistic Quantum Molecular Dynamics (UrQMD v4.0) transport model, the authors generate hadron yields for central (0–10 %) collisions in two distinct equations of state (EoS): a cascade mode without mean‑field potentials (soft EoS) and a mode with parity‑doublet chiral mean‑field (CMF) potentials (stiff EoS). The CMF EoS reduces compression, leading to a pronounced suppression of strange mesons (K⁺) and anti‑protons relative to the cascade case.

The simulated yields are then fitted with the Thermal‑FIST statistical‑model toolkit, which implements a Hadron Resonance Gas (HRG) in the grand‑canonical ensemble, including γ_s strangeness suppression and fixed charge‑to‑baryon ratio Q/A = 0.4. To probe the “missing‑hadron” effect, three hadron sets are defined:

• Set 1 (full): π±, K±, p, Λ, anti‑p, and deuterons;
• Set 2: same as Set 1 but without deuterons;
• Set 3: same as Set 2 but also without anti‑protons.

A uniform 10 % statistical error is assumed for all species, and χ² per degree of freedom (χ²/dof) is evaluated. Across all energies and both EoS, χ²/dof stays below unity, indicating an excellent description of the UrQMD yields despite the fact that UrQMD itself does not assume chemical equilibrium. Slightly larger χ² for Set 1 at the lowest energies is attributed to the simplified coalescence model for deuterons and to imperfect baryon stopping in the transport calculation.

The extracted (T, μ_B) points are plotted in the T–μ_B plane and compared with the phenomenological freeze‑out curve ⟨E⟩/N ≈ 1 GeV from Cleymans‑Redlich parametrisation, as well as with world‑wide thermal‑fit results. All three sets lie close to the parametrised line, but systematic shifts are evident: inclusion of anti‑protons raises T by ~10–15 MeV, and adding deuterons adds another ~5 MeV. This reflects the early production of anti‑protons (requiring a hotter source) and the need for a higher temperature to accommodate light nuclei yields. Switching from cascade to CMF EoS shifts μ_B upward by ~30–40 MeV, a consequence of the stiffer EoS demanding a larger baryon chemical potential to achieve the same net baryon number under reduced compression.

Using the fitted (T, μ_B) values, the authors compute the corresponding baryon density n_B (assuming an ideal HRG EoS) and display the results in the T–n_B plane. The CMF scenario yields ~10 % lower n_B at a given temperature than the cascade case, reflecting a lower entropy‑per‑baryon (e/N) in the stiff EoS. These differences are significant when one attempts to map freeze‑out points onto the QCD phase diagram.

The study draws several key conclusions: (1) Even non‑equilibrium transport simulations can be described by equilibrium HRG fits with high quality, underscoring that a good χ² does not guarantee true chemical equilibrium; (2) The choice of hadron species included in the fit and the underlying EoS introduce systematic biases of tens of MeV in T and μ_B, and of order 10 % in n_B; (3) Consequently, interpreting the chemical freeze‑out line as a direct indicator of QCD critical phenomena (e.g., the critical endpoint) must account for these systematic uncertainties. For the upcoming CBM experiment at FAIR, where precise mapping of the phase diagram is a primary goal, the authors recommend (i) more sophisticated coalescence treatments for light nuclei, (ii) systematic studies across centralities and system sizes, and (iii) combined analyses of experimental data with constraints on γ_s and volume to reduce model dependence.

In summary, the paper provides a thorough, model‑driven assessment of how methodological choices affect the extracted freeze‑out parameters in the high‑baryon‑density regime accessible at SIS100, highlighting the need for caution when linking freeze‑out systematics to fundamental QCD phase‑structure signatures.