Multi-strange and charmed hadrons: A novel probe for the QCD equation of state at high baryon densities

TL;DR

This work argues that sub-threshold production of strange and, for the first time, charm hadrons can serve as sensitive probes of the high-density QCD equation of state (EOS). Using the UrQMD transport model with both cascade and CMF-based equations of state, the authors study how production yields of kaons, multi-strange baryons, and charmed hadrons depend on the EOS in heavy-ion collisions at SIS100 energies, highlighting strong EOS sensitivity at high densities. They show that the centrality-dependent yield scaling parameter alpha for yields is a key observable, with distinct trends for strange and charm species and notable discrepancies with existing data for Xi, underscoring the need for reliable elementary cross sections near threshold. The study emphasizes that accurate interpretation requires solid p+p baseline cross sections and advocates dedicated p+p, p+A, and A+A measurements at FAIR to constrain the EOS. Overall, it outlines a concrete path to using multi-strange and charmed hadrons as high-density EOS probes.

Abstract

Nuclear experiments near and below the threshold of hyperon production have shown that the production of Kaons is a sensitive probe for the dense QCD equation of state. At beam energies up to 1.5AGeV, strangeness production can probe the equation of state for densities up to approximately twice nuclear saturation. In this paper we will discuss the possibilities of extending this range in density by the study of multi-strange baryons as well as charmed hadrons in the SIS100 beam energy range up to 10AGeV. Here, densities up to five times nuclear saturation can be reached and the production of multi-strange and charmed hadrons shows a strong sensitivity to the equation of state. On the other hand a precise prediction of the effect of the equation of state will require knowledge of the fundamental production cross section near the elementary production threshold in p+p collisions which is yet not measured for the hadrons discussed.

Figures (5)

• Figure 1: Upper panel: Integrated $4 \pi$ multiplicity per inelastic p+p event for several strange and charmed hadrons from UrQMD v4.0 (solid lines) and compared to experimental data Antinucci:1972ibRossi:1974if. Lower panel: Multiplicities per event for central (0-10$\%$) Au+Au reactions with UrQMD (lines) and compared to experimental data (symbols) HADES:2017jgzLi:2025yhe. The solid lines correspond to simulations with the CMF-equation of state (CMF) while the dashed lines are results with the UrQMD cascade mode (CAS)
• Figure 2: Beam energy dependence of the $\alpha$ parameter from the fit to the centrality dependence of Kaons and anti-Kaons in Au+Au collisions. The shaded areas with filled symbols denote the UrQMD results with the CMF equation of state while the open symbols are the results with the cascade mode (CAS). Experimental data for Kaons are shown as green symbols. The threshold energies for the production in elementary p+p collisions are indicated as vertical lines.
• Figure 3: Beam energy dependence of the $\alpha$ parameter from the fit to the centrality dependence of $\Xi^-$ and $\Omega^-$ in Au+Au collisions. The shaded areas with filled symbols denote the results from UrQMD with the CMF equation of state while the open symbols are the results with the cascade mode (CAS). Preliminary experimental data for $\Xi^-$ are shown as green symbols. The threshold energies for the production in elementary p+p collisions are indicated as vertical lines.
• Figure 4: Beam energy dependence of the $\alpha$ parameter from the fit to the centrality dependence of charm hadrons in Au+Au collisions. The shades areas with filled symbols denote the results with the CMF equation of state while the open symbols are the results with the cascade mode (CAS). The threshold energy for production in elementary p+p collisions is indicated as vertical line.
• Figure 5: The $\alpha$ parameter for the $\Xi$-baryon at a beam energy of $\sqrt{s_{\mathrm{NN}}}=3.5$ GeV for five different scenarios. The scenarios are described in the text. The green shaded area corresponds to the preliminary STAR results at that energy.