Search for the QCD Critical Point in High Energy Nuclear Collisions: A Status Report

TL;DR

The paper addresses locating the QCD critical point in high-energy nuclear collisions by analyzing net-proton fluctuations measured by STAR in the BES-II program. It uses cumulants $C_n$ and factorial cumulants $\kappa_n$ of (net-)proton numbers, comparing results to non-critical baselines from Lattice QCD, HRG, hydro with excluded-volume effects, and UrQMD, while developing methods to mitigate initial volume fluctuations. A key finding is a maximum deviation of $C_4/C_2$ around $\sqrt{s_{\rm NN}}\approx 20$ GeV at $2$–$5\sigma$, with low-energy trends suggesting attractive interactions, though not providing unambiguous evidence for a critical point due to finite-size and dynamical effects. The work emphasizes the need for final STAR FXT results down to $\sqrt{s_{\rm NN}}=4.5$ GeV and highlights future facilities CBM/MPD/HIAF and finite-size scaling approaches to robustly test critical fluctuations in high-baryon-density matter.

Abstract

We review recent results of net-proton multiplicity fluctuations from STAR experiment, aiming to locate the QCD critical point in high-energy nuclear collisions at RHIC. We show net-proton number cumulant and proton number factorial cumulant ratios up to fourth order using experimental data from RHIC BES-II Au+Au collisions in collider mode and fixed-target mode. The comparison is made between experimental data and non-critical model calculations from Lattice QCD, HRG, hydrodynamic simulations and transport model UrQMD. In addition, we discuss initial volume fluctuation effect, which plays significant role in fixed-target energies. Finally, an outlook on experimental research on the QCD critical point in future experiments will be presented.

Figures (6)

• Figure 1: Theoretical predictions on the QCD critical point from various approaches.
• Figure 2: Net-proton cumulant ratios: (a) $C_2/\langle p+\bar{p}\rangle$, (b) $C_3/C_1$, and (c) $C_4/C_2$ and proton factorial cumulant ratios: (d) $\kappa_2/\kappa_1$, (e) $\kappa_3/\kappa_1$, and (f) $\kappa_4/\kappa_1$ in Au+Au collisions from STAR at RHIC. Figure is taken from Reference STAR:2025zdq.
• Figure 3: Significance of deviation, (data$-$reference)/$\sigma_{\rm total}$, for (a) net-proton cumulant ratios $C_4/C_2$ in 0-5% Au+Au collisions STAR:2020tgaSTAR:2021iopSTAR:2021fgeSTAR:2022etb. References include the non-critical model calculations, such as the UrQMD transport model Bass:1998caBleicher:1999xi (blue square), HRG with canonical ensemble for baryon charge Braun-Munzinger:2020jbk (HRG CE, black cross), hydrodynamic model with excluded volume Vovchenko:2021kxx (Hydro EV, black triangle), and data from 70-80% peripheral collisions (red dots). Figure is taken from Reference STAR:2025zdq.
• Figure 4: Collision energy dependence of ratios for the cumulants of net-proton (top panels) and the factorial cumulant of protons (lower panels) in Au+Au collisions from STAR at RHIC. The red squares in the energy range $3<\sqrt{s_{\rm NN}} < 3.9$ GeV are the new results shown at Quark Matter 2025.
• Figure 5: Cumulants optimized from IVF correction method in UrQMD at $\sqrt{s_{\rm NN}} = 3.9$ GeV. Here black squares are from RefMult3-based centrality without Centrality Bin Width Correction(CBWC), green squares are from RefMult3-based centrality with CBWC, black circles are from $N_{\rm part}$-based centrality without CBWC, green circles are from $N_{\rm part}$-based centrality with CBWC.