Charged-Particle Multiplicity Dependence of Net-Proton Cumulants in Zr+Zr and Ru+Ru Collisions at $\sqrt{s_{NN}}$ = 200 GeV

TL;DR

This work addresses how higher-order cumulants of net-proton distributions depend on charged-particle multiplicity to probe the QCD phase diagram. It employs STAR measurements of cumulants up to $C_6$ and their ratios in isobar collisions at $\sqrt{s_{NN}}=200$ GeV, with comparisons to p+p, Au+Au, and lattice QCD-based crossover predictions (LGT/FRG). The main finding is that cumulants grow with multiplicity and high-order ratios trend downward toward LGT/FRG expectations, suggesting thermalized QCD matter undergoing a crossover at high multiplicity; HRG GCE and UrQMD fail to capture the centrality dependence. This supports a picture of the medium evolving toward a crossover regime with increasing multiplicity and motivates further high-statistics, multi-system studies to map the phase structure.

Abstract

We present measurements of cumulants of event-by-event net-proton distribution at mid-rapidity and their ratios up to the sixth order as a function of charged-particle multiplicity in Zr+Zr and Ru+Ru(isobars) collisions at a nucleon-nucleon center-of-mass energy ($\sqrt{s_{NN}}$) of 200 GeV. The data are collected from the STAR experiment with a total of two billion events recorded for each collision system. The measurements are compared with those obtained from p+p and Au+Au collision systems at the same center-of-mass energy. The higher-order cumulant ratios ($C_4/C_2$, $C_5/C_1$, and $C_6/C_2$) show an overall decreasing trend as a function of the charged-particle multiplicity across systems. The isobar results align with the Au+Au trends within uncertainties. The observations are compared with calculations from Lattice Gauge Theory (LGT) that include a quark-hadron crossover. The systematic behavior of the higher-order cumulant ratios shows that, overall, they progressively approach LGT predictions with increasing multiplicity within uncertainties. This could imply that the medium created in these heavy-ion collisions gradually evolves into thermalized QCD matter undergoing a crossover transition with multiplicity.

Figures (5)

• Figure 1: Panel (a): Energy loss ($\mathrm{d}E/\mathrm{d}x$) of charged particles in the TPC as a function of rigidity (p/q). The energy loss expectation from the Bichsel function is drawn as red lines for protons and antiprotons. The letter '$p$' stands for protons, '$\bar{p}$' antiprotons, '$K^{\pm}$' for charged kaons, '$\pi^{\pm}$' for charged pions. Panel (c): Reconstructed mass squared ($m^2$) of the particle tracks in TOF as a function of rigidity. The red dashed line indicates the $m^2$ range used for the (anti-)proton selection for the analysis, i.e., $0.6 < m^2 < 1.2\;GeV^2/c^4$. Panel (c): Kinematic acceptance in transverse momentum and rapidity. The rectangular region enclosed by black dashed lines shows the acceptance of selected tracks in this analysis. The z-scale for each of these plots represents track density.
• Figure 2: Upper plot: Charged-particle multiplicity distributions, $M_{\text{ch}}^{\text{TPC}}$, for Zr+Zr and Ru+Ru collisions at $\sqrt{\mathrm{s}_{_{\mathrm{NN}}}}$ = 200 GeV along with the ratio between the distributions (bottom panel). The vertical dashed magenta and cyan lines indicate the lower boundaries of the centrality classes in Zr+Zr and Ru+Ru collisions, respectively, for the top 5%, 20%, and 40% centralities. Lower plot: Net-proton multiplicity distributions, uncorrected for detector efficiency, in Zr+Zr and Ru+Ru collisions at $\sqrt{\mathrm{s}_{_{\mathrm{NN}}}}$ = 200 GeV for selected centralities.
• Figure 3: Net-proton cumulants from the first ($C_1$) to the sixth order ($C_6$) as a function of charged-particle multiplicity, $M_{\text{ch}}^{\text{TPC}}$, for Zr+Zr (cyan squares and open circles) and Ru+Ru (orange diamonds and filled circles) collisions at $\sqrt{\mathrm{s}_{_{\mathrm{NN}}}}$ = 200 GeV. Circle markers represent centrality-bin-width averaged cumulants for nine centrality classes from 0--5%, 5--10%, 10--20%, 20--30%, and so on, up to 70--80%. Each point is plotted with the corresponding statistical uncertainties. The inset panels present $C_5$ and $C_6$ results from 70--80% to 20--30% centrality. Systematic uncertainties are shown as colored bands on the data points (orange for Zr+Zr and blue for Ru+Ru collisions).
• Figure 4: The collision centrality dependence (shown as a function of average number of participating nucleons) of the net-proton cumulant ratios for Zr+Zr (open circles), Ru+Ru (filled circles) at $\sqrt{\mathrm{s}_{_{\mathrm{NN}}}}$ = 200 GeV. Results from Au+Au collisions STAR:2021iopSTAR:2021rlsSTAR:2022vlo (open triangles) at the same collision energy are also shown for comparison. Bars and colored bands on the data points represent statistical and systematic uncertainties, respectively. For Au+Au collisions STAR:2021iopSTAR:2021rlsSTAR:2022vlo, the most central point corresponds to the 0--40% centrality class. In the case of the $C_5/C_1$ and $C_6/C_2$ from the isobar collisions, the most central point corresponds to the 0--20% centrality class. Expectations from the UrQMD model, including statistical uncertainties, are shown as bands. The dashed line represents the calculations from the thermal model HRG in a grand canonical ensemble (HRG GCE). By definition, the HRG GCE expectation for $C_4/C_2$, $C_5/C_1$, and $C_6/C_2$ is unity.
• Figure 5: Net-proton cumulant ratios $C_4/C_2$, $C_5/C_1$, and $C_6/C_2$ from p+pSTAR:2023zhl (blue), Zr+Zr and Ru+Ru (black), and Au+Au STAR:2021iopSTAR:2021rlsSTAR:2022vlo (red markers) collisions at $\sqrt{\mathrm{s}_{_{\mathrm{NN}}}}$ = 200 GeV shown as a function of measured charged-particle multiplicity, $M_{\text{ch}}^{\text{TPC}}$. For better statistical precision, results from a wide 0--40% centrality are shown as the top centrality for the isobar and Au+Au collisions, along with those from 40--50%, 50--60%, 60--70% and 70--80% centrality classes. Model calculations from Lattice Gauge Theory (LGT) Bazavov:2020bjn (brown bands), FRG Fu:2021oaw (green bands), and HRG GCE (dashed lines at unity) are also shown. The $C_6/C_2$ (0-40%) data for Au+Au has been scaled down by factor of 0.5 for clarity of presentation.