Motivation

We present new 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 center-of-mass energy of \sqrtsNN~=~\SI{200}{GeV}. The data was collected from the STAR experiment and a total of two billion events for each colliding system. The measurements are compared to those obtained from p+p and Au+Au collisions at the same center-of-mass energy.  As the function of the charged-particle multiplicity, the high-order cumulant ratios of C₄/C₂, C₅/C₁, and C₆/C₂ decrease progressively from p+p to central Au+Au collisions. The observations are compared to calculations from the Lattice Gauge Theory (LGT) and various QCD-based models. The systematic trend of the high-order cumulant ratios shows they all approach the predictions from the LGT in the highest multiplicity limits within experimental uncertainties, suggesting the media created in these heavy-ion collisions gradually reach a thermalized QCD matter with a smooth crossover phase transition. 
 

Figures
Fig. 1

Fig1. caption: Left: particle energy loss per momentum times its charge inside the TPC. The theoretical energy loss curve using Bichsel formula is drawn, indicating the particles. The letter "p" stands for proton, "d'' for deuteron, "K'' for kaon, "pi'' for pion, and "e'' for electron. Middle: reconstructed mass squared of the particle tracks with momentum times charge in TOF. Red dashed line indicates the mass range used for the (anti-)proton selection for the analysis. Right: acceptance plot in transverse momentum and rapidity. The red dashed square shows the acceptance for the analysis.

Fig. 2

Fig. 2 caption:   Upper plot: charged-particle multiplicity distributions for the Zr+Zr and Ru+Ru collisions at \sqrtsNN~=~200~\si{GeV} and the ratio between the distributions of the Ru+Ru collisions and the Zr+Zr collisions (bottom panel). Vertical dashed magenta and cyan lines respectively represent the lower boundary for the centrality determinations for the Zr+Zr and Ru+Ru collisions. Lower plot: efficiency-uncorrected net-proton multiplicity distribution of Zr+Zr and Ru+Ru collisions at \sqrtsNN~=~200~\si{GeV} for selected centralities. Open markers represent the distribution for the Zr+Zr collisions and closed for the Ru+Ru collisions.

Fig. 3

Fig. 3 caption: Net-proton cumulants from the first C₁ to the sixth order C₆ as a function of charged-particle multiplicity for Zr+Zr orange squares and open circles) and Ru+Ru (cyan squares and filled circles) collisions at \sqrtsNN = 200 \si{GeV}. Circled points represent CBWC-corrected cumulants. Each point is plotted with the corresponding statistical uncertainties. In the insets, the top centralities are shown up to 20% collision centrality and systematic uncertainties are shown in colored bands (orange color for Zr+Zr and blue for Ru+Ru collisions).

Fig. 4

Fig. 4 caption: The collision centrality dependence (shown as a function of the number of participating nucleons) of the CBWC-corrected net-proton cumulant ratios for Zr+Zr (open circles), Ru+Ru  (filled circles), and Au+Au (open triangles) collisions at \sqrtsNN  =  200  \si{GeV}. Bars and colored bands on the markers represent statistical and systematic uncertainties, respectively. For Au+Au collisions  [1, 2, 3], the top centrality class corresponds to 0-40%. In the case of the C₅/C₁ and C₆/C₂ of the isobar collisions, the top centrality class corresponds to 0-20%. Results from the UrQMD are shown in bands. The dashed lines represent the HRG GCE calculations.

Fig. 5

Fig. 5 caption:  Net-proton cumulant ratios C₄/C₂, C₅/C₁, and C₆/C₂ from  p+p (blue), Zr+Zr and Ru+Ru (black), and Au+Au [1, 2, 3] (red) collisions at \sqrtsNN = 200 \si{GeV} shown as a function of the charged-particle multiplicity. The efficiencies of the charged-particle multiplicity are corrected to match that of the Au+Au collisions. For better statistical precision, a wider 0-40% centrality is shown as the top centrality for the isobar and Au+Au collisions. Model calculations from HRG GCE, PYTHIA, FRG [4], and Lattice Gauge Theory (LGT) [5] are shown, in dashed lines, green bands in multiplicity and gold bands in average, and red bands, respectively.

Tables
Tab. 1

Tab. 1 caption: The ⟨N_part⟩ with systematic uncertainties of the corresponding centrality using Glauber model and NBD fit of the Zr+Zr and Ru+Ru collisions.

Tab. 2


Tab. 2 caption: The slope of the linear fit on the net-proton cumulants C₄/C₂, C₅/C₁, and C₆/C₂ of the Zr+Zr and Ru+Ru collisions. The standard errors of the fits are also listed.

Summary

In this study, we investigated net-proton cumulants and their ratios up to the sixth order as a function of charged particle multiplicity in high statistics data of Zr+Zr and Ru+Ru collisions at √s_NN = 200 GeV. We observed systematic deviations between the isobar and Au+Au collisions at low order cumulant C₂/C₁. The high order cumulant ratios C₄/C₂, C₅/C₁, and C₆/C₂ of p+p, isobars, and Au+Au collisions showed decreasing trends as multiplicity increased. We point out that although decreasing trends are observed, each colliding system shows a different rate of decrease. The transport model UrQMD does not show the deviations of C₂/C₁ between the isobars and the Au+Au collisions. This indicates that the transport model does not fully explain the observed differences in the data. Including other cumulant ratios, the model shows quantitative discrepancy from the data. In the most central collision centrality of the heavy-ion collisions, the high order cumulant ratios became consistent with the LGT [5] and the FRG [4] calculations. These QCD thermodynamic models also show consistent results with the highest multiplicity results in p+p collisions data. This indicates that in the central heavy-ion collisions at top RHIC energy, thermalized QGP matter is formed and the transition to hadronic matter is a smooth crossover. This is a direct comparison between the data and the first principle QCD (LGT) calculations.

References

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arXiv:2001.08530, doi:10.1103/PhysRevD.101.074502.