Measurements of Proton High-Order Cumulants in $\sqrt{s_{NN}}=3\mathrm{GeV}$ $\mathrm{Au}+\mathrm{Au}$ Collisions and Implications for the QCD Critical Point

We report cumulants of the proton multiplicity distribution from dedicated fixed-target $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{s_{NN}}=3.0\mathrm{GeV}$, measured by the STAR experiment in the kinematic acceptance of rapidity ($y$) and transverse momentum ($p_T$) within $-0.5<y<0$ and $0.4<p_T<2.0\mathrm{GeV}/c$. In the most central 0%–5% collisions, a proton cumulant ratio is measured to be $C_4/C_2=-0.85\pm 0.09(\mathrm{stat})\pm 0.82(\mathrm{syst})$, which is $2\sigma$ below the Poisson baseline with respect to both the statistical and systematic uncertainties. The hadronic transport UrQMD model reproduces our $C_4/C_2$ in the measured acceptance. Compared to higher energy results and the transport model calculations, the suppression in $C_4/C_2$ is consistent with fluctuations driven by baryon number conservation and indicates an energy regime dominated by hadronic interactions. These data imply that the QCD critical region, if created in heavy-ion collisions, could only exist at energies higher than 3 GeV.

Figure 1

Reference multiplicity distributions obtained from $\sqrt{s_{NN}}=3.0\mathrm{GeV}$ data (black markers), GM (red histogram), and single and pileup contributions from unfolding. Vertical lines on markers represent statistical uncertainties. Single, pileup, and $\mathrm{single}+\mathrm{pileup}$ collisions are shown in solid blue markers, dashed green, and dashed magenta curves, respectively. Analysis is performed on 0%–5% central events, indicated by a black arrow.

Figure 2

Left panel (a): $dE/dx$ versus particle rigidity measured in the TPC; pion, kaon, proton, deuteron, and triton bands are labeled. The theory prediction for protons is plotted in red. The electron peak is in between the pion and kaon bands. Right panel (b): Analysis acceptance in transverse momentum versus proton rapidity ($y$) in the c.m. frame of $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{s_{NN}}=3.0\mathrm{GeV}$. The black box indicates the acceptance within $-0.5<y<0$ and $0.4<p_T<2.0\mathrm{GeV}/c$. The red dashed box indicates a narrower rapidity window $|y|<0.1$, the largest possible symmetric rapidity window from this data set. In both panels, the yellow-to-blue color scale indicates the intensity.

Figure 3

Centrality dependence of the proton cumulant ratios for $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{s_{NN}}=3.0\mathrm{GeV}$. Protons are from $-0.5<y<0$ and $0.4<p_T<2.0\mathrm{GeV}/c$. Systematic uncertainties are represented by gray bars. Statistical uncertainties are smaller than marker size. CBWC is applied to all cumulant ratios. While open squares represent the data without the VFC correction, blue triangles and red circles are the results with VFC using the $⟨N_{\mathrm{part}}⟩$ distributions from the UrQMD and Glauber models, respectively. UrQMD model results are represented as a gold dashed line.

Figure 4

Similar to Fig. 3: Rapidity and transverse momentum dependence of the proton cumulant ratios for 0%–5% central collisions. Black squares, red dots, and blue triangles stand for data without and with the VFC using Glauber and UrQMD, respectively.

Figure 5

Collision energy dependence of the ratios of cumulants $C_4/C_2$, for proton (squares) and net proton (red circles) from the top 0%–5% $\mathrm{Au}+\mathrm{Au}$ collisions at RHIC [14, 15]. The points for protons are shifted horizontally for clarity. The new result for proton from $\sqrt{s_{NN}}=3.0\mathrm{GeV}$ collisions is shown as a filled square. HADES data of $\sqrt{s_{NN}}=2.4\mathrm{GeV}$ 0%–10% collisions [52] is also shown. The vertical black and gray bars are the statistical and systematic uncertainties, respectively. In addition, results from the HRG model, based on both canonical ensemble and grand-canonical ensemble, and transport model UrQMD are presented.