Measurement of the Sixth-Order Cumulant of Net-Proton Multiplicity Distributions in $\mathrm{Au}+\mathrm{Au}$ Collisions at $\sqrt{s_{\mathit{NN}}}=27$, 54.4, and 200 GeV at RHIC

According to first-principle lattice QCD calculations, the transition from quark-gluon plasma to hadronic matter is a smooth crossover in the region ${\mu }_B\le T_c$. In this range the ratio, $C_6/C_2$, of net-baryon distributions are predicted to be negative. In this Letter, we report the first measurement of the midrapidity net-proton $C_6/C_2$ from 27, 54.4, and 200 GeV $\mathrm{Au}+\mathrm{Au}$ collisions at the Relativistic Heavy Ion Collider (RHIC). The dependence on collision centrality and kinematic acceptance in ($p_T$, $y$) are analyzed. While for 27 and 54.4 GeV collisions the $C_6/C_2$ values are close to zero within uncertainties, it is observed that for 200 GeV collisions, the $C_6/C_2$ ratio becomes progressively negative from peripheral to central collisions. Transport model calculations without critical dynamics predict mostly positive values except for the most central collisions within uncertainties. These observations seem to favor a smooth crossover in the high-energy nuclear collisions at top RHIC energy.

Figure 1

Event by event net-proton multiplicity $\mathrm{\Delta }{N}_p$ distributions for $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{s_{\mathit{NN}}}=27$, 54.4, and 200 GeV in 0%–10% (left) and 30%–40% (right) centralities at midrapidity ($|y|<0.5$) for the transverse momentum range of $0.4<p_T(\mathrm{GeV}/c)<2.0$. These distributions are normalized by the corresponding numbers of events and are not corrected for detector efficiencies. Statistical uncertainties are shown as vertical lines. The dashed lines show the Skellam distributions for each collision energy and centrality. The bottom panels show the ratio of the data to the Skellam expectations.

Figure 2

Net-proton $C_6/C_2$ as a function of rapidity (left) and transverse momentum acceptance (right) from $\sqrt{s_{\mathit{NN}}}=27$ (crosses), 54.4 (open squares), and 200 GeV (filled circles) $\mathrm{Au}+\mathrm{Au}$ collisions. The upper and lower plots are for 0%–10% and 30%–40% centralities, respectively. The error bars are statistical and caps are systematic errors. Points for different beam energies are staggered horizontally to improve clarity. UrQMD transport model results are shown as shaded and hatched bands. The Skellam expectation ($C_6/C_2=1$) is shown as long-dashed lines.

Figure 3

Collision centrality dependence of net-proton $C_6/C_2$ in $\mathrm{Au}+\mathrm{Au}$ collisions for $\sqrt{s_{\mathit{NN}}}=27$, 54.4, and 200 GeV within $|y|<0.5$ and $0.4<p_T(\mathrm{GeV}/c)<2.0$. The error bars are statistical and caps are systematic errors. Points for different beam energies are staggered horizontally to improve clarity. A shaded band shows the results from UrQMD model calculations. UrQMD calculations from the above three collision energies are consistent among them so they are merged in order to reduce statistical fluctuations. Details on these calculations can be found in Supplemental Material [24]. The lattice QCD calculations on net-baryon number fluctuations [17, 19] for $T=160\mathrm{MeV}$ and ${\mu }_B<110\mathrm{MeV}$ are shown as a blue band at $⟨N_{\mathrm{part}}⟩\approx 340$. The inset shows the expanded region of 40%–80% centrality.