Nonmonotonic Energy Dependence of Net-Proton Number Fluctuations

Nonmonotonic variation with collision energy ($\sqrt{s_{\mathrm{NN}}}$) of the moments of the net-baryon number distribution in heavy-ion collisions, related to the correlation length and the susceptibilities of the system, is suggested as a signature for the quantum chromodynamics critical point. We report the first evidence of a nonmonotonic variation in the kurtosis times variance of the net-proton number (proxy for net-baryon number) distribution as a function of $\sqrt{s_{\mathrm{NN}}}$ with $3.1\sigma$ significance for head-on (central) gold-on-gold ($\mathrm{Au}+\mathrm{Au}$) collisions measured solenoidal tracker at Relativistic Heavy Ion Collider. Data in noncentral $\mathrm{Au}+\mathrm{Au}$ collisions and models of heavy-ion collisions without a critical point show a monotonic variation as a function of $\sqrt{s_{\mathrm{NN}}}$.

Figure 1

Event-by-event net-proton number distributions for head-on (0%–5% central) $\mathrm{Au}+\mathrm{Au}$ collisions for nine $\sqrt{s_{\mathrm{NN}}}$ values measured by STAR. The distributions are normalized to the total number of events at each $\sqrt{s_{\mathrm{NN}}}$. The statistical uncertainties are smaller than the symbol sizes and the lines are shown to guide the eye. The distributions in this figure are not corrected for proton and antiproton detection efficiency. The deviation of the distribution for $\sqrt{s_{\mathrm{NN}}}=54.4\mathrm{GeV}$ from the general energy dependence trend is understood to be due to the reconstruction efficiency of protons and antiprotons being different compared to other energies.

Figure 2

Cumulants ($C_n$) of the net-proton distributions for central (0%–5%) and peripheral (70%–80%) $\mathrm{Au}+\mathrm{Au}$ collisions as a function of collision energy. The transverse momentum ($p_T$) range for the measurements is from 0.4 to $2\mathrm{GeV}/\mathrm{c}$, and the rapidity ($y$) range is $-0.5<y<0.5$.

Figure 3

Upper panels: $S\sigma$ (1) and $\kappa {\sigma }^2$ (2) of net-proton distributions for 0%–5% central $\mathrm{Au}+\mathrm{Au}$ collisions from $\sqrt{s_{\mathrm{NN}}}=7.7–62.4\mathrm{GeV}$. The bars on the data points are statistical and systematic uncertainties added in quadrature. The black solid lines are polynomial fit functions that best describe the data. The black dashed lines are the Poisson baselines. Lower panels: Derivative of the fitted polynomial as a function of $\sqrt{s_{\mathrm{NN}}}$. The bar and the shaded band on the derivatives represent the statistical and systematic uncertainties, respectively.

Figure 4

$S\sigma$ (1) and $\kappa {\sigma }^2$ (2) as a function of collision energy for net-proton distributions measured in $\mathrm{Au}+\mathrm{Au}$ collisions. The results are shown for central (0%–5%, filled circles) and peripheral (70%–80%, open squares) collisions within $0.4<p_T(\mathrm{GeV}/\mathrm{c})<2.0$ and $|y|<0.5$. The vertical narrow and wide bars represent the statistical and systematic uncertainties, respectively. Shown as an open triangle is the result from the High Acceptance Di-Electron Spectrometer (HADES) experiment [52] for 0%–10% $\mathrm{Au}+\mathrm{Au}$ collisions and $|y|<0.4$. The shaded green band is the estimated statistical uncertainty for the second beam energy scan (BES-II) at RHIC. The peripheral data points have been shifted along the $x$ axis for clarity of presentation. Results from different variants (GCE, EV, CE) of the HRG model [33, 49, 50], and a transport model calculation (UrQMD [31]) for central collisions (0%–5%) are shown as black, red, and blue bands and a gold band, respectively.