Beam Energy Dependence of Fifth and Sixth-Order Net-proton Number Fluctuations in Au+Au Collisions at RHIC

Abstract

We report the beam energy and collision centrality dependence of fifth and sixth order cumulants ($C_5$, $C_6$) and factorial cumulants ($\hat{I}{º}_5$, $\hat{I}{º}_6$) of net-proton and proton distributions, from $\sqrt{s_{NN}}=3-200$ GeV Au+Au collisions at RHIC. The net-proton cumulant ratios generally follow the hierarchy expected from QCD thermodynamics, except for the case of collisions at $\sqrt{s_{NN}}$ = 3 GeV. $C_6/C_2$ for 0-40\% centrality collisions is increasingly negative with decreasing $\sqrt{s_{NN}}$, while it is positive for the lowest $\sqrt{s_{NN}}$ studied. These observed negative signs are consistent with QCD calculations (at baryon chemical potential, $\hat{I}{¼}_B\le$ 110 MeV) that include a crossover quark-hadron transition. In addition, for $\sqrt{s_{NN}}\ge$ 11.5 GeV, the measured proton $\hat{I}{º}_n$, within uncertainties, does not support the two-component shape of proton distributions that would be expected from a first-order phase transition. Taken in combination, the hyper-order proton number fluctuations suggest that the structure of QCD matter at high baryon density, $\hat{I}{¼}_B\sim 750$ MeV ($\sqrt{s_{NN}}$ = 3 GeV) is starkly different from those at vanishing $\hat{I}{¼}_B\sim 20$MeV ($\sqrt{s_{NN}}$ = 200 GeV and higher).

10 pages, 8 figures