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

We report the beam energy and collision centrality dependence of fifth and sixth order cumulants (C-5, C-6) and factorial cumulants (kappa(5),kappa(6)) of net-proton and proton number distributions, from center-of mass energy ( root(NN)-N-s) 3 GeV to 200 GeV Au thorn Au collisions at RHIC. Cumulant ratios of net-proton (taken as proxy for net-baryon) We report the beam energy and collision centrality dependence of fifth and sixth order cumulants (C-5, C-6) and factorial cumulants (kappa(5), kappa(6)) of net-proton and proton number distributions, from center-of-mass energy (root(NN)-N-s) 3 GeV to 200 GeV Au thorn Au collisions at RHIC. Cumulant ratios of net-proton (taken sNN as proxy for net-baryon) distributions generally follow the hierarchy expected from QCD thermodynamics, except for the case of collisions at 3 GeV. The measured values of C-6/C-2 for 0%-40% centrality collisions show progressively negative trend with decreasing energy, while it is positive for the lowest energy studied. These observed negative signs are consistent with QCD calculations (for baryon chemical potential, mu(B) <= 110 MeV) which contains the crossover transition range. In addition, for energies above 7.7 GeV, the measured proton kappa(n), within uncertainties, does not support the two-component (Poisson thorn binomial) shape of proton number distributions that would be expected from a first-order phase transition. Taken in combination, the hyperorder proton number fluctuations suggest that the structure of QCD matter at high baryon density, mu(B) similar to 750 MeV at root(NN)-N-s = 3 GeV is starkly different from those at vanishing sNN mu(B) similar to 24 MeV at root(NN)-N-s = 200 GeV and higher collision energies. sNN