Measurement of the sixth-order cumulant of net-proton multiplicity distributions in Au+Au collisions at $\sqrt{s_{\rm NN}}=$ 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 $\mu_{\rm B}\leq T_{c}$. As a result, higher-order cumulants and their ratios are predicted to be negative, $C_{6}/C_{2}<0$, for example. In this paper, we report the first measurement of the midrapidity net-proton $C_{6}/C_{2}$ from 27, 54.4 and 200 GeV Au+Au collisions at 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 values around zero. These observations seem to favor a smooth crossover in the high energy nuclear collisions at RHIC.