Probing the nature of the QCD phase transition with higher-order net-proton number fluctuation and local parton density fluctuation measurements at RHIC-STAR

The moments of proton and net-proton multiplicity distributions are observables expected to be sensitive to the QCD critical point and the nature of the QCD phase transition from QGP to hadron gas. Hyper-order cumulants are measured in wide centrality bins in STAR BES-I data and found to be qualitatively consistent with trends predicted by lattice QCD which finds a cross-over phase transition at low $\mu_\text{B}$. Data collected at $\sqrt{s_{NN}}=3$ GeV in BES-II exhibit trends opposite of those observed in higher energy collisions which may suggest the dominance of hadronic interactions at this energy. The variance of proton multiplicity distributions in azimuthal partitions is measured to search for signals of clustering indicative of a first-order phase transition. A strong dependence on the event multiplicity is observed. This dependence is independent of energy in AMPT while in STAR data a significant trend with energy is observed.