Probing dense nuclear matter with event-by-event particle number fluctuations

Abstract The HADES experiment, located at the GSI Helmholtzzentrum für Schwerionenforschung in Darmstadt, investigates the equation of state (EoS) of Quantum Chromodynamics (QCD) matter created in central collisions of heavy- and medium-mass nuclei at beam energies of a few GeV, employing both electromagnetic and hadronic probes. In addition, the experiment maintains dedicated programs aimed at the study of hadron properties in p+p and pion-induced reactions. A particular focus of this report is the reconstruction of higher-order cumulant ratios of proton and light-nuclei multiplicity distributions in Ag+Ag collisions, which constitute sensitive probes of critical phenomena due to their direct connection, within the framework of statistical mechanics, to the EoS. Event-by-event (E-by-E) fluctuations are reconstructed using a novel probabilistic approach based on Fuzzy Logic, which effectively circumvents the limitations imposed by incomplete E-by-E particle identification in experimental data. Several strategies for efficiency correction are discussed, and a data-driven event-mixing technique is employed to account for volume (centrality) fluctuations. The fully corrected normalized factorial cumulants of the proton multiplicity distribution, including their acceptance dependence in rapidity, are presented and compared with canonical ensemble baseline calculations that incorporate correlations arising from local attractive interactions. The HADES results extend the trends observed by the STAR experiment toward lower collision energies for the measured cumulant ratios.