Cumulants and Correlation Functions vs the QCD phase diagram

Abstract: In this paper we discuss the relation of particle number cumulants and correlation functions. It is argued that measuring couplings of the genuine multi-particle correlation functions could provide cleaner information on possible non-trivial dynamics in heavy-ion collisions. We extract integrated multi-proton correlation functions from the presently available experimental data on proton cumulants. We find that the STAR data contain significant four-proton correlations, at least at the lower energies, with indication of changing dynamics in central collisions. We also find that these correlations are rather long-ranged in rapidity. Finally, using the Ising model, we demonstrate how the signs of the multi-proton correlation functions may be used to exclude certain regions of the phase diagram close to the critical point.