Cumulants and Correlation Functions vs the QCD phase diagram

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.