Cumulants vs correlation functions and the QCD phase diagram at low energies

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. * bzdak@fis.agh.edu.pl † vkoch@lbl.gov ‡ nstrodthoff@lbl.gov arXiv:1607.07375v2 [nucl-th]

Beam energy scan theory: Status and open questions

“…Recently, the existing results by the STAR collaboration [16] have been extended to lower beam energies by the measurements of the HADES collaboration in the recent Au+Au run at E lab = 1.23A GeV (see contributions by M. Lorenz and R. Holzmann). The idea to draw exclusion plots on the phase diagram based on extraced 2-,3-and 4-particle correlations [17] is intriguing, but at this point needs to await the finalized experimental data and more work on the theory side.…”

Correlation functions of net-proton multiplicity distributions in Au + Au collisions at energies available at the BNL Relativistic Heavy Ion Collider from a multiphase transport model

“…Recently, it was argued [20][21][22][23][24] that measuring multiparticle correlation function could provide cleaner information on the dynamics of critical fluctuations in heavy-ion collisions, since cumulants may mix correlations of different orders. By ignoring the contributions from antiprotons, various orders of correlation functions between protons can be extracted from the cumulants measured by the STAR experiment.…”

“…By ignoring the contributions from antiprotons, various orders of correlation functions between protons can be extracted from the cumulants measured by the STAR experiment. It was found that the strong enhancement of fourth-order cumulant at 7.7 GeV is due to large four-particle correlations, while the negative two-particle correlations are dominant at 19.6 GeV [22]. With removal of the four-particle correlation function from the cumulants, i.e., only the two- * Electronic address: lizm@mail.ccnu.edu.cn and three-particle correlation functions remain, the nonmonotonic behavior observed in the fourth-order proton cumulant disappears [25].…”