Bridging the gap between event-by-event fluctuation measurements and theory predictions in relativistic nuclear collisions

Abstract

We develop methods to deal with non-dynamical contributions to event-by-event fluctuation measurements of net-particle numbers in relativistic nuclear collisions. These contributions arise from impact parameter fluctuations and from the requirement of overall net-baryon number or net-charge conservation and may mask the dynamical fluctuations of interest, such as those due to critical endpoints in the QCD phase diagram. Within a model of independent particle sources we derive formulae for net-particle fluctuations and develop a rigorous approach to take into account contributions from participant fluctuations in realistic experimental environments and at any cumulant order. Interestingly, contributions from participant fluctuations to the second and third cumulants of net-baryon distributions are found to vanish at mid-rapidity for LHC energies while higher cumulants of even order are non-zero even when the net-baryon number at mid-rapidity is zero. At lower beam energies the effect of participant fluctuations increases and induces spurious higher moments. The necessary corrections become large and need to be carefully taken into account before comparison to theory. We also provide a procedure for selecting the optimal phase-space coverage of particles for fluctuation analyses and discuss quantitatively the necessary correction due to global charge conservation.

Energy dependence of strangeness production and event-byevent fluctuations

“…The analysis of experimental data was performed with the Identity Method [21][22][23][24][25]. Futhermore, based on the recently proposed model, it was demonstrated that non-dynamical fluctuations, such as those stemming from unavoidable fluctuations of participant nucleons are immaterial for the second cumulants of net-protons measured at LHC energies [18]. The obtained results for the second cumulants of net-protons, normalised to the Skellam baseline, are presented in the left panel of Figure 3.…”

“…It is argued that these deviations, as a functions of acceptance, are due to the global baryon conservation, which should be corrected for before comparison to theoretical calculations within GCE. For the second cumulants the contribution from the global baryon number conservation depends only on the acceptance factor α = n p / N 4π B with n p and N 4π B referring to the mean number of protons inside the acceptance and the mean number of baryons in the full phase space respectively [18]:…”

“…This is typically done by analysing the experimental data in a finite acceptance by imposing cuts on rapidity and/or transverse momentum of detected particles. However, if the selected acceptance window is too small, the possible dynamical correlations we are after will also be strongly reduced [17] and consequently, net-baryons will be distributed according to the difference of two independent Poisson distributions [18]. We remind that for the Poisson distribution, all its cumulants are equal to its mean.…”

Properties and uses of factorial cumulants in relativistic heavy-ion collisions

“…[22] for second order cumulant, non-equilibrium effects near the critical point also lead to the violation of the locality assumption. Third, other various effects in real heavyion collisions [1,13,16,18,19] have also be taken into account. We left the inclusion of these effects for future study.…”

“…In particular, the study of the non-Gaussianity of fluctuations is one of the central topics in this realm [7][8][9][10]. Active studies have been carried out theoretically [11][12][13][14][15][16][17][18][19][20][21][22][23], and experimentally by STAR and ALICE collaborations [24][25][26][27][28][29], as well as in the lattice QCD numerical simulations [30]. The fluctuation observables will also play crucial roles in the future heavy-ion experiments aiming at the study of extremely dense medium [31][32][33].…”