Measurement of the ratio of the sixth order to the second order cumulant of net-proton multiplicity distributions in relativistic heavy-ion collisions

Abstract

We investigate the measurement of the sixth order cumulant and its ratio to the second order cumulant (C 6 /C 2 ) in relativistic heavy-ion collisions. The influence of statistics and different methods of centrality bin width correction on C 6 /C 2 of net-proton multiplicity distributions is demonstrated. There is no satisfactory method to extract C 6 /C 2 with the current statistics recorded at lower energies by STAR at RHIC. With statistics comparable to the expected statistics at the planned future RHIC Beam Energy Scan II (BES II), no energy dependence of C 6 /C 2 is observed in central collisions using the UrQMD model. We find if the transition signal is as strong as predicted by the PQM model, then it is hopefully observed at the upcoming RHIC BES II.

Higher order net-proton number cumulants dependence on the centrality definition and other spurious effects

“…On the experimental side the measurements of these susceptibilities via event-by-event fluctuations has been pushed forward with experiments at RHIC [19][20][21][22][23] and at LHC [24,25]. In fact, first measurements of 6th order and even 8th order cumulants or moments of the distributions have been presented recently or are currently under investigation [26,27]. In spite of these progresses, a detailed understanding and interpretation of the measured moments is difficult due to (a) uncertainties in the centrality determination which is crucial to avoid volume fluctuations, (b) efficiency corrections, and (c) transverse momentum (p T ) cuts that have to be extrapolated to low p T on an event-by-event basis.…”

The sixth order cumulant of net-proton number in Binomial distribution at = 200 GeV *

“…However, it is a challenge for analysis of the high-order cumulants, which are up to the fifth, sixth, or even eighth order [36][37][38]. When the CBWC method is applied in cumulants calculations, the statistics in each are significantly limited in 0-10% centrality even with a few hundred million MB events.…”

“…As we mentioned, the required statistics are also related to the detail shape and width of the net-proton multiplicity distributions [36][37][38]. The behavior of the statistical dependency in different centralities requires a careful case-by-case study.…”

“…A critical issue is that the statistics in each of are still considerably limited even with 320M MB events. Our previous studies showed that we must check whether the statistics in each of are sufficient to satisfy the Central Limit Theorem (CLT) when applying the CBWC method in cumulants analysis [36][37][38]. It showed that 90M MB events are not sufficient for analysis of net-proton at GeV in the UrQMD model.…”