Influences of statistics and initial size fluctuation on high-order cumulants of conserved quantities in relativistic heavy ion collisions

Abstract

By the generator of the UrQMD model, event statistics for the products of kurtosis (κ) and variance (σ 2 ) of net-proton and net-charge multiplicity distributions are carefully studied. It is shown that the statistics at RHIC/BES below √ s N N < 19.6GeV are not sufficient for using the method of Centrality Bin Width Correction (CBWC). Corresponding results are systematically underestimated. A way to improve the CBWC method is proposed. It can remove the statistics dependence of the data and reduce the initial size fluctuation as well.

Influence of statistics on the measured moments of conserved quantities in relativistic heavy ion collisions

“…Moreover, it has been shown in Figure 1 in Ref. [23] that the fluctuation of many sub-samples are out of 3σ of expectation. So the deviation of average from its expectation due to insufficient statistics can not be ignored.…”

“…where X th is theoretical expectation and X exp is experimentally measured mean of moments with finite statistics. Consider the statistics at RHIC/BES I and its uncertainty of the measurements, the result is acceptable if d < 5% [23]. The statistics at RHIC/BES II has a few hundred millions, which is 1-2 magnitudes larger than those at RHIC/BES I.…”

The sixth order cumulant of net-proton number in Binomial distribution at $\sqrt{s_{NN}} = $ 200 GeV

“…A critical issue is that the statistics in each of N ch are still considerably limited even with 320M MB events. Our previous studies showed that we must check whether the statistics in each of N ch 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 netproton C 6 /C 2 at √ s N N = 11.5 GeV in the UrQMD model.…”

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

“…The effects of the acceptance cuts as well as efficiency corrections drastically influence the measured cumulants [21,22]. The initial size fluctuation is also one of the important non-critical effects which exists in all experiment event variables [23,24,25]. What we want to emphasize here is that the techniques to reduce those non-critical effects should be studied carefully case by case for different cumulants.…”

“…Similar with the previously published study on κσ 2 (C 4 /C 2 ) [25], we randomly divide the total number of events into 450, 225, 90, 45, 30, 15, 9, and 5 sub-samples. Correspondingly, the number of events for each kind of sub-sample are 1M, 2M, 5M, 10M, 15M, 30M, 50M, and 90M, respectively.…”