High cumulants of conserved charges and their statistical uncertainties

TL;DR

This paper investigates how high cumulants of conserved charges fluctuate and how their statistical uncertainties depend on the number of collision events, providing insights into their measurement reliability in heavy-ion collision experiments.

Contribution

It reveals the relationship between measured high cumulants and their uncertainties, and confirms the applicability of the three sigma rule above one million events.

Findings

Larger measured cumulants lead to larger estimated uncertainties.

Statistical uncertainties are correlated with cumulant values.

The three sigma rule holds for event counts above one million.

Abstract

We study the influence of measured high cumulants of conserved charges on their associated statistical uncertainties in relativistic heavy-ion collisions. With a given number of events, the measured cumulants randomly fluctuate with an approximately normal distribution, while the estimated statistical uncertainties are found to be correlated with corresponding values of the obtained cumulants. Generally, with a given number of events, the larger the cumulants we measure, the larger the statistical uncertainties that are estimated. The error-weighted averaged cumulants are dependent on statistics. Despite this effect, however, it is found that the three sigma rule of thumb is still applicable when the statistics are above one million.