Event-by-Event Efficiency Fluctuations and Efficiency Correction for Cumulants of Superposed Multiplicity Distributions in Relativistic Heavy-ion Collision Experiments

TL;DR

This study investigates how event-by-event efficiency fluctuations affect cumulant analysis in relativistic heavy-ion collisions, demonstrating that fluctuations can cause significant deviations in corrected cumulants, which can be mitigated by sub-event binning.

Contribution

The paper introduces a method to account for efficiency fluctuations in cumulant correction by using sub-event binning to reduce bias in heavy-ion collision analyses.

Findings

Efficiency fluctuations cause large deviations in cumulant corrections.

Sub-event binning effectively suppresses efficiency fluctuation effects.

Corrected cumulants can be accurately obtained by weighted averaging of sub-events.

Abstract

We performed systematic studies on the effects of event-by-event efficiency fluctuations on efficiency correction for cumulant analysis in relativistic heavy-ion collision experiments. Experimentally, particle efficiencies of events measured under different experimental conditions should be different. For fluctuation measurements, the final event-by-event multiplicity distributions should be the superposed distributions of various type of events measured under different conditions. We demonstrate efficiency fluctuation effects using numerical simulation, in which we construct an event ensemble consisting of events with two different efficiencies. By using the mean particle efficiencies, we find that the efficiency corrected cumulants show large deviations from the original inputs when the discrepancy between the two efficiencies is large. We further studied the effects of efficiency fluctuations for the cumulants of net-proton distributions by implementing the UrQMD events of Au+Au collisions at $\sqrt{s_{NN}}=7.7$ GeV in a realistic STAR detector acceptance. We consider the unequal efficiency in two sides of the Time Projection Chamber (TPC), multiplicity dependent efficiency, and the event-by-event variations of the collision vertex position along the longitudinal direction ($V_\mathrm{z}$). When the efficiencies fluctuate dramatically within the studied event sample, the effects of efficiency fluctuations have significant impacts on the efficiency corrections of cumulants with the mean efficiency. We find that this effect can be effectively suppressed by binning the entire event ensemble into various sub-event samples, in which the efficiency variations are relatively small. The final efficiency corrected cumulants can be calculated from the weighted average of the corrected factorial moments of the sub-event samples with the mean efficiency.