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We performed systematic studies on the effects of event-by-event efficiencyfluctuations on efficiency correction for cumulant analysis in relativisticheavy-ion collision experiments. Experimentally, particle efficiencies ofevents measured under different experimental conditions should be different.For fluctuation measurements, the final event-by-event multiplicitydistributions should be the superposed distributions of various type of eventsmeasured under different conditions. We demonstrate efficiency fluctuationeffects using numerical simulation, in which we construct an event ensembleconsisting of events with two different efficiencies. By using the meanparticle efficiencies, we find that the efficiency corrected cumulants showlarge deviations from the original inputs when the discrepancy between the twoefficiencies is large. We further studied the effects of efficiencyfluctuations for the cumulants of net-proton distributions by implementing theUrQMD events of Au+Au collisions at $\sqrt{s_{NN}}=7.7$ GeV in a realistic STARdetector acceptance. We consider the unequal efficiency in two sides of theTime Projection Chamber (TPC), multiplicity dependent efficiency, and theevent-by-event variations of the collision vertex position along thelongitudinal direction ($V_\mathrm{z}$). When the efficiencies fluctuatedramatically within the studied event sample, the effects of efficiencyfluctuations have significant impacts on the efficiency corrections ofcumulants with the mean efficiency. We find that this effect can be effectivelysuppressed by binning the entire event ensemble into various sub-event samples,in which the efficiency variations are relatively small. The final efficiencycorrected cumulants can be calculated from the weighted average of thecorrected factorial moments of the sub-event samples with the mean efficiency.

chinese physics c, high energy physics and nuclear physics/chinese physics c

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