Efficiency corrections for factorial moments and cumulants of overlapping sets of particles

TL;DR

This paper addresses the complexities of correcting for detection efficiency in measurements of factorial moments and cumulants involving overlapping particle sets, especially in heavy-ion experiments with sequential particle identification.

Contribution

It derives specific efficiency correction formulas for cases where detection efficiencies follow a binomial distribution in overlapping particle set measurements.

Findings

Derived correction formulas for overlapping sets with binomial efficiency.

Clarified the impact of sequential charge and particle identification.

Provided practical guidance for heavy-ion experiment data analysis.

Abstract

In this note we discuss subtleties associated with the efficiency corrections for measurements of off-diagonal cumulants and factorial moments for a situation when one deals with overlapping sets of particles, such as correlations between numbers of protons and positively charged particles. In particular, we discuss the situation commonly encountered in heavy-ion experiments, where first all charges are reconstructed and then protons are selected from these charges by an additional particle identification procedure. We present the efficiency correction formulas for the case when the detection efficiencies follow a binomial distribution.