Effects of the Detection Efficiency on Multiplicity Distributions

TL;DR

This paper examines how detection efficiency, especially when dependent on multiplicity, influences the shape and moments of Poisson, Binomial, and Negative Binomial distributions in experimental data analysis.

Contribution

It introduces a method to analyze the impact of multiplicity-dependent detection efficiency on key distribution characteristics.

Findings

Multiplicity-independent efficiency does not alter distribution shape.

Multiplicity-dependent efficiency causes deviations in distribution moments.

A procedure is provided to quantify these deviations.

Abstract

In this paper we investigate how a finite detection efficiency affects three popular multiplicity distributions, namely the Poisson, the Binomial and the Negative Binomial distributions. We found that a multiplicity-independent detection efficiency does not change the characteristic of a distribution, while a multiplicity-dependent detection efficiency does. We layout a procedure to study the deviation of moments and their derivative quantities from the baseline distribution due to a multiplicity-dependent detection efficiency.