Fuzzy logic for reconstructing arbitrary moments of multiplicity distributions

TL;DR

This paper introduces a new fuzzy logic-based framework for reconstructing arbitrary moments of multiplicity distributions, enhancing the robustness and extendability of the Identity Method in high-energy physics and other fields.

Contribution

A multivariate moment generation function framework is developed, enabling more robust and higher-order moment calculations within the Identity Method.

Findings

Framework improves accuracy of multiplicity distribution analysis

Extends the Identity Method to higher-order moments

Applicable to noisy, probabilistic signal identification in various fields

Abstract

The Identity Method is a statistical technique developed to reconstruct moments of multiplicity distributions of particles produced in high-energy nuclear collisions. The method leverages principles from fuzzy logic, allowing for a more nuanced representation of particle identification by assigning degrees of membership to different particle types based on detector signals. In this contribution, a new framework, based on a multivariate moment generation function, is developed that allows the derivation of the formulas used in the Identity Method in a more robust way. Moreover, within the introduced framework, the Identity Method is easily extended to cope with arbitrarily higher-order moments. The techniques developed here offer significant potential for improving the accuracy of multiplicity distribution analyses in high-energy nuclear collisions. While the primary focus of the work presented is on applications in high-energy particle and nuclear physics, it can also be applied in other areas where signal identification is probabilistic and data are noisy, such as in medical imaging, remote sensing, and various other fields of experimental science.