# Statistical moments in superposition models and strongly intensive measures

## TL;DR

This paper develops a comprehensive mathematical framework for moments in superposition models, introducing new strongly intensive measures to analyze particle production and fluctuations in high-energy collisions, aiding QCD phase transition studies.

## Contribution

It provides explicit formulas for moments in superposition models and introduces new strongly intensive fluctuation measures involving higher-rank moments.

## Key findings

- Derived formulas for moments of all orders in superposition models
- Introduced new strongly intensive measures involving higher moments
- Applied formalism to particle multiplicity differences

## Abstract

First, we present a concise glossary of formulas for composition of standard, cumulant, factorial, and factorial cumulant moments in superposition (compound) models, where final particles are created via independent emission from a collection of sources. Explicit mathematical formulas for the composed moments are given to all orders. We discuss the composition laws for various types of moments via the generating-function methods and list the formulas for the unfolding of the unwanted fluctuations. Second, the technique is applied to the difference of the scaled multiplicities of two particle types. This allows us for a systematic derivation and a simple algebraic interpretation of the so-called strongly intensive fluctuation measures. With the help of the formalism we obtain several new strongly intensive measures involving higher-rank moments. The reviewed as well as the new results may be useful in investigations of mechanisms of particle production and event-by-event fluctuations in high-energy nuclear and hadronic collisions, and in particular in the search for signatures of the QCD phase transition at a finite baryon density.