# Properties and uses of factorial cumulants in relativistic heavy-ion collisions

## TL;DR

This paper explores the properties and applications of factorial cumulants in analyzing particle number fluctuations in relativistic heavy-ion collisions, emphasizing their role in understanding critical phenomena and fluctuation observables.

## Contribution

It introduces the definition and properties of factorial cumulants for multi-species systems and proposes new methods to utilize them in fluctuation analysis.

## Key findings

- Factorial cumulants help interpret fluctuation data in heavy-ion collisions.
- They are useful in studying critical fluctuations and binomial distribution approximations.
- Novel methods for analyzing momentum and rapidity dependence of fluctuations.

## Abstract

We discuss properties and applications of factorial cumulants of various particle numbers and for their mixed channels measured by the event-by-event analysis in relativistic heavy-ion collisions. After defining the factorial cumulants for systems with multi-particle species, their properties are elucidated. The uses of the factorial cumulants in the study of critical fluctuations are discussed. We point out that factorial cumulants play useful roles in understanding fluctuation observables when they have underlying physics approximately described by the binomial distribution. As examples, we suggest novel utilization methods of the factorial cumulants in the study of the momentum cut and rapidity window dependences of fluctuation observables.