Modified Skellam, Poisson and Gaussian distributions in semi-open systems at charge-like conservation law

TL;DR

This paper introduces modified Skellam, Poisson, and Gaussian distributions that incorporate charge conservation constraints, enabling more accurate analysis of fluctuations in subsystems within high-multiplicity collisions and other scientific fields.

Contribution

It proposes new modified distributions that account for charge conservation in subsystems, extending their applicability to various scientific studies involving variable fluctuations.

Findings

Modified distributions effectively incorporate conservation laws.

Applicable to high-energy collision data analysis.

Useful in diverse scientific fluctuation studies.

Abstract

A modification of the Skellam and Poisson distributions is proposed for subsystems when the constraints imposed by the charge conservation law in the complete system are taken into account. Such distributions can be applied, for example, for an analysis of the fluctuations of baryon and net baryon numbers in certain pseudo-rapidity interval in $A+A$ and $p+p$ collisions with high multiplicities. The presented modified Skellam, Poisson and Gaussian distributions can be utilized also in various branches of science, when one studies the fluctuations of the two variables related to a subsystem, as well as the distribution of the difference of these variables, while the mentioned difference in the total system is fixed.