Multiplicity Distributions in Canonical and Microcanonical Statistical Ensembles

TL;DR

This paper introduces a Fourier-based method to calculate multiplicity distributions in statistical ensembles, demonstrating their convergence to normal distributions in large volumes and providing formulas for finite volume corrections and resonance effects.

Contribution

It presents a novel Fourier analysis technique for observables in statistical ensembles, including finite volume corrections and resonance decay effects.

Findings

Distributions tend to a multivariate normal in the thermodynamic limit

Finite volume corrections can be systematically calculated

Analytical formulas incorporate resonance decay and acceptance effects

Abstract

The aim of this paper is to introduce a new technique for calculation of observables, in particular multiplicity distributions, in various statistical ensembles at finite volume. The method is based on Fourier analysis of the grand canonical partition function. Taylor expansion of the generating function is used to separate contributions to the partition function in their power in volume. We employ Laplace's asymptotic expansion to show that any equilibrium distribution of multiplicity, charge, energy, etc. tends to a multivariate normal distribution in the thermodynamic limit. Gram-Charlier expansion allows additionally for calculation of finite volume corrections. Analytical formulas are presented for inclusion of resonance decay and finite acceptance effects directly into the system partition function. This paper consolidates and extends previously published results of current investigation into properties of statistical ensembles.