A Unified View of Multiplicity Distributions Based on a Pure Birth Process

Abstract

Various probability distributions which have been proposed to explain the charged particle multiplicity distributions in high energy collisions are shown to arise from the evolution equation of a pure birth process subject to appropriate initial conditions. For example, both the negative binomial distribution (NBD) as well as the partially coherent laser distribution (PCLD) can be obtained in this way. New interrelations between some of these probability distributions are also brought out.

Multiplicity distributions at high energies as a sum of Poissonian-like distributions

“…One can note [12,15] that the GS distribution is a particular case of the partially coherent laser distribution PCLD (see review of the PCLD in [7]). Indeed the p.g.f.…”

“…The GS distribution having the Poissonian as a particular case at r = 0 and known in mathematical statistics under the name of the Pólya-Aeppli distribution [11] has physical interpretation in the framework of different models [12][13][14], see discussion in Refs. [15,16].…”