A Bose–Einstein model of particle multiplicity distributions

Abstract

A model of particle production is developed based on a parallel with a theory of Bose-Einstein condensation and similarities with other critical phenomena such as critical opalescence. The role of a power law critical exponent τ and Levy index α are studied. Various features of this model are developed and compared with other commonly used models of particle production which are shown to differ by having different values for τ , α. While void scaling is a feature of this model, hierarchical structure is not a general property of it. The value of the exponent τ = 2 is a transition point associated with void and hierarchical scaling features. An exponent γ is introduced to describe enhanced fluctuations near a critical point. Experimentally determined properties of the void scaling function can be used to determine τ .

Critical exponents and particle multiplicity distributions in high energy collisions

“…The latter model is also connected to a Feynman-Wilson gas as discussed in detail in ref [14,6] and briefly mentioned below. These two specific models have been extended in a previous paper [4,5,6] and shown to be special cases of a more general model. A main element of this more general model is a power law critical exponent ) , ( − + e e ) , ( p e τ which appears in statistical physics, or a related Levy index α of probability theory.…”

“…Phenomenological models of hadron multiplicities have been applied to understanding high energy collisions [1][2][3][4][5][6][7][8]. Several of these models are based on specific statistical models of photon count distributions [9,10].…”

“…Details can be found in ref. [4,5] so we included only some fundamental defining equations and key factors to make this present paper self contained. Our focus here is to use a generalized model to try to extract an exponent or index from existing data.…”

“…Our focus here is to use a generalized model to try to extract an exponent or index from existing data. The count probability distribution for N-particles [1][2][3][4][5][6][7][8] can be obtained from a generating function…”

“…We next briefly discuss a generalized hypergeometric model that contains, as special cases, several models of particle multiplicity distributions and also features associated with Bose-Einstein condensation phenomena and critical opalescence [5] . It will allow us to study various situations in a unified way.…”