Development of particle multiplicity distributions using a general form of the grand canonical partition function
Abstract
Various phenomenological models of particle multiplicity distributions are discussed using a general form of a unified model which is based on the grand canonical partition function and Feynman's path integral approach to statistical processes. These models can be written as special cases of a more general distribution which has three control parameters which are a, x, z. The relation to these parameters to various physical quantities are discussed. A connection of the parameter a with Fisher's critical exponent τ is developed. Using this grand canonical approach, moments, cumulants and combinants are discussed and a physical interpretation of the combinants are given and their behavior connected to the critical exponent τ. Various physical phenomena such as hierarchical structure, void scaling relations, KobaNielsonOlesen or KNO scaling features, clan variables, and branching laws are shown in terms of this general approach. Several of these features which were previously developed in terms of the negative binomial distribution are found to be more general. Both hierarchical structure and void scaling relations depend on the Fisher exponent τ. Applications of our approach to the charged particle multiplicity distribution in jets of L3 and H1 data are given.
 Publication:

Nuclear Physics A
 Pub Date:
 January 2004
 DOI:
 10.1016/j.nuclphysa.2003.11.008
 arXiv:
 arXiv:nuclth/0304057
 Bibcode:
 2004NuPhA.730..514L
 Keywords:

 25.75.Dw;
 25.75.Gz;
 24.10.Pa;
 05.30.Jp;
 05.40.+j;
 Particle and resonance production;
 Particle correlations;
 Thermal and statistical models;
 Boson systems;
 Nuclear Theory
 EPrint:
 7 figures included