Scaling Laws in Hierarchical Clustering Models with Poisson Superposition

Abstract

Properties of cumulant- and combinant ratios are studied for multihadron final states composed of Poisson distributed clusters. The application of these quantities to ``detect'' clusters is discussed. For the scaling laws which hold in hierarchical clustering models (void scaling, combinant scaling) a generalization is provided. It is shown that testing hierarchical models is meaningful only for phase-space volumes not larger than the characteristic correlation length introduced by Poisson superposition. Violation of the scaling laws due to QCD effects is predicted.