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. hegyi@rmki.kfki.hu -2 -

Cumulants of QCD multiplicity distributions in small phase space bins

“…Its predictions have been confirmed by experiment [3]. From the theoretical side, those results imply that QCD distributions do not belong to the class of infinitely-divisible ones (in particular, they can not be fitted by the negative binomial distribution -NBD) and prohibit Poissonian cluster models [4].…”

Cell count moments in the halo model

“…where the number of clusters N h and the number of galaxies N i in each cluster are chosen randomly and at first we take the cluster occupation numbers N i to be independent and identically distributed. A similar sum over clusters arises in situations ranging from the distribution of particle multiplicities in hadron collisions at highenergy accelerators (Finkelstein 1988;Hegyi 1994;Tchikilev 1999) to the distribution of rainfall totals (Rodriguez-Iturbe, Cox & Isham 1987;Cowpertwait 1994;Evin & Favre 2008). We can characterize the net count distribution directly for small counts and in general using the generating function G(z).…”