Superclusters and hadronic multiplicity distribution

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Abstract
We have formulated a multiplicity distribution as a supercluster in hadronic production processes at high energy. This process creates unstable clusters at intermediate stages and hadrons at the final stage. It includes Poisson-weighted distributions and especially partially coherent distributions as a special case, and it is very flexible for phenomenological analyses. The associated Koba, Nielsen, and Olesen (KNO) limit and cumulant moments are analyzed in detail for finite and/or infinite cluster size and particle size per cluster. We demonstrate that in general a supercluster distribution does not need to be equivalent to a negative-binomial distribution to fit experimental data well. Furthermore, the requirement of such equivalence leads to many solutions, in which the average size of the cluster is not logarithmic (e.g., it may show a power behavior instead). We finally demonstrate that the broadening of the KNO scaling function at high energy does not need to stop early if a finite number of clusters are produced, and if the KNO scaling function of the cluster distribution itself remains nonasymptotic at high energy.