Multiplicity distributions in strong interactions: a generalized negative binomial model

A three-parameter discrete distribution is developed to describe the multiplicity distributions observed in total- and limited phase space volumes in different collision processes. The proability law is obtained by the Poisson transform of the KNO scaling function derived in Polyakovʹs similarity hypothesis for strong interactions as well as in perturbative QCD, ψ(z) α zα exp(−zμ). Various characteristics of the newly proposed distribution are investigated, e.g. its generating function, factorial moments, factorial cumulants. Several limiting and special cases are discussed. A comparison is made to the multiplicity data available in e+e− annihilations at the Z0 peak.