Multiplicity distributions in hadron interactions derived from the statistical bootstrap model

We give a self-contained (though sketchy) derivation of the charged multiplicity distribution of final hadrons in a simplified (only pions) version of the statistical bootstrap model (SBM). The analytical form of this distribution is determined by two prominent features of SBM: a singularity at some temperatureT ₀ (related to the phase transition hadrons → quark-gluon plasma) and the production of Poisson-distributed hadron clusters with well-defined decay structure. The multiplicity distribution of final hadrons has two free parameters: an average temperatureT and the mean number \(\bar N\) of clusters, both depending on the collision energy √s such that for √s→∞, the temperature tends to the limitT ₀ while \(\bar N\) may grow (very slowly) without bound. With these two free parameters we obtain reasonable to good fits to experimental data at energies ranging from √s=7.87 to 900 GeV (full and in some cases cut pseudorapidity). The average cluster sizes found in our fits are compatible with those inferred from (pseudo) rapidity correlations in the data. We discuss the relation of this model to the negative binomial distribution (NBD).