Multiparticle Spectra in Simple Theoretical Models: ACluster-Decomposition Analysis

We present a detailed investigation of inclusive and exclusive multiparticle spectra in several simple models of high-energy hadronic interactions. To clarify the origins of particular structure in these spectra we divide the study into two sections. First, we discuss models designed to isolate the features arising from kinematic constraints. Specifically, we treat both pure longitudinal phase space and a longitudinal phase space modified to produce a "leading-particle" effect. In the second section we consider examples of specific dynamical models. Here we investigate the simplified Chew-Pignotti model, in both the strong-ordered and general versions, and a "${\varphi }^3$-type" multiperipheral model. Our analysis is based on a cluster-decomposition approach analogous to that used in statistical mechanics. In particular, we apply a set of "cluster-function sum rules" to relate the correlations found in inclusive spectra to those observed in exclusive processes. Within the context of the models, we establish that these sum rules provide both an attractive qualitative picture of correlations in multiparticle spectra and a useful quantitative framework in which to calculate these correlations. We conclude with a discussion of the possible extensions of these cluster techniques to phenomenological analyses of high-energy interactions.