Analysis of correlation functions in multiperipheral cluster models with simultaneous emission of clusters of different multiplicity

Abstract

Experimental results indicate that the two-body correlation function ${f}_{2}^{\mathrm{ch}}$ is positive at laboratory momentum above about 50 GeV/c. To obtain positive ${f}_{2}$, we examine multiperipheral models modified to include more than one different vertex type, with more than one particle emitted at some vertices. We will show that in such models, ${f}_{2}={c}_{2}\mathrm{ln}(s)+\mathrm{constant}$ at high energy, and ${c}_{2}$ can be positive. Furthermore, $〈N〉$ and all correlation functions ${f}_{j}$ also go as ${c}_{j}\mathrm{ln}(s)$ at high $s$. As a result, the model features a special form of Koba-Nielsen-Olesen (KNO) scaling. We have made a numerical analysis of the model for clusters of up to eight particles emitted at the vertices, and we calculate the average multiplicity, the Mueller two-body correlation function, and the Mueller three-body correlation function. We obtain a favorable, through crude, fit to the experimental data.