212 Progress of Theoretical Physics 1 Vol. 51 1 No.1, January 1974 Multiplicity Distribution Model Based on Cluster Assumption in High-Energy Hadr.onie Collisions*' Kan-ichi YoKOYAMA, Hisakazu MINAKATA and Mikio NAMIKit Research Institute for Theoretical Physics Hiroshima University, T akehara, Hiroshima 725 tDepartment of Physics, Waseda University, Tokyo 160 (Received July 16, 1973) In order to describe the feature of correlations among produced particles. in high-energy hadronic collisions, a new type of multiplicity distribution is introduced. The distribution can be derived from some simple assumptions of clustering for produced particles, and it corresponds to a modified P6lya distribution in which two parameters are included besides the averaged multiplicity. Under some conditions given for these parameters in stochastic and clustering sense, it is shown ·that the distribution can lead to two- and three-particle correlation parameters consistent with the data in the GeV J c region of incident roo• mentum in proton-proton collisions. Some possible •parametrizations lead to the Koba-Nielsen· Olesen scaling as well as the above. § 1. Introduction Recently Koba, Nielsen and 61esen 1 > [KNO] predicted that the partial cr.oss section for producing n·charged particles in·multiple particle production should scale at asymptotic energies with an energy-independent ·function if; (z) (z; the normalized multiplicity n/(n) and (n); the averaged in the form . '(71)->oo (O'ine 1 ; the_ total inelastic cross section). After the KNO prediction, and Slattery 8 >·'> presented evidence for an onset of the KNO scaling already at present machine energies in the 50-300 Ge V / c regio_n of incident momentum in proton- proton collisions. The experimental data on 6 11 show that the function if; (i) can be approximated with any curve within a strip with a narrow width in the range of z from "'0.2 to "'3. 3 >• 4 > Apart from a question wheth_er or not such an ob- served weak (n)-dependence of the function if;(z) may really be accepted as strong evidence for the KNO scaling, 6 > the weak (n)-dependence itself is in determining as functions of (n) the values of higher correlation parameters (i.e., integrated Mueller correlation functions). which. are yery sensitive with respect to small variation of the function ¢ (z). Many models of multiple particle produc- *l Work prepared in part while one of the authors (K.Y;) stayed at Department of Physics, Waseda University, under support by the Japan Society for the P:i:orp.otion of Science. Downloaded from https://academic.oup.com/ptp/article-abstract/51/1/212/1841717 by guest on 23 May 2020