Negative binomial multiplicity distributions in continuous domains

Abstract

Prompted by experimental evidence on multiplicity distributions of particles produced in high energy collisions, we study the class of distributions of points in a continuous domain D 0, characterized by the property that the multiplicity of points in D 0 and in any subdomain D of D 0 has a negative binomial distribution. We show that a distribution of this class is completely determined by the two parameters Q 1( y) = dn/ dy and k(y) of the multiplicity distribution in infinitesimal neighbourhoods of all points y of D 0. We prove that the distribution can be constructed by N-fold convolution of identical uncorrelated “clan” distributions, the number N of clans being itself Poisson-distributed. The clan distribution, which involves all correlations of the original distribution, is found to be very simply expressed in terms of Q 1( y) and k( y).