Anomalous dimensions in multiparticle collisions and the empty bin effect

Abstract

Using the random cascade model, we systematically analyze various conditions where realistic multiparticle distributions from cascading processes are affected by systematic and statistical biases at high resolution. We show, both analytically and numerically, that the effect of such conditions (“empty bin effect”) is to produce, in some cases, a modification of the power law of factorial moments as a function of the bin size that is, of the anomalous dimensions governing the dynamical fluctuations. We examine how these may influence the intermittency analysis of multiparticle data. Simulations based on the α-model parametrization of random cascading are suggested to take into account the empty bin effects in the intermittency analysis. A systematic comparison of the fluctuation effects of known distributions, including the log-normal, negative binomial and Lévy-stable laws is performed in terms of the anomalous dimensions, in view of their use as useful approximations.