Fractal behavior of multiplicity fluctuations in high-energy collisions

It is shown that the multiplicity fluctuations of the particles produced in high-energy hadron collisions can be systematically quantified by the $G$ moments, which can be defined to suppress the statistical contributions. Expansion in terms of a set of basic functions $B_{q,k}\mathrm{}\left(M\right)\mathrm{}$ provides simple fractal interpretation for the asymptotic power-law behavior of $〈G_q〉$. The connection with the scaled factorial moments is investigated. An extension to nonintegral values of $q$ is considered. The generalized fractal dimension $D_q$ is determined. Calculations of all quantities involving multiplicity fluctuations are done using a Monte Carlo code (ECCO) based on the geometrical branching model, which has previously been shown to yield the correct degree of intermittency as determined by the NA22 experiment on hadronic collisions.