Levy stable law description of intermittent behaviour and quark-gluon plasma phase transitions

Levy stable laws are introduced to describe intermittency in multiparticle production, using a generalization of the central limit theorem applied to random cascading models. This gives a one-parameter family of representative models depending continuously on the Levy index μ. The multifractal spectrum, the associate 'free energy' and the phase diagram of random cascading are retrieved. This helps classifying intermittency patterns due to different kinds of a phase transitions, either thermal μ < 1: quark-gluon plasma, or non-thermal μ > 1: cascading process. Bin-bin factorial correlations are shown to be very sensitive to the Levy index μ. We suggest to measure them in heavy-ion reactions as a clear signal of a quark-gluon plasma and its decay into hadrons. (orig.)