A Monte Carlo Study of the Levy Stability and Multifractal Spectrum in e+e- collisions

The Levy stability analysis is carried out for e+e- collisions at Z^0 mass using Monte Carlo method. The Levy index \mu is found to be \mu=1.701 +- 0.043. The self-similar generalized dimensions D(q) and multi-fractal spectrum f(\alpha) are presented. The Renyi dimension D(q) decreases with increasing q. The self-similar multi-fractal spectrum is a convex curve with a maximum at q = 0, \alpha = 1.169 +- 0.011. The right-side part of the spectrum, corresponding to negative values of q is obtained through analytical continuation.