Monte Carlo Analysis of the Lévy Stability and Multi-fractal Spectrum in e⁺e^- Collisions

The Lévy stability analysis is carried out for e⁺e^- collisions at Z⁰ mass using the Monte Carlo method. The Lévy index μ is found to be μ = 1.701±0.043. The self-similar generalized dimensions D(q) and multi-fractal spectrum f(α) are presented. The Rényi dimension D(q) decreases with increasing q. The self-similar multi-fractal spectrum is a convex curve with a maximum at q = 0, α = 1.169±0.011. The right-hand side of the spectrum, corresponding to negative values of q, is obtained through analytical continuation.