Multifractal dimensions in QCD cascades

Particle production in small rapidity or angular intervals have fractal structures similar to a Cantor dust. In this paper we present analytical result for multifractal dimensions valid for high energies. For high moments the dimension is given by \(\sqrt {6\alpha _s /\pi } \) . The scaling properties seen in the partonic state are not so well reflected in the hadronic multiplicity moments or factorial moments. We show how to define new observables on the final hadronic state, which do scale well. This means that the multifractal dimensions can be well determined and compared with results from QCD.