Abstract
The $G$ moments for the multifractal analysis of multiparticle production are investigated in a model-independent way. By successive bin splitting and assuming the existence of a multiplicity splitting function that depends on multiplicity, but applicable at all steps of the splittings, we study the ergodicity of horizontal and vertical averaging, and derive a universality relation for the $G$ moments. It relates the $G$ moments for different initial multiplicities to a common scaling function ${\ensuremath{\Gamma}}_{p}(\ensuremath{\xi})$. The experimental verification of this scaling property would, on the one hand, signify self-similarity in the data, and, on the other, provide a convenient function for comparison not only among different experiments, but also between theory and experiment.
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