Multifractal structure of multiplicity distributions in particle collisions at high energies

Experimental data on the bin size dependence of charged hadron multiplicity distributions in proton-antiproton collisions and electron-positron annihilation are analyzed in terms of multifractals. Linear relations are found between 〈nlnn〉/〈n〉 and ln〈n〉, and also between ln〈${\mathit{n}}^{\mathit{q}}$〉 and ln〈n〉 for q=2,3,4,..., where n is the multiplicity in a single bin of the (pseudo) rapidity space and 〈 〉 stands for the event average. Generalized dimensions ${\mathit{D}}_{\mathit{q}}$ for q=0,1,2, . . . are determined from the slopes. Our result suggests a power law of the form 〈${\mathit{n}}^{\mathit{q}}$〉=c(〈n〉/${\mathit{n}}_0$ ${)}_{\mathit{q}}^{\mathit{b}}$.