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 [l angle][ital n]ln[ital n][r angle]/[l angle][ital n][r angle] and ln[l angle][ital n][r angle], and also between ln[l angle][ital n][sup [ital q]][r angle] and ln[l angle][ital n][r angle] for [ital q]=2,3,4,..., where [ital n] is the multiplicity in a single bin of the (pseudo) rapidity space and [l angle] [r angle] stands for the event average. Generalized dimensions [ital D][sub [ital q]] for [ital q]=0,1,2, . . . are determined from the slopes. Our result suggests a power law of the form [l angle][ital n][sup [ital q]][r angle]=[ital c]([l angle][ital n][r angle]/[ital n][sub 0])[sup [ital b]][sub [ital q]].