Factorial and fractal analysis of the multipion production process at 350 GeV/c

The self-similarity property of the multiparticle production process is investigated from different angles using 350 GeV/c ${\mathrm{\pi }}^{\mathrm{-}}$-AgBr data of our own. An intermittency analysis in pseudorapidity-azimuthal angle space shows that a one-dimensional analysis gives considerably underestimated exponent values and thus proves the necessity of probing higher dimensions. The study of factorial correlators at different bin widths reveals an approximate linearity of log-log plots of correlators versus the inverse rapidity distance over a limited region and bin width independence of correlators calculated at a small rapidity distance. A dimension-independent relation between factorial correlators and moments is utilized to eliminate the intermittency-nonintermittency ambiguity. A newly defined G moment, which can suppress the statistical bias, is used to extract the dynamical signals in the framework of a fractal analysis. It also indicates a rough link between factorial and fractal moment methods, which has been missing so far.