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FRACTAL STRUCTURES AND CORRELATIONS IN HADRONIC MULTIPARTICLE DISTRIBUTIONS

1989; World Scientific; Volume: 04; Issue: 20 Linguagem: Inglês

10.1142/s0217751x89002405

1793-656X

Peter Carruthers,

Computational Physics and Python Applications

Multihadron rapidity distributions exhibit highly irregular (perhaps fractal) event structure. Application of methods used in nonlinear dynamics to hadronic data is made uncertain by the relatively small number of particles in a given event. We analyze three standard methods to assess their applicability: the Hausdorff (box-counting) method, the correlation dimension, and the information dimension. The Hausdorff method can work for large multiplicities if the fractal set (strange attractor) has simple self-similar behavior. It is noted that addition of points from different events will doubtless erase sponge-like structure characteristic of the attractor. This defect is even greater for the information dimension, whose proper definition requires probabilities whose evaluation involves event averaging. For a fixed attractor, this is of no consequence; however, individual collisions differ by a "noise" effect. The correlation dimension, which has the merit of rapid computational convergence, depends only on relative rapidities |y i − y j | and therefore should not depend on overall rapidity shifts between events. Possible statistical independence of different subsets of a given partition of n particles is analyzed using factorial cumulant moments and information entropy. Additivity of constituent cumulants and entropies is characteristic of statistical independence. Conditional entropies are introduced and used to generalize conventional definitions of information entropy and its (Renyi) generalization.