Direct evidence for the validity of Hurst's empirical law in hadron production processes

We propose to use the rescaled range analysis to examine the records of rapidity-dependence of multiplicities in high-energy collision processes. We probe event by event the existence of global statistical dependence in the system of produced hadrons, and demonstrate the effectiveness of the above-mentioned statistical method by applying it to the cosmic-ray data of the JACEE collaboration, and by comparing the obtained results with other experimental results for similar reactions at accelerator and collider energies. We present experimental evidence for the validity of Hurst's empirical law, and the evidence for the existence of global statistical dependence, fractal dimension, and scaling behavior in such systems of hadronic matter. None of these features is directly related to the basis of the conventional physical picture. Hence, it is not clear whether (and if yes, how and why) these striking empirical regularities can be understood in terms of the conventional theory.