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A microscopic scenario of constituent interactions in high energy collisions of hadrons and nuclei is studied. The concept is based on the  z -scaling of inclusive spectra observed in a wide range of collision energies, multiplicity densities, momenta, and angles of detected particles. We bring arguments that, due to the fractality and self-similarity of the hadron interactions assumed in the  z -scaling scheme, there exists a conservation law of a new quantity named “fractal cumulativity.” The conserved quantity is proportional to the corresponding fractal dimensions and is a simple function of the respective momentum fractions. Based on statistical ideas and entropy considerations we demonstrate that the fractal dimensions possess quantum character.

Fractality in hadron interactions: a conservation law and quantization of fractal dimensions