Collective and fractal properties of pion jets in the space of 4-velocities at intermediate energies

Experimental results obtained by studying collective and fractal properties of soft pion jets in the space of relative 4-velocities at intermediate energies are presented. The mean square of the distance between secondary particles and the jet axis is found to be significantly smaller in the case of pion-proton interactions at initial energies of about 3 GeV than in the case of hadron-hadron collisions at similar energies. This reduction leads to a power-law dependence of this quantity on the interaction energy in the energy range between about 2 and 4 GeV, and this makes it possible to estimate the lower boundary of the region where color degrees of freedom manifest themselves in pion-jet production. The cluster dimensions of pion jets in various reactions were obtained for the first time. Fractional values of this dimension may be a manifestation of fractal properties of pion jets. The change in the mean kinetic energy of particles in the jet and the change in the fractal dimension in response to the change in the collision energy is compatible with the assumption that color degrees of freedom come into play in pion-jet production at intermediate energies.