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

Abstract

Experimental results are presented for study of collective and fractal properties of soft pion jets in the space of relative four-dimensional velocities. Significant decreasing is obtained for mean square of second particle distances from jet axis for pion-proton interactions at initial energies ∼ 3 GeV in comparison with hadron-nuclear collisions at close energies. The decreasing results in power dependence of distance variable on collision energy for range ∼ 2 − 4 GeV. The observation allows us to estimate the low boundary of manifestation of color degree of freedom in pion jet production. Cluster dimension values were deduced for pion jets in various reactions. Fractional values of this dimension indicate on the manifestation of fractal-like properties by pion jets. Changing of mean kinetic energy of jet particles and fractal dimension with initial energy increasing is consistent with suggestion for presence of color degrees of freedom in pion jet production at intermediate energies.

NICA fixed target mode: Soft jet studies in the relative 4-velocity space

“…The values of √ s c for the members of G are given in the Table 1. The estimates of √ s c for T k and D agree well with each other but exceed the values of √ s c obtained earlier in [5] on the basis of the b k ( √ s) dependence. This difference may be due both to physical reasons that lead to a sharper growth of T k and D in relation to b k and to a smaller size of the experimental-data samples in the case of the first two parameters.…”

Quark degrees of freedom in the production of soft pion jets

“…Thus, this investigation extended for the whole set G renders the results obtained earlier in [3,4] more reliable and furnishes an additional argument in support of the hypothesis that a changeover of dynamical interaction regimes occurs because of the onset of the experimental manifestation of quark degrees of freedom in the production of soft pion jets at √ s ∼ 3 GeV. This entails the respective transition from the description of the processes in question in terms of baryon-meson degrees of freedom to the use of quark-gluon degrees of freedom.…”

“…. Special features of this method in the case of the production of two jets were considered in detail in [2][3][4][5]. In that case, secondary particles refer to the region of target (beam) fragmentation if X k t ≥ (≤)X bnd X k b ≤ (≥)X bnd , where X k p = [m k (U k U r )][m p (U p U r )] −1 , p, r = t, b; p = r; m k is the mass of the kth secondary particle; m t/b is the mass of the target/beam particles; U k = P k /m k is the 4-velocity; k = t, b, 1, 2, .…”

“…Statistically acceptable values of χ 2 /ndf could be obtained for 45% of the samples [5]. Numerical values found for √ s c from a fit to G i ( √ s) for √ s < 4 GeV are summarized in the table, the values for b k being taken from [4]. The values of √ s c for the remaining two parameters from G are presented in the first rows for T k and D. Taking into account the sizes of samples of available experimental data and the behavior of T k ( √ s) and D( √ s), we can approximate the dependences in question by the function in (1) for √ s > 2 GeV.…”

“…Taking into account the results for b k ( √ s) in the region of √ s > 3.5 GeV [3,4] and the behavior of T k ( √ s) and D( √ s) in the above range of √ s, we approximated by the function in (2) the samples taken for T k and D and summed over the fragmentation regions. The numerical values of the fit parameters and the respective detailed discussion are presented in [5].…”