Strong evidences for correlated nonextensive quantum statistics in hadronic scatterings

In this paper the degrees of nonextensivity of the quantum systems composed of (J or θ) - quantum states in the spin (0-1/2+ → 0-1/2+) hadron-hadron scatterings are investigated. So, first we presented a complete statistical description of the nonextensive quantum systems from the (0-1/2+ → 0-1/2+) - scatterings in terms of the scattering entropies S J(p) and Sθ(q), p,q from R. Then, the nonextensivity indices of quantum states from the pion-nucleon and pion-nucleus scatterings, determined by the fit of the scattering entropies S J(p) and Sθ(q) with the optimal scattering entropies S J01(p) and Sθ01(q), are calculated from the available pion-nucleon experimental phase shifts. Therefore, we consider the maximum-entropy (MaxEnt) problem. In this paper we obtained a complete nonextensive statistical description of the quantum state in the (0-1/2+ → 0-1/2+) - scatterings. The equilibrium (or MaxEnt) distributions and optimal (J or θ) - scattering entropies are obtained in terms of the spin dμνJ(x) - functions and of corresponding reproducing kernel functions. The experimental determination of statistical behavior of the quantum scattering states in the pion-nucleon scattering was performed by the experimental fit of the (p,q)- nonextensivity indices using the available pion-nucleon experimental phase shifts. Hence, a separate p-fit of the experimental data on the scattering entropies SJ(p), p of (1/2,∞) with the 'equilibrium' entropy SJo1(p) allowed us to conclude that the (J,p)-statistics of the system of J-quantum states are subextensive with an index p slightly above 1/2, while a separate q-fit of the experimental entropies Sθ(q), q of (1/2,∞) with the optimal entropy Sθo1(q) proved that (θ ,q)- statistics of the θ -quantum states are superextensive with q ≥2. A two-parameter (p,q)-fit of the scattering entropies SJ(p) and Sθ(q) with the optimal scattering entropies SJo1(p) and Sθo1(q) entailed the conclusion that the best values for p are also in the range (0.5 ≤p≤0.6) but with the q-nonextensivities correlated by the Riesz-Thorin relation: 1/p + 1/q=2. The strong experimental evidence obtained here for the nonextensive statistical behavior of the (J,θ) -quantum scattering states in the pion-nucleon scattering can be interpreted as an indirect manifestation of the presence of the quarks and gluons as fundamental constituents of the scattering system having the strong-coupling long-distance regime required by the Quantum Chromodynamics. (authors)