Nonextensive quantum statistics and saturation of the PMD-SQS optimality limit in hadron-hadron scattering

In this paper, new results on the analysis in hadron-hadron scattering (πN , KN , KN , etc) are obtained by using the nonextensive quantum entropy and principle of minimum distance in the space of quantum states (PMD-SQS). So, using [SJ (p), Sθ(q), SJθ(p), SJθ(p, q)]-Tsallis-like scattering entropies, the optimality as well as the nonextensive statistical behavior of the [J and θ]-quantum systems of states produced in hadronic scatterings are investigated in an unified manner. A connection between optimal states obtained from the principle of minimum distance in the space of quantum states (PMD-SQS) [17] and the most stringent (MaxEnt) entropic bounds on Tsallis-like entropies for quantum scattering, is established. The generalized entropic uncertainty relations as well as the correlation between the nonextensivities p and q of the [J and θ]-statistics are proved. New results on the experimental tests of the saturation of the PMD-SQS-optimality limit, as well as on the test of optimal entropic bands obtained by using the experimental pion-nucleon, kaon-nucleon, antikaon-nucleon phase shifts, are presented. The nonextensivity indices p and q are determined from the experimental entropies by a fit with the optimal entropies [S J (p), S o1 θ (q), S o1 Jθ(p, q)]] obtained from the principle of minimum distance in the space of states. In this way strong experimental evidences for the p−nonextensivities index in the range p = 0.6 with q = p/(2p − 1) = 3, is obtained from the experimental data of the (πN,KN,KN)-scattering. The experimental evidence obtained here for the nonextensive statistical behavior of the (J, θ)−quantum scatterings states in the above hadron-hadron 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-range regime required by the Quantum Chromodynamics.