Saturation Of Optimal Entropic Resonance Limits In Pion-Nucleus Scattering In $\Delta (1236)$-Elementary Resonance Region

TL;DR

This study demonstrates that experimental scattering entropies in pion-nucleus interactions near the $236$ resonance align with theoretical optimal resonance predictions when nonextensivity indices follow a specific Riesz-Thorin-like relation.

Contribution

It introduces a correlation between nonextensivity indices that accurately describes experimental scattering entropies in the resonance region.

Findings

Experimental entropies match optimal resonance predictions.

Nonextensivity indices are linked by a Riesz-Thorin-like relation.

Results validate the entropic approach in resonance scattering analysis.

Abstract

In this paper, it is shown that the experimental values of the nonextensive scattering entropies $S_L (p)$ and $S_\theta (q)$ for the pion-nucleus ($\pi^0 He, \pi^0 C, \pi^0 O, \pi^0 Ca$) scatterings, in the energy region corresponding to $\Delta (1236)$ resonance in the elementary pion-nucleon interaction, are well described by the entropic optimal resonance predictions $S_L^o1 (p)$ and $S_\theta^o1 (q)$ and when the nonextensivities indices are correlated by a Riesz-Thorin-like relation: 1/2p+1/2q=1.