Scaling and s-channel helicity conservation via optimal state description of hadron-hadron scattering
type: Item
instance of: scholarly article
title: Scaling and s-channel helicity conservation via optimal state description of hadron-hadron scattering
zbMATH Open document ID: 0617.47010
DOI: 10.1007/BF00670413
author: D. B. Ion
published in: International Journal of Theoretical Physics
publication date: 1986-01-01T00:00:00Z
review text: This paper is a continuation and an extension of two previous papers [the author and \textit{H. Scutaru}, ibid. 24, 355-366 (1985; Zbl 0577.47011) and the author, ibid. 24, 1233-1258 (1985)] in which the two-body scattering amplitude is assumed to be an element of a reproducing kernel Hilbert space (RKHS). There it was shown that the RKHS has many special properties that make it an adequate variational space for the description of the scattering in terms of the minimum norm optimum principle and that the notions of optimal scattering state and the reproducing kernel (RK) of the RKHS associated to the scattering amplitude are the same. Then, the expansion of the scattering amplitude in terms of optimal states is an important alternative to partial wave analysis. The essential characteristic features of the two-body scattering as predicted by optimal state dominance are satisfied experimentally with high accuracy for meson-nucleon scattering at energies higher than 2 GeV. In this paper other two-important physical laws of the hadron-hadron scattering such as the scaling of the angular distributions and s-channel helicity conservation, are proved as special properties of the optimal state dominance. These results include in more general and exact form the scaling variables introduced empirically by many authors. Detailed comparisons of the optimal state predictions with the experimental data at low energies are of great importance since the Morrison D-resonances can be interpreted as optimal resonances. All these results can be extended to the many-body final state reactions.
Mathematics Subject Classification ID: 47A40
Mathematics Subject Classification ID: 81U99
Mathematics Subject Classification ID: 46E20
Mathematics Subject Classification ID: 81V25
zbMATH DE Number: 4000797
zbMATH Keywords: reproducing kernel Hilbert space
zbMATH Keywords: minimum norm optimum principle
zbMATH Keywords: optimal scattering state
zbMATH Keywords: scattering amplitude
zbMATH Keywords: two-body scattering
zbMATH Keywords: hadron- hadron scattering
zbMATH Keywords: scaling of the angular distributions
zbMATH Keywords: s-channel helicity conservation
zbMATH Keywords: Morrison D-resonances
zbMATH Keywords: optimal resonances
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4000797