Scaling and s-channel helicity conservation via optimal state description of hadron-hadron scattering
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.
scientific article; zbMATH DE number 4000797
scientific article