Symmetry of Strong Interactions

Abstract

The symmetry of strong interactions and weak interactions is formulated in terms of the four-dimensional charge space of SU(2) × SU (2) or O (4), where the isospin, τ, and the “hypercharge spin”, ζ, are considered as two independent spin matrices. The wave functions of baryons and mesons in this charge space are assumed to be composed of the eigenfunctions t of τ3 and s of ζ3, and to transform according to the representations (1/2, 0) and (0, 1/2), respectively. As the basic wave functions which span an irreducible representation space allowing the reflection operations in the charge space, which give rise to the transformations we need sixteen kinds of baryons and also sixteen kinds of mesons, if we assume that the ground state particles are described in terms of the bilinear products t*t, s*s t*s and s*t. The sixteen kinds of particles are made of a singlet, a triplet and a quartet which correspond to an octet in SU (3) symmetry and their countermultiplets which come out by exchanging t⇄s. Among the latter multiplets, a “hypercharge spin” triplet of baryons Z+ (Y=+2), Λ*(Y=0), Ω−(Y = −2) and of mesons D+ (Y=+2), D°(Y=0), D−(Y=−2) are introduced as the countermultiplets of ∑ hyperon and π meson, respectively. We also attempt to classify baryon isobars and meson isobars in terms of the higher configurations of t, t* and s, s*. It is remarkable that a new selection rule of “hypercharge independence” is very powerful in explaining the suppression of some of the decay modes which are otherwise hard to understand. It may also be satisfactory to see that the allowed modes are described in terms of Symmetric interactions, while the forbidden modes of decay are invoked in terms of the meso-strong symmetry breaking interactions on the basis of the present scheme of SU(2) × SU (2) symmetry. The possible experiments which could afford tests of the present scheme are cited within the framework of strong interactions only. We extend the theorem by Okun and Pomeranchuk for high energy scattering in the asymptotic region to include hypercharge independence in addition to charge independence, and obtain good results in the case of kaon-nucleon scattering; we also obtain predictions which can be easily tested by the experiments in the case of antiproton (proton)-nucleon scattering in the asymptotic region. Discussions are made on the various results deduced from the present scheme of SU (2) × SU (2), in comparison with those obtained from the SU (3) scheme.