Prog. Theor. Phys. Vol. 34 No. 1 (1965) pp. 20-45
An Approach to the Symmetry of Hadrons on the Basis of the Lie Group Sp(3). I
Department of Physics, University of Tokyo, Tokyo
(Received February 15, 1965)
On the basis of the unitary symplectic group Sp(3) of rank three, a symmetry scheme of hadrons is proposed in such a way that the product of Gell-Mann's octuplet scheme is succeeded to and some unsatisfactory aspects of his are improved. The 14-dimensional representation of Sp(3) is employed for the baryon and the ps-meson family, and the 21-dimensional one (adjoint representation) for the vector meson family. The octuple baryon multiplet and the octuple ps-meson one in Gell-Mann's scheme are embedded into the supermultiplets forming a giant multiplet in the 14-dimensional representation, in either case, and the octuple v-meson multiplet together with the singlet one is incorporated to the constituents of a giant multiplet for the 21-dimensional representation. The problem of the so-called φ-ω mixing is then discussed from the standpoint of this scheme.
As a consequence of the employment of the Lie group of rank three, a third additive quantum number called superstrangeness is introduced, which plays an important role in characterizing the postulated hadrons. As for the usual hadrons only, the quantum number imposes no further selection rule on the process in the strong interaction. On the other hand, it works so as to make the superstrage hadrons appear pair-wise in the creation and scattering process and materializes the gross structure of the baryon or the meson family regarded as a giant multiplet. The mass relations among the hadrons in this scheme contain Gell-Mann-Okubo's and allow the superstrange hadrons to be much heavier than the usual ones. The electromagnetic mass differences of hadrons and the magnetic moments of baryons are investigated in comparison with Coleman-Glashow's results.
DOI : 10.1143/PTP.34.20
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