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## Prog. Theor. Phys. Supplement Extra Number (1965) pp. 339-382

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# Spinor Model of Baryons and Mesons

Department of Physics, Nagoya University, Nagoya

### Abstract:

A unified model of baryons and mesons is presented based on the hypothesis that a strongly interacting particle originally has the internal configuration represented by three “triads", where a triad is by definition a light-like vector together with a rotational orientation around it, and the existence of three triads is related to the fact that our Minkowski space allows three independent light-like vectors. The assumed configuration implies twelve (real) independent internal coordinates. The SU(6) symmetry is contained there in conformity with relativity, which requires kinematical couplings to exist between internal and external motions. Characteristic to the model is, besides the SU(6), the existence of generators of a three-dimensional Lorentz group, which represents the extension, dilatation and vibration of the structure. These quantities play particularly important roles of controlling the IR (irreducible representation) of SU(6) and determining the mass operator. Eigenstates of the internal motion are first classified into "shells” by a pair of oscillator quantum numbers, and then each shell is subgrouped into super-multiplets corresponding to IR's of SU(6). The first mesonic shell has odd parity and contains 36 states which are divided into an SU(6) singlet (identified as X0(958) meson) and an SU(6) 35-plet. The predictions about spin, parity and charge-conjugation parity just agree with observations. In the model the IR's \underbar15 and \underbar20 of SU(6) do not occur in the shells of lower excitation.

DOI : 10.1143/PTPS.E65.339

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