Baryon Mass Spectra in a DynamicalS-WaveSU(6)Model

Some results on the mass spectra of the ${56}^{\mathrm{}(+)\mathrm{}}$ and the proposed ${70}^{\mathrm{}(-)\mathrm{}}$ and ${20}^{\mathrm{}(+)\mathrm{}}$ $\mathrm{SU}\left(6\right)\mathrm{}$ baryon multiplets are presented as calculated from a simple $S$-wave $\mathrm{SU}\left(6\right)\mathrm{}$-invariant dynamical model involving first-order mass deviations. We take the meson masses from experiment and obtain reasonable agreement with the experimentally known baryon masses. The masses of the missing members of the multiplets are estimated. The mass spectrum of the 70 is discussed in detail. A two-parameter calculation using the experimental 56 and 35 mass spectra yields a mass spectrum in qualitative agreement with a recent nondynamical calculation of Gyuk and Tuan, in which 6 parameters have been used. The three mixing angles occurring in the 70 are estimated from the model and found to be small. On this basis some new approximate mass rules are given. We derive explicit representations for the reduced matrix elements of the strong interaction mass operator for the $\mathrm{SU}\left(6\right)\mathrm{}$ 35, 56, 70, and 20 representations.