Higher Symmetries and the Neutron-Proton Magnetic-Moment Ratio

A quark model of $\mathrm{SU}\left(4\right)\mathrm{}$ is developed in which the quarks possess charge $\frac{2}{3}$ and $-\frac{1}{3}$ and baryon number $N=\frac{1}{3}$. The new particles predicted are characterized by a quantum number $W\ne 0$ (superstrangeness); they possess integer charge but fractional hypercharge $\frac{1}{3}$ or $\frac{2}{3}$, and are called hyperquarks. A spin extension of $\mathrm{SU}\left(4\right)\mathrm{}$ is formulated and leads to the study of the group $\mathrm{SU}\left(8\right)\mathrm{}$ and the subalgebra $\mathrm{SU}\left(4\right)\mathrm{}\otimes \mathrm{SU}\left(2\right)\mathrm{}$. The baryons and isobars are grouped in the representation 120 and the mesons in the adjoint representation 63. It is found that the $\frac{F}{D}$ ratio in $\mathrm{SU}\left(8\right)\mathrm{}$ is uniquely specified by the scheme. The ratio of the magnetic moments of the neutron and proton is uniquely determined by assuming that the magnetic-moment operator transforms as the adjoint representation of $\mathrm{SU}\left(8\right)\mathrm{}$, and by specifying the extended Gell-Mann-Nishijima relation for the quarks. The value $-\frac{2}{3}$ is found for the neutron-proton magnetic-moment ratio in agreement with the result found in $\mathrm{SU}\left(6\right)\mathrm{}$. The selection rules forbidding processes like $\phi \to \rho \pi$ and $\pi +N\to \pi +N+\phi$ are obtained from the conservation of the four quark spins. These results strongly indicate that the physical predictions of a symmetry scheme like $\mathrm{SU}\left(6\right)\mathrm{}$ are not unique and that there exists a hierarchy of symmetries all possessing equally good (or bad) physical predictions, but with new quantum numbers associated with superstrange particles.