Higher Symmetries and the Neutron-Proton Magnetic-Moment Ratio

Abstract

A quark model of $\mathrm{SU}(4)$ is developed in which the quarks possess charge $\frac{2}{3}$ and $\ensuremath{-}\frac{1}{3}$ and baryon number $N=\frac{1}{3}$. The new particles predicted are characterized by a quantum number $W\ensuremath{\ne}0$ (superstrangeness); they possess integer charge but fractional hypercharge $\frac{1}{3}$ or $\frac{2}{3}$, and are called hyperquarks. A spin extension of $\mathrm{SU}(4)$ is formulated and leads to the study of the group $\mathrm{SU}(8)$ and the subalgebra $\mathrm{SU}(4)\ensuremath{\bigotimes}\mathrm{SU}(2)$. 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 $\mathrm{SU}(8)$ 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 $\mathrm{SU}(8)$, and by specifying the extended Gell-Mann-Nishijima relation for the quarks. The value $\ensuremath{-}\frac{2}{3}$ is found for the neutron-proton magnetic-moment ratio in agreement with the result found in $\mathrm{SU}(6)$. The selection rules forbidding processes like $\ensuremath{\varphi}\ensuremath{\rightarrow}\ensuremath{\rho}\ensuremath{\pi}$ and $\ensuremath{\pi}+N\ensuremath{\rightarrow}\ensuremath{\pi}+N+\ensuremath{\varphi}$ are obtained from the conservation of the four quark spins. These results strongly indicate that the physical predictions of a symmetry scheme like $\mathrm{SU}(6)$ 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.