Unitary or Octal Symmetry?

Octal symmetry ($R_8=\mathrm{group}\mathrm{of}\mathrm{rotations}\mathrm{in}\mathrm{eight}\mathrm{dimensions}$) is applied to the strong interactions. If the existence of an octet $m$ and a singlet $\lambda$ of spinless mesons is assumed, a bootstrap mechanism allows the existence of 36 vector mesons with the coupling constants given by the $R_9$ group. Under $R_8\subset R_9$ the 36-plet of vector mesons splits in an octet $v^{\prime }$ [with $\eta \mathrm{}\left(780\right)\mathrm{}$, $K\left(730\right)\mathrm{}$, $\pi \mathrm{}\left(560\right)\mathrm{}$ as a possible identification] and a 28-plet $v$. From octal symmetry a multiplicative quantum number $N$ (block parity) is obtained which forbids the decay $v^{\prime }\to m+m$ and perhaps explains the small width of this octet. A reasonable mass formula allows us to predict the masses of the $v$, $v^{\prime }$ vector mesons and suitable candidates with the predicted masses are found. The partial widths for the $v\to m+m$ decays are consistent with the experimental data and in particular with ${\Gamma }_{K\left(1175\right)\mathrm{}\to K\pi }$, ${\Gamma }_{\pi \mathrm{}\left(1220\right)\mathrm{}\to \pi \pi }$ being small.