Decays of Positive-Parity Baryon Resonances in a BrokenŨ(12)

The simplest representations of $\mathrm{SU}\left(6\right)\mathrm{}$ and $\tilde{U}\mathrm{}\left(12\right)\mathrm{}$ which are capable of describing the low-lying positive-parity baryon resonances are the three-quark representations. All particle states in these multiplets are eigenstates of $W$ spin and $\mathrm{SU}{\mathrm{}\left(6\right)\mathrm{}}_W$, the subgroup of $\tilde{U}\mathrm{}\left(12\right)\mathrm{}$ and $U\left(6\right)\mathrm{}\times U\left(6\right)\mathrm{}$ which remains invariant for two-body decay processes, even when kinetic-energy terms and derivative couplings are included in the calculations. It is shown that $\mathrm{SU}{\mathrm{}\left(6\right)\mathrm{}}_W$ leads to various selection rules and to definite branching ratios for the decays of these resonances. The branching ratios for the decays of the spin -$\frac{3}{2}$, $\mathrm{SU}\left(3\right)\mathrm{}$-octet resonances in the 70 representation of $\mathrm{SU}\left(6\right)\mathrm{}$ and $\mathrm{SU}{\mathrm{}\left(6\right)\mathrm{}}_W$ are calculated. An attempt is made to include $\mathrm{SU}\left(3\right)\mathrm{}$ symmetry-breaking effects in a calculation of the decay rates of the ${\frac{3}{2}}^{+}$ decuplet within the 56 of $\mathrm{SU}{\mathrm{}\left(6\right)\mathrm{}}_W$.