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

Abstract

The simplest representations of $\mathrm{SU}(6)$ and $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{U}(12)$ 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 $\mathrm{SU}{(6)}_{W}$, the subgroup of $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{U}(12)$ and $U(6)\ifmmode\times\else\texttimes\fi{}U(6)$ 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 $\mathrm{SU}{(6)}_{W}$ 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 -$\frac{3}{2}$, $\mathrm{SU}(3)$-octet resonances in the 70 representation of $\mathrm{SU}(6)$ and $\mathrm{SU}{(6)}_{W}$ are calculated. An attempt is made to include $\mathrm{SU}(3)$ symmetry-breaking effects in a calculation of the decay rates of the ${\frac{3}{2}}^{+}$ decuplet within the 56 of $\mathrm{SU}{(6)}_{W}$.