Weak Interactions inSU(6)andŨ(12)

Abstract

Weak interactions are studied in $\mathrm{SU}(6)$ and $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{U}(12)$. The weak currents are assigned to the 35-dimensional representation of $\mathrm{SU}(6)$ [or the 143 in $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{U}(12)$], and the predictions of a Cabibbo-type theory are derived. For nonleptonic decay, the 35 has been shown to be inconsistent with experiment, and so we assign the effective Hamiltonian to an admixture of 35 and 405. This assignment is now consistent with experiment, and, when one extra assumption is made, it leads to the Lee-Sugawara triangle and the vanishing of $〈{\ensuremath{\Sigma}}^{+}|n{\ensuremath{\pi}}^{+}〉$ for parity-violating amplitudes. In $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{U}(12)$, the assignment 143+5940 yields the same results. Amplitudes for ${\ensuremath{\Omega}}^{\ensuremath{-}}$ decay modes are related to amplitudes of known decays, and the corresponding rates are calculated.