Unitary Symmetry and Hyperon Leptonic Decays

Abstract

The consequences (beyond the $\Delta I=\frac{1}{2}$ and $\Delta I=1\mathrm{}$ rules) of the most general form of the hypothesis that the weak-interaction currents transform like components of S${\mathrm{U}}_3$ octets are discussed. These are presented as relations between the $\Delta S=1\mathrm{}$ leptonic decays of ${\Xi }^{-}$ and ${\Xi }^0$ and those of $\Sigma$ and $\Lambda$. The only prediction for the branching ratios $B$ of $\Xi$ decays which can be compared to present experiments is $B({\Xi }^{-}\to \Lambda +e^{-}+\nu )+B({\Xi }^{-}\to {\Sigma }^0+e^{-}+\nu )\le (1.05\mathrm{}\pm 0.2)\times {10}^{-3\mathrm{}}.$ As yet the comparison is inconclusive. One additional relation among the leptonic decays of hyperons is found if the particular model of Cabibbo is assumed. Applications of these considerations to the determination of induced couplings are made.