Phenomenological Analysis of Hyperon Decay

The $\Delta I=\frac{1}{2}$ rule is incorporated into a previously discussed universal weak Yukawa interaction by assuming the simplest relation between chirality and charge operators. Expressing the $\Delta I=\frac{1}{2}$ rule by forming the $N$ and $\Xi$ isospinors into an isovector B and an isoscalar $B_0$, we assume B occurs (as in $\beta$ decay) with $g{\gamma }_{\mu }\frac{1}{2}(1+r{\gamma }_5)$ and $B_0$ (which has no $\beta$-decay counterpart) with $g{\gamma }_{\mu }\frac{1}{2}(1-r{\gamma }_5)$. Here $g$ is the constant previously fitted to the $\pi$ decay rate, and $r$ the ratio of Gamow-Teller and Fermi coupling constants. Depending on the sign taken between the B and $B_0$ interaction terms, $\Sigma$ decays into $n+{\pi }^{+}$ in pure $S$ and into $n+{\pi }^{-}$ in pure $P$ channels, or vice versa. In either case, ${\Sigma }^{+}\to p+{\pi }^0$ involves maximal $S-P$ interference and ${\alpha }^0=0.98\mathrm{}$. Decay into $I=\frac{1}{2}$ proceeds via ${\gamma }_{\mu }(\frac{1}{2}+\frac{3}{2}r{\gamma }_5)$ or ${\gamma }_{\mu }(\frac{3}{2}+\frac{1}{2}r{\gamma }_5)$, depending on whether ${\Sigma }^{-}$ decay is pure $S$ or pure $P$. The second case, but not the first, leads to a $\Lambda$-decay rate in agreement with experiment. In this case ${\alpha }_{\Lambda }=0.54\mathrm{}$, and in ${\Xi }^{-}$ decay, ${\alpha }_{\Xi }=0.64\mathrm{}$ and the calculated decay rate is 2.4×${10}^{-1\mathrm{}}$ ${\sec }^{-1\mathrm{}}$.