Weak Interactions andG2

Abstract

A speculative model of the weak interactions constructed in the framework of the $G_2$ symmetry scheme is discussed. The model leads to the existence of $\Delta Q=-\Delta S$ matrix elements in the vector interaction and their absence in the axial-vector contribution. In particular, it leads in a natural manner to the existence of ${\Sigma }^{+}\to n+e^{+}+\nu$ at a rate compatible with the present upper limit, to the existence of $\Delta Q=-\Delta S{\left(K^{\circ }\right)}_{e3\mathrm{}}$ decays, and to a strong inhibition of the reaction $K^{+}\to {\pi }^{+}+{\pi }^{+}+e^{-}+\overline{\nu }$. It also gives rise to rigorous predictions involving the ${\left(K^{+}\right)}_{e3\mathrm{}}$ and ${\left(K^{\circ }\right)}_{e3\mathrm{}}$ decays. The scheme allows for the possible violation of $\mathrm{CP}$ invariance in the ${\left(K^0\right)}_{e3\mathrm{}}$ and is qualitatively compatible with Sach's explanation of the order of magnitude of the $\mathrm{CP}$ violation in $K_2^{}{}_{}{}^0\to {\pi }^{+}+{\pi }^{-}$. Several qualitative and quantitative predictions, some of which hold to all orders in the symmetry-breaking interactions, are discussed and compared, whenever possible, with experimental information.