A Class of Gauge Theories with SuperweakCPViolation

A class of gauge theories is discussed in which the $\Delta S=0\mathrm{}$ and the $\Delta S=1\mathrm{}$ semileptonic decays are mediated by distinct intermediate bosons, whose mass ratio is related to the Cabibbo angle $\theta$. Common features of the models are as follows: $\theta$ is well defined only as the result of spontaneous symmetry breaking; $\mu$ decay and the semileptonic $\Delta S=0\mathrm{}$, $\Delta S=1\mathrm{}$ decays are in the ratio $1:{cos}^2\theta :{sin}^2\theta$ only if $\mathrm{CP}$ is maximally violated in the lepton sector; a breakdown of $\mu e$ universality related to $\mathrm{CP}$ violation; a superweak impact of $\mathrm{CP}$ violation on $K$ decays; the mediation through a neutral vector boson of nonleptonic decays which obey $\left|\Delta I\right|=\frac{1}{2}$; and an amplitude $\ll O\left(G\right)\mathrm{}$ for ${\nu }_{\mu }e$ scattering. Two distinct types of theories are discussed in detail. (a) The gauge group O(4) reported before. Here the $\mathrm{CP}$-violating parameter needs a renormalization. To $O\left(G\right)\mathrm{}$, ${\nu }_{\mu }$-nucleon reactions are possible only if a heavy lepton is produced. (b) $\mathrm{O}\mathrm{}\left(4\right)\mathrm{}\times \mathcal{G}$, where left- [right-] handed fermions are in $\mathrm{O}\mathrm{}\left(4\right)\mathrm{} \left[\mathcal{G}\right]$ but scalar with respect to $\mathcal{G} \left[\mathrm{O}\mathrm{}\right(4\left)\right]$. Here the $\mathrm{CP}$-violating parameter can be made finite if a constraint between electron and muon multiplets is satisfied. Further consequences for case (b) are: the ${\overline{\nu }}_e-e$ and ${\nu }_e-e$ elastic cross sections are ($1+sin2\left|\theta \right|$) times their respective $V-A$ values, and ${\nu }_{\mu }$-nucleon reactions are possible with or without production of a heavy lepton. However, the final hadronic state is necessarily "charmed." The example $\mathcal{G}=\mathrm{U}\mathrm{}\left(1\right)\mathrm{}$ is discussed in detail. The role of discrete symmetries is emphasized.