Heavy-electron mass andCPviolation in a gauge model

A renormalizable [$\mathrm{SU}\mathrm{}\left(2\right)\mathrm{}\times Y$] weak gauge model is studied in which spontaneous breakdown generates masses for all fermions except neutrinos and gauge bosons except the photon and at the same time destroys the original $P$ and $CP$ invariance of the Lagrangian. A connection between the heavy-electron-to-electron mass ratio and the size of $CP$ violation is pointed out. A free-quark-model calculation of lowest order $CP$ violation in the $K^0\leftrightarrow {\overline{K}}^0$ mass matrix is used to test whether the model can accommodate the measured $CP$ violation ($\left|\epsilon \right|=2\mathrm{}\times {10}^{-3\mathrm{}}$) and the bound on heavy-lepton mass ($M_E>1\mathrm{}$ GeV). Assuming reasonable and consistent values of certain quark and Higgs-particle mass ratios, it is found that the model is consistent with known weak-interaction phenomenology if the mass of the heavy electron is less than about 6 GeV. The dominant leptonic decays of the heavy electron, $E$, are $E^{-}\to l^{-}+\left({\overline{\nu }}_L^l\right)+{\nu }_R^e$, where (${\overline{\nu }}_L^l$) refers to the usual lepton ($l=e or \mu$) antineutrino but ${\nu }_R^e$ refers to a right-handed electron neutrino associated with the $E$.