Mixing Angle in Renormalizable Theories of Weak and Electromagnetic Interactions

It is suggested that the weak and electromagnetic interactions be incorporated into a theory based on an $\mathrm{SU}\mathrm{}\left(3\right)\mathrm{}\otimes \mathrm{SU}\mathrm{}\left(3\right)\mathrm{}$ gauge-invariant and parity-conserving Lagrangian, in which the lepton fields form a Konopinski-Mahmoud triplet ${\mu }^{+}$, $\nu$, $e^{-}$. The unobserved effects which would be produced by 10 of the 12 charged vector bosons in this theory are suppressed if the spontaneous breaking of $\mathrm{SU}\mathrm{}\left(3\right)\mathrm{}\otimes \mathrm{SU}\mathrm{}\left(3\right)\mathrm{}$ down to $\mathrm{SU}\mathrm{}\left(2\right)\mathrm{}\otimes \mathrm{U}\mathrm{}\left(1\right)\mathrm{}$ is much stronger than the spontaneous breaking of $\mathrm{SU}\mathrm{}\left(2\right)\mathrm{}\otimes \mathrm{U}\mathrm{}\left(1\right)\mathrm{}$ down to electromagnetic gauge invariance. The resulting theory is for most purposes equivalent to the previous $\mathrm{SU}\mathrm{}\left(2\right)\mathrm{}\otimes \mathrm{U}\mathrm{}\left(1\right)\mathrm{}$ model, but with mixing angle now fixed at 30°. In consequence, the mass of the charged vector boson which mediates the known weak interactions is now predicted to be 74.6 GeV. This model also provides a natural mechanism for producing an electron mass of order $\alpha m_{\mu }$.