Mixing Angle in Renormalizable Theories of Weak and Electromagnetic Interactions

Abstract

It is suggested that the weak and electromagnetic interactions be incorporated into a theory based on an $\mathrm{SU}(3)\ensuremath{\bigotimes}\mathrm{SU}(3)$ gauge-invariant and parity-conserving Lagrangian, in which the lepton fields form a Konopinski-Mahmoud triplet ${\ensuremath{\mu}}^{+}$, $\ensuremath{\nu}$, ${e}^{\ensuremath{-}}$. 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 $\mathrm{SU}(3)\ensuremath{\bigotimes}\mathrm{SU}(3)$ down to $\mathrm{SU}(2)\ensuremath{\bigotimes}\mathrm{U}(1)$ is much stronger than the spontaneous breaking of $\mathrm{SU}(2)\ensuremath{\bigotimes}\mathrm{U}(1)$ down to electromagnetic gauge invariance. The resulting theory is for most purposes equivalent to the previous $\mathrm{SU}(2)\ensuremath{\bigotimes}\mathrm{U}(1)$ model, but with mixing angle now fixed at 30\ifmmode^\circ\else\textdegree\fi{}. 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 $\ensuremath{\alpha}{m}_{\ensuremath{\mu}}$.