Calculation of the electron mass in terms of measured quantities in a left-right—symmetric model

We describe a class of left-right-symmetric models in which the electron mass can be calculated in terms of the fine-structure constant, the muon mass, and the Weinberg angle. We obtain $\frac{m_e}{m_{\mu }}=\frac{N\alpha }{\pi {{sin}^2\theta }_W}$. $N$ is a pure number depending on the particular model. In our approach the electron derives its mass not from the muon directly (as in most models where $m_e$ is calculated as a radiative effect) but from a lepton of large mass. (The mass of this heavy lepton does not appear in the expression for $\frac{m_e}{m_{\mu }}$ and thus is not considered by present data to have a definite value.) We present an illustrative model in which, for values of ${sin\theta }_W$ consistent with neutrino data, the mass of the electron comes out too large by roughly a factor of 2.