Calculating the electron mass in terms of measured quantities

We construct a class of 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 $\frac{m_e}{m_{\mu }}=N\left(\frac{\alpha }{\pi {{sin}^2\theta }_W}\right)$ where $N$ is a pure number of order 1 which depends on the specific model. (There are corrections to this formula which depend on parameters of the model, but which can be made arbitrarily small by arranging certain exotic gauge bosons to be heavy.) We show that within this class of models it is possible to obtain agreement with neutral-current data and the experimental value of $\frac{m_e}{m_{\mu }}$.