An Accurate Empirical Determination of the Mass of the Electron from Properties of the W Boson Vector

An accurate and empirical relationship between the electron mass and the mass of the W boson vector is proposed. The electron mass, calculated in this way, differs from the experimental value by 25 ppm and can be improved up to about 7.3 ppm; the error arises from the uncertainty of the boson mass. By calculating the vacuum expectation value of the Wilson loop (rectangle ) for a gauge field, it becomes necessary to compare the Bohr energy of a suitably chosen particle-antiparticle pair with the time scale determined by the electron mass, possibly corrected for the value of the electron's gyromagnetic ratio. It is demonstrated that by appropriately choosing an off-shell pair, a Bohr energy can be determined that agrees with the mass value of the electron-positron pair. From these considerations, a dependence on the square of the fine-structure constant α, the mass of the W boson, and the cosine of an angle compatible with the Weinberg angle is deduced. Once appropriately validated, the theory allows for the deduction of the electron's coupling constant with the Higgs field and reduces the number of free parameters in the Standard Model.