Electromagnetic Violation of Conservation of Vector Current

The electromagnetic violation of vector current conservation is considered and the strong interaction renormalization of the $\beta$-decay coupling constant $G_{\mathrm{V}}$ in the presence of electromagnetism is estimated. It is shown that the existing discrepancy between the $G_{\mathrm{V}}$ and the $\mu$-decay coupling constant $G_{\mu }$ may be due to such a renormalization. In this demonstration, use is made of a hypothetical scalar particle with isotopic spin unity. This particle has been used as an auxiliary means and the final results do not depend on the parameters of such a particle. It is shown that this particle has interactions with other particles only if the electromagnetic mass splitting of the isotopic multiplets is not neglected. Other properties of this particle are discussed.