Weak-Interaction Model with Finite Self-Masses of Leptons

Abstract

We propose a model of the weak interactions for leptons, including scalar intermediate bosons ${C}^{\ifmmode\pm\else\textpm\fi{}}$ with a negative metric in addition to the usual weak vector bosons ${B}^{\ifmmode\pm\else\textpm\fi{}}$. With this modification, problems of divergence and high-energy behavior are greatly reduced. If the logarithmic weak and electromagnetic self-mass divergences are assumed to cancel each other, the coupling constant $g$ and the mass ${m}_{B}$$(={m}_{C})$ of the weak boson are predicted to be ${g}^{2}=\frac{3}{2}{e}^{2}$ and ${m}_{B}=137.7{m}_{p}(\ensuremath{\simeq}\frac{{m}_{p}}{\ensuremath{\alpha}})$ (where ${m}_{p}$ is the proton mass), respectively. The finite self-masses are $\ensuremath{\delta}{m}_{l}\ensuremath{\simeq}(\frac{3{e}^{2}}{16{\ensuremath{\pi}}^{2}}){m}_{l}$ $\mathrm{ln}{(\frac{{m}_{B}}{{m}_{l}})}^{2}$ ($\ensuremath{\simeq}0.044{m}_{e}$ for an electron). It is shown that the renormalization of both the electromagnetic and weak interactions can be consistently accomplished in spite of the existence of the parity-violating interaction. The contributions of the weak interaction to the anomalous magnetic moments of leptons are calculated to be $\frac{1}{2}({g}_{l}\ensuremath{-}2)=\ensuremath{-}\frac{G{{m}_{l}}^{2}}{12\sqrt{2}{\ensuremath{\pi}}^{2}}$ (\ensuremath{\simeq}-7.7 \ifmmode\times\else\texttimes\fi{} ${10}^{\ensuremath{-}10}$ for $\ensuremath{\mu}$). Various weak reactions of leptons are discussed. For example, $\ensuremath{\sigma}({\ensuremath{\nu}}_{\ensuremath{\mu}}+e\ensuremath{\rightarrow}\ensuremath{\mu}+{\ensuremath{\nu}}_{e})$ approaches a constant value $\frac{{G}^{2}{{m}_{B}}^{2}}{\ensuremath{\pi}}\ensuremath{\simeq}2.8\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}34}$ ${\mathrm{cm}}^{2}$ at high energies.