Some Physical Constraints on Gauge Models of Weak Interactions

Abstract

Recently proposed models of weak interactions based on spontaneously broken gauge symmetry contain additional interactions arising from exchange of the scalar Higgs particles and/or neutral vector bosons. Further, higher-order corrections are finite, and therefore should be taken seriously. We investigate what constraints on parameters of models are imposed by consideration of Higgs-particle exchange and of higher-order effects in $K$ decays. To bring out the main points we shall focus mainly on the SO(3) models of Georgi and Glashow. In the 5-quark version of the Georgi-Glashow model, the Higgs scalar couples strongly to ($\overline{\ensuremath{\lambda}}\mathfrak{N}$), and to ($\overline{e}e$), so that processes such as ${K}^{+}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{+}+e+\overline{e}$ decay can occur already in lowest order. Thus a stringent lower bound (${m}_{\ensuremath{\varphi}}\ensuremath{\ge}10$ GeV) is imposed on the mass of the scalar particle. For the process ${K}_{L}\ensuremath{\rightarrow}\ensuremath{\mu}+\overline{\ensuremath{\mu}}$, which occurs in second order, we find the amplitude to be of order ${G}_{F}\ensuremath{\alpha}{sin\ensuremath{\theta}}_{C}$ and independent of the value of ${M}_{W}$. This is clearly in contradiction with experiment and rules out the 5-quark version. We analyze also an 8-quark version of the model, in which extra quarks are used to suppress the amplitudes for ${K}_{L}\ensuremath{\rightarrow}\ensuremath{\mu}+\overline{\ensuremath{\mu}}$ and ${K}^{0}\ensuremath{\leftrightarrow}{\overline{K}}^{0}$: The amplitudes are of order ${G}_{F}\ensuremath{\alpha}(\frac{\ensuremath{\Delta}{m}^{2}}{{{M}_{W}}^{2}})$, where $\ensuremath{\Delta}{m}^{2}$ is the difference between the squared masses of "charmed" and "uncharmed" quarks. It is also shown that in this version single-scalar-particle exchange is altogether forbidden and the constraint on ${m}_{\ensuremath{\varphi}}$ is accordingly eliminated. Constraints similar to those found for the Georgi-Glashow models also apply to other spontaneously broken gauge models of weak interactions.