Models for weak currents with Han-Nambu three-triplets

Abstract

A mechanism introduced by Stech to suppress $\ensuremath{\Delta}S=1$ neutral currents is adapted to the Han-Nambu model. Consequences of different schemes arising from the freedom in baryon number assignment are investigated. Though first order processes are eliminated in all of these models, only two of them give sufficiently small second-order rates for ${K}_{L}^{0}\ensuremath{\rightarrow}{\ensuremath{\mu}}^{+}{\ensuremath{\mu}}^{\ensuremath{-}}$. In these cases, it is possible to obtain $sin{\ensuremath{\theta}}_{C}=\frac{1}{3\sqrt{2}}\ensuremath{\cong}0.235$ in a rather natural manner. These two models and one of the others can be extended to SU(2)\ensuremath{\bigotimes}U(1) gauge theories of weak and electromagnetic interactions which are anomaly-free in the quark sector and thus require heavy leptons to cancel leptonic anomalies. The rates for neutral events in inclusive neutrino-nucleon reactions predicted by these gauge theories are compatible with experimental results when ${sin}^{2}{\ensuremath{\theta}}_{W}\ensuremath{\cong}\frac{1}{3}$. The models giving acceptable ${K}_{L}^{0}\ensuremath{\rightarrow}{\ensuremath{\mu}}^{+}{\ensuremath{\mu}}^{\ensuremath{-}}$ rates do not predict any enhancement of neutrino-nucleon total cross sections associated with the production of SU(3)\ensuremath{''} nonsinglet states. None of the above schemes helps explain the $\ensuremath{\Delta}T=\frac{1}{2}$ rule.