Unified gauge theories with right-handed currents and heavy fermions

Gauge models with heavy fermions and right-handed currents are discussed based on the gauge groups ${\mathrm{SU}\mathrm{}\left(2\right)\mathrm{}}_A\times \mathrm{U}\mathrm{}\left(1\right)\mathrm{}\times {\mathrm{SU}\mathrm{}\left(4\right)\mathrm{}}^{\prime },{\mathrm{SU}\mathrm{}\left(2\right)\mathrm{}}_A\times {\mathrm{SU}\mathrm{}\left(2\right)\mathrm{}}_B\times {\mathrm{SU}\mathrm{}\left(4\right)\mathrm{}}^{\prime }$, and SU(4) × SU${\mathrm{}\left(4\right)\mathrm{}}^{\prime }$ and are constructed so as to lead to the $\Delta I=\frac{1}{2}$ rule. SU(4) × SU${\mathrm{}\left(4\right)\mathrm{}}^{\prime }$ is advocated as the ultimate unifying gauge group of nature, and it is shown how at various stages of spontaneous breakdown both the ${\mathrm{SU}\mathrm{}\left(2\right)\mathrm{}}_A\times {\mathrm{SU}\mathrm{}\left(2\right)\mathrm{}}_B\times {\mathrm{SU}\mathrm{}\left(4\right)\mathrm{}}^{\prime }$ and ${\mathrm{SU}\mathrm{}\left(2\right)\mathrm{}}_A\times \mathrm{U}\mathrm{}\left(1\right)\mathrm{}\times {\mathrm{SU}\mathrm{}\left(4\right)\mathrm{}}^{\prime }$ groups manifest themselves. We also show that $\mathrm{CP}$ violation takes an interesting complexion in these models and leads to exactly the relations ${\eta }_{+-}\simeq {\eta }_{00}$ in $K_L\to 2\pi$ decays. Furthermore, we show that the magnitude of $\mathrm{CP}$ violation is related to gauge interactions that violate the heavy quark degeneracy.