SU(4) × U(1) gauge theory. II.CPnonconservation

We exploit the higher symmetry inherent in an SU(4) × U(1) gauge theory to construct a spontaneously broken theory of $\mathrm{CP}$ nonconservation. Higgs multiplets in the adjoint representation of SU(4) contain both even and odd $\mathrm{CP}$ fields; thus, requiring the simultaneous nonvanishing of the vacuum expectation values of these fields leads to $\mathrm{CP}$ noninvariance of the vacuum. We find that all the $\mathrm{CP}$-nonconserving effects are mediated in our theory by the superheavy gauge bosons of the broken SU(4) × U(1) symmetry. In fact, the very existence of $\mathrm{CP}$ violation sets an upper limit on the masses of these bosons. In our model the dominant $\mathrm{CP}$ effect lies in the neutral kaon system and is found to arise through a direct ($\Delta S=2\mathrm{}$) $K_1-K_2$ transition. The model has all the features of a superweak theory, with a neutron electric dipole moment substantially smaller than ${10}^{-24\mathrm{}}e$ cm.