Class of gauge theories with superweak CP violation

A class of gauge theories is discussed in which the Δ S=0 and the Δ S=1 semileptonic decays are mediated by distinct intermediate bosons, whose mass ratio is related to the Cabibbo angle θ. Common features of the models are as follows: θ is well defined only as the result of spontaneous symmetry breaking; μ decay and the semileptonic Δ S=0, Δ S=1 decays are in the ratio 1:cos²θ:sin²θ only if CP is maximally violated in the lepton sector; a breakdown of μ e universality related to CP violation; a superweak impact of CP violation on K decays; the mediation through a neutral vector boson of nonleptonic decays which obey |Δ I|=1/2; and an amplitude ≪O(G) for ${\nu }_{\mu }e$ scattering. Two distinct types of theories are discussed in detail. (a) The gauge group O(4) reported before. Here the CP-violating parameter needs a renormalization. To O(G), ${\nu }_{\mu }$-nucleon reactions are possible only if a heavy lepton is produced. (b) O(4)×G, where left- [right-] handed fermions are in O(4) [G] but scalar with respect to G [O(4)]. Here the CP-violating parameter can be made finite if a constraint between electron and muon multiplets is satisfied. Further consequences for case (b) are: the ν̄ₑ-e and νₑ-e elastic cross sections are (1+sin2|θ|) times their respective V-A values, and ${\nu }_{\mu }$-nucleon reactions are possible with or without production of a heavy lepton. However, the final hadronic state is necessarily "charmed." The example G=U(1) is discussed in detail. The role of discrete symmetries is emphasized.