Soft superweak CP violation and the strong CP puzzle

We discuss a class of models in which CP is violated softly in a heavy sector adjoined to the standard model. Heavy-sector loops produce the observed CP violation in kaon physics, yielding a tiny and probably undetectable value for ϵ′. All other CP-violating parameters in the effective low-energy standard model, including the area of the unitarity triangle and θ, are finite, calculable and can be made very small. The leading contribution to θ comes from a four-loop graph. These models offer a natural realization of superweak CP violation and can resolve the strong CP puzzle. In one realization of this idea, CP is violated in the mass matrix of heavy majorana neutrinos.