Aspects of soft and spontaneous CP violation - art. no. 036004.

We study four different models for CP violation: the standard Kobayashi-Mas kawa (KM) model, the aspen model of spontaneous breaking, and two models of soft breaking. In all except the standard model, the strong CP problem is addressed and solved. Testable predictions for the area of the unitarity tr iangle and for (epsilon'/epsilon)(K) are emphasized. The issue of CP violat ion may well become the first place where the standard model of particle th eory is shown definitively to be deficient. There are two reasons for expec ting this to happen: (1) the strong CP problem is still not understood in t he unadorned standard model and (2) the KM mechanism, although unquestionab ly present may not provide the full explanation of epsilon(K) and (epsilon' /epsilon)(K). [S0556-2821(99)04003-5].