SUPERSYMMETRY AND THE NELSON-BARR MECHANISM

One possible solution to the strong CP problem is that CP is an exact symmetry, spontaneously broken at some scale. Some years ago, Nelson a nd Barr suggested a mechanism for obtaining theta = 0 at the tree leve l in this framework and showed that radiative corrections were small i n some nonsupersymmetric models. Further investigations suggested that the same could be true in supersymmetric theories. In this paper we s how that such solutions assume extraordinarily high degrees of degener acy among squark masses and among other supersymmetry-breaking paramet ers. We argue, using naturalness as well as expectations from string t heory, that this is not very plausible.