Strong CP and Low-energy Supersymmetry

A spontaneously-broken CP provides an alternative to the KM mechanism for CP violation with the advantage that the strong CP problem is solved. We consider, for such a model with a new gauged U(1), the incorporation of low-energy supersymmetry and find the constraints on alignment and squark degeneracy. The conclusion is that although the $\bar{\theta}$ constraints are much less severe than in other generic schemes with supersymmetry breaking and spontaneous CP violation, one restriction remains stronger than needed in the MSSM for suppression of FCNC.