Spontaneous CP violation in Supersymmetric theories

We study the minimal version of the supersymmetric standard model with spontaneous CP breaking. In this model, the KM matrix is real and contributions to $\varepsilon$ arise from box diagrams involving squarks. We analyze the region of the parameter space which corresponds to values for $\varepsilon$, $\varepsilon^\prime/\varepsilon$ and the neutron electric dipole moment (NEDM) in agreement with the experimental data. We show that the CP violating phases must be of $\calo (10^{-2})$ and the NEDM lies near its present experimental limit.