SpontaneousCPviolation in supersymmetric theories

We study the minimal version of the supersymmetric standard model with spontaneous $\mathrm{CP}$ breaking. In this model, the Kobayashi-Maskawa 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 $\varepsilon$, $\frac{{\varepsilon }^{\prime }}{\varepsilon }$, and the neutron electric dipole moment (NEDM) in agreement with the experimental data. We show that the $\mathrm{CP}$-violating phases must be of order ${10}^{-2\mathrm{}}$ and the NEDM lies near its present experimental limit.