Solution to the small-phase problem of supersymmetry

It is a well-known problem that in supersymmetric models there are new CP-violating phases which, if unsuppressed, would give a neutron electric dipole moment (EDM) ${10}^2$ to ${10}^3$ times the present experimental limit. Here we propose that these new phases are suppressed by CP invariance, which is broken spontaneously at a high scale and that this breaking shows up at low energies only through the phases of the gaugino masses. This can well fit both ε and ε’ of the neutral kaon system. The EDM of the neutron and the electron should be not much below present limits. A model incorporating these ideas in an economical way is presented.