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CP violation in supersymmetric theories

We review the present status of CP violating problem in supersymmetric extensions of the standard model. We analyze the constraints imposed by the experimental limits of the electron, neutron, and mercury electric dipole moments on the supersymmetric CP phases and show that only the scenarios with flavour-off- diagonal CP violation remain attractive. These scenarios require hermitian Yukawa matrices which naturally arise in models with left-right symmetry or a SU(3) flavour symmetry. In this case, epsilon_K and epsilon'/epsilon can be saturated by a small non-universality of the soft scalar masses through the gluino and chargino contributions respectively. The model also predicts a strong correlation between A_{CP}(b-> s gamma) and the neutron electric dipole moment. In this framework, the standard model gives a the leading contribution to the CP asymmetry in B ->psi K_S decay, while the dominant chargino contribution to this asymmetry is < 0.2. Thus, no constraint is set on the non-universality of this model by the recent BaBar and Belle measureets.