EDM-free supersymmetric CP violation with non-universal soft terms

Non-universality in the soft breaking terms is a common feature in most superstring inspired SUSY models. This property is required to obtain sizeable CP violation effects from SUSY and, on the other hand, can be used to avoid the electric dipole moment (EDM) constraints. We take advantage of these qualities and explore a class of SUSY models based on type I string theory where scalar masses, gaugino masses and trilinear couplings are non-universal. In this framework, we show that, in the presence of large SUSY phases, the bounds on the electric dipole moments can be controlled without fine-tuning. At the same time, we find that these phases, free from EDM constraints, lead to large contributions to the observed CP phenomena in Kaon system and, in particular, to direct CP violation in e′/e.