Solving the supersymmetric CP problem with Abelian horizontal symmetries

Models that combine Abelian horizontal symmetries and spontaneous CP violation can (i) explain the smallness and hierarchy in quark parameters; (ii) satisfactorily suppress supersymmetric contributions to flavor changing neutral current processes; (iii) solve the mu-problem; and (iv) suppress supersymmetric contributions to CP violating observables to an acceptable level. The CKM phase is Omicron(1) and responsible, through Standard Model box diagrams, to epsilon(K). The supersymmetric CP violating phases are suppressed, phi(A)