Solving the Supersymmetric CP Problem with Abelian Horizontal Symmetries

Abstract

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 $μ$-problem; and (iv) suppress supersymmetric contributions to CP violating observables to an acceptable level. The CKM phase is $Ø(1)$ and responsible, through Standard Model box diagrams, to $ε_K$. The supersymmetric CP violating phases are suppressed, $ϕ_A\simλ^6$ and $ϕ_B\simλ^{8}$ ($λ\sim0.2$), leading to an electric dipole moment of the neutron that is about 2--3 orders of magnitude below the experimental bound.