A Supersymmetric Solution to CP Problems

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We analyze the minimal supersymmetric left-right model with non-renormalizable interactions induced by higher scale physics and study its CP violating properties. We show that it: (i) solves the strong CP problem; (ii) predicts the neutron electric dipole moment well within experimental limits (thus solving the usual SUSY CP problem). In addition, it automatically conserves R-parity. The key points are that the parity symmetry forces the Yukawa couplings to be hermitean, while supersymmetry ensures that the scalar potential has a minimum with real higgs doublet vacuum expectation values. Gluino and B-L gaugino masses are automatically real. The observed CP violation in the kaon system comes, as in the Standard Model, from the Kobayashi-Maskawa-type phases. These solutions are valid for any value of the right-handed breaking scale Mᵣ, as long as the effective theory below Mᵣ has only two Higgs doublets that couple fully to fermions. (i.e. the theory below Mᵣ is MSSM-like.) The potentially dangerous SU(2)ₗ gaugino one-loop contributions to Θ below Mᵣ can be avoided if the left-right symmetry originates from a unified theory in which the SU(2)ₗ,ᵣ gaugino masses are real. As an example, we show how the left-right symmetry can be embedded in an SO(10) theory.