Supersymmetric solution to CP problems

We analyze the minimal supersymmetric left-right model with nonrenormalizable interactions induced by higher scale physics and study its CP-violating properties. We show that it (i) solves the strong CP problem, and (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 Hermitian, 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 contributions from the SU(2)L gaugino one-loop diagram as well as from some higher dimensional terms to bar Θ below MR can be avoided if the left-right symmetry originates from a unified theory such as SO(10) and we discuss how this embedding is achieved for the SO(10) case. copyright 1996 The American Physical Society