Supersymmetric solution toCPproblems

Abstract

We analyze the minimal supersymmetric left-right model with nonrenormalizable interactions induced by higher scale physics and study its $\mathrm{CP}$-violating properties. We show that it (i) solves the strong $\mathrm{CP}$ problem, and (ii) predicts the neutron electric dipole moment well within experimental limits (thus solving the usual SUSY $\mathrm{CP}$ 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 $\mathrm{CP}$ 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 $M_R$, as long as the effective theory below $M_R$ has only two Higgs doublets that couple fully to fermions (i.e., the theory below $M_R$ is MSSM-like.) The potentially dangerous contributions from the $\mathrm{SU}{\mathrm{}\left(2\right)\mathrm{}}_L$ gaugino one-loop diagram as well as from some higher dimensional terms to $\overline{\Theta }$ below $M_R$ 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.