We propose a simultaneous solution to the strong $\mathrm{CP}$ problem and the supersymmetry (SUSY) phase problem based on parity symmetry realized when the supersymmetric standard model is embedded into a left-right symmetric framework at a scale near $2\times {10}^{16}\hspace{0.5em}\mathrm{GeV},$ as suggested by neutrino masses and gauge coupling unification. In this class of models, owing to parity, SUSY contributions to the muon anomalous magnetic moment can be naturally large without conflicting with the electric dipole moments (EDM’s) of the electron and the neutron. The strong CP-violation parameter $\overline{\theta }$ is zero at the tree level, also due to parity $\mathrm{}\left(P\right),$ but is induced due to P-violating effects below the unification scale. We estimate the induced $\overline{\theta }$ to be $<~{10}^{-16},$ if we adopt a constrained supersymmetric spectrum with universal scalar masses. In the more general SUSY-breaking scenario, after imposing flavor changing constraints, we find $\overline{\theta }\sim {(10\mathrm{}}^{-8}-{10}^{-10}),$ which is compatible with, but not much below, the present limit on the neutron EDM. We also argue that potential nonperturbative corrections to $\overline{\theta }$ from quantum gravitational effects are not excessive in these models.

• Received 24 July 2001

DOI:https://doi.org/10.1103/PhysRevD.65.016005