Solution to the strongCPproblem without an axion
We present a solution to the strong $\mathrm{CP}$ problem using softly broken parity invariance in the context of left-right-symmetric gauge models with a "seesaw" mechanism for quark masses. A distinguishing feature of the model is that the first nonvanishing contribution to $\overline{\ensuremath{\theta}}$ arises only at the two-loop level, whereas the electric dipole moment of the neutron ${d}_{n}^{e}$ is generated at the one-loop level via weak $\mathrm{CP}$ violation. For the ${W}_{R}$ mass at the TeV scale, we estimate ${d}_{e}^{n}\ensuremath{\approx}{10}^{\ensuremath{-}25}\ensuremath{-}{10}^{\ensuremath{-}26}$ ecm and $\overline{\ensuremath{\theta}}\ensuremath{\le}{10}^{\ensuremath{-}12}$.