Abstract
We find a solution to the strong $CP$ problem that may be testable at the LHC and future colliders. In this solution $CP$ is broken by parity conserving terms, while parity breaking vacuum expectation values conserve $CP$. The quark mass matrix is Hermitian at the tree level, and the strong $CP$ phase is generated only in loops where $CP$ and $P$ violating sectors interact. A full vectorlike quark family with parity symmetric mass terms that violate $CP$ softly is predicted. Since no Higgs vacuum expectation values [other than the $SU(2{)}_{L}$ breaking weak-scale vacuum expectation value] contribute to the masses of the new quarks, they can be naturally light, independent of parity breaking and other high energy scales.
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