P/CP Conserving CP/P Violation Solves Strong CP Problem

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 VEVs conserve CP. The quark mass matrix is Hermitian at the tree-level and strong CP phase is generated only in loops where CP and P violating sectors interact. A full vector-like quark family with parity symmetric mass-terms that violate CP softly is predicted. Since no Higgs VEVs (other than the SU(2)_L breaking weak-scale VEV) contribute to the masses of the new quarks, they can be naturally light, independent of parity breaking and other high energy scales.