Colorful Mirror Solution to the Strong CP Problem

We propose theories of a complete mirror world with parity (P) solving the strong CP problem. P exchanges the entire standard model with its mirror copy. We derive bounds on the two new mass scales that arise: v^{'} where parity and mirror electroweak symmetry are spontaneously broken, and v_{3} where the color groups break to the diagonal strong interactions. The strong CP problem is solved even if v_{3}≪v^{'}, when heavy colored states at the scale v_{3} may be accessible at LHC and future colliders. Furthermore, we argue that the breaking of P introduces negligible contributions to θ[over ¯]_{QCD}, starting at three-loop order. The symmetry breaking at v_{3} can be made dynamical, without introducing an additional hierarchy problem.