Lawrence Berkeley National Laboratory

We propose theories of a complete mirror world with parity (P) solving the strong CP problem. P exchanges the entire Standard Model (SM) 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 $v_3 \ll v^{\prime}$, when heavy coloured 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 $\bar \theta_\text{QCD}$, starting at three-loop order. The symmetry breaking at $v_3$ can be made dynamical, without introducing an additional hierarchy problem.