A 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 (SM) with its mirror copy. We derive bounds on the two new mass scales that arise: $v^{\mathrm{\prime }}$ 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 $v_3\ll v^{\mathrm{\prime }}$, 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.