CP alone allows the QCD theta angle to be 0 or pi; choosing a gauge group with enlarged theta periodicity forces CP to select 0, eliminating the excluded pi value.
A Colorful Mirror Solution to the Strong CP Problem
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abstract
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.
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When CP requires $\bar\theta=0$, not $\bar\theta=\pi$
CP alone allows the QCD theta angle to be 0 or pi; choosing a gauge group with enlarged theta periodicity forces CP to select 0, eliminating the excluded pi value.