Solutions of the Strong CP Problem based on the spontaneous breaking of CP must feature a non-generic structure and simultaneously explain a coincidence between a priori unrelated CP-even and CP-odd mass scales. We show that these properties can emerge from gauge invariance and a CP-conserving, but otherwise generic, physics at the Planck scale. In our scenarios no fundamental scalar is introduced beyond the Standard Model Higgs doublet, and CP is broken at naturally small scales by a confining non-abelian dynamics. This approach is remarkably predictive: robustness against uncontrollable UV corrections to the QCD topological angle requires one or more families of vector-like quarks below a few 10’s of TeV, hence potentially accessible at colliders. Because CP violation is communicated to the SM at these super-soft scales, our solution of the Strong CP Problem is not spoiled by the presence of heavy new states motivated by other puzzles in physics beyond the Standard Model. In addition, these models generically predict a dark sector that may lead to interesting cosmological signatures.

基于 CP 自发断裂的强 CP 问题的解决方案必须具有非一般结构，并同时解释先验无关的 CP 偶数和 CP 奇数质量尺度之间的巧合。我们表明，这些属性可以从规范不变性和 CP 守恒中出现，但在普朗克尺度上是通用的物理。在我们的场景中，除了标准模型希格斯双峰之外没有引入任何基本标量，并且 CP 在自然小尺度上被限制性非阿贝尔动力学打破。这种方法具有显着的预测性：针对 QCD 拓扑角的不可控制的 UV 校正的鲁棒性需要一个或多个低于几十 TeV 的类矢量夸克，因此可能在对撞机处访问。因为 CP 违规是以这些超软尺度传达给 SM，我们对强 CP 问题的解决方案并没有被标准模型之外的物理学中的其他难题所激发的重新状态的存在所破坏。此外，这些模型通常会预测一个可能导致有趣的宇宙学特征的暗区。