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.
We analyze the Nelson-Barr approach to the Strong CP Problem. We derive the necessary conditions in order to simultaneously reproduce the CKM phase and the quark masses. Then we quantify the irreducible contributions to the QCD topological angle, namely the corrections arising from loops of the colored fermion mediators that characterize these models. Corrections analytic in the couplings first arise at 3-loop order and are safely below current bounds; non-analytic effects are 2-loop order and decouple as the mediators exceed a few TeV. We discuss collider, electroweak, and flavor bounds and argue that most of the parameter space above the TeV scale is still allowed in models with down-type mediators, whereas other scenarios are more severely constrained. With two or more families of mediators the dominant experimental bound is due to the neutron electric dipole moment.
We present a model that solves the strong CP problem via an axion parametrically heavier than the standard one. Within this picture the Standard Model quarks are embedded into a larger non-abelian Grand Color group that at high scales splits into ordinary QCD and an additional confining dynamics under which exotic chiral fermions are charged. Crucially, the vacuum expectation value of the axion is automatically relaxed to zero because the only renormalizable source of explicit CP violation, beyond those encoded in the topological angles, is contained in the Standard Model Yukawa couplings, and is therefore very suppressed. The Grand Color axion potential is controlled by the scale of the new confining group and is much larger than the QCD contribution, such that its dynamics is less exposed to the so-called “axion quality problem”. Potentially observable corrections to the effective topological angle can also arise, in our model as well as in a large class of heavy axion scenarios, from non-renormalizable Peccei-Quinn-conserving interactions, which introduce a new “heavy axion quality problem”. Our model has a very minimal field content, it relies entirely on gauge invariance and does not require the introduction of additional symmetries beyond the usual one postulated by Peccei and Quinn. The phenomenology is very rich and can be tested at colliders as well as via cosmological observations. A particularly interesting portion of parameter space predicts a visible Grand Color axion of mass above the GeV and decay constant larger than a few TeV.
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