Sliding Naturalness: New Solution to the Strong-$CP$ and Electroweak-Hierarchy Problems

We present a novel framework to solve simultaneously the electroweak-hierarchy problem and the strong-$CP$ problem. A small but finite Higgs vacuum expectation value and a small $\theta$ angle are selected after the QCD phase transition, without relying on the Peccei-Quinn mechanism or other traditional solutions. We predict a distinctive pattern of correlated signals at hadronic EDM, fuzzy dark matter, and axion experiments.

Figure 1

Example potentials $V({\varphi }_{\pm })$ that select the weak scale. If $⟨h⟩\gtrsim v$ the local minimum of $V({\varphi }_{-})$ is destabilized (left panel), so that the field rolls down towards its deep global minimum (not shown in the plot) and the Universe rapidly crunches. Conversely, the local minimum of $V({\varphi }_{+})$ is generated only if $⟨h⟩\gtrsim v$ and $\theta \lesssim {\theta }_{\max }$.

Figure 2

Parameter space for which ${\varphi }_{+}$ constitutes the totality of DM of the Universe, as function of the ${\varphi }_{+}$ mass and the $\theta$ angle today. Bounds [26] and future prospects [38, 39, 40] from hadronic EDM searches are shown. New ideas involving molecular compounds could further improve the red dashed line [54, 55, 56, 57, 58]. We also plot constraints on fuzzy DM from Lyman-$\alpha$ forest [41, 42, 43, 44, 45, 46], measurements of the subhalo mass function [47] and the Eridanus II dwarf galaxy [48]. Tensions in the fit to other dwarf galaxies point to a similar constraint as Eridanus [49, 50]. We shade the area where multiple observations disfavor the corresponding DM mass hypotheses [51]. The dashed lines correspond to the potential sensitivity from future observations in 21 cm cosmology (HERA) [52] and by the Vera Rubin Observatory [53].