Sliding Naturalness

Abstract: 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.