Phenomenology of relaxion-Higgs mixing

We show that the relaxion generically stops its rolling at a point that breaks CP leading to relaxion-Higgs mixing. This opens the door to a variety of observational probes since the possible relaxion mass spans a broad range from sub-eV to the GeV scale. We derive constraints from current experiments (fifth force, astrophysical and cosmological probes, beam dump, flavour, LEP and LHC) and present projections from future experiments such as NA62, SHiP and PIXIE. We find that a large region of the parameter space is already under the experimental scrutiny. All the experimental constraints we derive are equally applicable for general Higgs portal models. In addition, we show that simple multiaxion (clockwork) UV completions suffer from a mild fine tuning problem, which increases with the number of sites. These results favour a cut-off scale lower than the existing theoretical bounds.