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.Comment: 46 pages, 6 figures, v3: typos fixed, references added, version
matches the version published in JHE
