  The recently proposed multi-phase criticality principle in Coleman-Weinberg
models can provide a new explanation for the hierarchy between the electroweak
and new physics scales. When applied to the Standard Model, a Higgs boson as
light as the pseudo-Goldstone boson of broken scale invariance occurs. The
suppressed mixing between the two light fields still carries information about
the large scale of symmetry breaking, albeit up to logarithmic corrections. In
this work we probe this scenario with the present LHC data and assess the
impact of future lepton and hadron colliders. Our results show that the
multi-phase criticality can easily explain the apparent absence of new physics
at the energy scales tested in current experiments.
