Fifth forces, Higgs portals and broken scale invariance
  We study the relationship between the strength of fifth forces and the origin
of scale breaking in the Standard Model (SM) of particle physics. We start with
a light scalar field that is conformally coupled to a toy SM matter sector
through a Weyl rescaling of the metric. After appropriately normalizing the
fields, the conformally coupled scalar only interacts directly with the
would-be Higgs field through kinetic-mixing and Higgs-portal terms. Thus, for
the first time, we describe the equivalence of conformally coupled
scalar-tensor modifications of gravity and Higgs-portal theories, and we find
that the usual tree-level fifth forces only emerge if there is mass mixing
between the conformally coupled scalar and the Higgs field. The strength of the
fifth force, mediated by the light scalar, then depends on whether the mass of
the Higgs arises from an explicit symmetry-breaking term or a spontaneous
mechanism of scale breaking. Solar System tests of gravity and the
non-observation of fifth forces therefore have the potential to provide
information about the structure of the Higgs sector and the origin of its
symmetry breaking, setting an upper bound on the magnitude of any explicit
scale-breaking terms. These results demonstrate the phenomenological importance
(both for cosmology and high-energy physics) of considering how scalar-tensor
modifications of gravity are embedded within extensions of the SM.
