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.