# Fifth forces and discrete symmetry breaking

## TL;DR

This paper explores how light scalar fields coupled to the Higgs can produce fifth forces, linking modifications of gravity to the Higgs sector and dark matter, with implications for galaxy dynamics.

## Contribution

It reveals that Yukawa-like fifth forces are tied to Higgs-scalar mixing and symmetry breaking, connecting scalar-tensor theories to Higgs-portal models and dark matter phenomenology.

## Key findings

- Fifth forces arise from scalar-Higgs mixing.
- Non-observation constrains Higgs sector structure.
- Scalar-tensor theories can be equivalent to Higgs-portal models.

## Abstract

Modifications of general relativity often involve coupling additional scalar fields to the Ricci scalar, leading to scalar-tensor theories of Brans-Dicke type. If the additional scalar fields are light, they can give rise to long-range fifth forces, which are subject to stringent constraints from local tests of gravity. In this talk, we show that Yukawa-like fifth forces only arise for the Standard Model (SM) due to a mass mixing of the additional scalar with the Higgs field, and we emphasise the pivotal role played by discrete and continuous symmetry breaking. Quite remarkably, if one assumes that sufficiently light, non-minimally coupled scalar fields exist in nature, the non-observation of fifth forces has the potential to tell us about the structure of the SM Higgs sector and the origin of its symmetry breaking. Moreover, with these observations, we argue that certain classes of scalar-tensor theories are, up to and including their dimension-four operators, equivalent to Higgs-portal theories. In this way, ultra-light dark matter models may also exhibit fifth-force phenomenology, and we consider the impact on the dynamics of disk galaxies as an example.