Screening the Higgs portal

Light scalar fields that couple to matter through the Higgs portal mediate long-range fifth forces. We show how the mixing of a light scalar with the Higgs field can lead to this fifth force being screened around macroscopic objects. This behavior can only be seen by considering both scalar fields as dynamical, and is missed if the mixing between the Higgs field and the scalar field is not taken into account. We explain under which conditions the naive "integrating-out" procedure fails, i.e., when the mass matrix of the Higgs-scalars system has a nearly vanishing mass eigenvalue. The resulting flat direction in field space can be lifted at the quadratic order in the presence of matter and the resulting fifth force mediated by the Higgs portal can be screened either when the gravitating objects are large enough or their surface Newton potential exceeds a threshold. Finally we discuss the implications of these results for nearly massless relaxion models.