  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 behaviour 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.

High Energy Physics - Phenomenology;Cosmology and Nongalactic Astrophysics;High Energy Physics - Theory