  We study the on-shell version of the Higgs mechanism in effective theories
(EFTs) containing particles of different spins, focusing on contact terms as a
simple starting point. We derive the massive contact terms and their
coefficients from the massless amplitudes of the EFT above the symmetry
breaking scale, by covariantizing the massless contact terms under the massive
little group. In the little-group-covariant massive-spinor formalism, this
notationally amounts to bolding spinor labels. Mass-suppressed contributions to
the contact-term coefficients arise from higher-point contact terms with
additional soft Higgs legs. We apply this procedure to obtain massive
four-point amplitudes featuring scalars, spin 1/2 fermions and vectors, in the
standard-model EFT. The subleading helicity-flipped components of each massive
contact term, which are dictated by little-group covariance, are associated
with the residues of factorizable massless amplitudes. Extra "frozen" Higgses
emitted from each leg of a massless contact term supply the additional
light-like momentum component, needed to form a massive leg of the same
polarization. As another application, we derive various components of massive
three-point amplitudes from massless amplitudes with up to three additional
Higgses, in a standard-model-like toy model.
