  Heavy WIMP (weakly-interacting-massive-particle) effective field theory is
used to compute the WIMP-nucleon scattering rate for general heavy electroweak
multiplets through order $m_W/M$, where $m_W$ and $M$ denote the electroweak
and WIMP mass scales. The lightest neutral component of such an electroweak
multiplet is a candidate dark matter particle, either elementary or composite.
Existing computations for certain representations of electroweak
$\mathrm{SU(2)}_W\times \mathrm{U(1)}_Y$ reveal a cancellation of amplitudes
from different effective operators at leading and subleading orders in $1/M$,
yielding small cross sections that are below current dark matter direct
detection experimental sensitivities. We extend those computations and consider
all low-spin (spin-0, spin-1/2, spin-1, spin-3/2) heavy electroweak multiplets
with arbitrary $\mathrm{SU(2)}_W\times \mathrm{U(1)}_Y$ representations and
provide benchmark cross section results for dark matter direct detection
experiments. For most self-conjugate TeV WIMPs with isospin $\le 3$, the cross
sections are below current experimental limits but within reach of
next-generation experiments. An exception is the case of pure electroweak
doublet, where WIMPs are hidden below the neutrino floor.
