  We perform a detailed study of an effective field theory which includes the
Standard Model particle content extended by a pair of Weyl fermionic
SU(2)-doublets with opposite hypercharges. A discrete symmetry guarantees that
a linear combination of the doublet components is stable and can act as a
candidate particle for Dark Matter. The dark sector fermions interact with the
Higgs and gauge bosons through renormalizable $d=4$ operators, and
non-renormalizable $d=5$ operators that appear after integrating out extra
degrees of freedom above the TeV scale. We study collider, cosmological and
astrophysical probes for this effective theory of Dark Matter. We find that a
WIMP with a mass nearby to the electroweak scale, and thus observable at LHC,
is consistent with collider and astrophysical data only when fairly large
magnetic dipole moment transition operators with the gauge bosons exist,
together with moderate Yukawa interactions.
