  We consider models where a hidden U(1)' interacts with the Standard Model via
kinetic mixing. We assume the dark matter is neutral under this U(1)', but
interacts with it via higher dimension operators. In particular, we consider a
hidden dipole operator for fermionic dark matter, and charge radius and
Rayleigh operators for scalar dark matter. These models naturally explain the
absence of direct detection signals, but allow for a thermal cosmology. LHC
searches for the Z' represent a powerful probe.
