  We study the direct-detection rate for axial-vectorial dark matter scattering
off nuclei in an $\mathrm{SU}(2)\times \mathrm{U}(1)$ invariant effective
theory and compare it against the LHC reach. Current constraints from direct
detection experiments are already bounding the mediator mass to be well into
the TeV range for WIMP-like scenarios. This motivates a consistent and
systematic exploration of the parameter space to map out possible regions where
the rates could be suppressed. We do indeed find such regions and proceed to
construct consistent UV models that generate the relevant effective theory. We
then discuss the corresponding constraints from both collider and
direct-detection experiments on the same parameter space. We find a benchmark
scenario, where even for future XENONnT experiment, LHC constraints will have a
greater sensitivity to the mediator mass.
