  Effective contact operators provide the simplest parameterization of dark
matter searches at colliders. However, light mediator can significantly change
the sensitivity and search strategies. Considering simple models of mediators
is an important next-step for collider searches. In this paper, we consider the
case of a $t$-channel mediator. Its presence opens up new contributions to the
monojet$+\displaystyle{\not{E}}_T$ searches and can change the reach
significantly. We also study the complementarity between searches for processes
of monojet$+\displaystyle{\not{E}}_T$ and direct pair production of the
mediators. Mediator pair production also gives important contribution to a
CMS-like monojet$+\displaystyle{\not{E}}_T$ search where a second hard jet is
allowed.There is a large region of parameter space in which the
monojet$+\displaystyle{\not{E}}_T$ search provides the stronger limit. Assuming
the relic abundance of the dark matter is thermally produced within the
framework of this model, we find that in the Dirac fermion dark matter case,
there is no region in the parameter space that satisfies the combined
constraint of monojet$+\displaystyle{\not{E}}_T$ search and direct detection;
whereas in the Majorana fermion dark matter case, the mass of dark matter must
be larger than about 100 GeV. If the relic abundance requirement is not
assumed, the discovery of the $t$-channel mediator predicts additional new
physics.
