  The general strategy for dark matter (DM) searches at colliders currently
relies on simplified models. In this paper, we propose a new $t$-channel
UV-complete simplified model that improves the existing simplified DM models in
two important respects: (i) we impose the full SM gauge symmetry including the
fact that the left-handed and the right-handed fermions have two independent
mediators with two independent couplings, and (ii) we include the
renormalization group evolution when we derive the effective Lagrangian for
DM-nucleon scattering from the underlying UV complete models by integrating out
the $t$-channel mediators. The first improvement will introduce a few more new
parameters compared with the existing simplified DM models. In this study we
look at the effect this broader set of free parameters has on direct detection
and the mono-$X$ + MET ($X$=jet,$W,Z$) signatures at 13 TeV LHC while
maintaining gauge invariance of the simplified model under the full SM gauge
group. We find that the direct detection constraints require DM masses less
than 10 GeV in order to produce phenomenologically interesting collider
signatures. Additionally, for a fixed mono-W cross section it is possible to
see very large differences in the mono-jet cross section when the usual
simplified model assumptions are loosened and isospin violation between RH and
LH DM-SM quark couplings are allowed.
