Simplified DM models with the full SM gauge symmetry : the case of $t$-channel colored scalar mediators

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.