Dark Matter Direct Detection in $t$-channel mediator models

We perform a comprehensive study of the Direct Detection phenomenology of singlet Dark Matter $t$-channel portal models. For that purpose, we present a complete one-loop matching onto a Heavy Dark-Matter Effective Field Theory, leading to a complete computation of the loop induced direct detection cross-section for both scalar and fermionic Dark Matter candidates. The results are compared with current and future bounds from Direct Detection experiments, as well as with the requirement of the correct Dark Matter relic density.