A comprehensive analysis of cosmological and collider constraints is presented for three simplified models characterised by a dark matter candidate (real scalar, Majorana fermion and real vector) and a coloured mediator (fermion, scalar and fermion respectively) interacting with the right-handed up quark of the Standard Model. Constraints from dark matter direct and indirect detection and relic density are combined with bounds originating from the re-interpretation of a full LHC run 2 ATLAS search targeting final states with multiple jets and missing transverse energy. Projections for the high-luminosity phase of the LHC are also provided to assess future exclusion and discovery reaches, which show that analogous future search strategies will not allow for a significant improvement compared with the present status. From the cosmological point of view, we demonstrate that thermal dark matter is largely probed (and disfavoured) by constraints from current direct and indirect detection experiments. These bounds and their future projections have moreover the potential of probing the whole parameter space when combined with the expectation of the high-luminosity phase of the LHC.

8 pages, 3 figures, version accepted by PLB