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We enumerate the set of simplified models which match onto the complete setof gauge invariant effective operators up to dimension six describinginteractions of a singlet-like Majorana fermion dark matter with the standardmodel. Tree level matching conditions for each case are worked out in the largemediator mass limit, defining a one to one correspondence between the effectiveoperator coefficients and the simplified model parameters for weaklyinteracting models. Utilizing such a mapping, we compute the dark matterannihilation rate in the early universe, as well as other low-energyobservables like nuclear recoil rates using the effective operators, while thesimplified models are used to compute the dark matter production rates at highenergy colliders like LEP, LHC and future lepton colliders. Combining allrelevant constraints with a profile likelihood analysis, we then discuss thecurrently allowed parameter regions and prospects for future searches in termsof the effective operator parameters, reducing the model dependence to aminimal level. In the parameter region where such a model-independent analysisis applicable, and leaving aside the special dark matter mass regions where theannihilation proceeds through an s-channel Z or Higgs boson pole, the currentconstraints allow effective operator suppression scales ($\Lambda$) of theorder of a few hundred GeV for dark matter masses $m_\chi >$ 20 GeV at $95\%$C.L., while the maximum allowed scale is around $3$ TeV for $m_\chi \sim\mathcal{O}(1\,{\rm TeV})$. An estimate of the future reach of ton-scale directdetection experiments and planned electron-positron colliders show that most ofthe remaining regions can be probed, apart from dark matter masses near half ofthe Z-boson mass (with $500\,{\rm GeV} < \Lambda < 2\,{\rm TeV} $) and thosebeyond the kinematic reach of the future lepton colliders.

Effective Theory of WIMP Dark Matter supplemented by Simplified Models: Singlet-like Majorana fermion case