Effective theory of WIMP dark matter supplemented by simplified models: Singlet-like Majorana fermion case

Abstract

We enumerate the set of simplified models which match onto the complete set of gauge invariant effective operators up to dimension six describing interactions of a singlet-like Majorana fermion dark matter with the standard model. Tree level matching conditions for each case are worked out in the large mediator mass limit, defining a one to one correspondence between the effective operator coefficients and the simplified model parameters for weakly interacting models. Utilizing such a mapping, we compute the dark matter annihilation rate in the early universe, as well as other low-energy observables like nuclear recoil rates using the effective operators, while the simplified models are used to compute the dark matter production rates at high energy colliders like LEP, LHC and future lepton colliders. Combining all relevant constraints with a profile likelihood analysis, we then discuss the currently allowed parameter regions and prospects for future searches in terms of the effective operator parameters, reducing the model dependence to a minimal level. In the parameter region where such a model-independent analysis is applicable, and leaving aside the special dark matter mass regions where the annihilation proceeds through an s-channel Z or Higgs boson pole, the current constraints allow effective operator suppression scales ($\Lambda$) of the order 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 direct detection experiments and planned electron-positron colliders show that most of the remaining regions can be probed, apart from dark matter masses near half of the Z-boson mass (with $500\,{\rm GeV} < \Lambda < 2\,{\rm TeV} $) and those beyond the kinematic reach of the future lepton colliders.