  Conventional approaches to describe dark matter phenomenology at collider and
(in)direct detection experiments in the form of dark matter effective field
theory or simplified models suffer in general from drawbacks regarding validity
at high energies and/or generality, limiting their applicability. In order to
avoid these shortcomings, we propose a hybrid framework in the form of an
effective theory, including, however, both the dark matter states and a
mediator connecting the former to the Standard Model fields. Since the
mediation can be realized through rather light new dynamical fields allowing
for non-negligible collider signals in missing energy searches, the framework
remains valid for the phenomenologically interesting parameter region, while
retaining correlations dictated by gauge symmetry. Moreover, a richer
new-physics sector can be consistently included via higher-dimensional
operators. Interestingly, for fermionic and scalar dark matter with a
(pseudo-)scalar mediator, the leading effects originate from dimension-five
operators, allowing to capture them with a rather small set of new couplings.
We finally examine the correlations between constraints from reproducing the
correct relic density, direct-detection experiments, and mono-jet and
Higgs+missing energy signatures at the LHC.
