Abstract
We discuss simple extensions of the Standard Model featuring a (fermionic) stable DM candidate interacting with SM fermions through a mediator. These kind of models offer a wide phenomenology but result, at the same time, particularly manageable, given the limited number of free-parameters, and offer a broad LHC phenomenology. We will discuss the impact Direct and Indirect Dark Matter searches, assuming the latter to be thermal WIMPs. We will show in particular that the combinations of the limits on the DM Spin Independent and Spin Dependent scattering cross-section on nuclei already exclude large portions of the parameter space favored by DM relic density, in particular if, in addition, a DM Indirect signal, like the Galactic Center gamma-ray excess is required.
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