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Abstract. We examine Simplified Models in which fermionic DM interacts with Standard Model (SM) fermions via the exchange of an s-channel scalar mediator. The single-mediator version of this model is not gauge invariant, and instead we must consider models with two scalar mediators which mix and interfere. The minimal gauge invariant scenario involves the mixing of a new singlet scalar with the Standard Model Higgs boson, and is tightly constrained. We construct two Higgs doublet model (2HDM) extensions of this scenario, where the singlet mixes with the 2nd Higgs doublet. Compared with the one doublet model, this provides greater freedom for the masses and mixing angle of the scalar mediators, and their coupling to SM fermions. We outline constraints on these models, and discuss Yukawa structures that allow enhanced couplings, yet keep potentially dangerous flavour violating processes under control. We examine the direct detection phenomenology of these models, accounting for interference of the scalar mediators, and interference of different quarks in the nucleus. Regions of parameter space consistent with direct detection measurements are determined.

We consider loop level contributions to dark matter scattering off nucleons in cases where the spin independent scattering cross section is absent or suppressed at tree level. In the case of a pseudoscalar interaction, for which the tree level cross section is both spin-dependent and suppressed by 4 powers of the exchanged momentum, we show that loop diagrams give rise to a nonzero spin independent cross section. Importantly, if the pseudoscalar interaction is formulated using a gauge invariant framework, loop effects generate an effective χχh vertex and result in a scattering cross section that is within reach of current or forthcoming experiments. We also consider the case of inelastic dark matter, for which the tree-level direct detection cross section is negligible when the inelastic χ 1 N → χ 2 N process is kinematically suppressed. In this case, loop diagrams generate an interaction with both initial and final χ 1 states and hence permit measurable, spin independent, χ 1 N → χ 1 N elastic scattering. As such, we are able to probe parameter space that was previously considered inaccessible to direct detection.