Self-consistent Dark Matter Simplified Models with an s-channel scalar mediator

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 process 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.