$Z$ boson mediated dark matter beyond the effective theory

Direct detection bounds are beginning to constrain a very simple model of weakly interacting dark matter---a Majorana fermion with a coupling to the $Z$ boson. In a particularly straightforward gauge-invariant realization, this coupling is introduced via a higher-dimensional operator. While attractive in its simplicity, this model generically induces a large $\rho$ parameter. An ultraviolet completion that avoids an overly large contribution to $\rho$ is the singlet-doublet model. We revisit this model, focusing on the Higgs blind spot region of parameter space where spin-independent interactions are absent. This model successfully reproduces dark matter with direct detection mediated by the $Z$ boson, but whose cosmology may depend on additional couplings and states. Future direct detection experiments should effectively probe a significant portion of this parameter space, aside from a small coannihilating region. As such, $Z$-mediated thermal dark matter as realized in the singlet-doublet model represents an interesting target for future searches.