$Z$ 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.

Figure 1

Constraints on $g_A\equiv c{v}^2/(2{\mathrm{\Lambda }}^2)$ as a function of $m_{\chi }$ for $Z$-mediated DM. The black solid line indicates where the thermal relic abundance matches the observed abundance [5]. The orange dotted (dot-dashed) line corresponds to omitting higher-dimensional couplings to $Zhh$ (and $Zh$), in violation of gauge invariance. The shaded (dashed) blue region is excluded by PandaX (LZ), with bounds obtained as described in the text. The purple shaded region is excluded by IceCube (IC). Invisible $Z$ decay limits (${\mathrm{\Gamma }}_Z$) are shown in gray. Pink shaded regions indicate where $T<-0.09$ (upper, darker) and $T<-0.01$ (lower, lighter), corresponding to $2\sigma$ excluded regions depending on if $S$ is nonzero or zero, respectively. Green shaded regions indicate where the EFT is precarious, taking $c_{\max }=4\pi$ (upper, darker) or 1 (lower, lighter).

Figure 2

Constraints on the singlet-doublet model at the Higgs blind spot. The blind spot condition fixes $y^c$ via (10), while $M_D$ (contours in blue) is set by demanding that the thermal relic abundance matches the observed DM abundance. Shown in red are current bounds from PandaX (solid curves, shaded region) and prospective bounds from Xenon1T (thick dashed curve) and LZ (thin dashed curve) on ${\sigma }_{\mathrm{SD}}$. In the shaded gray region, the DM-$Z$ is at least 95% of that in the $Z$-mediated model of the previous section.

Figure 3

Similar to Fig. 2, but with $y^c$ deviating from the Higgs blind spot by ${\delta }_{y^c}=-0.3$; see Eq. (13). Mirroring the previous figure, contours of $M_D$ are shown in blue. Current and projected limits on ${\sigma }_{\mathrm{SD}}$ (${\sigma }_{\mathrm{SI}}$) are shown in red (orange).