# Vector Mediator coupling only to 1st generation quarks, Majorana Dark Matter¶

This is the model discussed in the ‘white paper’ [116]. Some later results are also discussed in [110]. It is a simplified model with a dark matter Majorana fermion, $$\psi$$, which interacts with the SM through a new vector particle, $$Z^\prime$$. The couplings of the mediator $$Z^\prime$$ to the dark matter $$\psi$$ and to the SM are specified as

\begin{aligned} \label{eq:vector_mediator} {\cal L} \supset {{g_{\rm DM}}}\,\overline{\psi} \gamma_{\mu}\gamma_5 \psi\,Z'^{\mu} + {{g_{q}}}\sum_{q} \bar q \gamma_{\mu} q \,Z'^{\mu} \,,\end{aligned}

where the sum in the second term includes only the first generation SM quarks, $$q \in \{u,d\}$$. The model has only four free parameters - two couplings and two masses: $$g_{\rm DM}$$, $$g_{q}$$, $$M_\psi \equiv {{M_{\rm DM}}}$$, and $$M_{Z^{\prime}}$$. The width of the mediator, $$\Gamma_{Z'}$$, is determined by these four parameters.

Following Ref. [203] the mediator couples to dark matter and to the SM quarks through an axial-vector and vector current, respectively. An axial-vector coupling of the mediator to dark matter leads to spin-dependent dark matter-nucleon interactions and thus weaker bounds from direct dark matter searches. Such a coupling structure naturally arises for Majorana fermion dark matter.

To investigate the exclusion power of the particle-level measurements considered, we scanned a range in plausible mediator masses ($$M_{Z^{\prime}}$$) and dark matter masses ($$M_{\rm DM}$$) within this model for three choices of the coupling of the mediator to the SM ($$g_{q}$$). The results at the time are shown in the paper [116]. By now, however, most of the parameter plane is excluded for all of them except the “challenging” scenario, which ($${{g_{q}}}= 0.25, {{g_{\rm DM}}}= 1$$:) is also a common benchmark choice for other studies of similar models, e.g. LPCC led studies (see Vector mediator, Dirac fermion DM ) and is the only one updated here. (Rivet 2.7.x, 30/4/2019)

(NB the lowest mass point generated is $$M_{\rm Z^\prime}= 10$$ GeV, so the limit does not really extend to zero):

The rather odd shapes comes from the fact that different signatures and measurements affect different areas and they don’t quite overlap. At low $$M_{Z^{\prime}}$$, vector-boson-plus-jet measurements have most sensitivity (see heatmap the CMS photon analyses [138] below left as an example). At low $$M_{\rm DM}$$, the ATLAS missing-energy-plus-jet measurement [6] (again, see below, second left). At higher $$M_{\rm DM}$$ and $$M_{Z^{\prime}}$$, the dijet analyses have most impact (again, see below, right and second right).

Heatmaps for photons, missing energy, 8 TeV and 13 TeV jets.

J M Butterworth, D Grellscheid, M Krämer, B Sarrazin, D Yallup