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

This is the model discussed in the ‘white paper’ [114]. Some later results are also discussed in [109]. 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

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. [201] 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 [114]. 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 [136] 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*