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

*Jon Butterworth, David Grellscheid, Michael Krämer, Bjorn Sarrazin, David Yallup*

This is the model discussed in the ‘white paper’ [133]. Some later results are also discussed in [129]. 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. [170] 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 [133]. 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 or Axial-Vector mediator, Dirac fermion DM ) and is the only one updated here.
(*Last updated Contur 2.0.x, Rivet 3.1.4, Herwig 7.2.2, 23/05/2021, using correlation information from the experimental measurements where available.*)

The purple line indicates the perturbative unitarity constraint. At low \(M_{Z^{\prime}}\), vector-boson-plus-jet measurements (especially photon-plus-jet) have sensitivity. At low \(M_{\rm DM}\), the ATLAS missing-energy-plus-jet measurement [7] dominates. At higher \(M_{\rm DM}\) and \(M_{Z^{\prime}}\), the dijet analyses have most impact ([198], [179], [3]).

NB the lowest mass point generated is \(M_{\rm Z^\prime}= 10\) GeV, so the limit does not really extend to zero. For a zoom on the low mass region in a similar model, see Vector or Axial-Vector mediator, Dirac fermion DM.

The model files are available in the DM_vector_mediator_UFO directory here