Vector Mediator coupling only to 1st generation quarks, Majorana Dark Matter (2019)

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

This is the model discussed in the ‘white paper’ [146]. Some later results are also discussed in [139]. 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. [186] 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 [146]. 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 (2022) ) 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 [9] dominates. At higher \(M_{\rm DM}\) and \(M_{Z^{\prime}}\), the dijet analyses have most impact ([216], [195], [4]).

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 (2022).

The model files are available in the DM_vector_mediator_UFO directory here