Vector Mediator coupling only to 1st generation quarks, Majorana Dark Matter
============================================================================
This is the model discussed in the 'white paper' :cite:`Butterworth:2016sqg`.
Some later results are also discussed in :cite:`Butterworth:2019wnt`.
It is a simplified model with a
dark matter Majorana fermion, :math:`\psi`, which interacts with the SM through a new vector particle, :math:`Z^\prime`.
The couplings of the mediator :math:`Z^\prime` to the dark matter :math:`\psi` and to the SM are specified as
.. math::
\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, :math:`q \in \{u,d\}`. The model
has only four free parameters - two couplings and two masses: :math:`g_{\rm DM}`, :math:`g_{q}`,
:math:`M_\psi \equiv {{M_{\rm DM}}}`, and :math:`M_{Z^{\prime}}`. The width of the mediator, :math:`\Gamma_{Z'}`,
is determined by these four parameters.
Following Ref. :cite:`Kahlhoefer:2015bea` 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
(:math:`M_{Z^{\prime}}`) and dark matter masses (:math:`M_{\rm DM}`) within this model for three choices of the coupling of the mediator to the
SM (:math:`g_{q}`).
The results at the time are shown in the paper :cite:`Butterworth:2016sqg`. By now, however, most of the parameter plane is excluded for all
of them except the "challenging" scenario, which (:math:`{{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 :doc:`../dmsimpspin1/index` ) and is the only one updated here. (Rivet 2.7.x, 30/4/2019)
(NB the lowest mass point generated is :math:`M_{\rm Z^\prime}= 10` GeV, so the limit does not really extend to zero):
.. image:: images/combinedHybrid.png
The rather odd shapes comes from the fact that different signatures and measurements affect different areas and they don't quite overlap.
At low :math:`M_{Z^{\prime}}`, vector-boson-plus-jet measurements have most sensitivity (see heatmap the CMS photon analyses
:cite:`Chatrchyan:2013mwa` below left as an example).
At low :math:`M_{\rm DM}`, the ATLAS missing-energy-plus-jet measurement :cite:`Aaboud:2017buf` (again, see below, second left).
At higher :math:`M_{\rm DM}` and :math:`M_{Z^{\prime}}`, the dijet analyses have most impact (again, see below, right and second right).
.. image:: images/CMS_7_GAMMAMesh.png
:scale: 40%
.. image:: images/ATLAS_13_METJETMesh.png
:scale: 40%
.. image:: images/CMS_8_JETSMesh.png
:scale: 40%
.. image:: images/ATLAS_13_JETSMesh.png
:scale: 40%
Heatmaps for photons, missing energy, 8 TeV and 13 TeV jets.
*J M Butterworth, D Grellscheid, M Krämer, B Sarrazin, D Yallup*