# Simplified Vector Dark Matter Model (3 generations)¶

This is a small generalisation of the model discussed in the ‘white paper’ [42]. 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 now runs over all three generations SM quarks, \(q \in \{u,d\}\). Again, 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. The differences with the 1st-generation only model will be:

- Slightly higher production cross section for the \(Z^{\prime}\) due to the strange, charm and bottom content of the proton
- Higher BR for \(Z^{\prime}\) to decay back to quarks rather than DM, for any given \(g_{\rm DM}\).
- For high enough \(M_{Z^{\prime}}\), top quark decays open up, with their distinctive final states

To investigate the exclusion power of the particle-level measurements considered, we scan a range in plausible mediator masses (\(M_{Z^{\prime}}\)) and dark matter masses (\(M_{\rm DM}\)) within this model thse choices of coupling:

- an ‘optimistic’ scenario \({{g_{q}}}= 0.5, {{g_{\rm DM}}}= 1\):
- a ‘challenging’ scenario \({{g_{q}}}= 0.25, {{g_{\rm DM}}}= 1\):

## Heatmaps for three-generation Vector DM model¶

The sensitivities derived from multiple distributions such as those discussed in the previous section are combined into heatmaps’ which delineate exclusion regions and contours in the parameter space of \(M_{\rm DM}\)and \(M_{Z^{\prime}}\).

Heatmaps displaying 2D parameter space scans in mass in planes corresponding to a fixed \(g_{\rm DM}=1\) and variable \(g_{q}\). The confidence level of exclusion represented corresponds to testing the full signal strength hypothesis against the null background-only hypothesis. The combination of measurements entering into the confidence level presented here is the maximally sensitive allowed grouping, considering all available measurements.

Legend:

Heatmaps for \(g_{q}=0.25\) , \(g_{DM} = 1\)

Heatmap and contour for all available data (measurements from 7, 8 and 13 TeV runs in Rivet/Contrib as of 2018/03/24)

To see where the sensitivity comes from, here’s what we have from the inclusive, dijet and multijet measurements:

this is the exclusion from the W+jet and Z+jet measurements. Top quark measurements also contribute here:

and here’s what the various diboson measurements do.

The photon measurements (inclusive, photon+jet, diphoton) don’t add anything significant for this model.

And higher coupling: Heatmaps for \(g_{q}=0.5\) , \(g_{DM} = 1\)

Heatmap and contour for all available data in Rivet as of 21/9/2017.

Previous versions:

## Comparison to Data¶

Some examples for this model:

- Exclusion of \(M_{Z^\prime} = 500\) GeV, \(M_\chi = 400\) GeV by 7 TeV measurements involving charged leptons

Explanation of Contur plot format

The sensitivities derived from multiple distributions such as those discussed in the previous section are combined into heatmaps’ which delineate exclusion regions and contours in the parameter space of \(M_{\rm DM}\)and \(M_{Z^{\prime}}\).

## Discussion¶

The measurements have more sensitivity to this model for a given coupling than the 1st-generation-only one
(note that the main plots are for \(g_{q} = 0.25\) not \(0.5\)). The main effect seems to be not so much the marginally
increased production cross section or increased BR to jets, but the presence of top quarks and the inclusion of several top measurements from ATLAS and
CMS. You can see the sudden switch-on of \(t\bar{t}\) production at \(M_{Z^{\prime}} = 350\) GeV in the heatmaps. Note that
a dedicated study using ATLAS \(t\bar{t}\) measurements to constrain top production via *scalar* resonances is presented
in [37].

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