Vector or Axial-Vector mediator, Dirac fermion DM

Jon Butterworth, Charlie Velasquez, Yoran Yeh

This class of models is one of those considered in the ATLAS search summary [24], updated here: https://atlas.web.cern.ch/Atlas/GROUPS/PHYSICS/PUBNOTES/ATL-PHYS-PUB-2022-036/ We compare equivalent scenarios here (see [130] for an early set of results):

Vector mediator

ATLAS Searches

../../_images/ATLAS_VV_noLep.png

Contur

../../_images/dominantPools0_smbg.png

(Contur 2.3.1, Rivet 3.1.6, Herwig 7.2, 26/07/2022, using correlation info)

In the heatmap above, the dotted line delineates the expected region of 95% exclusion, using the Standard Model (SM) predictions and the data uncertainties. The solid line delineates the actual 95% exclusion region, calculated using the SM as the background. The dashed line is the same as the solid line but delineates the 68% (2-sigma) exclusion region.

The colour of each square indicates which analysis pool contributes the largest exclusion (when using the SM as the background), the analysis pools corresponds to measurements shown on the sidebar of the heatmap. It can be seen that over most of the region, top measurements are the most sensitive. The switch-on of \(t\bar{t}\) production at \(M_{Z^{\prime}} = 350\) GeV can be seen, when the lepton and missing energy analyses become important, with the boosted hadronic top measurement [22], taking over above a higher threshold, due to the high transverse momentum cut on the tops. In the ATLAS search result, the dijet channel dominates at the highest \(M_{\rm Z^\prime}\) region, The dijet measurements are less sensitive, likely because they currently only includes 3.2/fb of data, while the search uses the full run 2 139/fb. Likewise the missing energy measurement [7] which contributes at low masses only uses 3.2/fb of data.

The fact that the photon measurements dominate at very high massess comes from the fact that a SM prediction is available in this region, but with no uncertainites evaluated. The sensitivity is in any case very small.

The white line delineates the region of 95% exclusion when the data are assumed to be equal to the SM (the mode in which Contur has been run in several previous studies). This includes some data sets for which the SM predictions are not yet available in Contur. If the data are close to the SM and the uncertainties on the SM prediction are small compared to the measurement uncertainties, then the black and white solid lines should be similar. Although they are close, it can be seen that the solid white line is a little higher in mass than the dotted and solid black lines, which may be due to the theoretical uncertainties in the standard model predictions, which are neglected for the white line. Differences can also be caused when the SM undershoots the data, as it does in some regions. It can also be seen that at low \(M_{\rm Z^\prime}\), the whole region is excluded under this assumption.

The low \(M_{\rm Z^\prime}\) region is interesting. The lowest mass bins in the plots above are 10 GeV, so the impression that the sensitivity (when data are used as SM background) goes down to zero is misleading. To look at this region more closely, we extend the lower bin to 4 GeV and expanding the low mass region using a log scale.

../../_images/dominantPools0_smbg1.png

(Contur 2.3.1, Rivet 3.1.6, Herwig 7.2, 26/07/2022)

The sensitivity when data are used as background here comes from \(\gamma +\) jets and \(W,Z +\) jets measurements, where the \(Z^\prime\) decays hadronically. Most of the analyses are not used for the black lines, and do not show in the colour key, because the SM predictions are not (yet) available in Contur. The sensitvity arises from marginal contributions from many analyses, so in the mode (using data as background) such a situation should be treated with caution. Nevertheless it illustrates the fact that these measurements do probe the model in that region, and is worth following up.

Jet measurements contribute the largest exclusion using the SM as the background. There is a region centred on \(M_{\rm Z^\prime} = 45\) GeV that is expected to be excluded at 95% (dotted black line) but is only excluded at somewhere between 68 and 95%. This arises from the fact that SM theoretical predictions for the inclusive jet transverse momentum undershoot the data in this region.

Another scenario has the mediator coupling to quarks set to 0.1, and a coupling of 0.01 to leptons.

ATLAS Searches

../../_images/ATLAS_VV_Lep.png

Contur

Here the upper mass limits evaluated using the data as background or the SM as background are very close indeed. The measurements responsible for the highest exclusion using SM as background are shown in the heatmap below.

../../_images/dominantPools0_smbg2.png

(Contur 2.3.1, Rivet 3.1.6, Herwig 7.2, 26/08/2022)

The sensitivity is limited at higher \(M_{\rm Z^\prime}\) compared to the searches because the missing energy [7] and dijet measurements [3] only use 3.2/fb of data

As with the first set of model parameters, the sensitivity apparently extends to lower masses than seen in the ATLAS combined search results, with the caveat as above - the lowest mass point generated is \(M_{\rm Z^\prime}= 10\) GeV Below, the \(M_{\rm Z^\prime}\) is generated on a log scale for \(M_{\rm Z^\prime} \ge 4\) GeV, so the low mass regime can be seen in more detail. The measurements responsible for the highest exclusion using SM as background are shown in the heatmap below.

../../_images/dominantPools0_smbg3.png

(Contur 2.3.1, Rivet 3.1.6, Herwig 7.2, 03/08/2022, using correlation info)

Axial-Vector mediator

As with the vector case, the coupling to quarks is set to 0.25, no coupling to leptons.

ATLAS Searches

See https://atlas.web.cern.ch/Atlas/GROUPS/PHYSICS/PUBNOTES/ATL-PHYS-PUB-2020-021/

../../_images/ATLAS_AA_noLep.png

Contur

../../_images/dominantPools0_smbg4.png

(Contur 2.3.1, Rivet 3.1.6, Herwig 7.2, 26/07/2022)

../../_images/dominantPools0_smbg5.png

(Contur 2.3.1, Rivet 3.1.6, Herwig 7.2, 26/07/2022)

As with the vector case, the coupling to quarks is set to 0.1, but now the coupling to leptons is also 0.1.

ATLAS Searches

../../_images/ATLAS_AA_Lep.png

Contur

../../_images/dominantPools0_smbg6.png

(Contur 2.3.1, Rivet 3.1.6, Herwig 7.2, 26/07/2022)

Lepton signatures now dominate due to the higher coupling compared to that used in the vector case, with the 13 TeV 139/fb dilepton resonance search from ATLAS extending the sensitivity at high mass, in this case to cover the whole plane. The low-mass zoom is shown below.

../../_images/dominantPools0_smbg7.png

(Contur 2.3.1, Rivet 3.1.6, Herwig 7.2, 03/08/2022)

Summary

When the coupling to the SM quarks is 0.25, the measurments in Contur have less sensitivity than the searches at high \(M_{\rm Z^\prime}\), because the dijet measurement in the end drives this region, and the available measurement only uses 36/fb, while the searches use 139/fb. The top measurements are quite powerful, particularly the ATLAS fully-hadronic boosted top measurement [22].

When the coupling to the SM quarks is reduced to 0.1, and some coupling to the SM leptons is introduced, the limits from measurements at higher DM masses are again limited, primarily due to the lack of high-luminosity measurments of dijets and of missing energy.

In both cases, \(\gamma +\) jets and \(W,Z +\) jets measurements ahve the potential to extend the reach to lower \(M_{\rm Z^\prime}\), beyond that of the searches.

The model files are available in the DMsimp_s_spin1 directory here