CMSEXO22011 ; CERNEP2024032  
Search for heavy neutral leptons in final states with electrons, muons, and hadronically decaying tau leptons in protonproton collisions at $ \sqrt{s} = $ 13 TeV  
CMS Collaboration  
29 February 2024  
JHEP 06 (2024) 123  
Abstract: A search for heavy neutral leptons (HNLs) of Majorana or Dirac type using protonproton collision data at $ \sqrt{s} = $ 13 TeV is presented. The data were collected by the CMS experiment at the CERN LHC and correspond to an integrated luminosity of 138 fb$ ^{1} $. Events with three charged leptons (electrons, muons, and hadronically decaying tau leptons) are selected, corresponding to HNL production in association with a charged lepton and decay of the HNL to two charged leptons and a standard model (SM) neutrino. The search is performed for HNL masses between 10 GeV and 1.5 TeV. No evidence for an HNL signal is observed in data. Upper limits at 95% confidence level are found for the squared coupling strength of the HNL to SM neutrinos, considering exclusive coupling of the HNL to a single SM neutrino generation, for both Majorana and Dirac HNLs. The limits exceed previously achieved experimental constraints for a wide range of HNL masses, and the limits on tau neutrino coupling scenarios with HNL masses above the W boson mass are presented for the first time.  
Links: eprint arXiv:2403.00100 [hepex] (PDF) ; CDS record ; inSPIRE record ; HepData record ; CADI line (restricted) ; 
Figures  
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Figure 1:
Examples of Feynman diagrams for production and decay of an HNL (indicated with the symbol $ \mathrm{N} $) resulting in final states with three charged leptons. The production processes DY (upper row and lower left) and VBF (lower right) are shown, with decays mediated by a W boson (upper row and lower right) or a Z boson (lower left). In the left column, HNLs of Majorana type with an LNV decay are shown, whereas the right column has HNLs of Dirac type with an LNC decay. The leptons that couple directly to the HNL (indicated with the symbol $\ell$) are restricted to the SM generation that couples with the HNL, whereas the leptons from the W and Z boson decays (indicated with the symbol $ \ell^\prime $) can be from any SM generation. 
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Figure 1a:
Examples of Feynman diagrams for production and decay of an HNL (indicated with the symbol $ \mathrm{N} $) resulting in final states with three charged leptons. The production processes DY (upper row and lower left) and VBF (lower right) are shown, with decays mediated by a W boson (upper row and lower right) or a Z boson (lower left). In the left column, HNLs of Majorana type with an LNV decay are shown, whereas the right column has HNLs of Dirac type with an LNC decay. The leptons that couple directly to the HNL (indicated with the symbol $\ell$) are restricted to the SM generation that couples with the HNL, whereas the leptons from the W and Z boson decays (indicated with the symbol $ \ell^\prime $) can be from any SM generation. 
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Figure 1b:
Examples of Feynman diagrams for production and decay of an HNL (indicated with the symbol $ \mathrm{N} $) resulting in final states with three charged leptons. The production processes DY (upper row and lower left) and VBF (lower right) are shown, with decays mediated by a W boson (upper row and lower right) or a Z boson (lower left). In the left column, HNLs of Majorana type with an LNV decay are shown, whereas the right column has HNLs of Dirac type with an LNC decay. The leptons that couple directly to the HNL (indicated with the symbol $\ell$) are restricted to the SM generation that couples with the HNL, whereas the leptons from the W and Z boson decays (indicated with the symbol $ \ell^\prime $) can be from any SM generation. 
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Figure 1c:
Examples of Feynman diagrams for production and decay of an HNL (indicated with the symbol $ \mathrm{N} $) resulting in final states with three charged leptons. The production processes DY (upper row and lower left) and VBF (lower right) are shown, with decays mediated by a W boson (upper row and lower right) or a Z boson (lower left). In the left column, HNLs of Majorana type with an LNV decay are shown, whereas the right column has HNLs of Dirac type with an LNC decay. The leptons that couple directly to the HNL (indicated with the symbol $\ell$) are restricted to the SM generation that couples with the HNL, whereas the leptons from the W and Z boson decays (indicated with the symbol $ \ell^\prime $) can be from any SM generation. 
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Figure 1d:
Examples of Feynman diagrams for production and decay of an HNL (indicated with the symbol $ \mathrm{N} $) resulting in final states with three charged leptons. The production processes DY (upper row and lower left) and VBF (lower right) are shown, with decays mediated by a W boson (upper row and lower right) or a Z boson (lower left). In the left column, HNLs of Majorana type with an LNV decay are shown, whereas the right column has HNLs of Dirac type with an LNC decay. The leptons that couple directly to the HNL (indicated with the symbol $\ell$) are restricted to the SM generation that couples with the HNL, whereas the leptons from the W and Z boson decays (indicated with the symbol $ \ell^\prime $) can be from any SM generation. 
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Figure 2:
Comparison of observed (points) and predicted (coloured histograms) distributions in the lowmass selection for the 0$ \tau_{\mathrm{h}} $ categories combined. Important input variables to the BDT training are shown: $ \min m({\ell}^{+}{\ell}^{}) $ (upper left), $ m_{\mathrm{T}} $ (upper right), $ \Delta R $ between the two leptons used for $ \min m({\ell}^{+}{\ell}^{}) $ ($ \Delta R[\min m({\ell}^{+}{\ell}^{})] $, lower left), $ m(3\ell) $ (lower right). The predicted background yields are shown before the fit to the data (``prefit''). The HNL predictions for three different $ m_{\mathrm{N}} $ values with exclusive coupling to tau neutrinos are shown with coloured lines, and are normalized to the total background yield. The vertical bars on the points represent the statistical uncertainties in the data, and the hatched bands the total uncertainties in the predictions. The last bins include the overflow contributions. In the lower panels, the ratios of the event yield in data to the overall sum of the predictions are shown. 
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Figure 2a:
Comparison of observed (points) and predicted (coloured histograms) distributions in the lowmass selection for the 0$ \tau_{\mathrm{h}} $ categories combined. Important input variables to the BDT training are shown: $ \min m({\ell}^{+}{\ell}^{}) $ (upper left), $ m_{\mathrm{T}} $ (upper right), $ \Delta R $ between the two leptons used for $ \min m({\ell}^{+}{\ell}^{}) $ ($ \Delta R[\min m({\ell}^{+}{\ell}^{})] $, lower left), $ m(3\ell) $ (lower right). The predicted background yields are shown before the fit to the data (``prefit''). The HNL predictions for three different $ m_{\mathrm{N}} $ values with exclusive coupling to tau neutrinos are shown with coloured lines, and are normalized to the total background yield. The vertical bars on the points represent the statistical uncertainties in the data, and the hatched bands the total uncertainties in the predictions. The last bins include the overflow contributions. In the lower panels, the ratios of the event yield in data to the overall sum of the predictions are shown. 
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Figure 2b:
Comparison of observed (points) and predicted (coloured histograms) distributions in the lowmass selection for the 0$ \tau_{\mathrm{h}} $ categories combined. Important input variables to the BDT training are shown: $ \min m({\ell}^{+}{\ell}^{}) $ (upper left), $ m_{\mathrm{T}} $ (upper right), $ \Delta R $ between the two leptons used for $ \min m({\ell}^{+}{\ell}^{}) $ ($ \Delta R[\min m({\ell}^{+}{\ell}^{})] $, lower left), $ m(3\ell) $ (lower right). The predicted background yields are shown before the fit to the data (``prefit''). The HNL predictions for three different $ m_{\mathrm{N}} $ values with exclusive coupling to tau neutrinos are shown with coloured lines, and are normalized to the total background yield. The vertical bars on the points represent the statistical uncertainties in the data, and the hatched bands the total uncertainties in the predictions. The last bins include the overflow contributions. In the lower panels, the ratios of the event yield in data to the overall sum of the predictions are shown. 
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Figure 2c:
Comparison of observed (points) and predicted (coloured histograms) distributions in the lowmass selection for the 0$ \tau_{\mathrm{h}} $ categories combined. Important input variables to the BDT training are shown: $ \min m({\ell}^{+}{\ell}^{}) $ (upper left), $ m_{\mathrm{T}} $ (upper right), $ \Delta R $ between the two leptons used for $ \min m({\ell}^{+}{\ell}^{}) $ ($ \Delta R[\min m({\ell}^{+}{\ell}^{})] $, lower left), $ m(3\ell) $ (lower right). The predicted background yields are shown before the fit to the data (``prefit''). The HNL predictions for three different $ m_{\mathrm{N}} $ values with exclusive coupling to tau neutrinos are shown with coloured lines, and are normalized to the total background yield. The vertical bars on the points represent the statistical uncertainties in the data, and the hatched bands the total uncertainties in the predictions. The last bins include the overflow contributions. In the lower panels, the ratios of the event yield in data to the overall sum of the predictions are shown. 
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Figure 2d:
Comparison of observed (points) and predicted (coloured histograms) distributions in the lowmass selection for the 0$ \tau_{\mathrm{h}} $ categories combined. Important input variables to the BDT training are shown: $ \min m({\ell}^{+}{\ell}^{}) $ (upper left), $ m_{\mathrm{T}} $ (upper right), $ \Delta R $ between the two leptons used for $ \min m({\ell}^{+}{\ell}^{}) $ ($ \Delta R[\min m({\ell}^{+}{\ell}^{})] $, lower left), $ m(3\ell) $ (lower right). The predicted background yields are shown before the fit to the data (``prefit''). The HNL predictions for three different $ m_{\mathrm{N}} $ values with exclusive coupling to tau neutrinos are shown with coloured lines, and are normalized to the total background yield. The vertical bars on the points represent the statistical uncertainties in the data, and the hatched bands the total uncertainties in the predictions. The last bins include the overflow contributions. In the lower panels, the ratios of the event yield in data to the overall sum of the predictions are shown. 
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Figure 3:
Comparison of observed (points) and predicted (coloured histograms) distributions in the lowmass selection for the 1$ \tau_{\mathrm{h}} $ categories combined. Important input variables to the BDT training are shown: $ \min m({\ell}^{+}{\ell}^{}) $ (upper left), $p_{\mathrm{T}}(\ell_{3})$ (upper right), $ m(3\ell) $ (lower left), $ L_{\mathrm{T}} $ (lower right). The predicted background yields are shown before the fit to the data (``prefit''). The HNL predictions for three different $ m_{\mathrm{N}} $ values with exclusive coupling to tau neutrinos are shown with coloured lines, and are normalized to the total background yield. The vertical bars on the points represent the statistical uncertainties in the data, and the hatched bands the total uncertainties in the predictions. The last bins include the overflow contributions. In the lower panels, the ratios of the event yield in data to the overall sum of the predictions are shown. 
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Figure 3a:
Comparison of observed (points) and predicted (coloured histograms) distributions in the lowmass selection for the 1$ \tau_{\mathrm{h}} $ categories combined. Important input variables to the BDT training are shown: $ \min m({\ell}^{+}{\ell}^{}) $ (upper left), $p_{\mathrm{T}}(\ell_{3})$ (upper right), $ m(3\ell) $ (lower left), $ L_{\mathrm{T}} $ (lower right). The predicted background yields are shown before the fit to the data (``prefit''). The HNL predictions for three different $ m_{\mathrm{N}} $ values with exclusive coupling to tau neutrinos are shown with coloured lines, and are normalized to the total background yield. The vertical bars on the points represent the statistical uncertainties in the data, and the hatched bands the total uncertainties in the predictions. The last bins include the overflow contributions. In the lower panels, the ratios of the event yield in data to the overall sum of the predictions are shown. 
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Figure 3b:
Comparison of observed (points) and predicted (coloured histograms) distributions in the lowmass selection for the 1$ \tau_{\mathrm{h}} $ categories combined. Important input variables to the BDT training are shown: $ \min m({\ell}^{+}{\ell}^{}) $ (upper left), $p_{\mathrm{T}}(\ell_{3})$ (upper right), $ m(3\ell) $ (lower left), $ L_{\mathrm{T}} $ (lower right). The predicted background yields are shown before the fit to the data (``prefit''). The HNL predictions for three different $ m_{\mathrm{N}} $ values with exclusive coupling to tau neutrinos are shown with coloured lines, and are normalized to the total background yield. The vertical bars on the points represent the statistical uncertainties in the data, and the hatched bands the total uncertainties in the predictions. The last bins include the overflow contributions. In the lower panels, the ratios of the event yield in data to the overall sum of the predictions are shown. 
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Figure 3c:
Comparison of observed (points) and predicted (coloured histograms) distributions in the lowmass selection for the 1$ \tau_{\mathrm{h}} $ categories combined. Important input variables to the BDT training are shown: $ \min m({\ell}^{+}{\ell}^{}) $ (upper left), $p_{\mathrm{T}}(\ell_{3})$ (upper right), $ m(3\ell) $ (lower left), $ L_{\mathrm{T}} $ (lower right). The predicted background yields are shown before the fit to the data (``prefit''). The HNL predictions for three different $ m_{\mathrm{N}} $ values with exclusive coupling to tau neutrinos are shown with coloured lines, and are normalized to the total background yield. The vertical bars on the points represent the statistical uncertainties in the data, and the hatched bands the total uncertainties in the predictions. The last bins include the overflow contributions. In the lower panels, the ratios of the event yield in data to the overall sum of the predictions are shown. 
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Figure 3d:
Comparison of observed (points) and predicted (coloured histograms) distributions in the lowmass selection for the 1$ \tau_{\mathrm{h}} $ categories combined. Important input variables to the BDT training are shown: $ \min m({\ell}^{+}{\ell}^{}) $ (upper left), $p_{\mathrm{T}}(\ell_{3})$ (upper right), $ m(3\ell) $ (lower left), $ L_{\mathrm{T}} $ (lower right). The predicted background yields are shown before the fit to the data (``prefit''). The HNL predictions for three different $ m_{\mathrm{N}} $ values with exclusive coupling to tau neutrinos are shown with coloured lines, and are normalized to the total background yield. The vertical bars on the points represent the statistical uncertainties in the data, and the hatched bands the total uncertainties in the predictions. The last bins include the overflow contributions. In the lower panels, the ratios of the event yield in data to the overall sum of the predictions are shown. 
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Figure 4:
Comparison of observed (points) and predicted (coloured histograms) distributions in the highmass selection for the 0$ \tau_{\mathrm{h}} $ categories combined. Important input variables to the BDT training are shown: $ \Delta R[\min m({\ell}^{+}{\ell}^{})] $ (upper left), $ m_{\mathrm{T}} $ (upper right), $p_{\mathrm{T}}(\ell_{3})$ (lower left), $ p_{\mathrm{T}}^\text{miss} $ (lower right). The predicted background yields are shown before the fit to the data (``prefit''). The HNL predictions for three different $ m_{\mathrm{N}} $ values with exclusive coupling to tau neutrinos are shown with coloured lines, and are normalized to the total background yield. The vertical bars on the points represent the statistical uncertainties in the data, and the hatched bands the total uncertainties in the predictions. The last bins include the overflow contributions. In the lower panels, the ratios of the event yield in data to the overall sum of the predictions are shown. 
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Figure 4a:
Comparison of observed (points) and predicted (coloured histograms) distributions in the highmass selection for the 0$ \tau_{\mathrm{h}} $ categories combined. Important input variables to the BDT training are shown: $ \Delta R[\min m({\ell}^{+}{\ell}^{})] $ (upper left), $ m_{\mathrm{T}} $ (upper right), $p_{\mathrm{T}}(\ell_{3})$ (lower left), $ p_{\mathrm{T}}^\text{miss} $ (lower right). The predicted background yields are shown before the fit to the data (``prefit''). The HNL predictions for three different $ m_{\mathrm{N}} $ values with exclusive coupling to tau neutrinos are shown with coloured lines, and are normalized to the total background yield. The vertical bars on the points represent the statistical uncertainties in the data, and the hatched bands the total uncertainties in the predictions. The last bins include the overflow contributions. In the lower panels, the ratios of the event yield in data to the overall sum of the predictions are shown. 
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Figure 4b:
Comparison of observed (points) and predicted (coloured histograms) distributions in the highmass selection for the 0$ \tau_{\mathrm{h}} $ categories combined. Important input variables to the BDT training are shown: $ \Delta R[\min m({\ell}^{+}{\ell}^{})] $ (upper left), $ m_{\mathrm{T}} $ (upper right), $p_{\mathrm{T}}(\ell_{3})$ (lower left), $ p_{\mathrm{T}}^\text{miss} $ (lower right). The predicted background yields are shown before the fit to the data (``prefit''). The HNL predictions for three different $ m_{\mathrm{N}} $ values with exclusive coupling to tau neutrinos are shown with coloured lines, and are normalized to the total background yield. The vertical bars on the points represent the statistical uncertainties in the data, and the hatched bands the total uncertainties in the predictions. The last bins include the overflow contributions. In the lower panels, the ratios of the event yield in data to the overall sum of the predictions are shown. 
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Figure 4c:
Comparison of observed (points) and predicted (coloured histograms) distributions in the highmass selection for the 0$ \tau_{\mathrm{h}} $ categories combined. Important input variables to the BDT training are shown: $ \Delta R[\min m({\ell}^{+}{\ell}^{})] $ (upper left), $ m_{\mathrm{T}} $ (upper right), $p_{\mathrm{T}}(\ell_{3})$ (lower left), $ p_{\mathrm{T}}^\text{miss} $ (lower right). The predicted background yields are shown before the fit to the data (``prefit''). The HNL predictions for three different $ m_{\mathrm{N}} $ values with exclusive coupling to tau neutrinos are shown with coloured lines, and are normalized to the total background yield. The vertical bars on the points represent the statistical uncertainties in the data, and the hatched bands the total uncertainties in the predictions. The last bins include the overflow contributions. In the lower panels, the ratios of the event yield in data to the overall sum of the predictions are shown. 
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Figure 4d:
Comparison of observed (points) and predicted (coloured histograms) distributions in the highmass selection for the 0$ \tau_{\mathrm{h}} $ categories combined. Important input variables to the BDT training are shown: $ \Delta R[\min m({\ell}^{+}{\ell}^{})] $ (upper left), $ m_{\mathrm{T}} $ (upper right), $p_{\mathrm{T}}(\ell_{3})$ (lower left), $ p_{\mathrm{T}}^\text{miss} $ (lower right). The predicted background yields are shown before the fit to the data (``prefit''). The HNL predictions for three different $ m_{\mathrm{N}} $ values with exclusive coupling to tau neutrinos are shown with coloured lines, and are normalized to the total background yield. The vertical bars on the points represent the statistical uncertainties in the data, and the hatched bands the total uncertainties in the predictions. The last bins include the overflow contributions. In the lower panels, the ratios of the event yield in data to the overall sum of the predictions are shown. 
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Figure 5:
Comparison of observed (points) and predicted (coloured histograms) distributions in the WZ CR. The leading lepton $ p_{\mathrm{T}} $ (upper left) and $ \eta $ (upper right), as well as $ p_{\mathrm{T}}^\text{miss} $ (lower left) and $ \min m({\ell}^{+}{\ell}^{}) $ (lower right) are shown. The vertical bars on the points represent the statistical uncertainties in the data, and the hatched bands the total uncertainties in the predictions. The last bins include the overflow contributions. In the lower panels, the ratios of the event yield in data to the overall sum of the predictions are shown. 
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Figure 5a:
Comparison of observed (points) and predicted (coloured histograms) distributions in the WZ CR. The leading lepton $ p_{\mathrm{T}} $ (upper left) and $ \eta $ (upper right), as well as $ p_{\mathrm{T}}^\text{miss} $ (lower left) and $ \min m({\ell}^{+}{\ell}^{}) $ (lower right) are shown. The vertical bars on the points represent the statistical uncertainties in the data, and the hatched bands the total uncertainties in the predictions. The last bins include the overflow contributions. In the lower panels, the ratios of the event yield in data to the overall sum of the predictions are shown. 
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Figure 5b:
Comparison of observed (points) and predicted (coloured histograms) distributions in the WZ CR. The leading lepton $ p_{\mathrm{T}} $ (upper left) and $ \eta $ (upper right), as well as $ p_{\mathrm{T}}^\text{miss} $ (lower left) and $ \min m({\ell}^{+}{\ell}^{}) $ (lower right) are shown. The vertical bars on the points represent the statistical uncertainties in the data, and the hatched bands the total uncertainties in the predictions. The last bins include the overflow contributions. In the lower panels, the ratios of the event yield in data to the overall sum of the predictions are shown. 
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Figure 5c:
Comparison of observed (points) and predicted (coloured histograms) distributions in the WZ CR. The leading lepton $ p_{\mathrm{T}} $ (upper left) and $ \eta $ (upper right), as well as $ p_{\mathrm{T}}^\text{miss} $ (lower left) and $ \min m({\ell}^{+}{\ell}^{}) $ (lower right) are shown. The vertical bars on the points represent the statistical uncertainties in the data, and the hatched bands the total uncertainties in the predictions. The last bins include the overflow contributions. In the lower panels, the ratios of the event yield in data to the overall sum of the predictions are shown. 
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Figure 5d:
Comparison of observed (points) and predicted (coloured histograms) distributions in the WZ CR. The leading lepton $ p_{\mathrm{T}} $ (upper left) and $ \eta $ (upper right), as well as $ p_{\mathrm{T}}^\text{miss} $ (lower left) and $ \min m({\ell}^{+}{\ell}^{}) $ (lower right) are shown. The vertical bars on the points represent the statistical uncertainties in the data, and the hatched bands the total uncertainties in the predictions. The last bins include the overflow contributions. In the lower panels, the ratios of the event yield in data to the overall sum of the predictions are shown. 
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Figure 6:
Comparison of observed (points) and predicted (coloured histograms) distributions in the ZZ CR. The leading lepton $ p_{\mathrm{T}} $ (upper left), $ m({\ell}^{+}{\ell}^{}) $ of $ \mathrm{Z}_2 $ ($ m(\mathrm{Z}_2) $, upper right), $ p_{\mathrm{T}}^\text{miss} $ (lower left), and $ \min m({\ell}^{+}{\ell}^{}) $ (lower right) are shown. The ZZ prediction is scaled with a normalization factor of 1.12, as discussed in the text. The vertical bars on the points represent the statistical uncertainties in the data, and the hatched bands the total uncertainties in the predictions. The last bins include the overflow contributions. In the lower panels, the ratios of the event yield in data to the overall sum of the predictions are shown. 
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Figure 6a:
Comparison of observed (points) and predicted (coloured histograms) distributions in the ZZ CR. The leading lepton $ p_{\mathrm{T}} $ (upper left), $ m({\ell}^{+}{\ell}^{}) $ of $ \mathrm{Z}_2 $ ($ m(\mathrm{Z}_2) $, upper right), $ p_{\mathrm{T}}^\text{miss} $ (lower left), and $ \min m({\ell}^{+}{\ell}^{}) $ (lower right) are shown. The ZZ prediction is scaled with a normalization factor of 1.12, as discussed in the text. The vertical bars on the points represent the statistical uncertainties in the data, and the hatched bands the total uncertainties in the predictions. The last bins include the overflow contributions. In the lower panels, the ratios of the event yield in data to the overall sum of the predictions are shown. 
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Figure 6b:
Comparison of observed (points) and predicted (coloured histograms) distributions in the ZZ CR. The leading lepton $ p_{\mathrm{T}} $ (upper left), $ m({\ell}^{+}{\ell}^{}) $ of $ \mathrm{Z}_2 $ ($ m(\mathrm{Z}_2) $, upper right), $ p_{\mathrm{T}}^\text{miss} $ (lower left), and $ \min m({\ell}^{+}{\ell}^{}) $ (lower right) are shown. The ZZ prediction is scaled with a normalization factor of 1.12, as discussed in the text. The vertical bars on the points represent the statistical uncertainties in the data, and the hatched bands the total uncertainties in the predictions. The last bins include the overflow contributions. In the lower panels, the ratios of the event yield in data to the overall sum of the predictions are shown. 
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Figure 6c:
Comparison of observed (points) and predicted (coloured histograms) distributions in the ZZ CR. The leading lepton $ p_{\mathrm{T}} $ (upper left), $ m({\ell}^{+}{\ell}^{}) $ of $ \mathrm{Z}_2 $ ($ m(\mathrm{Z}_2) $, upper right), $ p_{\mathrm{T}}^\text{miss} $ (lower left), and $ \min m({\ell}^{+}{\ell}^{}) $ (lower right) are shown. The ZZ prediction is scaled with a normalization factor of 1.12, as discussed in the text. The vertical bars on the points represent the statistical uncertainties in the data, and the hatched bands the total uncertainties in the predictions. The last bins include the overflow contributions. In the lower panels, the ratios of the event yield in data to the overall sum of the predictions are shown. 
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Figure 6d:
Comparison of observed (points) and predicted (coloured histograms) distributions in the ZZ CR. The leading lepton $ p_{\mathrm{T}} $ (upper left), $ m({\ell}^{+}{\ell}^{}) $ of $ \mathrm{Z}_2 $ ($ m(\mathrm{Z}_2) $, upper right), $ p_{\mathrm{T}}^\text{miss} $ (lower left), and $ \min m({\ell}^{+}{\ell}^{}) $ (lower right) are shown. The ZZ prediction is scaled with a normalization factor of 1.12, as discussed in the text. The vertical bars on the points represent the statistical uncertainties in the data, and the hatched bands the total uncertainties in the predictions. The last bins include the overflow contributions. In the lower panels, the ratios of the event yield in data to the overall sum of the predictions are shown. 
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Figure 7:
Comparison of observed (points) and predicted (coloured histograms) distributions in the $ \mathrm{Z}\gamma $ CR. The leading lepton $ p_{\mathrm{T}} $ (upper left) and $ \eta $ (upper right), $ p_{\mathrm{T}}^\text{miss} $ (lower left), and $ m_{\mathrm{T}} $ (lower right) are shown. The $ \mathrm{Z}\gamma $ prediction is scaled with a normalization factor of 1.11, as discussed in the text. The vertical bars on the points represent the statistical uncertainties in the data, and the hatched bands the total uncertainties in the predictions. The last bins include the overflow contributions. In the lower panels, the ratios of the event yield in data to the overall sum of the predictions are shown. 
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Figure 7a:
Comparison of observed (points) and predicted (coloured histograms) distributions in the $ \mathrm{Z}\gamma $ CR. The leading lepton $ p_{\mathrm{T}} $ (upper left) and $ \eta $ (upper right), $ p_{\mathrm{T}}^\text{miss} $ (lower left), and $ m_{\mathrm{T}} $ (lower right) are shown. The $ \mathrm{Z}\gamma $ prediction is scaled with a normalization factor of 1.11, as discussed in the text. The vertical bars on the points represent the statistical uncertainties in the data, and the hatched bands the total uncertainties in the predictions. The last bins include the overflow contributions. In the lower panels, the ratios of the event yield in data to the overall sum of the predictions are shown. 
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Figure 7b:
Comparison of observed (points) and predicted (coloured histograms) distributions in the $ \mathrm{Z}\gamma $ CR. The leading lepton $ p_{\mathrm{T}} $ (upper left) and $ \eta $ (upper right), $ p_{\mathrm{T}}^\text{miss} $ (lower left), and $ m_{\mathrm{T}} $ (lower right) are shown. The $ \mathrm{Z}\gamma $ prediction is scaled with a normalization factor of 1.11, as discussed in the text. The vertical bars on the points represent the statistical uncertainties in the data, and the hatched bands the total uncertainties in the predictions. The last bins include the overflow contributions. In the lower panels, the ratios of the event yield in data to the overall sum of the predictions are shown. 
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Figure 7c:
Comparison of observed (points) and predicted (coloured histograms) distributions in the $ \mathrm{Z}\gamma $ CR. The leading lepton $ p_{\mathrm{T}} $ (upper left) and $ \eta $ (upper right), $ p_{\mathrm{T}}^\text{miss} $ (lower left), and $ m_{\mathrm{T}} $ (lower right) are shown. The $ \mathrm{Z}\gamma $ prediction is scaled with a normalization factor of 1.11, as discussed in the text. The vertical bars on the points represent the statistical uncertainties in the data, and the hatched bands the total uncertainties in the predictions. The last bins include the overflow contributions. In the lower panels, the ratios of the event yield in data to the overall sum of the predictions are shown. 
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Figure 7d:
Comparison of observed (points) and predicted (coloured histograms) distributions in the $ \mathrm{Z}\gamma $ CR. The leading lepton $ p_{\mathrm{T}} $ (upper left) and $ \eta $ (upper right), $ p_{\mathrm{T}}^\text{miss} $ (lower left), and $ m_{\mathrm{T}} $ (lower right) are shown. The $ \mathrm{Z}\gamma $ prediction is scaled with a normalization factor of 1.11, as discussed in the text. The vertical bars on the points represent the statistical uncertainties in the data, and the hatched bands the total uncertainties in the predictions. The last bins include the overflow contributions. In the lower panels, the ratios of the event yield in data to the overall sum of the predictions are shown. 
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Figure 8:
Comparison of the number of observed (points) and predicted (coloured histograms) events in the SR bins, shown for the 0$ \tau_{\mathrm{h}} $ (left column) and 1$ \tau_{\mathrm{h}} $ (right column) categories combined. The La18 and Lb18 (upper row), Ha1Ha9 (middle row), and Hb116 (lower row) are displayed. The predicted background yields are shown with the values of the normalizations and nuisance parameters obtained in backgroundonly fits applied (``postfit''). The HNL predictions for three different $ m_{\mathrm{N}} $ values with exclusive coupling to tau neutrinos are shown with coloured lines. The vertical bars on the points represent the statistical uncertainties in the data, and the hatched bands the total uncertainties in the background predictions as obtained from the fits. In the lower panels, the ratios of the event yield in data to the overall sum of the background predictions are shown. 
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Figure 8a:
Comparison of the number of observed (points) and predicted (coloured histograms) events in the SR bins, shown for the 0$ \tau_{\mathrm{h}} $ (left column) and 1$ \tau_{\mathrm{h}} $ (right column) categories combined. The La18 and Lb18 (upper row), Ha1Ha9 (middle row), and Hb116 (lower row) are displayed. The predicted background yields are shown with the values of the normalizations and nuisance parameters obtained in backgroundonly fits applied (``postfit''). The HNL predictions for three different $ m_{\mathrm{N}} $ values with exclusive coupling to tau neutrinos are shown with coloured lines. The vertical bars on the points represent the statistical uncertainties in the data, and the hatched bands the total uncertainties in the background predictions as obtained from the fits. In the lower panels, the ratios of the event yield in data to the overall sum of the background predictions are shown. 
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Figure 8b:
Comparison of the number of observed (points) and predicted (coloured histograms) events in the SR bins, shown for the 0$ \tau_{\mathrm{h}} $ (left column) and 1$ \tau_{\mathrm{h}} $ (right column) categories combined. The La18 and Lb18 (upper row), Ha1Ha9 (middle row), and Hb116 (lower row) are displayed. The predicted background yields are shown with the values of the normalizations and nuisance parameters obtained in backgroundonly fits applied (``postfit''). The HNL predictions for three different $ m_{\mathrm{N}} $ values with exclusive coupling to tau neutrinos are shown with coloured lines. The vertical bars on the points represent the statistical uncertainties in the data, and the hatched bands the total uncertainties in the background predictions as obtained from the fits. In the lower panels, the ratios of the event yield in data to the overall sum of the background predictions are shown. 
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Figure 8c:
Comparison of the number of observed (points) and predicted (coloured histograms) events in the SR bins, shown for the 0$ \tau_{\mathrm{h}} $ (left column) and 1$ \tau_{\mathrm{h}} $ (right column) categories combined. The La18 and Lb18 (upper row), Ha1Ha9 (middle row), and Hb116 (lower row) are displayed. The predicted background yields are shown with the values of the normalizations and nuisance parameters obtained in backgroundonly fits applied (``postfit''). The HNL predictions for three different $ m_{\mathrm{N}} $ values with exclusive coupling to tau neutrinos are shown with coloured lines. The vertical bars on the points represent the statistical uncertainties in the data, and the hatched bands the total uncertainties in the background predictions as obtained from the fits. In the lower panels, the ratios of the event yield in data to the overall sum of the background predictions are shown. 
png pdf 
Figure 8d:
Comparison of the number of observed (points) and predicted (coloured histograms) events in the SR bins, shown for the 0$ \tau_{\mathrm{h}} $ (left column) and 1$ \tau_{\mathrm{h}} $ (right column) categories combined. The La18 and Lb18 (upper row), Ha1Ha9 (middle row), and Hb116 (lower row) are displayed. The predicted background yields are shown with the values of the normalizations and nuisance parameters obtained in backgroundonly fits applied (``postfit''). The HNL predictions for three different $ m_{\mathrm{N}} $ values with exclusive coupling to tau neutrinos are shown with coloured lines. The vertical bars on the points represent the statistical uncertainties in the data, and the hatched bands the total uncertainties in the background predictions as obtained from the fits. In the lower panels, the ratios of the event yield in data to the overall sum of the background predictions are shown. 
png pdf 
Figure 8e:
Comparison of the number of observed (points) and predicted (coloured histograms) events in the SR bins, shown for the 0$ \tau_{\mathrm{h}} $ (left column) and 1$ \tau_{\mathrm{h}} $ (right column) categories combined. The La18 and Lb18 (upper row), Ha1Ha9 (middle row), and Hb116 (lower row) are displayed. The predicted background yields are shown with the values of the normalizations and nuisance parameters obtained in backgroundonly fits applied (``postfit''). The HNL predictions for three different $ m_{\mathrm{N}} $ values with exclusive coupling to tau neutrinos are shown with coloured lines. The vertical bars on the points represent the statistical uncertainties in the data, and the hatched bands the total uncertainties in the background predictions as obtained from the fits. In the lower panels, the ratios of the event yield in data to the overall sum of the background predictions are shown. 
png pdf 
Figure 8f:
Comparison of the number of observed (points) and predicted (coloured histograms) events in the SR bins, shown for the 0$ \tau_{\mathrm{h}} $ (left column) and 1$ \tau_{\mathrm{h}} $ (right column) categories combined. The La18 and Lb18 (upper row), Ha1Ha9 (middle row), and Hb116 (lower row) are displayed. The predicted background yields are shown with the values of the normalizations and nuisance parameters obtained in backgroundonly fits applied (``postfit''). The HNL predictions for three different $ m_{\mathrm{N}} $ values with exclusive coupling to tau neutrinos are shown with coloured lines. The vertical bars on the points represent the statistical uncertainties in the data, and the hatched bands the total uncertainties in the background predictions as obtained from the fits. In the lower panels, the ratios of the event yield in data to the overall sum of the background predictions are shown. 
png pdf 
Figure 9:
Comparison of the observed (points) and predicted (coloured histograms) BDT output distributions of the lowmass selection, shown for the $ \mathrm{e}\mathrm{e}\mathrm{e} $ and $ \mathrm{e}\mathrm{e}\mu $ channels combined (left column) and the $ \mathrm{e}\mu\mu $ and $ \mu\mu\mu $ channels combined (right column). The output scores BDT(1040, e, 0$ \tau_{\mathrm{h}} $) (upper left), BDT(1040, $ \mu $, 0$ \tau_{\mathrm{h}} $) (upper right), BDT(5075, e, 0$ \tau_{\mathrm{h}} $) (lower left), and BDT(5075, $ \mu $, 0$ \tau_{\mathrm{h}} $) (lower right) are displayed. The predicted background yields are shown with the values of the normalizations and nuisance parameters obtained in backgroundonly fits applied (``postfit''). The HNL predictions for three different $ m_{\mathrm{N}} $ values with exclusive coupling to electron (left column) or muon (right column) neutrinos are shown with coloured lines. The vertical bars on the points represent the statistical uncertainties in the data, and the hatched bands the total uncertainties in the background predictions as obtained from the fits. In the lower panels, the ratios of the event yield in data to the overall sum of the background predictions are shown. 
png pdf 
Figure 9a:
Comparison of the observed (points) and predicted (coloured histograms) BDT output distributions of the lowmass selection, shown for the $ \mathrm{e}\mathrm{e}\mathrm{e} $ and $ \mathrm{e}\mathrm{e}\mu $ channels combined (left column) and the $ \mathrm{e}\mu\mu $ and $ \mu\mu\mu $ channels combined (right column). The output scores BDT(1040, e, 0$ \tau_{\mathrm{h}} $) (upper left), BDT(1040, $ \mu $, 0$ \tau_{\mathrm{h}} $) (upper right), BDT(5075, e, 0$ \tau_{\mathrm{h}} $) (lower left), and BDT(5075, $ \mu $, 0$ \tau_{\mathrm{h}} $) (lower right) are displayed. The predicted background yields are shown with the values of the normalizations and nuisance parameters obtained in backgroundonly fits applied (``postfit''). The HNL predictions for three different $ m_{\mathrm{N}} $ values with exclusive coupling to electron (left column) or muon (right column) neutrinos are shown with coloured lines. The vertical bars on the points represent the statistical uncertainties in the data, and the hatched bands the total uncertainties in the background predictions as obtained from the fits. In the lower panels, the ratios of the event yield in data to the overall sum of the background predictions are shown. 
png pdf 
Figure 9b:
Comparison of the observed (points) and predicted (coloured histograms) BDT output distributions of the lowmass selection, shown for the $ \mathrm{e}\mathrm{e}\mathrm{e} $ and $ \mathrm{e}\mathrm{e}\mu $ channels combined (left column) and the $ \mathrm{e}\mu\mu $ and $ \mu\mu\mu $ channels combined (right column). The output scores BDT(1040, e, 0$ \tau_{\mathrm{h}} $) (upper left), BDT(1040, $ \mu $, 0$ \tau_{\mathrm{h}} $) (upper right), BDT(5075, e, 0$ \tau_{\mathrm{h}} $) (lower left), and BDT(5075, $ \mu $, 0$ \tau_{\mathrm{h}} $) (lower right) are displayed. The predicted background yields are shown with the values of the normalizations and nuisance parameters obtained in backgroundonly fits applied (``postfit''). The HNL predictions for three different $ m_{\mathrm{N}} $ values with exclusive coupling to electron (left column) or muon (right column) neutrinos are shown with coloured lines. The vertical bars on the points represent the statistical uncertainties in the data, and the hatched bands the total uncertainties in the background predictions as obtained from the fits. In the lower panels, the ratios of the event yield in data to the overall sum of the background predictions are shown. 
png pdf 
Figure 9c:
Comparison of the observed (points) and predicted (coloured histograms) BDT output distributions of the lowmass selection, shown for the $ \mathrm{e}\mathrm{e}\mathrm{e} $ and $ \mathrm{e}\mathrm{e}\mu $ channels combined (left column) and the $ \mathrm{e}\mu\mu $ and $ \mu\mu\mu $ channels combined (right column). The output scores BDT(1040, e, 0$ \tau_{\mathrm{h}} $) (upper left), BDT(1040, $ \mu $, 0$ \tau_{\mathrm{h}} $) (upper right), BDT(5075, e, 0$ \tau_{\mathrm{h}} $) (lower left), and BDT(5075, $ \mu $, 0$ \tau_{\mathrm{h}} $) (lower right) are displayed. The predicted background yields are shown with the values of the normalizations and nuisance parameters obtained in backgroundonly fits applied (``postfit''). The HNL predictions for three different $ m_{\mathrm{N}} $ values with exclusive coupling to electron (left column) or muon (right column) neutrinos are shown with coloured lines. The vertical bars on the points represent the statistical uncertainties in the data, and the hatched bands the total uncertainties in the background predictions as obtained from the fits. In the lower panels, the ratios of the event yield in data to the overall sum of the background predictions are shown. 
png pdf 
Figure 9d:
Comparison of the observed (points) and predicted (coloured histograms) BDT output distributions of the lowmass selection, shown for the $ \mathrm{e}\mathrm{e}\mathrm{e} $ and $ \mathrm{e}\mathrm{e}\mu $ channels combined (left column) and the $ \mathrm{e}\mu\mu $ and $ \mu\mu\mu $ channels combined (right column). The output scores BDT(1040, e, 0$ \tau_{\mathrm{h}} $) (upper left), BDT(1040, $ \mu $, 0$ \tau_{\mathrm{h}} $) (upper right), BDT(5075, e, 0$ \tau_{\mathrm{h}} $) (lower left), and BDT(5075, $ \mu $, 0$ \tau_{\mathrm{h}} $) (lower right) are displayed. The predicted background yields are shown with the values of the normalizations and nuisance parameters obtained in backgroundonly fits applied (``postfit''). The HNL predictions for three different $ m_{\mathrm{N}} $ values with exclusive coupling to electron (left column) or muon (right column) neutrinos are shown with coloured lines. The vertical bars on the points represent the statistical uncertainties in the data, and the hatched bands the total uncertainties in the background predictions as obtained from the fits. In the lower panels, the ratios of the event yield in data to the overall sum of the background predictions are shown. 
png pdf 
Figure 10:
Comparison of the observed (points) and predicted (coloured histograms) BDT output distributions of the lowmass selection, shown for the 0$ \tau_{\mathrm{h}} $ channels combined (left column) and the 1$ \tau_{\mathrm{h}} $ channels combined (right column). The output scores BDT(1040, $ \tau $, 0$ \tau_{\mathrm{h}} $) (upper left), BDT(1040, $ \tau $, 1$ \tau_{\mathrm{h}} $) (upper right), BDT(5075, $ \tau $, 0$ \tau_{\mathrm{h}} $) (lower left), and BDT(5075, $ \tau $, 0$ \tau_{\mathrm{h}} $) (lower right) are displayed. The predicted background yields are shown with the values of the normalizations and nuisance parameters obtained in backgroundonly fits applied (``postfit''). The HNL predictions for three different $ m_{\mathrm{N}} $ values with exclusive coupling to tau neutrinos are shown with coloured lines. The vertical bars on the points represent the statistical uncertainties in the data, and the hatched bands the total uncertainties in the background predictions as obtained from the fits. In the lower panels, the ratios of the event yield in data to the overall sum of the background predictions are shown. 
png pdf 
Figure 10a:
Comparison of the observed (points) and predicted (coloured histograms) BDT output distributions of the lowmass selection, shown for the 0$ \tau_{\mathrm{h}} $ channels combined (left column) and the 1$ \tau_{\mathrm{h}} $ channels combined (right column). The output scores BDT(1040, $ \tau $, 0$ \tau_{\mathrm{h}} $) (upper left), BDT(1040, $ \tau $, 1$ \tau_{\mathrm{h}} $) (upper right), BDT(5075, $ \tau $, 0$ \tau_{\mathrm{h}} $) (lower left), and BDT(5075, $ \tau $, 0$ \tau_{\mathrm{h}} $) (lower right) are displayed. The predicted background yields are shown with the values of the normalizations and nuisance parameters obtained in backgroundonly fits applied (``postfit''). The HNL predictions for three different $ m_{\mathrm{N}} $ values with exclusive coupling to tau neutrinos are shown with coloured lines. The vertical bars on the points represent the statistical uncertainties in the data, and the hatched bands the total uncertainties in the background predictions as obtained from the fits. In the lower panels, the ratios of the event yield in data to the overall sum of the background predictions are shown. 
png pdf 
Figure 10b:
Comparison of the observed (points) and predicted (coloured histograms) BDT output distributions of the lowmass selection, shown for the 0$ \tau_{\mathrm{h}} $ channels combined (left column) and the 1$ \tau_{\mathrm{h}} $ channels combined (right column). The output scores BDT(1040, $ \tau $, 0$ \tau_{\mathrm{h}} $) (upper left), BDT(1040, $ \tau $, 1$ \tau_{\mathrm{h}} $) (upper right), BDT(5075, $ \tau $, 0$ \tau_{\mathrm{h}} $) (lower left), and BDT(5075, $ \tau $, 0$ \tau_{\mathrm{h}} $) (lower right) are displayed. The predicted background yields are shown with the values of the normalizations and nuisance parameters obtained in backgroundonly fits applied (``postfit''). The HNL predictions for three different $ m_{\mathrm{N}} $ values with exclusive coupling to tau neutrinos are shown with coloured lines. The vertical bars on the points represent the statistical uncertainties in the data, and the hatched bands the total uncertainties in the background predictions as obtained from the fits. In the lower panels, the ratios of the event yield in data to the overall sum of the background predictions are shown. 
png pdf 
Figure 10c:
Comparison of the observed (points) and predicted (coloured histograms) BDT output distributions of the lowmass selection, shown for the 0$ \tau_{\mathrm{h}} $ channels combined (left column) and the 1$ \tau_{\mathrm{h}} $ channels combined (right column). The output scores BDT(1040, $ \tau $, 0$ \tau_{\mathrm{h}} $) (upper left), BDT(1040, $ \tau $, 1$ \tau_{\mathrm{h}} $) (upper right), BDT(5075, $ \tau $, 0$ \tau_{\mathrm{h}} $) (lower left), and BDT(5075, $ \tau $, 0$ \tau_{\mathrm{h}} $) (lower right) are displayed. The predicted background yields are shown with the values of the normalizations and nuisance parameters obtained in backgroundonly fits applied (``postfit''). The HNL predictions for three different $ m_{\mathrm{N}} $ values with exclusive coupling to tau neutrinos are shown with coloured lines. The vertical bars on the points represent the statistical uncertainties in the data, and the hatched bands the total uncertainties in the background predictions as obtained from the fits. In the lower panels, the ratios of the event yield in data to the overall sum of the background predictions are shown. 
png pdf 
Figure 10d:
Comparison of the observed (points) and predicted (coloured histograms) BDT output distributions of the lowmass selection, shown for the 0$ \tau_{\mathrm{h}} $ channels combined (left column) and the 1$ \tau_{\mathrm{h}} $ channels combined (right column). The output scores BDT(1040, $ \tau $, 0$ \tau_{\mathrm{h}} $) (upper left), BDT(1040, $ \tau $, 1$ \tau_{\mathrm{h}} $) (upper right), BDT(5075, $ \tau $, 0$ \tau_{\mathrm{h}} $) (lower left), and BDT(5075, $ \tau $, 0$ \tau_{\mathrm{h}} $) (lower right) are displayed. The predicted background yields are shown with the values of the normalizations and nuisance parameters obtained in backgroundonly fits applied (``postfit''). The HNL predictions for three different $ m_{\mathrm{N}} $ values with exclusive coupling to tau neutrinos are shown with coloured lines. The vertical bars on the points represent the statistical uncertainties in the data, and the hatched bands the total uncertainties in the background predictions as obtained from the fits. In the lower panels, the ratios of the event yield in data to the overall sum of the background predictions are shown. 
png pdf 
Figure 11:
Comparison of the observed (points) and predicted (coloured histograms) BDT output distributions of the highmass selection, shown for the $ \mathrm{e}\mathrm{e}\mathrm{e} $ and $ \mathrm{e}\mathrm{e}\mu $ channels combined (left column) and the $ \mathrm{e}\mu\mu $ and $ \mu\mu\mu $ channels combined (right column). The output scores BDT(85150, e, 0$ \tau_{\mathrm{h}} $) (upper left), BDT(85150, $ \mu $, 0$ \tau_{\mathrm{h}} $) (upper right), BDT(200250, e, 0$ \tau_{\mathrm{h}} $) (middle left), BDT(200250, $ \mu $, 0$ \tau_{\mathrm{h}} $) (middle right), BDT(300400, e, 0$ \tau_{\mathrm{h}} $) (lower left), and BDT(300400, $ \mu $, 0$ \tau_{\mathrm{h}} $) (lower right) are displayed. Notations as in Fig. 9. 
png pdf 
Figure 11a:
Comparison of the observed (points) and predicted (coloured histograms) BDT output distributions of the highmass selection, shown for the $ \mathrm{e}\mathrm{e}\mathrm{e} $ and $ \mathrm{e}\mathrm{e}\mu $ channels combined (left column) and the $ \mathrm{e}\mu\mu $ and $ \mu\mu\mu $ channels combined (right column). The output scores BDT(85150, e, 0$ \tau_{\mathrm{h}} $) (upper left), BDT(85150, $ \mu $, 0$ \tau_{\mathrm{h}} $) (upper right), BDT(200250, e, 0$ \tau_{\mathrm{h}} $) (middle left), BDT(200250, $ \mu $, 0$ \tau_{\mathrm{h}} $) (middle right), BDT(300400, e, 0$ \tau_{\mathrm{h}} $) (lower left), and BDT(300400, $ \mu $, 0$ \tau_{\mathrm{h}} $) (lower right) are displayed. Notations as in Fig. 9. 
png pdf 
Figure 11b:
Comparison of the observed (points) and predicted (coloured histograms) BDT output distributions of the highmass selection, shown for the $ \mathrm{e}\mathrm{e}\mathrm{e} $ and $ \mathrm{e}\mathrm{e}\mu $ channels combined (left column) and the $ \mathrm{e}\mu\mu $ and $ \mu\mu\mu $ channels combined (right column). The output scores BDT(85150, e, 0$ \tau_{\mathrm{h}} $) (upper left), BDT(85150, $ \mu $, 0$ \tau_{\mathrm{h}} $) (upper right), BDT(200250, e, 0$ \tau_{\mathrm{h}} $) (middle left), BDT(200250, $ \mu $, 0$ \tau_{\mathrm{h}} $) (middle right), BDT(300400, e, 0$ \tau_{\mathrm{h}} $) (lower left), and BDT(300400, $ \mu $, 0$ \tau_{\mathrm{h}} $) (lower right) are displayed. Notations as in Fig. 9. 
png pdf 
Figure 11c:
Comparison of the observed (points) and predicted (coloured histograms) BDT output distributions of the highmass selection, shown for the $ \mathrm{e}\mathrm{e}\mathrm{e} $ and $ \mathrm{e}\mathrm{e}\mu $ channels combined (left column) and the $ \mathrm{e}\mu\mu $ and $ \mu\mu\mu $ channels combined (right column). The output scores BDT(85150, e, 0$ \tau_{\mathrm{h}} $) (upper left), BDT(85150, $ \mu $, 0$ \tau_{\mathrm{h}} $) (upper right), BDT(200250, e, 0$ \tau_{\mathrm{h}} $) (middle left), BDT(200250, $ \mu $, 0$ \tau_{\mathrm{h}} $) (middle right), BDT(300400, e, 0$ \tau_{\mathrm{h}} $) (lower left), and BDT(300400, $ \mu $, 0$ \tau_{\mathrm{h}} $) (lower right) are displayed. Notations as in Fig. 9. 
png pdf 
Figure 11d:
Comparison of the observed (points) and predicted (coloured histograms) BDT output distributions of the highmass selection, shown for the $ \mathrm{e}\mathrm{e}\mathrm{e} $ and $ \mathrm{e}\mathrm{e}\mu $ channels combined (left column) and the $ \mathrm{e}\mu\mu $ and $ \mu\mu\mu $ channels combined (right column). The output scores BDT(85150, e, 0$ \tau_{\mathrm{h}} $) (upper left), BDT(85150, $ \mu $, 0$ \tau_{\mathrm{h}} $) (upper right), BDT(200250, e, 0$ \tau_{\mathrm{h}} $) (middle left), BDT(200250, $ \mu $, 0$ \tau_{\mathrm{h}} $) (middle right), BDT(300400, e, 0$ \tau_{\mathrm{h}} $) (lower left), and BDT(300400, $ \mu $, 0$ \tau_{\mathrm{h}} $) (lower right) are displayed. Notations as in Fig. 9. 
png pdf 
Figure 11e:
Comparison of the observed (points) and predicted (coloured histograms) BDT output distributions of the highmass selection, shown for the $ \mathrm{e}\mathrm{e}\mathrm{e} $ and $ \mathrm{e}\mathrm{e}\mu $ channels combined (left column) and the $ \mathrm{e}\mu\mu $ and $ \mu\mu\mu $ channels combined (right column). The output scores BDT(85150, e, 0$ \tau_{\mathrm{h}} $) (upper left), BDT(85150, $ \mu $, 0$ \tau_{\mathrm{h}} $) (upper right), BDT(200250, e, 0$ \tau_{\mathrm{h}} $) (middle left), BDT(200250, $ \mu $, 0$ \tau_{\mathrm{h}} $) (middle right), BDT(300400, e, 0$ \tau_{\mathrm{h}} $) (lower left), and BDT(300400, $ \mu $, 0$ \tau_{\mathrm{h}} $) (lower right) are displayed. Notations as in Fig. 9. 
png pdf 
Figure 11f:
Comparison of the observed (points) and predicted (coloured histograms) BDT output distributions of the highmass selection, shown for the $ \mathrm{e}\mathrm{e}\mathrm{e} $ and $ \mathrm{e}\mathrm{e}\mu $ channels combined (left column) and the $ \mathrm{e}\mu\mu $ and $ \mu\mu\mu $ channels combined (right column). The output scores BDT(85150, e, 0$ \tau_{\mathrm{h}} $) (upper left), BDT(85150, $ \mu $, 0$ \tau_{\mathrm{h}} $) (upper right), BDT(200250, e, 0$ \tau_{\mathrm{h}} $) (middle left), BDT(200250, $ \mu $, 0$ \tau_{\mathrm{h}} $) (middle right), BDT(300400, e, 0$ \tau_{\mathrm{h}} $) (lower left), and BDT(300400, $ \mu $, 0$ \tau_{\mathrm{h}} $) (lower right) are displayed. Notations as in Fig. 9. 
png pdf 
Figure 12:
The 95% CL limits on $ V_{\mathrm{e}\mathrm{N}}^2 $ (upper row), $ V_{\mu\mathrm{N}}^2 $ (middle row), and $ V_{\tau\mathrm{N}}^2 $ (lower row) as functions of $ m_{\mathrm{N}} $ for a Majorana (left) and Dirac (right) HNL. The area above the solid (dashed) black curve indicates the observed (expected) exclusion region. Previous results from the DELPHI Collaboration [142] are shown for reference. The previous CMS result ``3\ell prompt (2016)'' [46] is shown to highlight the improvements achieved in our analysis, and the results ``3\ell displaced'' [50], ``2\ell displaced'' [52], and ``$ t $channel VBF'' [143] are shown to highlight the complementarity to other search strategies. 
png pdf 
Figure 12a:
The 95% CL limits on $ V_{\mathrm{e}\mathrm{N}}^2 $ (upper row), $ V_{\mu\mathrm{N}}^2 $ (middle row), and $ V_{\tau\mathrm{N}}^2 $ (lower row) as functions of $ m_{\mathrm{N}} $ for a Majorana (left) and Dirac (right) HNL. The area above the solid (dashed) black curve indicates the observed (expected) exclusion region. Previous results from the DELPHI Collaboration [142] are shown for reference. The previous CMS result ``3\ell prompt (2016)'' [46] is shown to highlight the improvements achieved in our analysis, and the results ``3\ell displaced'' [50], ``2\ell displaced'' [52], and ``$ t $channel VBF'' [143] are shown to highlight the complementarity to other search strategies. 
png pdf 
Figure 12b:
The 95% CL limits on $ V_{\mathrm{e}\mathrm{N}}^2 $ (upper row), $ V_{\mu\mathrm{N}}^2 $ (middle row), and $ V_{\tau\mathrm{N}}^2 $ (lower row) as functions of $ m_{\mathrm{N}} $ for a Majorana (left) and Dirac (right) HNL. The area above the solid (dashed) black curve indicates the observed (expected) exclusion region. Previous results from the DELPHI Collaboration [142] are shown for reference. The previous CMS result ``3\ell prompt (2016)'' [46] is shown to highlight the improvements achieved in our analysis, and the results ``3\ell displaced'' [50], ``2\ell displaced'' [52], and ``$ t $channel VBF'' [143] are shown to highlight the complementarity to other search strategies. 
png pdf 
Figure 12c:
The 95% CL limits on $ V_{\mathrm{e}\mathrm{N}}^2 $ (upper row), $ V_{\mu\mathrm{N}}^2 $ (middle row), and $ V_{\tau\mathrm{N}}^2 $ (lower row) as functions of $ m_{\mathrm{N}} $ for a Majorana (left) and Dirac (right) HNL. The area above the solid (dashed) black curve indicates the observed (expected) exclusion region. Previous results from the DELPHI Collaboration [142] are shown for reference. The previous CMS result ``3\ell prompt (2016)'' [46] is shown to highlight the improvements achieved in our analysis, and the results ``3\ell displaced'' [50], ``2\ell displaced'' [52], and ``$ t $channel VBF'' [143] are shown to highlight the complementarity to other search strategies. 
png pdf 
Figure 12d:
The 95% CL limits on $ V_{\mathrm{e}\mathrm{N}}^2 $ (upper row), $ V_{\mu\mathrm{N}}^2 $ (middle row), and $ V_{\tau\mathrm{N}}^2 $ (lower row) as functions of $ m_{\mathrm{N}} $ for a Majorana (left) and Dirac (right) HNL. The area above the solid (dashed) black curve indicates the observed (expected) exclusion region. Previous results from the DELPHI Collaboration [142] are shown for reference. The previous CMS result ``3\ell prompt (2016)'' [46] is shown to highlight the improvements achieved in our analysis, and the results ``3\ell displaced'' [50], ``2\ell displaced'' [52], and ``$ t $channel VBF'' [143] are shown to highlight the complementarity to other search strategies. 
png pdf 
Figure 12e:
The 95% CL limits on $ V_{\mathrm{e}\mathrm{N}}^2 $ (upper row), $ V_{\mu\mathrm{N}}^2 $ (middle row), and $ V_{\tau\mathrm{N}}^2 $ (lower row) as functions of $ m_{\mathrm{N}} $ for a Majorana (left) and Dirac (right) HNL. The area above the solid (dashed) black curve indicates the observed (expected) exclusion region. Previous results from the DELPHI Collaboration [142] are shown for reference. The previous CMS result ``3\ell prompt (2016)'' [46] is shown to highlight the improvements achieved in our analysis, and the results ``3\ell displaced'' [50], ``2\ell displaced'' [52], and ``$ t $channel VBF'' [143] are shown to highlight the complementarity to other search strategies. 
png pdf 
Figure 12f:
The 95% CL limits on $ V_{\mathrm{e}\mathrm{N}}^2 $ (upper row), $ V_{\mu\mathrm{N}}^2 $ (middle row), and $ V_{\tau\mathrm{N}}^2 $ (lower row) as functions of $ m_{\mathrm{N}} $ for a Majorana (left) and Dirac (right) HNL. The area above the solid (dashed) black curve indicates the observed (expected) exclusion region. Previous results from the DELPHI Collaboration [142] are shown for reference. The previous CMS result ``3\ell prompt (2016)'' [46] is shown to highlight the improvements achieved in our analysis, and the results ``3\ell displaced'' [50], ``2\ell displaced'' [52], and ``$ t $channel VBF'' [143] are shown to highlight the complementarity to other search strategies. 
Tables  
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Table 1:
Requirements on the lightlepton $ p_{\mathrm{T}} $ values in the online and offline selections. The first two columns give the numbers of electrons and muons in the event ($ N_{\mathrm{e}} $ and $ N_{\mu} $). The third column lists the $ p_{\mathrm{T}} $ thresholds on the reconstructed electrons and muons in the online trigger selection, where the indices 1, 2, and 3 refer to the highest $ p_{\mathrm{T}} $, secondhighest $ p_{\mathrm{T}} $, and thirdhighest $ p_{\mathrm{T}} $ lepton, respectively. The fourth column lists the offline event selection requirements applied in addition to the baseline requirements of $ p_{\mathrm{T}^{\ell_1} > $ 15 GeV and $ p_{\mathrm{T}^{\ell_{2,3}} > $ 10 GeV, where $\ell$ refers to reconstructed leptons of any flavour. For the $ \mathrm{e}\mu $ trigger, the requirements are given for the highest and secondhighest $ p_{\mathrm{T}} $ light lepton, referred to as $ \ell_1 $ and $ \ell_2 $ to indicate that a $ \tau_{\mathrm{h}} $ present in the event is not considered for the ordering. The values in parentheses give the thresholds applied in 2017 and 2018, where they are different from 2016. All events are required to pass the conditions of at least one of the rows. 
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Table 2:
Definitions of the search regions (SRs) for events in the lowmass (upper part) and highmass (lower part) selections. 
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Table 3:
Relative impacts of the uncertainty sources in fits for six different fit models specified with $ m_{\mathrm{N}} $ value and coupling scenario, where the relative impact is defined as the ratio between the uncertainty from the respective source and the total uncertainty in the HNL signal strength. The symbol ``$ \text{} $'' indicates that the corresponding uncertainty source is not applicable. 
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Table 4:
Summary of the selections, categories, and distributions used in the maximum likelihood fits for the HNL signal points. 
Summary 
A search for heavy neutral leptons (HNLs) produced in protonproton collisions at $ \sqrt{s} = $ 13 TeV has been presented. The data were collected with the CMS experiment at the LHC and correspond to an integrated luminosity of 138 fb$ ^{1} $. Events with three charged leptons (electrons, muons, and hadronically decaying tau leptons) are selected, and dedicated identification criteria based on machine learning techniques are applied to reduce the contribution from nonprompt leptons not originating from the hard scattering process. Remaining standard model (SM) background contributions with nonprompt leptons are estimated from control samples in data, whereas other SM contributions that mostly stem from diboson production are estimated from Monte Carlo event simulations. A combination of categorization by kinematic properties and machine learning discriminants achieves optimal separation of the predicted signal and SM background contributions. No significant deviations from the SM predictions are observed. Exclusion limits at 95% confidence level are evaluated, assuming exclusive HNL couplings to a single generation of SM neutrinos in the mass range 10 GeV1.5 TeV, for both Majorana and Dirac HNLs. These results exceed previous experimental constraints over large parts of the mass range. Constraints on tau neutrino couplings for HNL masses above the W boson mass are presented for the first time. 
References  
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