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CMS-PAS-EXO-21-011
Search for long-lived heavy neutral leptons in proton-proton collision events with a lepton and a jet from a secondary vertex at $ \sqrt{s}= $ 13 TeV
Abstract: A search for long-lived heavy neutral leptons (HNLs) using proton-proton collision data with an integrated luminosity corresponding to 138 fb$ ^{-1} $ collected at $ \sqrt{s}= $ 13 TeV with the CMS detector at the CERN LHC is presented. The HNLs are searched for in events with a secondary vertex, corresponding to the semileptonic decay of a long-lived HNL. The final states include the presence of a charged lepton originating from the primary vertex, as well as a second charged lepton and a hadronic jet that are associated with the secondary vertex. No excess of events above the standard model expectation is observed. Exclusion limits at 95% confidence level are evaluated on the HNL masses and the mixing parameters with the standard model neutrinos in the mass range 1-16 GeV, with excluded squared mixing parameter values reaching as low as 10$^{-7} $.
Figures & Tables Summary References CMS Publications
Figures

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Figure 1:
Example of LO Feynman diagrams for HNL production and decay resulting in a final state with two charged leptons and two quarks. In the left diagram, the HNL is a Dirac particle and thus the two charged leptons must have opposite charge. In the right diagram, the HNL is a Majorana particle and the two charged leptons can have the same charge.

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Figure 1-a:
Example of LO Feynman diagrams for HNL production and decay resulting in a final state with two charged leptons and two quarks. In the left diagram, the HNL is a Dirac particle and thus the two charged leptons must have opposite charge. In the right diagram, the HNL is a Majorana particle and the two charged leptons can have the same charge.

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Figure 1-b:
Example of LO Feynman diagrams for HNL production and decay resulting in a final state with two charged leptons and two quarks. In the left diagram, the HNL is a Dirac particle and thus the two charged leptons must have opposite charge. In the right diagram, the HNL is a Majorana particle and the two charged leptons can have the same charge.

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Figure 2:
Selection efficiencies of nonprompt electrons (upper) and muons (lower), evaluated in simulated HNL signal events as a function of generated lepton $ p_{\mathrm{T}} $ (left) and of the transverse displacement $ L_{xy} $ of the generated SV (right). The error bars in the plot represent statistical uncertainties.

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Figure 2-a:
Selection efficiencies of nonprompt electrons (upper) and muons (lower), evaluated in simulated HNL signal events as a function of generated lepton $ p_{\mathrm{T}} $ (left) and of the transverse displacement $ L_{xy} $ of the generated SV (right). The error bars in the plot represent statistical uncertainties.

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Figure 2-b:
Selection efficiencies of nonprompt electrons (upper) and muons (lower), evaluated in simulated HNL signal events as a function of generated lepton $ p_{\mathrm{T}} $ (left) and of the transverse displacement $ L_{xy} $ of the generated SV (right). The error bars in the plot represent statistical uncertainties.

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Figure 2-c:
Selection efficiencies of nonprompt electrons (upper) and muons (lower), evaluated in simulated HNL signal events as a function of generated lepton $ p_{\mathrm{T}} $ (left) and of the transverse displacement $ L_{xy} $ of the generated SV (right). The error bars in the plot represent statistical uncertainties.

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Figure 2-d:
Selection efficiencies of nonprompt electrons (upper) and muons (lower), evaluated in simulated HNL signal events as a function of generated lepton $ p_{\mathrm{T}} $ (left) and of the transverse displacement $ L_{xy} $ of the generated SV (right). The error bars in the plot represent statistical uncertainties.

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Figure 3:
SV reconstruction efficiency in simulated HNL signal events as a function of the SV displacement for vertices with a nonprompt muon (left) or electron (right).

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Figure 3-a:
SV reconstruction efficiency in simulated HNL signal events as a function of the SV displacement for vertices with a nonprompt muon (left) or electron (right).

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Figure 3-b:
SV reconstruction efficiency in simulated HNL signal events as a function of the SV displacement for vertices with a nonprompt muon (left) or electron (right).

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Figure 4:
The $ m(\ell_1,\text{SV}) $ distribution of predicted events yields after applying the selection summarized in Table 1, for the OS $ \mathrm{e}\mathrm{e} $ (upper left), SS $ \mathrm{e}\mathrm{e} $ (upper right), OS $ \mu\mu $ (middle left), SS $ \mu\mu $ (middle right), OS and SS $ \mathrm{e}\mu $ (lower left), and OS and SS $ \mu\mathrm{e} $ (lower right) categories. The filled histograms display the predicted background yields. The lines show the predicted yields fro three HNL signal scenarios, with $ m_{\mathrm{N}} = $ 2 GeV and $ |V_{\ell{\mathrm{N}} }|^2=4\times10^{-4} $ (HNL2), $ m_{\mathrm{N}} = $ 6 GeV and $ |V_{\ell{\mathrm{N}} }|^2=4\times10^{-6} $ (HNL6), and $ m_{\mathrm{N}} = $ 10 GeV and $ |V_{\ell{\mathrm{N}} }|^2=4\times10^{-8} $ (HNL10). The last bins include overflow contributions.

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Figure 4-a:
The $ m(\ell_1,\text{SV}) $ distribution of predicted events yields after applying the selection summarized in Table 1, for the OS $ \mathrm{e}\mathrm{e} $ (upper left), SS $ \mathrm{e}\mathrm{e} $ (upper right), OS $ \mu\mu $ (middle left), SS $ \mu\mu $ (middle right), OS and SS $ \mathrm{e}\mu $ (lower left), and OS and SS $ \mu\mathrm{e} $ (lower right) categories. The filled histograms display the predicted background yields. The lines show the predicted yields fro three HNL signal scenarios, with $ m_{\mathrm{N}} = $ 2 GeV and $ |V_{\ell{\mathrm{N}} }|^2=4\times10^{-4} $ (HNL2), $ m_{\mathrm{N}} = $ 6 GeV and $ |V_{\ell{\mathrm{N}} }|^2=4\times10^{-6} $ (HNL6), and $ m_{\mathrm{N}} = $ 10 GeV and $ |V_{\ell{\mathrm{N}} }|^2=4\times10^{-8} $ (HNL10). The last bins include overflow contributions.

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Figure 4-b:
The $ m(\ell_1,\text{SV}) $ distribution of predicted events yields after applying the selection summarized in Table 1, for the OS $ \mathrm{e}\mathrm{e} $ (upper left), SS $ \mathrm{e}\mathrm{e} $ (upper right), OS $ \mu\mu $ (middle left), SS $ \mu\mu $ (middle right), OS and SS $ \mathrm{e}\mu $ (lower left), and OS and SS $ \mu\mathrm{e} $ (lower right) categories. The filled histograms display the predicted background yields. The lines show the predicted yields fro three HNL signal scenarios, with $ m_{\mathrm{N}} = $ 2 GeV and $ |V_{\ell{\mathrm{N}} }|^2=4\times10^{-4} $ (HNL2), $ m_{\mathrm{N}} = $ 6 GeV and $ |V_{\ell{\mathrm{N}} }|^2=4\times10^{-6} $ (HNL6), and $ m_{\mathrm{N}} = $ 10 GeV and $ |V_{\ell{\mathrm{N}} }|^2=4\times10^{-8} $ (HNL10). The last bins include overflow contributions.

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Figure 4-c:
The $ m(\ell_1,\text{SV}) $ distribution of predicted events yields after applying the selection summarized in Table 1, for the OS $ \mathrm{e}\mathrm{e} $ (upper left), SS $ \mathrm{e}\mathrm{e} $ (upper right), OS $ \mu\mu $ (middle left), SS $ \mu\mu $ (middle right), OS and SS $ \mathrm{e}\mu $ (lower left), and OS and SS $ \mu\mathrm{e} $ (lower right) categories. The filled histograms display the predicted background yields. The lines show the predicted yields fro three HNL signal scenarios, with $ m_{\mathrm{N}} = $ 2 GeV and $ |V_{\ell{\mathrm{N}} }|^2=4\times10^{-4} $ (HNL2), $ m_{\mathrm{N}} = $ 6 GeV and $ |V_{\ell{\mathrm{N}} }|^2=4\times10^{-6} $ (HNL6), and $ m_{\mathrm{N}} = $ 10 GeV and $ |V_{\ell{\mathrm{N}} }|^2=4\times10^{-8} $ (HNL10). The last bins include overflow contributions.

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Figure 4-d:
The $ m(\ell_1,\text{SV}) $ distribution of predicted events yields after applying the selection summarized in Table 1, for the OS $ \mathrm{e}\mathrm{e} $ (upper left), SS $ \mathrm{e}\mathrm{e} $ (upper right), OS $ \mu\mu $ (middle left), SS $ \mu\mu $ (middle right), OS and SS $ \mathrm{e}\mu $ (lower left), and OS and SS $ \mu\mathrm{e} $ (lower right) categories. The filled histograms display the predicted background yields. The lines show the predicted yields fro three HNL signal scenarios, with $ m_{\mathrm{N}} = $ 2 GeV and $ |V_{\ell{\mathrm{N}} }|^2=4\times10^{-4} $ (HNL2), $ m_{\mathrm{N}} = $ 6 GeV and $ |V_{\ell{\mathrm{N}} }|^2=4\times10^{-6} $ (HNL6), and $ m_{\mathrm{N}} = $ 10 GeV and $ |V_{\ell{\mathrm{N}} }|^2=4\times10^{-8} $ (HNL10). The last bins include overflow contributions.

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Figure 4-e:
The $ m(\ell_1,\text{SV}) $ distribution of predicted events yields after applying the selection summarized in Table 1, for the OS $ \mathrm{e}\mathrm{e} $ (upper left), SS $ \mathrm{e}\mathrm{e} $ (upper right), OS $ \mu\mu $ (middle left), SS $ \mu\mu $ (middle right), OS and SS $ \mathrm{e}\mu $ (lower left), and OS and SS $ \mu\mathrm{e} $ (lower right) categories. The filled histograms display the predicted background yields. The lines show the predicted yields fro three HNL signal scenarios, with $ m_{\mathrm{N}} = $ 2 GeV and $ |V_{\ell{\mathrm{N}} }|^2=4\times10^{-4} $ (HNL2), $ m_{\mathrm{N}} = $ 6 GeV and $ |V_{\ell{\mathrm{N}} }|^2=4\times10^{-6} $ (HNL6), and $ m_{\mathrm{N}} = $ 10 GeV and $ |V_{\ell{\mathrm{N}} }|^2=4\times10^{-8} $ (HNL10). The last bins include overflow contributions.

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Figure 4-f:
The $ m(\ell_1,\text{SV}) $ distribution of predicted events yields after applying the selection summarized in Table 1, for the OS $ \mathrm{e}\mathrm{e} $ (upper left), SS $ \mathrm{e}\mathrm{e} $ (upper right), OS $ \mu\mu $ (middle left), SS $ \mu\mu $ (middle right), OS and SS $ \mathrm{e}\mu $ (lower left), and OS and SS $ \mu\mathrm{e} $ (lower right) categories. The filled histograms display the predicted background yields. The lines show the predicted yields fro three HNL signal scenarios, with $ m_{\mathrm{N}} = $ 2 GeV and $ |V_{\ell{\mathrm{N}} }|^2=4\times10^{-4} $ (HNL2), $ m_{\mathrm{N}} = $ 6 GeV and $ |V_{\ell{\mathrm{N}} }|^2=4\times10^{-6} $ (HNL6), and $ m_{\mathrm{N}} = $ 10 GeV and $ |V_{\ell{\mathrm{N}} }|^2=4\times10^{-8} $ (HNL10). The last bins include overflow contributions.

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Figure 5:
Distributions of the PFN score for $ \mathrm{K^0_S}\to\pi^{+}\pi^{-} $ decays in $ \mathrm{Z}\to\mu^{+}\mu^{-} $ events, using the low-mass PFNs for the electron (left) and muon (right) channels, where the higher-$ p_{\mathrm{T}} \pi^{\pm} $ is treated as lepton. The selected data are compared with simulated DY events with the same selection.

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Figure 5-a:
Distributions of the PFN score for $ \mathrm{K^0_S}\to\pi^{+}\pi^{-} $ decays in $ \mathrm{Z}\to\mu^{+}\mu^{-} $ events, using the low-mass PFNs for the electron (left) and muon (right) channels, where the higher-$ p_{\mathrm{T}} \pi^{\pm} $ is treated as lepton. The selected data are compared with simulated DY events with the same selection.

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Figure 5-b:
Distributions of the PFN score for $ \mathrm{K^0_S}\to\pi^{+}\pi^{-} $ decays in $ \mathrm{Z}\to\mu^{+}\mu^{-} $ events, using the low-mass PFNs for the electron (left) and muon (right) channels, where the higher-$ p_{\mathrm{T}} \pi^{\pm} $ is treated as lepton. The selected data are compared with simulated DY events with the same selection.

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Figure 6:
Illustration of the target and sideband region definitions for the ABCD method applied to the SR, in terms of $ N $ (jets), $ m(\ell_1,\text{SV}) $, and the PFN score.

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Figure 7:
PFN scores in data in the VR, shown for the electron (left) and muon (right) trainings with the low- (upper) and high-mass (lower) samples. The distributions are normalized to unity to facilitate a shape comparison.

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Figure 7-a:
PFN scores in data in the VR, shown for the electron (left) and muon (right) trainings with the low- (upper) and high-mass (lower) samples. The distributions are normalized to unity to facilitate a shape comparison.

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Figure 7-b:
PFN scores in data in the VR, shown for the electron (left) and muon (right) trainings with the low- (upper) and high-mass (lower) samples. The distributions are normalized to unity to facilitate a shape comparison.

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Figure 7-c:
PFN scores in data in the VR, shown for the electron (left) and muon (right) trainings with the low- (upper) and high-mass (lower) samples. The distributions are normalized to unity to facilitate a shape comparison.

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Figure 7-d:
PFN scores in data in the VR, shown for the electron (left) and muon (right) trainings with the low- (upper) and high-mass (lower) samples. The distributions are normalized to unity to facilitate a shape comparison.

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Figure 8:
Predicted and observed event yields in the CR for the low- (upper) and high-mass (lower) PFNs in the SS categories, binned flavor channel, $ m_{\text{SV}} $ (as specified below the flavor channel), and $ \Delta_{\mathrm{2D}} $. The hashed bands represent the total uncertainty in the background prediction. The lower panels show the data-to-prediction ratio and the background prediction uncertainty includes both statistical (blue) and systematic (green) contributions.

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Figure 8-a:
Predicted and observed event yields in the CR for the low- (upper) and high-mass (lower) PFNs in the SS categories, binned flavor channel, $ m_{\text{SV}} $ (as specified below the flavor channel), and $ \Delta_{\mathrm{2D}} $. The hashed bands represent the total uncertainty in the background prediction. The lower panels show the data-to-prediction ratio and the background prediction uncertainty includes both statistical (blue) and systematic (green) contributions.

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Figure 8-b:
Predicted and observed event yields in the CR for the low- (upper) and high-mass (lower) PFNs in the SS categories, binned flavor channel, $ m_{\text{SV}} $ (as specified below the flavor channel), and $ \Delta_{\mathrm{2D}} $. The hashed bands represent the total uncertainty in the background prediction. The lower panels show the data-to-prediction ratio and the background prediction uncertainty includes both statistical (blue) and systematic (green) contributions.

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Figure 9:
Predicted and observed event yields in the CR for the low- (upper) and high-mass (lower) PFNs in the OS categories, binned flavor channel, $ m_{\text{SV}} $ (as specified below the flavor channel), and $ \Delta_{\mathrm{2D}} $. The hashed bands represent the total uncertainty in the background prediction. The lower panels show the data-to-prediction ratio and the background prediction uncertainty includes both statistical (blue) and systematic (green) contributions.

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Figure 9-a:
Predicted and observed event yields in the CR for the low- (upper) and high-mass (lower) PFNs in the OS categories, binned flavor channel, $ m_{\text{SV}} $ (as specified below the flavor channel), and $ \Delta_{\mathrm{2D}} $. The hashed bands represent the total uncertainty in the background prediction. The lower panels show the data-to-prediction ratio and the background prediction uncertainty includes both statistical (blue) and systematic (green) contributions.

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Figure 9-b:
Predicted and observed event yields in the CR for the low- (upper) and high-mass (lower) PFNs in the OS categories, binned flavor channel, $ m_{\text{SV}} $ (as specified below the flavor channel), and $ \Delta_{\mathrm{2D}} $. The hashed bands represent the total uncertainty in the background prediction. The lower panels show the data-to-prediction ratio and the background prediction uncertainty includes both statistical (blue) and systematic (green) contributions.

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Figure 10:
Predicted and observed SR event yields for the SS categories of the low-mass (upper) and high-mass (lower) PFNs, binned flavor channel, $ m_{\text{SV}} $ (as specified below the flavor channel), and $ \Delta_{\mathrm{2D}} $. The hashed band represents the total systematic and statistical uncertainty in the background prediction. Signal predictions are shown for two HNL production hypotheses: $ m_{\mathrm{N}} = $ 3 and 5 GeV with $ |V_{\ell{\mathrm{N}} }|^2=2\times10^{-6} $. The lower panels show the data-to-prediction ratio and the background prediction uncertainty is split into statistical (blue) and systematic (green) contributions.

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Figure 10-a:
Predicted and observed SR event yields for the SS categories of the low-mass (upper) and high-mass (lower) PFNs, binned flavor channel, $ m_{\text{SV}} $ (as specified below the flavor channel), and $ \Delta_{\mathrm{2D}} $. The hashed band represents the total systematic and statistical uncertainty in the background prediction. Signal predictions are shown for two HNL production hypotheses: $ m_{\mathrm{N}} = $ 3 and 5 GeV with $ |V_{\ell{\mathrm{N}} }|^2=2\times10^{-6} $. The lower panels show the data-to-prediction ratio and the background prediction uncertainty is split into statistical (blue) and systematic (green) contributions.

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Figure 10-b:
Predicted and observed SR event yields for the SS categories of the low-mass (upper) and high-mass (lower) PFNs, binned flavor channel, $ m_{\text{SV}} $ (as specified below the flavor channel), and $ \Delta_{\mathrm{2D}} $. The hashed band represents the total systematic and statistical uncertainty in the background prediction. Signal predictions are shown for two HNL production hypotheses: $ m_{\mathrm{N}} = $ 3 and 5 GeV with $ |V_{\ell{\mathrm{N}} }|^2=2\times10^{-6} $. The lower panels show the data-to-prediction ratio and the background prediction uncertainty is split into statistical (blue) and systematic (green) contributions.

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Figure 11:
Predicted and observed SR event yields for the OS categories of the low-mass (upper) and high-mass (lower) PFNs, binned flavor channel, $ m_{\text{SV}} $ (as specified below the flavor channel), and $ \Delta_{\mathrm{2D}} $. The hashed band represents the total systematic and statistical uncertainty in the background prediction. Signal predictions are shown for two HNL production hypotheses: $ m_{\mathrm{N}} = $ 3 and 5 GeV with $ |V_{\ell{\mathrm{N}} }|^2=2\times10^{-6} $. The lower panels show the data-to-prediction ratio and the background prediction uncertainty is split into statistical (blue), main systematic (green), and DY scale factor (red) contributions.

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Figure 11-a:
Predicted and observed SR event yields for the OS categories of the low-mass (upper) and high-mass (lower) PFNs, binned flavor channel, $ m_{\text{SV}} $ (as specified below the flavor channel), and $ \Delta_{\mathrm{2D}} $. The hashed band represents the total systematic and statistical uncertainty in the background prediction. Signal predictions are shown for two HNL production hypotheses: $ m_{\mathrm{N}} = $ 3 and 5 GeV with $ |V_{\ell{\mathrm{N}} }|^2=2\times10^{-6} $. The lower panels show the data-to-prediction ratio and the background prediction uncertainty is split into statistical (blue), main systematic (green), and DY scale factor (red) contributions.

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Figure 11-b:
Predicted and observed SR event yields for the OS categories of the low-mass (upper) and high-mass (lower) PFNs, binned flavor channel, $ m_{\text{SV}} $ (as specified below the flavor channel), and $ \Delta_{\mathrm{2D}} $. The hashed band represents the total systematic and statistical uncertainty in the background prediction. Signal predictions are shown for two HNL production hypotheses: $ m_{\mathrm{N}} = $ 3 and 5 GeV with $ |V_{\ell{\mathrm{N}} }|^2=2\times10^{-6} $. The lower panels show the data-to-prediction ratio and the background prediction uncertainty is split into statistical (blue), main systematic (green), and DY scale factor (red) contributions.

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Figure 12:
Exclusion limits at 95% CL on $ |V_{\mathrm{e}{\mathrm{N}} }|^2 $ (upper row), $ |V_{\mu{\mathrm{N}} }|^2 $ (middle row), and $ |V_{\mathrm{e}{\mathrm{N}} }V_{\mu{\mathrm{N}} }|^2/(|V_{\mathrm{e}{\mathrm{N}} }|^2+|V_{\mu{\mathrm{N}} }|^2) $ (lower row) as a function of $ m_{\mathrm{N}} $ for a Majorana (left) and Dirac (right) HNL. The solid (dashed) black curve indicates the observed (expected) exclusion, where the parameter combinations inside the curve are excluded.

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Figure 12-a:
Exclusion limits at 95% CL on $ |V_{\mathrm{e}{\mathrm{N}} }|^2 $ (upper row), $ |V_{\mu{\mathrm{N}} }|^2 $ (middle row), and $ |V_{\mathrm{e}{\mathrm{N}} }V_{\mu{\mathrm{N}} }|^2/(|V_{\mathrm{e}{\mathrm{N}} }|^2+|V_{\mu{\mathrm{N}} }|^2) $ (lower row) as a function of $ m_{\mathrm{N}} $ for a Majorana (left) and Dirac (right) HNL. The solid (dashed) black curve indicates the observed (expected) exclusion, where the parameter combinations inside the curve are excluded.

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Figure 12-b:
Exclusion limits at 95% CL on $ |V_{\mathrm{e}{\mathrm{N}} }|^2 $ (upper row), $ |V_{\mu{\mathrm{N}} }|^2 $ (middle row), and $ |V_{\mathrm{e}{\mathrm{N}} }V_{\mu{\mathrm{N}} }|^2/(|V_{\mathrm{e}{\mathrm{N}} }|^2+|V_{\mu{\mathrm{N}} }|^2) $ (lower row) as a function of $ m_{\mathrm{N}} $ for a Majorana (left) and Dirac (right) HNL. The solid (dashed) black curve indicates the observed (expected) exclusion, where the parameter combinations inside the curve are excluded.

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Figure 12-c:
Exclusion limits at 95% CL on $ |V_{\mathrm{e}{\mathrm{N}} }|^2 $ (upper row), $ |V_{\mu{\mathrm{N}} }|^2 $ (middle row), and $ |V_{\mathrm{e}{\mathrm{N}} }V_{\mu{\mathrm{N}} }|^2/(|V_{\mathrm{e}{\mathrm{N}} }|^2+|V_{\mu{\mathrm{N}} }|^2) $ (lower row) as a function of $ m_{\mathrm{N}} $ for a Majorana (left) and Dirac (right) HNL. The solid (dashed) black curve indicates the observed (expected) exclusion, where the parameter combinations inside the curve are excluded.

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Figure 12-d:
Exclusion limits at 95% CL on $ |V_{\mathrm{e}{\mathrm{N}} }|^2 $ (upper row), $ |V_{\mu{\mathrm{N}} }|^2 $ (middle row), and $ |V_{\mathrm{e}{\mathrm{N}} }V_{\mu{\mathrm{N}} }|^2/(|V_{\mathrm{e}{\mathrm{N}} }|^2+|V_{\mu{\mathrm{N}} }|^2) $ (lower row) as a function of $ m_{\mathrm{N}} $ for a Majorana (left) and Dirac (right) HNL. The solid (dashed) black curve indicates the observed (expected) exclusion, where the parameter combinations inside the curve are excluded.

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Figure 12-e:
Exclusion limits at 95% CL on $ |V_{\mathrm{e}{\mathrm{N}} }|^2 $ (upper row), $ |V_{\mu{\mathrm{N}} }|^2 $ (middle row), and $ |V_{\mathrm{e}{\mathrm{N}} }V_{\mu{\mathrm{N}} }|^2/(|V_{\mathrm{e}{\mathrm{N}} }|^2+|V_{\mu{\mathrm{N}} }|^2) $ (lower row) as a function of $ m_{\mathrm{N}} $ for a Majorana (left) and Dirac (right) HNL. The solid (dashed) black curve indicates the observed (expected) exclusion, where the parameter combinations inside the curve are excluded.

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Figure 12-f:
Exclusion limits at 95% CL on $ |V_{\mathrm{e}{\mathrm{N}} }|^2 $ (upper row), $ |V_{\mu{\mathrm{N}} }|^2 $ (middle row), and $ |V_{\mathrm{e}{\mathrm{N}} }V_{\mu{\mathrm{N}} }|^2/(|V_{\mathrm{e}{\mathrm{N}} }|^2+|V_{\mu{\mathrm{N}} }|^2) $ (lower row) as a function of $ m_{\mathrm{N}} $ for a Majorana (left) and Dirac (right) HNL. The solid (dashed) black curve indicates the observed (expected) exclusion, where the parameter combinations inside the curve are excluded.
Tables

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Table 1:
Selection criteria for electrons and muons. Numbers in parentheses indicate values applied in the 2017--2018 data sets, when different from those for 2016.

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Table 2:
Event selection criteria.

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Table 3:
Definition of target and sideband regions used in the ABCD background estimation method for the signal (SR), validation (VR), and control (CR) regions.

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Table 4:
Summary of systematic uncertainty sources in the signal and background prediction.

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Table 5:
Summary of the most stringent observed limits of $ |V_{\ell{\mathrm{N}} }|^2 $ for Majorana and Dirac type HNL in this search.
Summary
A search for long-lived heavy neutral leptons (HNLs) in proton-proton collision events with one prompt lepton, one nonprompt lepton, and one jet from a secondary vertex has been presented. The data set corresponds to 138 fb$ ^{-1} $ and was collected by the CMS experiment at the LHC. A dedicated machine-learning method is applied to identify the secondary vertex associated with the HNL decay. No excess of events above the background prediction obtained from control samples in data is found. Exclusion limits at 95% confidence level are evaluated on the HNL mass and mixing parameter with standard model neutrinos. The obtained exclusion limits covering HNL masses from 1 to 16 GeV and squared mixing parameters as low as 2.6 $ \times$ 10$^{-7} $, depending on the scenario. These results exceed previous experimental constraints in the mass range 11--16 GeV for HNLs coupling to electrons or muons and provide the most stringent limits to date.
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