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CMS-EXO-20-009 ; CERN-EP-2021-264

Search for long-lived heavy neutral leptons with displaced vertices in proton-proton collisions at $\sqrt{s} = $ 13 TeV

CMS Collaboration

14 January 2022

JHEP 07 (2022) 081

Abstract: A search for heavy neutral leptons (HNLs), the right-handed Dirac or Majorana neutrinos, is performed in final states with three charged leptons (electrons or muons) using proton-proton collision data collected by the CMS experiment at $\sqrt{s} = $ 13 TeV at the CERN LHC. The data correspond to an integrated luminosity of 138 fb$^{-1}$. The HNLs could be produced through mixing with standard model neutrinos $\nu$. For small values of the HNL mass ($ < $ 20 GeV) and the square of the HNL-$\nu$ mixing parameter (10$^{-7}$-10$^{-2}$), the decay length of these particles can be large enough so that the secondary vertex of the HNL decay can be resolved with the CMS silicon tracker. The selected final state consists of one lepton emerging from the primary proton-proton collision vertex, and two leptons forming a displaced, secondary vertex. No significant deviations from the standard model expectations are observed, and constraints are obtained on the HNL mass and coupling strength parameters, excluding previously unexplored regions of parameter space in the mass range 1-20 GeV and squared mixing parameter values as low as 10$^{-7}$.

Links: e-print arXiv:2201.05578 [hep-ex] (PDF) ; CDS record ; inSPIRE record ; HepData record ; CADI line (restricted) ;

Figures
png pdf	Figure 1: Typical diagrams for the production and decay of an HNL through its mixing with an SM neutrino, leading to final states with three charged leptons and a neutrino. The HNL decay is mediated by either a W* (upper row) or a Z* (lower row) boson. In the diagrams on the left, the HNL is assumed to be a Majorana neutrino, thus $\ell$ and $\ell'$ in the W*-mediated diagram can have the same electric charge, and lepton number can be violated. In the diagrams on the right, the HNL decay conserves lepton number and can be either a Majorana or a Dirac particle, and, therefore, $\ell$ and $\ell'$ in the W*-mediated diagram have always opposite charge. The present study only considers the LNC case, thus $\ell$ and $\ell'$ (or $\nu_{\ell'}$) are always of the same flavor. In the case of the HNL decay mediated by a Z* boson, only the case where $\ell$ and $\ell''$ are of the same flavor is considered.
png pdf	Figure 1-a: Typical diagram for the production and decay of an HNL through its mixing with an SM neutrino, leading to final states with three charged leptons and a neutrino. Here, the HNL decay is mediated by a W* boson. The HNL is assumed to be a Majorana neutrino, thus $\ell$ and $\ell'$ can have the same electric charge, and lepton number can be violated. The present study only considers the LNC case, thus $\ell$ and $\ell'$ are always of the same flavor.
png pdf	Figure 1-b: Typical diagram for the production and decay of an HNL through its mixing with an SM neutrino, leading to final states with three charged leptons and a neutrino. Here, the HNL decay is mediated by a W* boson. The HNL decay conserves lepton number and can be either a Majorana or a Dirac particle, and, therefore, $\ell$ and $\ell'$ have always opposite charge. The present study only considers the LNC case, thus $\ell$ and $\ell'$ are always of the same flavor.
png pdf	Figure 1-c: Typical diagram for the production and decay of an HNL through its mixing with an SM neutrino, leading to final states with three charged leptons and a neutrino. Here, the HNL decay is mediated by a Z* boson. The HNL is assumed to be a Majorana neutrino. The present study only considers the LNC case, thus $\ell$ and $\nu_{\ell'}$ are always of the same flavor. In the case of the HNL decay mediated by a Z* boson, only the case where $\ell$ and $\ell''$ are of the same flavor is considered.
png pdf	Figure 1-d: Typical diagram for the production and decay of an HNL through its mixing with an SM neutrino, leading to final states with three charged leptons and a neutrino. Here, the HNL decay is mediated by a Z* boson. The HNL decay conserves lepton number and can be either a Majorana or a Dirac particle. The present study only considers the LNC case, thus $\ell$ and $\nu_{\ell'}$ are always of the same flavor. In the case of the HNL decay mediated by a Z* boson, only the case where $\ell$ and $\ell''$ are of the same flavor is considered.
png pdf	Figure 2: Distribution of kinematic properties of the generated leptons for simulated HNL signal events: the ${p_{\mathrm {T}}}$ of ${\ell _3}$ (left), the $m({\ell _2} {\ell _3})$ variable (center), and the angular separation between ${\ell _1}$ and ${\ell _3}$ (right). Predictions are shown for several benchmark hypotheses for Majorana HNL production: ${m_\mathrm{N}} =$ 2 GeV and $ {{| {V_{\mathrm{N} \ell}} |}^2} = $ 1.2$\times$10$^{-4}$ (HNL2), ${m_\mathrm{N}} =$ 6 GeV and $ {{| {V_{\mathrm{N} \ell}} |}^2} = $ 4.1$\times$10$^{-6}$ (HNL6), ${m_\mathrm{N}} =$ 12 GeV and $ {{| {V_{\mathrm{N} \ell}} |}^2} = $ 1.0$\times$10$^{-5}$ (HNL12).
png pdf	Figure 2-a: Distribution of the ${p_{\mathrm {T}}}$ of ${\ell _3}$ for simulated HNL signal events. Predictions are shown for several benchmark hypotheses for Majorana HNL production: ${m_\mathrm{N}} =$ 2 GeV and $ {{| {V_{\mathrm{N} \ell}} |}^2} = $ 1.2$\times$10$^{-4}$ (HNL2), ${m_\mathrm{N}} =$ 6 GeV and $ {{| {V_{\mathrm{N} \ell}} |}^2} = $ 4.1$\times$10$^{-6}$ (HNL6), ${m_\mathrm{N}} =$ 12 GeV and $ {{| {V_{\mathrm{N} \ell}} |}^2} = $ 1.0$\times$10$^{-5}$ (HNL12).
png pdf	Figure 2-b: Distribution of the $m({\ell _2} {\ell _3})$ variable for simulated HNL signal events. Predictions are shown for several benchmark hypotheses for Majorana HNL production: ${m_\mathrm{N}} =$ 2 GeV and $ {{| {V_{\mathrm{N} \ell}} |}^2} = $ 1.2$\times$10$^{-4}$ (HNL2), ${m_\mathrm{N}} =$ 6 GeV and $ {{| {V_{\mathrm{N} \ell}} |}^2} = $ 4.1$\times$10$^{-6}$ (HNL6), ${m_\mathrm{N}} =$ 12 GeV and $ {{| {V_{\mathrm{N} \ell}} |}^2} = $ 1.0$\times$10$^{-5}$ (HNL12).
png pdf	Figure 2-c: Distribution of the angular separation between ${\ell _1}$ and ${\ell _3}$ for simulated HNL signal events. Predictions are shown for several benchmark hypotheses for Majorana HNL production: ${m_\mathrm{N}} =$ 2 GeV and $ {{| {V_{\mathrm{N} \ell}} |}^2} = $ 1.2$\times$10$^{-4}$ (HNL2), ${m_\mathrm{N}} =$ 6 GeV and $ {{| {V_{\mathrm{N} \ell}} |}^2} = $ 4.1$\times$10$^{-6}$ (HNL6), ${m_\mathrm{N}} =$ 12 GeV and $ {{| {V_{\mathrm{N} \ell}} |}^2} = $ 1.0$\times$10$^{-5}$ (HNL12).
png pdf	Figure 3: Comparison between the number of observed events in data and the background predictions (shaded histograms, stacked) in the control regions for eeX (upper) and $ \mu \mu $X (lower) final states. The hashed band indicates the total systematic and statistical uncertainty in the background prediction. The lower panels indicate the ratio between data and prediction, and missing points indicate that the ratio lies outside the axis range. The uncertainty band assigned to the background prediction includes statistical and systematic contributions. Small contributions from background processes that are estimated from simulation are collectively referred to as "Other''.
png pdf	Figure 3-a: Comparison between the number of observed events in data and the background predictions (shaded histograms, stacked) in the control regions for the eeX final state. The hashed band indicates the total systematic and statistical uncertainty in the background prediction. The lower panel indicates the ratio between data and prediction, and missing points indicate that the ratio lies outside the axis range. The uncertainty band assigned to the background prediction includes statistical and systematic contributions. Small contributions from background processes that are estimated from simulation are collectively referred to as "Other''.
png pdf	Figure 3-b: Comparison between the number of observed events in data and the background predictions (shaded histograms, stacked) in the control regions for the $ \mu \mu $X final state. The hashed band indicates the total systematic and statistical uncertainty in the background prediction. The lower panel indicates the ratio between data and prediction, and missing points indicate that the ratio lies outside the axis range. The uncertainty band assigned to the background prediction includes statistical and systematic contributions. Small contributions from background processes that are estimated from simulation are collectively referred to as "Other''.
png pdf	Figure 4: Comparison between the observed number of events in data and simulation for converted photons. Events are selected in the final states with three (upper left) or four (upper right, lower) leptons, with one (or two) of the leptons identified as displaced electron(s). The distributions are shown for the displaced electron displacement $d$ (upper left) and reconstructed invariant mass of four leptons (upper right). Additionally, the ${\Delta _{\text {2D}}}$ variable is presented (lower). The simulated events correspond to the processes with external conversions, ${\mathrm{Z} \gamma ^{(*)}}$; internally converted photons, $\mathrm{Z} (\gamma ^{*})$; and other processes with the production of vector bosons and top quarks. The hashed band represents the statistical uncertainty in the simulation. The lower panels indicate the ratio between data and prediction.
png pdf	Figure 4-a: Comparison between the observed number of events in data and simulation for converted photons. Events are selected in the final states with three leptons, with one (or two) of the leptons identified as displaced electron(s). The distribution of the displaced electron displacement $d$ is presented. The simulated events correspond to the processes with external conversions, ${\mathrm{Z} \gamma ^{(*)}}$; internally converted photons, $\mathrm{Z} (\gamma ^{*})$; and other processes with the production of vector bosons and top quarks. The hashed band represents the statistical uncertainty in the simulation. The lower panel indicates the ratio between data and prediction.
png pdf	Figure 4-b: Comparison between the observed number of events in data and simulation for converted photons. Events are selected in the final states with four leptons, with one (or two) of the leptons identified as displaced electron(s). The distribution of the reconstructed invariant mass of four leptons is presented. The simulated events correspond to the processes with external conversions, ${\mathrm{Z} \gamma ^{(*)}}$; internally converted photons, $\mathrm{Z} (\gamma ^{*})$; and other processes with the production of vector bosons and top quarks. The hashed band represents the statistical uncertainty in the simulation. The lower panel indicates the ratio between data and prediction.
png pdf	Figure 4-c: Comparison between the observed number of events in data and simulation for converted photons. Events are selected in the final states with four leptons, with one (or two) of the leptons identified as displaced electron(s). The distribution of the ${\Delta _{\text {2D}}}$ variable is presented. The simulated events correspond to the processes with external conversions, ${\mathrm{Z} \gamma ^{(*)}}$; internally converted photons, $\mathrm{Z} (\gamma ^{*})$; and other processes with the production of vector bosons and top quarks. The hashed band represents the statistical uncertainty in the simulation. The lower panel indicates the ratio between data and prediction.
png pdf	Figure 5: The invariant mass distribution of the $\mathrm{K^0_S}$ candidates reconstructed using the $\pi^{\pm} \pi^{\mp}$ tracks for various displacement regions. The fitted $\mathrm{K^0_S}$ candidate mass in data in each region is also shown. The lowermost plot shows the $\mathrm{K^0_S}$ candidate yield after subtracting the background in data and in simulation, as well as their ratio, as a function of radial distance of the $\mathrm{K^0_S}$ vertex to the PV. The simulated yields are scaled to match the data in the lowest displacement bin.
png pdf	Figure 5-a: The invariant mass distribution of the $\mathrm{K^0_S}$ candidates reconstructed using the $\pi^{\pm} \pi^{\mp}$ tracks for 0 $< {\Delta _{\text {2D}}} <$ 0.5. The fitted $\mathrm{K^0_S}$ candidate mass in data in each region is also shown.
png pdf	Figure 5-b: The invariant mass distribution of the $\mathrm{K^0_S}$ candidates reconstructed using the $\pi^{\pm} \pi^{\mp}$ tracks for 0.5 $< {\Delta _{\text {2D}}} <$ 1.5. The fitted $\mathrm{K^0_S}$ candidate mass in data in each region is also shown.
png pdf	Figure 5-c: The invariant mass distribution of the $\mathrm{K^0_S}$ candidates reconstructed using the $\pi^{\pm} \pi^{\mp}$ tracks for 1.5 $< {\Delta _{\text {2D}}} <$ 4.0. The fitted $\mathrm{K^0_S}$ candidate mass in data in each region is also shown.
png pdf	Figure 5-d: The invariant mass distribution of the $\mathrm{K^0_S}$ candidates reconstructed using the $\pi^{\pm} \pi^{\mp}$ tracks for 4.0 $< {\Delta _{\text {2D}}} <$ 20.0. The fitted $\mathrm{K^0_S}$ candidate mass in data in each region is also shown.
png pdf	Figure 5-e: The plot shows the $\mathrm{K^0_S}$ candidate yield after subtracting the background in data and in simulation, as well as their ratio, as a function of radial distance of the $\mathrm{K^0_S}$ vertex to the PV. The simulated yields are scaled to match the data in the lowest displacement bin.
png pdf	Figure 6: Comparison between the number of observed events in data and the background predictions (shaded histograms, stacked) for the ${\Delta _{\text {2D}}}$ variable in eeX (left) and $ \mu \mu $X (right) final states. Events in the overflow bin are included in the last bin. The hashed band indicates the total systematic and statistical uncertainty in the background prediction. The lower panels indicate the ratio between data and prediction. Predictions for signal events are shown for several benchmark hypotheses for Majorana HNL production: ${m_\mathrm{N}} =$ 2 GeV and ${{| {V_{\mathrm{N} \ell}} |}^2} = $ 0.8$\times$10$^{-4}$ (HNL2), ${m_\mathrm{N}} =$ 6 GeV and ${{| {V_{\mathrm{N} \ell}} |}^2} = $ 1.3$\times$10$^{-6}$ (HNL6), ${m_\mathrm{N}} =$ 12 GeV and ${{| {V_{\mathrm{N} \ell}} |}^2} = $ 1.0$\times$10$^{-6}$ (HNL12).
png pdf	Figure 6-a: Comparison between the number of observed events in data and the background predictions (shaded histograms, stacked) for the ${\Delta _{\text {2D}}}$ variable in the eeX final state. Events in the overflow bin are included in the last bin. The hashed band indicates the total systematic and statistical uncertainty in the background prediction. The lower panels indicate the ratio between data and prediction. Predictions for signal events are shown for several benchmark hypotheses for Majorana HNL production: ${m_\mathrm{N}} =$ 2 GeV and ${{| {V_{\mathrm{N} \ell}} |}^2} = $ 0.8$\times$10$^{-4}$ (HNL2), ${m_\mathrm{N}} =$ 6 GeV and ${{| {V_{\mathrm{N} \ell}} |}^2} = $ 1.3$\times$10$^{-6}$ (HNL6), ${m_\mathrm{N}} =$ 12 GeV and ${{| {V_{\mathrm{N} \ell}} |}^2} = $ 1.0$\times$10$^{-6}$ (HNL12).
png pdf	Figure 6-b: Comparison between the number of observed events in data and the background predictions (shaded histograms, stacked) for the ${\Delta _{\text {2D}}}$ variable in the $ \mu \mu $X final state. Events in the overflow bin are included in the last bin. The hashed band indicates the total systematic and statistical uncertainty in the background prediction. The lower panels indicate the ratio between data and prediction. Predictions for signal events are shown for several benchmark hypotheses for Majorana HNL production: ${m_\mathrm{N}} =$ 2 GeV and ${{| {V_{\mathrm{N} \ell}} |}^2} = $ 0.8$\times$10$^{-4}$ (HNL2), ${m_\mathrm{N}} =$ 6 GeV and ${{| {V_{\mathrm{N} \ell}} |}^2} = $ 1.3$\times$10$^{-6}$ (HNL6), ${m_\mathrm{N}} =$ 12 GeV and ${{| {V_{\mathrm{N} \ell}} |}^2} = $ 1.0$\times$10$^{-6}$ (HNL12).
png pdf	Figure 7: Comparison between the number of observed events in data and the background predictions (shaded histograms, stacked) for the $m({\ell _2} {\ell _3})$ variable in eeX (left) and $ \mu \mu $X (right) final states. Events in the overflow bin are included in the last bin. The hashed band indicates the total systematic and statistical uncertainty in the background prediction. The lower panels indicate the ratio between data and prediction, and missing points indicate that the ratio lies outside the axis range. Predictions for signal events are shown for several benchmark hypotheses for Majorana HNL production: ${m_\mathrm{N}} =$ 2 GeV and ${{| {V_{\mathrm{N} \ell}} |}^2} = $ 0.8$\times$10$^{-4}$ (HNL2), ${m_\mathrm{N}} =$ 6 GeV and ${{| {V_{\mathrm{N} \ell}} |}^2} = $ 1.3$\times$10$^{-6}$ (HNL6), ${m_\mathrm{N}} =$ 12 GeV and ${{| {V_{\mathrm{N} \ell}} |}^2} = $ 1.0$\times$10$^{-6}$ (HNL12). Small contributions from background processes that are estimated from simulation are collectively referred to as "Other''.
png pdf	Figure 7-a: Comparison between the number of observed events in data and the background predictions (shaded histograms, stacked) for the $m({\ell _2} {\ell _3})$ variable in the eeX final state. Events in the overflow bin are included in the last bin. The hashed band indicates the total systematic and statistical uncertainty in the background prediction. The lower panels indicate the ratio between data and prediction, and missing points indicate that the ratio lies outside the axis range. Predictions for signal events are shown for several benchmark hypotheses for Majorana HNL production: ${m_\mathrm{N}} =$ 2 GeV and ${{| {V_{\mathrm{N} \ell}} |}^2} = $ 0.8$\times$10$^{-4}$ (HNL2), ${m_\mathrm{N}} =$ 6 GeV and ${{| {V_{\mathrm{N} \ell}} |}^2} = $ 1.3$\times$10$^{-6}$ (HNL6), ${m_\mathrm{N}} =$ 12 GeV and ${{| {V_{\mathrm{N} \ell}} |}^2} = $ 1.0$\times$10$^{-6}$ (HNL12). Small contributions from background processes that are estimated from simulation are collectively referred to as "Other''.
png pdf	Figure 7-b: Comparison between the number of observed events in data and the background predictions (shaded histograms, stacked) for the $m({\ell _2} {\ell _3})$ variable in the $ \mu \mu $X final state. Events in the overflow bin are included in the last bin. The hashed band indicates the total systematic and statistical uncertainty in the background prediction. The lower panels indicate the ratio between data and prediction, and missing points indicate that the ratio lies outside the axis range. Predictions for signal events are shown for several benchmark hypotheses for Majorana HNL production: ${m_\mathrm{N}} =$ 2 GeV and ${{| {V_{\mathrm{N} \ell}} |}^2} = $ 0.8$\times$10$^{-4}$ (HNL2), ${m_\mathrm{N}} =$ 6 GeV and ${{| {V_{\mathrm{N} \ell}} |}^2} = $ 1.3$\times$10$^{-6}$ (HNL6), ${m_\mathrm{N}} =$ 12 GeV and ${{| {V_{\mathrm{N} \ell}} |}^2} = $ 1.0$\times$10$^{-6}$ (HNL12). Small contributions from background processes that are estimated from simulation are collectively referred to as "Other''.
png pdf	Figure 8: Comparison between the number of observed events in data and the background predictions (shaded histograms, stacked) in the search regions for eeX (upper) and $ \mu \mu $X (lower) final states. The hashed band indicates the total systematic and statistical uncertainty in the background prediction. The lower panels indicate the ratio between data and prediction, and missing points indicate that the ratio lies outside the axis range. Predictions for signal events are shown for several benchmark hypotheses for Majorana HNL production: ${m_\mathrm{N}} =$ 2 GeV and ${{| {V_{\mathrm{N} \ell}} |}^2} = $ 0.8$\times$10$^{-4}$ (HNL2), ${m_\mathrm{N}} =$ 6 GeV and ${{| {V_{\mathrm{N} \ell}} |}^2} = $ 1.3$\times$10$^{-6}$ (HNL6), ${m_\mathrm{N}} =$ 12 GeV and ${{| {V_{\mathrm{N} \ell}} |}^2} = $ 1.0$\times$10$^{-6}$ (HNL12). The uncertainty band assigned to the background prediction includes statistical and systematic contributions. Small contributions from background processes that are estimated from simulation are collectively referred to as "Other''.
png pdf	Figure 8-a: Comparison between the number of observed events in data and the background predictions (shaded histograms, stacked) in the search regions for the eeX final states. The hashed band indicates the total systematic and statistical uncertainty in the background prediction. The lower panels indicate the ratio between data and prediction, and missing points indicate that the ratio lies outside the axis range. Predictions for signal events are shown for several benchmark hypotheses for Majorana HNL production: ${m_\mathrm{N}} =$ 2 GeV and ${{| {V_{\mathrm{N} \ell}} |}^2} = $ 0.8$\times$10$^{-4}$ (HNL2), ${m_\mathrm{N}} =$ 6 GeV and ${{| {V_{\mathrm{N} \ell}} |}^2} = $ 1.3$\times$10$^{-6}$ (HNL6), ${m_\mathrm{N}} =$ 12 GeV and ${{| {V_{\mathrm{N} \ell}} |}^2} = $ 1.0$\times$10$^{-6}$ (HNL12). The uncertainty band assigned to the background prediction includes statistical and systematic contributions. Small contributions from background processes that are estimated from simulation are collectively referred to as "Other''.
png pdf	Figure 8-b: Comparison between the number of observed events in data and the background predictions (shaded histograms, stacked) in the search regions for the $ \mu \mu $X final states. The hashed band indicates the total systematic and statistical uncertainty in the background prediction. The lower panels indicate the ratio between data and prediction, and missing points indicate that the ratio lies outside the axis range. Predictions for signal events are shown for several benchmark hypotheses for Majorana HNL production: ${m_\mathrm{N}} =$ 2 GeV and ${{| {V_{\mathrm{N} \ell}} |}^2} = $ 0.8$\times$10$^{-4}$ (HNL2), ${m_\mathrm{N}} =$ 6 GeV and ${{| {V_{\mathrm{N} \ell}} |}^2} = $ 1.3$\times$10$^{-6}$ (HNL6), ${m_\mathrm{N}} =$ 12 GeV and ${{| {V_{\mathrm{N} \ell}} |}^2} = $ 1.0$\times$10$^{-6}$ (HNL12). The uncertainty band assigned to the background prediction includes statistical and systematic contributions. Small contributions from background processes that are estimated from simulation are collectively referred to as "Other''.
png pdf	Figure 9: The 95% CL limits on ${{| {V_{\mathrm{N} \mathrm{e}}} |}^2}$ (left) and ${{| {V_{\mathrm{N} \mu}} |}^2}$ (right) as functions of ${m_\mathrm{N}}$ for a Majorana HNL. The area inside the solid (dashed) black curve indicates the observed (expected) exclusion region. Results from the DELPHI [18] and the CMS [20,19] Collaborations are shown for reference.
png pdf	Figure 9-a: The 95% CL limits on ${{| {V_{\mathrm{N} \mathrm{e}}} |}^2}$ as functions of ${m_\mathrm{N}}$ for a Majorana HNL. The area inside the solid (dashed) black curve indicates the observed (expected) exclusion region. Results from the DELPHI [18] and the CMS [20,19] Collaborations are shown for reference.
png pdf	Figure 9-b: The 95% CL limits on ${{| {V_{\mathrm{N} \mu}} |}^2}$ as functions of ${m_\mathrm{N}}$ for a Majorana HNL. The area inside the solid (dashed) black curve indicates the observed (expected) exclusion region. Results from the DELPHI [18] and the CMS [20,19] Collaborations are shown for reference.
png pdf	Figure 10: The 95% CL limits on ${{| {V_{\mathrm{N} \mathrm{e}}} |}^2}$ (left) and ${{| {V_{\mathrm{N} \mu}} |}^2}$ (right) as functions of ${m_\mathrm{N}}$ for a Dirac HNL. The area inside the solid (dashed) black curve indicates the observed (expected) exclusion region. Results from the DELPHI [18] and the CMS [20,19] Collaborations are shown for reference.
png pdf	Figure 10-a: The 95% CL limits on ${{| {V_{\mathrm{N} \mathrm{e}}} |}^2}$ as functions of ${m_\mathrm{N}}$ for a Dirac HNL. The area inside the solid (dashed) black curve indicates the observed (expected) exclusion region. Results from the DELPHI [18] and the CMS [20,19] Collaborations are shown for reference.
png pdf	Figure 10-b: The 95% CL limits on ${{| {V_{\mathrm{N} \mu}} |}^2}$ as functions of ${m_\mathrm{N}}$ for a Dirac HNL. The area inside the solid (dashed) black curve indicates the observed (expected) exclusion region. Results from the DELPHI [18] and the CMS [20,19] Collaborations are shown for reference.

Tables
png pdf	Table 1: Baseline selection criteria (left) and dilepton invariant mass vetoes (right) applied in the analysis. The width of the vetoed range for the meson resonances reflects the experimental resolution of the dilepton invariant mass reconstruction.
png pdf	Table 2: Definition of kinematic regions in terms of dilepton invariant mass $m({\ell _2} {\ell _3})$ and SV displacement ${\Delta _{\text {2D}}}$.
png pdf	Table 3: Number of predicted and observed events in the eeX final states. The quoted uncertainties include statistical and systematic components.
png pdf	Table 4: Number of predicted and observed events in the $ \mu \mu $X final states. The quoted uncertainties include statistical and systematic components.
png pdf	Table 5: Number of predicted signal events in the eeX final states. The results are presented for several benchmark signal hypotheses for Majorana HNL production: ${m_\mathrm{N}} =$ 2 GeV and ${{| {V_{\mathrm{N} \ell}} |}^2} = $ 0.8$\times$10$^{-4}$ (HNL2), ${m_\mathrm{N}} =$ 6 GeV and ${{| {V_{\mathrm{N} \ell}} |}^2} = $ 1.3$\times$10$^{-6}$ (HNL6), ${m_\mathrm{N}} =$ 12 GeV and ${{| {V_{\mathrm{N} \ell}} |}^2} = $ 1.0$\times$10$^{-6}$ (HNL12). The quoted uncertainties include statistical and systematic components.
png pdf	Table 6: Number of predicted signal events in the $ \mu \mu $X final states. The results are presented for several benchmark signal hypotheses for Majorana HNL production: ${m_\mathrm{N}} =$ 2 GeV and ${{| {V_{\mathrm{N} \ell}} |}^2} = $ 0.8$\times$10$^{-4}$ (HNL2), ${m_\mathrm{N}} =$ 6 GeV and ${{| {V_{\mathrm{N} \ell}} |}^2} = $ 1.3$\times$10$^{-6}$ (HNL6), ${m_\mathrm{N}} =$ 12 GeV and ${{| {V_{\mathrm{N} \ell}} |}^2} = $ 1.0$\times$10$^{-6}$ (HNL12). The quoted uncertainties include statistical and systematic components.

Summary

A search for heavy neutral leptons (HNLs) has been performed in the decays of W bosons produced in proton-proton collisions at $\sqrt{s} = $ 13 TeV and collected by the CMS experiment at the LHC. The analysis uses a data set corresponding to an integrated luminosity of 138 fb$^{-1}$. Events with three charged leptons are selected, and dedicated methods are applied to identify two displaced leptons consistent with the decay of a long-lived HNL in the mass range 1-20 GeV. Novel methods have been developed to estimate relevant background contributions from control samples in data, addressing one of the important challenges in this type of search at the LHC. No significant deviation from the standard model predictions is observed. Exclusion limits are evaluated at 95% confidence level on the coupling strengths of HNLs to standard model neutrinos as functions of the HNL mass, covering HNL masses from 1 up to 16.5 GeV and squared mixing parameters as low as 3.2$\times$10$^{-7}$, depending on the scenario. These results exceed previous experimental constraints in the mass range 3-14 (1-16.5) GeV for HNLs coupling to electrons (muons) and provide the most stringent limits to date.

Additional Figures
png pdf	Additional Figure 1: Covariance matrix for the background prediction in the signal region bins for the eeX (a) and $ {\mu} {\mu} $X (b) final states. The bin labels specify the channel, the $m(\ell_2,\ell_3)$ bin in GeV, and the $\Delta _{\text {2D}}$ bin in cm.
png pdf	Additional Figure 1-a: Covariance matrix for the background prediction in the signal region bins for the eeX final state. The bin labels specify the channel, the $m(\ell_2,\ell_3)$ bin in GeV, and the $\Delta _{\text {2D}}$ bin in cm.
png pdf	Additional Figure 1-b: Covariance matrix for the background prediction in the signal region bins for the $ {\mu} {\mu} $X final state. The bin labels specify the channel, the $m(\ell_2,\ell_3)$ bin in GeV, and the $\Delta _{\text {2D}}$ bin in cm.
png pdf	Additional Figure 2: Correlation matrix obtained from the covariance matrix for the background prediction in the signal region bins for the eeX (a) and $ {\mu} {\mu} $X (b) final states. The coefficients are obtained from the background-only fit. The bin labels specify the channel, the $m(\ell_2,\ell_3)$ bin in GeV, and the $\Delta _{\text {2D}}$ bin in cm.
png pdf	Additional Figure 2-a: Correlation matrix obtained from the covariance matrix for the background prediction in the signal region bins for the eeX final state. The coefficients are obtained from the background-only fit. The bin labels specify the channel, the $m(\ell_2,\ell_3)$ bin in GeV, and the $\Delta _{\text {2D}}$ bin in cm.
png pdf	Additional Figure 2-b: Correlation matrix obtained from the covariance matrix for the background prediction in the signal region bins for the $ {\mu} {\mu} $X final state. The coefficients are obtained from the background-only fit. The bin labels specify the channel, the $m(\ell_2,\ell_3)$ bin in GeV, and the $\Delta _{\text {2D}}$ bin in cm.

Additional Tables
png pdf	Additional Table 1: Number of predicted signal events in the eeX final states. The results are presented for several benchmark signal hypotheses for Majorana HNL production: $m_{\mathrm {N}} = $ 4 GeV and $ {| V_{\mathrm {N}} |}^2=$ 0.8$\times$10$^{-4}$ (HNL4), $m_{\mathrm {N}} = $ 8 GeV and $ {| V_{\mathrm {N}} |}^2=$ 1.3$\times$10$^{-6}$ (HNL8), $m_{\mathrm {N}} = $ 10 GeV and $ {| V_{\mathrm {N}} |}^2=$ 1.0$\times$10$^{-6}$ (HNL10). The quoted uncertainties include statistical and systematic components.
png pdf	Additional Table 2: Number of predicted signal events in the $ {\mu} {\mu} $X final states. The results are presented for several benchmark signal hypotheses for Majorana HNL production: $m_{\mathrm {N}} = $ 4 GeV and $ {| V_{\mathrm {N}} |}^2=$ 0.8$\times$10$^{-4}$ (HNL4), $m_{\mathrm {N}} = $ 8 GeV and $ {| V_{\mathrm {N}} |}^2=$ 1.3$\times$10$^{-6}$ (HNL8), $m_{\mathrm {N}} = $ 10 GeV and $ {| V_{\mathrm {N}} |}^2=$ 1.0$\times$10$^{-6}$ (HNL10). The quoted uncertainties include statistical and systematic components.
png pdf	Additional Table 3: Mean lifetime and production cross section for HNLs of Majorana nature, for different masses and coupling strengths, assuming the decay to three charged leptons and coupling to only electrons or muons, as evaluated from simulated event samples.

References
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