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| CMS-PAS-EXO-24-015 | ||
| Search for long-lived heavy neutral leptons in proton-proton collisions with one prompt muon and a secondary vertex from two displaced muons | ||
| CMS Collaboration | ||
| 2026-03-24 | ||
| Abstract: A search for heavy neutral leptons (HNLs) is performed in final states with three muons, with one originating from the prompt primary interaction vertex and the other two originate from a common displaced vertex. The analysis strategy is optimized for large HNL decay lengths by considering very displaced muons reconstructed only outside the tracker of the CMS experiment at the CERN LHC. This enhances the analysis reach in the high HNL lifetime region, corresponding to low HNL masses and small mixing with standard model neutrinos, where prompt and tracker-based displaced analyses have limited acceptance. The analysed proton-proton collision data correspond to integrated luminosities of 138 fb$ ^{-1} $ recorded at a centre-of-mass energy of 13 TeV in 2016 $ {-} $ 2018, and of 34.6 fb$ ^{-1} $ recorded at 13.6 TeV in 2022. No excess over the background prediction is found. Exclusion limits at 95% confidence level are set on the HNL mixing parameter as a function of its mass, in the mass range 1 $ {-} $ 5 GeV. | ||
| Links: CDS record (PDF) ; CADI line (restricted) ; | ||
| Figures | |
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Figure 1:
Feynman diagrams for the production of an HNL (denoted as $ \mathrm{N} $) through its mixing with an SM neutrino, resulting in a final state with three charged leptons and a neutrino. In the used notation, \ell originates from the primary $ \mathrm{W^-} $ decay, {\HepParticle\ell\prime} from the HNL decay directly, and {\HepParticle\ell\prime\prime} from the leptonic decay of the virtual electroweak boson. The HNL decay is mediated by a {\HepParticleW\ast} boson in the upper row and by a $ \mathrm{Z}^{*} $ boson in the lower row. On the left, the HNL is assumed to be a Majorana neutrino, allowing \ell and {\HepParticle\ell\prime} to have the same charge in the {\HepParticleW\ast} -mediated diagram, with consequent lepton-number violation. On the right, instead, the HNL can be either a Dirac or a Majorana particle. |
png pdf |
Figure 1-a:
Feynman diagrams for the production of an HNL (denoted as $ \mathrm{N} $) through its mixing with an SM neutrino, resulting in a final state with three charged leptons and a neutrino. In the used notation, \ell originates from the primary $ \mathrm{W^-} $ decay, {\HepParticle\ell\prime} from the HNL decay directly, and {\HepParticle\ell\prime\prime} from the leptonic decay of the virtual electroweak boson. The HNL decay is mediated by a {\HepParticleW\ast} boson in the upper row and by a $ \mathrm{Z}^{*} $ boson in the lower row. On the left, the HNL is assumed to be a Majorana neutrino, allowing \ell and {\HepParticle\ell\prime} to have the same charge in the {\HepParticleW\ast} -mediated diagram, with consequent lepton-number violation. On the right, instead, the HNL can be either a Dirac or a Majorana particle. |
png pdf |
Figure 1-b:
Feynman diagrams for the production of an HNL (denoted as $ \mathrm{N} $) through its mixing with an SM neutrino, resulting in a final state with three charged leptons and a neutrino. In the used notation, \ell originates from the primary $ \mathrm{W^-} $ decay, {\HepParticle\ell\prime} from the HNL decay directly, and {\HepParticle\ell\prime\prime} from the leptonic decay of the virtual electroweak boson. The HNL decay is mediated by a {\HepParticleW\ast} boson in the upper row and by a $ \mathrm{Z}^{*} $ boson in the lower row. On the left, the HNL is assumed to be a Majorana neutrino, allowing \ell and {\HepParticle\ell\prime} to have the same charge in the {\HepParticleW\ast} -mediated diagram, with consequent lepton-number violation. On the right, instead, the HNL can be either a Dirac or a Majorana particle. |
png pdf |
Figure 1-c:
Feynman diagrams for the production of an HNL (denoted as $ \mathrm{N} $) through its mixing with an SM neutrino, resulting in a final state with three charged leptons and a neutrino. In the used notation, \ell originates from the primary $ \mathrm{W^-} $ decay, {\HepParticle\ell\prime} from the HNL decay directly, and {\HepParticle\ell\prime\prime} from the leptonic decay of the virtual electroweak boson. The HNL decay is mediated by a {\HepParticleW\ast} boson in the upper row and by a $ \mathrm{Z}^{*} $ boson in the lower row. On the left, the HNL is assumed to be a Majorana neutrino, allowing \ell and {\HepParticle\ell\prime} to have the same charge in the {\HepParticleW\ast} -mediated diagram, with consequent lepton-number violation. On the right, instead, the HNL can be either a Dirac or a Majorana particle. |
png pdf |
Figure 1-d:
Feynman diagrams for the production of an HNL (denoted as $ \mathrm{N} $) through its mixing with an SM neutrino, resulting in a final state with three charged leptons and a neutrino. In the used notation, \ell originates from the primary $ \mathrm{W^-} $ decay, {\HepParticle\ell\prime} from the HNL decay directly, and {\HepParticle\ell\prime\prime} from the leptonic decay of the virtual electroweak boson. The HNL decay is mediated by a {\HepParticleW\ast} boson in the upper row and by a $ \mathrm{Z}^{*} $ boson in the lower row. On the left, the HNL is assumed to be a Majorana neutrino, allowing \ell and {\HepParticle\ell\prime} to have the same charge in the {\HepParticleW\ast} -mediated diagram, with consequent lepton-number violation. On the right, instead, the HNL can be either a Dirac or a Majorana particle. |
png pdf |
Figure 2:
Distributions of $ \Delta\phi(\mu_0,\mu_1) $ (upper left), $ \Delta\phi(\mu_0,\mu_2) $ (upper right), $ \Delta R(\mu_1,\mu_2) $ (middle left), $ p_{\mathrm{T}}(\mu_1,\mu_2) $ (middle right), $ \cos\theta(\mu_1,\mu_2) $ (lower left), and $ m(\mu_0,\mu_1,\mu_2) $ (lower right), shown for HNL predictions with three different $ m_{\mathrm{N}} $ values after the muon selection and compared to data from the control region with inverted tracker veto on $ \mu_1 $. The HNL predictions are scaled with a single normalization factor such that the integral of the HNL prediction with $ m_{\mathrm{N}}= $ 2 GeV matches the integral of the data distribution, with relative normalization differences between different HNL hypotheses retained. Overflow contributions are included in the last bin of the histograms. |
png pdf |
Figure 2-a:
Distributions of $ \Delta\phi(\mu_0,\mu_1) $ (upper left), $ \Delta\phi(\mu_0,\mu_2) $ (upper right), $ \Delta R(\mu_1,\mu_2) $ (middle left), $ p_{\mathrm{T}}(\mu_1,\mu_2) $ (middle right), $ \cos\theta(\mu_1,\mu_2) $ (lower left), and $ m(\mu_0,\mu_1,\mu_2) $ (lower right), shown for HNL predictions with three different $ m_{\mathrm{N}} $ values after the muon selection and compared to data from the control region with inverted tracker veto on $ \mu_1 $. The HNL predictions are scaled with a single normalization factor such that the integral of the HNL prediction with $ m_{\mathrm{N}}= $ 2 GeV matches the integral of the data distribution, with relative normalization differences between different HNL hypotheses retained. Overflow contributions are included in the last bin of the histograms. |
png pdf |
Figure 2-b:
Distributions of $ \Delta\phi(\mu_0,\mu_1) $ (upper left), $ \Delta\phi(\mu_0,\mu_2) $ (upper right), $ \Delta R(\mu_1,\mu_2) $ (middle left), $ p_{\mathrm{T}}(\mu_1,\mu_2) $ (middle right), $ \cos\theta(\mu_1,\mu_2) $ (lower left), and $ m(\mu_0,\mu_1,\mu_2) $ (lower right), shown for HNL predictions with three different $ m_{\mathrm{N}} $ values after the muon selection and compared to data from the control region with inverted tracker veto on $ \mu_1 $. The HNL predictions are scaled with a single normalization factor such that the integral of the HNL prediction with $ m_{\mathrm{N}}= $ 2 GeV matches the integral of the data distribution, with relative normalization differences between different HNL hypotheses retained. Overflow contributions are included in the last bin of the histograms. |
png pdf |
Figure 2-c:
Distributions of $ \Delta\phi(\mu_0,\mu_1) $ (upper left), $ \Delta\phi(\mu_0,\mu_2) $ (upper right), $ \Delta R(\mu_1,\mu_2) $ (middle left), $ p_{\mathrm{T}}(\mu_1,\mu_2) $ (middle right), $ \cos\theta(\mu_1,\mu_2) $ (lower left), and $ m(\mu_0,\mu_1,\mu_2) $ (lower right), shown for HNL predictions with three different $ m_{\mathrm{N}} $ values after the muon selection and compared to data from the control region with inverted tracker veto on $ \mu_1 $. The HNL predictions are scaled with a single normalization factor such that the integral of the HNL prediction with $ m_{\mathrm{N}}= $ 2 GeV matches the integral of the data distribution, with relative normalization differences between different HNL hypotheses retained. Overflow contributions are included in the last bin of the histograms. |
png pdf |
Figure 2-d:
Distributions of $ \Delta\phi(\mu_0,\mu_1) $ (upper left), $ \Delta\phi(\mu_0,\mu_2) $ (upper right), $ \Delta R(\mu_1,\mu_2) $ (middle left), $ p_{\mathrm{T}}(\mu_1,\mu_2) $ (middle right), $ \cos\theta(\mu_1,\mu_2) $ (lower left), and $ m(\mu_0,\mu_1,\mu_2) $ (lower right), shown for HNL predictions with three different $ m_{\mathrm{N}} $ values after the muon selection and compared to data from the control region with inverted tracker veto on $ \mu_1 $. The HNL predictions are scaled with a single normalization factor such that the integral of the HNL prediction with $ m_{\mathrm{N}}= $ 2 GeV matches the integral of the data distribution, with relative normalization differences between different HNL hypotheses retained. Overflow contributions are included in the last bin of the histograms. |
png pdf |
Figure 2-e:
Distributions of $ \Delta\phi(\mu_0,\mu_1) $ (upper left), $ \Delta\phi(\mu_0,\mu_2) $ (upper right), $ \Delta R(\mu_1,\mu_2) $ (middle left), $ p_{\mathrm{T}}(\mu_1,\mu_2) $ (middle right), $ \cos\theta(\mu_1,\mu_2) $ (lower left), and $ m(\mu_0,\mu_1,\mu_2) $ (lower right), shown for HNL predictions with three different $ m_{\mathrm{N}} $ values after the muon selection and compared to data from the control region with inverted tracker veto on $ \mu_1 $. The HNL predictions are scaled with a single normalization factor such that the integral of the HNL prediction with $ m_{\mathrm{N}}= $ 2 GeV matches the integral of the data distribution, with relative normalization differences between different HNL hypotheses retained. Overflow contributions are included in the last bin of the histograms. |
png pdf |
Figure 2-f:
Distributions of $ \Delta\phi(\mu_0,\mu_1) $ (upper left), $ \Delta\phi(\mu_0,\mu_2) $ (upper right), $ \Delta R(\mu_1,\mu_2) $ (middle left), $ p_{\mathrm{T}}(\mu_1,\mu_2) $ (middle right), $ \cos\theta(\mu_1,\mu_2) $ (lower left), and $ m(\mu_0,\mu_1,\mu_2) $ (lower right), shown for HNL predictions with three different $ m_{\mathrm{N}} $ values after the muon selection and compared to data from the control region with inverted tracker veto on $ \mu_1 $. The HNL predictions are scaled with a single normalization factor such that the integral of the HNL prediction with $ m_{\mathrm{N}}= $ 2 GeV matches the integral of the data distribution, with relative normalization differences between different HNL hypotheses retained. Overflow contributions are included in the last bin of the histograms. |
png pdf |
Figure 3:
Observed (black points) and predicted (blue histograms) yields in the low-$ p_{\mathrm{T}} $ validation region in \Run2 (left) and in 2022 with relaxed DSA isolation requirements (right). The grey bands represent the statistical uncertainty in the background prediction. The lower panels show the ratio between observed and predicted yields in each bin. Both predicted and observed yields are exactly zero in the last two bins by construction of the low-$ p_{\mathrm{T}} $ validation region. |
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Figure 3-a:
Observed (black points) and predicted (blue histograms) yields in the low-$ p_{\mathrm{T}} $ validation region in \Run2 (left) and in 2022 with relaxed DSA isolation requirements (right). The grey bands represent the statistical uncertainty in the background prediction. The lower panels show the ratio between observed and predicted yields in each bin. Both predicted and observed yields are exactly zero in the last two bins by construction of the low-$ p_{\mathrm{T}} $ validation region. |
png pdf |
Figure 3-b:
Observed (black points) and predicted (blue histograms) yields in the low-$ p_{\mathrm{T}} $ validation region in \Run2 (left) and in 2022 with relaxed DSA isolation requirements (right). The grey bands represent the statistical uncertainty in the background prediction. The lower panels show the ratio between observed and predicted yields in each bin. Both predicted and observed yields are exactly zero in the last two bins by construction of the low-$ p_{\mathrm{T}} $ validation region. |
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Figure 4:
Observed (black points) and predicted (blue histograms) yields in the sideband with at least one non-isolated DSA muon of the low-$ p_{\mathrm{T}} $ validation region (left) and the signal region (right) in \Run2. The grey bands represent the statistical uncertainty in the background prediction. The lower panels show the ratio between observed and predicted yields in each bin. In the left figure, both predicted and observed yields are exactly zero in the last two bins by construction of the low-$ p_{\mathrm{T}} $ validation region. |
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Figure 4-a:
Observed (black points) and predicted (blue histograms) yields in the sideband with at least one non-isolated DSA muon of the low-$ p_{\mathrm{T}} $ validation region (left) and the signal region (right) in \Run2. The grey bands represent the statistical uncertainty in the background prediction. The lower panels show the ratio between observed and predicted yields in each bin. In the left figure, both predicted and observed yields are exactly zero in the last two bins by construction of the low-$ p_{\mathrm{T}} $ validation region. |
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Figure 4-b:
Observed (black points) and predicted (blue histograms) yields in the sideband with at least one non-isolated DSA muon of the low-$ p_{\mathrm{T}} $ validation region (left) and the signal region (right) in \Run2. The grey bands represent the statistical uncertainty in the background prediction. The lower panels show the ratio between observed and predicted yields in each bin. In the left figure, both predicted and observed yields are exactly zero in the last two bins by construction of the low-$ p_{\mathrm{T}} $ validation region. |
png pdf |
Figure 5:
Observed (black points) and predicted (blue histograms) yields in the inverted tracker veto validation region in \Run2 (left) and in 2022 with relaxed DSA isolation requirements (right). The grey bands represent the statistical uncertainty in the background prediction. The lower panels show the ratio between observed and predicted yields in each bin. |
png pdf |
Figure 5-a:
Observed (black points) and predicted (blue histograms) yields in the inverted tracker veto validation region in \Run2 (left) and in 2022 with relaxed DSA isolation requirements (right). The grey bands represent the statistical uncertainty in the background prediction. The lower panels show the ratio between observed and predicted yields in each bin. |
png pdf |
Figure 5-b:
Observed (black points) and predicted (blue histograms) yields in the inverted tracker veto validation region in \Run2 (left) and in 2022 with relaxed DSA isolation requirements (right). The grey bands represent the statistical uncertainty in the background prediction. The lower panels show the ratio between observed and predicted yields in each bin. |
png pdf |
Figure 6:
Observed (black points) and predicted (blue histograms) yields in the signal region in \Run2 (left) and in 2022 (right). The grey bands represent the total uncertainty in the background prediction. The green and orange histograms show the signal distributions for two different hypotheses, corresponding to $ m_{\mathrm{N}}= $ 1 and 3 GeV, and respective $ |V_{\mathrm{N}\mu}|^2 $ values equal to the smallest excluded values at 95% CL by Ref. [36]. The lower panels show the ratio between observed yields and predicted background yields in each bin. |
png pdf |
Figure 6-a:
Observed (black points) and predicted (blue histograms) yields in the signal region in \Run2 (left) and in 2022 (right). The grey bands represent the total uncertainty in the background prediction. The green and orange histograms show the signal distributions for two different hypotheses, corresponding to $ m_{\mathrm{N}}= $ 1 and 3 GeV, and respective $ |V_{\mathrm{N}\mu}|^2 $ values equal to the smallest excluded values at 95% CL by Ref. [36]. The lower panels show the ratio between observed yields and predicted background yields in each bin. |
png pdf |
Figure 6-b:
Observed (black points) and predicted (blue histograms) yields in the signal region in \Run2 (left) and in 2022 (right). The grey bands represent the total uncertainty in the background prediction. The green and orange histograms show the signal distributions for two different hypotheses, corresponding to $ m_{\mathrm{N}}= $ 1 and 3 GeV, and respective $ |V_{\mathrm{N}\mu}|^2 $ values equal to the smallest excluded values at 95% CL by Ref. [36]. The lower panels show the ratio between observed yields and predicted background yields in each bin. |
png pdf |
Figure 7:
Exclusion limits at 95% CL on $ |V_{\mathrm{N}\mu}|^2 $ as a function of $ m_{\mathrm{N}} $ for a Majorana HNL, obtained with the combination of \Run2 and 2022 data. The solid (dashed) black curve indicates the observed (expected) exclusion, where the parameter combinations inside the curve are excluded. |
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Figure 8:
Lower expected exclusion limits at 95% CL on $ |V_{\mathrm{N}\mu}|^2 $ as a function of $ m_{\mathrm{N}} $ for a Majorana HNL, obtained with the combination of \Run2 and 2022 data (solid black line), compared with the expected limits obtained by other CMS analyses in the same mass range (dashed coloured lines). |
| Tables | |
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Table 1:
Summary of event selection criteria. |
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Table 2:
Cumulative selection efficiency after each kinematic selection criterion with \Run2 (upper) and 2022 (lower) conditions. The efficiencies are evaluated for three signal samples: $ m_{\mathrm{N}}= $ 2 GeV with $ |V_{\mathrm{N}\mu}|^2=1.61\times10^{-5} $, $ m_{\mathrm{N}}= $ 3 GeV with $ |V_{\mathrm{N}\mu}|^2=4.87\times10^{-6} $, and $ m_{\mathrm{N}}= $ 4 GeV with $ |V_{\mathrm{N}\mu}|^2=2.14\times10^{-6} $. The denominator for each efficiency corresponds to the signal yield after the prompt and displaced muon selections described in Section 5.1. |
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Table 3:
Definition of the signal region bins. |
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Table 4:
Definition of the regions used in the ABCD method. |
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Table 5:
Observed yields in the regions B, C, D for the selection with relaxed DSA isolation requirements, and corresponding transfer factor obtained as the ratio of events in the regions C and D. |
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Table 6:
Observed yields in the regions A, B, C, D for the low-$ p_{\mathrm{T}} $ validation region with relaxed DSA isolation requirements, and predicted yield in region A using the ABCD method. |
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Table 7:
Definition of the regions used in the ABCD method for the inverted tracker veto validation region. |
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Table 8:
Observed yields in the regions $ \text{B}^\prime $, $ \text{B}^{\prime\prime} $, $ \text{D}^\prime $, $ \text{D}^{\prime\prime} $ for the inverted tracker veto validation region with relaxed DSA isolation requirements, and predicted yield in region $ \text{B}^\prime $ using the ABCD method. |
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Table 9:
Magnitude of the systematic uncertainty on the signal yields in the four search regions. Details on each source of systematic uncertainty are provided in the text. The numbers in the table are computed for an HNL signal corresponding to $ m_{\mathrm{N}}= $ 3 GeV and $ |V_{\mathrm{N}\mu}|^2= $ 4.9e-6, but no significant variation is observed for different signal hypotheses. |
| Summary |
| A search for heavy neutral leptons (HNLs) has been performed using proton-proton collision events with one prompt muon and two highly displaced muons. The analysed data set was recorded by the CMS experiment at the LHC and corresponds to an integrated luminosity of 138 fb$ ^{-1} $ recorded at $ \sqrt{s}= $ 13 TeV in 2016--2018 and 34.6 fb$ ^{-1} $ recorded at $ \sqrt{s}= $ 13.6 TeV in 2022. The target process is HNL production in association with a prompt muon through decays of W bosons, with a delayed HNL decay to two muons and one standard model neutrino. The two displaced muons are reconstructed using only information from the CMS muon system, thus significantly extending the sensitivity of the analysis to HNLs with longer decay lengths compared to previous searches for long-lived HNLs. No significant deviation from the SM background estimated from control samples in data is found. Exclusion limits at 95% confidence level are set on the HNL mixing parameter as a function of its mass. This analysis surpasses previous experimental results in terms of the sensitivity to HNLs with masses between 2.5 and 4.2 GeV. |
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