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CMS-EXO-22-019 ; CERN-EP-2024-053

Search for long-lived heavy neutrinos in the decays of B mesons produced in proton-proton collisions at $ \sqrt{s} = $ 13 TeV

CMS Collaboration

7 March 2024

Submitted to J. High Energy Phys.

Abstract: A search for long-lived heavy neutrinos (N) in the decays of B mesons produced in proton-proton collisions at $ \sqrt{s} = $ 13 TeV is presented. The data sample corresponds to an integrated luminosity of 41.6 fb$ ^{-1} $ collected in 2018 by the CMS experiment at the CERN LHC, using a dedicated data stream that enhances the number of recorded events containing B mesons. The search probes heavy neutrinos with masses in the range 1 $ < m_\mathrm{N} < $ 3 GeV and decay lengths in the range 10$^{-2}$ $ < c\tau_{\mathrm{N}} < $ 10$^{4} $ mm, where $ \tau_\mathrm{N} $ is the N proper mean lifetime. Signal events are defined by the signature B $\to \ell_{\mathrm{B}} $NX; N $ \to \ell^{\pm} \pi^{\mp} $, where the leptons $ \ell_{\mathrm{B}} $ and $ \ell $ can be either a muon or an electron, provided that at least one of them is a muon. The hadronic recoil system, X, is treated inclusively and is not reconstructed. No significant excess of events over the standard model background is observed in any of the $ \ell^{\pm}\pi^{\mp} $ invariant mass distributions. Limits at 95% confidence level on the sum of the squares of the mixing amplitudes between heavy and light neutrinos, $ |V_\mathrm{N}|^2 $, and on $ c\tau_{\mathrm{N}} $ are obtained in different mixing scenarios for both Majorana and Dirac-like N particles. The most stringent upper limit $ |V_\mathrm{N}|^2 < $ 2.0 $\times$ 10$^{-5} $ is obtained at $ m_\mathrm{N}= $ 1.95 GeV for the Majorana case where N mixes exclusively with muon neutrinos. The limits on $ |V_\mathrm{N}|^2 $ for masses 1 $ < m_\mathrm{N} < $ 1.7 GeV are the most stringent from a collider experiment to date.

Links: e-print arXiv:2403.04584 [hep-ex] (PDF) ; CDS record ; inSPIRE record ; HepData record ; CADI line (restricted) ;

Figures
png pdf	Figure 1: Feynman diagrams showing the semileptonic (upper row) and leptonic (lower row) decay of a B meson into a lepton ($ \ell_{\mathrm{B}} $), a hadronic system (X) in case of the semileptonic decay, and a neutrino ($ \nu_{\ell_{\mathrm{B}}} $), which contains a small admixture of a heavy neutrino (N). The N mass eigenstate propagates and, according to its admixture of the neutrino flavour eigenstate ($ \nu_{\ell} $), decays weakly into a lepton $ \ell^{\pm} $ and a charged pion $ \pi^{\mp} $.
png pdf	Figure 1-a: Feynman diagrams showing the semileptonic (upper row) and leptonic (lower row) decay of a B meson into a lepton ($ \ell_{\mathrm{B}} $), a hadronic system (X) in case of the semileptonic decay, and a neutrino ($ \nu_{\ell_{\mathrm{B}}} $), which contains a small admixture of a heavy neutrino (N). The N mass eigenstate propagates and, according to its admixture of the neutrino flavour eigenstate ($ \nu_{\ell} $), decays weakly into a lepton $ \ell^{\pm} $ and a charged pion $ \pi^{\mp} $.
png pdf	Figure 1-b: Feynman diagrams showing the semileptonic (upper row) and leptonic (lower row) decay of a B meson into a lepton ($ \ell_{\mathrm{B}} $), a hadronic system (X) in case of the semileptonic decay, and a neutrino ($ \nu_{\ell_{\mathrm{B}}} $), which contains a small admixture of a heavy neutrino (N). The N mass eigenstate propagates and, according to its admixture of the neutrino flavour eigenstate ($ \nu_{\ell} $), decays weakly into a lepton $ \ell^{\pm} $ and a charged pion $ \pi^{\mp} $.
png pdf	Figure 2: Distribution of the displaced $ \mu^{\pm}\pi^{\mp} $ invariant mass (left) and $ L_{xy}/\sigma_{L_{xy}} $ (right) in data and in simulated event samples corresponding to two different signal hypotheses, in the Majorana scenario, and with the N mixing exclusively with the muon sector: $ m_\mathrm{N} = $ 1 GeV, $ c\tau_{\mathrm{N}} =$ 1000 mm, $ |V_\mathrm{N}|^2= |V_{\mu\mathrm{N}}|^2 = $ 5.4 $\times$ 10$^{-4} $; and $ m_\mathrm{N} = $ 2 GeV, $ c\tau_{\mathrm{N}} = $ 100 mm, $ |V_\mathrm{N}|^2=|V_{\mu\mathrm{N}}|^2=$ 1.7 $\times$ 10$^{-4} $. The signal distributions are scaled with factors given in the legend. The vertical lines show the statistical uncertainty in each bin.
png pdf	Figure 2-a: Distribution of the displaced $ \mu^{\pm}\pi^{\mp} $ invariant mass (left) and $ L_{xy}/\sigma_{L_{xy}} $ (right) in data and in simulated event samples corresponding to two different signal hypotheses, in the Majorana scenario, and with the N mixing exclusively with the muon sector: $ m_\mathrm{N} = $ 1 GeV, $ c\tau_{\mathrm{N}} =$ 1000 mm, $ |V_\mathrm{N}|^2= |V_{\mu\mathrm{N}}|^2 = $ 5.4 $\times$ 10$^{-4} $; and $ m_\mathrm{N} = $ 2 GeV, $ c\tau_{\mathrm{N}} = $ 100 mm, $ |V_\mathrm{N}|^2=|V_{\mu\mathrm{N}}|^2=$ 1.7 $\times$ 10$^{-4} $. The signal distributions are scaled with factors given in the legend. The vertical lines show the statistical uncertainty in each bin.
png pdf	Figure 2-b: Distribution of the displaced $ \mu^{\pm}\pi^{\mp} $ invariant mass (left) and $ L_{xy}/\sigma_{L_{xy}} $ (right) in data and in simulated event samples corresponding to two different signal hypotheses, in the Majorana scenario, and with the N mixing exclusively with the muon sector: $ m_\mathrm{N} = $ 1 GeV, $ c\tau_{\mathrm{N}} =$ 1000 mm, $ |V_\mathrm{N}|^2= |V_{\mu\mathrm{N}}|^2 = $ 5.4 $\times$ 10$^{-4} $; and $ m_\mathrm{N} = $ 2 GeV, $ c\tau_{\mathrm{N}} = $ 100 mm, $ |V_\mathrm{N}|^2=|V_{\mu\mathrm{N}}|^2=$ 1.7 $\times$ 10$^{-4} $. The signal distributions are scaled with factors given in the legend. The vertical lines show the statistical uncertainty in each bin.
png pdf	Figure 3: The distributions of the pion $ p_{\mathrm{T}} $ (upper left), $ m(\mu_{\mathrm{B}}\mu^\pm\pi^\mp) $ (upper right), $ \cos\theta $ (lower left), and pion $ d_{xy}/\sigma_{d_{xy}} $ (lower right) are shown for data, as well as for a signal hypothesis of $ m_\mathrm{N}= $ 2 GeV and $ c\tau_{\mathrm{N}}=$ 100 mm. The data correspond to an integrated luminosity of 5.2 fb$ ^{-1} $ and are selected in the mass window of size 10 $ \sigma $ around $ m_\mathrm{N}= $ 2 GeV. The distributions, which are normalized to unit area, are shown for the dimuon channel in category with high $ L_{xy}/\sigma_{L_{xy}} $, OS, and low $ \ell_{\mathrm{B}}\ell^\pm\pi^\mp\mathrm{ mass} $. The vertical lines show the statistical uncertainty in each bin.
png pdf	Figure 3-a: The distributions of the pion $ p_{\mathrm{T}} $ (upper left), $ m(\mu_{\mathrm{B}}\mu^\pm\pi^\mp) $ (upper right), $ \cos\theta $ (lower left), and pion $ d_{xy}/\sigma_{d_{xy}} $ (lower right) are shown for data, as well as for a signal hypothesis of $ m_\mathrm{N}= $ 2 GeV and $ c\tau_{\mathrm{N}}=$ 100 mm. The data correspond to an integrated luminosity of 5.2 fb$ ^{-1} $ and are selected in the mass window of size 10 $ \sigma $ around $ m_\mathrm{N}= $ 2 GeV. The distributions, which are normalized to unit area, are shown for the dimuon channel in category with high $ L_{xy}/\sigma_{L_{xy}} $, OS, and low $ \ell_{\mathrm{B}}\ell^\pm\pi^\mp\mathrm{ mass} $. The vertical lines show the statistical uncertainty in each bin.
png pdf	Figure 3-b: The distributions of the pion $ p_{\mathrm{T}} $ (upper left), $ m(\mu_{\mathrm{B}}\mu^\pm\pi^\mp) $ (upper right), $ \cos\theta $ (lower left), and pion $ d_{xy}/\sigma_{d_{xy}} $ (lower right) are shown for data, as well as for a signal hypothesis of $ m_\mathrm{N}= $ 2 GeV and $ c\tau_{\mathrm{N}}=$ 100 mm. The data correspond to an integrated luminosity of 5.2 fb$ ^{-1} $ and are selected in the mass window of size 10 $ \sigma $ around $ m_\mathrm{N}= $ 2 GeV. The distributions, which are normalized to unit area, are shown for the dimuon channel in category with high $ L_{xy}/\sigma_{L_{xy}} $, OS, and low $ \ell_{\mathrm{B}}\ell^\pm\pi^\mp\mathrm{ mass} $. The vertical lines show the statistical uncertainty in each bin.
png pdf	Figure 3-c: The distributions of the pion $ p_{\mathrm{T}} $ (upper left), $ m(\mu_{\mathrm{B}}\mu^\pm\pi^\mp) $ (upper right), $ \cos\theta $ (lower left), and pion $ d_{xy}/\sigma_{d_{xy}} $ (lower right) are shown for data, as well as for a signal hypothesis of $ m_\mathrm{N}= $ 2 GeV and $ c\tau_{\mathrm{N}}=$ 100 mm. The data correspond to an integrated luminosity of 5.2 fb$ ^{-1} $ and are selected in the mass window of size 10 $ \sigma $ around $ m_\mathrm{N}= $ 2 GeV. The distributions, which are normalized to unit area, are shown for the dimuon channel in category with high $ L_{xy}/\sigma_{L_{xy}} $, OS, and low $ \ell_{\mathrm{B}}\ell^\pm\pi^\mp\mathrm{ mass} $. The vertical lines show the statistical uncertainty in each bin.
png pdf	Figure 3-d: The distributions of the pion $ p_{\mathrm{T}} $ (upper left), $ m(\mu_{\mathrm{B}}\mu^\pm\pi^\mp) $ (upper right), $ \cos\theta $ (lower left), and pion $ d_{xy}/\sigma_{d_{xy}} $ (lower right) are shown for data, as well as for a signal hypothesis of $ m_\mathrm{N}= $ 2 GeV and $ c\tau_{\mathrm{N}}=$ 100 mm. The data correspond to an integrated luminosity of 5.2 fb$ ^{-1} $ and are selected in the mass window of size 10 $ \sigma $ around $ m_\mathrm{N}= $ 2 GeV. The distributions, which are normalized to unit area, are shown for the dimuon channel in category with high $ L_{xy}/\sigma_{L_{xy}} $, OS, and low $ \ell_{\mathrm{B}}\ell^\pm\pi^\mp\mathrm{ mass} $. The vertical lines show the statistical uncertainty in each bin.
png pdf	Figure 4: (Left) Performance of the pNN as a function of signal mass for events in the 50 $ < L_{xy}/\sigma_{L_{xy}} < $ 150, OS, and low $ \ell_{\mathrm{B}}\ell^\pm\pi^\mp\mathrm{ mass} $ category in the dimuon channel. The performance is shown by the AUC curve, where a value at unity corresponds to a perfect separation between signal and background. The different coloured curves correspond to different $ c\tau_{\mathrm{N}} $ hypotheses. (Right) Validation of the use of a pNN for intermediate $ m_\mathrm{N} $ mass points, for events in the 50 $ < L_{xy}/\sigma_{L_{xy}} < $ 150, OS and low $ \ell_{\mathrm{B}}\ell^\pm\pi^\mp\mathrm{ mass} $ category in the dimuon channel: a pNN trained on masses $ m_\mathrm{N} = $ 1.0, 1.5, 2.0, and 3.0 GeV (blue) and a NN trained on mass $ m_\mathrm{N}= $ 2 GeV (red). All the points have $ c\tau_{\mathrm{N}}=$ 10 mm. The full circles correspond to mass points on which the pNN and NN were trained on, while the open circles show mass points that have not been trained on.
png pdf	Figure 4-a: (Left) Performance of the pNN as a function of signal mass for events in the 50 $ < L_{xy}/\sigma_{L_{xy}} < $ 150, OS, and low $ \ell_{\mathrm{B}}\ell^\pm\pi^\mp\mathrm{ mass} $ category in the dimuon channel. The performance is shown by the AUC curve, where a value at unity corresponds to a perfect separation between signal and background. The different coloured curves correspond to different $ c\tau_{\mathrm{N}} $ hypotheses. (Right) Validation of the use of a pNN for intermediate $ m_\mathrm{N} $ mass points, for events in the 50 $ < L_{xy}/\sigma_{L_{xy}} < $ 150, OS and low $ \ell_{\mathrm{B}}\ell^\pm\pi^\mp\mathrm{ mass} $ category in the dimuon channel: a pNN trained on masses $ m_\mathrm{N} = $ 1.0, 1.5, 2.0, and 3.0 GeV (blue) and a NN trained on mass $ m_\mathrm{N}= $ 2 GeV (red). All the points have $ c\tau_{\mathrm{N}}=$ 10 mm. The full circles correspond to mass points on which the pNN and NN were trained on, while the open circles show mass points that have not been trained on.
png pdf	Figure 4-b: (Left) Performance of the pNN as a function of signal mass for events in the 50 $ < L_{xy}/\sigma_{L_{xy}} < $ 150, OS, and low $ \ell_{\mathrm{B}}\ell^\pm\pi^\mp\mathrm{ mass} $ category in the dimuon channel. The performance is shown by the AUC curve, where a value at unity corresponds to a perfect separation between signal and background. The different coloured curves correspond to different $ c\tau_{\mathrm{N}} $ hypotheses. (Right) Validation of the use of a pNN for intermediate $ m_\mathrm{N} $ mass points, for events in the 50 $ < L_{xy}/\sigma_{L_{xy}} < $ 150, OS and low $ \ell_{\mathrm{B}}\ell^\pm\pi^\mp\mathrm{ mass} $ category in the dimuon channel: a pNN trained on masses $ m_\mathrm{N} = $ 1.0, 1.5, 2.0, and 3.0 GeV (blue) and a NN trained on mass $ m_\mathrm{N}= $ 2 GeV (red). All the points have $ c\tau_{\mathrm{N}}=$ 10 mm. The full circles correspond to mass points on which the pNN and NN were trained on, while the open circles show mass points that have not been trained on.
png pdf	Figure 5: Branching fractions as functions of $ m_\mathrm{N} $ for $ {\mathrm{B}}_\mathrm{q}\to\mu\mathrm{N}\mathrm{X} $ decays, $ \mathrm{q} = (\mathrm{u}, \mathrm{d}, \mathrm{s}, \mathrm{c}) $, multiplied by the corresponding fragmentation fraction, $ f_{\mathrm{q}} $. Both leptonic and semileptonic decays are considered. The results are shown for the mixing scenario $ |V_\mathrm{N}|^2=|V_{\mu\mathrm{N}}|^2= $ 1. The branching fractions are computed based on the method described in Ref. [9].
png pdf	Figure 6: Distribution of the $ \mathrm{K}^\pm\mu^+\mu^- $ invariant mass for a luminosity of 0.77 fb$ ^{-1} $. A large signal is observed at the $ {\mathrm{B}}_{\mathrm{u}} $ mass. The blue curve shows the fit to signal plus background, while the orange, green, and red curves show the contributions from the signal, composite background, and combinatorial background, respectively.
png pdf	Figure 7: Distribution of the $ \mu^\pm\pi^\mp $ invariant mass in the mass window around 1.5 GeV in the high $ L_{xy}/\sigma_{L_{xy}} $, OS, and low $ \ell_{\mathrm{B}}\ell^\pm\pi^\mp\mathrm{ mass} $ category in the dimuon channel. The result of the background-only fit to the data (red) is shown together with the mass distribution expected from a Majorana signal with $ m_\mathrm{N}= $ 1.5 GeV and $ c\tau_{\mathrm{N}}=$ 500 mm, for the case in which the N mixes with the muon sector only (green).
png pdf	Figure 8: Fits of the mass distribution for a signal of mass $ m_\mathrm{N}= $ 1.0 GeV (upper left), 1.5 GeV (upper right), 2.0 GeV (lower left), and 2.5 GeV (lower right), in the high $ L_{xy}/\sigma_{L_{xy}} $, OS, and low $ \ell_{\mathrm{B}}\ell^\pm\pi^\mp\mathrm{ mass} $ category of the dimuon channel. The blue curve corresponds to signal-plus-background fit, while the green and red curves indicate its individual signal and background components, respectively. The yellow band shows the total post-fit systematic plus statistical uncertainty.
png pdf	Figure 8-a: Fits of the mass distribution for a signal of mass $ m_\mathrm{N}= $ 1.0 GeV (upper left), 1.5 GeV (upper right), 2.0 GeV (lower left), and 2.5 GeV (lower right), in the high $ L_{xy}/\sigma_{L_{xy}} $, OS, and low $ \ell_{\mathrm{B}}\ell^\pm\pi^\mp\mathrm{ mass} $ category of the dimuon channel. The blue curve corresponds to signal-plus-background fit, while the green and red curves indicate its individual signal and background components, respectively. The yellow band shows the total post-fit systematic plus statistical uncertainty.
png pdf	Figure 8-b: Fits of the mass distribution for a signal of mass $ m_\mathrm{N}= $ 1.0 GeV (upper left), 1.5 GeV (upper right), 2.0 GeV (lower left), and 2.5 GeV (lower right), in the high $ L_{xy}/\sigma_{L_{xy}} $, OS, and low $ \ell_{\mathrm{B}}\ell^\pm\pi^\mp\mathrm{ mass} $ category of the dimuon channel. The blue curve corresponds to signal-plus-background fit, while the green and red curves indicate its individual signal and background components, respectively. The yellow band shows the total post-fit systematic plus statistical uncertainty.
png pdf	Figure 8-c: Fits of the mass distribution for a signal of mass $ m_\mathrm{N}= $ 1.0 GeV (upper left), 1.5 GeV (upper right), 2.0 GeV (lower left), and 2.5 GeV (lower right), in the high $ L_{xy}/\sigma_{L_{xy}} $, OS, and low $ \ell_{\mathrm{B}}\ell^\pm\pi^\mp\mathrm{ mass} $ category of the dimuon channel. The blue curve corresponds to signal-plus-background fit, while the green and red curves indicate its individual signal and background components, respectively. The yellow band shows the total post-fit systematic plus statistical uncertainty.
png pdf	Figure 8-d: Fits of the mass distribution for a signal of mass $ m_\mathrm{N}= $ 1.0 GeV (upper left), 1.5 GeV (upper right), 2.0 GeV (lower left), and 2.5 GeV (lower right), in the high $ L_{xy}/\sigma_{L_{xy}} $, OS, and low $ \ell_{\mathrm{B}}\ell^\pm\pi^\mp\mathrm{ mass} $ category of the dimuon channel. The blue curve corresponds to signal-plus-background fit, while the green and red curves indicate its individual signal and background components, respectively. The yellow band shows the total post-fit systematic plus statistical uncertainty.
png pdf	Figure 9: Expected and observed 95% CL limits on $ |V_\mathrm{N}|^2 $ as a function of $ m_\mathrm{N} $, in the Majorana scenario. On the upper row, the limits are derived uniquely with the dimuon channel, and are shown for the mixing scenarios ($ r_\mathrm{e} $, $ r_\mu $, $ r_\tau $) $= $(0, 1, 0) on the left and for ($ r_\mathrm{e} $, $ r_\mu $, $ r_\tau $) $=$ (0, 1/2, 1/2) on the right; on the lower row, the limits are obtained with the dimuon and mixed-flavour channel combined, for the mixing scenarios ($ r_\mathrm{e} $, $ r_\mu $, $ r_\tau $) $=$ (1/2, 1/2, 0) on the left and for ($ r_\mathrm{e} $, $ r_\mu $, $ r_\tau $) $=$ (1/3, 1/3, 1/3) on the right. In the upper left figure, results from the CMS [21,23], ATLAS [17], LHCb [24], and Belle [14] Collaborations are shown as a comparison; in the other figures, results from the CMS Collaboration [22] are reported. The mass range with no results shown corresponds to the $ \mathrm{D^0} $ meson veto listed in the lower part of Table 1.
png pdf	Figure 9-a: Expected and observed 95% CL limits on $ |V_\mathrm{N}|^2 $ as a function of $ m_\mathrm{N} $, in the Majorana scenario. On the upper row, the limits are derived uniquely with the dimuon channel, and are shown for the mixing scenarios ($ r_\mathrm{e} $, $ r_\mu $, $ r_\tau $) $= $(0, 1, 0) on the left and for ($ r_\mathrm{e} $, $ r_\mu $, $ r_\tau $) $=$ (0, 1/2, 1/2) on the right; on the lower row, the limits are obtained with the dimuon and mixed-flavour channel combined, for the mixing scenarios ($ r_\mathrm{e} $, $ r_\mu $, $ r_\tau $) $=$ (1/2, 1/2, 0) on the left and for ($ r_\mathrm{e} $, $ r_\mu $, $ r_\tau $) $=$ (1/3, 1/3, 1/3) on the right. In the upper left figure, results from the CMS [21,23], ATLAS [17], LHCb [24], and Belle [14] Collaborations are shown as a comparison; in the other figures, results from the CMS Collaboration [22] are reported. The mass range with no results shown corresponds to the $ \mathrm{D^0} $ meson veto listed in the lower part of Table 1.
png pdf	Figure 9-b: Expected and observed 95% CL limits on $ |V_\mathrm{N}|^2 $ as a function of $ m_\mathrm{N} $, in the Majorana scenario. On the upper row, the limits are derived uniquely with the dimuon channel, and are shown for the mixing scenarios ($ r_\mathrm{e} $, $ r_\mu $, $ r_\tau $) $= $(0, 1, 0) on the left and for ($ r_\mathrm{e} $, $ r_\mu $, $ r_\tau $) $=$ (0, 1/2, 1/2) on the right; on the lower row, the limits are obtained with the dimuon and mixed-flavour channel combined, for the mixing scenarios ($ r_\mathrm{e} $, $ r_\mu $, $ r_\tau $) $=$ (1/2, 1/2, 0) on the left and for ($ r_\mathrm{e} $, $ r_\mu $, $ r_\tau $) $=$ (1/3, 1/3, 1/3) on the right. In the upper left figure, results from the CMS [21,23], ATLAS [17], LHCb [24], and Belle [14] Collaborations are shown as a comparison; in the other figures, results from the CMS Collaboration [22] are reported. The mass range with no results shown corresponds to the $ \mathrm{D^0} $ meson veto listed in the lower part of Table 1.
png pdf	Figure 9-c: Expected and observed 95% CL limits on $ |V_\mathrm{N}|^2 $ as a function of $ m_\mathrm{N} $, in the Majorana scenario. On the upper row, the limits are derived uniquely with the dimuon channel, and are shown for the mixing scenarios ($ r_\mathrm{e} $, $ r_\mu $, $ r_\tau $) $= $(0, 1, 0) on the left and for ($ r_\mathrm{e} $, $ r_\mu $, $ r_\tau $) $=$ (0, 1/2, 1/2) on the right; on the lower row, the limits are obtained with the dimuon and mixed-flavour channel combined, for the mixing scenarios ($ r_\mathrm{e} $, $ r_\mu $, $ r_\tau $) $=$ (1/2, 1/2, 0) on the left and for ($ r_\mathrm{e} $, $ r_\mu $, $ r_\tau $) $=$ (1/3, 1/3, 1/3) on the right. In the upper left figure, results from the CMS [21,23], ATLAS [17], LHCb [24], and Belle [14] Collaborations are shown as a comparison; in the other figures, results from the CMS Collaboration [22] are reported. The mass range with no results shown corresponds to the $ \mathrm{D^0} $ meson veto listed in the lower part of Table 1.
png pdf	Figure 9-d: Expected and observed 95% CL limits on $ |V_\mathrm{N}|^2 $ as a function of $ m_\mathrm{N} $, in the Majorana scenario. On the upper row, the limits are derived uniquely with the dimuon channel, and are shown for the mixing scenarios ($ r_\mathrm{e} $, $ r_\mu $, $ r_\tau $) $= $(0, 1, 0) on the left and for ($ r_\mathrm{e} $, $ r_\mu $, $ r_\tau $) $=$ (0, 1/2, 1/2) on the right; on the lower row, the limits are obtained with the dimuon and mixed-flavour channel combined, for the mixing scenarios ($ r_\mathrm{e} $, $ r_\mu $, $ r_\tau $) $=$ (1/2, 1/2, 0) on the left and for ($ r_\mathrm{e} $, $ r_\mu $, $ r_\tau $) $=$ (1/3, 1/3, 1/3) on the right. In the upper left figure, results from the CMS [21,23], ATLAS [17], LHCb [24], and Belle [14] Collaborations are shown as a comparison; in the other figures, results from the CMS Collaboration [22] are reported. The mass range with no results shown corresponds to the $ \mathrm{D^0} $ meson veto listed in the lower part of Table 1.
png pdf	Figure 10: Expected and observed 95% CL limits on $ |V_\mathrm{N}|^2 $ as a function of $ m_\mathrm{N} $, in the Dirac-like scenario. On the upper row, the limits are derived uniquely with the dimuon channel, and are shown for the mixing scenarios ($ r_\mathrm{e} $, $ r_\mu $, $ r_\tau $) $=$ (0, 1, 0) on the left and for ($ r_\mathrm{e} $, $ r_\mu $, $ r_\tau $) = (0, 1/2, 1/2) on the right; on the lower row, the limits are obtained with the dimuon and mixed-flavour channel combined, for the mixing scenarios ($ r_\mathrm{e} $, $ r_\mu $, $ r_\tau $) $=$ (1/2, 1/2, 0) on the left and for ($ r_\mathrm{e} $, $ r_\mu $, $ r_\tau $) $=$ (1/3, 1/3, 1/3) on the right. In the upper left figure, results from the CMS [21,23] and ATLAS [17] Collaborations are shown as a comparison; in the other figures, results from the CMS Collaboration [22] are reported. The mass range with no results shown corresponds to the $ \mathrm{D^0} $ meson veto listed in the lower part of Table 1.
png pdf	Figure 10-a: Expected and observed 95% CL limits on $ |V_\mathrm{N}|^2 $ as a function of $ m_\mathrm{N} $, in the Dirac-like scenario. On the upper row, the limits are derived uniquely with the dimuon channel, and are shown for the mixing scenarios ($ r_\mathrm{e} $, $ r_\mu $, $ r_\tau $) $=$ (0, 1, 0) on the left and for ($ r_\mathrm{e} $, $ r_\mu $, $ r_\tau $) = (0, 1/2, 1/2) on the right; on the lower row, the limits are obtained with the dimuon and mixed-flavour channel combined, for the mixing scenarios ($ r_\mathrm{e} $, $ r_\mu $, $ r_\tau $) $=$ (1/2, 1/2, 0) on the left and for ($ r_\mathrm{e} $, $ r_\mu $, $ r_\tau $) $=$ (1/3, 1/3, 1/3) on the right. In the upper left figure, results from the CMS [21,23] and ATLAS [17] Collaborations are shown as a comparison; in the other figures, results from the CMS Collaboration [22] are reported. The mass range with no results shown corresponds to the $ \mathrm{D^0} $ meson veto listed in the lower part of Table 1.
png pdf	Figure 10-b: Expected and observed 95% CL limits on $ |V_\mathrm{N}|^2 $ as a function of $ m_\mathrm{N} $, in the Dirac-like scenario. On the upper row, the limits are derived uniquely with the dimuon channel, and are shown for the mixing scenarios ($ r_\mathrm{e} $, $ r_\mu $, $ r_\tau $) $=$ (0, 1, 0) on the left and for ($ r_\mathrm{e} $, $ r_\mu $, $ r_\tau $) = (0, 1/2, 1/2) on the right; on the lower row, the limits are obtained with the dimuon and mixed-flavour channel combined, for the mixing scenarios ($ r_\mathrm{e} $, $ r_\mu $, $ r_\tau $) $=$ (1/2, 1/2, 0) on the left and for ($ r_\mathrm{e} $, $ r_\mu $, $ r_\tau $) $=$ (1/3, 1/3, 1/3) on the right. In the upper left figure, results from the CMS [21,23] and ATLAS [17] Collaborations are shown as a comparison; in the other figures, results from the CMS Collaboration [22] are reported. The mass range with no results shown corresponds to the $ \mathrm{D^0} $ meson veto listed in the lower part of Table 1.
png pdf	Figure 10-c: Expected and observed 95% CL limits on $ |V_\mathrm{N}|^2 $ as a function of $ m_\mathrm{N} $, in the Dirac-like scenario. On the upper row, the limits are derived uniquely with the dimuon channel, and are shown for the mixing scenarios ($ r_\mathrm{e} $, $ r_\mu $, $ r_\tau $) $=$ (0, 1, 0) on the left and for ($ r_\mathrm{e} $, $ r_\mu $, $ r_\tau $) = (0, 1/2, 1/2) on the right; on the lower row, the limits are obtained with the dimuon and mixed-flavour channel combined, for the mixing scenarios ($ r_\mathrm{e} $, $ r_\mu $, $ r_\tau $) $=$ (1/2, 1/2, 0) on the left and for ($ r_\mathrm{e} $, $ r_\mu $, $ r_\tau $) $=$ (1/3, 1/3, 1/3) on the right. In the upper left figure, results from the CMS [21,23] and ATLAS [17] Collaborations are shown as a comparison; in the other figures, results from the CMS Collaboration [22] are reported. The mass range with no results shown corresponds to the $ \mathrm{D^0} $ meson veto listed in the lower part of Table 1.
png pdf	Figure 10-d: Expected and observed 95% CL limits on $ |V_\mathrm{N}|^2 $ as a function of $ m_\mathrm{N} $, in the Dirac-like scenario. On the upper row, the limits are derived uniquely with the dimuon channel, and are shown for the mixing scenarios ($ r_\mathrm{e} $, $ r_\mu $, $ r_\tau $) $=$ (0, 1, 0) on the left and for ($ r_\mathrm{e} $, $ r_\mu $, $ r_\tau $) = (0, 1/2, 1/2) on the right; on the lower row, the limits are obtained with the dimuon and mixed-flavour channel combined, for the mixing scenarios ($ r_\mathrm{e} $, $ r_\mu $, $ r_\tau $) $=$ (1/2, 1/2, 0) on the left and for ($ r_\mathrm{e} $, $ r_\mu $, $ r_\tau $) $=$ (1/3, 1/3, 1/3) on the right. In the upper left figure, results from the CMS [21,23] and ATLAS [17] Collaborations are shown as a comparison; in the other figures, results from the CMS Collaboration [22] are reported. The mass range with no results shown corresponds to the $ \mathrm{D^0} $ meson veto listed in the lower part of Table 1.
png pdf	Figure 11: Observed 95% CL lower limits on $ c\tau_{\mathrm{N}} $ as functions of the mixing ratios ($ r_\mathrm{e} $, $ r_\mu $, $ r_\tau $) for fixed N masses of 1 GeV (upper row), 1.5 GeV (middle row), and 2 GeV (lower row), in the Majorana (left column) and Dirac-like (right column) scenarios. The red crosses indicate that there is no exclusion found for that point. The orientation of the value markers on each axis identifies the associated internal lines on the plot.
png pdf	Figure 11-a: Observed 95% CL lower limits on $ c\tau_{\mathrm{N}} $ as functions of the mixing ratios ($ r_\mathrm{e} $, $ r_\mu $, $ r_\tau $) for fixed N masses of 1 GeV (upper row), 1.5 GeV (middle row), and 2 GeV (lower row), in the Majorana (left column) and Dirac-like (right column) scenarios. The red crosses indicate that there is no exclusion found for that point. The orientation of the value markers on each axis identifies the associated internal lines on the plot.
png pdf	Figure 11-b: Observed 95% CL lower limits on $ c\tau_{\mathrm{N}} $ as functions of the mixing ratios ($ r_\mathrm{e} $, $ r_\mu $, $ r_\tau $) for fixed N masses of 1 GeV (upper row), 1.5 GeV (middle row), and 2 GeV (lower row), in the Majorana (left column) and Dirac-like (right column) scenarios. The red crosses indicate that there is no exclusion found for that point. The orientation of the value markers on each axis identifies the associated internal lines on the plot.
png pdf	Figure 11-c: Observed 95% CL lower limits on $ c\tau_{\mathrm{N}} $ as functions of the mixing ratios ($ r_\mathrm{e} $, $ r_\mu $, $ r_\tau $) for fixed N masses of 1 GeV (upper row), 1.5 GeV (middle row), and 2 GeV (lower row), in the Majorana (left column) and Dirac-like (right column) scenarios. The red crosses indicate that there is no exclusion found for that point. The orientation of the value markers on each axis identifies the associated internal lines on the plot.
png pdf	Figure 11-d: Observed 95% CL lower limits on $ c\tau_{\mathrm{N}} $ as functions of the mixing ratios ($ r_\mathrm{e} $, $ r_\mu $, $ r_\tau $) for fixed N masses of 1 GeV (upper row), 1.5 GeV (middle row), and 2 GeV (lower row), in the Majorana (left column) and Dirac-like (right column) scenarios. The red crosses indicate that there is no exclusion found for that point. The orientation of the value markers on each axis identifies the associated internal lines on the plot.
png pdf	Figure 11-e: Observed 95% CL lower limits on $ c\tau_{\mathrm{N}} $ as functions of the mixing ratios ($ r_\mathrm{e} $, $ r_\mu $, $ r_\tau $) for fixed N masses of 1 GeV (upper row), 1.5 GeV (middle row), and 2 GeV (lower row), in the Majorana (left column) and Dirac-like (right column) scenarios. The red crosses indicate that there is no exclusion found for that point. The orientation of the value markers on each axis identifies the associated internal lines on the plot.
png pdf	Figure 11-f: Observed 95% CL lower limits on $ c\tau_{\mathrm{N}} $ as functions of the mixing ratios ($ r_\mathrm{e} $, $ r_\mu $, $ r_\tau $) for fixed N masses of 1 GeV (upper row), 1.5 GeV (middle row), and 2 GeV (lower row), in the Majorana (left column) and Dirac-like (right column) scenarios. The red crosses indicate that there is no exclusion found for that point. The orientation of the value markers on each axis identifies the associated internal lines on the plot.

Tables
png pdf	Table 1: List of considered SM resonances and the corresponding vetoes in the various two-particle invariant mass spectra. The first seven lines consider any possible opposite-sign pair comprising the lepton originating from the B decay and either of the displaced $ \ell^{\pm} $ and $ \pi^{\mp} $. Events that fail the veto conditions are removed from the analysis. The last two lines pertain to the displaced $ \ell^{\pm}\pi^{\mp} $ candidate and indicate that the signal extraction is not performed and exclusion limits are not provided for $ m_\mathrm{N} $ in the vetoed regions. The presence of misidentified particles is also indicated. For the $ \mathrm{D^0} $ meson vetoes, the mass range is adjusted to account for the incorrect mass hypothesis assigned to the misidentified particle.
png pdf	Table 2: Summary of the event categorisation. The events are classified into 24 mutually exclusive categories.
png pdf	Table 3: Sources of systematic uncertainty affecting the expected signal event yield. The ranges given correspond to the uncertainties across the different event categories. The uncertainty in the integrated luminosity is not reported as it is incorporated in the uncertainty in the cross section measurement used to normalize the signal.
png pdf	Table 4: Summary of the most stringent upper limits on $ |V_\mathrm{N}|^2 $ at 95% CL. For each scenario, the minimum excluded value of $ |V_\mathrm{N}|^2 $ is reported together with the mass at which it occurs.
png pdf	Table 5: Summary of the most stringent lower limits on $ c\tau_{\mathrm{N}} $ at 95% CL, obtained for the mixing scenario ($r_\mathrm{e}$, $\,r_\mu$, $\,r_\tau$) $=$ (0, 1, 0). The maximum excluded value of $ c\tau_{\mathrm{N}} $ is reported for masses $ m_\mathrm{N} = $ 1.0, 1.5 and 2.0, and for the Majorana and Dirac-like scenarios.

Summary

A search for long-lived heavy neutrinos, N, in the leptonic and semileptonic decays of B mesons produced in proton-proton collisions at $ \sqrt{s}= $ 13 TeV has been performed. The search uses a special data sample, referred to as the B-parking data sample, accumulated by the CMS experiment during 2018. The sample corresponds to an integrated luminosity of 41.6 fb$ ^{-1} $ and contains of order 10^${10}$ $ \mathrm{b} \overline{\mathrm{b}} $ events. The search is based on the process $ {\mathrm{B}}\to\ell_{\mathrm{B}}\mathrm{N} \mathrm{X} $, $ \mathrm{N}\to \ell^{\pm}\pi^{\mp} $, where the charged leptons $ \ell_{\mathrm{B}} $ and $ \ell $ are required to be $ \ell_{\mathrm{B}}\ell=\mu\mu,\,\mu\mathrm{e},\,\mathrm{or }\mathrm{e}\mu $; the hadronic recoil system, X, is treated inclusively and is not reconstructed and the $ {\mathrm{B}} =({\mathrm{B}}_{{\mathrm{u}}} $, $ {\mathrm{B}}_{{\mathrm{d}}} $, $ {\mathrm{B}}_{{\mathrm{s}}} $, $ {\mathrm{B}}_{{\mathrm{c}}}) $ decays are summed. Results are reported for the N mass range 1 $ < m_{\mathrm{N}} < $ 3 GeV. The main elements of the search signature are (i) two charged leptons, at least one of which must be a muon that satisfies the B-parking trigger requirements, (ii) a displaced vertex associated with the $ \mathrm{N}\to\ell^{\pm}\pi^{\mp} $ decay, and (iii) a peak in the invariant mass distribution of the $ \ell^{\pm}\pi^{\mp} $ system consistent with the expected signal shape. Backgrounds, which arise primarily from strong-interaction processes, are suppressed using a parametric neural network that considers a broad range of event properties. A search for N states is performed using simultaneous maximum likelihood fits to the $ \ell^{\pm}\pi^{\mp} $ invariant mass distributions in 24 mutually exclusive event categories. No significant excess of events over the SM background is observed in any of the fit regions. The results are interpreted for the separate hypotheses of a Majorana or Dirac-like particle as (i) upper limits at 95% CL on $ |V_{\mathrm{N}}|^2 $ as functions of $ m_{\mathrm{N}} $, for representative scenarios specified by different values of the mixing ratios $ r_\mathrm{e} $, $ r_\mu $, and $ r_\tau $; and as (ii) lower limits at 95% CL on $ c\tau_{\mathrm{N}} $ for 66 combinations of $ r_\mathrm{e} $, $ r_\mu $, and $ r_\tau $ for signal masses $ m_\mathrm{N} = $ 1.0, 1.5, and 2.0 GeV. The most stringent limits are $ |V_{\mathrm{N}}|^2 < $ 2.0 $\times$ 10$^{-5} $ and $ c\tau_{\mathrm{N}} > $ 10.5 m, obtained for the Majorana and Dirac-like cases, respectively, and for the scenario in which the N mixes exclusively with the muon sector. This search provides the most stringent exclusion limits on $ |V_\mathrm{N}|^2 $ for masses 1 $ < m_\mathrm{N} < $ 1.7 GeV from a collider experiment to date. Assuming the benchmark scenario $ (r_\mathrm{e},\,r_\mu,\,r_\tau) = $ (0, 1, 0) and the Majorana hypothesis, the exclusion is improved by almost one order of magnitude compared to LHCb [24], and by up to a factor of about 2 compared to Belle [14] and the most stringent previous hadron collider result [23]. Furthermore, the first upper limits on $ |V_\mathrm{N}|^2 $ are set for the mass range 1 $ < m_\mathrm{N} < $ 2 GeV for the mixing scenarios $ (r_\mathrm{e},\,r_\mu,\,r_\tau) = $ (0, 1/2, 1/2), (1/2, 1/2, 0), and (1/3, 1/3, 1/3). Finally, lower limits on $ c\tau_{\mathrm{N}} $ in the form of ternary plots for masses $ m_\mathrm{N} \leq $ 2.0 GeV are presented for the first time.

Additional Figures
png pdf	Additional Figure 1: Observed limits on $ |V_\mathrm{N}|^2 $ as a function of the mixing ratios ($ r_\mathrm{e} $, $ r_\mu $, $ r_\tau $) for fixed N masses of 1 GeV (top row), 1.5 GeV (middle row), and 2 GeV (bottom row), in the Majorana (left column) and Dirac-like (right column) scenarios. The red crosses indicate that there is no exclusion found for that point. The orientation of the value markers on each axis identifies the associated internal lines on the plot.
png pdf	Additional Figure 1-a: Observed limits on $ |V_\mathrm{N}|^2 $ as a function of the mixing ratios ($ r_\mathrm{e} $, $ r_\mu $, $ r_\tau $) for fixed N masses of 1 GeV (top row), 1.5 GeV (middle row), and 2 GeV (bottom row), in the Majorana (left column) and Dirac-like (right column) scenarios. The red crosses indicate that there is no exclusion found for that point. The orientation of the value markers on each axis identifies the associated internal lines on the plot.
png pdf	Additional Figure 1-b: Observed limits on $ |V_\mathrm{N}|^2 $ as a function of the mixing ratios ($ r_\mathrm{e} $, $ r_\mu $, $ r_\tau $) for fixed N masses of 1 GeV (top row), 1.5 GeV (middle row), and 2 GeV (bottom row), in the Majorana (left column) and Dirac-like (right column) scenarios. The red crosses indicate that there is no exclusion found for that point. The orientation of the value markers on each axis identifies the associated internal lines on the plot.
png pdf	Additional Figure 1-c: Observed limits on $ |V_\mathrm{N}|^2 $ as a function of the mixing ratios ($ r_\mathrm{e} $, $ r_\mu $, $ r_\tau $) for fixed N masses of 1 GeV (top row), 1.5 GeV (middle row), and 2 GeV (bottom row), in the Majorana (left column) and Dirac-like (right column) scenarios. The red crosses indicate that there is no exclusion found for that point. The orientation of the value markers on each axis identifies the associated internal lines on the plot.
png pdf	Additional Figure 1-d: Observed limits on $ |V_\mathrm{N}|^2 $ as a function of the mixing ratios ($ r_\mathrm{e} $, $ r_\mu $, $ r_\tau $) for fixed N masses of 1 GeV (top row), 1.5 GeV (middle row), and 2 GeV (bottom row), in the Majorana (left column) and Dirac-like (right column) scenarios. The red crosses indicate that there is no exclusion found for that point. The orientation of the value markers on each axis identifies the associated internal lines on the plot.
png pdf	Additional Figure 1-e: Observed limits on $ |V_\mathrm{N}|^2 $ as a function of the mixing ratios ($ r_\mathrm{e} $, $ r_\mu $, $ r_\tau $) for fixed N masses of 1 GeV (top row), 1.5 GeV (middle row), and 2 GeV (bottom row), in the Majorana (left column) and Dirac-like (right column) scenarios. The red crosses indicate that there is no exclusion found for that point. The orientation of the value markers on each axis identifies the associated internal lines on the plot.
png pdf	Additional Figure 1-f: Observed limits on $ |V_\mathrm{N}|^2 $ as a function of the mixing ratios ($ r_\mathrm{e} $, $ r_\mu $, $ r_\tau $) for fixed N masses of 1 GeV (top row), 1.5 GeV (middle row), and 2 GeV (bottom row), in the Majorana (left column) and Dirac-like (right column) scenarios. The red crosses indicate that there is no exclusion found for that point. The orientation of the value markers on each axis identifies the associated internal lines on the plot.

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