CMSEXO22019 ; CERNEP2024053  
Search for longlived heavy neutrinos in the decays of B mesons produced in protonproton collisions at $ \sqrt{s} = $ 13 TeV  
CMS Collaboration  
7 March 2024  
JHEP 06 (2024) 183  
Abstract: A search for longlived heavy neutrinos (N) in the decays of B mesons produced in protonproton 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 Diraclike 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: eprint arXiv:2403.04584 [hepex] (PDF) ; CDS record ; inSPIRE record ; HepData record ; Physics Briefing ; CADI line (restricted) ; 
Figures & Tables  Summary  Additional Figures  References  CMS Publications 

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} $. 
png pdf 
Figure 1a:
Feynman diagrams showing the semileptonic (upper row) and leptonic (lower row) decay of a B meson into a lepton ($ \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} $. 
png pdf 
Figure 1b:
Feynman diagrams showing the semileptonic (upper row) and leptonic (lower row) decay of a B meson into a lepton ($ \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 2a:
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 2b:
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 3a:
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 3b:
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 3c:
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 3d:
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 4a:
(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 4b:
(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. [10]. 
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 backgroundonly 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 signalplusbackground fit, while the green and red curves indicate its individual signal and background components, respectively. The yellow band shows the total postfit systematic plus statistical uncertainty. 
png pdf 
Figure 8a:
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 signalplusbackground fit, while the green and red curves indicate its individual signal and background components, respectively. The yellow band shows the total postfit systematic plus statistical uncertainty. 
png pdf 
Figure 8b:
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 signalplusbackground fit, while the green and red curves indicate its individual signal and background components, respectively. The yellow band shows the total postfit systematic plus statistical uncertainty. 
png pdf 
Figure 8c:
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 signalplusbackground fit, while the green and red curves indicate its individual signal and background components, respectively. The yellow band shows the total postfit systematic plus statistical uncertainty. 
png pdf 
Figure 8d:
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 signalplusbackground fit, while the green and red curves indicate its individual signal and background components, respectively. The yellow band shows the total postfit 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 mixedflavour 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. n the upper left figure, results from the CMS [22,24], ATLAS [18], LHCb [25], and Belle [15] Collaborations are shown as a comparison; in the other figures, results from the CMS Collaboration [23] 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 9a:
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 mixedflavour 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. n the upper left figure, results from the CMS [22,24], ATLAS [18], LHCb [25], and Belle [15] Collaborations are shown as a comparison; in the other figures, results from the CMS Collaboration [23] 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 9b:
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 mixedflavour 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. n the upper left figure, results from the CMS [22,24], ATLAS [18], LHCb [25], and Belle [15] Collaborations are shown as a comparison; in the other figures, results from the CMS Collaboration [23] 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 9c:
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 mixedflavour 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. n the upper left figure, results from the CMS [22,24], ATLAS [18], LHCb [25], and Belle [15] Collaborations are shown as a comparison; in the other figures, results from the CMS Collaboration [23] 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 9d:
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 mixedflavour 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. n the upper left figure, results from the CMS [22,24], ATLAS [18], LHCb [25], and Belle [15] Collaborations are shown as a comparison; in the other figures, results from the CMS Collaboration [23] 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} $, in the Diraclike scenario. On the upper row, the limits are derived uniquely with the dimuon channel, and are shown for the mixing scenarios ($ r_\mathrm{e} $, $ r_\mu $, $ r_\tau $) $=$ (0, 1, 0) on the left and for ($ r_\mathrm{e} $, $ r_\mu $, $ r_\tau $) = (0, 1/2, 1/2) on the right; on the lower row, the limits are obtained with the dimuon and mixedflavour channel combined, for the mixing scenarios ($ 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 [22,24] and ATLAS [18] Collaborations are shown as a comparison; in the other figures, results from the CMS Collaboration [23] 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 10a:
Expected and observed 95% CL limits on $ V_\mathrm{N}^2 $ as a function of $ m_\mathrm{N} $, in the Diraclike scenario. On the upper row, the limits are derived uniquely with the dimuon channel, and are shown for the mixing scenarios ($ r_\mathrm{e} $, $ r_\mu $, $ r_\tau $) $=$ (0, 1, 0) on the left and for ($ r_\mathrm{e} $, $ r_\mu $, $ r_\tau $) = (0, 1/2, 1/2) on the right; on the lower row, the limits are obtained with the dimuon and mixedflavour channel combined, for the mixing scenarios ($ 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 [22,24] and ATLAS [18] Collaborations are shown as a comparison; in the other figures, results from the CMS Collaboration [23] 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 10b:
Expected and observed 95% CL limits on $ V_\mathrm{N}^2 $ as a function of $ m_\mathrm{N} $, in the Diraclike scenario. On the upper row, the limits are derived uniquely with the dimuon channel, and are shown for the mixing scenarios ($ r_\mathrm{e} $, $ r_\mu $, $ r_\tau $) $=$ (0, 1, 0) on the left and for ($ r_\mathrm{e} $, $ r_\mu $, $ r_\tau $) = (0, 1/2, 1/2) on the right; on the lower row, the limits are obtained with the dimuon and mixedflavour channel combined, for the mixing scenarios ($ 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 [22,24] and ATLAS [18] Collaborations are shown as a comparison; in the other figures, results from the CMS Collaboration [23] 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 10c:
Expected and observed 95% CL limits on $ V_\mathrm{N}^2 $ as a function of $ m_\mathrm{N} $, in the Diraclike scenario. On the upper row, the limits are derived uniquely with the dimuon channel, and are shown for the mixing scenarios ($ r_\mathrm{e} $, $ r_\mu $, $ r_\tau $) $=$ (0, 1, 0) on the left and for ($ r_\mathrm{e} $, $ r_\mu $, $ r_\tau $) = (0, 1/2, 1/2) on the right; on the lower row, the limits are obtained with the dimuon and mixedflavour channel combined, for the mixing scenarios ($ 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 [22,24] and ATLAS [18] Collaborations are shown as a comparison; in the other figures, results from the CMS Collaboration [23] 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 10d:
Expected and observed 95% CL limits on $ V_\mathrm{N}^2 $ as a function of $ m_\mathrm{N} $, in the Diraclike scenario. On the upper row, the limits are derived uniquely with the dimuon channel, and are shown for the mixing scenarios ($ r_\mathrm{e} $, $ r_\mu $, $ r_\tau $) $=$ (0, 1, 0) on the left and for ($ r_\mathrm{e} $, $ r_\mu $, $ r_\tau $) = (0, 1/2, 1/2) on the right; on the lower row, the limits are obtained with the dimuon and mixedflavour channel combined, for the mixing scenarios ($ 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 [22,24] and ATLAS [18] Collaborations are shown as a comparison; in the other figures, results from the CMS Collaboration [23] 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 Diraclike (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 11a:
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 Diraclike (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 11b:
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 Diraclike (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 11c:
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 Diraclike (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 11d:
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 Diraclike (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 11e:
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 Diraclike (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 11f:
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 Diraclike (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 twoparticle invariant mass spectra. The first seven lines consider any possible oppositesign 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 Diraclike scenarios. 
Summary 
A search for longlived heavy neutrinos, N, in the leptonic and semileptonic decays of B mesons produced in protonproton collisions at $ \sqrt{s}= $ 13 TeV has been performed. The search uses a special data sample, referred to as the Bparking 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 Bparking 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 stronginteraction 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 Diraclike 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 Diraclike 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 [25], and by up to a factor of about 2 compared to Belle [15] and the most stringent previous hadron collider result [24]. 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 Diraclike (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 1a:
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 Diraclike (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 1b:
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 Diraclike (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 1c:
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 Diraclike (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 1d:
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 Diraclike (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 1e:
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 Diraclike (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 1f:
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 Diraclike (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. 
References  
1  S. Bilenky  Neutrino oscillations: From a historical perspective to the present status  NPB 908 (2016) 2  1602.00170 
2  J. Silk et al  Particle dark matter: observations, models and searches  Cambridge Univ. Press, Cambridge, ISBN~9781107653924, 2010 link 

3  G. R. Farrar and M. E. Shaposhnikov  Baryon asymmetry of the universe in the standard electroweak theory  PRD 50 (1994) 774  hepph/9305275 
4  T. Asaka, S. Blanchet, and M. Shaposhnikov  The nuMSM, dark matter and neutrino masses  PLB 631 (2005) 151  hepph/0503065 
5  T. Asaka and M. Shaposhnikov  The $ \nu $MSM, dark matter and baryon asymmetry of the universe  PLB 620 (2005) 17  hepph/0505013 
6  S. Dodelson and L. M. Widrow  Sterileneutrinos as dark matter  PRL 72 (1994) 17  hepph/9303287 
7  M. Fukugita and T. Yanagida  Baryogenesis without grand unification  PLB 174 (1986) 45  
8  P. Minkowski  $ \mu \to e\gamma $ at a rate of one out of $ 10^{9} $ muon decays?  PLB 67 (1977) 421  
9  K. N. Abazajian et al.  Light sterile neutrinos: a white paper  fermilab pub, 2012  1204.5379 
10  K. Bondarenko, A. Boyarsky, D. Gorbunov, and O. Ruchayskiy  Phenomenology of GeVscale heavy neutral leptons  JHEP 11 (2018) 032  1805.08567 
11  CHARM Collaboration  A search for decays of heavy neutrinos in the mass range 0.5  2.8 GeV  PLB 166 (1986) 473  
12  NuTeVE815 Collaboration  Search for neutral heavy leptons in a highenergy neutrino beam  PRL 83 (1999) 4943  hepex/9908011 
13  R. Barouki, G. Marocco, and S. Sarkar  Blast from the past II: Constraints on heavy neutral leptons from the BEBC WA66 beam dump experiment  SciPost Phys. 13 (2022) 118  2208.00416 
14  WA66 Collaboration  Search for heavy neutrino decays in the BEBC beam dump experiment  PLB 160 (1985) 207  
15  Belle Collaboration  Search for heavy neutrinos at Belle  PRD 87 (2013) 071102  1301.1105 
16  BABAR Collaboration  Search for heavy neutral leptons using tau lepton decays at BABAR  PRD 107 (2023) 052009  2207.09575 
17  ATLAS Collaboration  Search for heavy neutral leptons in decays of $ W $ bosons produced in 13 TeV $ pp $ collisions using prompt and displaced signatures with the ATLAS detector  JHEP 10 (2019) 265  1905.09787 
18  ATLAS Collaboration  Search for heavy neutral leptons in decays of W bosons using a dilepton displaced vertex in $ \sqrt{s}= $ 13 TeV pp collisions with the ATLAS detector  PRL 131 (2023) 061803  2204.11988 
19  CMS Collaboration  Search for heavy neutral leptons in events with three charged leptons in protonproton collisions at $ \sqrt{s} = $ 13 TeV  PRL 120 (2018) 221801  CMSEXO17012 1802.02965 
20  CMS Collaboration  Search for heavy Majorana neutrinos in samesign dilepton channels in protonproton collisions at $ \sqrt{s}= $ 13 TeV  JHEP 01 (2019) 122  CMSEXO17028 1806.10905 
21  CMS Collaboration  Search for heavy neutrinos and thirdgeneration leptoquarks in hadronic states of two $ \tau $ leptons and two jets in protonproton collisions at $ \sqrt{s} = $ 13 TeV  JHEP 03 (2019) 170  CMSEXO17016 1811.00806 
22  CMS Collaboration  Search for longlived heavy neutral leptons with displaced vertices in protonproton collisions at $ \sqrt{\mathrm{s}} $ =13 TeV  JHEP 07 (2022) 081  CMSEXO20009 2201.05578 
23  CMS Collaboration  Search for longlived heavy neutral leptons with lepton flavour conserving or violating decays to a jet and a charged lepton  link  CMSEXO21013 2312.07484 
24  CMS Collaboration  Search for longlived heavy neutral leptons decaying in the CMS muon detectors in protonproton collisions at $ \sqrt{s} $ = 13 TeV  2, 2024  CMSEXO22017 2402.18658 
25  LHCb Collaboration  Search for Majorana neutrinos in $ B^ \to \pi^+\mu^\mu^ $ decays  PRL 112 (2014) 131802  1401.5361 
26  LHCb Collaboration  Search for heavy neutral leptons in $ W^+\to\mu^{+}\mu^{\pm}\text{jet} $ decays  EPJC 81 (2021) 248  2011.05263 
27  CMS Collaboration  Enriching the physics program of the CMS experiment via data scouting and data parking  Submitted to Phys. Rep, 2024  CMSEXO23007 2403.16134 
28  CMS Collaboration  Test of lepton flavor universality in B$ ^{\pm} \to $ K$ ^{\pm}\mu^+\mu^ $ and B$ ^{\pm} \to $ K$ ^{\pm} $e$ ^+ $e$ ^ $ decays in protonproton collisions at $ \sqrt{s} $ = 13 TeV  link  CMSBPH22005 2401.07090 
29  F. F. Deppisch, P. S. Bhupal Dev, and A. Pilaftsis  Neutrinos and Collider Physics  New J. Phys. 17 (2015) 075019  1502.06541 
30  Particle Data Group  Review of particle physics  PTEP 2022 (2022) 083C01  
31  M. Drewes  The phenomenology of right handed neutrinos  Int. J. Mod. Phys. E 22 (2013) 1330019  1303.6912 
32  P. Hernández, J. JonesPérez, and O. SuarezNavarro  Majorana vs pseudoDirac neutrinos at the ILC  EPJC 79 (2019) 220  1810.07210 
33  CMS Collaboration  HEPData record for this analysis  link  
34  CMS Collaboration  Performance of the CMS Level1 trigger in protonproton collisions at $ \sqrt{s} = $ 13 TeV  JINST 15 (2020) P10017  CMSTRG17001 2006.10165 
35  CMS Collaboration  The CMS trigger system  JINST 12 (2017) P01020  CMSTRG12001 1609.02366 
36  CMS Collaboration  The CMS experiment at the CERN LHC  JINST 3 (2008) S08004  
37  CMS Collaboration  CMS luminosity measurement for the 2018 datataking period at $ \sqrt{s} = $ 13 TeV  CMS Physics Analysis Summary, 2019 link 
CMSPASLUM18002 
38  LHCb Collaboration  Measurement of the $ B_c^ $ meson production fraction and asymmetry in 7 and 13 TeV $ pp $ collisions  PRD 100 (2019) 112006  1910.13404 
39  T. Sjöstrand et al.  An introduction to PYTHIA 8.2  Comput. Phys. Commun. 191 (2015) 159  1410.3012 
40  CMS Collaboration  Extraction and validation of a new set of CMS PYTHIA8 tunes from underlyingevent measurements  EPJC 80 (2020) 4  CMSGEN17001 1903.12179 
41  NNPDF Collaboration  Parton distributions from highprecision collider data  EPJC 77 (2017) 663  1706.00428 
42  D. J. Lange  The EvtGen particle decay simulation package  NIM A 462 (2001) 152  
43  C.H. Chang, J.X. Wang, and X.G. Wu  BCVEGPY2.0: A Upgrade version of the generator BCVEGPY with an addendum about hadroproduction of the Pwave B(c) states  Comput. Phys. Commun. 174 (2006) 241  hepph/0504017 
44  GEANT4 Collaboration  GEANT 4a simulation toolkit  NIM A 506 (2003) 250  
45  CMS Collaboration  Performance of the CMS muon detector and muon reconstruction with protonproton collisions at $ \sqrt{s}= $ 13 TeV  JINST 13 (2018) P06015  CMSMUO16001 1804.04528 
46  CMS Collaboration  Particleflow reconstruction and global event description with the CMS detector  JINST 12 (2017) P10003  CMSPRF14001 1706.04965 
47  CMS Collaboration  CMS tracking performance results from early LHC operation  EPJC 70 (2010) 1165  CMSTRK10001 1007.1988 
48  CMS Collaboration  Electron and photon reconstruction and identification with the CMS experiment at the CERN LHC  JINST 16 (2021) P05014  CMSEGM17001 2012.06888 
49  K. Prokofiev and T. Speer  A kinematic and a decay chain reconstruction library  in 14th International Conference on Computing in HighEnergy and Nuclear Physics, 2005  
50  P. Baldi et al.  Parameterized neural networks for highenergy physics  EPJC 76 (2016) 235  1601.07913 
51  K. Fukushima  Visual feature extraction by a multilayered network of analog threshold elements  IEEE Transactions on Systems Science and Cybernetics 5 (1969) 322  
52  F. Chollet et al.  Keras  link  
53  M. Abadi et al.  TensorFlow: A system for largescale machine learning  in Proceedings of the 12th USENIX Conference on Operating Systems Design and Implementation, OSDI'16, USENIX Association, 2016  1605.08695 
54  D. P. Kingma and J. Ba  Adam: A method for stochastic optimization  1412.6980  
55  F. Pedregosa et al.  Scikitlearn: Machine learning in Python  J. Mach. Learn. Res. 12 (2011) 2825  1201.0490 
56  CMS Collaboration  Measurement of the total and differential inclusive $ B^+ $ hadron cross sections in pp collisions at $ \sqrt{s} $ = 13 TeV  PLB 771 (2017) 435  CMSBPH15004 1609.00873 
57  M. J. Oreglia  A study of the reactions $ \psi^\prime \to \gamma \gamma \psi $  PhD thesis, Stanford University, . SLAC Report SLACR236, 1980 link 

58  J. E. Gaiser  Charmonium spectroscopy from radiative decays of the J/$ \psi $ and $ \psi^\prime $  PhD thesis, Stanford University, SLAC Report SLACR255, 1982  
59  P. D. Dauncey, M. Kenzie, N. Wardle, and G. J. Davies  Handling uncertainties in background shapes: the discrete profiling method  JINST 10 (2015) P04015  1408.6865 
60  R. A. Fisher  On the mathematical foundations of theoretical statistics  Phil. Trans. Roy. Soc. Lond. A 222 (1922) 309  
61  S. S. Wilks  The largesample distribution of the likelihood ratio for testing composite hypotheses  Annals Math. Statist. 9 (1938) 60  
62  A. L. Read  Presentation of search results: The $ CL_s $ technique  JPG 28 (2002) 2693  
63  G. Cowan, K. Cranmer, E. Gross, and O. Vitells  Asymptotic formulae for likelihoodbased tests of new physics  EPJC 71 (2011) 1554  1007.1727 
64  M. Drewes, J. Klarić, and J. LópezPavón  New benchmark models for heavy neutral lepton searches  EPJC 82 (2022) 1176  2207.02742 
65  B. Shuve and M. E. Peskin  Revision of the LHCb limit on Majorana neutrinos  PRD 94 (2016) 113007  1607.04258 
Compact Muon Solenoid LHC, CERN 