Searches for Heavy Neutral Leptons at FCC-ee in final states including a muon

. Searches for Heavy Neutral Leptons at FCC-ee in final states including a muon. L Bellagamba,aG Polesello,b,1N. Valle.b aINFN Sezione di Bologna, Viale C. Berti Pichat 6/2, 40127 Bologna, Italy bINFN Sezione di Pavia, Via Bassi 6, 27100 Pavia, Italy E-mail: [email protected],[email protected], [email protected] Abstract: The sensitivity of the CERN FCC-ee collider to the production of heavy neutral leptons (HNL) is investigated. The study focuses on a simplified model with a single lowmass HNL mixing with a muon, and addresses the fully leptonic and semileptonic decay modes of the HNL. Complete Monte Carlo analyses of signal and background based on a parametrised detector simulation are performed for the FCC-ee run at the Z-pole, resulting in an estimate of the intervals of the mixing parameter for which the FCC-ee will have a 95% CL sensitivity as a function of the HNL mass. 1Corresponding author. Contents 1 Introduction 1 2 The simulation setup 2 2.1 Model definition and signal generation 2 2.2 The IDEA detector and its simulation 3 3 Fully leptonic muon channel with µ+µ−ν¯νfinal state 4 3.1 Event processing and reconstruction 4 3.2 Final selection and signal sensitivity 6 4 Semi-leptonic muon channel with µνjj final state 8 4.1 Event reconstruction 9 4.2 Preselection 10 4.3 Prompt analysis 11 4.4 Long lived analysis 16 5 Combined results and conclusions 18 1 Introduction The next generation of proposed e+e−circular colliders, such as the CERN FCC-ee [1], will provide access to a broad range of physics studies. The production of HNLs has been identified as one of the most promising new physics channels for FCC-ee at the Z pole in a seminal paper of 2014 [2]. Several different decay channels and lifetime scenarios will be accessible at the FCC, yielding severe requirements on the performance of the detectors, which must be quantified through detailed studies taking into account realistic performance figures for the foreseen detectors. Detailed discussions of previous experimental studies targeting FCC-ee are contained in [3,4]. The present study aims to evaluate the sensitivity for the production of HNLs to the e+e−future collider, at the centre of mass energy √s= 91.2GeV and with target integrated luminosity Lint = 2.0×108pb−1, distributed over three energy points around the Zpeak corresponding to 6×1012 e+e−→Zinteractions. A HNL mass region ranging from 5GeV to 85 GeV is investigated. We study the production of HNL in Zdecay through mixing with light neutrinos. The HNLs decay to a virtual or real Zor Wvector boson and, respectively a light neutrino or a lepton. The vector boson decays in turn to two fermions, as shown in the diagrams of Figure 1. We concentrate on a benchmark model with a single light HNL mixing only with muons, so the model is defined in terms of two parameters: the HNL mass (MN1) and – 1 – Figure 1: Diagrams for production and decay of a heavy neutral lepton in the decay of a Zboson. the mixing parameter UµN with the active neutrino. Prompt and long-lived signatures are both possible, depending on the value of those parameters. Two decay channels are considered: •a fully leptonic final state µ+µ−ν, which yields a very clean final state signature, and is produced both through the mediation of a charged and a neutral vector boson. The branching fraction is approximately 5% over the parameter range of interest. •The semileptonic decay into µjj′, where j, j′are jets from q¯q′pairs coming from the charged vector boson coupling with HNL and the muon. This channel is the most copiously produced, with a total branching fraction of approximately 50% over the full HNL mass range of interest. Moreover, this channel, with a single neutrino in the final state, allows the complete reconstruction both of the mass of the HNL and of the energy of the recoiling neutrino from the Zdecay, providing a very strong handle for the reduction of non-resonant background sources. The present study complements and completes the results shown in the Snowmass reports [3,4], which focused on long-lived signatures, and for which the results including consideration of experimental effects were limited to leptonic decays of the HNL. The experimental sensitivity of a future circular e+e−collider to the prompt HNL decay in µjj′ has been studied in a master thesis [5] and in two papers focused on the CEPC collider in China [6,7]. We improve on the previous work by performing a full Monte Carlo study based on a parametrised simulation of the expected performance for the IDEA detector proposal [8]. Background studies rely on the centrally produced large background statistics for the FCC Physics-Experiment-Detector (PED) studies [9]. Both prompt and long-lived (LLP, long-lived particles) signatures are studied in an integrated environment, which offers the possibility of statistically combining the different channels studied. The paper is organised as follows. We first describe the generation of signal and background followed by a description of detector simulation and event reconstruction, with special focus on the reconstruction of vertices in the inner detector and of hadronic jets. In the following two sections, the fully leptonic and semi-leptonic analyses are described separately, arriving at the definition of optimal signal regions. Based on these selections, the – 2 – covered area for each analysis in the model parameter space is assessed. Finally, the results of the different analyses are combined and compared to existing experimental limits. 2 The simulation setup The discovery potential for Heavy Neutral Leptons with the IDEA detector [8] at FCC-ee is studied through a detailed Monte Carlo analysis. The generated events are passed through a parametrised simulation of the detector response, and physics objects for analysis are reconstructed from the output of the simulation. In the following, we provide some details on the event simulation procedure. 2.1 Model definition and signal generation The model of interest is implemented in the SM_HeavyN_LO [10–12] package, and signal samples were generated with MG5aMC@NLO [13]. The masses of the heavy neutrinos N2and N3were set to 10 TeV, and all mixing terms were set to zero, except for the mixining UµN between the muon and the HNL (N1) in the model. The associated production of a muon (anti)neutrino and the heavy neutrino N1was simulated at a centre-of-mass energy of 91.2GeV, with the N1directly decayed into the final state of interest in the MG5aMC@NLO process card, so as to have the correct decay kinematics. For the analysis addressing the semileptonic decay, a scan was performed on the mass of N1(MN1) between 5 and 85 GeV. For each mass a scan on UµN was performed in a range going from the minimal coupling yielding at least one event decaying within 2.5 meters of the centre of the detector for the full FCC-ee Z-pole statistics, to U2 µN = 5 ×10−4which is excluded by existing experiments. A total of 10k events were generated for each sample. For the fully leptonic case, a scan was performed over MN1between 10 and 50 GeV with a step of 5 GeV and for couplings UµN in the range from 10−2to 5×10−6. For each sample 2k events were generated. The LHE files generated with MG5aMC@NLO were hadronised with PYTHIA8 [14] and then fed into the DELPHES [15] fast simulation of the IDEA detector, based on the official data cards used for the "Winter2023" production of backgrounds [16]. For the backgrounds from Zdecays, the official samples produced by the central software group for the FCC PED studies under the tag “Winter2023” were used [9]. The total available Monte Carlo statistics correspond to the production of approximately 3×109 e+e−→Zevents. The irreducible background from the four-fermion process e+e−→µνjj was produced at LO with MG5aMC@NLO, including both the associated production of a real and a virtual W, and Z/γ production followed by the radiation of a virtual Woff one of the decay legs of the Z. The only generation-level requirements were that leptons and jets were produced within a pseudorapidity of ±5and that the invariant mass of the two jets was in excess of 5 GeV. The cross-section for the process is 3.2 fb, and a sample of 500k events was – 3 – produced, corresponding to approximately the full expected statistics for the FCC-ee run at the Zpole. The events were then processed through the same PYTHIA8-DELPHES chain as the signal events. 2.2 The IDEA detector and its simulation The IDEA detector concept is a proposal for a general-purpose detector for the FCC-ee. The design includes an inner detector composed of 5 Monolithic silicon pixel (MAPS) layers followed by a high-transparency and high-resolution drift chamber. Outside the inner detector is a dual-readout electromagnetic (EM) crystal calorimeter providing high-precision energy measurement of photons and electrons, followed by a superconducting solenoid producing a 2 T magnetic field. Outside the solenoid is located a dual-readout fibre calorimeter, providing, together with the EM calorimeter, high precision energy measurement of hadrons. The detector is completed by three µ-rwell layers for muon detection, embedded in the return yoke of the solenoid. The present analysis relies on the parametrised simulation in DELPHES of the inner detector for the estimate of the tracking and vertexing performance of IDEA, complemented by a parametrised simulation of the calorimeter response to reconstruct hadronic jets. The DELPHES simulation software relies on a full description of the geometry of the IDEA vertex detector and drift chamber and accounts for the finite detector resolution and for the multiple scattering in each tracker layer. It turns charged particles emitted within the angular acceptance of the tracker into five-parameter tracks (the helix parameters that describe the trajectory of the particle, including the transverse and longitudinal impact parameters), and determines the full covariance matrix of these parameters. Vertices are reconstructed using these tracks as input, based on a simple χ2minimisation with constraints, producing 3D vertices with their χ2and covariance matrix. More details on the vertexing code used here can be found in [17]. The calorimeter response is simulated by smearing the energy of electrons and photons based on the expected resolution of the crystal EM calorimeter, parametrised as σ(E) E=0.03 √E⊕0.005 ⊕0.002 E. The response for hadrons is parametrised as σ(E) E=0.3 √E⊕0.01 ⊕0.05 E, which is the expected response for the dual readout fiber calorimeter. From the tracks and energy depositions in the calorimeter, particle flow objects (PFOs) are built. Reconstructed tracks are used for charged particles. For neutrals, the PFOs are vectors with magnitude equal to the calorimetric energy measurement, and direction corresponding to the segment connecting the centre of the detector with the centre of the face of the hit calorimeter cell, smeared by the size of the cell. Hadronic jets are reconstructed giving collections of particle flow objects in input to the FASTJET package [18]. – 4 – 3 Fully leptonic muon channel with µ+µ−ν¯νfinal state The decay of the HNL into µµνµcan take place through the virtual exchange of an off-shell Zor a Wboson, and it has a branching fraction of ∼5% in the considered model. It is an experimentally clean channel with only two reconstructed muons in the detector and missing energy due to escaping neutrinos. The long-lived signature, which characterizes HNL decays in a significant portion of the parameter space, can be exploited to suppress the massive Standard Model background due to the decay of Zto muons, taus and heavy flavours and to the four fermion process e+e−→µµνν. 3.1 Event processing and reconstruction The signal and background events are generated and reconstructed using the DELPHES fast simulation as described in Section 2. A pre-selection is applied that requires two final-state muons with momentum larger than 3 GeV and nothing else in the detector. In addition, the two muon tracks are required to be fitted to a common vertex, and a cut on the χ2per degree of freedom, χ2/ndf <10, is applied to ensure a reasonable fit quality. The distance between the reconstructed vertex and the interaction point (IP) is the crucial parameter used to separate signal from background. Figures 2and 3show, for two generated points, the distribution of the transverse distance between the IP and the decay vertex at generator level (Dtruth xy ), before and after the pre-selection requirements (left), together with the corresponding pre-selection efficiency (right). At a large distance from the interaction point, the lower mass point, characterized by a much longer decay-length, exhibits a clear drop in the efficiency due to the acceptance of the central tracking detector. Muons without a track in the central tracking detector are not considered in the present analysis. Figure 2: Distribution of the transverse distance between the IP and the decay vertex at the generator level before and after the pre-selection requirements for 2k signal events generated at MN1= 20 GeV and U2 µN = 10−10 (left) and corresponding efficiency (right). The cross-sections of the simulated background samples are several orders of magnitude larger than the signal in a large part of the parameter space, and the generated statistics – 5 – Figure 3: Distribution of the transverse distance between the IP and the decay vertex at the generator level before and after the pre-selection requirements for 2k signal events generated at MN1= 40 GeV and U2 µN = 10−10 (left) and corresponding efficiency (right). is not sufficient to populate the tails of the distributions which contribute to the possible background. The samples can hence only suggest reasonable selection requirements for signal to background separation taking into account the intrinsic limitations of the study. The natural variable to consider for background rejection, taking advantage of the LLP topology of the signal, is the reconstructed transverse distance Dxy between the displaced vertex and the interaction point. Figure 4shows the distributions of Dxy for Z→µµ/ττ and Z→bb/cc, applying the pre-selection requirements and a further cuts cos(αµµ)>−0.95, where αµµ is the angle between the two reconstructed muon tracks at the decay vertex. The requirement on cos(αµµ)has a negligible impact on the signal efficiency and removes back-to-back topologies that could produce relatively large Dxy values due to poor vertex reconstruction. While Zdecays to muons produce prompt muons, Zdecays to taus or heavy quarks give rise to genuinely displaced vertices, arising from leptonic tau decays, semi-leptonic heavy-quark decays, and vector meson decays. However, as clearly shown in Figure 4, the background from heavy-quark production is strongly suppressed by the exclusive requirement of two final-state muons, while the τ-induced background exhibits a tail extending up to a few millimeters. 3.2 Final selection and signal sensitivity The strategy adopted in this study involves the variable Dxy to separate signal from background, following a conservative approach and assuming negligible background after the final selection requirements listed below: •2 tracks reconstructed as muons with momentum >3GeV and nothing else in the detector; •cos(αµµ)>−0.95; •a reconstructed vertex with Dxy >10 mm. – 6 – Figure 4:Dxy distribution for Z→µµ,Z→ττ and Z→bb/cc, applying pre-selection requirements and a cut on the angle between the two reconstructed muons to reject backto-back topology as described in the text. The inset shows the same distribution in linear scale. The plot has been normalized to a luminosity corresponding to 6×1012 Zevents. An improved background simulation will allow for future optimization of the selection, leveraging additional kinematic variables and potentially relaxing the Dxy requirement to enhance the sensitivity in the parameter space, especially towards higher masses. The signal efficiency for the selections described above is parameterized for each considered HNL mass as a function of log10(cτ), based on the generated grid of signal points. The results are presented in Figure 5, where the signal points in the parameter space are shown as blue dots. A very high efficiency, of order 80%, is obtained for the range of couplings for which the HNL mean decay length is comparable with the size of the inner detector. Since the adopted parametrisation has large fluctuations for low efficiency values, the efficiency is conservatively set to zero when its parametrised value falls below 10%. The final sensitivity for the HNL signal has been estimated at 95% CL assuming no SM background survives the final selection. The number of expected signal events, Nexp, is normalised to the production of 6×1012 Zbosons. Assuming negligible background and no observed events, the 95% CL limits on the number of signal events is N95 = 3. Figure 6shows 95% CL limit contours. The solid line represents the central limit, while the dashed lines correspond to relative shifts in signal efficiency by ±0.05, accounting for the uncertainty associated with the parametrization model. The threshold set at 0.1 for the signal efficiency induces a visible feature in the upper part of the exclusion curve, starting from the corner at high MN1and extending towards higher couplings. Couplings down to U2 µN ∼10−10 for a range of N1masses between 20 and 35 GeV can be excluded by this analysis. – 7 – Figure 5: Signal efficiency in the considered parameter space. The generated points are shown as blue dots. Figure 6:95% CL exclusion limits in the parameter space. The solid line represents the central limit while the dashed lines correspond to shifts in the signal efficiency by ±0.05. The effect of the threshold set at 0.1 for the signal efficiency determines the behaviour of the upper part of the exclusion curve from the corner at high MN1towards higher couplings. – 8 – Figure 12: Normalized distribution of the total reconstructed mass of the event for the backgrounds and three signal samples. The distribution are after preselection and for the prompt analysis. Sample Produced Preselection Selection Dvxp xy <0.5mm Dvxp xy <0.5mm Z→b¯ b9.36e+11 2.98e+10 5.57e+05 Z→c¯c6.96e+11 1.08e+10 4.76e+05 Z→s¯s9.36e+11 1.43e+08 7.68e+04 Z→u¯u, d ¯ d1.60e+12 2.32e+08 2.29e+04 Z→µ+µ−2.20e+11 1.21e+06 6.59e+03 Z→τ+τ−2.20e+11 1.38e+08 4.46e+05 µνqq′6.56e+05 4.91e+05 2.21e+05 Table 3: Background events passing each stage of the selection normalised to the expected statistics of the FCC-ee Z-pole run After these cuts a significant amount of backgrounds is still present, especially at high HNL masses, as shown in the right panel of Figure 10. Additional rejection can be achieved by considering a grid of test values for MN1. For each HNL test mass MN1, the Mvis variable has a peak around MN1, as shown in Figure 10. Similarly for a given value of MN1and e+e− collisions at the Z-pole the energy of the neutrino recoiling against the HNL, Eν(MN1), has a fixed value of: Eν(MN1) = M2 Z−M2 N1 2MZ .(4.1) The correlation between the two variables for the background is shown in the left panel of Figure 13. The resolution on Mvis obtained with the DELPHES simulation is shown in the right panel of Figure 13 for a signal with MN1= 50 GeV. The distribution is not gaussian, as the jets are reconstructed in DELPHES with an idealised version of the particle flow algorithm which does not account for uncertainties on the amount of calorimetric energy associated with a – 15 – Figure 13: Left: Distribution of Emiss versus Mvis for the backgrounds after selection cuts. The black rectangles show the effect of the mass selection for three values of the HNL test mass: 30, 60 and 80 GeV. Right: Distribution of the reconstructed visible mass for a signal point at MN1= 50 GeV. track. It is found that about 90% of the signal is contained within a mass window centred around the nominal visible mass with a width scaling approximately as 2×10%×pM/ GeV. A window in the (Mvis,Emiss) plane defined as: Mvis ∈MN1±2×10%pMN1/GeV Emiss ∈Eν(MN1)±2×10%pEν/GeV, shown in the left side of Figure 13 for three values of MN1, contains between 80 and 90% of the signal, except for the highest values of MN1, and selects only a small fraction of the background. After mass selection, for each point in the generated signal grid the numbers of signal and background events are calculated normalised to the expected statistics of the FCC-ee Zpole run. The statistical significance zfor each point is calculated based on the prescription in [19] and is shown in Figure 14. The line corresponding to z= 2, the 95% CL exclusion for the signal was calculated by interpolating through the generated points, which are shown as blue dots in the plot. 4.4 Long lived analysis As discussed above, long-lived signal regions are defined by the requirement Dvxp xy >0.5mm. This selection removes the irreducible 4-fermion background. The signal has a significant long-lived cross-section for MN1<70 GeV, a region in which Z→ττ is the dominant background, and the contribution from the decay of Zinto heavy quarks is strongly reduced. Therefore, as for the fully leptonic decays, we define a selection which reduces the backgrounds to zero, while maximising signal efficiency, and we define the 95% sensitivity area as the area where at least three signal events survive the selections for the expected integrated luminosity of the Z-pole run of the FCC-ee. – 16 – Figure 14: Map of the sensitivity zof the prompt analysis MN1−log10(U2 µN )plane. The generated points are shown as blue dots, and the line corresponding to z= 2 is shown in red. A selection on Mtot >85 GeV, ensuring that no neutrino is produced, strongly reduces Z→ττ. A veto on the topology where the muon and the leading jet are approximately back to back, and in the two-jet case where the jets are back to back, together with the request that Emiss >38 GeV fully eliminate the background for values of the HNL test mass smaller than or equal to 30 GeV. For higher HNL test masses, in the range 30-65 GeV, the additional contributions from heavy quarks demand more complex selection criteria, based on the same angular variables as for the prompt analysis. These criteria are shown in Table 1, and reduce the background to zero, while retaining high signal efficiency. The values of the selection efficiencies in the MN1−log10(U2 µN )plane are shown in Figure 15. On the left panel the total selection efficiency is displayed, incorporating both the request of a well-reconstructed vertex and the kinematic selection criteria; on the right panel we show the incremental efficiency of the kinematic selections. The latter is very high, between 75% and almost 100%, and for lower masses the experimental efficiency is completely dominated by the requirement that the decay occurs in the volume of the tracking detector and is reconstructed by the tracker. As explained in Section 2, for the Zdecay backgrounds only ∼3×109Monte Carlo events were generated, well short of the expected statistics at the FCC-ee Z-pole run. In order to have some confidence that the zero-event condition can be reached, the number of Zdecay events after selections as a function of Dvxp xy was fitted with an exponential for both signal regions defined above. It was found that for a cut Dvxp xy >0.1mm the extrapolated curve yields a prediction of less than one event in both cases, thus ensuring – 17 – Figure 15: Efficiency of the long-lived selections in the MN1−log10(U2 µN )plane. On the left: total selection efficiency; on the right: efficiency of the kinematic cuts with respect to the events with a reconstructed vertex in the inner tracker. The generated points are shown as blue dots. that no background from well-reconstructed events is left over. In addition, no ZMonte Carlo events would pass the selection Dvxp xy >0.2mm, and the reach curve was calculated for Dvxp xy >1,5 and 10 mm, in addition to the nominal Dvxp xy >0.5mm selection, to evaluate how much tighter cuts on the HNL decay length would affect the experimental reach. Figure 16: Curves bounding the areas where three events survive the long-lived selections in the MN1−log10(U2 µN )plane for four values of the threshold on the transverse position of the reconstructed decay vertex Dvxp xy . In Figure 16 we show the lines bounding the area with at least three detected events after selections in the MN1−log10(U2 µN )plane corresponding to the 95% CL experimental sensitivity. The results are given for the four different requirements on Dvxp xy given above. The extension of the sensitivity region towards low values of U2 µN is little affected by an increase in the threshold set on Dvxp xy . The main effect would be a reduction of the accessible – 18 – mass range towards high mass values. The loss in coverage towards higher U2 µN values would be compensated by a corresponding increase of the coverage of the prompt analysis. 5 Combined results and conclusions We have studied the experimental reach of the FCC-ee Z-pole run to the production of an HNL in a simplified benchmark model with a single experimentally accessible HNL mixing only with muons. Two different decay channels for the HNL were addressed, a semileptonic one into a muon and two jets, and a fully leptonic one into a µ+µ−pair and a neutrino. For the first case two analyses were performed, one addressing the ‘prompt’ decay of the HNL, and one addressing long-lived HNLs decaying after a measurable flight path in the detector; for the second channel only the long-lived signature was studied. The 95% CL coverages of the analyses in the MN1−U2 µN plane were obtained based on an analysis of simulated events. It is found that the long-lived analyses, thanks to the large Zstatistics allow very low values of the mixing to be reached, down to U2 µN ∼10−11 for MN1between 5 and ∼65 GeV. The ‘prompt’ analysis has larger backgrounds, but it is useful for covering higher values of U2 µN and MN1up to 85 GeV. The statistical combination of the two LLP channels was performed by summing the number of expected signal events after the selections described above for each of the two channels on a grid in the MN1−U2 µN plane. The 95% sensitivity region was calculated by interpolation as the area in which at least three signal events survive the selection, and is shown as a dashed dotted line in the left panel of Figure 17, whereas the semileptonic channel is shown as a full line, and the fully leptonic one as a dashed line. The combined Figure 17: Sensitivity limits at 95% confidence level in the MN1−U2 µN plane for the LLP analyses described in the text and for their statistical combination. Left panel: combination of the semileptonic and leptonic LLP analyses. Right panel: comparison of the coverage of the combined LLP analyses (full line) with the extrapolation to the full visible branching fraction of the HNL (dashed line), and with the line corresponding to three events with decay in the tracker (dotted line). analysis covers yields a gain of ∼10% in terms of covered values of U2 µN with respect to – 19 – the semileptonic analysis alone, corresponding to the ratio of the branching fractions of the two considered channels. The present study is based on two Monte Carlo analyses that cover between 55 and 60% of the visible HNL branching fractions. Channels which were not studied are dominated by the decay of the HNL into a neutrino and two jets via a virtual Z, and fully leptonic decays with a muon, a neutrino and an electron or a tau, via a virtual W. Under the assumption that the analysis efficiency will be the same as for the channels explicitly studied, the parameter space coverage for the combined analysis of all visible HNL decay channels can be calculated. The results are shown in the right panel of Figure 17, where the combined results of the two analyses of this paper are compared to the extrapolated reach for the complete visible decay channels and to the theoretical calculation of the line corresponding to three events decaying in the IDEA inner tracker based on the formulas of [20]. With the analysis of all decay channels, mixing values as small as approximately 70% of the theoretical limit could be covered. The results of the present study are compared with the existing experimental limits and with the expected limits for several proposed beam dump experiments in Figure 18. The theoretical curve corresponding to three HNL decaying within the volume of a detector with 4.5 m diameter and 11 m length is also shown. Thanks to the high Z statistics, these analyses could cover couplings down to U2 µN ∼10−11 for the kinematically accessible range of HNL masses. – 20 – 2510 50 100 MN 1 [GeV] 10 12 10 10 10 8 10 6 10 4 | UN |2 FCC-ee LLP N 1 jj FCC-ee prompt N 1 jj FCC-ee LLP N 1 FCC-ee theo LHC prompt LHC LLP SHiP MATHUSLA FASER2 AL3X Figure 18: Discovery potential in the MN1−U2 µN plane. The FCC-ee potential shown as a red (green) line for the prompt (long-lived) semileptonic analyses described in the text. The blue line shows the reach of the leptonic decay N1→µ+µ−ν. The dashed green line bounds the area where, out of 6×1012 Zbosons, three events with visible HNL decays inside the full IDEA detector are produced (based on the analytical formulas in [20]). The existing limits from LHC searches are given as turquoise areas. 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