EXO-22-011

EXO-22-011

# Search for heavy neutral leptons in final states with electrons, muons, and
hadronically decaying tau leptons in proton-proton collisions at
$\sqrt{s}=13\TeV$

The CMS Collaboration

###### Abstract

A search for heavy neutral leptons (HNLs) of Majorana or Dirac type using
proton-proton collision data at $\sqrt{s}=13\TeV$ is presented. The data were
collected by the CMS experiment at the CERN LHC and correspond to an
integrated luminosity of 138. Events with three charged leptons (electrons,
muons, and hadronically decaying tau leptons) are selected, corresponding to
HNL production in association with a charged lepton and decay of the HNL to
two charged leptons and a standard model (SM) neutrino. The search is
performed for HNL masses between 10and 1.5. No evidence for an HNL signal is
observed in data. Upper limits at 95% confidence level are found for the
squared coupling strength of the HNL to SM neutrinos, considering exclusive
coupling of the HNL to a single SM neutrino generation, for both Majorana and
Dirac HNLs. The limits exceed previously achieved experimental constraints for
a wide range of HNL masses, and the limits on tau neutrino coupling scenarios
with HNL masses above the boson mass are presented for the first time.

##  0.1 Introduction

The observation of neutrino oscillations [1, 2, 3] implies that neutrinos have
a nonzero mass [4]. Direct neutrino mass measurements [5, 6], as well as
constraints from cosmological observations [7, 8, 9], indicate that the
neutrino masses are much smaller than those of the other fermions in the
standard model (SM) of particle physics. A possible mechanism for the
generation of gauge-invariant neutrino mass terms and an explanation of their
small scale is the see-saw mechanism [10, 11, 12, 13, 14, 15, 16, 17], which
introduces new heavy neutral leptons (HNLs) with right-handed chirality that
are singlets under all SM gauge groups, but mix with the SM neutrinos. In
addition, HNL models can provide a viable dark matter candidate [18, 19], and
a mechanism to generate the matter-antimatter asymmetry of the universe [20,
21, 22].

Figure 1: Examples of Feynman diagrams for production and decay of an HNL
(indicated with the symbol $\mathrm{N}$) resulting in final states with three
charged leptons. The production processes DY (upper row and lower left) and
VBF (lower right) are shown, with decays mediated by a boson (upper row and
lower right) or a boson (lower left). In the left column, HNLs of Majorana
type with an LNV decay are shown, whereas the right column has HNLs of Dirac
type with an LNC decay. The leptons that couple directly to the HNL (indicated
with the symbol ) are restricted to the SM generation that couples with the
HNL, whereas the leptons from the and boson decays (indicated with the symbol
$\Pell^{\prime}$) can be from any SM generation.

We consider a simplified model with a single HNL (labelled $\mathrm{N}$ in
diagrams and formulas) of Majorana or Dirac type that couples through the
neutrino mixing matrix exclusively to a single generation of SM neutrinos [23,
24]. The signatures of such models in proton-proton ($\Pp\Pp$) collisions have
been studied extensively [25, 26, 27, 28, 17, 29, 30, 31]. We focus on the
production in association with a charged lepton $\HepParticle{\ell}{}{\pm}$,
which proceeds via the charged-current Drell–Yan (DY) process
$\PQq\PAQq^{\prime}\to\PWpm\to\mathrm{N}\HepParticle{\ell}{}{\pm}$ [32, 33] or
via the vector boson fusion (VBF) process
$\PQq\PGg\to\mathrm{N}\HepParticle{\ell}{}{\pm}\PQq^{\prime}$ [34, 35, 36,
37]. Several searches for this production mode have been performed by the
ATLAS, CMS, and LHCb experiments at the CERN LHC [38, 39, 40, 41, 42, 43, 44,
45, 46, 47, 48]. The fully leptonic decay channel
$\mathrm{N}\to\Pell\Pell\PGn$ results in final states with three charged
leptons, as illustrated in Fig. 1. Due to the assumption of an exclusive
coupling to a single SM generation, the charged lepton originating from the
HNL production and the one from the first decay vertex in the case of -boson-
mediated decays are necessarily of the same flavour and from the generation to
which the HNL couples. In the case of an HNL of Majorana type, both lepton
number violating (LNV) and lepton number conserving (LNC) decays are possible,
and as a result these two charged leptons can be of the same or opposite
charge. For an HNL of Dirac type, only LNC decays are possible and these two
charged leptons thus always have opposite charge.

In this article, we present a search for HNLs in events with three charged
leptons (electrons , muons , and hadronically decaying tau leptons
$\HepParticle{\PGt}{\mathrm{h}}{}$, in the following referred to as
“leptons”), using $\Pp\Pp$ collision data collected in 2016–2018 at
$\sqrt{s}=13\TeV$ and corresponding to an integrated luminosity of 138. We
select events with all possible combinations of three light leptons (electrons
and muons), resulting in the $\Pe\Pe\Pe$, $\Pe\Pe\PGm$, $\Pe\PGm\PGm$, and
$\PGm\PGm\PGm$ flavour channels, as well as events with one
$\HepParticle{\PGt}{\mathrm{h}}{}$ and any combination of two light leptons,
resulting in the $\Pe\Pe\HepParticle{\PGt}{\mathrm{h}}{}$,
$\Pe\PGm\HepParticle{\PGt}{\mathrm{h}}{}$, and
$\PGm\PGm\HepParticle{\PGt}{\mathrm{h}}{}$ flavour channels. Events with an
HNL decay mediated by a boson or with an LNC decay mediated by a boson result
in events with an opposite-sign same-flavour (OSSF) lepton pair, whereas
events without such a pair are only possible for an LNV decay. The HNL
scenarios with exclusive electron (muon) neutrino coupling are only probed in
the $\Pe\Pe\Pe$ and $\Pe\Pe\PGm$ ($\PGm\PGm\PGm$ and $\Pe\PGm\PGm$) channels.
In the scenario of exclusive tau neutrino couplings, the two tau leptons can
decay leptonically or hadronically, and thus the $\Pe\Pe\Pe$, $\Pe\Pe\PGm$,
$\Pe\PGm\PGm$, and $\PGm\PGm\PGm$ channels provide sensitivity to HNL events
where both tau leptons decay leptonically, whereas the
$\Pe\Pe\HepParticle{\PGt}{\mathrm{h}}{}$,
$\Pe\PGm\HepParticle{\PGt}{\mathrm{h}}{}$, and
$\PGm\PGm\HepParticle{\PGt}{\mathrm{h}}{}$ channels provide sensitivity where
one tau lepton each decays leptonically and hadronically. Two strategies based
on event categorization or on machine-learning discriminants are employed to
separate the HNL signal from the SM background, where diboson production is
the most important contribution. Our results are interpreted for HNL masses
$m_{\mathrm{N}}$ between 10and 1.5. To facilitate reinterpretations within
more general HNL models [49, 50], we provide tabulated results in the HEPData
record for this analysis [51].

The CMS Collaboration presented in Ref. [42] a search in events with three
light leptons using $\Pp\Pp$ collision data collected in 2016 at
$\sqrt{s}=13\TeV$ and corresponding to an integrated luminosity of 35.9,
constraining the mixing parameter $\abs{V_{\Pell\mathrm{N}}}^{2}$ between the
HNL and the SM neutrino generation for $m_{\mathrm{N}}$ between 1and 1.2. This
article supersedes those results, and improves them not only because of the
larger data set, but also from refined light-lepton identification (ID)
criteria, improved background estimation techniques, and signal-to-background
discrimination based on machine learning. Additionally, we include for the
first time in HNL searches at the LHC events with
$\HepParticle{\PGt}{\mathrm{h}}{}$ and use state-of-the-art
$\HepParticle{\PGt}{\mathrm{h}}{}$ ID techniques.

The mean lifetime of an HNL is proportional to
$m_{\mathrm{N}}^{-5}V_{\Pell\mathrm{N}}^{-2}$ [52]. The HNL events that have a
large decay length compared with the impact parameter resolution of the CMS
tracker have a reduced selection efficiency in this analysis because we
require that leptons originate from the primary interaction vertex (PV). Two
dedicated HNL searches presented by the CMS Collaboration, based on the same
$\Pp\Pp$ collision data set used in this analysis, reconstruct the secondary
HNL decay vertex in events with three light leptons [46] or apply a displaced
jet tagger to events with two light leptons [48], and constrain long-lived HNL
scenarios for $1<m_{\mathrm{N}}<20\GeV$. The results of this analysis are
complementary since they probe short-lived HNL scenarios with
$m_{\mathrm{N}}>10\GeV$ not excluded by the dedicated searches for long-lived
HNLs.

##  0.2 The CMS detector and event reconstruction

The central feature of the CMS apparatus is a superconducting solenoid of 6m
internal diameter, providing a magnetic field of 3.8T. Within the solenoid
volume are a silicon pixel and strip tracker, a lead tungstate crystal
electromagnetic calorimeter (ECAL), and a brass and scintillator hadron
calorimeter (HCAL), each composed of a barrel and two endcap sections. Forward
calorimeters extend the pseudorapidity ($\eta$) coverage provided by the
barrel and endcap detectors. Muons are measured in gas-ionization detectors
embedded in the steel flux-return yoke outside the solenoid. A more detailed
description of the CMS detector, together with a definition of the coordinate
system used and the relevant kinematic variables, is reported in Refs. [53,
54].

Events of interest are selected using a two-tiered trigger system. The first
level, composed of custom hardware processors, uses information from the
calorimeters and muon detectors to select events at a rate of around 100kHz
within a fixed latency of about 4 [55]. The second level, known as the high-
level trigger, consists of a farm of processors running a version of the full
event reconstruction software optimized for fast processing, and reduces the
event rate to around 1kHz before data storage [56].

The global event reconstruction with the particle-flow (PF) algorithm [57]
reconstructs and identifies each individual particle in an event, with an
optimized combination of all subdetector information. In this process, the
identification of the particle type (photon, electron, muon, charged or
neutral hadron) plays an important role in the determination of the particle
direction and energy. Photons are identified as ECAL energy clusters not
linked to the extrapolation of any charged-particle trajectory to the ECAL.
Electrons are identified as a charged-particle track and potentially many ECAL
energy clusters corresponding to the extrapolation of this track to the ECAL
and to possible bremsstrahlung photons emitted along the way through the
tracker material. Muons are identified as tracks in the central tracker
consistent with either a track or several hits in the muon system, and
associated with calorimeter deposits compatible with the muon hypothesis.
Charged hadrons are identified as charged-particle tracks neither identified
as electrons, nor as muons. Finally, neutral hadrons are identified as HCAL
energy clusters not linked to any charged-hadron trajectory, or as a combined
ECAL and HCAL energy excess with respect to the expected charged-hadron energy
deposit. The PV is taken to be the vertex corresponding to the hardest
scattering in the event, evaluated using tracking information alone, as
described in Section 9.4.1 of Ref. [58].

For each event, hadronic jets are clustered from these reconstructed particles
using the infrared and collinear safe anti-algorithm [59, 60] with a distance
parameter of 0.4. Jet momentum is determined as the vectorial sum of all
particle momenta in the jet, and is found from simulation to be, on average,
within 5–10% of the true momentum over the entire transverse momentum ()
spectrum and detector acceptance. Additional $\Pp\Pp$ interactions within the
same or nearby bunch crossings (pileup) can contribute additional tracks and
calorimetric energy depositions to the jet momentum. To mitigate this effect,
charged particles identified to be originating from pileup vertices are
discarded and an offset correction is applied to correct for remaining
contributions. Jet energy corrections are derived from simulation to bring the
measured response of jets to that of particle-level jets on average. In situ
measurements of the momentum balance in dijet, photon+jet, +jet, and multijet
events are used to correct for any residual differences in the jet energy
scale between data and simulation [61]. Only jets with $\pt>25\GeV$ and
$\abs{\eta}<2.4$ are considered in this analysis. Additional selection
criteria are applied to each jet to remove jets potentially dominated by
anomalous contributions from various subdetector components or reconstruction
failures [62].

The missing transverse momentum vector is computed as the negative sum of all
PF candidates in an event, and its magnitude is denoted as [63]. The is
modified to account for corrections to the energy scale of the reconstructed
jets in the event. Anomalous high-events can arise from a variety of
reconstruction failures, detector malfunctions, or noncollisional backgrounds.
Such events are rejected by event filters that identify more than 85% of the
spurious high-events with a mistagging rate of less than 0.1% [63].

The DeepJet algorithm [64, 65, 66] is applied to identify jets arising from
the hadronization of hadrons. We use a loose working point to tag jets as
“jets” with a selection efficiency for quark jets of more than 90%, and a
misidentification rate for quark jets (light quark and gluon jets) of 50
(20)%.

##  0.3 Event simulation

Event samples simulated with Monte Carlo event generators are used to evaluate
the signal selection efficiency, to predict background contributions, to train
machine learning discriminators, and to validate background estimation
techniques based on control samples in data. The simulated event samples are
processed with a full simulation of the CMS detector based on the toolkit
[67], and are reconstructed with the same software as the data samples.
Additional simulated pileup interactions are added to the simulated events to
match the observed pileup distribution as well, with a mean pileup of 23 (32)
in 2016 (2017–2018) [68]. Separate event samples are generated for each data-
taking year, reflecting the differences in the LHC running conditions and the
CMS detector performance.

For the signal process, event samples are generated with the v2.6.5 program
[69, 70], using a model that extends the SM particle content by up to three
right-handed neutrinos [26, 36, 37, 29]. The DY production process is
simulated for $m_{\mathrm{N}}<80\GeV$ at leading order (LO) in the strong
coupling , whereas the simulation is performed at next-to-LO (NLO) in all
other cases. In the matrix element calculation, the NNPDF3.1 [71] parton
distribution functions (PDFs) are used for the DY production process, and the
NNPDF31.luxQED [72, 73, 74] PDFs for the VBF production process. Separate
samples are generated for HNLs that couple to electron, muon, or tau
neutrinos, and for different $m_{\mathrm{N}}$ values between 10and 1.5. The
VBF samples are generated only for masses of at least 600, since the
contribution from VBF production is only relevant at high masses. For
$m_{\mathrm{N}}>30\GeV$, no HNL lifetime effects are included in the
simulation and a fixed value of $\abs{V_{\Pell\mathrm{N}}}^{2}=10^{-4}$ is
used. The HNL production cross section is proportional to
$\abs{V_{\Pell\mathrm{N}}}^{2}$ [37], and thus the generated samples can be
used to emulate any $\abs{V_{\Pell\mathrm{N}}}^{2}$ value by applying a
corresponding normalization factor. At 30and lower, we calculate the HNL mean
lifetime analytically [75] and include it in the simulation of the HNL decay.
Samples are generated with one fixed $\abs{V_{\Pell\mathrm{N}}}^{2}$ value
between $10^{-6}$ and $10^{-3}$ for each mass point, and we emulate other
$\abs{V_{\Pell\mathrm{N}}}^{2}$ values by reweighting the HNL decay length
distribution as described in Ref. [46]. In all cases, the samples are
generated assuming an HNL of Majorana nature, including both LNV and LNC
decays, and samples for a Dirac HNL are obtained by selecting only the subset
of simulated events with LNC decays and applying appropriate event weights.

Furthermore, the generator is used to simulate background samples at NLO for
$\PW\PZ$ and $\PZ\PGg$ diboson production, for Higgs boson () production in
association with a vector boson or a top quark pair (), for triboson
production, for production in association with a or boson, for $s$-channel and
$\PQt\PZ$ single top quark production, and for four top quark production. It
is also used at LO for DY vector boson production in association with jets
($\PZ\text{+jets}$ and $\PW\text{+jets}$), production in association with a
single top quark, production in association with two bosons, and three top
quark production. Background samples for -initiated $\PW\PW$ and $\PZ\PZ$
diboson production, gluon fusion and VBF production, production, and
$t$-channel and $\PQt\PW$ single-production are generated with the 2 program
[76, 77, 78, 79, 80, 81, 82, 83, 84] at NLO. The gluon-gluon-initiated
$\PZ\PZ$ diboson production is simulated with the v7.0.1 generator [85, 86,
87] at LO. In all cases, the NNPDF3.1 PDFs are used.

The generators are interfaced with the v8.230 program [88] for the underlying
event description with the CP5 tune [89], the parton shower simulation, and
hadronization. For samples simulated at LO (NLO), jets from matrix element
calculations are merged with those from the parton shower using the MLM [90]
(FxFx [91]) matching scheme. In samples for production, the decay to four
leptons is simulated with the JHUgen v5.2.5 program [92].

##  0.4 Lepton selection

Electrons are measured in the range $\abs{\eta}<2.5$, and their momentum is
estimated by combining the energy measurement in the ECAL with the momentum
measurement in the tracker [93, 94]. Electrons with $1.44<\abs{\eta}<1.57$ in
the transition region between the barrel and endcap are not considered in the
analysis because of performance limitations of the electron reconstruction in
this region. Muons are measured in the range $\abs{\eta}<2.4$, with detection
planes made using three technologies: drift tubes, cathode strip chambers, and
resistive plate chambers [95].

We select reconstructed electrons and muons with $\pt>10\GeV$ that are
compatible with originating from the PV and isolated from other particles in
the event. The relative isolation variable $I_{\text{rel}}$ is defined as the
scalar sum of all PF particles reconstructed within a cone around the lepton
direction divided by the lepton , with the cone size defined in terms of
$\Delta R=\sqrt{\smash[b]{(\Delta\eta)^{2}+(\Delta\phi)^{2}}}$, where
$\Delta\eta$ and $\Delta\phi$ are the $\eta$ and azimuthal angle difference
between the particle and the lepton. We use a variable cone size of 0.2 for
leptons with $\pt<50\GeV$, of $10\GeV/\pt$ for $50<\pt<200\GeV$, and of 0.05
for $\pt>200\GeV$, which improves the efficiency for high-leptons by removing
the accidental overlap with other particles [96]. Additionally, corrections
for pileup contributions to $I_{\text{rel}}$ are applied. All reconstructed
electrons and muons are required to have $I_{\text{rel}}<0.4$. For electrons,
we additionally require that there be at most one tracker layer that
contributes no hit on the track, to reduce contributions from photon
conversions [93]. For muons, we additionally apply the “medium” set of ID
criteria defined in Ref. [95].

Electrons and muons produced directly from the prompt decay of HNLs, and
bosons, or tau leptons are referred to as “prompt” leptons. Background
contributions with “nonprompt” leptons arise from events with genuine leptons
produced in hadron decays and photon conversions, as well as from evens with
jet constituents misidentified as leptons. To distinguish between prompt and
nonprompt electrons and muons, the two additional sets of ID criteria defined
in Ref. [97] are applied, labelled “loose” and “tight”. The tight ID is based
on a multivariate analysis (MVA) discriminant using the methods developed for
various CMS measurements and searches with multilepton signatures [98, 99,
100, 101, 102, 103], described in more detail for the case of muons in Ref.
[104]. Tight electrons and muons are required to have the MVA discriminant
exceed certain thresholds, resulting in a prompt electron (muon) selection
efficiency of about 85 (92)%. The misidentification rate for nonprompt
electrons (muons) is less than 0.6% (about 1%). The loose ID is defined by
requiring that electrons and muons either pass the tight ID, or pass selection
requirements on some properties that are also used as inputs to the MVA
discriminant.

Jets are used to reconstruct $\HepParticle{\PGt}{\mathrm{h}}{}$ candidates
with the hadrons-plus-strips algorithm [105], which combines one or three
tracks with energy deposits in the calorimeters, to identify the
$\HepParticle{\PGt}{\mathrm{h}}{}$ decay modes. Neutral pions are
reconstructed as ECAL energy deposition “strips” with dynamic size in
$\eta$–$\phi$ from reconstructed electrons and photons, where the strip size
varies as a function of the of the electron or photon candidate. The
$\HepParticle{\PGt}{\mathrm{h}}{}$ decay mode is then obtained by combining
the charged hadrons with the strips. We consider decay modes with one or three
charged hadrons, with or without neutral pions, and require the
$\HepParticle{\PGt}{\mathrm{h}}{}$ candidate to have $\pt>20\GeV$ and
$\abs{\eta}<2.3$.

To distinguish genuine $\HepParticle{\PGt}{\mathrm{h}}{}$ decays from jets
originating from the hadronization of quarks or gluons, and from electrons and
muons, the DeepTau algorithm is used [106]. Information from all individual
reconstructed particles near the $\HepParticle{\PGt}{\mathrm{h}}{}$ axis is
combined with properties of the $\HepParticle{\PGt}{\mathrm{h}}{}$ candidate
and the event to provide a multiclassification output equivalent to a Bayesian
probability of the $\HepParticle{\PGt}{\mathrm{h}}{}$ to originate from a
genuine tau lepton, the hadronization of a quark or gluon, an electron, or a
muon. We define a “loose” and a “tight” ID for
$\HepParticle{\PGt}{\mathrm{h}}{}$ by choosing different working points of the
DeepTau discriminant for genuine tau leptons. The rate of a jet to be
misidentified as $\HepParticle{\PGt}{\mathrm{h}}{}$ by the DeepTau algorithm
depends on the and quark flavour of the jet. We estimate it in simulated
events from boson production in association with jets to be 0.43% for a
genuine $\HepParticle{\PGt}{\mathrm{h}}{}$ identification efficiency of 70%.
The misidentification rate for electrons (muons) is 2.6 (0.03)% for a genuine
$\HepParticle{\PGt}{\mathrm{h}}{}$ identification efficiency of 80 ($>$99)%.

To avoid double counting of charged-particle candidates that pass both the
electron and muon reconstruction, we remove reconstructed electrons that are
within $\Delta R<0.05$ of any reconstructed muon. Furthermore, we require that
$\HepParticle{\PGt}{\mathrm{h}}{}$ candidates be separated from any
reconstructed electron or muon passing the tight working point by $\Delta
R>0.5$. Any jet that is within $\Delta R<0.4$ of any reconstructed electron or
muon that passes the loose ID or within $\Delta R<0.5$ of a
$\HepParticle{\PGt}{\mathrm{h}}{}$ candidate that passes the tight ID is
removed as well.

##  0.5 Event selection and search strategy

We analyse events that were collected with various triggers that require the
presence of one, two, or three light leptons, with thresholds that depend on
the data-taking year and the flavour combination of the reconstructed leptons,
as listed in Table 0.5. The efficiency of the trigger selection is larger than
90% for three-lepton events everywhere, approaching 100% for events with large
lepton .

Requirements on the light-lepton values in the online and offline selections.
The first two columns give the numbers of electrons and muons in the event
($N_{\Pe}$ and $N_{\PGm}$). The third column lists the thresholds on the
reconstructed electrons and muons in the online trigger selection. The fourth
column lists the offline event selection requirements applied in addition to
the baseline requirements of $\pt(\Pell_{1})>15\GeV$ and
$\pt(\Pell_{2,3})>10\GeV$. For the $\Pe\PGm$ trigger, the requirements are
given for the highest and second-highest light lepton, referred to as
$\Pl_{1}$ and $\Pl_{2}$. The values in parentheses give the thresholds applied
in 2017 and 2018, where they are different from 2016. All events are required
to pass the conditions of at least one of the rows.  $N_{\Pe}$ $N_{\PGm}$
Online selection Offline selection $\geq$1 $\pt(\Pe_{1})>27$ (32)
$\pt(\Pe_{1})>30$ (35) $\geq$1 $\pt(\PGm_{1})>24\GeV$ $\pt(\PGm_{1})>25\GeV$
$\geq$2 $\pt(\Pe_{1})>23\GeV$, $\pt(\Pe_{2})>12\GeV$ $\pt(\Pe_{1})>25\GeV$,
$\pt(\Pe_{2})>15\GeV$ $\geq$2 $\pt(\PGm_{1})>17\GeV$, $\pt(\PGm_{2})>8\GeV$
$\pt(\PGm_{1})>20\GeV$ $\geq$1 $\geq$1 $\pt(\Pl_{1})>23\GeV$, $\pt(\Pl_{2})>8$
(12) $\pt(\Pl_{1})>25\GeV$, $\pt(\Pl_{2})>10$ (15) $\geq$3
$\pt(\Pe_{1})>16\GeV$, $\pt(\Pe_{2})>12\GeV$, $\pt(\Pe_{3})>8\GeV$
$\pt(\Pe_{1})>25\GeV$, $\pt(\Pe_{2})>15\GeV$ $\geq$2 $\geq$1
$\pt(\Pe_{1,2})>12\GeV$, $\pt(\PGm_{1})>8\GeV$ $\pt(\Pe_{1})>25\GeV$,
$\pt(\Pe_{2})>15\GeV$ $\geq$1 $\geq$2 $\pt(\Pe_{1})>9\GeV$,
$\pt(\PGm_{1,2})>9\GeV$ $\geq$3 $\pt(\PGm_{1})>12$ (10), $\pt(\PGm_{2})>10$
(5), $\pt(\PGm_{3})>5\GeV$

We select events with exactly three leptons that pass the tight ID criteria.
For a sideband enriched in events with nonprompt leptons, we retain events
where at least one lepton fails the tight but passes the loose ID criteria.
Events with additional loose leptons or with at least one jet are removed, as
well as events where all leptons have the same charge. The highest (leading)
lepton, referred to as $\Pell_{1}$, is required to have
$\pt(\Pell_{1})>15\GeV$. To ensure a high trigger efficiency, higher
thresholds are applied to the leading and second-highest (subleading) light
lepton depending on the lepton flavours present in the event, as summarized in
Table 0.5. If OSSF lepton pairs are present in an event, they are required to
have an invariant mass
$m(\HepParticle{\ell}{}{+}\HepParticle{\ell}{}{-})>5\GeV$ to remove
contributions from low-mass resonances. Additionally, we require
$\abs{m(\HepParticle{\ell}{}{+}\HepParticle{\ell}{}{-})-m_{\PZ}}>15\GeV$ for
any OSSF lepton pair, where $m_{\PZ}=91.2\GeV$ is the boson mass [107], to
remove background events with bosons. While this removes HNL signal events
with decays mediated by an on-shell boson, the SM boson background is
overwhelming in this phase space and thus the loss of sensitivity incurred by
this requirement is negligible. Finally, events with jets are removed to
suppress background contributions with top quarks.

Events are categorized by the flavour of the selected leptons. For events with
only electrons and muons, this results in the four categories $\Pe\Pe\Pe$,
$\Pe\Pe\PGm$, $\Pe\PGm\PGm$, and $\PGm\PGm\PGm$. For events with exactly one
$\HepParticle{\PGt}{\mathrm{h}}{}$, we distinguish the three categories
$\Pe\Pe\HepParticle{\PGt}{\mathrm{h}}{}$,
$\Pe\PGm\HepParticle{\PGt}{\mathrm{h}}{}$, and
$\PGm\PGm\HepParticle{\PGt}{\mathrm{h}}{}$. We do not select events with more
than one $\HepParticle{\PGt}{\mathrm{h}}{}$, since the typically smaller
signal efficiency, higher background contamination, and lower resolution of
the $\HepParticle{\PGt}{\mathrm{h}}{}$ reconstruction compared with those for
electrons and muons result in a low signal acceptance and a significant
background yield for these events.

For HNL models with $m_{\mathrm{N}}$ below the boson mass $m_{\PW}=80.4\GeV$
[107], the HNL decay proceeds via a virtual or boson, resulting in typically
low-leptons. In the case of $m_{\mathrm{N}}>m_{\PW}$, the decay will first
proceed to an on-shell boson and a lepton, with a subsequent leptonic decay of
the boson, resulting in typically higher for at least one of the leptons.
Similarly for $m_{\mathrm{N}}>m_{\PZ}$, the decay via an on-shell boson also
results in events with leptons of typically higher . Other kinematic
properties of the final-state leptons will be significantly different as well
for the cases of $m_{\mathrm{N}}<m_{\PW}$ (“low mass”) and $>$$m_{\PW}$ (“high
mass”). Thus, we define two orthogonal event selections to target the two
separate mass ranges, by categorizing events with $\pt(\Pell_{1})<55\GeV$ as
low-mass and $>$55as high-mass events.

In the low-mass selection, events are further required to have
$\ptmiss<75\GeV$ to remove background contributions with SM neutrinos, such as
and diboson production, and to have a trilepton invariant mass
$m(3\Pell)<80\GeV$ to remove $\PZ\PGg$ photon conversion events. In the high-
mass selection, the subleading lepton is required to have
$\pt(\Pell_{2})>15\GeV$ to reduce background contributions with nonprompt
leptons, and events with an OSSF lepton pair and
$\abs{m(3\Pell)-m_{\PZ}}<15\GeV$ are removed to reduce $\PZ\PGg$ photon
conversion backgrounds. To remove background contributions with charge-
misidentified electrons, events in the high-mass selection with two same-sign
electrons and a muon are required to have consistent results between three
independent charge measurements [108] for the two electrons and to have a
dielectron mass more than 15away from $m_{\PZ}$. Although charge-misidentified
electrons can also play a role in other final states, their contribution to
the background is small in other flavour channels. Charge mismeasurement for
muons is negligible [109, 110].

Definitions of the search regions (SRs) for events in the low-mass (upper
part) and high-mass (lower part) selections.  OSSF pair $\pt(\Pell_{1})$
$m(3\Pell)$ $\min m(\HepParticle{\ell}{}{+}\HepParticle{\ell}{}{-})$ SR name
() () () () Low-mass selection No $<$30 $<$80 $<$10 any La1 10–20 La2 20–30
La3 $>$30 La4 30–55 $<$80 $<$10 any La5 10–20 La6 20–30 La7 $>$30 La8 Yes
$<$30 $<$80 $<$10 any Lb1 10–20 Lb2 20–30 Lb3 $>$30 Lb4 30–55 $<$80 $<$10 any
Lb5 10–20 Lb6 20–30 Lb7 $>$30 Lb8 High-mass selection No $>$55 $<$100 any
$<$100 Ha1 $>$100 Ha2 $>$100 $<$100 $<$100 Ha3 100–150 Ha4 150–250 Ha5 $>$250
Ha6 100–200 $<$100 Ha7 $>$100 Ha8 $>$200 any Ha9 Yes $>$55 $<$75 any $<$100
Hb1 100–200 Hb2 $>$200 Hb3 $>$105 $<$100 $<$100 Hb4 100–200 Hb5 200–300 Hb6
300–400 Hb7 $>$400 Hb8 100–200 $<$100 Hb9 100–200 Hb10 200–300 Hb11 $>$300
Hb12 $>$200 $<$100 Hb13 100–200 Hb14 200–300 Hb15 $>$300 Hb16

Following the strategy applied in Ref. [42], we define a number of orthogonal
search regions (SRs) by classifying the events according to several kinematic
variables that provide a good discrimination between signal and background
contributions, as summarized in Table 0.5. Events are first sorted based on
whether they have an OSSF lepton pair or not, since background processes with
a boson contribute primarily to the OSSF events. In the low-mass region, the
SRs are then defined in bins of $\pt(\Pell_{1})$ and the smallest invariant
mass of any opposite-sign (OS) lepton pair, $\min
m(\HepParticle{\ell}{}{+}\HepParticle{\ell}{}{-})$. The SRs with
$\pt(\Pell_{1})<30\GeV$ target HNL scenarios where $m_{\mathrm{N}}$ is close
to $m_{\PW}$, such that both the lepton from the HNL production and the
leptons from the HNL decay have low . The SRs with $30<\pt(\Pell_{1})<55\GeV$,
on the other hand, target HNL scenarios with a smaller $m_{\mathrm{N}}$, such
that the lepton from the HNL production can have a large . The $\min
m(\HepParticle{\ell}{}{+}\HepParticle{\ell}{}{-})$ variable is bounded to be
smaller than $m_{\mathrm{N}}$ for HNL signal events, and thus provides
sensitivity to distinguish different HNL signal scenarios.

In the high-mass region, the SRs are defined in bins of $\min
m(\HepParticle{\ell}{}{+}\HepParticle{\ell}{}{-})$, $m(3\Pell)$, and the
transverse mass calculated with and the lepton not used for $\min
m(\HepParticle{\ell}{}{+}\HepParticle{\ell}{}{-})$, defined as
$\mT=\sqrt{\smash[b]{2\ptmiss\pt(\Pell)(1-\cos\Delta\phi)}}$, where
$\Delta\phi$ is the $\phi$ angle between the lepton and . The variable $\min
m(\HepParticle{\ell}{}{+}\HepParticle{\ell}{}{-})$ again provides
discriminating power between different HNL masses, whereas is targeted at the
reconstruction of a resonance decaying into the third lepton and an SM
neutrino that causes the in the events. Although the HNL signal events have no
such resonance and thus are distributed towards high values, SM background
processes like $\PW\PZ$ production with $\PW\to\Pell\PGn$ decays will have a
distribution of mostly below $m_{\PW}$. Finally, $m(3\Pell)$ measures a lower
bound on the energy of the $s$-channel resonance that produced the leptons in
the event, with larger values as $m_{\mathrm{N}}$ increases due to the large
partonic centre-of-mass energy required to produce high-mass HNLs, and a
distribution at lower values for the SM backgrounds that generally have a
lower production threshold.

To further improve the separation of signal and background events, we employ
machine learning classifiers based on boosted decision trees (BDTs) as
implemented in the tmva package [111]. The classifiers are trained to
distinguish HNL signal events from background events taken from simulated
samples for the $\PZ\text{+jets}$, , and $\PW\PZ$ background processes, using
both selected and sideband events to also train against nonprompt-lepton
background events. We train separate BDTs for different HNL coupling scenarios
and $m_{\mathrm{N}}$ ranges, using different event selections and categories,
and label these trainings as “BDT($m_{\mathrm{N}}$, ,
$i$$\HepParticle{\PGt}{\mathrm{h}}{}$)”. The first argument specifies one of
the five $m_{\mathrm{N}}$ ranges (in ), where we use the low-mass (high-mass)
selection for the ranges 10–40 and 50–75(85–150, 200–250, and 300–400). The
second argument specifies the lepton flavour of the neutrino generation to
which the HNL couples exclusively. The third argument specifies the event
categories used in the training: for electron and muon neutrino couplings, the
event categories without $\HepParticle{\PGt}{\mathrm{h}}{}$ are used,
$\Pe\Pe\Pe$, $\Pe\Pe\PGm$, $\Pe\PGm\PGm$, and $\PGm\PGm\PGm$, labelled as
“0$\HepParticle{\PGt}{\mathrm{h}}{}$”. For tau neutrino couplings, separate
trainings are performed for final states with no
$\HepParticle{\PGt}{\mathrm{h}}{}$ at generator level, using the
0$\HepParticle{\PGt}{\mathrm{h}}{}$ event categories, and for final states
with at least one $\HepParticle{\PGt}{\mathrm{h}}{}$ at generator level, using
the $\Pe\Pe\HepParticle{\PGt}{\mathrm{h}}{}$,
$\Pe\PGm\HepParticle{\PGt}{\mathrm{h}}{}$, and
$\PGm\PGm\HepParticle{\PGt}{\mathrm{h}}{}$ event categories, labelled as
“1$\HepParticle{\PGt}{\mathrm{h}}{}$”.

The input variables to the BDTs are the kinematic properties of the
reconstructed leptons; invariant and transverse masses of different dilepton
and trilepton systems; the number of jets; kinematic properties of the
reconstructed jets; $\Delta R$ between different lepton and lepton-jet pairs;
; and the sum of the of all reconstructed jets (leptons), referred to as
($L_{\mathrm{T}}$). Additional input variables to the BDTs trained with the
low-mass selection are various $\Delta\phi$ between and leptons or jets.
Furthermore, the BDTs trained with the low-mass selection in the
0$\HepParticle{\PGt}{\mathrm{h}}{}$ categories have the flavours and charges
of the reconstructed electrons and muons as additional input variables. A
selection of the most discriminating variables used in the different trainings
is shown in Figs. 2–4. It can be seen that the different distributions provide
sensitivity to distinguish between HNL signal and background distributions,
but also show differences in the expected distributions for different
$m_{\mathrm{N}}$ values, which is the reason to train separate BDTs for
different mass ranges. Generally good agreement is observed between data and
background prediction.

Figure 2: Comparison of observed (points) and predicted (coloured histograms)
distributions in the low-mass selection for the
0$\HepParticle{\PGt}{\mathrm{h}}{}$ categories combined. Important input
variables to the BDT training are shown: $\min
m(\HepParticle{\ell}{}{+}\HepParticle{\ell}{}{-})$ (upper left), (upper
right), $\Delta R$ between the two leptons used for $\min
m(\HepParticle{\ell}{}{+}\HepParticle{\ell}{}{-})$ ($\Delta R[\min
m(\HepParticle{\ell}{}{+}\HepParticle{\ell}{}{-})]$, lower left), $m(3\Pell)$
(lower right). The predicted background yields are shown before the fit to the
data (“prefit”). The HNL predictions for three different $m_{\mathrm{N}}$
values with exclusive coupling to tau neutrinos are shown with coloured lines,
and are normalized to the total background yield. The vertical bars on the
points represent the statistical uncertainties in the data, and the hatched
bands the total uncertainties in the predictions. The last bins include the
overflow contributions. In the lower panels, the ratios of the event yield in
data to the overall sum of the predictions are shown.

Figure 3: Comparison of observed (points) and predicted (coloured histograms)
distributions in the low-mass selection for the
1$\HepParticle{\PGt}{\mathrm{h}}{}$ categories combined. Important input
variables to the BDT training are shown: $\min
m(\HepParticle{\ell}{}{+}\HepParticle{\ell}{}{-})$ (upper left),
$\pt(\Pell_{3})$ (upper right), $m(3\Pell)$ (lower left), $L_{\mathrm{T}}$
(lower right). The predicted background yields are shown before the fit to the
data (“prefit”). The HNL predictions for three different $m_{\mathrm{N}}$
values with exclusive coupling to tau neutrinos are shown with coloured lines,
and are normalized to the total background yield. The vertical bars on the
points represent the statistical uncertainties in the data, and the hatched
bands the total uncertainties in the predictions. The last bins include the
overflow contributions. In the lower panels, the ratios of the event yield in
data to the overall sum of the predictions are shown.

Figure 4: Comparison of observed (points) and predicted (coloured histograms)
distributions in the high-mass selection for the
0$\HepParticle{\PGt}{\mathrm{h}}{}$ categories combined. Important input
variables to the BDT training are shown: $\Delta R[\min
m(\HepParticle{\ell}{}{+}\HepParticle{\ell}{}{-})]$ (upper left), (upper
right), $\pt(\Pell_{3})$ (lower left), (lower right). The predicted background
yields are shown before the fit to the data (“prefit”). The HNL predictions
for three different $m_{\mathrm{N}}$ values with exclusive coupling to tau
neutrinos are shown with coloured lines, and are normalized to the total
background yield. The vertical bars on the points represent the statistical
uncertainties in the data, and the hatched bands the total uncertainties in
the predictions. The last bins include the overflow contributions. In the
lower panels, the ratios of the event yield in data to the overall sum of the
predictions are shown.

The BDTs calculate event scores based on these input variables, and the score
can be interpreted as a measure of how likely an event is to originate from
the HNL signals used in the respective BDT training. The agreement between
data and background prediction is validated for all BDT input variables and
output scores in the control regions (CRs) defined in Section 0.6, and good
agreement is found.

For the final results, we combine the approaches based on SRs and BDTs. In the
low-mass selection, the background events used in the BDT training
predominantly have an OSSF lepton pair, whereas the SRs with no OSSF pair have
only small background yields and no significant separation between signal and
background contributions is provided by the BDTs for these events. Thus, we
analyse together the BDT score distributions for the combined SRs with an OSSF
pair (Lb1–8, as defined in Table 0.5) and the yields in the SRs without an
OSSF pair (La1–8). In the high-mass selection, good sensitivity to the HNL
signal is provided by the BDT scores for $m_{\mathrm{N}}$ up to 400for
electron and muon neutrino couplings, whereas the low expected signal yields
for larger $m_{\mathrm{N}}$ or exclusive couplings to tau neutrinos result in
a loss of sensitivity for the BDT approach. Consequentially, we use the BDT
score distributions for the combined SRs Ha1–9 and Hb1–16 when targeting
$m_{\mathrm{N}}$ up to 400for electron or muon neutrino couplings, and the
yields in these SRs otherwise.

##  0.6 Background estimation

Background contributions from SM processes are estimated with a combination of
methods based on CRs in data and simulated event samples. We distinguish
between background contributions where all three selected leptons are prompt
and those that have at least one nonprompt lepton. For prompt-lepton
backgrounds, we additionally treat processes separately that have a charge-
misidentified electron (referred to as “charge misID”) or at least one lepton
originating from the conversion of a prompt photon produced at the interaction
point. Prompt-lepton backgrounds are estimated from the simulated event
samples discussed in Section 0.3, and are dominated by $\PW\PZ$ and $\PZ\PZ$
diboson production, where the latter includes resonant contributions from
$\PH\to\PZ\PZ$ production. All other prompt-lepton background contributions,
of which the largest is from associated top quark and triboson production, are
grouped together with charge-misID contributions as “Other” in the figures.

To validate the modelling of the dominant diboson background contributions in
the simulated event samples, we define three CRs that are orthogonal to the
SRs by the requirement of an OSSF lepton pair consistent with $m_{\PZ}$. These
CRs target $\PW\PZ$ and $\PZ\PZ$ production, as well as $\PZ\PGg$ production
with photon conversion. The total yield predicted by the SM backgrounds is
compared with the observed data yield, and a correction factor is derived
where necessary. Additionally, the distributions for several observables
relevant in the SR definitions and the BDTs are compared to ensure that these
background contributions are well modelled, and to derive uncertainties in the
background normalizations.

The $\PW\PZ$ CR is defined by selecting events with exactly three tight light
leptons with $\pt(\Pell_{1})>25\GeV$ and $\pt(\Pell_{2})>15\GeV$, where two
leptons form an OSSF pair with
$\abs{m(\HepParticle{\ell}{}{+}\HepParticle{\ell}{}{-})-m_{\PZ}}<15\GeV$.
Events with jets are excluded to reduce contributions from associated top
quark production, $\ptmiss>50\GeV$ is required to account for the SM neutrino
from the boson decay, and the requirement of $\abs{m(3\Pell)-m_{\PZ}}>15\GeV$
removes contributions with photon conversions. More than 80% of the events in
the CR originate from $\PW\PZ$ production. Signal contributions to this CR are
negligible, with predicted yields of signal processes not excluded by Ref.
[42] less than 0.5% of the total background yield for all mass points in this
analysis. The total yields observed in the data agree with the prediction. The
comparison of the distributions for several observables in Fig. 5 demonstrates
good agreement as well, with deviations smaller than 10% in most bins.

Figure 5: Comparison of observed (points) and predicted (coloured histograms)
distributions in the $\PW\PZ$ CR. The leading lepton (upper left) and $\eta$
(upper right), as well as (lower left) and $\min
m(\HepParticle{\ell}{}{+}\HepParticle{\ell}{}{-})$ (lower right) are shown.
The vertical bars on the points represent the statistical uncertainties in the
data, and the hatched bands the total uncertainties in the predictions. The
last bins include the overflow contributions. In the lower panels, the ratios
of the event yield in data to the overall sum of the predictions are shown.

The $\PZ\PZ$ CR is defined by selecting events with exactly four tight light
leptons with $\pt(\Pell_{1})>15\GeV$, where the four leptons form two OSSF
pairs with
$\abs{m(\HepParticle{\ell}{}{+}\HepParticle{\ell}{}{-})-m_{\PZ}}<15\GeV$ each.
In the case of four leptons of the same flavour, the pairs are chosen such
that the sum of the mass differences with respect to $m_{\PZ}$ is minimized.
The OSSF pair with the invariant mass further away from $m_{\PZ}$ is labelled
“$\PZ_{2}$”. Events with jets are removed to reduce contributions from
associated top quark production, and
$m(\HepParticle{\ell}{}{+}\HepParticle{\ell}{}{-})>12\GeV$ is required for
every OS lepton pair to remove contributions from low-mass resonances.
Contributions from background processes other than $\PZ\PZ$ production or from
signal contamination are negligible in this CR. We find the observed yields to
be larger than the prediction, and assign a scale factor of 1.12 to the
simulated $\PZ\PZ$ samples to correct for the difference in the total yield.
After applying the scale factor, good agreement between the prediction and the
observation is found across several observables, some of which are shown in
Fig. 6. Except for a few bins with lower statistical precision, the agreement
is generally better than 10%.

Figure 6: Comparison of observed (points) and predicted (coloured histograms)
distributions in the $\PZ\PZ$ CR. The leading lepton (upper left),
$m(\HepParticle{\ell}{}{+}\HepParticle{\ell}{}{-})$ of $\PZ_{2}$
($m(\PZ_{2})$, upper right), (lower left), and $\min
m(\HepParticle{\ell}{}{+}\HepParticle{\ell}{}{-})$ (lower right) are shown.
The $\PZ\PZ$ prediction is scaled with a normalization factor of 1.12, as
discussed in the text. The vertical bars on the points represent the
statistical uncertainties in the data, and the hatched bands the total
uncertainties in the predictions. The last bins include the overflow
contributions. In the lower panels, the ratios of the event yield in data to
the overall sum of the predictions are shown.

Background contributions from processes with photon conversions are also
estimated from simulated samples. The main photon conversion background arises
from $\PZ\PGg$ production, where the photon undergoes an asymmetric conversion
into two leptons of which one has very low and is not reconstructed. For the
$\PZ\PGg$ CR, events with exactly three tight light leptons with
$\pt(\Pell_{1})>15\GeV$ are selected. To select $\PZ\PGg$ events where the
photon is radiated from one of the leptons from the boson decay but at the
same time remove contributions from $\PZ\text{+jets}$ and $\PW\PZ$ production,
we require $\abs{m(3\Pell)-m_{\PZ}}<10\GeV$, as well as that two leptons form
an OSSF pair with
$\abs{m(\HepParticle{\ell}{}{+}\HepParticle{\ell}{}{-})-m_{\PZ}}>15\GeV$.
Events with jets are removed. In this CR, about 70% of the events originate
from photon conversions. Expected signal yields for processes not excluded by
Ref. [42] are below 0.5% of the total yield. To correct for differences in the
total yield between data and prediction, we apply a scale factor of 1.11 to
simulated $\PZ\PGg$ samples. Figure 7 shows the data and predicted
distributions for several observables, with the scale factor applied, and
exhibits agreement that is typically better than 10%.

Figure 7: Comparison of observed (points) and predicted (coloured histograms)
distributions in the $\PZ\PGg$ CR. The leading lepton (upper left) and $\eta$
(upper right), (lower left), and (lower right) are shown. The $\PZ\PGg$
prediction is scaled with a normalization factor of 1.11, as discussed in the
text. The vertical bars on the points represent the statistical uncertainties
in the data, and the hatched bands the total uncertainties in the predictions.
The last bins include the overflow contributions. In the lower panels, the
ratios of the event yield in data to the overall sum of the predictions are
shown.

Simulated event samples are used to predict background contributions with
charge-misID electrons. The misID rate in simulation depends strongly on the
material included in the detector model, and is validated by dedicated
measurements in data by comparing event yields with same- and opposite-sign
electron pairs [97]. It is found that the misidentification rate is
overestimated (underestimated) in 2016 (2017–2018) samples by about 10 (50)%,
and we apply correction factors to the normalization of the charge-misID
background correspondingly.

Nonprompt-lepton background contributions arise mostly from and
$\PZ\text{+jets}$ production with an additional nonprompt lepton. They are
especially relevant in the 1$\HepParticle{\PGt}{\mathrm{h}}{}$ categories. A
“tight-to-loose” ratio method [112, 100, 113] is applied to estimate the
nonprompt-lepton background contributions from control samples in data. The
tight-to-loose ratio is defined as the probability $f$ for a loose lepton to
also satisfy the tight ID selection. It is evaluated separately for the
different lepton flavours, and is measured as a function of and $\abs{\eta}$.
For electrons and muons, $f$ is measured in a sample enriched in SM events
composed uniquely of jets produced through the strong interaction selected
with nonisolated single-lepton triggers. For
$\HepParticle{\PGt}{\mathrm{h}}{}$, $f$ is measured in samples enriched in
$\PZ\text{+jets}$ and events. The measured values of $f$ are applied as
weights to events that pass the SR selection but have one or more leptons that
pass the loose and fail the tight selection. Both simulated events and data
samples enriched in nonprompt leptons are used to validate the tight-to-loose
ratio method for all lepton flavours. Good agreement of better than 30% is
found in these tests in the most relevant kinematic distributions, with larger
deviations up to 50% only for nonprompt electrons with $\pt>55\GeV$.

##  0.7 Systematic uncertainties

Multiple sources of systematic uncertainty affect the signal prediction, the
background event yields, and the distributions of the observables used for the
signal extraction. The sources and their correlations between the data-taking
years are described below, and their impact on the fits described in Section
0.9 is summarized in Table 0.7.

The integrated luminosities for the three data-taking years have individual
uncertainties between 1.2 and 2.5% [114, 115, 116], and the overall
uncertainty for the 2016–2018 period is 1.6%. This uncertainty affects the
normalization of the background contributions from simulated event samples, as
well as the extraction of cross section limits from the final estimate of the
limit on the number of signal events.

The distribution of the number of additional $\Pp\Pp$ interactions per event
in simulation is matched to data by reweighting the profile of the true number
of interactions to the one inferred from the instantaneous luminosity profile
in data. The systematic uncertainty is estimated from a variation of the total
inelastic cross section used for this reweighting by $\pm$4.6%, which is
treated as correlated among the data-taking years.

Relative impacts of the uncertainty sources in fits for six different fit
models specified with $m_{\mathrm{N}}$ value and coupling scenario, where the
relative impact is defined as the ratio between the uncertainty from the
respective source and the total uncertainty in the HNL signal strength. The
symbol “” indicates that the corresponding uncertainty source is not
applicable.  Uncertainty source $m_{\mathrm{N}}=40\GeV$
$m_{\mathrm{N}}=200\GeV$ Luminosity, pileup reweighting 5.0% 2.6% 11.3% 5.8%
7.6% 4.4% Trigger efficiency 2.4% 10.6% 26.4% 2.9% 6.9% 5.1% Light-lepton
selection efficiency & energy calibration 8.7% 15.5% 7.9% 10.4% 18.3% 1.2%
$\HepParticle{\PGt}{\mathrm{h}}{}$ selection efficiency 2.7% 14.2% Jet energy
calibration, , tagging efficiency 10.6% 8.4% 34.4% 8.6% 12.4% 24.0% $\PW\PZ$
background normalization 1.1% 9.6% 7.4% 2.8% 5.4% 4.0% $\PZ\PZ$ background
normalization 3.9% 9.9% 8.0% 4.1% 6.1% 6.5% $\PZ\PGg$ background normalization
7.4% 8.3% 5.1% 1.9% 1.5% 12.1% Other background normalization 1.4% 5.6% 1.6%
13.8% 6.3% 10.5% Nonprompt light-lepton background 10.8% 16.0% 20.9% 15.6%
26.4% 9.1% Nonprompt $\HepParticle{\PGt}{\mathrm{h}}{}$ background 14.3% 66.7%
HNL cross section prediction 4.7% 3.5% 3.8% 3.7% 3.0% 2.1% Total systematic
23.3% 25.5% 55.1% 27.7% 35.8% 75.5% Statistical 96.8% 96.5% 83.4% 96.1% 93.3%
65.5%

The trigger selection efficiency is measured in data and simulation with
independent trigger paths based on hadronic activity and signatures. The
efficiencies in data and simulation agree within 3%, which is assigned as a
systematic uncertainty that is correlated between the data-taking years.
Additionally, the statistical uncertainty in the measured trigger efficiencies
in data is considered, separately for each data-taking year.

During the 2016 and 2017 data-taking periods, a gradual shift in the timing of
the inputs of the ECAL level-1 trigger in the region $\abs{\eta}>2.0$ caused a
specific trigger inefficiency [55]. For events containing an electron (a jet)
with $\pt>50$ (100)in the region $2.5<\abs{\eta}<3.0$ the efficiency loss is
$\approx$10–20%, depending on , $\eta$, and time. Correction factors are
derived from data and applied to the acceptance evaluated by simulation, and
the impact on our results is small.

The efficiency of the tight ID selection of light leptons is measured in data
and simulation using a “tag-and-probe” method applied to
$\PZ\to\HepParticle{\ell}{}{+}\HepParticle{\ell}{}{-}$ events [117]. Per-
lepton corrections are derived separately for electrons, muons, and
$\HepParticle{\PGt}{\mathrm{h}}{}$. Statistical and systematic uncertainties
in the correction factors are included, with the former (latter) treated as
uncorrelated (correlated) between the data-taking years. Corrections for the
differences in the electron energy scale and resolution between data and
simulation are derived from $\PZ\to\Pe\Pe$ events using only ECAL information
[93], and systematic uncertainties are considered that are correlated between
the data-taking years.

Uncertainties in the jet energy scale and resolution are evaluated from the
variations of the reconstructed jets in simulated events [61]. The variation
due to the jet energy scale, as well as an additional variation to account for
the uncertainty in the contribution from unclustered PF particles [63], is
propagated to . The jet energy scale (jet energy resolution and unclustered
energy) variation is treated as correlated (uncorrelated) between the data-
taking years. Differences in the tagging efficiency between data and
simulation are corrected by applying scale factors to simulated events.
Uncertainties in the scale factors are evaluated by separate variations for
light- and heavy-flavour jets, where both correlated and uncorrelated
variations between the three data-taking years are considered [64].

Several uncertainties are considered for the normalization of the background
processes. For the dominant $\PW\PZ$, $\PZ\PZ$, and $\PZ\PGg$ contributions,
we assign an uncertainty of 10% each, corresponding to the level of agreement
in the CRs described in Section 0.6. The SM predictions for triboson
production have a precision of about 10% [118, 119, 120, 121, 122], which is
assigned as a normalization uncertainty to the triboson background. For
associated top quark production, a normalization uncertainty of 10% is
assigned, matching the experimental precision of the latest CMS measurements
of the most important contributions [103, 113]. The uncertainty in the charge-
misID contribution originates from the correction factors and is taken to be
15% [97]. For all remaining contributions in the “Other” category, we assign a
normalization uncertainty of 20% corresponding to the experimental precision
in the signal strength of production in association with a vector boson [123].

The uncertainties in the nonprompt background contributions stem from the
tight-to-loose ratio method. For nonprompt light leptons, a normalization
uncertainty of 30% is applied when the leading nonprompt lepton is a muon, and
a -dependent uncertainty when it is an electron. In the latter case, the
uncertainty is 15% for $\pt<35\GeV$ of the electron, 30% for $35<\pt<55\GeV$,
and 50% for $\pt>55\GeV$. In the case of nonprompt
$\HepParticle{\PGt}{\mathrm{h}}{}$ leptons, a normalization uncertainty of 30%
is assigned to account for observed differences in the validation, separately
for events with and without an OSSF lepton pair because of the different
composition of sources of nonprompt $\HepParticle{\PGt}{\mathrm{h}}{}$ leptons
in these two event selections.

The HNL signal samples for $m_{\mathrm{N}}<m_{\PW}$ are simulated at LO
accuracy, and their normalization is scaled with the ratio between the SM
cross sections of boson production evaluated at next-to-NLO with the v3.1
program [124, 125, 126, 127] and at LO with , using settings identical to
those of the signal samples. The uncertainty in the signal cross section is
then evaluated from the variations of the renormalization and factorization
scale and of the PDFs in the next-to-NLO calculation and amounts to 4% in
total [46]. For the HNL signal samples with $m_{\mathrm{N}}>m_{\PW}$, the
simulation is done at NLO accuracy, and no additional scale factor is applied.
From the evaluation of scale variations and the PDF choice, we find a signal
cross section uncertainty of 3 (15)% for the DY (VBF) production mode.

##  0.8 Results

For each HNL signal scenario, a binned likelihood function $L(r,\theta)$ is
constructed from the product of Poisson probabilities to obtain the observed
yields in the relevant distributions, given the HNL signal prediction scaled
with a signal strength $r$ and the SM background estimates. Additional terms
are included to account for the systematic uncertainty sources, where $\theta$
denotes the full set of corresponding nuisance parameters [128]. Statistical
uncertainties in the predicted yields are implemented through a single
nuisance parameter in each bin for all processes [129, 130]. We consider the
cases of exclusive HNL couplings to electron, muon, and tau neutrinos
separately, and use different distributions to construct $L$ depending on the
coupling scenario and $m_{\mathrm{N}}$, as listed in Table 0.8. To obtain
background-only fits, the maximum likelihood estimator of $\theta$ with a
fixed $r=0$ is evaluated for specific fit setups. In Fig. 8, the number of
observed events in data is compared with the background predictions in the
SRs, separately combined for the 0$\HepParticle{\PGt}{\mathrm{h}}{}$ and
1$\HepParticle{\PGt}{\mathrm{h}}{}$ categories, after simultaneous background-
only fits to the SRs of all flavour channels. Furthermore, the distributions
of the BDT output scores are compared between data and prediction in Figs.
9–11, after the background-only fits corresponding to the fit setups in Table
0.8 where the corresponding BDT is used. In all figures, the signal prediction
for several HNL mass points is shown as well, with
$\abs{V_{\Pell\mathrm{N}}}^{2}$ values chosen such that the predicted signal
yield matches roughly the total background yield.

Summary of the selections, categories, and distributions used in the maximum
likelihood fits for the HNL signal points.  HNL model Selection Categories
OSSF Fitted distributions (10–40, ) low mass
0$\HepParticle{\PGt}{\mathrm{h}}{}$ no La1–8
0$\HepParticle{\PGt}{\mathrm{h}}{}$ yes BDT(10–40, ,
0$\HepParticle{\PGt}{\mathrm{h}}{}$) (40–75, ) low mass
0$\HepParticle{\PGt}{\mathrm{h}}{}$ no La1–8
0$\HepParticle{\PGt}{\mathrm{h}}{}$ yes BDT(50–75, ,
0$\HepParticle{\PGt}{\mathrm{h}}{}$) (85–125, ) high mass
0$\HepParticle{\PGt}{\mathrm{h}}{}$ any BDT(85–150, ,
0$\HepParticle{\PGt}{\mathrm{h}}{}$) (125–250, ) high mass
0$\HepParticle{\PGt}{\mathrm{h}}{}$ any BDT(200–250, ,
0$\HepParticle{\PGt}{\mathrm{h}}{}$) (250–400, ) high mass
0$\HepParticle{\PGt}{\mathrm{h}}{}$ any BDT(300–400, ,
0$\HepParticle{\PGt}{\mathrm{h}}{}$) ($\geq$400, ) high mass
0$\HepParticle{\PGt}{\mathrm{h}}{}$ any Ha1–9, Hb1–16 (10–40, ) low mass
0$\HepParticle{\PGt}{\mathrm{h}}{}$ no La1–8
0$\HepParticle{\PGt}{\mathrm{h}}{}$ yes BDT(10–40, ,
0$\HepParticle{\PGt}{\mathrm{h}}{}$) (40–75, ) low mass
0$\HepParticle{\PGt}{\mathrm{h}}{}$ no La1–8
0$\HepParticle{\PGt}{\mathrm{h}}{}$ yes BDT(50–75, ,
0$\HepParticle{\PGt}{\mathrm{h}}{}$) (85–125, ) high mass
0$\HepParticle{\PGt}{\mathrm{h}}{}$ any BDT(85–150, ,
0$\HepParticle{\PGt}{\mathrm{h}}{}$) (125–200, ) high mass
0$\HepParticle{\PGt}{\mathrm{h}}{}$ any BDT(200–250, ,
0$\HepParticle{\PGt}{\mathrm{h}}{}$) (200–400, ) high mass
0$\HepParticle{\PGt}{\mathrm{h}}{}$ any BDT(300–400, ,
0$\HepParticle{\PGt}{\mathrm{h}}{}$) ($\geq$400, ) high mass
0$\HepParticle{\PGt}{\mathrm{h}}{}$ any Ha1–9, Hb1–16 (10–40, ) low mass
0$\HepParticle{\PGt}{\mathrm{h}}{}$ no La1–8
0$\HepParticle{\PGt}{\mathrm{h}}{}$ yes BDT(10–40, ,
0$\HepParticle{\PGt}{\mathrm{h}}{}$) 1$\HepParticle{\PGt}{\mathrm{h}}{}$ no
La1–8 1$\HepParticle{\PGt}{\mathrm{h}}{}$ yes BDT(10–40, ,
1$\HepParticle{\PGt}{\mathrm{h}}{}$) (40–75, ) low mass
0$\HepParticle{\PGt}{\mathrm{h}}{}$ no La1–8
0$\HepParticle{\PGt}{\mathrm{h}}{}$ yes BDT(50–75, ,
0$\HepParticle{\PGt}{\mathrm{h}}{}$) 1$\HepParticle{\PGt}{\mathrm{h}}{}$ no
La1–8 1$\HepParticle{\PGt}{\mathrm{h}}{}$ yes BDT(50–75, ,
1$\HepParticle{\PGt}{\mathrm{h}}{}$) ($\geq$85, ) high mass all any Ha1–9,
Hb1–16

Figure 8: Comparison of the number of observed (points) and predicted
(coloured histograms) events in the SR bins, shown for the
0$\HepParticle{\PGt}{\mathrm{h}}{}$ (left column) and
1$\HepParticle{\PGt}{\mathrm{h}}{}$ (right column) categories combined. The
La1–8 and Lb1–8 (upper row), Ha1–Ha9 (middle row), and Hb1–16 (lower row) are
displayed. The predicted background yields are shown with the values of the
normalizations and nuisance parameters obtained in background-only fits
applied (“postfit”). The HNL predictions for three different $m_{\mathrm{N}}$
values with exclusive coupling to tau neutrinos are shown with coloured lines.
The vertical bars on the points represent the statistical uncertainties in the
data, and the hatched bands the total uncertainties in the background
predictions as obtained from the fits. In the lower panels, the ratios of the
event yield in data to the overall sum of the background predictions are
shown.

Figure 9: Comparison of the observed (points) and predicted (coloured
histograms) BDT output distributions of the low-mass selection, shown for the
$\Pe\Pe\Pe$ and $\Pe\Pe\PGm$ channels combined (left column) and the
$\Pe\PGm\PGm$ and $\PGm\PGm\PGm$ channels combined (right column). The output
scores BDT(10–40, , 0$\HepParticle{\PGt}{\mathrm{h}}{}$) (upper left),
BDT(10–40, , 0$\HepParticle{\PGt}{\mathrm{h}}{}$) (upper right), BDT(50–75, ,
0$\HepParticle{\PGt}{\mathrm{h}}{}$) (lower left), and BDT(50–75, ,
0$\HepParticle{\PGt}{\mathrm{h}}{}$) (lower right) are displayed. The
predicted background yields are shown with the values of the normalizations
and nuisance parameters obtained in background-only fits applied (“postfit”).
The HNL predictions for three different $m_{\mathrm{N}}$ values with exclusive
coupling to electron (left column) or muon (right column) neutrinos are shown
with coloured lines. The vertical bars on the points represent the statistical
uncertainties in the data, and the hatched bands the total uncertainties in
the background predictions as obtained from the fits. In the lower panels, the
ratios of the event yield in data to the overall sum of the background
predictions are shown.

Figure 10: Comparison of the observed (points) and predicted (coloured
histograms) BDT output distributions of the low-mass selection, shown for the
0$\HepParticle{\PGt}{\mathrm{h}}{}$ channels combined (left column) and the
1$\HepParticle{\PGt}{\mathrm{h}}{}$ channels combined (right column). The
output scores BDT(10–40, , 0$\HepParticle{\PGt}{\mathrm{h}}{}$) (upper left),
BDT(10–40, , 1$\HepParticle{\PGt}{\mathrm{h}}{}$) (upper right), BDT(50–75, ,
0$\HepParticle{\PGt}{\mathrm{h}}{}$) (lower left), and BDT(50–75, ,
0$\HepParticle{\PGt}{\mathrm{h}}{}$) (lower right) are displayed. The
predicted background yields are shown with the values of the normalizations
and nuisance parameters obtained in background-only fits applied (“postfit”).
The HNL predictions for three different $m_{\mathrm{N}}$ values with exclusive
coupling to tau neutrinos are shown with coloured lines. The vertical bars on
the points represent the statistical uncertainties in the data, and the
hatched bands the total uncertainties in the background predictions as
obtained from the fits. In the lower panels, the ratios of the event yield in
data to the overall sum of the background predictions are shown.

Figure 11: Comparison of the observed (points) and predicted (coloured
histograms) BDT output distributions of the high-mass selection, shown for the
$\Pe\Pe\Pe$ and $\Pe\Pe\PGm$ channels combined (left column) and the
$\Pe\PGm\PGm$ and $\PGm\PGm\PGm$ channels combined (right column). The output
scores BDT(85–150, , 0$\HepParticle{\PGt}{\mathrm{h}}{}$) (upper left),
BDT(85–150, , 0$\HepParticle{\PGt}{\mathrm{h}}{}$) (upper right), BDT(200–250,
, 0$\HepParticle{\PGt}{\mathrm{h}}{}$) (middle left), BDT(200–250, ,
0$\HepParticle{\PGt}{\mathrm{h}}{}$) (middle right), BDT(300–400, ,
0$\HepParticle{\PGt}{\mathrm{h}}{}$) (lower left), and BDT(300–400, ,
0$\HepParticle{\PGt}{\mathrm{h}}{}$) (lower right) are displayed. Notations as
in Fig. 9.

The number of observed events in data is in good agreement with the SM
background expectations within the statistical and systematic uncertainties.
No significant excess is found for any final state or in any SR.

##  0.9 Interpretation

To derive exclusion limits at 95% confidence level () on HNL signal scenarios,
we apply the modified frequentist approach [131, 132, 128, 133]. Distributions
of the LHC test statistic [128], based on the profile likelihood method, are
evaluated in the asymptotic approximation [133] and used to calculate the
value [131, 132]. We exclude a signal scenario if the signal strength of $r=1$
is excluded at 95% or greater.

Figure 12: The 95% limits on $\abs{V_{\Pe\mathrm{N}}}^{2}$ (upper row),
$\abs{V_{\PGm\mathrm{N}}}^{2}$ (middle row), and
$\abs{V_{\PGt\mathrm{N}}}^{2}$ (lower row) as functions of $m_{\mathrm{N}}$
for a Majorana (left) and Dirac (right) HNL. The area above the solid (dashed)
black curve indicates the observed (expected) exclusion region. Previous
results from the DELPHI Collaboration [134] are shown for reference. The
previous CMS result “3prompt (2016)” [42] is shown to highlight the
improvements achieved in our analysis, and the results “3displaced” [46],
“2displaced” [48], and “$t$-channel VBF” [135] are shown to highlight the
complementarity to other search strategies.

The limits are obtained under the assumption of a Majorana or a Dirac HNL, and
are evaluated at a grid of points in the
$\big{(}m_{\mathrm{N}},\abs{V_{\Pell\mathrm{N}}}^{2}\big{)}$ parameter space.
For a Dirac HNL, the predicted signal yields are emulated from a subset of
events in the simulated Majorana samples by selecting only events in which the
leptons from the original boson decay and from the direct HNL decay have
opposite lepton number. For electron and muon neutrino couplings, masses of up
to 1.5are considered, whereas tau neutrino couplings are evaluated only up to
1since the exclusion limit passes above $\abs{V_{\PGt\mathrm{N}}}^{2}=1$
already at this mass point. The results are shown in Fig. 12. The obtained
limits are connected with straight lines between neighbouring mass points for
which the same fit distributions are used. For $m_{\mathrm{N}}$ values at
which the fit distributions change, the limits are evaluated for both
strategies and shown separately. Since the BDTs are trained with
nonoverlapping mass ranges, the sensitivity is generally different for two
strategies evaluated at the same $m_{\mathrm{N}}$ value, and we thus obtain
disjoint limit curves for several of these mass points. The expected and
observed exclusion limits generally agree within one standard deviation, with
a few exceptions discussed in the following.

For exclusive couplings to electron neutrinos and $m_{\mathrm{N}}<m_{\PW}$, we
exclude $\abs{V_{\Pe\mathrm{N}}}^{2}$ values for Majorana (Dirac) HNL of
4.8$\times 10^{-6}$ (2.23$\times 10^{-5}$) at a mass of 20, of 1.5$\times
10^{-5}$ (3.3$\times 10^{-5}$) at 60, and of 3.3$\times 10^{-4}$ (9.6$\times
10^{-4}$) at 75, which is the highest simulated mass point below $m_{\PW}$.
For masses below 30, the HNLs become long-lived and have a reduced selection
efficiency, with, , 16 times less events selected at $m_{\mathrm{N}}=10\GeV$
and $\abs{V_{\Pe\mathrm{N}}}^{2}=10^{-5}$ compared with a prompt HNL of the
same mass, resulting in less stringent limits. In the high-mass selection, we
exclude $\abs{V_{\Pe\mathrm{N}}}^{2}$ values for Majorana (Dirac) HNL of
1.2$\times 10^{-3}$ (1.5$\times 10^{-3}$) at 85, which is the lightest
simulated mass point above $m_{\PW}$, of 8.8$\times 10^{-4}$ (1.3$\times
10^{-3}$) at 100, and of 7.8$\times 10^{-2}$ (8.2$\times 10^{-2}$) at 600. The
most notable discrepancies between observed and expected limits are for HNL
masses between 250 and 400(125 and 250) in the case of a Majorana (Dirac) HNL,
caused by a small excess (deficit) in the last bin of the corresponding BDT
score distribution. Similarly a discrepancy is observed at HNL masses below
40in case of a Dirac HNL. This is due to a small excess in the relevant BDT
distribution, which leads the sensitivity in the Dirac requirement of an OSSF
electron pair in the final selection. Compared with the results of the
previous prompt HNL search presented in Ref. [42] for Majorana HNL, the limits
improve by up to one order of magnitude. For masses below 20, we exclude
short-lived HNL scenarios not excluded by the displaced HNL searches presented
in Refs. [46, 48]. The exclusion limits obtained by the DELPHI Collaboration
[134] for $m_{\mathrm{N}}<m_{\PW}$ are less stringent (similar) compared with
our results for the case of Majorana (Dirac) HNL.

Using the low-mass selection and considering exclusive couplings to muon
neutrinos, we find limits on $\abs{V_{\PGm\mathrm{N}}}^{2}$ for Majorana
(Dirac) HNL of 2.9$\times 10^{-6}$ (1.0$\times 10^{-5}$) at
$m_{\mathrm{N}}=20\GeV$, of 6.3$\times 10^{-6}$ (3.6$\times 10^{-5}$) at 60,
and of 2.0$\times 10^{-4}$ (1.3$\times 10^{-3}$) at 75. Below 30, the limits
are less stringent because of the impact of the long HNL lifetime, with 34
times fewer events selected at $m_{\mathrm{N}}=10\GeV$ and
$\abs{V_{\PGm\mathrm{N}}}^{2}=10^{-5}$ compared with a prompt HNL. Above
$m_{\PW}$, we exclude $\abs{V_{\PGm\mathrm{N}}}^{2}$ values for Majorana
(Dirac) HNL of 1.4$\times 10^{-3}$ (2.3$\times 10^{-3}$) at a mass of 85, of
1.1$\times 10^{-3}$ (1.9$\times 10^{-3}$) at 100, and of 6.0$\times 10^{-2}$
(9.1$\times 10^{-2}$) at 600. We improve the exclusion limits from the
previous prompt HNL search [42] by up to one order of magnitude, and
complement the limits from previous displaced HNL searches [46, 48] for short-
lived HNLs below 20. For $m_{\mathrm{N}}<m_{\PW}$, our exclusion limits are
more stringent (similar) in the case of Majorana (Dirac) HNLs compared with
the results of the DELPHI Collaboration [134]. Compared with a CMS result that
searches for high-mass Majorana HNLs with muon neutrino couplings in
$t$-channel VBF production [135], our results provide stricter exclusion
limits up to $m_{\mathrm{N}}\approx 700\GeV$.

The case of HNLs at the scale with exclusive tau neutrino couplings was probed
before only by the DELPHI Collaboration for $m_{\mathrm{N}}<m_{\PW}$ [134], by
the BaBar Collaboration for $m_{\mathrm{N}}<1.3\GeV$ [136], and recently by
the CMS Collaboration in displaced HNL searches for $m_{\mathrm{N}}<20\GeV$
[48]. Using the low-mass selection, we exclude Majorana (Dirac) HNLs with
$\abs{V_{\PGt\mathrm{N}}}^{2}$ values of 6.1$\times 10^{-4}$ (6.3$\times
10^{-4}$) at a mass of 20, of 1.8$\times 10^{-3}$ (1.9$\times 10^{-3}$) at 60,
and of 2.3$\times 10^{-2}$ (2.4$\times 10^{-2}$) at 75. The DELPHI limits for
$m_{\mathrm{N}}<m_{\PW}$ are up to two orders of magnitude more stringent than
our results. Above $m_{\PW}$, the tau neutrino couplings are probed for the
first time, and we find limits for Majorana (Dirac) HNLs of 3.0$\times
10^{-1}$ (2.7$\times 10^{-1}$) at 85, 1.1$\times 10^{-1}$ (8.6$\times
10^{-2}$) at 100, and 5.9$\times 10^{-1}$ (5.0$\times 10^{-2}$) at 600.

##  0.10 Summary

A search for heavy neutral leptons (HNLs) produced in proton-proton collisions
at $\sqrt{s}=13\TeV$ has been presented. The data were collected with the CMS
experiment at the LHC and correspond to an integrated luminosity of 138.
Events with three charged leptons (electrons, muons, and hadronically decaying
tau leptons) are selected, and dedicated identification criteria based on
machine learning techniques are applied to reduce the contribution from
nonprompt leptons not originating from the hard scattering process. Remaining
standard model (SM) background contributions with nonprompt leptons are
estimated from control samples in data, whereas other SM contributions that
mostly stem from diboson production are estimated from Monte Carlo event
simulations. A combination of categorization by kinematic properties and
machine learning discriminants achieves optimal separation of the predicted
signal and SM background contributions.

No significant deviations from the SM predictions are observed. Exclusion
limits at 95% confidence level are evaluated, assuming exclusive HNL couplings
to a single generation of SM neutrinos in the mass range 10–1.5, for both
Majorana and Dirac HNLs. These results exceed previous experimental
constraints over large parts of the mass range. Constraints on tau neutrino
couplings for HNL masses above the boson mass are presented for the first
time.

###### Acknowledgements.

We congratulate our colleagues in the CERN accelerator departments for the
excellent performance of the LHC and thank the technical and administrative
staffs at CERN and at other CMS institutes for their contributions to the
success of the CMS effort. In addition, we gratefully acknowledge the
computing centres and personnel of the Worldwide LHC Computing Grid and other
centres for delivering so effectively the computing infrastructure essential
to our analyses. Finally, we acknowledge the enduring support for the
construction and operation of the LHC, the CMS detector, and the supporting
computing infrastructure provided by the following funding agencies: SC
(Armenia), BMBWF and FWF (Austria); FNRS and FWO (Belgium); CNPq, CAPES,
FAPERJ, FAPERGS, and FAPESP (Brazil); MES and BNSF (Bulgaria); CERN; CAS,
MoST, and NSFC (China); MINCIENCIAS (Colombia); MSES and CSF (Croatia); RIF
(Cyprus); SENESCYT (Ecuador); ERC PRG, RVTT3 and MoER TK202 (Estonia); Academy
of Finland, MEC, and HIP (Finland); CEA and CNRS/IN2P3 (France); SRNSF
(Georgia); BMBF, DFG, and HGF (Germany); GSRI (Greece); NKFIH (Hungary); DAE
and DST (India); IPM (Iran); SFI (Ireland); INFN (Italy); MSIP and NRF
(Republic of Korea); MES (Latvia); LMTLT (Lithuania); MOE and UM (Malaysia);
BUAP, CINVESTAV, CONACYT, LNS, SEP, and UASLP-FAI (Mexico); MOS (Montenegro);
MBIE (New Zealand); PAEC (Pakistan); MES and NSC (Poland); FCT (Portugal);
MESTD (Serbia); MCIN/AEI and PCTI (Spain); MOSTR (Sri Lanka); Swiss Funding
Agencies (Switzerland); MST (Taipei); MHESI and NSTDA (Thailand); TUBITAK and
TENMAK (Turkey); NASU (Ukraine); STFC (United Kingdom); DOE and NSF (USA).
Individuals have received support from the Marie-Curie programme and the
European Research Council and Horizon 2020 Grant, contract Nos. 675440,
724704, 752730, 758316, 765710, 824093, 101115353, and COST Action CA16108
(European Union); the Leventis Foundation; the Alfred P. Sloan Foundation; the
Alexander von Humboldt Foundation; the Science Committee, project no. 22rl-037
(Armenia); the Belgian Federal Science Policy Office; the Fonds pour la
Formation à la Recherche dans l’Industrie et dans l’Agriculture (FRIA-
Belgium); the Agentschap voor Innovatie door Wetenschap en Technologie (IWT-
Belgium); the F.R.S.-FNRS and FWO (Belgium) under the “Excellence of Science –
EOS” – be.h project n. 30820817; the Beijing Municipal Science & Technology
Commission, No. Z191100007219010 and Fundamental Research Funds for the
Central Universities (China); the Ministry of Education, Youth and Sports
(MEYS) of the Czech Republic; the Shota Rustaveli National Science Foundation,
grant FR-22-985 (Georgia); the Deutsche Forschungsgemeinschaft (DFG), under
Germany’s Excellence Strategy – EXC 2121 “Quantum Universe” – 390833306, and
under project number 400140256 - GRK2497; the Hellenic Foundation for Research
and Innovation (HFRI), Project Number 2288 (Greece); the Hungarian Academy of
Sciences, the New National Excellence Program - ÚNKP, the NKFIH research
grants K 124845, K 124850, K 128713, K 128786, K 129058, K 131991, K 133046, K
138136, K 143460, K 143477, 2020-2.2.1-ED-2021-00181, and TKP2021-NKTA-64
(Hungary); the Council of Science and Industrial Research, India; ICSC –
National Research Centre for High Performance Computing, Big Data and Quantum
Computing, funded by the EU NexGeneration program (Italy); the Latvian Council
of Science; the Ministry of Education and Science, project no. 2022/WK/14, and
the National Science Center, contracts Opus 2021/41/B/ST2/01369 and
2021/43/B/ST2/01552 (Poland); the Fundação para a Ciência e a Tecnologia,
grant CEECIND/01334/2018 (Portugal); the National Priorities Research Program
by Qatar National Research Fund; MCIN/AEI/10.13039/501100011033, ERDF “a way
of making Europe”, and the Programa Estatal de Fomento de la Investigación
Científica y Técnica de Excelencia María de Maeztu, grant MDM-2017-0765 and
Programa Severo Ochoa del Principado de Asturias (Spain); the Chulalongkorn
Academic into Its 2nd Century Project Advancement Project, and the National
Science, Research and Innovation Fund via the Program Management Unit for
Human Resources & Institutional Development, Research and Innovation, grant
B37G660013 (Thailand); the Kavli Foundation; the Nvidia Corporation; the
SuperMicro Corporation; the Welch Foundation, contract C-1845; and the Weston
Havens Foundation (USA).

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##  .11 The CMS Collaboration

Yerevan Physics Institute, Yerevan, Armenia A. Hayrapetyan, A.
Tumasyan10009-0000-0684-6742

Institut für Hochenergiephysik, Vienna, Austria W. Adam0000-0001-9099-4341,
J.W. Andrejkovic, T. Bergauer0000-0002-5786-0293, S.
Chatterjee0000-0003-2660-0349, K. Damanakis0000-0001-5389-2872, M.
Dragicevic0000-0003-1967-6783, P.S. Hussain0000-0002-4825-5278, M.
Jeitler20000-0002-5141-9560, N. Krammer0000-0002-0548-0985, A.
Li0000-0002-4547-116X, D. Liko0000-0002-3380-473X, I.
Mikulec0000-0003-0385-2746, J. Schieck20000-0002-1058-8093, R.
Schöfbeck0000-0002-2332-8784, D. Schwarz0000-0002-3821-7331, M.
Sonawane0000-0003-0510-7010, S. Templ0000-0003-3137-5692, W.
Waltenberger0000-0002-6215-7228, C.-E. Wulz20000-0001-9226-5812

Universiteit Antwerpen, Antwerpen, Belgium M.R. Darwish30000-0003-2894-2377,
T. Janssen0000-0002-3998-4081, P. Van Mechelen0000-0002-8731-9051

Vrije Universiteit Brussel, Brussel, Belgium E.S. Bols0000-0002-8564-8732, N.
Breugelmans, J. D’Hondt0000-0002-9598-6241, S. Dansana0000-0002-7752-7471, A.
De Moor0000-0001-5964-1935, M. Delcourt0000-0001-8206-1787, F. Heyen, S.
Lowette0000-0003-3984-9987, I. Makarenko0000-0002-8553-4508, D.
Müller0000-0002-1752-4527, S. Tavernier0000-0002-6792-9522, M.
Tytgat40000-0002-3990-2074, G.P. Van Onsem0000-0002-1664-2337, S. Van
Putte0000-0003-1559-3606, D. Vannerom0000-0002-2747-5095

Université Libre de Bruxelles, Bruxelles, Belgium B.
Clerbaux0000-0001-8547-8211, A.K. Das, G. De Lentdecker0000-0001-5124-7693, H.
Evard0009-0005-5039-1462, L. Favart0000-0003-1645-7454, P.
Gianneios0009-0003-7233-0738, D. Hohov0000-0002-4760-1597, J.
Jaramillo0000-0003-3885-6608, A. Khalilzadeh, F.A. Khan0009-0002-2039-277X, K.
Lee0000-0003-0808-4184, M. Mahdavikhorrami0000-0002-8265-3595, A.
Malara0000-0001-8645-9282, S. Paredes0000-0001-8487-9603, L.
Thomas0000-0002-2756-3853, M. Vanden Bemden0009-0000-7725-7945, C. Vander
Velde0000-0003-3392-7294, P. Vanlaer0000-0002-7931-4496

Ghent University, Ghent, Belgium M. De Coen0000-0002-5854-7442, D.
Dobur0000-0003-0012-4866, Y. Hong0000-0003-4752-2458, J.
Knolle0000-0002-4781-5704, L. Lambrecht0000-0001-9108-1560, G. Mestdach, K.
Mota Amarilo0000-0003-1707-3348, C. Rendón, A. Samalan, K.
Skovpen0000-0002-1160-0621, N. Van Den Bossche0000-0003-2973-4991, J. van der
Linden0000-0002-7174-781X, L. Wezenbeek0000-0001-6952-891X

Université Catholique de Louvain, Louvain-la-Neuve, Belgium A.
Benecke0000-0003-0252-3609, A. Bethani0000-0002-8150-7043, G.
Bruno0000-0001-8857-8197, C. Caputo0000-0001-7522-4808, C.
Delaere0000-0001-8707-6021, I.S. Donertas0000-0001-7485-412X, A.
Giammanco0000-0001-9640-8294, Sa. Jain0000-0001-5078-3689, V. Lemaitre, J.
Lidrych0000-0003-1439-0196, P. Mastrapasqua0000-0002-2043-2367, T.T.
Tran0000-0003-3060-350X, S. Wertz0000-0002-8645-3670

Centro Brasileiro de Pesquisas Fisicas, Rio de Janeiro, Brazil G.A.
Alves0000-0002-8369-1446, E. Coelho0000-0001-6114-9907, C.
Hensel0000-0001-8874-7624, T. Menezes De Oliveira0009-0009-4729-8354, A.
Moraes0000-0002-5157-5686, P. Rebello Teles0000-0001-9029-8506, M. Soeiro, A.
Vilela Pereira50000-0003-3177-4626

Universidade do Estado do Rio de Janeiro, Rio de Janeiro, Brazil W.L. Aldá
Júnior0000-0001-5855-9817, M. Alves Gallo Pereira0000-0003-4296-7028, M.
Barroso Ferreira Filho0000-0003-3904-0571, H. Brandao
Malbouisson0000-0002-1326-318X, W. Carvalho0000-0003-0738-6615, J.
Chinellato6, E.M. Da Costa0000-0002-5016-6434, G.G. Da
Silveira70000-0003-3514-7056, D. De Jesus Damiao0000-0002-3769-1680, S.
Fonseca De Souza0000-0001-7830-0837, R. Gomes De Souza, M.
Macedo0000-0002-6173-9859, J. Martins80000-0002-2120-2782, C. Mora
Herrera0000-0003-3915-3170, L. Mundim0000-0001-9964-7805, H.
Nogima0000-0001-7705-1066, J.P. Pinheiro0000-0002-3233-8247, A.
Santoro0000-0002-0568-665X, A. Sznajder0000-0001-6998-1108, M.
Thiel0000-0001-7139-7963

Universidade Estadual Paulista, Universidade Federal do ABC, São Paulo, Brazil
C.A. Bernardes70000-0001-5790-9563, L. Calligaris0000-0002-9951-9448, T.R.
Fernandez Perez Tomei0000-0002-1809-5226, E.M. Gregores0000-0003-0205-1672, I.
Maietto Silverio0000-0003-3852-0266, P.G. Mercadante0000-0001-8333-4302, S.F.
Novaes0000-0003-0471-8549, B. Orzari0000-0003-4232-4743, Sandra S.
Padula0000-0003-3071-0559

Institute for Nuclear Research and Nuclear Energy, Bulgarian Academy of
Sciences, Sofia, Bulgaria A. Aleksandrov0000-0001-6934-2541, G.
Antchev0000-0003-3210-5037, R. Hadjiiska0000-0003-1824-1737, P.
Iaydjiev0000-0001-6330-0607, M. Misheva0000-0003-4854-5301, M.
Shopova0000-0001-6664-2493, G. Sultanov0000-0002-8030-3866

University of Sofia, Sofia, Bulgaria A. Dimitrov0000-0003-2899-701X, L.
Litov0000-0002-8511-6883, B. Pavlov0000-0003-3635-0646, P.
Petkov0000-0002-0420-9480, A. Petrov0009-0003-8899-1514, E.
Shumka0000-0002-0104-2574

Instituto De Alta Investigación, Universidad de Tarapacá, Casilla 7 D, Arica,
Chile S. Keshri0000-0003-3280-2350, S. Thakur0000-0002-1647-0360

Beihang University, Beijing, China T. Cheng0000-0003-2954-9315, T.
Javaid0009-0007-2757-4054, L. Yuan0000-0002-6719-5397

Department of Physics, Tsinghua University, Beijing, China Z.
Hu0000-0001-8209-4343, Z. Liang, J. Liu, K. Yi9,100000-0002-2459-1824

Institute of High Energy Physics, Beijing, China G.M.
Chen110000-0002-2629-5420, H.S. Chen110000-0001-8672-8227, M.
Chen110000-0003-0489-9669, F. Iemmi0000-0001-5911-4051, C.H. Jiang, A.
Kapoor120000-0002-1844-1504, H. Liao0000-0002-0124-6999, Z.-A.
Liu130000-0002-2896-1386, R. Sharma140000-0003-1181-1426, J.N. Song13, J.
Tao0000-0003-2006-3490, C. Wang11, J. Wang0000-0002-3103-1083, Z. Wang11, H.
Zhang0000-0001-8843-5209

State Key Laboratory of Nuclear Physics and Technology, Peking University,
Beijing, China A. Agapitos0000-0002-8953-1232, Y. Ban0000-0002-1912-0374, A.
Levin0000-0001-9565-4186, C. Li0000-0002-6339-8154, Q. Li0000-0002-8290-0517,
Y. Mao, S. Qian, S.J. Qian0000-0002-0630-481X, X. Sun0000-0003-4409-4574, D.
Wang0000-0002-9013-1199, H. Yang, L. Zhang0000-0001-7947-9007, Y. Zhao, C.
Zhou0000-0001-5904-7258

Sun Yat-Sen University, Guangzhou, China Z. You0000-0001-8324-3291

University of Science and Technology of China, Hefei, China K.
Jaffel0000-0001-7419-4248, N. Lu0000-0002-2631-6770

Nanjing Normal University, Nanjing, China G. Bauer15

Institute of Modern Physics and Key Laboratory of Nuclear Physics and Ion-beam
Application (MOE) - Fudan University, Shanghai, China X.
Gao160000-0001-7205-2318

Zhejiang University, Hangzhou, Zhejiang, China Z. Lin0000-0003-1812-3474, C.
Lu0000-0002-7421-0313, M. Xiao0000-0001-9628-9336

Universidad de Los Andes, Bogota, Colombia C. Avila0000-0002-5610-2693, D.A.
Barbosa Trujillo, A. Cabrera0000-0002-0486-6296, C. Florez0000-0002-3222-0249,
J. Fraga0000-0002-5137-8543, J.A. Reyes Vega

Universidad de Antioquia, Medellin, Colombia J. Mejia
Guisao0000-0002-1153-816X, F. Ramirez0000-0002-7178-0484, M.
Rodriguez0000-0002-9480-213X, J.D. Ruiz Alvarez0000-0002-3306-0363

University of Split, Faculty of Electrical Engineering, Mechanical Engineering
and Naval Architecture, Split, Croatia D. Giljanovic0009-0005-6792-6881, N.
Godinovic0000-0002-4674-9450, D. Lelas0000-0002-8269-5760, A.
Sculac0000-0001-7938-7559

University of Split, Faculty of Science, Split, Croatia M.
Kovac0000-0002-2391-4599, A. Petkovic, T. Sculac0000-0002-9578-4105

Institute Rudjer Boskovic, Zagreb, Croatia P. Bargassa0000-0001-8612-3332, V.
Brigljevic0000-0001-5847-0062, B.K. Chitroda0000-0002-0220-8441, D.
Ferencek0000-0001-9116-1202, K. Jakovcic, S. Mishra0000-0002-3510-4833, A.
Starodumov170000-0001-9570-9255, T. Susa0000-0001-7430-2552

University of Cyprus, Nicosia, Cyprus A. Attikis0000-0002-4443-3794, K.
Christoforou0000-0003-2205-1100, A. Hadjiagapiou, C. Leonidou, J.
Mousa0000-0002-2978-2718, C. Nicolaou, L. Paizanos, F.
Ptochos0000-0002-3432-3452, P.A. Razis0000-0002-4855-0162, H. Rykaczewski, H.
Saka0000-0001-7616-2573, A. Stepennov0000-0001-7747-6582

Charles University, Prague, Czech Republic M. Finger0000-0002-7828-9970, M.
Finger Jr.0000-0003-3155-2484, A. Kveton0000-0001-8197-1914

Escuela Politecnica Nacional, Quito, Ecuador E. Ayala0000-0002-0363-9198

Universidad San Francisco de Quito, Quito, Ecuador E. Carrera
Jarrin0000-0002-0857-8507

Academy of Scientific Research and Technology of the Arab Republic of Egypt,
Egyptian Network of High Energy Physics, Cairo, Egypt Y. Assran18,19, S.
Elgammal19

Center for High Energy Physics (CHEP-FU), Fayoum University, El-Fayoum, Egypt
M. Abdullah Al-Mashad0000-0002-7322-3374, M.A. Mahmoud0000-0001-8692-5458

National Institute of Chemical Physics and Biophysics, Tallinn, Estonia K.
Ehataht0000-0002-2387-4777, M. Kadastik, T. Lange0000-0001-6242-7331, S.
Nandan0000-0002-9380-8919, C. Nielsen0000-0002-3532-8132, J.
Pata0000-0002-5191-5759, M. Raidal0000-0001-7040-9491, L.
Tani0000-0002-6552-7255, C. Veelken0000-0002-3364-916X

Department of Physics, University of Helsinki, Helsinki, Finland H.
Kirschenmann0000-0001-7369-2536, K. Osterberg0000-0003-4807-0414, M.
Voutilainen0000-0002-5200-6477

Helsinki Institute of Physics, Helsinki, Finland S.
Bharthuar0000-0001-5871-9622, E. Brücken0000-0001-6066-8756, F.
Garcia0000-0002-4023-7964, K.T.S. Kallonen0000-0001-9769-7163, R. Kinnunen, T.
Lampén0000-0002-8398-4249, K. Lassila-Perini0000-0002-5502-1795, S.
Lehti0000-0003-1370-5598, T. Lindén0009-0002-4847-8882, L.
Martikainen0000-0003-1609-3515, M. Myllymäki0000-0003-0510-3810, M.m.
Rantanen0000-0002-6764-0016, H. Siikonen0000-0003-2039-5874, E.
Tuominen0000-0002-7073-7767, J. Tuominiemi0000-0003-0386-8633

Lappeenranta-Lahti University of Technology, Lappeenranta, Finland P.
Luukka0000-0003-2340-4641, H. Petrow0000-0002-1133-5485

IRFU, CEA, Université Paris-Saclay, Gif-sur-Yvette, France M.
Besancon0000-0003-3278-3671, F. Couderc0000-0003-2040-4099, M.
Dejardin0009-0008-2784-615X, D. Denegri, J.L. Faure, F.
Ferri0000-0002-9860-101X, S. Ganjour0000-0003-3090-9744, P.
Gras0000-0002-3932-5967, G. Hamel de Monchenault0000-0002-3872-3592, V.
Lohezic0009-0008-7976-851X, J. Malcles0000-0002-5388-5565, F.
Orlandi0009-0001-0547-7516, L. Portales0000-0002-9860-9185, J. Rander, A.
Rosowsky0000-0001-7803-6650, M.Ö. Sahin0000-0001-6402-4050, A. Savoy-
Navarro200000-0002-9481-5168, P. Simkina0000-0002-9813-372X, M.
Titov0000-0002-1119-6614, M. Tornago0000-0001-6768-1056

Laboratoire Leprince-Ringuet, CNRS/IN2P3, Ecole Polytechnique, Institut
Polytechnique de Paris, Palaiseau, France F. Beaudette0000-0002-1194-8556, A.
Buchot Perraguin0000-0002-8597-647X, P. Busson0000-0001-6027-4511, A.
Cappati0000-0003-4386-0564, C. Charlot0000-0002-4087-8155, M.
Chiusi0000-0002-1097-7304, F. Damas0000-0001-6793-4359, O.
Davignon0000-0001-8710-992X, A. De Wit0000-0002-5291-1661, I.T.
Ehle0000-0003-3350-5606, B.A. Fontana Santos Alves0000-0001-9752-0624, S.
Ghosh0009-0006-5692-5688, A. Gilbert0000-0001-7560-5790, R. Granier de
Cassagnac0000-0002-1275-7292, A. Hakimi0009-0008-2093-8131, B.
Harikrishnan0000-0003-0174-4020, L. Kalipoliti0000-0002-5705-5059, G.
Liu0000-0001-7002-0937, J. Motta0000-0003-0985-913X, M.
Nguyen0000-0001-7305-7102, C. Ochando0000-0002-3836-1173, R.
Salerno0000-0003-3735-2707, J.B. Sauvan0000-0001-5187-3571, Y.
Sirois0000-0001-5381-4807, A. Tarabini0000-0001-7098-5317, E.
Vernazza0000-0003-4957-2782, A. Zabi0000-0002-7214-0673, A.
Zghiche0000-0002-1178-1450

Université de Strasbourg, CNRS, IPHC UMR 7178, Strasbourg, France J.-L.
Agram210000-0001-7476-0158, J. Andrea0000-0002-8298-7560, D.
Apparu0009-0004-1837-0496, D. Bloch0000-0002-4535-5273, J.-M.
Brom0000-0003-0249-3622, E.C. Chabert0000-0003-2797-7690, C.
Collard0000-0002-5230-8387, S. Falke0000-0002-0264-1632, U.
Goerlach0000-0001-8955-1666, C. Grimault, R. Haeberle0009-0007-5007-6723,
A.-C. Le Bihan0000-0002-8545-0187, M. Meena0000-0003-4536-3967, G.
Saha0000-0002-6125-1941, M.A. Sessini0000-0003-2097-7065, P. Van
Hove0000-0002-2431-3381

Institut de Physique des 2 Infinis de Lyon (IP2I ), Villeurbanne, France D.
Amram, S. Beauceron0000-0002-8036-9267, B. Blancon0000-0001-9022-1509, G.
Boudoul0009-0002-9897-8439, N. Chanon0000-0002-2939-5646, D.
Contardo0000-0001-6768-7466, P. Depasse0000-0001-7556-2743, C.
Dozen220000-0002-4301-634X, H. El Mamouni, J. Fay0000-0001-5790-1780, S.
Gascon0000-0002-7204-1624, M. Gouzevitch0000-0002-5524-880X, C. Greenberg, G.
Grenier0000-0002-1976-5877, B. Ille0000-0002-8679-3878, E. Jourd‘huy, I.B.
Laktineh, M. Lethuillier0000-0001-6185-2045, L. Mirabito, S. Perries, A.
Purohit0000-0003-0881-612X, M. Vander Donckt0000-0002-9253-8611, P.
Verdier0000-0003-3090-2948, J. Xiao0000-0002-7860-3958

Georgian Technical University, Tbilisi, Georgia A.
Khvedelidze170000-0002-5953-0140, I. Lomidze0009-0002-3901-2765, Z.
Tsamalaidze170000-0001-5377-3558

RWTH Aachen University, I. Physikalisches Institut, Aachen, Germany V.
Botta0000-0003-1661-9513, L. Feld0000-0001-9813-8646, K.
Klein0000-0002-1546-7880, M. Lipinski0000-0002-6839-0063, D.
Meuser0000-0002-2722-7526, A. Pauls0000-0002-8117-5376, N.
Röwert0000-0002-4745-5470, M. Teroerde0000-0002-5892-1377

RWTH Aachen University, III. Physikalisches Institut A, Aachen, Germany S.
Diekmann0009-0004-8867-0881, A. Dodonova0000-0002-5115-8487, N.
Eich0000-0001-9494-4317, D. Eliseev0000-0001-5844-8156, F.
Engelke0000-0002-9288-8144, J. Erdmann0000-0002-8073-2740, M.
Erdmann0000-0002-1653-1303, P. Fackeldey0000-0003-4932-7162, B.
Fischer0000-0002-3900-3482, T. Hebbeker0000-0002-9736-266X, K.
Hoepfner0000-0002-2008-8148, F. Ivone0000-0002-2388-5548, A.
Jung0000-0002-2511-1490, M.y. Lee0000-0002-4430-1695, F.
Mausolf0000-0003-2479-8419, M. Merschmeyer0000-0003-2081-7141, A.
Meyer0000-0001-9598-6623, S. Mukherjee0000-0001-6341-9982, D.
Noll0000-0002-0176-2360, F. Nowotny, A. Pozdnyakov0000-0003-3478-9081, Y.
Rath, W. Redjeb0000-0001-9794-8292, F. Rehm, H. Reithler0000-0003-4409-702X,
U. Sarkar0000-0002-9892-4601, V. Sarkisovi0000-0001-9430-5419, A.
Schmidt0000-0003-2711-8984, A. Sharma0000-0002-5295-1460, J.L.
Spah0000-0002-5215-3258, A. Stein0000-0003-0713-811X, F. Torres Da Silva De
Araujo230000-0002-4785-3057, S. Wiedenbeck0000-0002-4692-9304, S. Zaleski

RWTH Aachen University, III. Physikalisches Institut B, Aachen, Germany C.
Dziwok0000-0001-9806-0244, G. Flügge0000-0003-3681-9272, W. Haj
Ahmad240000-0003-1491-0446, T. Kress0000-0002-2702-8201, A.
Nowack0000-0002-3522-5926, O. Pooth0000-0001-6445-6160, A.
Stahl0000-0002-8369-7506, T. Ziemons0000-0003-1697-2130, A.
Zotz0000-0002-1320-1712

Deutsches Elektronen-Synchrotron, Hamburg, Germany H. Aarup
Petersen0009-0005-6482-7466, M. Aldaya Martin0000-0003-1533-0945, J.
Alimena0000-0001-6030-3191, S. Amoroso, Y. An0000-0003-1299-1879, J.
Bach0000-0001-9572-6645, S. Baxter0009-0008-4191-6716, M.
Bayatmakou0009-0002-9905-0667, H. Becerril Gonzalez0000-0001-5387-712X, O.
Behnke0000-0002-4238-0991, A. Belvedere0000-0002-2802-8203, S.
Bhattacharya0000-0002-3197-0048, F. Blekman250000-0002-7366-7098, K.
Borras260000-0003-1111-249X, A. Campbell0000-0003-4439-5748, A.
Cardini0000-0003-1803-0999, C. Cheng, F. Colombina0009-0008-7130-100X, S.
Consuegra Rodríguez0000-0002-1383-1837, G. Correia Silva0000-0001-6232-3591,
M. De Silva0000-0002-5804-6226, G. Eckerlin, D. Eckstein0000-0002-7366-6562,
L.I. Estevez Banos0000-0001-6195-3102, O. Filatov0000-0001-9850-6170, E.
Gallo250000-0001-7200-5175, A. Geiser0000-0003-0355-102X, A.
Giraldi0000-0003-4423-2631, V. Guglielmi0000-0003-3240-7393, M.
Guthoff0000-0002-3974-589X, A. Hinzmann0000-0002-2633-4696, L.
Jeppe0000-0002-1029-0318, B. Kaech0000-0002-1194-2306, M.
Kasemann0000-0002-0429-2448, C. Kleinwort0000-0002-9017-9504, R.
Kogler0000-0002-5336-4399, M. Komm0000-0002-7669-4294, D.
Krücker0000-0003-1610-8844, W. Lange, D. Leyva Pernia0009-0009-8755-3698, K.
Lipka270000-0002-8427-3748, W. Lohmann280000-0002-8705-0857, F.
Lorkowski0000-0003-2677-3805, R. Mankel0000-0003-2375-1563, I.-A. Melzer-
Pellmann0000-0001-7707-919X, M. Mendizabal Morentin0000-0002-6506-5177, A.B.
Meyer0000-0001-8532-2356, G. Milella0000-0002-2047-951X, K. Moral
Figueroa0000-0003-1987-1554, A. Mussgiller0000-0002-8331-8166, L.P.
Nair0000-0002-2351-9265, A. Nürnberg0000-0002-7876-3134, Y. Otarid, J.
Park0000-0002-4683-6669, D. Pérez Adán0000-0003-3416-0726, E.
Ranken0000-0001-7472-5029, A. Raspereza0000-0003-2167-498X, D.
Rastorguev0000-0001-6409-7794, B. Ribeiro Lopes0000-0003-0823-447X, J.
Rübenach, L. Rygaard, A. Saggio0000-0002-7385-3317, M.
Scham29,260000-0001-9494-2151, S. Schnake260000-0003-3409-6584, P.
Schütze0000-0003-4802-6990, C. Schwanenberger250000-0001-6699-6662, D.
Selivanova0000-0002-7031-9434, K. Sharko0000-0002-7614-5236, M.
Shchedrolosiev0000-0003-3510-2093, R.E. Sosa Ricardo0000-0002-2240-6699, D.
Stafford, F. Vazzoler0000-0001-8111-9318, A. Ventura
Barroso0000-0003-3233-6636, R. Walsh0000-0002-3872-4114, D.
Wang0000-0002-0050-612X, Q. Wang0000-0003-1014-8677, Y.
Wen0000-0002-8724-9604, K. Wichmann, L. Wiens260000-0002-4423-4461, C.
Wissing0000-0002-5090-8004, Y. Yang0009-0009-3430-0558, A. Zimermmane Castro
Santos0000-0001-9302-3102

University of Hamburg, Hamburg, Germany A. Albrecht0000-0001-6004-6180, S.
Albrecht0000-0002-5960-6803, M. Antonello0000-0001-9094-482X, S.
Bein0000-0001-9387-7407, L. Benato0000-0001-5135-7489, S. Bollweg, M.
Bonanomi0000-0003-3629-6264, P. Connor0000-0003-2500-1061, K. El
Morabit0000-0001-5886-220X, Y. Fischer0000-0002-3184-1457, E.
Garutti0000-0003-0634-5539, A. Grohsjean0000-0003-0748-8494, J.
Haller0000-0001-9347-7657, H.R. Jabusch0000-0003-2444-1014, G.
Kasieczka0000-0003-3457-2755, P. Keicher, R. Klanner0000-0002-7004-9227, W.
Korcari0000-0001-8017-5502, T. Kramer0000-0002-7004-0214, C.c. Kuo, V.
Kutzner0000-0003-1985-3807, F. Labe0000-0002-1870-9443, J.
Lange0000-0001-7513-6330, A. Lobanov0000-0002-5376-0877, C.
Matthies0000-0001-7379-4540, L. Moureaux0000-0002-2310-9266, M. Mrowietz, A.
Nigamova0000-0002-8522-8500, Y. Nissan, A. Paasch0000-0002-2208-5178, K.J.
Pena Rodriguez0000-0002-2877-9744, T. Quadfasel0000-0003-2360-351X, B.
Raciti0009-0005-5995-6685, M. Rieger0000-0003-0797-2606, D.
Savoiu0000-0001-6794-7475, J. Schindler0009-0006-6551-0660, P.
Schleper0000-0001-5628-6827, M. Schröder0000-0001-8058-9828, J.
Schwandt0000-0002-0052-597X, M. Sommerhalder0000-0001-5746-7371, H.
Stadie0000-0002-0513-8119, G. Steinbrück0000-0002-8355-2761, A. Tews, M.
Wolf0000-0003-3002-2430

Karlsruher Institut fuer Technologie, Karlsruhe, Germany S.
Brommer0000-0001-8988-2035, M. Burkart, E. Butz0000-0002-2403-5801, T.
Chwalek0000-0002-8009-3723, A. Dierlamm0000-0001-7804-9902, A. Droll, N.
Faltermann0000-0001-6506-3107, M. Giffels0000-0003-0193-3032, A.
Gottmann0000-0001-6696-349X, F. Hartmann300000-0001-8989-8387, R.
Hofsaess0009-0008-4575-5729, M. Horzela0000-0002-3190-7962, U.
Husemann0000-0002-6198-8388, J. Kieseler0000-0003-1644-7678, M.
Klute0000-0002-0869-5631, R. Koppenhöfer0000-0002-6256-5715, J.M.
Lawhorn0000-0002-8597-9259, M. Link, A. Lintuluoto0000-0002-0726-1452, B.
Maier0000-0001-5270-7540, S. Maier0000-0001-9828-9778, S.
Mitra0000-0002-3060-2278, M. Mormile0000-0003-0456-7250, Th.
Müller0000-0003-4337-0098, M. Neukum, M. Oh0000-0003-2618-9203, E.
Pfeffer0009-0009-1748-974X, M. Presilla0000-0003-2808-7315, G.
Quast0000-0002-4021-4260, K. Rabbertz0000-0001-7040-9846, B.
Regnery0000-0003-1539-923X, N. Shadskiy0000-0001-9894-2095, I.
Shvetsov0000-0002-7069-9019, H.J. Simonis0000-0002-7467-2980, M.
Toms0000-0002-7703-3973, N. Trevisani0000-0002-5223-9342, R.F. Von
Cube0000-0002-6237-5209, M. Wassmer0000-0002-0408-2811, S.
Wieland0000-0003-3887-5358, F. Wittig, R. Wolf0000-0001-9456-383X, X.
Zuo0000-0002-0029-493X

Institute of Nuclear and Particle Physics (INPP), NCSR Demokritos, Aghia
Paraskevi, Greece G. Anagnostou, G. Daskalakis0000-0001-6070-7698, A.
Kyriakis, A. Papadopoulos30, A. Stakia0000-0001-6277-7171

National and Kapodistrian University of Athens, Athens, Greece P.
Kontaxakis0000-0002-4860-5979, G. Melachroinos, Z.
Painesis0000-0001-5061-7031, A. Panagiotou, I. Papavergou0000-0002-7992-2686,
I. Paraskevas0000-0002-2375-5401, N. Saoulidou0000-0001-6958-4196, K.
Theofilatos0000-0001-8448-883X, E. Tziaferi0000-0003-4958-0408, K.
Vellidis0000-0001-5680-8357, I. Zisopoulos0000-0001-5212-4353

National Technical University of Athens, Athens, Greece G.
Bakas0000-0003-0287-1937, T. Chatzistavrou, G. Karapostoli0000-0002-4280-2541,
K. Kousouris0000-0002-6360-0869, I. Papakrivopoulos0000-0002-8440-0487, E.
Siamarkou, G. Tsipolitis, A. Zacharopoulou

University of Ioánnina, Ioánnina, Greece K. Adamidis, I. Bestintzanos, I.
Evangelou0000-0002-5903-5481, C. Foudas, C. Kamtsikis, P. Katsoulis, P.
Kokkas0009-0009-3752-6253, P.G. Kosmoglou Kioseoglou0000-0002-7440-4396, N.
Manthos0000-0003-3247-8909, I. Papadopoulos0000-0002-9937-3063, J.
Strologas0000-0002-2225-7160

HUN-REN Wigner Research Centre for Physics, Budapest, Hungary M.
Bartók310000-0002-4440-2701, C. Hajdu0000-0002-7193-800X, D.
Horvath32,330000-0003-0091-477X, K. Márton, A.J. Rádl340000-0001-8810-0388, F.
Sikler0000-0001-9608-3901, V. Veszpremi0000-0001-9783-0315

MTA-ELTE Lendület CMS Particle and Nuclear Physics Group, Eötvös Loránd
University, Budapest, Hungary M. Csanád0000-0002-3154-6925, K.
Farkas0000-0003-1740-6974, A. Fehérkuti350000-0002-5043-2958, M.M.A.
Gadallah360000-0002-8305-6661, Á. Kadlecsik0000-0001-5559-0106, P.
Major0000-0002-5476-0414, K. Mandal0000-0002-3966-7182, G.
Pásztor0000-0003-0707-9762, G.I. Veres0000-0002-5440-4356

Faculty of Informatics, University of Debrecen, Debrecen, Hungary P. Raics, B.
Ujvari0000-0003-0498-4265, G. Zilizi0000-0002-0480-0000

Institute of Nuclear Research ATOMKI, Debrecen, Hungary G. Bencze, S. Czellar,
J. Molnar, Z. Szillasi

Karoly Robert Campus, MATE Institute of Technology, Gyongyos, Hungary T.
Csorgo350000-0002-9110-9663, F. Nemes350000-0002-1451-6484, T.
Novak0000-0001-6253-4356

Panjab University, Chandigarh, India J. Babbar0000-0002-4080-4156, S.
Bansal0000-0003-1992-0336, S.B. Beri, V. Bhatnagar0000-0002-8392-9610, G.
Chaudhary0000-0003-0168-3336, S. Chauhan0000-0001-6974-4129, N.
Dhingra370000-0002-7200-6204, A. Kaur0000-0002-1640-9180, A.
Kaur0000-0003-3609-4777, H. Kaur0000-0002-8659-7092, M.
Kaur0000-0002-3440-2767, S. Kumar0000-0001-9212-9108, K.
Sandeep0000-0002-3220-3668, T. Sheokand, J.B. Singh0000-0001-9029-2462, A.
Singla0000-0003-2550-139X

University of Delhi, Delhi, India A. Ahmed0000-0002-4500-8853, A.
Bhardwaj0000-0002-7544-3258, A. Chhetri0000-0001-7495-1923, B.C.
Choudhary0000-0001-5029-1887, A. Kumar0000-0003-3407-4094, A.
Kumar0000-0002-5180-6595, M. Naimuddin0000-0003-4542-386X, K.
Ranjan0000-0002-5540-3750, S. Saumya0000-0001-7842-9518

Saha Institute of Nuclear Physics, HBNI, Kolkata, India S.
Baradia0000-0001-9860-7262, S. Barman380000-0001-8891-1674, S.
Bhattacharya0000-0002-8110-4957, S. Das Gupta, S. Dutta0000-0001-9650-8121, S.
Dutta, S. Sarkar

Indian Institute of Technology Madras, Madras, India M.M.
Ameen0000-0002-1909-9843, P.K. Behera0000-0002-1527-2266, S.C.
Behera0000-0002-0798-2727, S. Chatterjee0000-0003-0185-9872, G.