HIG-21-010

HIG-21-010

# Search for a charged Higgs boson decaying into a heavy neutral Higgs boson
and a $\PW$ boson in proton-proton collisions at $\sqrt{s}=13\TeV$

###### Abstract

A search for a charged Higgs boson decaying into a heavy neutral Higgs boson
and a boson is presented. The analysis targets the decay into a pair of tau
leptons with at least one of them decaying hadronically and with an additional
electron or muon present in the event. The search is based on proton-proton
collision data recorded by the CMS experiment during 2016–2018 at
$\sqrt{s}=13\TeV$, corresponding to an integrated luminosity of 138. The data
are consistent with standard model background expectations. Upper limits at
95% confidence level are set on the product of the cross section and branching
fraction for an in the mass range of 300–700, assuming an with a mass of 200.
The observed limits range from 0.085pb for an mass of 300to 0.019pb for a mass
of 700\. These are the first limits on production in the $\PHpm\to\PH\PWpm$
decay channel at the LHC.

##  0.1 Introduction

The experimental confirmation of the Brout–Englert–Higgs mechanism [1, 2, 3,
4, 5, 6] at the CERN LHC [7, 8, 9] has provided the long-sought solution to
the electroweak symmetry breaking problem. It has also further established the
standard model (SM) of particle physics as a successful theory. Subsequent
precision measurements of the couplings of the observed Higgs boson with the
SM particles are in agreement with expectations, with an experimental
precision of $\approx$5–33% [10, 11, 12, 13]. Regardless of the success it has
achieved, the SM is still considered to be an effective field theory valid
only at low energies because of its inability to address various fundamental
theoretical problems and compelling observations in nature such as the
naturalness problem, the vacuum metastability, the conjectured cosmological
inflation, and the matter-antimatter asymmetry of our universe.

Numerous theoretical models have been proposed to remedy the shortcomings of
the SM, many of which predict that the Higgs sector must also be extended.
Minimal extensions known as two-Higgs-doublet models (2HDMs) [14, 15, 16, 17]
include a second complex doublet and are classified into four types according
to the couplings of the Higgs doublets to fermions. The two-doublet structure
gives rise to five physical Higgs bosons via spontaneous symmetry breaking:
two neutral $CP$-even particles and with $m_{\Ph}\leq m_{\PH}$, one neutral
$CP$-odd particle , and two charged Higgs bosons . In these models the ratio
of the vacuum expectation values of the two Higgs doublets, $\tan\beta$, and
the mixing angle, $\alpha$, between and are free parameters. These can be
tuned to the alignment limit $\sin(\beta-\alpha)=1$ whereby aligns with the
properties of the SM Higgs boson with $m_{\Ph}$ = 125 [18], while the
additional Higgs bosons may appear at the scale or below it [19].

Three mass regions are conveniently defined for the classification of charged
Higgs bosons: light ($\smash[b]{m_{\PHpm}<m_{\PQt}-m_{\PQb}}$), intermediate
($\smash[b]{m_{\PHpm}\approx m_{\PQt}}$), and heavy
($\smash[b]{m_{\PHpm}>m_{\PQt}+m_{\PQb}}$), where $m_{\PHpm}$, $m_{\PQt}$, and
$m_{\PQb}$ represent the masses of the charged Higgs boson, the top and bottom
quarks, respectively. The search described in this paper is focused on a heavy
, whose production at the LHC would take place predominantly in association
with top and bottom quarks. The associated top quark production dominates and
can be described in the four- and five-flavor scheme (4FS and 5FS), which
yield consistent results at sufficiently high order of perturbation theory
[20]. The corresponding leading-order (LO) Feynman diagrams are shown in Fig.
1, with charge-conjugate processes implied.

Figure 1:  Leading order Feynman diagrams for the production of a heavy
$\PH^{+}$ at the LHC through $\Pp\Pp\to\PQt(\PQb)\PH^{+}$ in the 4FS (left)
and 5FS (right).

When considering 2HDMs, the decay branching fractions $\mathcal{B}$ of can
vary significantly between different models. Under the enforcement of the Z2
symmetry there are four types of 2HDMs which, for $\tan\beta=1$, lead to the
channels $\PHpm\to\PGt^{\pm}\PGnGt$ and $\PHpm\to\PQc\PQs$ being dominant in
the light-region. In the heavy-$\Hpm$ region, the decay mode
$\PHpm\to\PQt\PQb$ dominates, with some competition from the
$\PHpm\to\Ph\PWpm$ and $\PHpm\to\PH\PWpm$ decay modes. This behavior also
holds in the alignment limit with the only difference being that
$\mathcal{B}(\PHpm\to\PH\PWpm)$ increases faster with $m_{\PHpm}$, while
$\mathcal{B}(\PHpm\to\Ph\PWpm)$ vanishes completely. At larger values of
$\tan\beta$, the interplay between the channels $\PHpm\to\PH\PWpm$ and
$\PHpm\to\Ph\PWpm$ becomes more intricate, with the former becoming important
once kinematically attainable and the latter dominating because of the large
phase space available.

The importance of the potential interference between the $\PHpm\to\PH\PWpm$
and $\PHpm\to\Ph\PWpm$ channels is difficult to quantify as it highly depends
on the considered parameter space. In general, however, a large
$\PHpm\to\Ph\PWpm$ coupling is always associated with a small
$\PHpm\to\PH\PWpm$ coupling, and vice versa. As discussed in Ref. [21],
assuming a misalignment of $\approx$0.1 with $\sin(\beta-\alpha)=0.9$,
$\mathcal{B}(\PHpm\to\Ph\PWpm)$ is suppressed by a factor of $\approx$100 with
respect to $\mathcal{B}(\PHpm\to\PH\PWpm)$, while the interference between
$\PHpm\to\PH\PWpm$ and $\PHpm\to\Ph\PWpm$ is also expected to be suppressed by
at least a factor of $\approx$10 compared to the contribution from
$\PHpm\to\PH\PWpm$ itself. In this paper, we focus on the $\PHpm\to\PH\PWpm$
decay mode and neglect completely the $\PHpm\to\Ph\PWpm$ decay mode, as well
as their interference. For the neutral Higgs boson, typically the most
frequent final states close to the alignment limit are the $\PQb\PQb$ and
$\PGt\PGt$, while the $\PW\PW$, $\PZ\PZ$, and $\cPgg\cPgg$ channels are
experimentally the cleanest ones. However, the aforementioned decay rates are
model-dependent and are affected, directly or indirectly, by the value of
$m_{\PH}$.

Since no charged scalar boson exists in the SM, a discovery of a charged Higgs
boson would provide unequivocal proof of physics beyond the SM. To date,
various searches for an signature have been conducted by the ATLAS and CMS
Collaborations in proton-proton ($\Pp\Pp$) collisions at $\sqrt{s}=7$, 8, and
13. Searches for a light include the channels $\PHpm\to\PGt^{\pm}\PGnGt$ [22,
23, 24, 25], $\PHpm\to\PQc\PQs$ [26, 27], $\PHpm\to\PQc\PQb$ [28], and
$\PHpm\to\PWpm\PSA$ [29]. In the heavy-region, the searches include the
channels $\PHpm\to\PQt\PQb$ [23, 30, 31, 32] and $\PHpm\to\PGt^{\pm}\PGnGt$
[22, 23, 24, 33, 34]. Charged-current processes from low-energy flavor
observables, such as tauonic meson decays and the $\PQb\to\PQs\gamma$
transition, have yielded indirect lower limits on $m_{\PHpm}$ [35, 36].
Searches for $\PHpm\to\PWpm\PZ$ decays predicted in Higgs triplet models [37,
38, 39] have also been conducted in the vector boson ($\PV=\PZ$ or $\PW$)
fusion production mode [40, 41, 42, 43]. Finally, the ATLAS Collaboration has
set limits on production with a search for dijet resonances in events with an
isolated charged lepton [44]. No evidence of a charged Higgs boson has been
reported in any of the aforementioned searches. Searches for additional heavy
neutral Higgs bosons have also been performed at experiments at LEP [45] and
the Tevatron [46, 47, 48, 49]. These are superseded by searches performed by
the ATLAS and CMS Collaborations in the $\PQb\PQb$ [50, 51, 52, 53],
$\PGm\PGm$ [54, 55, 56, 57], and $\PGt\PGt$ [54, 58, 59, 60, 61, 62, 63, 64,
65] final states.

In this paper, a direct search for a heavy is performed through the
$\PHpm\to\PH\PWpm$ and $\PH\to\PGt\PGt$ decay modes, targeting the
$\PHpm\to\PH\PWpm$ decay channel for the first time at the LHC. In this search
it is assumed that the boson has a mass of $m_{\PH}=200\GeV$. This particular
choice appears as a benchmark point in various scenarios such as extended
Inert Doublet Models aiming to provide a viable Dark Matter candidate [66,
67], in 2HDM frameworks with new sources of CP-violation [68] or a strong
first order electroweak phase transition [69] which are needed for a
successful electroweak baryogenesis. Such heavy neutral scalars have also been
proposed to address flavor puzzles such as the anomalous magnetic moment of
the muon [70].

The search focuses on an associated production with a hadronically decaying
top quark, in final states with at least one tau lepton decaying hadronically
() and exactly one isolated lepton ($\ell=\Pe,\,\PGm$), as shown in Fig. 2.
Four distinct final states are targeted: $\Pe\tauh$, $\PGm\tauh$,
$\Pe\tauh\tauh$, and $\PGm\tauh\tauh$. For the $\ell\tauh$ final states,
candidate events contain one candidate, one isolated lepton, missing
transverse momentum (), and three additional hadronic jets from boson decays
andquarks. The $\ell\tauh$ search employs a multivariate analysis (MVA)
classifier based on boosted decision tree with gradient boost (BDTG) to
distinguish the signal from backgrounds. For the $\ell\tauh\tauh$ final
states, candidate events are selected by requiring one additional candidate
and by relaxing the hadronic jet multiplicity requirement to at least two. In
these final states, the transverse mass of the charged Higgs boson, , is used
to distinguish signal from backgrounds. Upper limits on the product of the
production cross section, $\sigma_{\PHpm}$, and the branching fraction
$\mathcal{B}(\PHpm\to\PH\PWpm,\PH\to\PGt\PGt)$ for the decay chain
$\PHpm\to\PH\PWpm$ with $\PH\to\PGt\PGt$, are presented as functions of
$m_{\PHpm}$.

Figure 2:  Feynman diagrams showing the signal processes targeted by this
analysis, with the production of a heavy $\PH^{+}$ in the 4FS, followed by the
$\PH^{+}\to\PH\PWp$ and $\PH\to\PGt\PGt$ decays, resulting in $\ell\tauh$
(left) and $\ell\tauh\tauh$ (right) final states. Contributions to the
$\ell\tauh$ final state may also arise from the right diagram when one from
the $\PH\to\PGt\PGt$ decay is not reconstructed.

The paper is organized as follows. A brief description of the CMS detector is
given in Section 0.2, while the collision data and simulated samples are
discussed in Section 0.3. Section 0.4 describes the global event
reconstruction and physics object identification, followed by the event
selection in Section 0.5. Background estimation, search strategy, and
systematic uncertainties are described in Sections 0.6, 0.7, and 0.8,
respectively. Finally, the results are presented in Section 0.9 and summarized
in Section 0.10.

##  0.2 The CMS detector

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, each composed of a barrel and two endcap sections. Forward
calorimeters extend the pseudorapidity ($\eta$) coverage provided by the
barrel and endcap detectors up to $\abs{\eta}=5$. Muons are detected in gas-
ionization chambers embedded in the steel flux-return yoke outside the
solenoid.

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 time interval of less than 4 [71]. The second level, known as the
high-level trigger (HLT), 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 [72].

A more detailed description of the CMS detector, together with a definition of
the coordinate system used and the relevant kinematic variables, can be found
in Ref. [73].

##  0.3 Collision data and simulated samples

The analysis presented in this paper uses $\Pp\Pp$ collision data collected
with the CMS experiment at $\sqrt{s}=13\TeV$ during the years 2016, 2017, and
2018. The corresponding integrated luminosities are 36.3, 41.5, and 59.8,
respectively, amounting to a total of 138. The aforementioned data were
collected with the use of single-electron and single-muon triggers with
isolation criteria. The trigger thresholds are mentioned in Section 0.5.

Simulated events are used to model the signal and background processes using
various Monte Carlo (MC) event generators. The signal samples are generated
with the generator [74] v2.2.2 for 2016 (v2.4.2 for 2017–2018) using the 4FS
at next-to-LO (NLO) precision in quantum chromodynamics (QCD). The decays of
the resonances are generated with madspin [75] to preserve spin-correlation
and finite-width effects. Both charge-conjugate signal processes are generated
with four mass hypotheses $m_{\PHpm}=300$, 400, 500, and 700and under the
assumption that $m_{\Ph}=125\GeV$ and $m_{\PH}=200\GeV$.

The top quark-antiquark pair ($\ttbar$) production constitutes an important
background that contributes significantly to all final states considered. It
is simulated with NLO precision in QCD using the v2.0 [76, 77, 78, 79, 80, 81]
generator. Its cross section is obtained from the TOP++ v2.0 [82] calculation
that includes next-to-NLO (NNLO) corrections in QCD and resummation of the
next-to-next-to-leading logarithmic soft-gluon terms. Other important sources
of background include single top quark production (single ), $\PQt\PAQt\PX$
with $\PX=\PW$, , , or , and electroweak processes including +jets with
$\PV=\PZ$ or $\PW$and diboson ($\PW\PZ$, $\PZ\PZ$, $\PW\PW$) production. For
the single samples, the $t$-channel process is generated with v2.0 at NLO
precision in QCD using the 4FS [83] and interfaced with madspin for simulating
the top quark decay. The $s$-channel process is simulated using , while the
production via the $\PQt\PW$-channel is simulated at NLO in QCD using the 5FS
and v2.0 [84]. The production of in association with or boson is simulated
with NLO precision in QCD using . The $\ttbar\Ph$ background process is
generated using v2.0 at NLO [85], with a Higgs boson mass of 125 . The top
quark mass is set to $m_{\PQt}=172.5\GeV$. The +jets samples are generated at
LO precision using , with up to four partons included in the matrix element
(ME) calculations. Finally, the diboson processes are generated at LO
precision using v8.212 [86] .

For processes generated at LO precision in QCD, the MLM matching and merging
procedure is used [87], whereby partons from the ME calculation are matched to
the jets reconstructed after the perturbative shower. For processes generated
at NLO precision in QCD with the generator, the events from the ME
characterized by different parton multiplicities are merged with the FxFx
procedure [88]. The matching between the ME calculation and the parton shower
in v2.0 is controlled by the damping factor $h_{\text{damp}}$, which has a
value set to $h_{\text{damp}}=1.379m_{\PQt}$. It is used to limit the
resummation of higher-order effects by the Sudakov form factor to below a
given scale.

For the generation of the above-mentioned simulated processes, the parton
distribution functions (PDFs) are parameterized using NNPDF3.0 [89] for 2016
(NNPDF3.1 [90] for 2017–2018). The PDFs in the ME calculations are at NLO for
NNPDF3.0 and at NNLO for NNPDF3.1. The parton shower and fragmentation are
modeled with the generator v8.212 for 2016 samples (v8.230 for 2017–2018). The
parameters affecting the description of the underlying event are set to the
CUETP8M1 tune [91] for 2016 (CP5 tune [92] for 2017–2018). The response of the
CMS detector is simulated using v9.4 [93] and reconstructed using the same
version of the CMS software as that used for the collision data.

The effect of additional inelastic $\Pp\Pp$ interactions within the same or
nearby bunch crossings, henceforth referred to as pileup, is taken into
account by generating concurrent minimum bias events. All simulated events are
weighted to match the pileup distributions observed in the data. The average
number of pileup in the 2016 data set was 23, increasing to 32 during the
2017–2018 data taking.

##  0.4 Object reconstruction

The global event reconstruction is based on the particle-flow (PF) algorithm
[94], which uses an optimized combination of information from the elements of
the CMS detector to reconstruct individual particles in an event. It
categorizes these PF candidates as photons, electrons, muons, charged hadrons,
and neutral hadrons. Higher-level objects are reconstructed from combinations
of the PF candidates. The primary $\Pp\Pp$ interaction vertex (PV) is taken to
be the vertex corresponding to the hardest scattering in the event, evaluated
using tracking information alone. More specifically, the individual tracks
originating from the same candidate vertex are clustered using the anti-
algorithm with a distance parameter of 0.4 [95], as implemented in the library
[96]. For each PV candidate the $\sum\pt^{2}$ value is computed by considering
the clustered jets, the remaining single tracks, and the neutral particle
contributions inferred from the negative vector sum of the of those jets. The
PV with the largest $\sum\pt^{2}$ is chosen as the one corresponding to the
hard scattering. All other candidate vertices are attributed to pileup, with
the exception of secondary vertices that are transversely displaced from the
PV and indicative of decays of long-lived particles emerging from it.

Electrons are identified as charged-particle tracks that are potentially
associated with ECAL energy clusters and bremsstrahlung photons emitted while
traversing the tracker material. Their momentum is estimated by combining the
energy measurement in the ECAL with the momentum measurement in the tracker.
The momentum resolution for electrons with $\pt\approx 45\GeV$ from
$\Z\rightarrow\Pe\Pe$ decays ranges from 1.7 to 4.5%. It is generally better
in the barrel region than in the endcaps, and also it depends on the
bremsstrahlung energy emitted by the electron as it traverses the material in
front of the ECAL. An MVA discriminant [97] is used to achieve better
discrimination of prompt isolated electrons from other electron candidates,
mainly originating from photon conversions, jet misidentification, and
semileptonic hadron decays. It requires as input several variables describing
the shapes of the energy deposits in the ECAL and the track quality. In this
paper, a medium (loose) working point with an identification efficiency of 90
($>$99)% is used for selecting (vetoing) electrons, corresponding to a rate of
jets misidentified as electrons of $\approx$1 (20)%.

Muons are reconstructed 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. They are measured in
the range of $\abs{\eta}<2.4$, with detection planes using three technologies:
drift tubes, cathode strip chambers, and resistive plate chambers. Their
momentum is obtained from the curvature of the corresponding tracks in the
silicon tracker, with a relative resolution of 1 and 3% for muons with up to
100in the barrel and endcaps, respectively. The resolution in the barrel is
better than 7% for muons with up to 1 [98]. To increase the purity of prompt
muons originating at the PV, a set of discriminants is employed based on the
track fit quality, the number of hits per track, and the degree of
compatibility of the information from the tracker and muon systems. A tight
(loose) working point with an efficiency of $\approx$95 (99)% is used for
selecting (vetoing) muons, in order to suppress muons from decays in flight
and misidentified muons from hadronic punch-through.

Both prompt and displaced reconstructed leptons are used in this analysis,
with the latter exclusively used in the validation of the background
estimation, described in detail in Section 0.6. In both cases the background
contributions from misidentified leptons are further suppressed by applying
stringent requirements on the lepton isolation. The relative lepton isolation
variable $I_{\text{rel}}$ is employed to ensure that the leptons are not
associated with any significant electromagnetic or hadronic activity in the
detector. It is defined as the scalar sum, normalized to the lepton , of all
PF candidates within a cone of radius $\Delta
R=\sqrt{\smash[b]{(\Delta\eta)^{2}+(\Delta\phi)^{2}}}<0.3$ (0.4) around the
electron (muon) direction at the PV, where $\phi$ is the azimuthal angle in
radians. The lepton itself is excluded from the calculation. To mitigate any
effects due to contamination from pileup, only PF candidates whose tracks are
associated with the PV are taken into account. For neutral hadrons and
photons, where the absence of an associated track precludes an unambiguous
association with the PV, an estimate of the pileup contribution is subtracted
from their energy sums [99]. A tight (loose) isolation criterion with
discriminant $I_{\text{rel}}<0.15$ (0.25) is used in lepton selection (veto).
The three-dimensional impact parameter significance, which is the impact
parameter value normalized to its uncertainty, can also be used to further
suppress electrons from photon conversions and muons originating from in-
flight decays of hadrons. Its value is required to be less than ten for prompt
electrons, or greater than three for all displaced electrons or muons.

Jets are reconstructed from PF candidates using the anti-algorithm [95], as
implemented in the package [96], with a distance parameter of 0.4. The jet
momentum is determined as the vectorial sum of all particle momenta in the
jet. It is found from simulation to be within 5–10% of the true momentum, over
the whole spectrum and detector acceptance. Pileup can contribute additional
tracks and calorimetric energy depositions, increasing the apparent jet
momentum. To mitigate this effect, tracks identified to be originating from
pileup vertices are discarded and an offset correction is applied to correct
for remaining contributions [99]. Jet energy corrections are derived from
simulation studies so that the average measured energy of jets becomes
identical to that of particle-level jets. In situ measurements of the momentum
balance in dijet, photon+jet, +jet, and multijet events are used to determine
any residual differences between the jet energy scale in data and in
simulation, and appropriate corrections are applied to simulated events [100].
After the corrections, the jet energy resolution amounts typically to 15–20%
at 30, 10% at 100, and 5% at 1 [100].

The identification of jets that originate from the hadronization of quarks (
jets) is performed with the DeepJet multiclass flavor-tagging algorithm, as
described in Refs. [101, 102, 103, 101]. In this analysis, a medium working
point of this algorithm is chosen that corresponds to a -jet identification
efficiency of $\approx$80%. The associated misidentification rate for jets
originating from light quarks and gluons (quarks) is 1 (15)% [102].

The candidates are reconstructed with the hadrons-plus-strips algorithm, as
described in Ref. [104]. It uses clustered anti-jets as seeds to reconstruct
decay modes with one charged hadron and up to two neutral pions (one-prong),
or three charged hadrons and up to one neutral pion (three-prong). The neutral
pions, which decay promptly to a photon pair, are reconstructed as strips of
-dependent size in the $\eta\text{-}\phi$ plane from reconstructed electrons
and photons contained in the jet. These strips are narrow in $\eta$ but wide
in $\phi$ to allow for the broadening of ECAL energy deposits due to photon
conversions. The decay mode is then obtained by combining the charged hadrons
with the strips, resulting in a reconstruction efficiency of $\approx$80%. To
efficiently discriminate the decays against jets originating from the
hadronization of quarks or gluons, and against electrons or muons, the DeepTau
[105, 106] multiclass identification algorithm is used. It exploits the
reconstructed event quantities by combining low-level information from the
tracking, calorimeter, and muon detectors with high-level properties of the
candidate and other PF candidates in its vicinity. The multiclassification
output $y_{\alpha}$ represents a Bayesian probability that the candidate
originates from a lepton ($\alpha=\Pe$, ), the hadronization of a quark or
gluon ($\alpha=j$), or a genuine ($\alpha=\PGt$). The aforementioned output
enables the definition of three discriminators according to the ratio
$D_{\alpha}=y_{\PGt}/(y_{\PGt}+y_{\alpha})$ with $\alpha=\Pe$, , $j$. For this
analysis, medium and tight working points of $D_{\Pe}$ and $D_{\PGm}$ are used
with efficiencies of 62 and 70% and misidentification rates of 0.2 and 0.03%,
respectively. For $D_{j}$, the medium and loose working points are used with
efficiencies of 49 and 70% for misidentification rates of 0.4 and 5%,
respectively, for candidates with up to 200. The selected candidates that pass
the loose but fail the medium $D_{j}$ working point are referred to as anti-
isolated ’s and are solely used in the background estimation as described in
Section 0.6.

The is computed as the negative vector sum of the transverse momenta of all PF
candidates in an event, and its magnitude is denoted as [107]. The is modified
to account for corrections to the energy scale of the reconstructed jets in
the event. The scalar sum of all selected leptons and objects in an event is
denoted as $L_{\mathrm{T}}$, while the corresponding sum over all selected
jets is designated as . In addition, we define $S_{\mathrm{T}}$ as the scalar
sum of , $L_{\mathrm{T}}$, and in the event. The transverse mass of charged
Higgs boson candidates is calculated as:

$\mT=\sqrt{(\ET^{1}+\ET^{2}+\ET^{\PW}+\ptmiss)^{2}-\abs{\ptvec^{1}+\ptvec^{2}+\ptvec^{\PW}+\ptvecmiss}^{2}},$
(1)

where $\ET^{1}$, $\ET^{2}$, and $\ET^{\PW}$ are the total visible transverse
energies of the two tau lepton and boson decay products, respectively, and
$\ptvec^{1}$, $\ptvec^{2}$, and $\ptvec^{\PW}$ the corresponding transverse
momentum vectors.

Hadronic decays of top quarks are reconstructed and identified using a
resolved top quark ($\PQt^{\text{res}}$) tagger that is based on a fully
connected neural network implemented using Keras [108] and TensorFlow [109]
software packages. It targets top quarks whose decay products are resolved as
three separate anti-jets with a distance parameter of 0.4. It is trained on
simulated events to discriminate between three-jet combinations originating
from the decay of top quarks (signal) and other combinatorial three-jet
systems (background). For training, the signal $\PQt^{\text{res}}$ candidates
are matched to the generated top quark decay products with one-to-one jet-to-
quark matching, while the $\PQt^{\text{res}}$ candidates with at least one
unmatched jet are considered as combinatorial background.

This MVA classifier utilizes high-level information from each of the three
seed jets, such as invariant masses, angular separations, jet flavor, and jet
shape variables. All the selected variables are uncorrelated with the top
quark mass to minimize possible correlations between the $\PQt^{\text{res}}$
candidate mass and the associated classifier output. To improve the stability
and performance of the learning algorithm, the input features are transformed
such that they are distributed in similar ranges and not influenced by
outliers. This tagger uses the robust scaler preprocessing method via scikit-
learn tool [110]. Furthermore to prevent mass sculpting effects, the algorithm
uses the sample-reweighting technique to decorrelate the classifier’s output
from the top quark mass. The mass information is removed from all the input
features by reweighting the combinatorial background data sets so that the
$\PQt^{\text{res}}$ candidate mass distribution matches that of the signal.

The performance of the $\PQt^{\text{res}}$ tagger is expressed as a receiver
operating characteristic curve and it is shown in Fig. 3. The loose, medium,
and tight working points are established at 10, 5, and 1% background
misidentification probability. The corresponding identification efficiencies
are 91, 81, and 47%, respectively. The loose working point is employed in this
analysis.

Figure 3: Receiver operating characteristic curve of the $\PQt^{\text{res}}$
tagger. The cross-, triangle-, and star-shaped markers indicate the loose,
medium, and tight working points with 10, 5, and 1% background
misidentification probability. The corresponding identification efficiencies
are 91, 81, and 47%, respectively.

The misidentification rate and tagging efficiency of the $\PQt^{\text{res}}$
tagger have been estimated and compared in data and simulation to extract
data-to-simulation corrections, using a sample of lepton+jets, dominated by
the semileptonic events. The events are characterized by large , exactly one
muon identified as tight with $\pt>50\GeV$ and at least four jets with
$\pt>40\GeV$ and $\abs{\eta}<2.4$, of which at least one is b tagged. The jet
closest to the muon is considered as the b jet from the leptonic top quark
decay. The three-jet system with a mass closest to the top quark mass is
selected as the hadronic $\PQt^{\text{res}}$ candidate. The misidentification
rate is measured using events in which the $\PQt^{\text{res}}$ candidate mass,
$m_{\PQt^{\text{res}}}$, falls outside a mass window of 130–210, and the
sample is dominated by the combinatorial background. Events where
$m_{\PQt^{\text{res}}}$ is within the mass window are used to measure the
$\PQt^{\text{res}}$ tagging efficiency, after subtracting from data the
contributions from non-top quark processes and the combinatorial background,
as estimated from simulations. The misidentification rate and tagging
efficiency for the 2017 data set are shown in Fig. 4 as a function of the
$\PQt^{\text{res}}$ candidate for the loose working point. The data-to-
simulation corrections are defined as the ratio data/simulation, in bins of
the $\PQt^{\text{res}}$ candidate. Similar behavior was also observed for the
2016 and 2018 data.

Figure 4:  Misidentification rate (left) and $\PQt^{\text{res}}$ -tagging
efficiency (right) in data and simulation, as a function of the
$\PQt^{\text{res}}$ candidate for the loose working point, using the 2017
data.

##  0.5 Event selection

The analysis is conducted in the mutually exclusive $\Pe\tauh$, $\PGm\tauh$,
$\Pe\tauh\tauh$, and $\PGm\tauh\tauh$ final states. The event selection
strategy is independently optimized for each final state to improve the
suppression of backgrounds while maintaining a large signal selection
efficiency. The selection of signal candidate events at the trigger level is
based on the presence of at least a single isolated lepton. More specifically,
for the $\Pe\tauh$ and $\Pe\tauh\tauh$ channels the online HLT requires the
presence of an isolated electron with a threshold of 27, 32, and 32for the
data-taking years 2016, 2017, and 2018, respectively. For the $\PGm\tauh$ and
$\PGm\tauh\tauh$ channels, an isolated muon is required, with thresholds of
24, 27, and 24for the three years. The HLT objects are geometrically matched
to analogous offline objects that satisfy the $\pt$, $\eta$, $I_{\text{rel}}$
criteria described in the following, in addition to the object identification
requirements given in Section 0.4.

To ensure high trigger efficiency, the offline $\pt$ and $\eta$ requirements
for prompt electrons (muons) are $\pt>30$, 35, 35 (26, 29, 26)and
$\abs{\eta}\leq 2.1$ (2.4) for the 2016, 2017, and 2018 data-taking periods.
Selected electrons (muons) are also required to pass medium (tight)
identification criteria and satisfy $I_{\text{rel}}<0.15$ for all three years.
Only events with exactly one such electron (muon) are accepted. Furthermore,
events with any additional electrons or muons fulfilling looser identification
criteria are also discarded, provided that the electron (muon) candidates
satisfy the requirements of $\pt>10\GeV$, $\abs{\eta}\leq 2.4$ (2.5), and
$I_{\text{rel}}<0.25$. This helps to avoid the incorrect assignment of objects
in the transverse mass reconstruction and the inadvertent smearing of its
Jacobian peak, and ensures the orthogonality between final states with
different lepton flavors.

In both the $\ell\tauh$ and $\ell\tauh\tauh$ final states, all candidates are
required to have $\pt>20\GeV$ and $\abs{\eta}<2.3$. They must be well
separated in $\eta\text{-}\phi$ space from the trigger lepton and other
candidates, such that $\Delta R(\tauh,\ell/\tauh)>0.5$. To reduce the
contribution of electrons, muons, or jets mimicking a object, the medium,
tight, and medium working points of the $D_{\Pe}$, $D_{\PGm}$, and $D_{j}$
discriminants are chosen, irrespective of final state, or year of data taking.
In the $\ell\tauh$ final states, the events are classified according to the
sum of the electric charge of the selected lepton and objects,
$Q_{\ell\tauh}$, in units of the electron charge $e$. Both the opposite-sign
(OS) case with $\abs{Q_{\ell\tauh}}=0$ and the same-sign (SS) case with
$\abs{Q_{\ell\tauh}}=2$ are considered as separate categories. The
categorisation of the $\ell\tauh$ final states into OS and SS significantly
improves the expected sensitivity over the entire $m_{\PHpm}$ region
considered. Events in the $\ell\tauh$ SS category arise when one of the tau
leptons from the $\PH\to\PGt\PGt$ decay is not reconstructed or identified. It
has significantly smaller contributions from SM processes with a top quark in
the final state than the $\ell\tauh$ OS category. In the $\ell\tauh\tauh$
final states, the two candidates are required to be OS with
$\abs{Q_{\tauh\tauh}}=0$.

The $\ell\tauh$ final states are required to contain at least three jets with
$\pt>30\GeV$ and $\abs{\eta}<2.4$, for all data-taking years. Slightly
modified criteria are used for the $\ell\tauh\tauh$ final states, with the
multiplicity requirement reduced to two and the pseudorapidity extended to
$\abs{\eta}<4.7$, in order to increase the signal acceptance. All selected
jets must be well separated from the reconstructed objects such that $\Delta
R(j,\tauh)>0.5$. We denote the selected jet with the highest (second-highest)
in each event as $j_{1}$ ($j_{2}$). For all final states considered, at least
one of the selected jets is required to pass the medium working point of the
DeepJet jet identification algorithm.

To further suppress multijet events with nonprompt leptons and jets
misidentified as , the $\ell\tauh$ ($\ell\tauh\tauh$) final states require the
presence of moderate magnitude of missing transverse momentum of $\ptmiss\geq
40$ (30). For the $\ell\tauh\tauh$ final state, the requirement
$S_{\mathrm{T}}>400\GeV$ is also used as it considerably improves the expected
sensitivity. A summary of the event selection criteria for all final states is
shown in Table 0.5. They result in a total of 6 signal regions (SRs) per year
of data taking; $\Pe\tauh$ OS, $\Pe\tauh$ SS, $\PGm\tauh$ OS, $\PGm\tauh$ SS,
$\Pe\tauh\tauh$, and $\PGm\tauh\tauh$. They are complemented by the various
control regions (CRs) and validation regions (VRs) described in Section 0.6,
which are used to predict the dominant backgrounds in the statistical
inference of the signal.

Offline selections applied to the reconstructed objects to obtain the SRs of
the $\ell\tauh$ and $\ell\tauh\tauh$ final states. The , , and
$S_{\mathrm{T}}$ variables are reported in units of , and $Q$ in units of $e$.
Selection criteria that depend on the year of data taking are presented in
parentheses with the order corresponding to (2016, 2017, 2018). The symbol
$\star$ is used to represent an electron (muon) for the $\Pe\tauh$
($\PGm\tauh$) final states, and a object in the $\Pe\tauh\tauh$ and
$\PGm\tauh\tauh$ final states.  Object Selection Signal Regions $\Pe\tauh$
$\PGm\tauh$ $\Pe\tauh\tauh$ $\PGm\tauh\tauh$ Prompt electrons $N$ $=$1 $=$0
$=$1 $=$0 $\pt$ $>$(30, 35, 35) $>$10 $>$(30, 35, 35) $>$10 $\abs{\eta}$
$<$2.1 $<$2.5 $<$2.1 $<$2.5 $I_{\text{rel}}$ $<$0.15 $<$0.25 $<$0.15 $<$0.25
Prompt muons $N$ $=$0 $=$1 $=$0 $=$1 $\pt$ $>$10 $>$(26, 29, 26) $>$10 $>$(26,
29, 26) $\abs{\eta}$ $<$2.4 $<$2.4 $<$2.4 $<$2.4 $I_{\text{rel}}$ $<$0.25
$<$0.15 $<$0.25 $<$0.15 objects $N$ $=$1 $=$2 $\pt$ $>$20 $>$20 $\abs{\eta}$
$<$2.3 $<$2.3 $\abs{Q_{\star\tauh}}$ $=$0, 2 $=$0 Jets $N$ $\geq$3 $\geq$2
$\pt$ $>$30 $>$30 $\abs{\eta}$ $<$2.4 $<$4.7 jets $N$ $\geq$1 $\geq$1 $\pt$
$>$30 $>$30 $\abs{\eta}$ $<$2.4 $<$2.4 Event-based $\ptmiss$ $>$40 $>$30
$S_{\mathrm{T}}$ $>$400

##  0.6 Background estimation

The dominant background for all the final states considered stems from +jets
and productions. This can be decomposed into events with genuine candidates,
and events with leptons or jets misidentified as candidates. Backgrounds from
events with genuine candidates, together with events involving electrons or
muons misidentified as objects ($\ell\to\tauh$) are estimated from simulation.
The reconstructed candidate is matched to a generator-level tau lepton,
electron, or muon using a cone of $\Delta R=0.1$. Backgrounds from jets
misidentified as candidates ($j\to\tauh$) are estimated using control samples
in data by the use of misidentification rates. These misidentification rates
are measured in dedicated CRs that are enriched in jets misidentified as
candidates, and mimic as closely as possible the composition and kinematic
properties of the corresponding SRs. The CRs are required to be orthogonal to
all SRs and have negligible signal contamination. Then, the misidentification
rate is defined as:

$\mathcal{R}_{j\to\tauh}=\frac{N^{\text{CR}}_{\text{nominal
}\tauh}}{N^{\text{CR}}_{\text{loose},\tauh}}$ (2)

where $N^{\text{CR}}_{\text{nominal }\tauh}$ is the number of events in the CR
satisfying the nominal selection criteria, and $N^{\text{CR}}_{\text{loose
}\tauh}$ is the corresponding number of events in the CR satisfying loose
selection criteria. For both the numerator and denominator in Eq. (2) a
correction is applied to remove events containing jets originating from a
genuine candidate or from a lepton misidentified as a candidate.

The misidentification rate measurements are performed in different CRs,
separately for each final state and data-taking period. In the $\ell\tauh$
channels, the CRs are selected with the nominal criteria used in defining the
SRs, but with the following modifications. The criterion is inverted such that
$\ptmiss<40\GeV$, while the requirement of exactly one $\PQt^{\text{res}}$
object is also introduced to suppress contributions from +jets processes. The
motivation for these selections is twofold: to enforce orthogonality with the
SRs, and to ensure that the obtained regions are enriched in . A second set of
CRs, orthogonal to all other CRs and SRs, is also used with alternative
selection criteria that are introduced to enhance electroweak contributions.
More specifically, the requirement is removed, the jet multiplicity is
inverted, and the requirement of exactly one $\PQt^{\text{res}}$ object is
also imposed. These auxiliary CRs are used to quantify systematic
uncertainties related to differences in sample composition between the SRs and
the CRs, and in particular the relative contribution of and electroweak
processes. The misidentification rates are measured as a function of the
candidate , separately for one- and three-prong decays, and individually for
the central ($\abs{\eta}\leq 1.5$) and forward regions ($\abs{\eta}\geq 1.5$)
of the detector.

In the $\ell\tauh\tauh$ channels, the misidentification rates are measured
using similar event selection as in the SRs, except that the two objects are
required to be SS with $\abs{Q_{\tauh\tauh}}=2$, and no requirement is imposed
on the $S_{\mathrm{T}}$ variable. To compensate for the lower statistical
precision relative to the $\ell\tauh$ final states, the misidentification
rates are parametrized in the and decay mode of the objects, without
separating the central and forward regions of the detector.

The predicted number of events with misidentified objects in the SRs is
derived using the fake factor method [111] by applying the misidentification
rates evaluated in the CRs to events with anti-isolated objects:

$N_{j\to\tauh}^{\text{SR}}=\sum\limits_{i}w_{i}^{\text{CR}}N_{\text{one anti-
isolated
}\tauh,i}^{\text{SR}}-\sum\limits_{i}w_{i,~{}1}^{\text{CR}}w_{i,~{}2}^{\text{CR}}N_{\text{two
anti-isolated}\tauh,i}^{\text{SR}}.$ (3)

The index $i$ refers to each bin of the parametrization and $w_{i}$ to the
corresponding normalization weight. The term $N_{\text{anti-isolated
}\tauh,i}^{\text{SR}}$ refers to number of events with anti-isolated objects
in the SR of interest, after subtracting events with jets originating from a
genuine or from a lepton misidentified as a candidate. The normalization
weight for a given parametrization bin $i$ is given by:

$w_{i}^{\text{CR}}=\frac{\mathcal{R}_{j\to\tauh,~{}i}}{1-\mathcal{R}_{j\to\tauh,~{}i}}$
(4)

for each event with a single anti-isolated candidate present. In the
$\ell\tauh\tauh$ final states, Eq. (4) must be applied to each of the two
candidates that are present. It thus accounts for the case where only one of
the candidate is a misidentified , but also includes cases whereby both
candidates are misidentified and one of them passes all nominal identification
criteria. In order to account for this double counting, the number of
misidentified events is predicted by the weighted sum of the number of events
with one anti-isolated candidate minus the weighted number of events with two
anti-isolated candidates.

The validity of the extracted misidentification rates is verified by defining
additional VRs with either anti-isolated or isolated candidates, mutually
orthogonal to both the SRs and CRs. The misidentification rates are used to
normalize the misidentified samples from the anti-isolated VRs to a signal-
depleted VR with isolated candidates, where the obtained background prediction
is compared with the observed data. This validation is performed separately
for all channels and data-taking periods.

In the $\ell\tauh$ channels, the VRs are defined by selecting events with the
same selection criteria as those used for the SRs. However, instead of
requiring the presence of one jet in the $\Pe\tauh$ ($\PGm\tauh$) region, a
low-loosely identified and loosely isolated displaced muon (electron) is
required. In the $\ell\tauh\tauh$ channels, the validation of the background
estimation is performed using two VRs. The first VR is defined by using
similar event selections to the SRs but vetoing events with identified jets,
while also removing any requirements on the $S_{\mathrm{T}}$ variable. For the
second VR, events are selected with identical criteria as for the SR, except
that the $S_{\mathrm{T}}$ requirement is inverted to satisfy
$S_{\mathrm{T}}<400\GeV$. A summary of the event selection criteria for the
CRs and the VRs used is shown in Table 0.6, indicating only selections that
are different than their respective SRs defined in Table 0.5.

Offline selections applied to the reconstructed objects to obtain the CRs and
VRs for the misidentified candidate background estimation in the $\ell\tauh$
and $\ell\tauh\tauh$ final states. Only differences with respect to the
corresponding SRs are shown. The , , and $S_{\mathrm{T}}$ variables are
reported in units of , and $Q$ in units of $e$. The symbol $\star$ is used to
represent an electron (muon) for the $\Pe\tauh$ ($\PGm\tauh$) final states,
and a object in the $\Pe\tauh\tauh$ and $\PGm\tauh\tauh$ final states.  Object
Selection Control Regions Validation Regions $\ell\tauh$ $\ell\tauh\tauh$
$\Pe\tauh$ $\PGm\tauh$ $\ell\tauh\tauh$ Displaced electrons $N$ $=$1 $\pt$
$>$10 $\abs{\eta}$ $<$2.5 $I_{\text{rel}}$ $<$0.25 Displaced muons $N$ $=$1
$\pt$ $>$10 $\abs{\eta}$ $<$2.4 $I_{\text{rel}}$ $<$0.25 objects
$\abs{Q_{\star\tauh}}$ $=$2 jets $N$ $\geq$0 $\geq$0 $=$0 $\PQt^{\text{res}}$
$N$ $=$1 Event-based $\ptmiss$ $<$40 $S_{\mathrm{T}}$ $>$0 $>$0 $<400$

##  0.7 Search strategy

To maximize the sensitivity of the search, the discriminating variable used to
separate between the signal and background processes is chosen separately for
the $\ell\tauh$ and $\ell\tauh\tauh$ final states. For the latter, the search
strategy focuses on the reconstruction of the full decay chain in order to
search for localized excesses in the spectrum, as per Eq. (1). For the
hypothetical signal, the distribution should possess a Jacobian peak with an
endpoint at $\mT=m_{\PHpm}$ that remains unchanged by the transverse motion of
the mother particle. For the $\ell\tauh$ final states, the ambiguity in the
selection of the jets that go into the calculation results in a combinatorial
background that smears the discriminating power of the variable. Thus, while
still valuable, the is not an optimal variable for signal extraction in the
$\ell\tauh$ channels.

In order to enhance the signal and background separation in the $\ell\tauh$
final states, an MVA BDTG classifier is employed using the TMVA [112]
framework. The training was performed separately for each simulated signal
sample, final state, and data-taking period. The inclusive +jets and simulated
samples were used to train against the background, weighted according to their
cross-sections. A total of 12 input variables were used for the training of
the BDTG classifiers and include kinematic variables of individual physics
objects, as well as event-based variables. They are summarized in Table 0.7.

The complete set of discriminating variables used in the training of the BDTG
classifier employed in the search strategy of the $\ell\tauh$ final states.
Variable Description $\Delta\phi(\tauh,\ptvecmiss)$ azimuthal angle between
the and objects $\Delta\phi(\ell,\ptvecmiss)$ azimuthal angle between the
$\ell$ and objects
$\frac{\pt^{j_{1}j_{2}}-\pt^{\PHpm}}{\pt^{j_{1}j_{2}}+\pt^{\PHpm}}$ ratio of
sums calculated from $\ell$, , $j_{1}$, $j_{2}$ and
$\frac{\pt^{j_{1}j_{2}}}{\HT}$ ratio of of the first two leading jets and the
$\mT(\ell,\tauh,j_{1},j_{2},\ptvecmiss)$ reconstructed from $\ell$, , $j_{1}$,
$j_{2}$, and  $\frac{\pt^{j_{3}}}{\HT}$ ratio of the of the third leading jet
and the  $m(\ell,\,\tauh)$ invariant mass of the $\ell$ and objects
$\frac{\pt^{j_{1}j_{2}}+L_{\mathrm{T}}}{\HT}$ ratio of of first two leading
jets plus $L_{\mathrm{T}}$ and the  $\mT(\ell,\ptvecmiss)$ reconstructed from
the $\ell$ and objects $\pt^{\tauh}$ transverse momentum of object
$N_{\text{jets}}$ number of selected jets in the event $N_{\PQt^{\text{res}}}$
number of selected $\PQt^{\text{res}}$ objects in the event

Three of these variables are shown in Fig. 5 for the $\PGm\tauh$ final state
and the 2018 data-taking period. Figure 5 (top left) shows the azimuthal angle
between the and , denoted as $\Delta\phi(\PGm,\ptvecmiss)$. In the same figure
(top right) the ratio of the of the third leading jet and the , denoted as
${\pt^{j_{3}}/{\HT}}$ is shown. Finally, the transverse mass
$\mT(\PGm,\tauh,j_{1},j_{2},\ptvecmiss)$ reconstructed from the selected , ,
$j_{1}$, $j_{2}$, and objects is shown in Fig. 5 (bottom). Instead of being
used as an input to the BDTG, the event-variable $Q_{\ell\tauh}$ is used for
the categorization of $\ell\tauh$ events, as it increases signal sensitivity
over the entire mass spectrum. In particular, the SS selection significantly
suppresses the contribution that dominates the OS category, leaving the
misidentified as the dominant background.

Figure 5:  Three of the BDTG input variables used for the $\PGm\tauh$ final
state, assuming a signal with mass $m_{\PHpm}=500\GeV$and 2018 data-taking
conditions: the azimuthal angle between the and objects (top left), the ratio
of the of the third leading jet and the (top right), and the transverse mass
reconstructed from the , , $j_{1}$, $j_{2}$, and objects (bottom). Both signal
and background distributions are normalized to unit area.

##  0.8 Systematic uncertainties

The systematic uncertainties from various experimental and theoretical sources
can affect the expected event yield (rate uncertainties), the shape of the fit
discriminant (shape uncertainties), or both. Log-normal (Gaussian) a priori
distributions are assumed for rate (shape) uncertainties. Partial and complete
correlations between the uncertainties in different categories and years are
taken into account, depending on the way they are derived. All experimental
sources are treated as correlated across categories but as uncorrelated across
years, unless otherwise specified. All theoretical sources are treated as
correlated across all categories and years. A summary of all sources of
systematic uncertainties discussed in this section is given in Table 0.8.2.

Apart from the various experimental uncertainties, the statistical analysis of
the results employs an uncertainty model that also accounts for uncertainties
due to the limited population of template distributions in signal and
background modeling. These statistical uncertainties can lead to fluctuations
in nominal predictions and their effect is individually incorporated for each
template bin with the Barlow–Beeston lite approach [113, 114]. Each bin is
assigned a combined statistical uncertainty, and these uncertainties are
treated as uncorrelated among other bins, categories, channels, and data sets.

###  0.8.1 Experimental sources

The integrated luminosity for each year of data taking is measured
individually with an uncertainty in the 1.2–2.5% range [115, 116, 117]. The
total integrated luminosity for the period 2016–2018 has an uncertainty of
1.6%. The improvement in precision reflects the uncorrelated time evolution of
some systematic effects. These effects are applied as rate uncertainties to
all simulated processes and thus only affect the expected yield of events, but
not the individual shapes of the fit discriminants.

Uncertainties related to the electron and muon trigger efficiencies arise from
the fact that simulated events are corrected to match the efficiencies
measured in data. The uncertainties in the corrections, which depend on the
and $\eta$ of the trigger object, lead to rate and shape effects in the fit
discriminants that amount to 1–4%.

During the 2016–2017 data taking, a gradual shift in the timing of the ECAL
inputs to the first-level trigger in the region of $\abs{\eta}>2.0$ caused a
trigger inefficiency of $\approx$10–20% for events containing an electron
(jet) with $\pt\gtrsim 50$ (100)and in the region $2.5<\abs{\eta}<3.0$,
depending on , $\eta$, and time. Corresponding correction factors were derived
from data and applied to the acceptance evaluated from simulation. The related
uncertainties, which are treated as correlated between the two years and all
categories, are found to affect the expected event yields by $\approx$1% when
propagated to the final fit discriminants.

The uncertainty due to the pileup modeling in simulated samples is estimated
by varying the total inelastic $\Pp\Pp$ cross section used to estimate the
number of pileup events in data. The nominal value of 69.2mb is varied by 5%
[118, 119] and the effect is propagated through all event selections. The
resulting uncertainty amounts to up to 5.5%, and is treated as correlated
across all categories and years.

Uncertainties associated with the identification efficiency for electrons and
muons are propagated as variations to the final fit discriminants. They are
treated as correlated across all categories and years and result in shape-
altering variations that change the total event yield by about 0.1–2.4%. The
uncertainty related to the vetoing of leptons passing loose selection criteria
is between 0.1 and 2.0%.

The uncertainties associated with the identification efficiency are evaluated
in bins of the object and range between 0.1 and 5.3%. The energy scale
uncertainties are found to be up to about 2.0%, depending on the decay mode of
the object. For the energy and momentum scale of electrons and muons
misidentified as candidates, the relevant corrections depend on the and decay
mode of the candidate and their uncertainties are of $\mathcal{O}(1\%)$. The
above-mentioned uncertainties lead to shape effects and are treated as
uncorrelated across $\pt$ bins and decay modes.

The jet energy scale uncertainties are specified as functions of jet and
$\eta$ and are treated as correlated across all categories and years. They are
estimated by shifting the energy of jets and propagating these shifts through
the analysis selections. This results in rate- and shape-altering variations
of $\mathcal{O}(5\%)$. The energy resolution of simulated jets is adjusted to
match the resolution observed in data. The uncertainties in the jet energy
resolution are evaluated by smearing the jet energies around their nominal
values. These are treated as uncorrelated across the years and correlated
across categories and result in an overall effect of $\mathcal{O}(5\%)$.

Jet energy uncertainties are also propagated to the calculation to account for
the fact that it primarily relies on the accurate measurement of the
reconstructed physics objects. Another uncertainty in the measurement is
related to the unclustered energy in the event. It refers to jets with
$\pt<10\GeV$ and PF candidates not clustered into jets. This unclustered
energy scale uncertainty impacts both the rate and the shape of the fit
discriminants and has an overall effect of up to 2.4%.

The efficiency of classifying jets as b tagged is different in data than in
simulation. To correct for this effect -dependent corrections are
incorporated. The systematic uncertainties in these tagging and mistagging
efficiency corrections are treated as rate and shape altering. They are found
to have an effect of $\mathcal{O}(5\%)$ in the expected event yields.

The uncertainties associated with the $\PQt^{\text{res}}$ tagging and
mistagging efficiency corrections are only relevant for the $\ell\tauh$
categories. They are evaluated in bins of of the selected $\PQt^{\text{res}}$
and the various sources of uncertainty are treated as uncorrelated. These
include effects due to the generator-level matching definition, the damping of
radiation with high , the modeling of the first emission, the scale radiation,
the color reconnection strength, the assumed value of the top quark mass, and
the tuning of the underlying event parameters. These are propagated to the fit
discriminants of the $\ell\tauh$ final states as shape uncertainties and are
found to change the total event yield by about 5% for tagging and 8% for
mistagging.

For the misidentified background estimation three distinct components of
uncertainties are defined. The first component is the statistical uncertainty
associated with the evaluation of the misidentification rates in the dedicated
CRs. The various parametrization bins that are used in the $\ell\tauh$ and
$\ell\tauh\tauh$ channels for this measurement, as described in Section 0.6,
are treated as uncorrelated. The propagation of the statistical uncertainty in
the final fit discriminants has an overall effect of $\mathcal{O}(10\%)$. The
second component is concerned with a rate and shape-altering uncertainties
implemented to address the level of agreement of closure tests in the VRs.
Their impact on the expected event yield is $\mathcal{O}(10\%)$. The third
component accounts for the difference in sample composition between the CRs in
which the misidentification rates are determined, and the SRs in which they
are applied. It is treated as uncorrelated between the parametrization bins
and when propagated to the final fit discriminants brings about an overall
effect of up to 18%.

###  0.8.2 Theoretical sources

The systematic uncertainties related to theoretical considerations mainly
arise due to missing higher-order QCD corrections and uncertainties in the PDF
sets. An additional source of uncertainty concerns the assumed values of the
top quark mass $m_{\PQt}$ and that of the strong coupling in parton showers
[120]. These affect both the total and differential cross sections of the
processes, yielding uncertainties on the overall normalization of the
simulated processes and the acceptance of the event selection. All effects are
taken into account as rate uncertainties.

For the and single processes, the effect of $m_{\PQt}$ on the cross sections
is evaluated by varying its nominal value of 172.5by 1.0. The effects from the
renormalization and factorization (RF) scales on the acceptance and cross
sections are evaluated by varying them independently by factors of one-half
and two with respect to their nominal values, respectively. Extreme variations
where one scale is varied by one-half and the other one by two are excluded.
The effect on the event yield from simulated events is then calculated by
enveloping the maximum variation with respect to the nominal fit
discriminants, as recommended in Ref. [121].

The PDF uncertainties are also treated as fully correlated for all processes
and categories. They are also correlated between simulated samples that share
the same dominant partons in the initial state of the ME calculations [122].

Summary of all sources of systematic uncertainties discussed in the text. The
first column identifies the source of uncertainty and, where applicable, the
process that it applies to. The second column indicates with a check mark
$\checkmark$ or dash whether or not the nuisance parameter also affects the
shape of the fit discriminant. The third column, which is subdivided into four
event categories, presents the percentage % impact of these nuisance
parameters on the expected event yields, before simultaneous fitting the data
for the background-only hypothesis. A range of such values represents the
minimum and maximum values observed through the different samples and data
eras, with apparent disparities also attributed to the limited sample size of
minor backgrounds. The last two columns indicate whether or not the nuisance
parameters are correlated across years and categories. A dagger $\dagger$
designates that a nuisance parameter is only partially correlated across years
or categories.  Category Correlated across Uncertainty source Shape $\Pe\tauh$
$\PGm\tauh$ $\Pe\tauh\tauh$ $\PGm\tauh\tauh$ Years Categories Experimental
Integrated luminosity 1.2–2.5 $\checkmark^{\dagger}$ $\checkmark$ Trigger
efficiency $\checkmark$ 0.9–4.2 0.5–2.9 1.2–3.0 0.1–0.3 $\checkmark$ Trigger
timing inefficiency $\checkmark$ 0.1–0.3 0.1–0.3 $\checkmark$ Pileup
$\checkmark$ 0.2–2.9 0.1–1.6 0.1–5.5 0.1–2.3 $\checkmark$ $\checkmark$
Electron identification $\checkmark$ 0.1–2.4 0.1–1.9 $\checkmark$ $\checkmark$
Muon identification $\checkmark$ 0.4–1.6 0.1–1.1 $\checkmark$ $\checkmark$
Lepton veto 0.1–2.0 0.1–2.0 0.1–2.0 0.1–2.0 $\checkmark$ identification
$\checkmark$ 0.1–3.6 0.1–3.2 4.2–5.2 4.3–5.3 $\checkmark$ energy scale
$\checkmark$ 0.2–1.8 0.2–0.4 0.8–1.5 0.8–1.2 $\checkmark$ $\Pe\to\tauh$
misidentification $\checkmark$ 0.2–1.5 0.1–0.4 0.3–0.6 0.2–0.6 $\checkmark$
$\PGm\to\tauh$ misidentification $\checkmark$ 0.1–1.6 0.1–0.3 0.1–0.3 0.1–0.3
$\checkmark$ Jet energy scale $\checkmark$ 1.1–4.9 1.2–4.2 1.6–3.6 1.6–2.4
$\checkmark$ $\checkmark$ Jet energy resolution $\checkmark$ 0.3–3.1 0.3–3.1
1.1–4.6 1.2–3.1 $\checkmark$ jet identification $\checkmark$ 2.5–5.4 2.5–5.1
2.4–4.2 3.2–4.2 $\checkmark$ jet misidentification $\checkmark$ 2.4–4.1
2.2–4.5 1.0–2.6 1.7–2.5 $\checkmark$ Unclustered energy scale $\checkmark$
0.1–1.9 0.2–1.5 0.5–1.7 0.3–2.4 $\checkmark$ $\PQt^{\text{res}}$ tagging
$\checkmark$ 1.5–7.6 1.3–7.5 $\checkmark$ $\PQt^{\text{res}}$ mistagging
$\checkmark$ 1.7–4.9 1.7–5.4 $\checkmark$ $j\to\tauh$ misidentification
$\checkmark$ 17.8–21.1 18.2–22.4 14.8 10.5 Theoretical Top quark mass
($\ttbar$) 2.2 $\checkmark$ $\checkmark$ Top quark mass (single ) 2.8
$\checkmark$ $\checkmark$ Acceptance (RF scale, PDF) 5.3 $\checkmark$
$\checkmark$ Acceptance (RF scale, PDF) $-2.8$ to $+2.0$ $\checkmark$
$\checkmark$ Acceptance single (RF scale, PDF) $-2.0$ to $+0.3$ $\checkmark$
$\checkmark$ Acceptance $\PQt\PAQt\PX$ (RF scale, PDF) 2.0 $\checkmark$
$\checkmark$ Acceptance EW (RF scale, PDF) $<$1.0 $\checkmark$ $\checkmark$
Cross section (RF scale, PDF) $-4.8$ to 5.5 $\checkmark$ $\checkmark$ Cross
section single (RF scale, PDF) 5.3 $\checkmark$ $\checkmark$ Cross section
$\PQt\PAQt\PX$ (RF scale, PDF) 2.2 $\checkmark$ $\checkmark$ Cross section EW
(RF scale, PDF) 5.4 $\checkmark$ $\checkmark$

##  0.9 Results

Binned MVA output distributions in the $\ell\tauh$ analysis and distributions
in the $\ell\tauh\tauh$ analysis are used to test the compatibility of the
observed data with the presence or absence of a signal. Data are split in 6
categories determined by the lepton flavor in the final state (or ), for each
of the three years of data taking. For the $\ell\tauh$ final states the number
of categories is double due to the consideration of the sum of the electric
charge of the lepton and objects. Therefore there are 18 categories in total;
12 associated with the $\ell\tauh$ analysis and 6 with the $\ell\tauh\tauh$
analysis. A simultaneous binned maximum likelihood fit is performed over all
categories and data sets. The likelihood incorporates all the systematic
uncertainties described in Section 0.8 as nuisance parameters, with shape
variations taken into account via continuous morphing [114].

No significant excess is found in any of the categories considered. The
distributions for the fit performed under the background-only hypothesis are
shown in Figs. 6 and 7 for the $\ell\tauh$ and $\ell\tauh\tauh$ final states,
respectively, whereby all categories for each individual final state are added
into a single distribution. For the $\ell\tauh\tauh$ final states, the
distributions are binned with variable width and according to the statistical
precision of the samples. In order to retain the shape of the distributions,
each bin is divided by their width. The pre-fit contribution of a hypothetical
$\PHpm\to\PH\PWpm$ signal with masses $m_{\PHpm}=500\GeV$and $m_{\PH}=200\GeV$
is also shown, normalized assuming that the product of the cross section and
branching fraction
$\sigma_{\PHpm}\mathcal{B}(\PHpm\to\PH\PWpm,\PH\to\PGt\PGt)$ is 1pb. Tabulated
results are provided in the HEPData record for this analysis [123].

Figure 6:  The MVA output of the BDTG for the $\Pe\tauh$ (left) and
$\PGm\tauh$ (right) final states used in the limit extraction, after a
background-only fit to the data. The data sets of all categories have been
added. The pre-fit contribution from $\PHpm\to\PH\PWpm$ with masses
$m_{\PHpm}=500\GeV$and $m_{\PH}=200\GeV$ and
$\sigma_{\PHpm}\mathcal{B}(\PHpm\to\PH\PWpm,\PH\to\PGt\PGt)=1\unit{pb}$ is
also shown.

Figure 7:  The distributions for the $\Pe\tauh\tauh$ (left) and
$\PGm\tauh\tauh$ (right) final states used in the limit extraction, after a
background-only fit to the data. The data sets of all categories have been
added. The pre-fit contribution from $\PHpm\to\PH\PWpm$ with masses
$m_{\PHpm}=500\GeV$and $m_{\PH}=200\GeV$ and
$\sigma_{\PHpm}\mathcal{B}(\PHpm\to\PH\PWpm,\PH\to\PGt\PGt)=1\unit{pb}$ is
also shown. The brackets $\langle\cdot\rangle$ signify that the plotted
variable is averaged over an interval in which the event frequency may have
changed considerably.

The event rates, with the expected yields from the SM backgrounds normalized
as resulting from a background-only fit to the data, are shown in Fig. 8, for
all data sets and final states considered.

Figure 8:  Observed event yields (black markers) for the 18 categories
considered in this analysis, grouped into data sets that are represented by
vertical dashed lines. The expected event yields (stacked histograms)
resulting from a background-only fit to the data are also shown, broken down
into various background processes. The solid red line represents the expected
signal yields from $\PHpm\to\PH\PWpm$ with masses $m_{\PHpm}=500\GeV$and
$m_{\PH}=200\GeV$, assuming
$\sigma_{\PHpm}\mathcal{B}(\PHpm\to\PH\PWpm,\PH\to\PGt\PGt)=1\unit{pb}$.

Upper limits on $\sigma_{\PHpm}\mathcal{B}(\PHpm\to\PH\PWpm,\PH\to\PGt\PGt)$
for a potential signal are computed at the 95% , using the modified
frequentist criterion [124, 125]. The definition of the profile likelihood
test statistic is as defined in Ref. [126], using the asymptotic approximation
[127].

The upper limit with all final states, categories, and years combined is shown
in Fig. 9 (left). The observed upper limit on
$\sigma_{\PHpm}\mathcal{B}(\PHpm\to\PH\PWpm,\PH\to\PGt\PGt)$ varies between
0.085pb at 300to 0.019pb at 700. In the same figure (right), the expected
sensitivity from each contributing final state is also shown. The
$\ell\tauh\tauh$ final states are the most sensitive in the whole $m_{\PHpm}$
range from 300 to 700, while the $\ell\tauh$ final states improve the overall
sensitivity by 20–35%.

Figure 9:  Expected and observed upper limits at 95% on the product of cross
section and branching fraction
$\sigma_{\PHpm}\mathcal{B}(\PHpm\to\PH\PWpm,\PH\to\PGt\PGt)$ as a function of
$m_{\PHpm}$ and assuming $m_{\PH}=200\GeV$ for the combination of all final
states considered (left). The observed upper limits are represented by a solid
black line and circle markers. The median expected limit (dashed line), 68%
(inner green band), and 95% (outer yellow band) confidence intervals are also
shown. The relative expected contributions of each final state to the overall
combination are also presented (right). The black solid line corresponds to
the combined expected limit, while the red dash-dotted, green dashed, blue
dashed-dotted, and orange dashed lines represent the relative contributions
from the $\Pe\tauh$, $\PGm\tauh$, $\Pe\tauh\tauh$, and $\PGm\tauh\tauh$
channels, respectively.

##  0.10 Summary

Results are presented from a search for a charged Higgs boson decaying into a
heavy neutral Higgs boson and a boson. Events are selected with exactly one
isolated electron or muon, targeting event topologies whereby the decays into
a pair of tau leptons with at least one decaying hadronically (). Four
distinct final states are considered: $\Pe\tauh$, $\PGm\tauh$,
$\Pe\tauh\tauh$, and $\PGm\tauh\tauh$. The analysis uses proton-proton
collision data recorded by the CMS detector at $\sqrt{s}=13\TeV$,
corresponding to an integrated luminosity of 138. No significant deviation is
observed from standard model expectations. Upper limits at 95% confidence
level are set on the product of the cross section and branching fraction for
an in the mass range of 300–700, assuming an with a mass of 200. The observed
limits range from 0.085pb for an mass of 300to 0.019pb for a mass of 700.
These are the first limits on production in the $\PHpm\to\PH\PWpm$ decay
channel at the LHC.

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