SUS-21-007

SUS-21-007

# Search for supersymmetry in final states with a single electron or muon
using angular correlations and heavy-object identification in proton-proton
collisions at $\sqrt{s}=13\TeV$

###### Abstract

A search for supersymmetry is presented in events with a single charged
lepton, electron or muon, and multiple hadronic jets. The data correspond to
an integrated luminosity of 138of proton-proton collisions at a center-of-mass
energy of 13, recorded by the CMS experiment at the CERN LHC. The search
targets gluino pair production, where the gluinos decay into final states with
the lightest supersymmetric particle (LSP) and either a top quark-antiquark ()
pair, or a light-flavor quark-antiquark () pair and a virtual or on-shell
boson. The main backgrounds, pair and $\PW\text{+jets}$ production, are
suppressed by requirements on the azimuthal angle between the momenta of the
lepton and of its reconstructed parent boson candidate, and by top quark and
boson identification based on a machine-learning technique. The number of
observed events is consistent with the expectations from standard model
processes. Limits are evaluated on supersymmetric particle masses in the
context of two simplified models of gluino pair production. Exclusions for
gluino masses reach up to 2130 (2280)at 95% confidence level for a model with
gluino decay to a pair (a pair and a boson) and the LSP. For the same models,
limits on the mass of the LSP reach up to 1270 (1220).

##  0.1 Introduction

Supersymmetry (SUSY) [1, 2, 3, 4, 5, 6] is an appealing extension of the
standard model (SM) of particle physics, which is able to address several
shortcomings of the SM by introducing a new symmetry that predicts
superpartners to the existing bosons and fermions. The supersymmetric partner
of the gluon is the gluino (). The superpartners of the electroweak gauge
bosons and the Higgs bosons mix to form mass eigenstates called neutralinos ()
and charginos (). In SUSY models that conserve $R$-parity [7], the SUSY
particles have to be produced in pairs and the lightest SUSY particle (LSP) is
stable, providing a possible dark matter candidate.

The search in this paper targets final states containing a single lepton
(electron or muon), missing transverse momentum, and large hadronic activity.
The proton-proton ($\Pp\Pp$) collision data at $\sqrt{s}=13\TeV$ recorded by
the CMS experiment at the CERN LHC during 2016–2018 and corresponding to an
integrated luminosity of 138are used. By defining exclusive search regions
(SRs) with and without tagging requirements, the search is sensitive to
different SUSY models. The sensitivity is further enhanced by using a large
number of SR bins defined by several variables characterizing the event
topology and kinematical properties. The results are interpreted in terms of
simplified SUSY models [8, 9, 10, 11, 12].

The diagrams of the specific $R$-parity conserving models of gluino pair
production that are used to interpret the results are shown in Fig. 1. The
results of the search with at least one -tagged jet, referred to as “multi-
analysis”, are interpreted in terms of the simplified model, labeled as
“T1tttt” (left), where the gluino always decays to a top quark-antiquark pair
() and the lightest neutralino (), which is the LSP. The top quarks will decay
into a bottom quark (quark) and a boson, which further decays hadronically or
into a lepton and a neutrino. The observations in the SR bins with no -tagged
jets, referred to as “zero- analysis”, are interpreted in the model labeled as
“T5qqqqWW” (right). In this model, each gluino decays to a light-flavor quark-
antiquark pair of different quark flavors ($\qqbar^{\prime}$) and the lightest
chargino (), which then decays further to a and a boson, which finally decays
hadronically or into a lepton and a neutrino. In T5qqqqWW, the boson can be
virtual, depending on the mass difference between the lightest chargino () and
the lightest neutralino (). The mass of the is fixed at the value halfway
between the masses of the and the .

Figure 1: Diagrams showing the simplified SUSY models T1tttt (left) and
T5qqqqWW (right).

Searches targeting gluino pair production in the single-lepton final state
have been performed by both the ATLAS [13, 14, 15, 16, 17] and CMS [18, 19,
20, 21, 20, 22, 23] Collaborations. The investigated models have also been
tested by ATLAS [24, 25, 26, 27] and CMS [28, 29, 30, 31, 32, 33, 34, 35] in
other final states. The results presented in this paper supersede the CMS
search presented in Ref. [19], which follows a similar strategy and uses data
recorded in 2016, corresponding to an integrated luminosity of 35.9.
Improvements stem not only from the larger analyzed data set, but also from
significantly reduced SM background contributions in the SR. This is achieved
by requiring at least one jet to be consistent with a hadronically decaying
top quark (boson) in the multi- (zero-) final states as determined by
multivariate classifiers.

Tabulated results are provided in the HEPData record for this analysis [36].

##  0.2 The CMS detector

The CMS apparatus is a multipurpose, nearly hermetic detector, designed to
trigger on and identify electrons, muons, photons, and charged and neutral
hadrons [37, 38, 39]. The detector comprises an all-silicon inner tracker and
by the crystal electromagnetic calorimeter (ECAL) and brass-scintillator
hadron calorimeters (HCAL), operating inside a 3.8T superconducting solenoid,
with data from the gas-ionization muon detectors embedded in the flux-return
yoke outside the solenoid. Each of these parts of the detector is composed of
a cylindrical barrel section and two endcap sections. The pseudorapidity
($\eta$) coverage of the barrel and endcap detectors is extended by forward
calorimeters that lie very close to the LHC beam line. Outside the solenoid,
the returning magnetic flux is guided through a steel return yoke. Gas-
ionization detectors are sandwiched in between the layers of the return yoke
and are used to detect muons.

The events used in the search were collected 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 [40]. 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
[41]. The CMS detector is described in more detail, along with the coordinate
system and basic kinematic variables, in Ref. [42].

##  0.3 Simulation

Simulated background events are used to optimize the event selection and test
the background estimation, which is mainly based on control samples in data.
The SM processes are simulated with different Monte Carlo (MC) event
generators: Events for , $\PW\text{+jets}$, and Drell–Yan (DY) production, as
well as for the background from SM events composed uniquely of jets produced
through the strong interaction, referred to as quantum chromodynamics (QCD)
multijet events, are simulated using the event generator at leading order (LO)
(versions 2.2.2 for 2016 and 2.4.2 for 2017 and 2018) [43]. The events are
generated with up to three additional partons in the matrix-element
calculations, while the $\PW\text{+jets}$ and DY events are generated with up
to four additional partons. Single top quark events produced through the $s$
channel; events containing a pair produced in association with a boson, a
boson, or a photon; and rare events such as those containing multiple
electroweak or Higgs bosons (, , , and ) are generated with at next-to-LO
(NLO) [44]. Events containing a single top quark produced through the $t$
channel and $\PQt\PW$ production, as well as $\PW\PW$ and $\ttbar\PH$ events,
are calculated at NLO with the v1 (v2) [45, 46, 47, 48, 49, 50, 51, 52]
program for 2016 (2017 and 2018). The $\PZ\PZ$ events are generated at NLO
with either or , depending on the decay mode, while $\PW\PZ$ production is
simulated at LO with 8.226 (8.230) [53] for 2016 (2017 and 2018). The
normalization of the simulated background samples is performed using the most
accurate cross section calculations available [48, 49, 43, 54, 55, 56, 57, 58,
59, 60, 61, 62, 63, 64, 65], which typically correspond to NLO or next-to-NLO
(NNLO) accuracy.

Simulated signal events are used to optimize the event selection and to
estimate the signal acceptance and selection efficiency. They are generated
using at LO including up to two additional partons in the matrix-element
calculations. The production cross sections are determined with approximate
NNLO plus next-to-next-to-leading logarithmic (NNLL) corrections [66, 67, 68,
69, 70, 71, 72, 73, 74, 75, 76]. The signal events are produced on a two-
dimensional grid for different gluino and LSP masses.

The parton showering and hadronization for all simulated samples is performed
with the 8.226 (8.230) program for 2016 (2017 and 2018). For samples that are
simulated at NLO with , the partons from the matrix-element calculations are
matched to those from the parton showers using the FxFx [44] scheme, while for
samples simulated at LO the MLM scheme [77] is adopted. The CUETP8M1 [78]
8.226 tune is used for both SM and signal samples for the analysis of the 2016
data. For 2017 and 2018, the CP5 (CP2) [79] tunes are used for the SM
background (signal) samples. Simulated background samples generated at LO
(NLO) with the CUETP8M1 tune use the NNPDF3.0LO (NNPDF3.0NLO) [80] sets for
the parton distribution functions (PDFs), respectively. For signal samples,
the NNPDF3.1LO was used [81]. The samples using the CP2 or CP5 tune use the
NNPDF3.1LO or NNPDF3.1NNLO sets, respectively.

Simulated SM events are processed through a -based [82] simulation of the CMS
detector, while the simulated signal events are processed through the CMS fast
simulation program [83, 84] in order to save computing time. The results of
the fast simulation are found to be generally consistent with the -based
simulation.

All simulated events are generated with nominal distributions of additional
$\Pp\Pp$ interactions per bunch crossing and nearby bunch crossings, referred
to as pileup. Any residual difference between the pileup distribution used in
the simulation and the one observed in the data is corrected via a weighting
procedure applied to the simulated events.

In order to improve the modeling of additional jets originating mainly from
initial-state radiation (ISR) in events containing , the prediction is
compared to data in a -enriched dileptonic control region, and scale factors
(SF) are extracted that are applied to the 2016–2018 simulation as well as to
the SUSY signal simulation. The simulation of the years 2017 and 2018 is
performed with an updated tune resulting in a good agreement between
simulation and data, such that no SF are needed.

##  0.4 Object reconstruction

The “particle-flow” (PF) algorithm [85] aims to reconstruct and identify each
particle in an event, with an optimized combination of information from the
various elements of the CMS detector, and classifies each either as a photon,
electron, muon, charged hadron, or a neutral hadron. The energy of charged
hadrons is determined from a combination of their momentum measured in the
tracker and the matching ECAL and HCAL energy deposits, corrected for the
response function of the calorimeters to hadronic showers. The energy of
neutral hadrons is obtained from the corresponding corrected ECAL and HCAL
energies. The primary vertex (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. [86].

The energy and momentum of electrons is determined from a combination of the
electron momentum at the PV as determined by the tracker, the energy of the
corresponding ECAL cluster, and the energy sum of all bremsstrahlung photons
spatially compatible with originating from the electron track [37]. For
electrons with transverse momentum $\pt\approx 45\GeV$ from $\PZ\to\EE$
decays, the momentum resolution ranges from 1.7 to 4.5%. It is generally
better in the barrel region than in the endcaps, and also depends on the
bremsstrahlung energy emitted by the electron as it traverses the material in
front of the ECAL.

The energy of muons is obtained from the curvature of the corresponding track.
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. Matching muons to tracks measured in the tracker results in a
relative resolution of 1% in the barrel and 3% in the endcaps for muons with
up to 100, and of better than 7% in the barrel for muons with up to 1 [38].

A relative isolation variable is defined as the sum of all objects within a
cone around the lepton candidate (excluding the candidate itself), divided by
the lepton . This analysis uses the so-called mini-isolation variable
($I_{\text{mini}}$), which is an optimized version [21] of the originally
proposed mini-isolation in Ref. [87]. The cone size $R$, referring to the
distance in the $\phi$–$\eta$ plane (where $\phi$ is the azimuthal angle),
depends on the of the lepton: for $\pt<50\GeV$, $R=0.2$; for $50<\pt<200\GeV$,
$R=10\GeV/\pt$; and for $\pt>200\GeV$, $R=0.05$.

Two categories of leptons are defined, denoted by “veto leptons” and “good
leptons”, in the range of $\abs{\eta}<2.4$ and with a minimum threshold of 10
and 25, respectively. Muons that fulfill the “loose” working point (WP) of the
standard muon identification (ID) criteria [38] are defined as “veto muons”.
The dedicated “veto” WP of the standard electron ID criteria [37] is used to
define “veto electrons”. We use a common requirement of $I_{\text{mini}}<0.4$
for all veto leptons, whereas for good muons (electrons) $I_{\text{mini}}<0.2$
(0.1) is required. The use of $I_{\text{mini}}$ enhances the selection
efficiency of signal events that contain a large amount of hadronic energy
compared to an isolation definition with a fixed cone size. The efficiency for
reconstructing a veto muon exceeds 99% and is equal to 95% for a veto
electron. The “medium” WP of the muon ID criteria with an efficiency of more
than 98% is used to select good muons. Good electrons are selected using the
“tight” WP of the electron ID criteria with an efficiency of 70%. A conversion
veto and the requirement of zero lost hits in the tracker are applied for good
electrons to reject converted photons.

Jets are clustered with the anti-algorithm [88, 89] with a distance parameter
$R$ of 0.4 (AK4), or, in order to identify large-radius jets, with $R=0.8$
(AK8). The jet is determined from the vectorial sum of all particles in the
jet, and is found from simulation to be, on average, within 5 to 10% of the
true over the whole spectrum and detector acceptance. Pileup interactions
contribute additional tracks and calorimetric energy depositions, increasing
the apparent jet momentum. To mitigate this effect, different strategies are
applied. For AK4 jets, tracks identified to be originating from pileup
vertices are discarded and a correction for remaining contributions is applied
[90]. For AK8 jets, the pileup per particle identification algorithm [90, 91]
is used, which makes use of local shape information, event pileup properties,
and tracking information. A local shape variable is defined, which
distinguishes between collinear and soft diffuse distributions of other
particles surrounding the particle under consideration. The former is
attributed to particles originating from the hard scatter and the latter to
particles originating from pileup interactions. Charged particles identified
to be originating from pileup vertices are discarded. For each neutral
particle, a local shape variable is computed using the surrounding charged
particles compatible with the primary vertex within the tracker acceptance
($\abs{\eta}<2.5$), and using both charged and neutral particles in the region
outside of the tracker coverage. The momenta of the neutral particles are then
rescaled according to their probability to originate from the primary
interaction vertex deduced from the local shape variable, superseding the need
for jet-based pileup corrections [90]. In the following, “jet” will refer to
AK4 jets, unless specified otherwise.

We apply jet energy corrections, derived from simulation studies, to match the
average measured energy of jets 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 in
the analysis [92]. For the fast simulation that is used for the signal,
dedicated jet energy corrections are applied.

Additional selection criteria are applied to each jet to remove jets
potentially affected by instrumental effects or reconstruction failures [90].
The jets are selected with $\pt>30\GeV$ and $\abs{\eta}<2.4$. The jets that
lie within a cone of $R=0.4$ around any good or veto lepton are removed, to
avoid double counting.

To identify jets originating from quarks we use an inclusive deep neural
network based combined secondary vertex tagger is used at the medium WP [93].
The efficiency to identify jets varies between 50 and 70%, depending on the
jet , with a misidentification probability of 10–15% for jets and 1–5% for
light-flavor quark and gluon jets, also depending on the jet .

AK8 jets are selected with $\pt>200\GeV$ and $\abs{\eta}<2.4$. In order to
identify hadronic decays of top quarks and bosons with a large Lorentz boost,
we apply a dedicated algorithm that is based on convolutional neural networks,
the DeepAK8 algorithm [94]. It is a multiclass classifier for top quark,
boson, boson, Higgs boson, and QCD jets, and takes input from all the PF
candidates and secondary vertices associated with the AK8 jet.

Hadronically decaying top quarks with $\pt>400\GeV$ are usually merged into
one large-radius jet, and are identified using the DeepAK8 algorithm at an
efficiency of $\approx$68% and a mistagging rate of $\approx$8%, as computed
in a $\PW\text{+jets}$ sample. The dominant source of the mistagging rate
stems from QCD multijet events. Top quarks with $\pt<400\GeV$ are usually not
boosted enough to be caught in one large-radius jet cone, and therefore are
identified by a resolved top quark tagging (tagging) algorithm, as used in
Ref. [95]. It identifies hadronically decaying top quarks whose decay products
form three individual jets. A boosted decision tree is used to distinguish
between trijet combinations whose three jets all match the decay products of a
top quark versus those that do not. It uses high-level information such as the
invariant mass of the trijet as well as information from each jet. The
resolved tagger yields an efficiency of $\approx$42%, while the mistagging
rate is $\approx$4%.

To avoid double counting, a cross cleaning between resolved and merged tags is
performed by first reconstructing the merged top quarks as identified by the
DeepAK8 algorithm. In the next step, resolved top quark candidates that
contain any jet within a cone of radius $R=0.8$ of the merged top quark (, the
cone of the AK8 jet classified as a top quark by the DeepAK8) are removed. In
the following, $n_{\PQt}$ is used to denote the number of identified tags.

Hadronically decaying bosons are identified with the DeepAK8 algorithm as
well. For the zero- analysis, this tagging algorithm utilizes AK8 jets to
identify hadronically decaying bosons with $\pt>200\GeV$. The efficiency for
boson tagging is $\approx$62%, while the mistagging rate is $\approx$7%. The
number of identified bosons is denoted as $n_{\PW}$.

All mistagging rates for the heavy object taggers were measured in
$\PW\text{+jets}$ data samples, where the decays leptonically. The
efficiencies of these taggers were measured using MC simulation samples of
hadronic and decays.

The missing transverse momentum vector is computed as the negative vector sum
of all the PF candidates in an event, and its magnitude is denoted as [96].
The is modified to account for corrections to the energy scale of the
reconstructed jets in the event. Anomalous high-events can occur because of a
variety of reconstruction failures, detector malfunctions, or noncollision
backgrounds. Such events are rejected by event filters that are designed to
identify more than 85–90% of the spurious high-events with an error rate of
less than 0.1%.

Two kinematic variables are used to describe the energy scale of an event: The
$L_{\mathrm{T}}$ variable is defined as the scalar sum of the lepton and
$\ptmiss$, reflecting the “leptonic” energy scale of the event. The variable
reflects the “hadronic” energy scale of the event. It denotes the scalar sum
of all selected jets.

In the second half of the 2018 data-taking period, a detector malfunction
prevented the readout from a small fraction of the HCAL. This is taken into
account by reweighting simulated events such that it reflects the overall 2018
efficiency of the HCAL in the relevant region.

##  0.5 Baseline event selection

Events are selected with a combination of HLT paths, relying on the kinematic
variables of reconstructed leptons, , , or combinations thereof, to maximize
the trigger efficiency. The main HLT path requires a loosely isolated lepton
with $\pt>15\GeV$ and greater than a threshold equal to 350, 400, and 450for
2016, 2017, and 2018, respectively. The additional HLT paths require greater
than a threshold equal to 100, 110, and 120for the three data-taking years;
isolated electrons with $\pt>27$ (35)in 2016 (2017 and 2018); isolated muons
with $\pt>24\GeV$; or leptons with no isolation requirement and a higher
threshold of 105 or 115for electrons (depending on the year), or 50for muons.
The trigger efficiency is measured in control samples recorded either with
single-lepton triggers or with triggers based on an requirement. For the
electron channel, it is found to be 98, 93, and 97% in 2016, 2017, and 2018,
respectively, while for the muon channel it is 99% for all three data-taking
years. The inefficiency is mainly caused by the lepton selection in the
trigger. The uncertainty in the measured trigger efficiencies is about 1%.

For the baseline event selection, one good lepton with $\pt>25\GeV$ is
required, and events with additional veto leptons with $\pt>10\GeV$ are
removed. Events with two genuine leptons, of which one is not identified,
constitute one of the main backgrounds in the SR bins. In order to reduce this
background contribution, we remove events with an isolated track that could
stem from leptons that are not well identified, but are not removed by the
requirement of no veto leptons. Charged particle tracks from the PV with
$\pt>5\GeV$ are selected, and an isolation variable $I_{\text{rel}}$ is
defined as the sum of all tracks within a cone of $R=0.3$ around the track
candidate (excluding the candidate itself), divided by the track . The
isolated tracks considered here come from two different sources, one is from
isolated leptons that satisfy looser ID criteria than lepton candidates, and
the other from isolated charged hadrons. Charged hadron (lepton) candidates
are required to satisfy $I_{\text{rel}}<0.1$ (0.2). In case of multiple
isolated track candidates in an event, the one with the highest that has the
opposite charge with respect to the selected lepton is chosen. Events with
such isolated tracks are rejected if the variable [97], calculated from the
momenta of the isolated track and the selected lepton, is below 60 (80)for
isolated tracks associated with charged hadrons (leptons).

Furthermore, we require $\HT>500\GeV$ and $L_{\mathrm{T}}>250\GeV$. The usage
of $L_{\mathrm{T}}$ instead of $\ptmiss$ allows the analysis to be not only
sensitive to events with high $\ptmiss$, but also to signal events with very
low $\ptmiss$ but higher lepton . A minimum number of three jets is required
for the baseline selection, and the two highest jets are required to fulfill
$\pt>80\GeV$.

Events are selected exclusively for the multi- or the zero- analysis,
depending on the number of -tagged jets in the event. Events in the multi-
analysis are additionally required to contain at least one tag. The baseline
event selection is summarized in Table 0.5.

Baseline event selection.  One good lepton with $\pt>25\GeV$ No additional
veto lepton with $\pt>10\GeV$ No isolated track with $\pt>5\GeV$ with
$\mTii<60$ (80)for hadronic (leptonic) tracks $L_{\mathrm{T}}>250\GeV$
$\HT>500\GeV$ Number of AK4 jets $n_{\text{jet}}\geq 3$ At least 2 jets with
$\pt>80\GeV$ $n_{\PQb}\geq 1$ and $n_{\PQt}\geq 1$ (multi- analysis) or
$n_{\PQb}=0$ (zero- analysis)

##  0.6 Search strategy and background estimation

The central kinematic variable of this analysis is the absolute value of the
azimuthal angle $\Delta\phi$ between the of a hypothetical boson decaying
leptonically and that of the decay lepton

$\Delta\phi=\sphericalangle(\ptvec^{\Pell},\ptvec^{\PW}),$ (1)

where the of the boson candidate is reconstructed as
$\ptvec^{\PW}=\ptvec^{\Pell}+\ptvecmiss$. After the baseline event selection,
the main backgrounds are events containing one lepton and jets from or
$\PW\text{+jets}$ decays. These backgrounds contain both one prompt lepton and
one neutrino from the boson decay in the final state. Since the neutrino and
lepton are boosted in the direction of the momentum of the boson and the
neutrino is the only source of , a small $\Delta\phi$ value is expected. On
the other hand, the SUSY models with two neutralinos in the final state break
this correlation, because the neutralinos cannot be detected in the CMS
detector and both of them will contribute to the , randomizing its direction.
This behavior is indeed observed in Fig. 2 showing simulated $\Delta\phi$
distributions. While most background contributions are at low $\Delta\phi$
values, the signal is almost flat over the whole range.

Figure 2: Signal and background distributions of the $\Delta\phi$ variable, as
predicted by simulation, for the multi- analysis, requiring
$n_{\text{jet}}\geq 6$, $L_{\mathrm{T}}>250\GeV$, $\HT>500\GeV$ (left), and
the zero- analysis, requiring $n_{\text{jet}}\geq 6$,
$L_{\mathrm{T}}>350\GeV$, $\HT>750\GeV$ (right). The predicted signal
distributions are also shown for two representative combinations of (gluino,
neutralino) masses with large (2.2, 0.1)and small (1.8, 1.3)mass differences.

The effect of the tagging in the multi- analysis is shown in Fig. 3 for the
sum of all background contributions and for two representative signal models
with a (gluino, neutralino) mass of (2.2, 0.1)and (1.8, 1.3). While the
background in the SR at high $\Delta\phi$ is reduced by an order of magnitude
when requiring one tag, the signal yield is only slightly decreased.
Therefore, one tag is always required, and a few SR bins are defined to have
two or more. When applying boson tagging at the “tight” WP in the zero-
analysis, the signal is reduced by about 40%, while the $\PW\text{+jets}$
background is reduced by more than 90%. The SR bins are split to contain
events with either $n_{\PW}=0$ or $n_{\PW}\geq 1$.

Figure 3: Distributions of $\Delta\phi$ as obtained from simulation, requiring
various tag multiplicities for the total background (left) and for the signal
in two representative combinations of (gluino, neutralino) masses with large
(2.2, 0.1)and small (1.8, 1.3)mass difference (right).

The $\Delta\phi$ variable is used to further suppress the background
contributions. The regions with large $\Delta\phi$ above a threshold value
$\Delta\phi_{0}$ are defined as SRs, while those with small $\Delta\phi$
values are used as control regions (CRs). For the multi- analysis, the SR is
defined by $\Delta\phi>0.75$, whereas in the zero- analysis the $\Delta\phi$
threshold depends on $L_{\mathrm{T}}$ and ranges between 0.5 and 1. This
accounts for a possible higher boost of the boson and correspondingly smaller
$\Delta\phi$ at larger values of $L_{\mathrm{T}}$. The SR is split into bins
of $n_{\text{jet}}$, $n_{\PQb}$, $L_{\mathrm{T}}$, and , and further
categorized by $n_{\PQt}$ ($n_{\PW}$) for the multi- (zero-) analysis. The
different SRs must provide good sensitivity for the different signal models
and signal parameters, while ensuring sufficient statistical accuracy in CRs
to predict the background in the corresponding SR.

The principal tool to estimate the background contributions in the SR bins is
a transfer factor, called $R^{\mathrm{CS}}$, from CR to SR, which is measured
in data with lower jet multiplicity, for each SR bin separately. For this
estimation, we split the regions into a low-$n_{\text{jet}}$ region, which is
called the sideband (SB), and a high-$n_{\text{jet}}$ region, which is called
the mainband (MB). Both of these bands are further divided by $\Delta\phi$
into a CR (with $\Delta\phi<\Delta\phi_{0}$) and an SR (with
$\Delta\phi>\Delta\phi_{0}$) as described above. This method can be considered
as a factorization approach in $\Delta\phi$ and jet multiplicity with four
regions indexed by pairs of CR or SR and SB or MB. We note that signal
contamination in the SB SR, SB CR, and MB CR is small, typically $<$0.5% for
both multi- and zero- analysis, and is taken into account in the final fit.

To account for possible deviations from the factorization assumption in the
extrapolation from SB to MB, we define multiplicative correction factors
$\kappa$, determined from simulations, as described in Sections 0.6.1 and
0.6.2.

In the multi- analysis, the background is dominated by events. In regions with
one -tagged jet and four or five jets, about 80% events and 15 to 20%
$\PW\text{+jets}$ and single top quark events are expected, with small
contributions from QCD multijet events. In all other multi- regions, the
background contribution is completely dominant. With only one SM process
dominating the background contribution, a single $R^{\mathrm{CS}}$ factor is
defined in the multi- analysis for each SR bin, after having subtracted the
small QCD multijets contribution in the SB. The background estimation is
performed for each year and explained in detail in Section 0.6.1.

In the zero- analysis, backgrounds from production are suppressed and
contributions from $\PW\text{+jets}$ production are found to be of the same
size. Here, an extension of the multi- strategy is employed, which takes into
account differences in the $R^{\mathrm{CS}}$ values for these two backgrounds,
for all years combined, as detailed in Section 0.6.2.

An overview of the ($n_{\text{jet}}$, $n_{\PQb}$) regions used in this
analysis is given in Fig. 4. The multi- and the zero- analysis share SB
regions, but their MB SR bins are exclusive and are never used simultaneously,
since the results are interpreted in different simplified models.

Figure 4: Overview of the regions used to calculate $R^{\mathrm{CS}}$ for the
multi- (left) and zero- (right) analysis. For the multijet (QCD) fit, the
electron () sample is used, while the muon () sample is used for the
determination of $R^{\mathrm{CS}}_{\PW}$.

###  0.6.1 Background estimate in the multi- final state

In the multi- analysis, the predicted number $N^{\text{MB,SR}}_{\text{Pred}}$
of background events in each MB SR bin is given as the sum of the number of
background events from and electroweak processes
$N^{\text{MB,SR}}_{\text{Pred,EW}}$ and the number of QCD multijet events
$N^{\text{MB,SR}}_{\text{Pred,QCD}}$:

$N^{\text{MB,SR}}_{\text{Pred}}=N^{\text{MB,SR}}_{\text{Pred,EW}}+N^{\text{MB,SR}}_{\text{Pred,QCD}}\;.$
(2)

The generic label “EW” refers to all backgrounds other than QCD multijet
events. About 10–15% of the SM background events in the SB CR are expected to
be QCD multijet events, while this fraction is significantly smaller in the MB
SR. This background contribution is estimated independently from a fit to
data, as described in Section 0.6.4. The multijet background is subtracted
from the number of background events when calculating the transfer factor
$R^{\mathrm{CS}}_{\text{data}}$ from data:

$R^{\mathrm{CS}}_{\text{data}}\big{(}n_{\text{jet}}\in[4,5]\big{)}=\frac{N^{\text{SB,SR}}_{\text{data}}-N^{\text{SB,SR}}_{\text{Pred,QCD}}}{N^{\text{SB,CR}}_{\text{data}}-N^{\text{SB,CR}}_{\text{Pred,QCD}}}\;.$
(3)

Here, $N^{\text{SB,SR}}_{\text{data}}$ is the number of events in the SB SR,
while $N^{\text{SB,CR}}_{\text{data}}$ corresponds to the number of events in
the SB CR. The independently estimated number of multijet events for these two
regions are $N^{\text{SB,SR}}_{\text{Pred,QCD}}$ and
$N^{\text{SB,CR}}_{\text{Pred,QCD}}$.

The SB region, where $R^{\mathrm{CS}}$ is determined for each SR bin, is
required to have four or five jets, while the MB region must satisfy
$n_{\text{jet}}\in[6,8]$ or $n_{\text{jet}}\geq 9$. This is represented
graphically in Fig. 5 (left). The $R^{\mathrm{CS}}$ factor is calculated
separately for each search bin in $L_{\mathrm{T}}$, , $n_{\PQb}$, and
$n_{\PQt}$. At very high , $R^{\mathrm{CS}}$ is determined jointly across all
three $n_{\PQb}$ bins to increase the number of events, as the overall
uncertainty of the background prediction for several of the search bins is
dominated by the statistical uncertainty of the yield in the SB SR.

Figure 5: Graphical presentation of the regions indexed by pairs of SB or MB
and CR or SR: for the multi- (left) and for the zero- (middle and right)
analysis. The value of $\Delta\phi$ separating CR and SR is labeled as
$\Delta\phi_{0}$. It is independent of the SR bin for the multi- analysis with
a value of 0.75, but varies from 0.5 to 1 among the zero- SR bins.

Small differences in $R^{\mathrm{CS}}$ between SB and MB are corrected by the
additional factor $\kappa_{\text{EW}}$, which is determined in simulation as
the ratio of the $R^{\mathrm{CS}}$ for simulated events:

$\kappa_{\text{EW}}=\frac{R^{\mathrm{CS}}_{\text{MC,EW}}\big{(}n_{\text{jet}}\text{
as in
MB}\big{)}}{R^{\mathrm{CS}}_{\text{MC,EW}}\big{(}n_{\text{jet}}\in[4,5]\big{)}}\;.$
(4)

For the multi- analysis, the label “$n_{\text{jet}}\text{ as in MB}$” refers
to either $n_{\text{jet}}\in[6,8]$ or $n_{\text{jet}}\geq 9$, depending on the
specific search bin. The $\kappa_{\text{EW}}$ factor is determined separately
for each search bin, except that a common $\kappa_{\text{EW}}$ factor is
applied for the $n_{\PQb}\geq 2$ search bins with the same and
$L_{\mathrm{T}}$, since the $\kappa_{\text{EW}}$ factors are found to be
nearly independent of $n_{\PQb}$. In general, these correction factors are
found to be close to unity, within 20–30%. With these definitions, the number
of predicted EW events in the MB SR is given by:

$N^{\text{MB,SR}}_{\text{Pred,EW}}=\kappa_{\text{EW}}R^{\mathrm{CS}}_{\text{data}}\big{(}n_{\text{jet}}\in[4,5]\big{)}\Big{(}N^{\text{MB,CR}}_{\text{data}}-N^{\text{MB,CR}}_{\text{Pred,QCD}}\Big{)}.$
(5)

For events containing one lepton and jets from production, $R^{\mathrm{CS}}$
typically has values of 0.01 to 0.02, depending on the search bin. Similar
values, ranging from 0.01 to 0.04, are found for $\PW\text{+jets}$ events. In
events with more than one high-neutrino, , in events in which both bosons
decay leptonically, $R^{\mathrm{CS}}$ is higher with values of around 0.5.
This is expected, since a large fraction of background events at high
$\Delta\phi$ is due to the dileptonic background, while the low-$\Delta\phi$
region is dominated by events with only one neutrino. A larger
$R^{\mathrm{CS}}$ is also expected for events with three neutrinos, such as
$\ttbar\PZ$, when the system decays into a lepton and jets and the boson
decays to two neutrinos.

A small fraction of the background arises from dileptonic events in which one
lepton is undetected. Having fewer jets than single-lepton events, these
events tend to populate the SB. At the same time their $\Delta\phi$
distribution is flatter, leading to an overestimate of $R^{\mathrm{CS}}$.
Accordingly a separate correction is developed as described in Section 6.3.

###  0.6.2 Background estimate in the zero- final state

Unlike the multi- analysis, where we have only one dominant background in each
bin, the SR bins in the zero- analysis require the prediction of two
backgrounds of almost the same size, and $\PW\text{+jets}$ events. These
background contributions are estimated by applying the $R^{\mathrm{CS}}$
method separately for each of the two components. Since we split these two
contributions in the background estimation, we typically have smaller bin
counts compared to the multi- and consequently larger statistical
fluctuations. To guarantee sufficient statistical precision, we perform the
prediction for the full data set instead of separate estimations for 2016,
2017, and 2018.

This strategy implies the use of two sidebands enriched in $\PW\text{+jets}$
(SB) and events (SB’), respectively. We decompose the total background in each
bin, for example in the MB SR, as:

$N^{\text{MB,SR}}_{\text{Pred}}=N^{\text{MB,SR}}_{\text{Pred,\PW}}+N^{\text{MB,SR}}_{\text{Pred,\ttbar}}+N^{\text{MB,SR}}_{\text{MC,other}}+N^{\text{MB,SR}}_{\text{Pred,QCD}}\;,$
(6)

where the numbers of predicted $\PW\text{+jets}$ and events are denoted by
$N^{\text{MB,SR}}_{\text{Pred,\PW}}$ and
$N^{\text{MB,SR}}_{\text{Pred,\ttbar}}$, respectively. We also include
$\PW\PW$ and $\PW\PZ$ events, where the boson decays leptonically and the
second or the boson hadronically, as a part of $\PW\text{+jets}$ estimation,
since they have similar kinematic properties and $R^{\mathrm{CS}}$ values. All
other diboson events are treated as part of the rare backgrounds, which are
estimated from simulation and denoted by $N^{\text{MB,SR}}_{\text{MC,other}}$.
The small contribution of the QCD multijet background is fixed to the yield
estimated from data as described in Section 0.6.4 and noted as
$N^{\text{MB,SR}}_{\text{Pred,QCD}}$.

The and the $\PW\text{+jets}$ contributions are estimated with an
$R^{\mathrm{CS}}$ method in a similar way as described in the previous
section. The $R^{\mathrm{CS}}$ values for $\PW\text{+jets}$ and events are
measured in separate SB regions with different -tagged jet requirements, as
laid out in Fig. 5 middle and right, respectively.

Similarly to Eq. (3), the value of $R^{\mathrm{CS}}$ for events is calculated
in the multi- sideband (SB’) with $n_{\text{jet}}\in[4,5]$ and $n_{\PQb}\geq
1$. The differences are the definition of $\Delta\phi_{0}$ and the
requirements that define the corresponding search bins:

$R^{\mathrm{CS}}_{\text{data}}\big{(}n_{\text{jet}}\in[4,5],n_{\PQb}\geq
1\big{)}=\frac{N^{\text{SB',SR}}_{\text{data}}-N^{\text{SB',SR}}_{\text{Pred,QCD}}}{N^{\text{SB',CR}}_{\text{data}}-N^{\text{SB',CR}}_{\text{Pred,QCD}}}\;.$
(7)

A correction factor $\kappa_{\PQb}$, defined in Eq. (8) and appearing in Eq.
(11) below, accounts for the difference of $R^{\mathrm{CS}}_{\ttbar}$ between
samples with zero -tagged jets and samples with at least one -tagged jet and
also takes into account non-background components in the EW category. It is
taken from simulation:

$\kappa_{\PQb}=\frac{R^{\mathrm{CS}}_{\ttbar}\big{(}n_{\text{jet}}\in[4,5],n_{\PQb}=0\big{)}}{R^{\mathrm{CS}}_{\text{EW}}\big{(}n_{\text{jet}}\in[4,5],n_{\PQb}\geq
1\big{)}}\text{, where
}R^{\mathrm{CS}}_{\text{MC}}=\frac{N^{\text{SB',SR}}_{\text{MC}}}{N^{\text{SB',CR}}_{\text{MC}}}\text{
and }\text{MC}\in[\ttbar,\text{EW}].$ (8)

A second factor $\kappa_{\ttbar}$, defined in Eq. (9) and appearing in Eq.
(11) below, corrects for a residual dependence of $R^{\mathrm{CS}}_{\ttbar}$
on $n_{\text{jet}}$, in analogy to the $\kappa_{\text{EW}}$ factor defined in
Section 0.6.1. It is defined as:

$\kappa_{\ttbar}=\frac{R^{\mathrm{CS}}_{\ttbar}\big{(}n_{\text{jet}}\text{ as
in
MB},n_{\PQb}=0\big{)}}{R^{\mathrm{CS}}_{\ttbar}\big{(}n_{\text{jet}}\in[4,5],n_{\PQb}=0\big{)}}\;.$
(9)

Similar to the multi- analysis, the number of simulated dilepton events in the
factor $\kappa_{\ttbar}$ is corrected by the slight difference in the
$n_{\text{jet}}$ shape measured in dilepton and one-lepton CRs, as described
in Section 0.6.3. The product of both correction factors $\kappa_{\PQb}$ and
$\kappa_{\ttbar}$ has typical values of 0.7 to 1.0 and statistical
uncertainties from the simulation are propagated to the predicted yields.

Finally, the fraction of and $\PW\text{+jets}$ events in the MB CR is
estimated by a template fit to the $n_{\PQb}$ distribution for each search
bin. The number of QCD events in these fits is consistently fixed to the
number of events predicted from data as described in Section 0.6.4, while all
other rare backgrounds are taken from simulation and fixed in the fit as well.
The templates are taken from simulation. Only the number of and
$\PW\text{+jets}$ events is adjusted in the fit. The fractions are:

$f_{\text{MC}}^{\text{MB,CR}}=\frac{N^{\text{MB,CR}}_{\text{fit,MC}}}{N^{\text{MB,CR}}_{\text{data}}},\text{
with }\text{MC}\in[\ttbar,\PW\text{+jets}].$ (10)

The uncertainties in these two components are propagated as systematic
uncertainties to the final prediction.

The final prediction is:

$N^{\text{MB,SR}}_{\text{Pred,\ttbar}}=\underbrace{\kappa_{\PQb}\kappa_{\ttbar}R^{\mathrm{CS}}_{\text{data}}\big{(}n_{\PQb}\geq
1,n_{\text{jet}}\in[4,5]\big{)}}_{\text{transfer
factor}}\underbrace{f_{\ttbar}^{\text{MB,CR}}N^{\text{MB,CR}}_{\text{data}}}_{\text{\makebox[0.0pt]{\ttbar
contribution in the control region}}}\;.$ (11)

The $\PW\text{+jets}$ contribution $N^{\text{MB,SR}}_{\text{Pred,\PW}}$ is
also estimated using an $R^{\mathrm{CS}}$ method. The zero- SB is chosen with
$n_{\text{jet}}\in[3,4]$, $n_{\PQb}=0$. With respect to the SB used for the
estimate of $R^{\mathrm{CS}}_{\ttbar}$, a lower jet multiplicity is chosen in
order to limit the contamination from events. Here we select only events where
the lepton is identified as a muon, since this sample has a negligible
contamination from QCD multijet events, contrary to the electron channel. A
systematic uncertainty is derived from simulation to cover potential
differences between the muon and the combined electron and muon samples.

The fit of the $n_{\PQb}$ distribution is also performed in the SB to
determine the fraction $f_{\ttbar}^{\text{SB,CR}}$, since the contamination is
significant and cannot be ignored. Examples of these fits are shown in Fig. 6.

Figure 6: Results of fits to the $n_{\PQb}$ multiplicity for control regions
for the muon channel and with the requirements $3\leq n_{\text{jet}}\leq 4$,
$250<L_{\mathrm{T}}<350\GeV$, $500<\HT<750\GeV$, $n_{\PW}\geq 1$,
$\Delta\phi<1$ (left) and $3\leq n_{\text{jet}}\leq 4$,
$350<L_{\mathrm{T}}<450\GeV$, $\HT>1000\GeV$, $n_{\PW}\geq 0$, $\Delta\phi<1$
(right). The shaded area shows the fit uncertainty of the total background.

The yields are then subtracted in the numerator and denominator when
determining $R^{\mathrm{CS}}$ for the $\PW\text{+jets}$ estimate:

$R^{\text{CS,corr}}_{\text{data}}\big{(}n_{\text{jet}}\in[3,4],n_{\PQb}=0,n_{\PGm}=1\big{)}=\frac{N^{\text{SB,SR}}_{\text{data}}-f_{\ttbar}^{\text{SB,CR}}\kappa_{\PQb}R^{\mathrm{CS}}_{\text{data}}\big{(}n_{\text{jet}}\in[4,5],n_{\PQb}\geq
1\big{)}N^{\text{SB,CR}}_{\text{data}}}{\Big{(}1-f_{\ttbar}^{\text{SB,CR}}\Big{)}N^{\text{SB,CR}}_{\text{data}}}\;.$
(12)

Similarly, a factor $\kappa_{\PW}$, defined in Eq. (13) and appearing in Eq.
(14), corrects for a residual dependence of $R^{\mathrm{CS}}_{\PW}$ on the jet
multiplicity; its typical values are 0.7 to 1.1. In addition, $\kappa_{\PW}$
also provides the extrapolation from the muon to the electron channel:

$\kappa_{\PW}=\frac{R^{\mathrm{CS}}_{\PW}\big{(}n_{\text{jet}}\text{ as in
MB},n_{\PQb}=0,n_{\Pell}=1\big{)}}{R^{\mathrm{CS}}_{\PW\text{+other}}\big{(}n_{\text{jet}}\in[3,4],n_{\PQb}=0,n_{\PGm}=1\big{)}}\text{,
where
}R^{\mathrm{CS}}_{\text{MC}}=\frac{N^{\text{SB,SR}}_{\text{MC}}}{N^{\text{SB,CR}}_{\text{MC}}}\text{
and }\text{MC}\in[\PW,\PW\text{+other}].$ (13)

The final prediction of the $\PW\text{+jets}$ background is then given by:

$N^{\text{MB,SR}}_{\text{Pred,\PW}}=\underbrace{\kappa_{\PW}R^{\text{CS,corr}}_{\text{data}}\big{(}n_{\text{jet}}\in[3,4],n_{\PQb}=0,n_{\PGm}=1\big{)}}_{\text{transfer
factor}}\underbrace{f_{\PW}^{\text{MB,CR}}N^{\text{MB,CR}}_{\text{data}}}_{\text{\makebox[0.0pt]{\PW
contribution in the control region}}}\;.$ (14)

###  0.6.3 Dilepton control region correction

The background prediction is sensitive to the extrapolation of
$R^{\mathrm{CS}}$ from the low-$n_{\text{jet}}$ SB to the MB regions with
higher jet multiplicities. The $R^{\mathrm{CS}}$ values differ significantly
for events with only one genuine lepton compared to events with two genuine
leptons (mainly dileptonic ), where one lepton is not identified or lost. In
the first case, the $R^{\mathrm{CS}}$ values are of the order 0.01–0.02, while
for dileptonic events the value is around 0.5. In the latter case, the
$\ptmiss$ in the event is not only caused by the neutrino of a leptonically
decaying boson, but also by the second genuine lepton that is not identified,
mostly because it is a hadronically decaying lepton leading to more neutrinos
in the event, or because it is out of acceptance. This leads to more events in
the high-$\Delta\phi$ region and a significantly higher $R^{\mathrm{CS}}$. In
general, the prediction is not affected by the different $R^{\mathrm{CS}}$ of
the different processes, if the ratio of events with one genuine lepton to
events with two genuine leptons (one lost or not identified) is the same for
all $n_{\text{jet}}$ regions.

Small differences can be corrected with an additional $n_{\text{jet}}$
dependent correction factor that is applied to genuine simulated dilepton
events. The high-purity dilepton events are transformed artificially into
typical single-lepton events by removing the second lepton, as described in
the following. The dilepton control sample is selected by requiring two
leptons of opposite charge. In order to reduce the DY background in the multi-
analysis, the invariant mass of same-flavor leptons is required to be more
than 10away from the boson mass peak. For the zero- analysis, where the DY
background is more important because of the zero tag requirement, we allow
only two leptons of different flavor. To simulate the feed-down of the
dileptonic events into the single-lepton selection, one of the two leptons is
removed from the event. Since these “lost leptons” are mainly from
$\PGt\to\text{hadrons}+\PGn$ decays, we replace the removed lepton with a jet
with 2/3 of the original lepton’s to model the typical visible energy of a
lepton, accounting for the missing momentum caused by the neutrino from the
lepton decay. In the next step $L_{\mathrm{T}}$, $\Delta\phi$, and values of
the now “single-lepton” event (with the additional “jet”) are recalculated. In
order to maximize the number of events, no $\Delta\phi$ requirement is
applied, and all events are used twice, with each reconstructed lepton being
considered as the lost lepton.

In the events with one genuine lepton in the zero- analysis, a change in the
background composition (mainly and $\PW\text{+jets}$) could lead to a change
of the correction factor. The size of this additional change is hard to
determine and it is desirable to disentangle these two effects. In order to
tackle this issue, we normalize these two backgrounds using weights extracted
after performing the template fit on the tag multiplicity.

The correction factor, $w_{\text{DL}}$, is determined as a function of
$n_{\text{jet}}$ for each event from a linear fit to the double ratio between
data over MC yields for dilepton (transformed to “single-lepton”) and single-
lepton events of the form:

$w_{\text{DL}}=a+b\big{(}n_{\text{jet}}-\langle n_{\text{jet}}\rangle\big{)},$
(15)

where $a$ is the constant, $b$ is the slope, and $\langle
n_{\text{jet}}\rangle$ is the weighted mean. The correction factor is applied
as a weight to all simulated events that are flagged as dileptonic from
generator level information.

As an example, the evaluation using 2018 data is shown in Fig. 7. The jet
multiplicity distributions are separately shown for single-lepton (after the
single-lepton baseline selection but excluding the SRs) and for dilepton
events, both for the multi- and the zero- analysis. Additionally, the fitted
double ratio is provided.

Figure 7: The upper row shows the jet multiplicity distribution after the
single-lepton baseline selection excluding the SRs for the multi- analysis
(left) and for the zero- analysis (right). The middle row contains the
dilepton CRs, again for the multi- analysis (left) and for the zero- analysis
(right). The simulation is normalized to data with the SF mentioned in the
plot. The double ratio of the single-lepton and dilepton ratio between data
and simulation together with fit results and their uncertainties is shown in
the lower row for the multi- (left) and the zero- (right) analysis. The fits
are performed for each data-taking year; 2018 is shown as an example.

The uncertainties in the templates are considered as a source of systematic
uncertainty in the analysis and are discussed in Section 0.7.

###  0.6.4 Estimation of QCD multijet background

The QCD multijet events that pass the event selection typically have a
reconstructed electron that originates from misidentified jets or from photon
conversions in the inner detector. This background contribution is estimated
from the yield of “anti-selected” electron candidates that pass looser
identification and isolation requirements and fail the tighter criteria for
selected electrons. Muons contribute naturally much less to this background,
but are nevertheless studied in the same way. The transfer factor
$F_{\mathrm{SA}}$ from the anti-selected to the selected lepton sample is
extracted in a multijet-enriched control sample with zero -tagged jets and
three or four other jets and therefore fewer prompt leptons.

The estimation method applied here is very similar to the procedure developed
in previous CMS analyses [98, 99]. It relies on the $L_{\mathrm{P}}$ variable,
which reflects the effective lepton polarization in the decay, defined as:

$L_{\mathrm{P}}=\frac{\pt^{\Pell}}{\pt^{\PW}}\cos(\Delta\phi).$ (16)

Here, $\Delta\phi$ is again the angle between the transverse components of the
momenta of lepton and reconstructed boson, as defined in Eq. (1). According to
the simulation, the selected lepton events comprise a mixture of EW and QCD
backgrounds. In contrast, the anti-selected electron events are clearly
dominated by QCD background, as intended by the modified electron
identification requirements. As shown in Fig. 8 for the electron channel, the
EW background peaks around $L_{\mathrm{P}}=0$ and falls off towards higher
values of $L_{\mathrm{P}}$, while the QCD background peaks around unity. There
is disagreement between the observed data and MC in the region of high
$L_{\mathrm{P}}$, however the effect of this disagreement will be negligible
for the fit to estimate the QCD yields.

Figure 8: The prefit $L_{\mathrm{P}}$ distribution for selected (left) and
anti-selected (right) electron candidates in the baseline QCD selection, with
modified requirements of $n_{\text{jet}}\in[3,4]$ and $n_{\PQb}=0$.

Therefore, the number of EW and QCD events can be determined with template
fits in $L_{\mathrm{P}}$ to the selected and to the anti-selected lepton
candidates. The shape of the templates is taken from the corresponding
simulated samples. The ratio of QCD events in selected to anti-selected lepton
events is then determined from data requiring zero tags and three or four
jets:

$F_{\mathrm{SA}}\big{(}L_{\mathrm{T}},n_{\PQb}=0,n_{\text{jet}}\in[3,4]\big{)}=\frac{N_{\text{QCD
selected}}^{\text{fit,
data}}\big{(}L_{\mathrm{T}},n_{\PQb}=0,n_{\text{jet}}\in[3,4]\big{)}}{N_{\text{QCD
anti-selected}}^{\text{fit,
data}}\big{(}L_{\mathrm{T}},n_{\PQb}=0,n_{\text{jet}}\in[3,4]\big{)}}\;.$ (17)

This ratio is calculated in bins of $L_{\mathrm{T}}$, but inclusively in ,
since the probability to misidentify jets as electrons is expected to be
independent on the number of jets and . Typically, the $F_{\mathrm{SA}}$
varies between 0.2 for smaller and 0.3 for large values of $L_{\mathrm{T}}$.
This ratio is finally used to predict the QCD background for the SR bins with
higher jet or -jet multiplicities bin by bin:

$N_{\text{QCD
selected}}^{\text{Pred}}\big{(}n_{\text{jet}},n_{\PQb}\big{)}=F_{\mathrm{SA}}\big{(}L_{\mathrm{T}},n_{\PQb}=0,n_{\text{jet}}\in[3,4]\big{)}N_{\text{QCD
anti-selected}}^{\text{data}}\big{(}n_{\text{jet}},n_{\PQb}\big{)}.$ (18)

##  0.7 Systematic uncertainties

Our search results are subject to various systematic uncertainty sources
related to the experimental apparatus and theoretical models. The
uncertainties can influence the background estimations and/or modify the
signal predictions. The impact of the uncertainties is evaluated individually
for the multi- and the zero- analysis, and also separately for the and
$\PW\text{+jets}$ background predictions in the zero- analysis. This is done
by varying the yields of the MC simulation used to calculate the correction
factors $\kappa_{\text{EW}}$ or $\kappa_{\PQb}$, $\kappa_{\ttbar}$ and
$\kappa_{\PW}$, for various uncertainty sources split by year. The results are
summarized in Tables 0.7 and 0.7, respectively. In addition, the impact of
uncertainties on the yield predictions for two representative signal points
for each analysis are shown in Tables 0.7 and 0.7. For the multi- analysis,
the uncertainty has a very high maximum value for T1tttt(2.2, 0.1) in one bin
with low sensitivity to the signal.

Summary of systematic uncertainties in the background prediction for the
multi- analysis. For each uncertainty source, the median, minimal (min), and
maximal (max) impact on the total background prediction is shown in order of
decreasing importance, where these quantities refer to the set of MB SR bins.
Uncertainty source Total background median [min, max] [%] Jet energy
corrections 3.8 [0.2, 36.3] QCD multijet 3.8 [0.8, 71.0] $\ttbar\PV$ cross
sections 2.8 [0.1, 22.6] ISR modeling 2.3 [0.4, 20.3] Pileup modeling 2.3
[0.1, 18.6] Dileptonic correction 2.2 [0.4, 12.3] cross section 1.6 [0.1,
23.7] $\PW\text{+jets}$ polarization 0.6 [0.1, 4.4] tagging (efficiency) 0.6
[0.1, 5.7] $\PW\text{+jets}$ cross section 0.4 [0.1, 7.7] tagging
(misidentification) 0.3 [0.1, 8.4] Lepton efficiency 0.2 [0.1, 1.6]

Summary of systematic uncertainties in the background prediction for the zero-
analysis. For each uncertainty source, the median, minimal (min), and maximal
(max) impact on the , $\PW\text{+jets}$, and total background prediction is
shown in order of decreasing importance for the total background, where these
quantities refer to the set of MB SR bins.  Uncertainty source
$\PW\text{+jets}$ Total background median [min, max] [%] median [min, max] [%]
median [min, max] [%] QCD multijet 5.2 [1.5, 27.6] $\ttbar\PV$ cross sections
0.9 [0.2, 5.3] 0.3 [0.1, 2.1] 4.0 [1.0, 19.6] Jet energy corrections 1.4 [0.1,
34.4] 1.2 [0.1, 22.0] 3.5 [0.5, 40.5] Pileup modeling 0.5 [0.1, 5.5] 0.6 [0.1,
4.8] 1.2 [0.1, 13.1] Dileptonic correction 2.0 [0.2, 13.7] 0.1 [0.1, 0.9] 0.8
[0.1, 4.7] $\PW\text{+jets}$ cross section 0.6 [0.1, 2.6] 1.5 [0.1, 13.7] 0.7
[0.1, 4.5] tagging (efficiency) 0.3 [0.1, 2.7] 0.1 [0.1, 1.8] 0.6 [0.2, 4.6]
$\PW\text{+jets}$ polarization 0.2 [0.1, 2.9] 0.8 [0.1, 7.6] 0.4 [0.1, 4.1]
Lepton efficiency 0.1 [0.1, 1.4] 0.1 [0.1, 1.6] 0.4 [0.1, 2.3] cross section
1.3 [0.1, 10.3] 0.3 [0.1, 3.2] Integrated luminosity 0.3 [0.1, 1.0] ISR
modeling 0.5 [0.1, 14.1] 0.1 [0.1, 4.4] tagging (misidentification) 0.1 [0.1,
0.5] 0.1 [0.1, 0.3] 0.1 [0.1, 0.7]

Summary of the main systematic uncertainties in the signal prediction for the
multi- analysis, for two representative combinations of (gluino, neutralino)
masses with large (2.2, 0.1)and small (1.8, 1.3)mass differences. For each
uncertainty source, the median, minimal (min), and maximal (max) impact on the
total background prediction is shown in order of decreasing importance for the
T1tttt(1.8, 1.3)signal, where these quantities refer to the set of MB SR bins.
Uncertainty source T1tttt(1.8, 1.3) T1tttt(2.2, 0.1) median [min, max] [%]
median [min, max] [%] tagging 10.0 [10.0, 10.0] 10.0 [10.0, 10.0] Jet energy
corrections 10.4 [0.1, 62.0] 8.8 [0.1, 58.8] 8.4 [1.0, 73.3] 4.2 [0.1, 129.2]
ISR modeling 4.7 [0.1, 50.9] 6.2 [0.1, 27.1] tagging (efficiency) 4.6 [0.1,
15.9] 7.3 [0.1, 26.9] Integrated luminosity 1.6 [1.6, 1.6] 1.6 [1.6, 1.6]
tagging (misidentification) 0.5 [0.1, 8.9] 0.6 [0.1, 7.4]

Summary of the main systematic uncertainties in the signal prediction for the
zero- analysis, for two representative combinations of (gluino, neutralino)
masses with large (2.2, 0.1)and small (1.8, 1.3)mass differences. For each
uncertainty source, the median, minimal (min), and maximal (max) impact on the
total background prediction is shown in order of decreasing importance for the
T5qqqqWW(1.8, 1.3)signal, where these quantities refer to the set of MB SR
bins.  Uncertainty source T5qqqqWW(1.8, 1.3) T5qqqqWW(2.2, 0.1) median [min,
max] [%] median [min, max] [%] boson tagging 10.0 [10.0, 10.0] 10.0 [10.0,
10.0] Jet energy corrections 6.2 [0.8, 72.5] 5.1 [0.1, 50.0] 4.0 [0.1, 28.4]
4.9 [0.1, 63.9] ISR modeling 1.8 [0.1, 11.3] 1.7 [0.1, 14.8] Integrated
luminosity 1.6 [1.6, 1.6] 1.6 [1.6, 1.6] tagging (efficiency) 0.5 [0.2, 5.9]
1.3 [0.2, 6.0] tagging (misidentification) 0.2 [0.1, 0.9] 0.4 [0.1, 1.1]

One common large systematic uncertainty is given by the jet energy
corrections, which are varied within their uncertainty [92] as a function of
jet and $\eta$, and these changes are propagated to all observables. The SF
related to the efficiencies for identifying leptons as well as quark jets, and
the misidentification of the quark, light quark, or gluon jets are scaled up
and down according to their uncertainties in the efficiency. The uncertainty
in the pileup is determined by varying the inelastic $\Pp\Pp$ cross-section of
69mb by $\pm$5% [100]. All these uncertainties apply to both the background
prediction and the signal yield.

The integrated luminosities of the 2016, 2017, and 2018 data-taking periods
are individually measured with uncertainties in the 1.2–2.5% range [101, 102,
103], while the total integrated luminosity has an uncertainty of 1.6%.

Changes in the polarization of bosons can affect the $\Delta\phi$ variable.
Thus, events are reweighted using the factor
$w=1+\alpha(1-\cos\theta^{\ast})^{2}$, where $\theta^{\ast}$ is the angle
between the charged lepton and boson in the boson rest frame. In
$\PW\text{+jets}$ events, we take $\alpha$ to be 0.1, guided by the
theoretical uncertainty and measurements found in Refs. [104, 105, 98, 106].
For +jets events, we take $\alpha=0.05$ [107, 108, 109, 110]. For
$\PW\text{+jets}$ events, where the initial state can have different
polarizations for and bosons, we take as uncertainty the larger change in
$\kappa$ resulting from reweighting only the bosons in the sample, and from
reweighting all bosons.

While the $\PW\text{+jets}$ and backgrounds are estimated from data, a change
in their relative contribution can lead to changes in the $R^{\mathrm{CS}}$ at
low jet multiplicities of the SB. Therefore, the inclusive $\PW\text{+jets}$
and cross sections are varied by 30% above and below the nominal value [111]
to account for possible biases in the estimation of the background
composition, which only affects the calculation of the $\kappa$ factors. The
small contribution of produced with an additional vector boson ($\ttbar\PV$)
is varied by 100% to account for the uncertainty in the theoretical
prediction. Uncertainties in the signal cross section are shown as explicit
variations of the mass limits (Section 0.9).

The QCD uncertainty includes the statistical uncertainties in the anti-
selected region. As $F_{\mathrm{SA}}$ is calculated for events with 3–4 jets,
we apply an additional relative uncertainty that is larger for SR bins with
higher jet multiplicities. An uncertainty of 30% for events with 6–8 jets, or
50% for events with least 9 jets in the multi- analysis is applied on the QCD
background estimate. For the zero- analysis, we take an uncertainty of 15% for
events with 5 jets, 30% for events with 6–7 jets, and 50% for events with at
least 8 jets.

Since we consider a signal with multiple top quarks (bosons) in the multi-
(zero-) analysis, the related tagging uncertainties have been investigated.
The taggers are described in detail in Section 0.4. The background estimation
is not sensitive to details of the and boson tagging performance, therefore a
systematic uncertainty is only assigned for the signal efficiency. The
systematic uncertainties in the tagging efficiency and mistagging rate are
estimated as follows: The relative yields of events with different tag
multiplicities are used to extract an overall efficiency and mistagging rate.
A difference of 5% is observed, and the systematic uncertainty is taken to be
twice this quantity, namely 10%. For boson tagging, the efficiency and
mistagging rates are extracted from a full comparison of data and simulation.
A total uncertainty of 10% is found to account for all differences between
data and simulation.

The SF applied to correct the ISR in signal samples and 2016 , with values
typically around 0.94, is varied by 4–5% (Section 0.3).

Because the signal samples use fast simulation, an additional uncertainty is
taken into account. The analysis is performed twice, once using the generated
and once using the reconstructed for signal events. A flat uncertainty equal
to one-half the difference between the acceptances is applied.

Lastly, systematic uncertainties related to the dileptonic correction
explained in Section 0.6.3 have to be taken into account. The systematic
variations around that new central value are determined by varying the fit to
the double ratio by the following uncertainties: the variation of the constant
value $a$ is extracted as the quadratic sum of the deviation of the central
value of $a$ from unity and by the uncertainty in $a$ that is extracted from
the fit itself. The variation of the slope $b$ is determined as the quadratic
sum of the deviation of $b$ from zero and the uncertainty in $b$ as given by
the fit.

##  0.8 Results

Observed number of events in the MB SR bins of the multi- analysis, together
with the predicted yields for background and two T1tttt ($m_{\PSg}$,
$m_{\PSGczDo}$) signal points. All bins are defined with $\Delta\phi>0.75$.
$n_{\text{jet}}$ $n_{\PQb}$ $L_{\mathrm{T}}$ [] [] $n_{\PQt}$ Bin name T1tttt
signal events Predicted Observed (1.8, 1.3) (2.2, 0.1) background events
events [6, 8] 1 [250, 450] [500, 1500] 1 A1a $1.2\pm 0.1$ $<$0.1 $576\pm 29$
570 $\geq$2 A1b $0.07\pm 0.02$ $<$0.1 $13\pm 2$ 14 $>$1500 1 A2a $<$0.1
$0.01\pm 0.01$ $47\pm 7$ 42 $\geq$2 A2b $<$0.1 $0.04\pm 0.01$ $5\pm 1$ 3 [450,
600] $>$500 1 A3a $0.44\pm 0.06$ $0.04\pm 0.01$ $31\pm 6$ 16 $\geq$2 A3b
$0.03\pm 0.02$ $0.06\pm 0.01$ $1.0\pm 0.3$ 1 $>$600 $>$500 1 A4a $0.18\pm
0.04$ $0.44\pm 0.02$ $7\pm 2$ 8 $\geq$2 A4b $<$0.1 $0.48\pm 0.02$ $1.0\pm 0.5$
0 2 [250, 450] [500, 1500] 1 B1a $2.3\pm 0.1$ $0.01\pm 0.01$ $532\pm 26$ 586
$\geq$2 B1b $0.28\pm 0.04$ $0.01\pm 0.01$ $16\pm 2$ 19 $>$1500 1 B2a $<$0.1
$0.03\pm 0.01$ $30\pm 5$ 34 $\geq$2 B2b $<$0.1 $0.06\pm 0.01$ $3.4\pm 0.8$ 1
[450, 600] $>$500 1 B3a $1.0\pm 0.1$ $0.07\pm 0.01$ $27\pm 6$ 34 $\geq$2 B3b
$0.06\pm 0.02$ $0.09\pm 0.01$ $1.1\pm 0.5$ 2 $>$600 $>$500 1 B4a $0.37\pm
0.05$ $0.67\pm 0.03$ $6.2\pm 1.6$ 6 $\geq$2 B4b $0.07\pm 0.02$ $0.80\pm 0.03$
$0.23\pm 0.08$ 0 $\geq$3 [250, 450] [500, 1500] 1 C1a $3.0\pm 0.1$ $0.01\pm
0.01$ $115\pm 7$ 105 $\geq$2 C1b $0.43\pm 0.06$ $<$0.1 $6\pm 1$ 3 $>$1500 1
C2a $0.01\pm 0.01$ $0.03\pm 0.01$ $7\pm 2$ 10 $\geq$2 C2b $<$0.1 $0.07\pm
0.01$ $1.0\pm 0.4$ 2 [450, 600] $>$500 1 C3a $1.1\pm 0.1$ $0.06\pm 0.01$ $5\pm
1$ 4 $\geq$2 C3b $0.24\pm 0.04$ $0.10\pm 0.01$ $0.63\pm 0.43$ 0 $>$600 $>$500
1 C4a $0.42\pm 0.05$ $0.67\pm 0.02$ $1.4\pm 0.4$ 4 $\geq$2 C4b $0.05\pm 0.02$
$0.76\pm 0.03$ $0.05\pm 0.04$ 0 $\geq$9 1 [250, 450] [500, 1500] 1 D1a
$0.62\pm 0.06$ $<$0.1 $32\pm 3$ 26 $\geq$2 D1b $0.12\pm 0.03$ $<$0.1 $2.1\pm
0.6$ 4 $>$1500 1 D2a $0.02\pm 0.01$ $0.01\pm 0.01$ $6\pm 1$ 11 $\geq$2 D2b
$0.02\pm 0.01$ $0.02\pm 0.01$ $1.0\pm 0.3$ 2 [450, 600] $>$500 $\geq$1 D3
$0.34\pm 0.05$ $0.04\pm 0.01$ $2.3\pm 0.6$ 2 $>$600 $>$500 $\geq$1 D4 $0.23\pm
0.04$ $0.40\pm 0.02$ $0.6\pm 0.3$ 0 2 [250, 450] [500, 1500] 1 E1a $1.5\pm
0.1$ $0.01\pm 0.01$ $35\pm 3$ 35 $\geq$2 E1b $0.55\pm 0.06$ $<$0.1 $3.2\pm
0.7$ 2 $>$1500 1 E2a $0.05\pm 0.02$ $0.02\pm 0.01$ $8\pm 2$ 6 $\geq$2 E2b
$0.04\pm 0.02$ $0.05\pm 0.01$ $1.0\pm 0.4$ 2 [450, 600] $>$500 1 E3a $0.75\pm
0.07$ $0.04\pm 0.01$ $1.7\pm 0.5$ 1 $\geq$2 E3b $0.19\pm 0.03$ $0.06\pm 0.01$
$0.2\pm 0.1$ 0 $>$600 $>$500 1 E4a $0.50\pm 0.05$ $0.30\pm 0.02$ $0.9\pm 0.4$
1 $\geq$2 E4b $0.21\pm 0.04$ $0.55\pm 0.02$ $0.06\pm 0.04$ 0 $\geq$3 [250,
450] [500, 1500] 1 F1a $3.2\pm 0.1$ $0.01\pm 0.01$ $13\pm 2$ 7 $\geq$2 F1b
$1.27\pm 0.08$ $<$0.1 $2.4\pm 0.8$ 2 $>$1500 1 F2a $0.04\pm 0.02$ $0.03\pm
0.01$ $4\pm 1$ 0 $\geq$2 F2b $0.07\pm 0.02$ $0.09\pm 0.01$ $0.7\pm 0.3$ 0
[450, 600] $>$500 $\geq$1 F3 $1.7\pm 0.1$ $0.16\pm 0.01$ $1.1\pm 0.4$ 2 $>$600
$>$500 $\geq$1 F4 $1.0\pm 0.1$ $1.30\pm 0.03$ $0.24\pm 0.16$ 2

Observed number of events in the MB SR bins of the zero- analysis, together
with the predicted yields for background and two T5qqqqWW ($m_{\PSg}$,
$m_{\PSGczDo}$) signal points.  $n_{\text{jet}}$ $L_{\mathrm{T}}$ [] []
$\Delta\phi$ $n_{\PW}$ Bin name T5qqqqWW signal events Predicted Observed
(1.8, 1.3) (2.2, 0.1) background events events 5 [250, 350] [500, 750] $>$1 0
G0a $1.2\pm 0.1$ $<$0.1 $342\pm 24$ 333 $\geq$1 G0b $0.46\pm 0.08$ $<$0.1
$70\pm 8$ 77 $>$750 0 G1a $0.35\pm 0.07$ $0.03\pm 0.01$ $292\pm 22$ 304
$\geq$1 G1b $0.14\pm 0.04$ $0.02\pm 0.01$ $69\pm 10$ 62 [350, 450] [500, 750]
$>$1 0 G2a $1.8\pm 0.2$ $<$0.1 $71\pm 8$ 63 $\geq$1 G2b $0.60\pm 0.09$ $<$0.1
$14\pm 5$ 25 $>$750 0 G3a $0.44\pm 0.08$ $0.04\pm 0.01$ $66\pm 8$ 44 $\geq$1
G3b $0.24\pm 0.06$ $0.03\pm 0.01$ $14\pm 4$ 13 [450, 650] [500, 750] $>$0.75 0
G4a $2.1\pm 0.2$ $<$0.1 $52\pm 7$ 45 $\geq$1 G4b $1.1\pm 0.1$ $<$0.1 $12\pm 3$
9 [750, 1250] 0 G5a $0.9\pm 0.1$ $0.03\pm 0.01$ $42\pm 6$ 35 $\geq$1 G5b
$0.35\pm 0.07$ $<$0.1 $10\pm 3$ 6 $>$1250 0 G6a $<$0.1 $0.17\pm 0.02$ $16\pm
3$ 19 $\geq$1 G6b $<$0.1 $0.13\pm 0.02$ $3\pm 1$ 3 $>$650 [500, 1250] $>$0.5 0
G7a $1.3\pm 0.1$ $0.13\pm 0.02$ $33\pm 8$ 32 $\geq$1 G7b $0.30\pm 0.06$
$0.04\pm 0.01$ $7\pm 2$ 8 $>$1250 0 G8a $0.15\pm 0.05$ $1.78\pm 0.07$ $11\pm
3$ 8 $\geq$1 G8b $0.04\pm 0.02$ $1.08\pm 0.05$ $0.6\pm 0.4$ 2 [6, 7] [250,
350] [500, 1000] $>$1 0 H1a $2.6\pm 0.2$ $<$0.1 $281\pm 22$ 292 $\geq$1 H1b
$1.3\pm 0.1$ $<$0.1 $71\pm 9$ 71 $>$1000 0 H2a $0.23\pm 0.06$ $0.05\pm 0.01$
$121\pm 11$ 121 $\geq$1 H2b $0.18\pm 0.05$ $0.02\pm 0.01$ $29\pm 5$ 21 [350,
450] [500, 1000] $>$1 0 H3a $3.1\pm 0.2$ $<$0.1 $51\pm 6$ 71 $\geq$1 H3b
$1.6\pm 0.2$ $0.01\pm 0.01$ $12\pm 3$ 15 $>$1000 0 H4a $0.31\pm 0.07$ $0.09\pm
0.01$ $31\pm 7$ 21 $\geq$1 H4b $0.12\pm 0.04$ $0.08\pm 0.01$ $6\pm 2$ 6 [450,
650] [500, 750] $>$0.75 0 H5a $3.1\pm 0.2$ $<$0.1 $19\pm 4$ 17 $\geq$1 H5b
$1.6\pm 0.2$ $<$0.1 $5\pm 2$ 9 [750, 1250] 0 H6a $2.8\pm 0.2$ $0.01\pm 0.01$
$29\pm 4$ 18 $\geq$1 H6b $1.4\pm 0.1$ $<$0.1 $7\pm 2$ 4 $>$1250 0 H7a $0.4\pm
0.07$ $0.45\pm 0.03$ $15\pm 3$ 14 $\geq$1 H7b $0.2\pm 0.05$ $0.33\pm 0.03$
$3\pm 1$ 1 $>$650 [500, 1250] $>$0.5 0 H8a $2.5\pm 0.2$ $0.09\pm 0.01$ $13\pm
3$ 17 $\geq$1 H8b $0.9\pm 0.1$ $0.05\pm 0.01$ $4\pm 1$ 4 $>$1250 0 H9a $0.8\pm
0.1$ $3.9\pm 0.1$ $9\pm 3$ 6 $\geq$1 H9b $0.34\pm 0.07$ $2.44\pm 0.08$ $2\pm
1$ 1 $\geq$8 [250, 350] [500, 1000] $>$1 0 I1a $0.8\pm 0.1$ $<$0.1 $23\pm 5$
25 $\geq$1 I1b $0.33\pm 0.07$ $<$0.1 $7\pm 3$ 5 $>$1000 0 I2a $0.30\pm 0.07$
$0.04\pm 0.01$ $22\pm 5$ 23 $\geq$1 I2b $0.16\pm 0.05$ $0.01\pm 0.01$ $8\pm 2$
12 [350, 450] [500, 1000] $>$1 0 I3a $0.8\pm 0.1$ $<$0.1 $3.0\pm 0.7$ 10
$\geq$1 I3b $0.36\pm 0.07$ $<$0.1 $1.1\pm 0.4$ 0 $>$1000 0 I4a $0.57\pm 0.09$
$0.07\pm 0.01$ $5\pm 1$ 5 $\geq$1 I4b $0.36\pm 0.07$ $0.06\pm 0.01$ $3\pm 1$ 2
[450, 650] [500, 1250] $>$0.75 0 I5a $1.5\pm 0.1$ $<$0.1 $3.4\pm 0.9$ 4
$\geq$1 I5b $1.0\pm 0.1$ $<$0.1 $0.5\pm 0.3$ 1 $>$1250 0 I6a $0.40\pm 0.07$
$0.26\pm 0.03$ $2.6\pm 0.8$ 2 $\geq$1 I6b $0.18\pm 0.05$ $0.17\pm 0.02$
$0.5\pm 0.3$ 2 $>$650 [500, 1250] $>$0.5 $\geq$0 I7 $1.4\pm 0.1$ $0.02\pm
0.01$ $1.5\pm 0.6$ 2 $>$1250 I8 $1.4\pm 0.1$ $3.58\pm 0.09$ $1.5\pm 0.7$ 1

The observed data yields and the predicted background contributions for the
multi- analysis are given in Table 0.8 and shown in Fig. 9 for the MB SR for
the combination of all three data-taking years. Good agreement is observed for
almost all search bins, except for the last bin where two events are observed,
against an expected value of $0.24\pm 0.16$. The observed limit is about one
standard deviation lower than expected, because of the number of excess events
in the last search bin.

Table 0.8 and Fig. 10 show the background predictions for the zero- analysis
and the data yields in the MB SR. Here, we observe good agreement in almost
all bins as well, and a deviation from the prediction is observed only for
bins that are dominated by the background. Namely, the bins G2b, H3a, and I3a,
among the 50 zero- bins, contain more observed events than expected by at
least one standard deviation.

Figure 9: Observed event yields in the MB SRs of the multi- analysis compared
to signal and background predictions. The relative fraction of the different
SM EW background contributions determined in simulation is shown by the
stacked, colored histograms, normalized so that their sum is equal to the
background estimated using data control regions. The QCD background is
predicted using the $L_{\mathrm{P}}$ method. The signal is shown for two
representative combinations of (gluino, neutralino) masses with large (2.2,
0.1)and small (1.8, 1.3)mass differences.  Figure 10: Observed event yields in
the MB SRs of the zero- analysis compared to signal and background
predictions. The $\PW\text{+jets}$, , and QCD predictions are extracted from
data control samples, while the other background contributions are estimated
from simulation. The signal is shown for two representative combinations of
(gluino, neutralino) masses with large (2.2, 0.1)and small (1.8, 1.3)mass
differences.

##  0.9 Interpretation

To evaluate exclusion limits on the simplified SUSY models considered in this
search, a likelihood function is defined that includes all SB and MB CRs and
SRs. For the multi- analysis, the measurement is performed for each set of
four bins (SB CR, SB SR, MB CR and MB SR), as defined for the
$R^{\mathrm{CS}}$ method in Section 0.6.1. The number of entries in the bins
are modeled by a product of Poisson distributions taking into account that the
$R^{\mathrm{CS}}$ method represents a factorization approach, which constrains
the rate parameter for the background estimate in the signal region. Multijet
background and rare processes are treated as independent contributions. The
systematic uncertainties enter the likelihood as nuisance parameters and are
taken into account as a product of log-normal distributions. For the zero-
analysis, the bins are defined in Section 0.6.1. The template fit on the
$n_{\PQb}$ distributions is performed separately. Thus, only the SB’ CR, SB’
SR, SB SR and MB SR search bins enter the likelihood. The different
constraints on the rate parameters implied by the extended $R^{\mathrm{CS}}$
method are taken into account in a similar way and the systematic
uncertainties are again modeled by log-normal distributions. We set upper
limits on the production cross section at 95% confidence level (). These are
estimated with the modified frequentist method [112, 113] using the asymptotic
approximation [114]. The method is used with the test statistic
$q_{\mu}=-2\ln\lambda_{\mu}$, where $\lambda_{\mu}$ refers to the ratio of the
maximized likelihood for a given signal strength $\mu$ to the unconditional
likelihood maximized for all parameters, including $\mu$. The $\PSg\PSg$ pair
production cross section is calculated at approximate NNLO and NNLL accuracy,
and exclusion limits are set as a function of the ($m_{\PSg}$, $m_{\PSGczDo}$)
hypothesis.

For the T1tttt model, which describes gluino pair production with each gluino
decaying to a pair and a , the cross section limits are obtained using the
multi- analysis. They are shown in Fig. 11 (left) as functions of $m_{\PSg}$
and $m_{\PSGczDo}$, assuming branching fractions of 100%. The observed limit
is about one standard deviation lower than the expected one, which is caused
by the observation of two events in the last bin, while only $0.24\pm 0.16$
events are expected.

The results of the zero- analysis are interpreted in the T5qqqqWW model, in
which pair-produced gluinos decay to a (light) quark-antiquark pair and a
chargino, which further decays to a boson and the . The observed limit, shown
in Fig. 11 (right), agrees with the expected limit over most of the mass
range.

Figure 11: Cross section limits at 95% for the T1tttt (left) and for the
T5qqqqWW (right) model, as functions of the gluino and LSP masses, assuming a
branching fraction of 100%. The mass of the intermediate chargino is taken to
be halfway between the gluino and the neutralino masses. The solid black
(dashed red) lines correspond to the observed (expected) mass limits, with the
thicker lines representing the central values and the thinner lines
representing the $\pm 1\sigma$ uncertainty bands related to the theoretical
(experimental) uncertainties.

##  0.10 Summary

A search for supersymmetry has been performed using a sample of proton-proton
collisions at $\sqrt{s}=13\TeV$ corresponding to an integrated luminosity of
138, recorded by the CMS experiment in 2016–2018. Events with a single charged
lepton (electron or muon) and multiple jets are selected. Top quark and boson
identification algorithms based on machine-learning techniques are employed to
suppress the main background contributions in the analysis. Various exclusive
search regions are defined that differ in the number of jets, the number of
jets identified as stemming from quarks, the number of hadronically decaying
top quarks or bosons, the scalar sum of all jet transverse momenta, and the
scalar sum of the missing transverse momentum and the transverse momentum of
the lepton.

To reduce the main background processes from and $\PW\text{+jets}$ production,
the presence of a lepton produced in the leptonic decay of a boson in the
event is exploited. Under the hypothesis that all of the missing transverse
momentum in the event originates from the neutrino produced in a leptonic
boson decay, the boson momentum is calculated. The requirement of a large
azimuthal angle between the directions of the lepton and of the reconstructed
boson decaying leptonically, notably reduces the background contributions.

The event yields observed in data are consistent with the expectations from
the SM processes, which are estimated using control samples in data. Exclusion
limits on the supersymmetric particle masses in the context of two simplified
models of gluino pair production are evaluated.

For the T1tttt simplified model, where each gluino decays to a top quark-
antiquark pair and the lightest neutralino, the excluded gluino masses reach
up to 2130, while the excluded neutralino masses reach up to 1270. This result
extends the exclusion limit on gluino (neutralino) masses from a previous CMS
search [19] by about 320 (170).

The second simplified model, T5qqqqWW, also targets gluino pair production,
but with decays to a light-flavor quark-antiquark pair and a chargino, which
decays to a boson and the lightest neutralino. The chargino mass in this decay
channel is assumed to be $m_{\PSGcpmDo}=0.5(m_{\PSg}+m_{\PSGczDo})$. The
excluded gluino masses reach up to 2280, while the excluded neutralino masses
reach up to 1220. This corresponds to an improvement on gluino (neutralino)
masses by about 380 (270)in comparison with the previous result [19],
extending the existing limit from ATLAS [13] on the neutralino mass in the
compressed region by about 150.

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