SUS-19-006

SUS-19-006

# Search for supersymmetry in proton-proton collisions at 13in final states
with jets and missing transverse momentum

###### Abstract

Results are reported from a search for supersymmetric particles in the final
state with multiple jets and large missing transverse momentum. The search
uses a sample of proton-proton collisions at $\sqrt{s}=13\TeV$ collected with
the CMS detector in 2016–2018, corresponding to an integrated luminosity of
137, representing essentially the full LHC Run 2 data sample. The analysis is
performed in a four-dimensional search region defined in terms of the number
of jets, the number of tagged bottom quark jets, the scalar sum of jet
transverse momenta, and the magnitude of the vector sum of jet transverse
momenta. No significant excess in the event yield is observed relative to the
expected background contributions from standard model processes. Limits on the
pair production of gluinos and squarks are obtained in the framework of
simplified models for supersymmetric particle production and decay processes.
Assuming the lightest supersymmetric particle to be a neutralino, lower limits
on the gluino mass as large as 2000 to 2310are obtained at $95\%$ confidence
level, while lower limits on the squark mass as large as 1190 to 1630are
obtained, depending on the production scenario.

##  0.1 Introduction

The search for particles and interactions beyond the standard model (SM) is a
major goal of experiments at the CERN LHC. The search described here focuses
on experimental signatures in which a proton-proton ($\Pp\Pp$) collision
produces at least two jets (collimated sprays of particles), in conjunction
with large unbalanced (“missing”) momentum in the direction transverse to the
beam axis. The jets result from the production and hadronization of energetic
quarks or gluons that could be generated in the decay chains of new heavy
particles. The jets are classified according to whether their properties are
consistent with a jet initiated by the production of a bottom quark ( jet), a
key experimental signature in many models of new-particle production. The
large missing transverse momentum is typically associated with the production
of a stable, weakly interacting particle that is not detected by the
apparatus. In this analysis, this quantity is inferred from the total momentum
of the observed jets in the transverse plane, which should sum to
approximately zero if there are no unobserved particles. Signatures of this
type have been studied extensively by both the ATLAS and CMS Collaborations
[1, 2, 3, 4, 5, 6, 7, 8]. This signature arises frequently in theoretical
models based on supersymmetry (SUSY) [9, 10, 11, 12, 13, 14, 15, 16, 17, 18]
as well as in a broad range of other theories [19, 20, 21, 22, 23, 24]
extending the SM.

The analysis uses a sample of $\Pp\Pp$ collision events at $\sqrt{s}=13\TeV$
recorded with the CMS detector in 2016–2018, corresponding to an integrated
luminosity of 137. This represents essentially the complete CMS Run 2 data
sample and is about four times larger than the 2016 data sample alone, which
was used in the previous analysis based on this methodology [8].

The motivation for searches for new physics in the final state with jets and
large missing transverse momentum arises from several considerations.
Astrophysical observations provide compelling evidence for the existence of
dark matter, known empirically to be the dominant component of matter in the
universe. A weakly interacting massive particle (WIMP) is one class of
candidates for dark matter. However, the SM does not contain such a particle.
Within the SM, the Higgs boson presents special theoretical challenges.
Assuming that the Higgs boson is a fundamental particle, its spin-0 nature
implies that the physical mass of the Higgs boson, as a quantity in the SM, is
unstable against corrections from quantum-loop processes. In the absence of
extreme fine tuning [25, 26, 27, 28] that would precisely cancel these
effects, the Higgs boson mass is generically driven to the cutoff scale of
validity of the theory, which could be as high as the Planck scale of quantum
gravity. The instability of the Higgs boson mass, and with it, that of the
entire electroweak scale (including the $\PW$ and $\PZ$ boson masses), is
known as the gauge hierarchy problem. This problem has been a major challenge
confronting theoretical particle physics for several decades. The discovery by
ATLAS and CMS of a Higgs boson with a mass around 125has strongly highlighted
this puzzle. The concept of “naturalness,” [26, 27, 28], which refers to the
degree of fine tuning of parameters, has been discussed extensively as an
important, yet difficult to quantify, consideration in assessing theoretical
scenarios.

Theories postulating physics beyond the SM, such as SUSY, can potentially
address these problems. Supersymmetry relates each SM bosonic field degree of
freedom to a corresponding fermionic superpartner field, and vice versa. Each
spin $J=1/2$ particle in the SM (the quarks and leptons) therefore has a spin
$J=0$ superpartner, so the SUSY spectrum contains a large number of scalar
quarks (squarks, $\PSQ$) and scalar leptons (sleptons, $\PSl$). The SUSY
partners of the SM gauge bosons ($J=1$) are referred to as gauginos ($J=1/2$).
For example, the superpartner of the gluon is a gluino ($\PSg$). The minimal
supersymmetric SM (MSSM) [16, 17, 18] contains five Higgs bosons ($J=0$) plus
the usual four electroweak gauge bosons ($J=1$) of the SM. In the MSSM, the
partners of the Higgs and gauge bosons map onto a set of four $J=1/2$
higgsinos and four electroweak gauginos. Because of possible mixing among
these particles, these superpartners are generically referred to as
electroweakinos, four of which are electrically neutral (neutralinos,
$\PSGc_{i}^{0}$, $i=1,\ldots,4$) and four of which are charged (charginos,
$\PSGc_{j}^{\pm}$, $j=1,2$). Supersymmetry provides a dark matter candidate if
the lightest supersymmetric particle (LSP) is stable and has no electric or
color charge. Stability of the LSP is guaranteed if the model conserves $R$
parity [15, 29], which also implies that SUSY particles are produced in pairs.
In this scenario, which is assumed in this paper, the lightest neutralino is
the LSP and could be a WIMP dark matter candidate.

Because gluinos and squarks carry color charges, like their SM partners, they
can be produced via the strong interaction: they therefore have the highest
production cross sections among SUSY particles for a given mass. The absence
of signals for these particles has so far led to lower limits on their masses
of roughly $m_{\PSg}\approx 2\TeV$ for gluinos and $m_{\sQua}\approx 1\TeV$
for light-flavored squarks [1, 30, 4, 5, 6, 7, 8], although these results are
model dependent. The present search focuses on processes involving the
production of colored SUSY particles, either gluinos or squarks. Once the SUSY
particles are produced, they typically decay via a sequence of processes that
generates jets, leptons, and large missing transverse momentum (), where is
the vector sum of the particles in an event. Large is a feature of models in
which the masses involved in the decay chains allow the LSP to carry
substantial transverse momentum (). So that this study is orthogonal to ones
explicitly requiring leptons, and to help enable a well-structured and
independent set of SUSY searches in CMS, the present search vetoes events in
which leptons (electrons or muons) are detected above a certain threshold in .

##  0.2 Analysis methodology

The basic approach of the analysis involves defining search regions in a four-
dimensional space specified by key event variables that characterize the
topology and kinematics of the events: the total number of jets
($N_{\text{jet}}$), the number of tagged jets ($N_{{\cPqb}\text{-jet}}$), the
scalar sum of jet (), and the magnitude of the vector sum of the jets (). The
variable is used to estimate the missing transverse momentum in the event. For
all-hadronic events, is similar to , but is less susceptible to uncertainties
in the modeling of soft energy deposits.

In total, there are 174 exclusive analysis bins in the four-dimensional search
region, which together provide sensitivity to a wide range of SUSY scenarios.
In each of the 174 analysis bins, the background from SM processes is
evaluated using event yields measured in corresponding control samples in the
data, in conjunction with correction factors obtained from Monte Carlo (MC)
simulated event samples. The principal sources of background arise from
several SM processes: production of a top quark, either through top quark-
antiquark () pair production or, less often, a single top quark; production of
an on- or off-mass-shell $\PW$ or $\PZ$ boson (+jets and +jets events,
respectively); and production of multijet events through quantum
chromodynamics (QCD) processes. Both top quark and +jets events can exhibit
significant and thus contribute to the background if a boson decays to a
neutrino and an undetected or out-of-acceptance charged lepton, including a
$\tau$ lepton with either a leptonic or hadronic decay. These backgrounds are
determined using a single-lepton control sample. Similarly, +jets events can
exhibit significant if the boson decays to two neutrinos. This background is
determined using a control sample of +jets events, in conjunction with a
control sample in which a boson decays into an $\EE$ or $\MM$ pair.
Significant in QCD multijet events can arise if the of a jet is mismeasured,
if a jet falls outside the acceptance of the jet selection, or from jets that
produce one or more neutrinos. The QCD background contribution is evaluated
using specially defined control samples together with the “rebalance and
smear” technique [31, 32, 8].

The search is performed using methodologies similar to those presented in Ref.
[8]. The search regions, however, have been optimized for the larger amount of
data, and refinements to the background estimation procedures have been
implemented. The main difference with respect to Ref. [8] is that for the
evaluation of background from top quark and +jets events, we now implement a
transfer factor method rather than construct event-by-event background
predictions separately for events with a hadronic tau lepton decay and for
events with an electron or a muon. Also, the larger data set of the current
analysis allows us to evaluate the background from
$\cPZ(\to\cPgn\cPagn)$+jets events, in the cases with
$N_{{\cPqb}\text{-jet}}>0$, using extrapolation factors based entirely on
data, rather than relying on simulation for these extrapolations when
$N_{\text{jet}}\geq 9$.

The interpretation of the results is performed using a set of representative
SUSY models, each of which is characterized by a small number of mass
parameters. For this purpose, we use so-called simplified models [33, 34, 35,
36]. For gluino pair production, the T1tttt, T1bbbb, T1qqqq, and T5qqqqVV [37]
simplified models are considered (Fig. 1). In the T1tttt model, each gluino
undergoes a three-body decay $\PSg\to\ttbar\PSGczDo$, where $\PSGczDo$ is the
LSP. The T1bbbb and T1qqqq models are the same as the T1tttt model, except the
system is replaced by bottom quark-antiquark ($\bbbar$) or light-flavored (, ,
, ) quark-antiquark ($\qqbar$) pairs, respectively. In the T5qqqqVV scenario,
each gluino decays to a light-flavored pair and either to the next-to-lightest
neutralino or to the lightest chargino $\PSGc_{1}^{\pm}$. The probability for
the decay to proceed via the , $\PSGcpDo$, or $\PSGc_{1}^{-}$ is 1/3 for each
channel. The ($\PSGc_{1}^{\pm}$) subsequently decays to the and to an on- or
off-mass-shell ($\PW^{\pm}$) boson. In this model, we assign
$m_{\PSGc_{1}^{\pm}}=m_{\PSGczDt}=0.5(m_{\PSGczDo}+m_{\PSg})$.

Figure 1:  Diagrams for the simplified models with direct gluino pair
production considered in this study: (upper left) T1tttt, (upper right)
T1bbbb, (lower left) T1qqqq, and (lower right) T5qqqqVV.

Figure 2:  Diagrams for the simplified models with direct squark pair
production considered in this study: (left) T2tt, (middle) T2bb, and (right)
T2qq.

For squark-antisquark production, three simplified models are considered,
denoted T2tt, T2bb, and T2qq (Fig. 2). In the T2tt model, top squark-
antisquark production is followed by the decay of the (anti)squark to a top
(anti)quark and the . The T2bb and T2qq models are the same as T2tt except
with bottom squarks and quarks, or light-flavored squarks and quarks,
respectively, in place of the top squarks and quarks.

##  0.3 Detector and trigger

A detailed description of the CMS detector, along with a definition of the
coordinate system and pertinent kinematic variables, is given in Ref. [38].
Briefly, a cylindrical superconducting solenoid with an inner diameter of 6m
provides a 3.8T axial magnetic field. Within the cylindrical volume are a
silicon pixel and strip tracker, a lead tungstate crystal electromagnetic
calorimeter (ECAL), and a brass and scintillator hadron calorimeter (HCAL).
The tracking detectors cover the range $\abs{\eta}<2.5$, where $\eta$ is the
pseudorapidity. The ECAL and HCAL, each composed of a barrel and two endcap
sections, cover $\abs{\eta}<3.0$. Forward calorimeters extend the coverage to
$3.0<\abs{\eta}<5.2$. Muons are measured within $\abs{\eta}<2.4$ by gas-
ionization detectors embedded in the steel flux-return yoke outside the
solenoid. The detector is nearly hermetic, permitting accurate measurements of
.

The CMS trigger is described in Ref. [39]. For this analysis, signal event
candidates were recorded by requiring at the trigger level to exceed a
threshold that varied between 100 and 120, depending on the LHC instantaneous
luminosity. The efficiency of this trigger is measured in data and is found to
exceed 97% for events satisfying the event selection criteria described below.
Additional triggers requiring the presence of charged leptons, photons, or
minimum values of are used to select control samples for the evaluation of
backgrounds, as described below.

##  0.4 Event reconstruction

Individual particles are reconstructed with the CMS particle-flow (PF)
algorithm [40], which identifies them as photons, charged hadrons, neutral
hadrons, electrons, or muons. To improve the quality of the photon and
electron reconstruction, additional criteria are imposed on the
$\sigma_{\eta\eta}$ variable [41], which is a measure of the width of the ECAL
shower shape with respect to the $\eta$ coordinate, and on the ratio of
energies associated with the photon or electron candidate in the HCAL and ECAL
[41, 42]. For muon candidates [43], more stringent requirements are imposed on
the matching between silicon tracker and muon detector track segments. Photon
and electron candidates are restricted to $\abs{\eta}<2.5$ and muon candidates
to $\abs{\eta}<2.4$.

The reconstructed vertex with the largest value of summed physics-object
$\pt^{2}$ is taken to be the primary $\Pp\Pp$ interaction vertex, where the
physics objects are the jets, clustered using the jet finding algorithm [44,
45] with the charged particle tracks assigned to the vertex as inputs, and the
associated missing transverse momentum, taken as the negative vector sum of
the of those jets. Charged particle tracks associated with vertices other than
the primary vertex are removed from further consideration. The primary vertex
is required to lie within 24cm of the center of the detector in the direction
along the beam axis and within 2cm in the plane transverse to that axis.

To suppress jets erroneously identified as leptons and genuine leptons from
hadron decays, electron and muon candidates are subjected to an isolation
requirement. The isolation criterion is based on the variable $I$, which is
the scalar sum of charged hadron, neutral hadron, and photon PF candidates
within a cone of radius $\Delta
R=\sqrt{\smash[b]{(\Delta\phi)^{2}+(\Delta\eta)^{2}}}$ around the lepton
direction, divided by the lepton , where $\phi$ is the azimuthal angle. The
expected contributions of neutral particles from extraneous $\Pp\Pp$
interactions (pileup) are subtracted [46]. The radius of the cone is 0.2 for
lepton $\pt<50\GeV$, $10\GeV/\pt$ for $50\leq\pt\leq 200\GeV$, and 0.05 for
$\pt>200\GeV$. The decrease in cone size with increasing lepton accounts for
the increased collimation of the decay products from the lepton’s parent
particle as the Lorentz boost of the parent particle increases [47]. The
isolation requirement is $I<0.1$ (0.2) for electrons (muons).

To further suppress leptons from hadron decays and also single-prong hadronic
$\tau$ lepton decays, charged particle tracks not identified as an isolated
electron or muon, including PF electrons and muons, are subjected to a track
isolation requirement. (Note that PF electrons and muons that do not satisfy
the isolation requirements of the previous paragraph are not considered to be
electron and muon candidates in this analysis.) To be identified as an
isolated track, the scalar sum of all other charged particle tracks within a
cone of radius 0.3 around the track direction, divided by the track , must be
less than 0.2 if the track is identified as a PF electron or muon and less
than 0.1 otherwise. Isolated tracks are required to satisfy $\abs{\eta}<2.4$.

Similarly, we require photon candidates to be isolated. The photon isolation
requirement is based on the individual sums of energy from charged hadrons,
neutral hadrons, and electromagnetic particles, excluding the photon candidate
itself, within a cone of radius $\Delta R=0.3$ around the photon candidate’s
direction, corrected for pileup [41]. Each of the three individual sums is
required to lie below a (different) threshold that depends on whether the
photon appears in the barrel or endcap calorimeter.

Jets are defined by clustering PF candidates using the anti-jet algorithm [44,
45] with a distance parameter of 0.4. Jet quality criteria [48, 49] are
imposed to eliminate jets from spurious sources such as electronics noise. The
jet energies are corrected for the nonlinear response of the detector [50] and
to account for the expected contributions of neutral particles from pileup
[46]. Jets are required to have $\pt>30\GeV$.

The identification of jets ( jet tagging) is performed by applying, to the
selected jet sample, a version of the combined secondary vertex algorithm
based on deep neural networks (DeepCSV) [51]. The medium working point of this
algorithm is used. The tagging efficiency for jets with $\pt\approx 30\GeV$ is
65%. The corresponding misidentification probability for gluon and up, down,
and strange quark jets is 1.6% while that for charm quark jets is 13%.

##  0.5 Event selection and search regions

Events considered as signal candidates are required to satisfy:

  * •

$N_{\text{jet}}\geq 2$, where jets must appear within $\abs{\eta}<2.4$;

  * •

$\HT>300\GeV$, where is the scalar sum of jets with $\abs{\eta}<2.4$;

  * •

$\mht>300\GeV$, where is the magnitude of , the negative of the vector sum of
jets with $\abs{\eta}<5$; an extended $\eta$ range is used to calculate so
that it better represents the total missing momentum in an event;

  * •

$\mht<\HT$, because events with $\mht>\HT$ are likely to arise from
mismeasurement;

  * •

no identified isolated electron or muon candidate with $\pt>10\GeV$;

  * •

no isolated track with $\mT<100\GeV$ and $\pt>10\GeV$ ($\pt>5\GeV$ if the
track is identified as a PF electron or muon), where is the transverse mass
[52] formed from and the isolated-track vector, with the negative of the
vector sum of all PF objects with appropriate calibration applied as explained
in Ref. [53]; the requirement restricts the veto to situations consistent with
a boson decay;

  * •

no identified, isolated photon candidate with $\pt>100\GeV$; this requirement
has a minimal impact on signal efficiency and is implemented to make the
analysis orthogonal to SUSY searches based on events with photons and missing
transverse energy, which typically require photon $\pt\gtrsim 100\GeV$ (e.g.,
Ref. [54]);

  * •

$\Delta\phi_{\mht,\mathrm{j_{i}}}>0.5$ for the two highest jets j1 and j2,
with $\Delta\phi_{\mht,\mathrm{j_{i}}}$ the azimuthal angle between and the
vector of jet ji; if $N_{\text{jet}}\geq 3$, then, in addition,
$\Delta\phi_{\mht,\mathrm{j}_{3}}>0.3$ for the third-highest jet j3; if
$N_{\text{jet}}\geq 4$, then, yet in addition,
$\Delta\phi_{\mht,\mathrm{j}_{4}}>0.3$ for the fourth-highest jet j4; all
considered jets must have $\abs{\eta}<2.4$; these requirements suppress
background from QCD events, for which is usually aligned along a jet
direction.

In addition, anomalous events with reconstruction failures or that arise from
noise or beam halo interactions are removed [53].

The search is performed in a four-dimensional region defined by exclusive
intervals in $N_{\text{jet}}$, $N_{{\cPqb}\text{-jet}}$, , and . The search
intervals in $N_{\text{jet}}$ and $N_{{\cPqb}\text{-jet}}$ are:

  * •

$N_{\text{jet}}$: 2–3, 4–5, 6–7, 8–9, $\geq$10;

  * •

$N_{{\cPqb}\text{-jet}}$: either 0, 1, 2, $\geq$3 (for intervals with
$N_{\text{jet}}\geq 4$), or 0, 1, $\geq$2 (for the $N_{\text{jet}}=2$–3
interval).

For and , 10 kinematic intervals are defined, as indicated in Table 0.5 and
Fig. 3. For $N_{\text{jet}}\geq 8$, the kinematic intervals labeled 1 and 4
are discarded because of the small numbers of events. The total number of
search bins in the four-dimensional space is 174.

Figure 3:  Schematic illustration of the 10 kinematic search intervals in the
versus plane. The diagonal line delineating the leftmost edge of regions 1, 4,
7, and 9 corresponds to the restriction $\mht<\HT$. Regions 1 and 4 are
excluded for $N_{\text{jet}}\geq 8$. The rightmost and topmost bins are
unbounded, extending to $\HT=\infty$ and $\mht=\infty$, respectively.

Definition of the search intervals in the and variables. Intervals 1 and 4 are
discarded for $N_{\text{jet}}\geq 8$. In addition, regions with $\mht>\HT$ are
excluded as illustrated in Fig. 3.  Interval [] [] 1 300–350 300–600 2 300–350
600–1200 3 300–350 $>$1200 4 350–600 350–600 5 350–600 600–1200 6 350–600
$>$1200 7 600–850 600–1200 8 600–850 $>$1200 9 $>$850 850–1700 10 $>$850
$>$1700

##  0.6 Simulated event samples

The evaluation of background (Section 0.7) is primarily based on data control
regions. Samples of MC simulated SM events are used to evaluate multiplicative
transfer factors that account for kinematic or other selection criteria
differences between the data control and signal regions and to validate the
analysis procedures.

The SM production of , +jets, +jets, +jets, and QCD events is simulated
using the 2.2.2 [55, 56] event generator with leading order (LO) precision.
The events are generated with up to three additional partons in the matrix
element calculations. The +jets, +jets, and +jets events are generated with
up to four additional partons. Single top quark events produced through the
$s$ channel, diboson events such as those originating from $\PW\PW$,
$\cPZ\cPZ$, or $\cPZ\PH$ production (with $\PH$ a Higgs boson), and rare
events such as those from $\ttbar\PW$, $\ttbar\cPZ$, and $\PW\PW\cPZ$
production, are generated with 2.2.2 at next-to-leading order (NLO) [57],
except that $\PW\PW$ events in which both bosons decay leptonically are
generated using the v2.0 [58, 59, 60, 61, 62] program at NLO. This same
generator is used to describe single top quark events produced through the $t$
and $\cPqt\PW$ channels. The detector response is modeled with the [63] suite
of programs. Normalization of the simulated background samples is performed
using the most accurate cross section calculations available [61, 62, 55, 64,
65, 66, 67, 68, 69, 70, 71, 72], which generally correspond to NLO or next-to-
NLO (NNLO) precision.

Samples of simulated signal events are generated at LO using 2.2.2, with up to
two additional partons included in the matrix element calculations. The
production cross sections are determined with approximate NNLO plus next-to-
next-to-leading logarithmic (NNLL) accuracy [73, 74, 75, 76, 77, 78, 79, 80,
81, 82, 83, 84]. Events with gluino (squark) pair production are generated for
a range of gluino $m_{\PSg}$ (squark $m_{\PSQ}$) and LSP $m_{\PSGczDo}$ mass
values, with $m_{\PSGczDo}<m_{\PSg}$ ($m_{\PSGczDo}<m_{\PSQ}$). The ranges of
mass considered vary according to the model, but are generally from around
600–2500for $m_{\PSg}$, 200–1700for $m_{\PSQ}$, and 0–1500for $m_{\PSGczDo}$
(see Section 0.9). For the T5qqqqVV model, the masses of the intermediate and
$\PSGc_{1}^{\pm}$ are given by the mean of $m_{\PSGczDo}$ and $m_{\PSg}$, as
was already stated in the introduction. The gluinos and squarks decay
according to the phase space model [85]. To render the computational
requirements manageable, the detector response is described using the CMS fast
simulation program [86, 87], which yields results that are generally
consistent with the -based simulation. To improve the consistency of the fast
simulation description with respect to that based on , we apply a correction
of 1% to account for differences in the efficiency of the jet quality
requirements [48, 49], corrections of 5–12% to account for differences in the
jet tagging efficiency, and corrections of 0–14% to account for differences in
the modeling of and .

All simulated samples make use of the 8.205 [85] program to describe parton
showering and hadronization. The CUETP8M1 [88] (CP5 [89]) 8.205 tune was used
to produce the SM background samples for the analysis of the 2016 (2017 and
2018) data, with signal samples based on the CUETP8M1 tune for 2016 and on the
CP2 tune [89] for 2017 and 2018. Simulated samples generated at LO (NLO) with
the CUETP8M1 tune use the nnpdf2.3lo (nnpdf2.3nlo) [90] parton distribution
function (PDF), while those using the CP2 or CP5 tune use the nnpdf3.1lo
(nnpdf3.1nnlo) [91] PDF. The simulated events are generated with a
distribution of $\Pp\Pp$ interactions per bunch crossing that is adjusted to
match the corresponding pileup distribution measured in data.

To improve the description of initial-state radiation (ISR), the prediction is
compared to data in a control region enriched in events: two leptons
($\Pe\Pe$, $\Pgm\Pgm$, or $\Pe\Pgm$) and two tagged jets are required. The
number of all remaining jets in the event is denoted
$N_{\text{jet}}^{\text{ISR}}$. A correction factor is applied to simulated and
signal events so that the $N_{\text{jet}}^{\text{ISR}}$ distribution agrees
with that in data. The correction is found to be unnecessary for samples that
are generated with the CP5 tune, so it is not applied to those samples. The
central value of the correction ranges from 0.92 for
$N_{\text{jet}}^{\text{ISR}}=1$ to 0.51 for $N_{\text{jet}}^{\text{ISR}}\geq
6$. From studies with a single-lepton data control sample, dominated by
events, the associated systematic uncertainty is taken to be 20% of the
correction for events and 50% of the correction for signal events, where the
larger uncertainty in the latter case accounts for possible differences
between signal and event production.

##  0.7 Background evaluation

The evaluation of the SM backgrounds is primarily based on data control
regions (CRs). Signal events, if present, could populate the CRs, an effect
known as signal contamination. The impact of signal contamination is accounted
for in the interpretation of the results (Section 0.9). Signal contamination
is negligible for all CRs except for the single-lepton CR described in Section
0.7.1. Similarly, it is negligible for all signal models except those that can
produce an isolated track or lepton. With respect to the models examined here,
signal contamination is relevant only for the T1tttt, T5qqqqVV, and T2tt
models.

###  0.7.1 Background from top quark and +jets events: “lost leptons”

The background from the SM production of , single top quark, and +jets events
originates from bosons that decay leptonically to yield a neutrino and a
charged lepton. The charged lepton can be an electron, a muon, or a lepton.
The lepton can decay leptonically to produce an electron or a muon or it can
decay hadronically, in each case yielding at least one additional neutrino.
For boson decays that produce electrons or muons, top quark and +jets events
can enter as background to the signal region if there is large from the
neutrino(s) and if the electron or muon lies outside the analysis acceptance,
is not reconstructed, or is not isolated. For boson decays that produce a
hadronically decaying lepton, top quark and +jets events can enter as
background if there is large from the neutrinos. Collectively, the background
from events with top quark and +jets production is referred to in this paper
as the “lost-lepton” background.

To evaluate the lost-lepton background, a single-lepton (, ) CR is selected
using the same trigger and event selection criteria used for signal events,
except the electron and muon vetoes are inverted and the isolated-track veto
is not applied. Exactly one isolated electron or muon is required to be
present. The single-electron and single-muon samples are combined to form a
single CR. The transverse mass formed from and the lepton vector is required
to satisfy $\mT<100\GeV$. This requirement has a high efficiency for SM events
while reducing potential contamination from signal events with large .

The signal contamination in the resulting CR is generally small, with a
typical value of 7, 3, and 1% for the T1tttt, T5qqqqVV, and T2tt model,
respectively. The contamination tends to be larger in search regions with
large values of $N_{\text{jet}}$, $N_{{\cPqb}\text{-jet}}$, , and/or , while
it is usually negligible in search regions with small and . For certain values
of $m_{\PSg}$ or $m_{\sTop}$ and $m_{\PSGczDo}$, the contamination can be as
large as 30–50, 4–12, and 20–50% for the respective model. In a narrow
diagonal range in the $m_{\PSGczDo}$ versus $m_{\sTop}$ plane, for which
$m_{\sTop}-m_{\PSGczDo}\approx m_{\PQt}$, the signal contamination for the
T2tt model can even be as large as around 90% at small $m_{\PSGczDo}$. Because
of this large contamination, this diagonal region is excluded from the
analysis as explained in Section 0.9 (see Fig. 14 (upper left)).

Figure 4:  (upper) The number of lost-lepton events in simulation, integrated
over and , as a function of $N_{\text{jet}}$ and $N_{{\cPqb}\text{-jet}}$.
(middle) Corresponding results from simulation for the number of events in the
single-lepton control region. (lower) The ratio of the simulated lost-lepton
to the single-lepton results, with statistical uncertainties (too small to be
visible). These ratios are equivalent to the transfer factors used in the
evaluation of the lost-lepton background, except integrated over and .

The lost-lepton background is evaluated by applying an MC-derived
multiplicative transfer factor to the observed single-lepton CR yields, with a
separate transfer factor determined for each of the 174 search bins. The
transfer factor is defined by the ratio, in simulation, of the number of lost-
lepton events in a search bin to the number of events in the corresponding bin
of the single-lepton CR, following normalization to the same integrated
luminosity. The simulated events are corrected to account for differences with
respect to data in the lepton, isolated track, and jet tagging efficiencies.

The upper panel of Fig. 4 shows the simulated results, as a function of
$N_{\text{jet}}$ and $N_{{\cPqb}\text{-jet}}$, for the number of lost-lepton
events. The corresponding results from simulation for the number of events in
the single-lepton CR are shown in the middle panel of Fig. 4. The ratio of the
results in the upper to the middle panels, equivalent to the transfer factor
integrated over and , is shown in the lower panel. At lower values of
$N_{\text{jet}}$, the distributions are enhanced in +jets events, for which a
larger fraction of leptons lie outside the kinematic acceptance of the
analysis compared to events. This reduces the event acceptance in the single-
lepton CR, increasing the value of the integrated transfer factors above unity
as seen in the lower panel of Fig. 4 for $2\leq N_{\text{jet}}\leq 3$. As
$N_{{\cPqb}\text{-jet}}$ increases, the probability for a lepton to fail the
isolation requirement increases, leading to a larger rate of lost-lepton
events and to an increase in the integrated transfer factors. This latter
effect is especially visible for $2\leq N_{\text{jet}}\leq 3$ in Fig. 4
(lower).

The dominant uncertainty in the lost-lepton background prediction is
statistical, arising from the limited number of events in the CR. Other
uncertainties are evaluated to account for the lepton and jet tagging scale
factors, the selection requirement, the PDFs, the renormalization and
factorization scales [92], and the jet energy corrections. These uncertainties
are summed in quadrature to obtain the total uncertainty in the lost-lepton
background prediction.

###  0.7.2 Background from $\cPZ(\to\cPgn\cPagn)$+jets events

The background from +jets events with $\cPZ\to\cPgn\cPagn$ decay is evaluated
using a CR with a single photon (+jets CR), in conjunction with a
$\cPZ(\to\ell^{+}\ell^{-})$+jets CR in which the boson decays to an $\EE$ or
$\MM$ pair. The method relies on the kinematic similarity between the
production of bosons and photons. The $\cPZ(\to\cPgn\cPagn)$+jets background
in search bins with $N_{{\cPqb}\text{-jet}}=0$ is determined by applying
multiplicative transfer factors from simulation to the observed rate of +jets
events, analogous to the method described in Section 0.7.1 for the evaluation
of the lost-lepton background. A correction is made to the normalization based
on the observed rate of $\cPZ(\to\ell^{+}\ell^{-})$+jets CR events. An
extrapolation to the search bins with $N_{{\cPqb}\text{-jet}}\geq 1$ is then
made based on factors constructed from the $\cPZ(\to\ell^{+}\ell^{-})$+jets
data. We follow this procedure in order to take advantage of both the higher
statistical precision of the +jets CR and the more direct transfer factors of
the $\cPZ\to\ell^{+}\ell^{-}$ CR, while preserving the
$N_{{\cPqb}\text{-jet}}$–$N_{\text{jet}}$ correlation observed in the latter.

#### The +jets events

Events in the +jets CR were collected using a single-photon trigger, with an
online threshold that varied between 180 and 190, depending on the data
collection period. In the offline analysis, events are required to contain
exactly one photon with $\pt>200\GeV$. In each CR event, the photon serves as
a proxy for a boson and is removed to emulate the undetected boson in
$\cPZ\to\cPgn\cPagn$ decays. To ensure that the kinematics of the +jets
events match those expected for $\cPZ(\to\cPgn\cPagn)$+jets events, jets are
reclustered after removing the photon and all event-level variables are
recomputed. The same event selection criteria used to select signal events are
then applied except, in addition, we require $N_{{\cPqb}\text{-jet}}=0$.

The +jets CR contains nonnegligible contributions from photons produced in
neutral meson decays. These photons are referred to as “nonprompt.” The
contamination of the CR from nonprompt photons, and thus the purity of signal
photons in the sample, is evaluated using a binned maximum likelihood fit to
the distribution of the photon candidate’s charged hadron isolation variable.
The fit is based on templates for nonprompt and signal photons. For signal
photons, the template is taken from simulation, using the nominal photon
selection criteria. For nonprompt photons, three different versions of the
template are made: i) from simulation using the nominal criteria; ii) from
simulation in a high-$\sigma_{\eta\eta}$ sideband (defined by inverting the
$\sigma_{\eta\eta}$ selection criterion), where nonprompt photon production is
expected to dominate; and iii) from data in this same high-$\sigma_{\eta\eta}$
sideband. The arithmetic mean of the three nonprompt templates is used in the
fit, with the variation in the results obtained using the three templates
individually defining a systematic uncertainty. The purity is determined as a
function of and typically exceeds 90%.

In the generation of simulated +jets events, photons that are approximately
collinear with a parton ($\Delta R<0.4$) are removed to improve the fraction
of events with well-isolated photons and thus the statistical precision of the
sample. A correction denoted $\mathcal{F}_{\text{dir}}$ is evaluated to
account for a bias from this requirement, using simulated events with a looser
restriction on the angular separation between the generator-level photons and
partons. The corrections are typically less than 10%. A systematic uncertainty
in the correction given by $0.30(1-\mathcal{F}_{\text{dir}})$ is determined by
evaluating the level of agreement between simulation and data in the
distribution of the angular separation between a photon and the nearest jet,
and the effect of changing the definition of collinear photons in the
simulation.

#### The $\cPZ(\to\ell^{+}\ell^{-})$+jets events

The $\cPZ(\to\ell^{+}\ell^{-})$+jets CR, collected using single-lepton
triggers, is selected by requiring two oppositely charged electrons or muons
with a dilepton invariant mass $m_{\ell\ell}$ within 15of the boson mass. The
selection requirements for electrons and muons are the same as those described
in Section 0.4, including the isolation requirements. To suppress events, the
of the dilepton system is required to exceed 200. Similar to the +jets CR,
the lepton pair in each $\cPZ(\to\ell^{+}\ell^{-})$+jets event is removed to
emulate the undetected boson in $\cPZ(\to\cPgn\cPagn)$+jets events, following
which jets are reclustered and the event-level quantities recalculated.

Top quark pair production typically constitutes $<$5% of the observed dilepton
event yield, except for events with $N_{{\cPqb}\text{-jet}}\geq 2$ where it
can comprise up to $\approx$15% of the sample. Using fits to the observed
$m_{\ell\ell}$ distribution, the purity $\beta^{\text{data}}_{\ell\ell}$ of
the $\cPZ(\to\ell^{+}\ell^{-})$+jets sample is evaluated for each individual
$N_{\text{jet}}$ and $N_{{\cPqb}\text{-jet}}$ region.

#### The $\cPZ(\to\cPgn\cPagn)$+jets background prediction

For each of the 46 search bins with $N_{{\cPqb}\text{-jet}}=0$, the
$\cPZ(\to\cPgn\cPagn)$+jets background is evaluated according to:

$\left.N_{\cPZ\to\cPgn\cPagn}^{\text{pred}}\right|_{N_{{\cPqb}\text{-jet}}=0}=\langle\rho\rangle{\mathcal{R}_{\cPZ\to\cPgn\cPagn/\gamma}^{\text{sim}}}\mathcal{F}_{\text{dir}}\beta_{\gamma}N_{\gamma}^{\text{data}}\,/\,\mathcal{C}_{\text{data/sim}}^{\gamma},$
(1)

where $N_{\gamma}^{\text{data}}$ is the number of observed events in the
+jets CR, $\mathcal{R}_{\cPZ\to\cPgn\cPagn/\gamma}^{\text{sim}}$ is the
transfer factor, $\mathcal{C}_{\text{data/sim}}^{\gamma}$ accounts for the
trigger efficiency and for differences between data and simulation in the
photon reconstruction efficiency [41], and $\beta_{\gamma}$ is the photon
purity. The transfer factors, which account for known differences between
photon and boson production, are given by the ratio from simulation of the
rates of $\cPZ(\to\cPgn\cPagn)$+jets events to +jets events in the 46 bins.
For the photon selection criteria used in this analysis, the transfer factor
has a value of around 0.5, with a relatively mild dependence on the signal
region kinematics. The distribution of $N_{\gamma}^{\text{data}}$, along with
the simulated results for signal and nonprompt +jets events, is shown in Fig.
5 (upper). Figure 5 (lower) shows the transfer factors
$\mathcal{R}_{\cPZ\to\cPgn\cPagn/\gamma}^{\text{sim}}$.

Figure 5:  (upper) The number of events in the +jets control region for data
and simulation. (lower) The transfer factors
$\mathcal{R}_{\cPZ\to\cPgn\cPagn/\gamma}^{\text{sim}}$ from simulation. The
respective results are shown for the 46 search bins with
$N_{{\cPqb}\text{-jet}}=0$. The 10 results (8 for $N_{\text{jet}}\geq 8$)
within each region delineated by vertical dashed lines correspond sequentially
to the 10 (8) kinematic intervals in and listed in Table 0.5 and Fig. 3. The
uncertainties are statistical only. For the upper plot, the simulated results
show the stacked event rates for the +jets and nonprompt MC event samples,
where “nonprompt” refers to SM MC events other than +jets. The simulated
nonprompt results are dominated by events from the QCD sample. Because of
limited statistical precision in the simulated event samples at large
$N_{\text{jet}}$, the transfer factors determined for the $8\leq
N_{\text{jet}}\leq 9$ region are also used for the $N_{\text{jet}}>10$ region.

The term denoted $\langle\rho\rangle$ in Eq. (1) accounts for possible
residual mismodeling of
$\mathcal{R}_{\cPZ\to\cPgn\cPagn/\gamma}^{\text{sim}}$. The value of
$\langle\rho\rangle$ is expected to be close to unity, with possible
deviations due to differences in missing higher-order terms between the +jets
and +jets simulation. It is the average over all search bins with
$N_{{\cPqb}\text{-jet}}=0$ of the double ratio

$\rho=\frac{\mathcal{R}_{\cPZ\to\ell^{+}\ell^{-}/\gamma}^{\text{data}}}{\mathcal{R}_{\cPZ\to\ell^{+}\ell^{-}/\gamma}^{\text{sim}}}=\frac{N_{\cPZ\to\ell^{+}\ell^{-}}^{\text{data}}}{N_{\cPZ\to\ell^{+}\ell^{-}}^{\text{sim}}}\frac{N_{\gamma}^{\text{sim}}}{N_{\gamma}^{\text{data}}}\frac{\beta^{\text{data}}_{\ell\ell}}{\mathcal{C}_{\text{data/sim}}^{\ell\ell}}\frac{\mathcal{C}_{\text{data/sim}}^{\gamma}}{\mathcal{F}_{\text{dir}}\beta_{\gamma}},$
(2)

where $N_{\cPZ\to\ell^{+}\ell^{-}}^{\text{data}}$ and
$N_{\cPZ\to\ell^{+}\ell^{-}}^{\text{sim}}$ represent the number of events in
the observed and simulated $\cPZ\to\ell^{+}\ell^{-}$ CR, respectively,
$N_{\gamma}^{\text{sim}}$ is the number of events in the simulated +jets CR,
and $\mathcal{C}_{\text{data/sim}}^{\ell\ell}$ accounts for the trigger
efficiency and for differences between data and simulation in the lepton
reconstruction efficiencies in $\cPZ(\to\ell^{+}\ell^{-})$+jets events [42,
43]. The event yields in the $\cPZ(\to\ell^{+}\ell^{-})$+jets CR are too
small to allow a meaningful determination of $\rho$ in all search bins and
thus we calculate the average $\langle\rho\rangle$ and apply it to all bins.

From studies of the variation of $\rho$ with , , and $N_{\text{jet}}$, we
observe a mild trend in $\rho$ with respect to . This trend is parameterized
as $\rho(\HT)=0.86+(2.0\times 10^{-4})\text{min}(\HT,900\GeV)$. Using this
parameterization, an event-by-event weight is applied to each simulated +jets
CR event before it enters Eq. (1). Prior to this event weighting, we find
$\langle\rho\rangle=0.95$. Following the event weighting,
$\langle\rho\rangle=1.00$. It is this latter value of $\langle\rho\rangle$,
along with its uncertainty, that enters Eq. (1). In each bin, the residual
deviation of $\rho$ from unity as a function of is added in quadrature with
the associated statistical uncertainty, and analogously but separately for and
$N_{\text{jet}}$, and the largest of the three resulting terms is taken as the
corresponding systematic uncertainty in the background prediction. The values
of this bin-dependent uncertainty range from 1 to 13%.

To evaluate the $\cPZ(\to\cPgn\cPagn)$+jets background for search bins with
$N_{{\cPqb}\text{-jet}}\geq 1$, we assume that the relative population of
$\cPZ(\to\cPgn\cPagn)$+jets events in the –plane is independent of
$N_{{\cPqb}\text{-jet}}$ for fixed $N_{\text{jet}}$. A systematic uncertainty
deduced from a closure test (described below) is assigned to account for this
assumption, where “closure test” refers to a check of the ability of the
method, applied to simulated event samples, to correctly predict the genuine
number of background events in simulation. We extend the result from Eq. (1)
using extrapolation factors $\mathcal{F}_{\mathrm{j},\PQb}^{\text{data}}$ from
$\cPZ(\to\ell^{+}\ell^{-})$+jets data, as follows:

$\left(N^{\text{pred}}_{\cPZ\to\cPgn\cPagn}\right)_{j,b,k}=\left(N^{\text{pred}}_{\cPZ\to\cPgn\cPagn}\right)_{j,0,k}\mathcal{F}_{\mathrm{j},\PQb}^{\text{data}}\equiv\left(N^{\text{pred}}_{\cPZ\to\cPgn\cPagn}\right)_{j,0,k}\frac{\left(N_{\cPZ\to\ell^{+}\ell^{-}}^{\text{data}}\beta^{\text{data}}_{\ell\ell}\right)_{j,b}}{\left(N_{\cPZ\to\ell^{+}\ell^{-}}^{\text{data}}\beta^{\text{data}}_{\ell\ell}\right)_{j,0}},$
(3)

where $j$ corresponds to the five $N_{\text{jet}}$ regions, $b$ to the four
$N_{{\cPqb}\text{-jet}}$ regions (three for $N_{\text{jet}}\leq 3$), and $k$
to the 10 kinematic regions of and (Table 0.5). The data used and the
resulting extrapolation factors $\mathcal{F}_{\mathrm{j},\PQb}^{\text{data}}$
are shown in Fig. 6.

Figure 6:  (upper) The observed event yield in the
$\cPZ(\to\ell^{+}\ell^{-})$+jets control region, integrated over and , as a
function of $N_{\text{jet}}$ and $N_{{\cPqb}\text{-jet}}$. The uncertainties
are statistical only. The stacked histograms show the corresponding results
from simulation. (lower) The extrapolation factors
$\mathcal{F}_{\mathrm{j},\PQb}^{\text{data}}$ with their statistical
uncertainties.

The rare process $\ttbar\cPZ$ and the even more rare processes $\PZ\PZ$,
$\PW\PW\PZ$, $\PW\PZ\PZ$, and $\PZ\PZ\PZ$ can also contribute to the
background. Those processes with a counterpart when the boson is replaced with
a photon are already accounted for in $N_{\gamma}^{\text{data}}$ and thus are
automatically included in the background estimate. We assume that the ratio of
the rate of the rare process to its counterpart with a photon, , the ratio of
$\ttbar\PZ$ (with $\PZ\to\cPgn\cPagn)$ to $\ttbar\gamma$ events, equals
$\mathcal{R}_{\cPZ\to\cPgn\cPagn/\gamma}^{\text{sim}}$.

A closure test of the procedure is performed by treating event yields from the
$\cPZ(\to\ell^{+}\ell^{-})$+jets simulation as data, as shown in Fig. 7.
Based on this study, the following systematic uncertainties are assigned. For
$N_{\text{jet}}=2$–3, a systematic uncertainty of 15 and 30% is assigned to
the $N_{{\cPqb}\text{-jet}}=1$ and $\geq$2 regions, respectively. For
$N_{\text{jet}}\geq 4$, a systematic uncertainty of 15 and 30% is assigned to
the $N_{{\cPqb}\text{-jet}}=1$–2 and $\geq$3 regions. These uncertainties
account for correlations between $N_{{\cPqb}\text{-jet}}$ and the and/or
variables in the shape of the $\cPZ\to\cPgn\cPagn$ prediction.

Figure 7:  Prediction from simulation for the
$\cPZ(\to\ell^{+}\ell^{-})$+jets event yields in the 174 search bins as
determined by computing the $\mathcal{F}_{\mathrm{j},\PQb}^{\text{data}}$
factors (Eq. (3)) and the $N_{{\cPqb}\text{-jet}}=0$ event yields in the same
manner as for data, in comparison to the corresponding direct
$\cPZ(\to\ell^{+}\ell^{-})$+jets prediction from simulation. The 10 results
(8 for $N_{\text{jet}}\geq 8$) within each region delineated by vertical
dashed lines correspond sequentially to the 10 (8) kinematic intervals in and
listed in Table 0.5 and Fig. 3. For bins with $N_{\text{jet}}\geq 10$, some
points do not appear in the upper panel because they lie below the minimum of
the displayed range. In the case that the direct expected yield is zero, there
is no result in the lower, ratio panel. The pink bands show the statistical
uncertainties in the prediction, scaled to correspond to the integrated
luminosity of the data, combined with the systematic uncertainty attributable
to the kinematic (and ) dependence. The black error bars show the statistical
uncertainties in the simulation. For bins corresponding to
$N_{{\cPqb}\text{-jet}}=0$, the agreement is exact by construction.

###  0.7.3 Background from QCD events

The QCD background comprises only a small fraction ($<$5%) of the total
background but, because it typically arises from the mismeasurement of jet ,
is difficult to evaluate with simulation. We use data to model this
background, exploiting knowledge of the jet energy resolution. Briefly, the
method employs a set of CR events collected using triggers requiring to exceed
various thresholds between 200 and 1050, with no condition on . Corresponding
prescale factors ranging from around 10 000 to 1 are applied, where a prescale
factor reduces the recorded event rate relative to the raw trigger rate in
order to maintain a manageable data flow. The jet momenta in each CR event are
adjusted so that the event has well-balanced jet , consistent with the
kinematics of a generator-level (, ideally measured) QCD event. This step is
called rebalancing. The rebalancing step removes the intrinsic from the event,
thus effectively eliminating the contributions of events like +jets and
+jets events that can have genuine [31]. The jet momenta are then smeared
according to the known detector jet resolution in order to determine the
probability that a given event will populate a given search bin. This latter
step is the smear stage. The so-called rebalance and smear (R&S) method was
introduced in Refs. [31, 32] and was further developed in Ref. [4].

To rebalance an event, a Bayesian inference procedure is used, in which the of
each jet in a CR event is varied within its uncertainty to maximize the
probability:

$\mathcal{P}(\vec{\mathcal{J}}_{\text{true}}|\vec{\mathcal{J}}_{\text{meas}})\sim\mathcal{P}(\vec{\mathcal{J}}_{\text{meas}}|\vec{\mathcal{J}}_{\text{true}})\,\pi(\vec{H}^{\text{miss}}_{\mathrm{T},\text{true}},\Delta{\phi}_{\mathrm{j}_{1(\PQb)},\text{true}}),$
(4)

where
$\mathcal{P}(\vec{\mathcal{J}}_{\text{true}}|\vec{\mathcal{J}}_{\text{meas}})$
is the posterior probability density for a given configuration of jets with
true (or ideal) momentum assignments $\vec{\mathcal{J}}_{\text{true}}$, given
a configuration of measured jet momenta $\vec{\mathcal{J}}_{\text{meas}}$. The
$\mathcal{P}(\vec{\mathcal{J}}_{\text{meas}}|\vec{\mathcal{J}}_{\text{true}})$
term, taken to be the product of the individual jet response functions of all
jets in an event, is the likelihood to observe a configuration of measured jet
momenta given a configuration of jets with a particular set of true momenta.
The jet response functions are constructed from the distributions in
simulation of the ratio of the reconstructed jet to the of well-matched
generator-level jets. The response functions are derived as a function of jet
and $\eta$ and are corrected to account for differences in the jet response
shape between data and simulation. The
$\pi(\vec{H}^{\text{miss}}_{\mathrm{T},\text{true}},\Delta{\phi}_{\mathrm{j}_{1(\PQb)},\text{true}})$
term is the prior distribution, determined as a function of the true (i.e.,
generator level) and $\Delta{\phi}_{\mathrm{j}_{1(\PQb)}}$, where
$\Delta{\phi}_{\mathrm{j}_{1(\PQb)}}$ is the azimuthal angle between and
either the highest jet in the event (for $N_{{\cPqb}\text{-jet}}=0$), or the
highest tagged jet (for $N_{{\cPqb}\text{-jet}}\geq 1$). This prior represents
the distribution of the magnitude and direction of the genuine expected in QCD
events.

After the transverse momenta of the individual jets have been adjusted
according to the posterior probability density in Eq. (4), the jet values are
smeared by rescaling them using factors sampled randomly from the jet response
functions. This sampling is performed numerous times for each rebalanced
event. Each event is then weighted by the inverse of the number of times it is
smeared. Events are smeared in up to 1000 independent trials, with a final
target event weight of 0.05, equal to the prescale value of the trigger that
collected the seed event divided by the number of times the event was reused
in the smearing step.

The R&S procedure produces a sample of events that closely resembles the
original sample of CR events, except with the contributions of the electroweak
backgrounds effectively removed. The resulting events are subjected to the
signal event selection criteria of Section 0.5 to obtain the QCD background
prediction in each search bin. The overall normalization is adjusted based on
a scaling factor derived from a QCD-dominated CR selected by inverting the
$\Delta\phi$ selection criteria and requiring $N_{{\cPqb}\text{-jet}}=0$ and
$250<\mht<300\GeV$. The $\Delta\phi$ selection criteria are inverted by
requiring at least one of the two (for $N_{\text{jet}}=2$), three (for
$N_{\text{jet}}=3$), or four (for $N_{\text{jet}}\geq 4$) highest jets in an
event to fail at least one of the corresponding
$\Delta\phi_{\mht,\mathrm{j_{i}}}$ requirements given in Section 0.5. The
normalization scale factors typically have values around 1.4.

Comparisons between the predicted QCD background yields and observations are
examined as a function of , , $N_{\text{jet}}$, and $N_{{\cPqb}\text{-jet}}$,
both in a CR defined by inverting the $\Delta\phi$ requirements and in a low-
sideband defined by $250<\mht<300\GeV$. As examples, Fig. 8 shows the
distribution of in the inverted-$\Delta\phi$ CR and the distribution of in the
low-sideband.

Figure 8:  The observed and predicted distributions of (left) in the
inverted-$\Delta\phi$ control region and (right) in the low-sideband. The
uncertainties are statistical only. The lower panels show the ratios of the
observed to the predicted distributions, with their statistical uncertainties.
The hatched regions indicate the total uncertainties in the predictions, with
statistical and systematic uncertainties combined in quadrature.

Figure 9 shows the observed and predicted event yields in 174 analysis control
bins defined using the same criteria as for the search bins except with the
inverted-$\Delta\phi$ requirement. For all these validation tests,
contributions from QCD events are evaluated using the R&S method,
contributions from top quarks and +jets events are evaluated using the lost-
lepton method described in Section 0.7.1, and contributions from
$\cPZ(\to\cPgn\cPagn)$+jets events are taken from simulation.

The principal uncertainty in the R&S QCD background prediction is systematic,
associated with the uncertainty in the shape of the jet response functions.
This uncertainty is evaluated by varying the jet energy resolution scale
factors within their uncertainties, resulting in uncertainties in the
prediction that range from 30–70%, depending on the search bin. Smaller
uncertainties related to the trigger and the finite size of the seed sample
are evaluated, as well as a nonclosure uncertainty that accounts for
inaccuracies identified from simulation-based studies.

Figure 9:  Distribution of observed and predicted event yields in the
inverted-$\Delta\phi$ control region analysis bins. The uncertainties are
statistical only. The labeling of the bin numbers is the same as in Fig. 7.
The lower panel shows the ratio of the observed to the predicted event yields,
with their statistical uncertainties. The hatched region indicates the total
uncertainty in the prediction, with statistical and systematic uncertainties
combined in quadrature.

##  0.8 Signal systematic uncertainties

Systematic uncertainties in the yield of signal events, averaged over all
search bins. The variations correspond to different signal models and choices
for the SUSY particle masses. Results reported as 0.0 correspond to values
less than 0.05%.  Item Relative uncertainty (%) Renormalization and
factorization scales $\mu_{\text{R}}$ & $\mu_{\text{F}}$ 0.0–5.7 Initial-state
radiation 0.0–14 Jet energy scale 0.0–14 Jet energy resolution 0.0–10 Pileup
modeling 0.0–2.4 Isolated-lepton & isolated-track vetoes 2.0 (T1tttt,
T5qqqqVV, and T2tt models) Integrated luminosity 2.3–2.5 Trigger efficiency
(statistical) 0.2–2.6 Trigger efficiency (systematic) 2.0 Statistical
uncertainty in simulated samples 1.2–31 and modeling 0.0–11 Jet quality
requirements 1.0 Total 4.0–33

Systematic uncertainties in the signal event yield are listed in Table 0.8. To
evaluate the uncertainty associated with the renormalization
($\mu_{\text{R}}$) and factorization ($\mu_{\text{F}}$) scales, each scale is
varied independently by a factor of 2.0 and 0.5 [92, 93, 94]. The
uncertainties associated with $\mu_{\text{R}}$, $\mu_{\text{F}}$, and ISR,
integrated over all search bins, typically lie below 0.1%. Nonetheless, they
can be as large as the maximum values noted in Table 0.8 if $\Delta m\approx
0$, where $\Delta m$ is the difference between the gluino or squark mass and
the sum of the masses of the particles into which the gluino or squark decays.
For example, for the T1tttt model, $\Delta
m=m_{\PSg}-(m_{\PSGczDo}+2m_{\PQt})$, with $m_{\PQt}$ the top quark mass. The
uncertainties associated with the jet energy scale and jet energy resolution
are evaluated as functions of jet and $\eta$. To evaluate the uncertainty
associated with the pileup reweighting, the value of the total inelastic cross
section is varied by 5% [95]. The isolated-lepton and isolated-track vetoes
have a minimal impact on the T1bbbb, T1qqqq, T2bb, and T2qq models because
events in these models rarely contain an isolated lepton. Thus, the associated
uncertainty is negligible ($\lesssim$0.1%). The systematic uncertainty in the
determination of the integrated luminosity varies between 2.3 and 2.5% [96,
97, 98], depending on the year of data collection.

Systematic uncertainties in the signal predictions associated with the jet
tagging and misidentification efficiencies are also evaluated. These
uncertainties do not affect the signal yield but can potentially alter the
shape of signal distributions. The systematic uncertainties associated with
$\mu_{\text{R}}$, $\mu_{\text{F}}$, ISR, jet energy scale, jet energy
resolution, the trigger, statistical precision in the event samples, and
modeling can also affect the shapes of the signal distributions. We account
for these potential changes in shape, , migration of events among search bins,
in the limit setting procedure described in Section 0.9.

##  0.9 Results

Figure 10 presents the observed numbers of events in the 174 search bins. The
data are shown in comparison to the stacked pre-fit predictions for the SM
backgrounds, where “pre-fit” refers to the predictions determined as described
in Section 0.7, before constraints from the fitting procedure have been
applied. Numerical values are given in Appendix .11. The uncertainties in the
background predictions are mainly from systematic uncertainties in the
transfer factors, statistical uncertainties in control sample yields, and
systematic uncertainties in the modeling of the search variables. Appendix .11
lists the overall statistical and systematic uncertainties for the individual
background components and for their sum. In addition to the finely segmented
search bins of Fig. 10, we determine the results for 12 aggregate search bins,
each representing a potentially interesting signal topology. These results are
presented in Appendix .12.

The observed event counts are consistent with the predicted backgrounds. Thus
we do not obtain evidence for supersymmetry.

Figure 10:  The observed numbers of events and pre-fit SM background
predictions in the 174 search bins of the analysis, where “pre-fit” means
there is no constraint from the likelihood fit. The labeling of the bin
numbers is the same as in Fig. 7. Numerical values are given in Appendix .11.
The hatching indicates the total uncertainty in the background predictions.
The lower panel displays the fractional differences between the data and SM
predictions.

Figure 11:  One-dimensional projections of the data and pre-fit SM predictions
in , $N_{\text{jet}}$, and $N_{{\cPqb}\text{-jet}}$. The hatched regions
indicate the total uncertainties in the background predictions. The
(unstacked) results for two example signal scenarios are shown in each
instance, one with $\Delta m\gg 0$ and the other with $\Delta m\approx 0$,
where $\Delta m$ is the difference between the gluino or squark mass and the
sum of the masses of the particles into which it decays.

Figure 12:  One-dimensional projections of the data and pre-fit SM predictions
in either , $N_{\text{jet}}$, or $N_{{\cPqb}\text{-jet}}$ after applying
additional selection criteria, given in the figure legends, to enhance the
sensitivity to the (upper left) T1tttt, (upper right) T1bbbb, (middle left)
T1qqqq, (middle right) T2tt, (lower left) T2bb, and (lower right) T2qq signal
processes. The (unstacked) results for two example signal scenarios are shown
in each instance, one with $\Delta m\gg 0$ and the other with $\Delta m\approx
0$, where $\Delta m$ is the difference between the gluino or squark mass and
the sum of the masses of the particles into which it decays.

Figure 11 presents one-dimensional projections of the data and SM predictions
in , $N_{\text{jet}}$, and $N_{{\cPqb}\text{-jet}}$. Additional projections
are shown in Fig. 12. For these latter results, criteria have been imposed, as
indicated in the legends, to enhance the sensitivity for a particular signal
process. For both Figs. 11 and 12, two example signal distributions are shown:
one with $\Delta m\gg 0$ and one with $\Delta m\approx 0$, where both example
scenarios lie well within the parameter space excluded by the present study.
The notation $\Delta m\gg 0$ means that the mass difference $\Delta m$ is
large compared to the sum of the masses of the particles into which the gluino
or squark decays.

Upper limits are evaluated for the production cross sections of the signal
scenarios using a likelihood fit. The SUSY signal strength $\mu$, defined by
the ratio of cross sections
$\mu\equiv\sigma_{\text{SUSY}}/\sigma_{\text{SM}}$, the signal uncertainties
described in Section 0.8, the predicted SM background contributions shown in
Fig. 10, the uncertainties in these backgrounds listed in Appendix .11, and
the control sample yields are all inputs to the fit. The background
uncertainties, uncertainties in the signal shape and normalization, and
control sample statistical uncertainties are assigned as nuisance parameters,
which are constrained in the fit.

For the models of gluino (squark) pair production, the limits are derived as a
function of $m_{\PSg}$ ($m_{\PSQ}$) and $m_{\PSGczDo}$. All 174 search bins
are used for each choice of the SUSY particle masses. The likelihood function
is given by a product of probability density functions, one for each search
bin. Each of these is a product of Poisson functions for the CR yields and
log-normal constraint functions for the nuisance parameters. Correlations
among bins are taken into account. The signal yield uncertainties associated
with the renormalization and factorization scales, ISR, jet energy scale, jet
tagging, pileup, and statistical fluctuations are evaluated as a function of
$m_{\PSg}$ and $m_{\PSGczDo}$, or $m_{\PSQ}$ and $m_{\PSGczDo}$. The test
statistic is $q_{\mu}=-2\ln(\mathcal{L}_{\mu}/\mathcal{L}_{\text{max}})$,
where $\mathcal{L}_{\text{max}}$ is the maximum likelihood determined by
allowing all parameters including the SUSY signal strength $\mu$ to vary, and
$\mathcal{L}_{\mu}$ is the maximum likelihood for a fixed signal strength.
Limits are set under the asymptotic approximation [99], with $q_{\mu}$
approximated with an Asimov data set and used in conjunction with the
criterion described in Refs. [100, 101].

Figure 13:  The 95% upper limits on the production cross sections of the
(upper left) T1tttt, (upper right) T1bbbb, (lower left) T1qqqq, and (lower
right) T5qqqqVV signal models as a function of the gluino and LSP masses
$m_{\PSg}$ and $m_{\PSGczDo}$. The thick solid (black) curves show the
observed exclusion limits assuming the approximate-NNLO+NNLL cross sections
[73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84]. The thin solid (black)
curves show the changes in these limits as the signal cross sections are
varied by their theoretical uncertainties [102]. The thick dashed (red) curves
present the expected limits under the background-only hypothesis, while the
two sets of thin dotted (red) curves indicate the region containing 68 and 95%
of the distribution of limits expected under this hypothesis.

We evaluate 95% confidence level () upper limits on the signal cross sections.
The approximate NNLO+NNLL cross section is used to determine corresponding
exclusion curves. Before computing these limits, the signal yields are
corrected to account for the predicted signal contamination in the CRs from
the signal model under consideration. Beyond the observed exclusion limits, we
derive expected exclusion limits by evaluating the test statistic using the
predicted numbers of background events with their expected Poisson
fluctuations.

The results for the T1tttt, T1bbbb, T1qqqq, and T5qqqqVV models are shown in
Fig. 13. Depending on the value of $m_{\PSGczDo}$, gluinos with masses as
large as 2180, 2310, 2000, and 2030, respectively, are excluded. These results
significantly extend those of our previous study [8], for which the
corresponding limits are 1960, 1950, 1825, and 1800.

Figure 14:  The 95% upper limits on the production cross sections of the
(upper left) T2tt, (upper right) T2bb, and (lower) T2qq signal models as a
function of the squark and LSP masses $m_{\PSQ}$ and $m_{\PSGczDo}$. The
meaning of the curves is described in the Fig. 13 caption. For the T2tt model,
we do not present cross section upper limits in the unshaded diagonal region
at low $m_{\PSGczDo}$ for the reason discussed in the text. The diagonal
dotted line shown for this model corresponds to
$m_{\sTop}-m_{\PSGczDo}=m_{\PQt}$.

Figure 14 shows the corresponding results for the T2tt, T2bb, and T2qq models.
Squarks with masses up to 1190, 1220, and 1630, respectively, are excluded,
compared to 960, 990, and 1390in our previous study [8]. Note that for the
T2tt model we do not present cross section upper limits at small values of
$m_{\PSGczDo}$ if $m_{\sTop}-m_{\PSGczDo}\approx m_{\PQt}$, corresponding to
the unshaded diagonal region at low $m_{\PSGczDo}$ in Fig. 14 (upper left),
because signal events are essentially indistinguishable from SM events in this
region, resulting in large signal contamination of the CRs and rendering the
signal event acceptance difficult to model.

In addition to the main T2qq model, with four mass-degenerate squark flavors
(up, down, strange, and charm), each arising from two different quark spin
states, Fig. 14 (lower) shows the results should only one of these eight
states (“Single ”) be accessible at the LHC. In this case, the upper limit on
the squark mass is reduced to 1130.

##  0.10 Summary

Using essentially the full CMS Run 2 data sample of proton-proton collisions
at $\sqrt{s}=13\TeV$, corresponding to an integrated luminosity of
137collected in 2016–2018, a search for supersymmetry has been performed based
on events containing multiple jets and large missing transverse momentum. The
event yields are measured in 174 nonoverlapping search bins defined in a four-
dimensional space of missing transverse momentum (), the scalar sum of jet
transverse momenta (), the number of jets, and the number of tagged bottom
quark jets. The events are required to satisfy $\mht>300\gev$, $\HT>300\gev$,
and to have at least two jets with transverse momentum $\pt>30\gev$. Events
with isolated high leptons or photons are vetoed.

The results are compared to the expected number of background events from
standard model (SM) processes. The principal backgrounds arise from events
with neutrino production or jet mismeasurement. The SM background is evaluated
using control regions in data supplemented by information from Monte Carlo
event simulation. The observed event yields are found to be consistent with
the SM background and no evidence for supersymmetry is obtained.

The results are interpreted in the context of simplified models for gluino and
squark pair production. For the gluino models, each of the produced gluinos
decays either to a pair and an undetected, stable, lightest supersymmetric
particle, assumed to be the neutralino (T1tttt model); to a $\bbbar$ pair and
the (T1bbbb model); to a light-flavored (, , , ) pair and the (T1qqqq model);
or to a light-flavored quark and antiquark and either the second-lightest
neutralino or the lightest chargino $\PSGc_{1}^{\pm}$, followed by decay of
the ($\PSGc_{1}^{\pm}$) to the and an on- or off-mass-shell ($\PW^{\pm}$)
boson (T5qqqqVV model). For the squark models, each of the produced squarks
decays either to a top quark and the (T2tt model), to a bottom quark and the
(T2bb model), or to a light-flavored quark and the (T2qq model).

Using the predicted cross sections with next-to-leading order plus approximate
next-to-leading logarithm accuracy as a reference, gluinos with masses as
large as from 2000 to 2310are excluded at 95% confidence level, depending on
the signal model. The corresponding limits on the masses of directly produced
squarks range from 1190 for top squarks to 1630for light-flavored squarks. The
results presented here supersede those of Ref. [8], extending the mass limits
of this previous study by, typically, 200or more.

###### Acknowledgements.

We congratulate our colleagues in the CERN accelerator departments for the
excellent performance of the LHC and thank the technical and administrative
staffs at CERN and at other CMS institutes for their contributions to the
success of the CMS effort. In addition, we gratefully acknowledge the
computing centers and personnel of the Worldwide LHC Computing Grid for
delivering so effectively the computing infrastructure essential to our
analyses. Finally, we acknowledge the enduring support for the construction
and operation of the LHC and the CMS detector provided by the following
funding agencies: BMBWF and FWF (Austria); FNRS and FWO (Belgium); CNPq,
CAPES, FAPERJ, FAPERGS, and FAPESP (Brazil); MES (Bulgaria); CERN; CAS, MoST,
and NSFC (China); COLCIENCIAS (Colombia); MSES and CSF (Croatia); RPF
(Cyprus); SENESCYT (Ecuador); MoER, ERC IUT, PUT and ERDF (Estonia); Academy
of Finland, MEC, and HIP (Finland); CEA and CNRS/IN2P3 (France); BMBF, DFG,
and HGF (Germany); GSRT (Greece); NKFIA (Hungary); DAE and DST (India); IPM
(Iran); SFI (Ireland); INFN (Italy); MSIP and NRF (Republic of Korea); MES
(Latvia); LAS (Lithuania); MOE and UM (Malaysia); BUAP, CINVESTAV, CONACYT,
LNS, SEP, and UASLP-FAI (Mexico); MOS (Montenegro); MBIE (New Zealand); PAEC
(Pakistan); MSHE and NSC (Poland); FCT (Portugal); JINR (Dubna); MON, RosAtom,
RAS, RFBR, and NRC KI (Russia); MESTD (Serbia); SEIDI, CPAN, PCTI, and FEDER
(Spain); MOSTR (Sri Lanka); Swiss Funding Agencies (Switzerland); MST
(Taipei); ThEPCenter, IPST, STAR, and NSTDA (Thailand); TUBITAK and TAEK
(Turkey); NASU and SFFR (Ukraine); STFC (United Kingdom); DOE and NSF (USA).
Individuals have received support from the Marie-Curie program and the
European Research Council and Horizon 2020 Grant, contract Nos. 675440,
752730, and 765710 (European Union); the Leventis Foundation; the A.P. Sloan
Foundation; the Alexander von Humboldt Foundation; the Belgian Federal Science
Policy Office; the Fonds pour la Formation à la Recherche dans l’Industrie et
dans l’Agriculture (FRIA-Belgium); the Agentschap voor Innovatie door
Wetenschap en Technologie (IWT-Belgium); the F.R.S.-FNRS and FWO (Belgium)
under the “Excellence of Science – EOS” – be.h project n. 30820817; the
Beijing Municipal Science & Technology Commission, No. Z181100004218003; the
Ministry of Education, Youth and Sports (MEYS) of the Czech Republic; the
Lendület (“Momentum”) Program and the János Bolyai Research Scholarship of the
Hungarian Academy of Sciences, the New National Excellence Program ÚNKP, the
NKFIA research grants 123842, 123959, 124845, 124850, 125105, 128713, 128786,
and 129058 (Hungary); the Council of Science and Industrial Research, India;
the HOMING PLUS program of the Foundation for Polish Science, cofinanced from
European Union, Regional Development Fund, the Mobility Plus program of the
Ministry of Science and Higher Education, the National Science Center
(Poland), contracts Harmonia 2014/14/M/ST2/00428, Opus 2014/13/B/ST2/02543,
2014/15/B/ST2/03998, and 2015/19/B/ST2/02861, Sonata-bis 2012/07/E/ST2/01406;
the National Priorities Research Program by Qatar National Research Fund; the
Ministry of Science and Education, grant no. 3.2989.2017 (Russia); the
Programa Estatal de Fomento de la Investigación Científica y Técnica de
Excelencia María de Maeztu, grant MDM-2015-0509 and the Programa Severo Ochoa
del Principado de Asturias; the Thalis and Aristeia programs cofinanced by EU-
ESF and the Greek NSRF; the Rachadapisek Sompot Fund for Postdoctoral
Fellowship, Chulalongkorn University and the Chulalongkorn Academic into Its
2nd Century Project Advancement Project (Thailand); the Welch Foundation,
contract C-1845; and the Weston Havens Foundation (USA).

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##  .11 Numerical results for the full set of search bins

In this appendix, we present numerical values for the results in the 174
search bins shown in Fig. 10.

Table 1: Observed number of events and pre-fit background predictions in the
$2\leq N_{\text{jet}}\leq 3$ search bins. For the background predictions, the
first uncertainty is statistical and the second systematic.

Bin |  |  | $N_{\text{jet}}$ | $N_{{\cPqb}\text{-jet}}$ | Lost-lepton | $\cPZ\to\cPgn\cPagn$ | QCD | Total | Observed
---|---|---|---|---|---|---|---|---|---
[] | [] | background | background | background | background
1 | 300–350 | 300–600 | 2–3 | 0 | $38\,870\pm 320\pm 580$ | $89\,100\pm 200\pm 2600$ | $1800\pm 1000^{+1200}_{-800}$ | $129\,800\pm 1100\pm 2800$ | 130 718
2 | 300–350 | 600–1200 | 2–3 | 0 | $2760\pm 61\pm 39$ | $4970\pm 50\pm 150$ | $330\pm 180\pm 160$ | $8060\pm 200\pm 220$ | 7820
3 | 300–350 |  $\geq$1200 | 2–3 | 0 | $181\pm 17\pm 3$ | $308\pm 12\pm 18$ | $62\pm 34\pm 27$ | $552\pm 40\pm 32$ | 514
4 | 350–600 | 350–600 | 2–3 | 0 | $26\,230\pm 240\pm 540$ | $78\,000\pm 200\pm 2200$ | $660\pm 360\pm 300$ | $104\,900\pm 500\pm 2300$ | 100 828
5 | 350–600 | 600–1200 | 2–3 | 0 | $5319\pm 81\pm 78$ | $14\,570\pm 80\pm 430$ | $210\pm 110\pm 100$ | $20\,100\pm 160\pm 450$ | 19 319
6 | 350–600 |  $\geq$1200 | 2–3 | 0 | $279\pm 21\pm 6$ | $689\pm 17^{+41}_{-36}$ | $29\pm 16\pm 13$ | $997\pm 32\pm 40$ | 933
7 | 600–850 | 600–1200 | 2–3 | 0 | $1220\pm 43\pm 25$ | $6290\pm 50\pm 370$ | $11.1\pm 6.0^{+5.4}_{-5.1}$ | $7520\pm 70\pm 360$ | 6786
8 | 600–850 |  $\geq$1200 | 2–3 | 0 | $52\pm 9\pm 2$ | $240\pm 11\pm 15$ | $0.73\pm 0.65^{+0.31}_{-0.07}$ | $293\pm 14\pm 16$ | 277
9 |  $\geq$850 | 850–1700 | 2–3 | 0 | $116\pm 14\pm 3$ | $1088\pm 23\pm 98$ | $0.35\pm 0.21\pm 0.15$ | $1205\pm 28\pm 98$ | 933
10 |  $\geq$850 |  $\geq$1700 | 2–3 | 0 | $1.8^{+4.1}_{-1.5}\pm 0.1$ | $48.9^{+5.3}_{-4.8}\pm 0.5$ | $0.02\pm 0.02^{+0.01}_{-0.00}$ | $50.7^{+6.7}_{-5.0}\pm 5.1$ | 50
11 | 300–350 | 300–600 | 2–3 | 1 | $5590\pm 100\pm 100$ | $9800\pm 20\pm 1500$ | $360\pm 200^{+330}_{-160}$ | $15\,800\pm 200\pm 1500$ | 15 272
12 | 300–350 | 600–1200 | 2–3 | 1 | $436\pm 25\pm 6$ | $616\pm 6\pm 95$ | $99\pm 54^{+79}_{-45}$ | $1150\pm 60\pm 110$ | 1177
13 | 300–350 |  $\geq$1200 | 2–3 | 1 | $27.4^{+7.9}_{-6.3}\pm 0.4$ | $38.4\pm 1.5\pm 6.1$ | $18\pm 10^{+14}_{-8}$ | $84\pm 13^{+15}_{-10}$ | 71
14 | 350–600 | 350–600 | 2–3 | 1 | $3237\pm 75\pm 99$ | $8600\pm 20\pm 1300$ | $124\pm 67^{+96}_{-57}$ | $11\,900\pm 100\pm 1300$ | 11 121
15 | 350–600 | 600–1200 | 2–3 | 1 | $757\pm 32\pm 14$ | $1780\pm 10\pm 270$ | $48\pm 27^{+38}_{-21}$ | $2590\pm 40\pm 270$ | 2530
16 | 350–600 |  $\geq$1200 | 2–3 | 1 | $36.7^{+8.9}_{-7.3}\pm 0.5$ | $86\pm 2\pm 14$ | $9.1\pm 5.0^{+6.9}_{-4.1}$ | $132\pm 10\pm 15$ | 127
17 | 600–850 | 600–1200 | 2–3 | 1 | $162\pm 17\pm 4$ | $710\pm 10\pm 120$ | $2.3\pm 1.3^{+1.8}_{-1.0}$ | $880\pm 20\pm 110$ | 728
18 | 600–850 |  $\geq$1200 | 2–3 | 1 | $2.7^{+3.5}_{-1.7}\pm 0.1$ | $29.5\pm 1.3\pm 4.8$ | $0.12\pm 0.10^{+0.09}_{-0.02}$ | $32.3^{+3.8}_{-2.1}\pm 4.8$ | 31
19 |  $\geq$850 | 850–1700 | 2–3 | 1 | $8.7^{+5.2}_{-3.5}\pm 0.2$ | $124\pm 3\pm 22$ | $0.10\pm 0.07^{+0.07}_{-0.02}$ | $133\pm 5\pm 22$ | 112
20 |  $\geq$850 |  $\geq$1700 | 2–3 | 1 | $0.0^{+3.6}_{-0.0}\pm 0.0$ | $6.0\pm 0.7\pm 1.1$ | $0.03^{+0.04+0.02}_{-0.03-0.00}$ | $6.0^{+3.6}_{-0.6}\pm 1.1$ | 5
21 | 300–350 | 300–600 | 2–3 |  $\geq$2 | $706\pm 37\pm 13$ | $940\pm 2\pm 290$ | $66^{+68+72}_{-66-0}$ | $1710\pm 80\pm 290$ | 1787
22 | 300–350 | 600–1200 | 2–3 |  $\geq$2 | $96\pm 13\pm 1$ | $71\pm 1\pm 22$ | $19\pm 11^{+19}_{-8}$ | $186\pm 18^{+29}_{-23}$ | 148
23 | 300–350 |  $\geq$1200 | 2–3 |  $\geq$2 | $3.5^{+4.7}_{-2.3}\pm 0.1$ | $4.4\pm 0.2\pm 1.4$ | $2.2\pm 1.3^{+2.1}_{-0.9}$ | $10.2^{+4.8+2.5}_{-2.6-1.7}$ | 11
24 | 350–600 | 350–600 | 2–3 |  $\geq$2 | $362\pm 27\pm 14$ | $810\pm 2\pm 250$ | $13\pm 8^{+13}_{-5}$ | $1190\pm 30\pm 250$ | 1159
25 | 350–600 | 600–1200 | 2–3 |  $\geq$2 | $166\pm 18\pm 5$ | $201\pm 1\pm 61$ | $5.1\pm 3.3^{+5.1}_{-1.8}$ | $373\pm 18\pm 62$ | 322
26 | 350–600 |  $\geq$1200 | 2–3 |  $\geq$2 | $6.0^{+4.8}_{-2.9}\pm 0.1$ | $9.9\pm 0.2\pm 3.1$ | $1.5\pm 0.9^{+1.5}_{-0.6}$ | $17.5^{+4.9+3.4}_{-3.1-3.1}$ | 13
27 | 600–850 | 600–1200 | 2–3 |  $\geq$2 | $17.5^{+7.6}_{-5.6}\pm 0.3$ | $72\pm 1\pm 22$ | $0.09\pm 0.09^{+0.09}_{-0.00}$ | $89\pm 7\pm 22$ | 50
28 | 600–850 |  $\geq$1200 | 2–3 |  $\geq$2 | $0.0^{+2.9}_{-0.0}\pm 0.0$ | $3.4\pm 0.1\pm 1.0$ | $0.08\pm 0.08^{+0.07}_{-0.00}$ | $3.4^{+2.9}_{-0.2}\pm 1.0$ | 4
29 |  $\geq$850 | 850–1700 | 2–3 |  $\geq$2 | $0.0^{+4.4}_{-0.0}\pm 0.0$ | $12.5\pm 0.3\pm 4.0$ | $0.09\pm 0.07^{+0.09}_{-0.02}$ | $12.6^{+4.5}_{-0.3}\pm 4.0$ | 9
30 |  $\geq$850 |  $\geq$1700 | 2–3 |  $\geq$2 | $0.0^{+3.7}_{-0.0}\pm 0.0$ | $0.68\pm 0.07\pm 0.22$ | $0.04\pm 0.04^{+0.03}_{-0.00}$ | $0.7^{+3.7}_{-0.1}\pm 0.2$ | 0

Table 2: Observed number of events and pre-fit background predictions in the
$4\leq N_{\text{jet}}\leq 5$ search bins. For the background predictions, the
first uncertainty is statistical and the second systematic.

Bin |  |  | $N_{\text{jet}}$ | $N_{{\cPqb}\text{-jet}}$ | Lost-lepton | $\cPZ\to\cPgn\cPagn$ | QCD | Total | Observed
---|---|---|---|---|---|---|---|---|---
[] | [] | background | background | background | background
31 | 300–350 | 300–600 | 4–5 | 0 | $8720\pm 110\pm 120$ | $13\,930\pm 70\pm 590$ | $630\pm 350^{+410}_{-290}$ | $23\,280\pm 370^{+740}_{-660}$ | 23 241
32 | 300–350 | 600–1200 | 4–5 | 0 | $2990\pm 48\pm 54$ | $3960\pm 40\pm 150$ | $490\pm 260\pm 230$ | $7440\pm 270\pm 280$ | 7277
33 | 300–350 |  $\geq$1200 | 4–5 | 0 | $216\pm 14\pm 5$ | $317\pm 12\pm 18$ | $230\pm 120\pm 100$ | $760\pm 120\pm 100$ | 726
34 | 350–600 | 350–600 | 4–5 | 0 | $5230\pm 90\pm 160$ | $11\,410\pm 70\pm 450$ | $180\pm 100\pm 80$ | $16\,820\pm 150\pm 490$ | 16 720
35 | 350–600 | 600–1200 | 4–5 | 0 | $4654\pm 59\pm 68$ | $9000\pm 60\pm 350$ | $210\pm 110\pm 100$ | $13\,870\pm 140\pm 370$ | 13 837
36 | 350–600 |  $\geq$1200 | 4–5 | 0 | $364\pm 17\pm 6$ | $680\pm 17\pm 37$ | $104\pm 56\pm 45$ | $1148\pm 61\pm 59$ | 1141
37 | 600–850 | 600–1200 | 4–5 | 0 | $428\pm 19\pm 9$ | $1592\pm 25\pm 94$ | $5.1\pm 2.8\pm 2.3$ | $2025\pm 32\pm 94$ | 2028
38 | 600–850 |  $\geq$1200 | 4–5 | 0 | $72.2^{+8.1}_{-7.3}\pm 1.1$ | $225\pm 10\pm 14$ | $1.9\pm 1.1\pm 0.8$ | $299\pm 13\pm 14$ | 291
39 |  $\geq$850 | 850–1700 | 4–5 | 0 | $42.4\pm 6.9\pm 0.8$ | $351\pm 13\pm 32$ | $0.13\pm 0.09\pm 0.5$ | $393\pm 15\pm 32$ | 360
40 |  $\geq$850 |  $\geq$1700 | 4–5 | 0 | $6.1^{+3.3}_{-2.3}\pm 0.1$ | $38.4\pm 4.2\pm 4.4$ | $0.06\pm 0.05^{+0.02}_{-0.01}$ | $44.6^{+5.5}_{-4.6}\pm 4.4$ | 51
41 | 300–350 | 300–600 | 4–5 | 1 | $4217\pm 69\pm 77$ | $2850\pm 15\pm 450$ | $220\pm 120^{+200}_{-100}$ | $7290\pm 140\pm 480$ | 7157
42 | 300–350 | 600–1200 | 4–5 | 1 | $1389\pm 35\pm 23$ | $850\pm 10\pm 130$ | $260\pm 140^{+210}_{-120}$ | $2500\pm 150^{+250}_{-180}$ | 2387
43 | 300–350 |  $\geq$1200 | 4–5 | 1 | $93\pm 10\pm 3$ | $69\pm 3\pm 11$ | $93\pm 50^{+71}_{-43}$ | $255\pm 51^{+72}_{-44}$ | 229
44 | 350–600 | 350–600 | 4–5 | 1 | $2068\pm 50\pm 41$ | $2330\pm 10\pm 370$ | $64\pm 35^{+49}_{-29}$ | $4460\pm 60\pm 370$ | 4317
45 | 350–600 | 600–1200 | 4–5 | 1 | $1777\pm 40\pm 29$ | $1910\pm 10\pm 300$ | $92\pm 50^{+73}_{-42}$ | $3780\pm 70\pm 300$ | 3822
46 | 350–600 |  $\geq$1200 | 4–5 | 1 | $112\pm 11\pm 3$ | $148\pm 4\pm 24$ | $45\pm 24^{+34}_{-21}$ | $305\pm 27^{+42}_{-32}$ | 350
47 | 600–850 | 600–1200 | 4–5 | 1 | $107\pm 11\pm 3$ | $332\pm 5\pm 54$ | $1.8\pm 1.1^{+1.5}_{-0.8}$ | $441\pm 12\pm 54$ | 388
48 | 600–850 |  $\geq$1200 | 4–5 | 1 | $23.1^{+5.5}_{-4.6}\pm 0.4$ | $48.6\pm 2.2\pm 8.0$ | $0.78\pm 0.51^{+0.59}_{-0.27}$ | $72.5\pm 5.5\pm 8.1$ | 74
49 |  $\geq$850 | 850–1700 | 4–5 | 1 | $9.4^{+4.0}_{-3.0}\pm 0.3$ | $73\pm 3\pm 13$ | $0.12\pm 0.09^{+0.09}_{-0.03}$ | $82\pm 5\pm 13$ | 73
50 |  $\geq$850 |  $\geq$1700 | 4–5 | 1 | $1.0^{+2.3}_{-0.8}\pm 0.0$ | $8.3\pm 1.0\pm 1.6$ | $0.03^{+0.04+0.02}_{-0.03-0.00}$ | $9.4^{+2.5}_{-1.2}\pm 1.6$ | 14
51 | 300–350 | 300–600 | 4–5 | 2 | $1806\pm 49\pm 30$ | $468\pm 2\pm 79$ | $68\pm 45^{+74}_{-24}$ | $2340\pm 70^{+110}_{-90}$ | 2505
52 | 300–350 | 600–1200 | 4–5 | 2 | $687\pm 26\pm 10$ | $144\pm 1\pm 24$ | $71\pm 39^{+70}_{-32}$ | $902\pm 47^{+75}_{-41}$ | 864
53 | 300–350 |  $\geq$1200 | 4–5 | 2 | $34.0^{+7.4}_{-6.2}\pm 0.7$ | $12.0\pm 0.4\pm 2.1$ | $24\pm 13^{+23}_{-11}$ | $70\pm 14^{+23}_{-11}$ | 72
54 | 350–600 | 350–600 | 4–5 | 2 | $820\pm 35\pm 20$ | $381\pm 2\pm 64$ | $17\pm 10^{+17}_{-7}$ | $1218\pm 36\pm 68$ | 1208
55 | 350–600 | 600–1200 | 4–5 | 2 | $794\pm 29\pm 12$ | $324\pm 2\pm 54$ | $23\pm 13^{+23}_{-10}$ | $1141\pm 32\pm 58$ | 1180
56 | 350–600 |  $\geq$1200 | 4–5 | 2 | $47.8^{+8.2+1.1}_{-7.2-1.1}$ | $25.6^{+0.6+4.4}_{-0.6-4.4}$ | $12^{+7+12}_{-7-5}$ | $85^{+11+12}_{-10-7}$ | 78
57 | 600–850 | 600–1200 | 4–5 | 2 | $37.1^{+8.0}_{-6.7}\pm 0.7$ | $55.5\pm 0.9\pm 9.6$ | $0.45\pm 0.30^{+0.45}_{-0.16}$ | $93.1^{+8.0}_{-6.8}\pm 9.7$ | 98
58 | 600–850 |  $\geq$1200 | 4–5 | 2 | $8.8^{+5.3}_{-3.5}\pm 0.1$ | $8.4\pm 0.4\pm 1.5$ | $0.20\pm 0.18^{+0.19}_{-0.02}$ | $17.4^{+5.3}_{-3.6}\pm 1.5$ | 15
59 |  $\geq$850 | 850–1700 | 4–5 | 2 | $1.2^{+2.8}_{-1.0}\pm 0.0$ | $12.0\pm 0.4\pm 2.2$ | $0.09\pm 0.07^{+0.09}_{-0.02}$ | $13.3^{+2.8}_{-1.1}\pm 2.2$ | 15
60 |  $\geq$850 |  $\geq$1700 | 4–5 | 2 | $0.0^{+2.6}_{-0.0}\pm 0.0$ | $1.44\pm 0.16\pm 0.28$ | $0.04\pm 0.04^{+0.03}_{-0.00}$ | $1.5^{+2.6}_{-0.1}\pm 0.3$ | 1
61 | 300–350 | 300–600 | 4–5 |  $\geq$3 | $147\pm 15\pm 2$ | $40\pm 0\pm 14$ | $4.4\pm 4.2^{+6.1}_{-0.2}$ | $192\pm 15\pm 15$ | 222
62 | 300–350 | 600–1200 | 4–5 |  $\geq$3 | $76.7\pm 9.0\pm 1.3$ | $13.5\pm 0.1\pm 4.8$ | $9\pm 6^{+12}_{-3}$ | $99\pm 10^{+13}_{-6}$ | 92
63 | 300–350 |  $\geq$1200 | 4–5 |  $\geq$3 | $5.8^{+3.9}_{-2.5}\pm 0.1$ | $1.14\pm 0.04\pm 0.41$ | $3.7\pm 2.2^{+4.7}_{-1.5}$ | $10.6^{+4.5+4.7}_{-3.3-1.5}$ | 5
64 | 350–600 | 350–600 | 4–5 |  $\geq$3 | $73\pm 11\pm 1$ | $33\pm 0\pm 12$ | $1.2\pm 1.1^{+1.6}_{-0.1}$ | $107\pm 11\pm 12$ | 111
65 | 350–600 | 600–1200 | 4–5 |  $\geq$3 | $92^{+11+2}_{-10-2}$ | $30^{+0+11}_{-0-11}$ | $3.2^{+2.0+4.2}_{-2.0-1.2}$ | $125^{+11+12}_{-10-11}$ | 138
66 | 350–600 |  $\geq$1200 | 4–5 |  $\geq$3 | $5.0^{+3.4}_{-2.2}\pm 0.1$ | $2.45\pm 0.06\pm 0.87$ | $1.8\pm 1.2^{+2.3}_{-0.6}$ | $9.3^{+3.6+2.5}_{-2.5-1.1}$ | 5
67 | 600–850 | 600–1200 | 4–5 |  $\geq$3 | $1.3^{+2.9}_{-1.1}\pm 0.0$ | $4.9\pm 0.1\pm 1.8$ | $0.10^{+0.12+0.13}_{-0.10-0.00}$ | $6.3^{+2.9}_{-1.1}\pm 1.8$ | 5
68 | 600–850 |  $\geq$1200 | 4–5 |  $\geq$3 | $0.0^{+2.6}_{-0.0}\pm 0.0$ | $0.79\pm 0.04\pm 0.28$ | $0.10^{+0.12+0.13}_{-0.10-0.00}$ | $0.9^{+2.6}_{-0.1}\pm 0.3$ | 0
69 |  $\geq$850 | 850–1700 | 4–5 |  $\geq$3 | $0.0^{+3.2}_{-0.0}\pm 0.0$ | $1.05\pm 0.04\pm 0.38$ | $0.10\pm 0.09^{+0.13}_{-0.02}$ | $1.2^{+3.2}_{-0.1}\pm 0.4$ | 1
70 |  $\geq$850 |  $\geq$1700 | 4–5 |  $\geq$3 | $0.0^{+2.3}_{-0.0}\pm 0.0$ | $0.13\pm 0.01\pm 0.05$ | $0.04^{+0.05+0.05}_{-0.04-0.00}$ | $0.2^{+2.3}_{-0.0}\pm 0.1$ | 0

Table 3: Observed number of events and pre-fit background predictions in the
$6\leq N_{\text{jet}}\leq 7$ search bins. For the background predictions, the
first uncertainty is statistical and the second systematic.

Bin |  |  | $N_{\text{jet}}$ | $N_{{\cPqb}\text{-jet}}$ | Lost-lepton | $\cPZ\to\cPgn\cPagn$ | QCD | Total | Observed
---|---|---|---|---|---|---|---|---|---
[] | [] | background | background | background | background
71 | 300–350 | 300–600 | 6–7 | 0 | $686\pm 29\pm 11$ | $761\pm 17\pm 63$ | $144\pm 83^{+92}_{-61}$ | $1590\pm 90^{+110}_{-90}$ | 1480
72 | 300–350 | 600–1200 | 6–7 | 0 | $967\pm 25\pm 14$ | $873\pm 18\pm 65$ | $280\pm 140\pm 130$ | $2110\pm 140\pm 150$ | 1993
73 | 300–350 |  $\geq$1200 | 6–7 | 0 | $121.5\pm 8.8\pm 2.8$ | $116.8\pm 7.3\pm 9.2$ | $172\pm 86\pm 74$ | $410\pm 87\pm 75$ | 362
74 | 350–600 | 350–600 | 6–7 | 0 | $353\pm 21\pm 8$ | $514\pm 14\pm 40$ | $33\pm 20\pm 14$ | $901\pm 32\pm 44$ | 847
75 | 350–600 | 600–1200 | 6–7 | 0 | $1219\pm 28\pm 28$ | $1540\pm 20\pm 110$ | $130\pm 65\pm 63$ | $2890\pm 80\pm 130$ | 2842
76 | 350–600 |  $\geq$1200 | 6–7 | 0 | $208\pm 11\pm 4$ | $258\pm 11\pm 18$ | $81\pm 40\pm 35$ | $547\pm 43\pm 39$ | 553
77 | 600–850 | 600–1200 | 6–7 | 0 | $76.1^{+1.0}_{-1.0}\pm 1.0$ | $182\pm 8\pm 15$ | $1.70\pm 0.88\pm 0.81$ | $259\pm 11\pm 15$ | 245
78 | 600–850 |  $\geq$1200 | 6–7 | 0 | $29.7\pm 4.2\pm 0.5$ | $72.8\pm 5.6\pm 5.7$ | $2.3\pm 1.2\pm 1.0$ | $104.8^{+7.4}_{-6.7}\pm 5.8$ | 122
79 |  $\geq$850 | 850–1700 | 6–7 | 0 | $18.5\pm 3.5\pm 0.3$ | $35.2\pm 3.6\pm 3.8$ | $0.10\pm 0.07^{+0.04}_{-0.02}$ | $53.8^{+5.4}_{-4.7}\pm 3.9$ | 55
80 |  $\geq$850 |  $\geq$1700 | 6–7 | 0 | $4.3^{+2.0}_{-1.4}\pm 0.2$ | $12.7\pm 2.3\pm 1.9$ | $0.05\pm 0.04^{+0.02}_{-0.01}$ | $17.0^{+3.2}_{-2.6}\pm 1.9$ | 20
81 | 300–350 | 300–600 | 6–7 | 1 | $675\pm 25\pm 12$ | $248\pm 6\pm 45$ | $42\pm 22^{+27}_{-20}$ | $965\pm 34\pm 53$ | 946
82 | 300–350 | 600–1200 | 6–7 | 1 | $950\pm 26\pm 15$ | $289\pm 6\pm 52$ | $115\pm 58\pm 55$ | $1355\pm 63\pm 77$ | 1282
83 | 300–350 |  $\geq$1200 | 6–7 | 1 | $105.6^{+9.1}_{-8.4}\pm 2.7$ | $39.3\pm 2.5\pm 7.1$ | $57\pm 28\pm 24$ | $201\pm 30\pm 26$ | 197
84 | 350–600 | 350–600 | 6–7 | 1 | $252\pm 16\pm 5$ | $168\pm 5\pm 30$ | $9.5\pm 5.0\pm 4.3$ | $429\pm 18\pm 31$ | 425
85 | 350–600 | 600–1200 | 6–7 | 1 | $1050\pm 28\pm 19$ | $510\pm 8\pm 91$ | $53\pm 27\pm 26$ | $1614\pm 39\pm 96$ | 1521
86 | 350–600 |  $\geq$1200 | 6–7 | 1 | $155\pm 11\pm 4$ | $86\pm 4\pm 15$ | $26\pm 13\pm 11$ | $268\pm 17\pm 20$ | 269
87 | 600–850 | 600–1200 | 6–7 | 1 | $34.7^{+5.4}_{-4.8}\pm 0.6$ | $60\pm 3\pm 11$ | $0.69\pm 0.41^{+0.33}_{-0.28}$ | $95\pm 6\pm 11$ | 90
88 | 600–850 |  $\geq$1200 | 6–7 | 1 | $25.9\pm 4.3\pm 0.4$ | $24.4\pm 1.9\pm 4.4$ | $0.59\pm 0.34\pm 0.25$ | $50.9^{+5.1}_{-4.4}\pm 4.4$ | 49
89 |  $\geq$850 | 850–1700 | 6–7 | 1 | $7.9^{+2.9}_{-2.2}\pm 0.1$ | $11.5\pm 1.1\pm 2.3$ | $0.05\pm 0.04^{+0.02}_{-0.00}$ | $19.4^{+3.2}_{-2.5}\pm 2.3$ | 17
90 |  $\geq$850 |  $\geq$1700 | 6–7 | 1 | $1.5^{+2.0}_{-1.0}\pm 0.0$ | $4.29^{+0.85}_{-0.72}\pm 0.95$ | $0.04^{+0.05+0.02}_{-0.04-0.00}$ | $5.9^{+2.2}_{-1.2}\pm 0.9$ | 7
91 | 300–350 | 300–600 | 6–7 | 2 | $376\pm 19\pm 8$ | $64\pm 2\pm 13$ | $9.8\pm 5.5^{+6.3}_{-4.2}$ | $450\pm 20\pm 16$ | 450
92 | 300–350 | 600–1200 | 6–7 | 2 | $693\pm 23\pm 10$ | $76\pm 2\pm 15$ | $34\pm 17\pm 16$ | $803\pm 28\pm 25$ | 797
93 | 300–350 |  $\geq$1200 | 6–7 | 2 | $46.7^{+6.4}_{-5.7}\pm 0.7$ | $10.5\pm 0.7\pm 2.1$ | $18.7\pm 9.4\pm 8.1$ | $76\pm 11\pm 8$ | 84
94 | 350–600 | 350–600 | 6–7 | 2 | $120\pm 12\pm 2$ | $43.6\pm 1.2\pm 8.9$ | $2.1\pm 1.2\pm 0.9$ | $165\pm 12\pm 9$ | 188
95 | 350–600 | 600–1200 | 6–7 | 2 | $661\pm 23\pm 11$ | $134\pm 2\pm 27$ | $14.6\pm 7.5\pm 7.0$ | $809\pm 24\pm 30$ | 762
96 | 350–600 |  $\geq$1200 | 6–7 | 2 | $66.6\pm 7.3\pm 2.2$ | $22.8\pm 0.9\pm 4.6$ | $7.5\pm 3.8\pm 3.2$ | $96.9\pm 8.3\pm 6.0$ | 106
97 | 600–850 | 600–1200 | 6–7 | 2 | $19.3^{+4.7}_{-3.9}\pm 0.3$ | $15.7\pm 0.7\pm 3.2$ | $0.15\pm 0.10\pm 0.06$ | $35.2\pm 4.3\pm 3.2$ | 32
98 | 600–850 |  $\geq$1200 | 6–7 | 2 | $8.0^{+3.2}_{-2.4}\pm 0.2$ | $6.5\pm 0.5\pm 1.3$ | $0.09\pm 0.07^{+0.04}_{-0.01}$ | $14.5^{+3.3}_{-2.4}\pm 1.3$ | 14
99 |  $\geq$850 | 850–1700 | 6–7 | 2 | $1.8^{+1.7}_{-1.0}\pm 0.0$ | $2.98\pm 0.30\pm 0.65$ | $0.05\pm 0.04^{+0.02}_{-0.01}$ | $4.8^{+1.8}_{-1.0}\pm 0.7$ | 9
100 |  $\geq$850 |  $\geq$1700 | 6–7 | 2 | $0.5^{+1.2}_{-0.4}\pm 0.0$ | $1.15^{+0.23}_{-0.19}\pm 0.28$ | $0.02\pm 0.02^{+0.01}_{-0.00}$ | $1.7^{+1.2}_{-0.5}\pm 0.3$ | 1
101 | 300–350 | 300–600 | 6–7 |  $\geq$3 | $67.8^{+8.8}_{-7.9}\pm 1.6$ | $8.8\pm 0.2\pm 3.7$ | $1.4\pm 1.0^{+0.9}_{-0.4}$ | $78.0\pm 8.5\pm 4.0$ | 86
102 | 300–350 | 600–1200 | 6–7 |  $\geq$3 | $136\pm 11\pm 2$ | $10.5\pm 0.2\pm 4.3$ | $7.4\pm 4.2^{+3.6}_{-3.2}$ | $154\pm 11\pm 6$ | 167
103 | 300–350 |  $\geq$1200 | 6–7 |  $\geq$3 | $15.7^{+4.1}_{-3.4}\pm 0.2$ | $1.44\pm 0.09\pm 0.59$ | $3.9\pm 2.2\pm 1.7$ | $21.1\pm 4.3\pm 1.8$ | 16
104 | 350–600 | 350–600 | 6–7 |  $\geq$3 | $20.6^{+5.3}_{-4.3}\pm 0.5$ | $6.0\pm 0.2\pm 2.5$ | $0.68\pm 0.62^{+0.31}_{-0.07}$ | $27.2^{+5.4}_{-4.4}\pm 2.5$ | 28
105 | 350–600 | 600–1200 | 6–7 |  $\geq$3 | $137\pm 11\pm 4$ | $18.5\pm 0.3\pm 7.6$ | $2.8\pm 1.6\pm 1.3$ | $158\pm 11\pm 9$ | 115
106 | 350–600 |  $\geq$1200 | 6–7 |  $\geq$3 | $15.4^{+4.4}_{-3.5}\pm 0.6$ | $3.1\pm 0.1\pm 1.3$ | $1.7\pm 1.0^{+0.8}_{-0.7}$ | $20.2^{+4.5}_{-3.7}\pm 1.6$ | 23
107 | 600–850 | 600–1200 | 6–7 |  $\geq$3 | $4.1^{+2.5}_{-1.7}\pm 0.0$ | $2.16\pm 0.10\pm 0.89$ | $0.05^{+0.06+0.02}_{-0.05-0.00}$ | $6.3^{+2.5}_{-1.7}\pm 0.9$ | 6
108 | 600–850 |  $\geq$1200 | 6–7 |  $\geq$3 | $2.1^{+2.0}_{-1.1}\pm 0.0$ | $0.89\pm 0.07\pm 0.37$ | $0.07\pm 0.06^{+0.03}_{-0.01}$ | $3.0^{+2.0}_{-1.1}\pm 0.4$ | 2
109 |  $\geq$850 | 850–1700 | 6–7 |  $\geq$3 | $0.0^{+1.2}_{-0.0}\pm 0.0$ | $0.41\pm 0.04\pm 0.17$ | $0.05\pm 0.04^{+0.02}_{-0.01}$ | $0.5^{+1.2}_{-0.1}\pm 0.2$ | 1
110 |  $\geq$850 |  $\geq$1700 | 6–7 |  $\geq$3 | $0.0^{+1.9}_{-0.0}\pm 0.0$ | $0.16\pm 0.03\pm 0.07$ | $0.02\pm 0.02^{+0.01}_{-0.00}$ | $0.2^{+1.9}_{-0.0}\pm 0.1$ | 1

Table 4: Observed number of events and pre-fit background predictions in the
$8\leq N_{\text{jet}}\leq 9$ search bins. For the background predictions, the
first uncertainty is statistical and the second systematic.

Bin |  |  | $N_{\text{jet}}$ | $N_{{\cPqb}\text{-jet}}$ | Lost-lepton | $\cPZ\to\cPgn\cPagn$ | QCD | Total | Observed
---|---|---|---|---|---|---|---|---|---
[] | [] | background | background | background | background
111 | 300–350 | 600–1200 | 8–9 | 0 | $139.5\pm 9.5\pm 1.9$ | $60.0\pm 4.6\pm 9.7$ | $58\pm 29\pm 28$ | $258\pm 31\pm 30$ | 245
112 | 300–350 |  $\geq$1200 | 8–9 | 0 | $31.0\pm 4.3\pm 1.1$ | $25.1\pm 3.5\pm 2.7$ | $57\pm 28\pm 24$ | $113\pm 29\pm 25$ | 88
113 | 350–600 | 600–1200 | 8–9 | 0 | $136.1\pm 9.3\pm 1.7$ | $123\pm 7\pm 14$ | $30\pm 15\pm 14$ | $289\pm 19\pm 20$ | 280
114 | 350–600 |  $\geq$1200 | 8–9 | 0 | $49.9\pm 5.3\pm 0.9$ | $52.2\pm 4.8\pm 5.4$ | $27\pm 14\pm 12$ | $129\pm 16\pm 13$ | 104
115 | 600–850 | 600–1200 | 8–9 | 0 | $6.6^{+2.3}_{-1.8}\pm 0.2$ | $13.9\pm 2.4\pm 1.5$ | $0.37\pm 0.21\pm 0.17$ | $20.9^{+3.5}_{-2.9}\pm 1.5$ | 28
116 | 600–850 |  $\geq$1200 | 8–9 | 0 | $6.1^{+2.1}_{-1.6}\pm 0.1$ | $12.9\pm 2.4\pm 1.6$ | $0.79\pm 0.44\pm 0.34$ | $19.7\pm 3.0\pm 1.6$ | 22
117 |  $\geq$850 | 850–1700 | 8–9 | 0 | $1.1^{+1.1}_{-0.6}\pm 0.0$ | $4.1^{+1.5}_{-1.2}\pm 0.6$ | $0.06\pm 0.04^{+0.03}_{-0.02}$ | $5.3^{+1.9}_{-1.3}\pm 0.6$ | 2
118 |  $\geq$850 |  $\geq$1700 | 8–9 | 0 | $1.5^{+1.2}_{-0.7}\pm 0.1$ | $2.2^{+1.3}_{-0.9}\pm 0.3$ | $0.02\pm 0.02^{+0.01}_{-0.00}$ | $3.7^{+1.8}_{-1.1}\pm 0.3$ | 1
119 | 300–350 | 600–1200 | 8–9 | 1 | $183\pm 11\pm 3$ | $37\pm 3\pm 11$ | $27\pm 13\pm 13$ | $247\pm 18\pm 17$ | 229
120 | 300–350 |  $\geq$1200 | 8–9 | 1 | $43.8\pm 5.3\pm 0.7$ | $13.8\pm 1.9\pm 3.8$ | $24\pm 12\pm 10$ | $82\pm 13\pm 11$ | 68
121 | 350–600 | 600–1200 | 8–9 | 1 | $176\pm 11\pm 3$ | $75\pm 4\pm 21$ | $10.9\pm 5.5\pm 5.3$ | $262\pm 13\pm 22$ | 224
122 | 350–600 |  $\geq$1200 | 8–9 | 1 | $68.4\pm 6.5\pm 1.2$ | $29.5\pm 2.7\pm 8.1$ | $9.8\pm 5.0\pm 4.2$ | $107.8\pm 8.5\pm 9.3$ | 90
123 | 600–850 | 600–1200 | 8–9 | 1 | $3.4^{+2.0}_{-1.4}\pm 0.2$ | $8.7\pm 1.5\pm 2.4$ | $0.10\pm 0.08^{+0.05}_{-0.02}$ | $12.2\pm 2.3\pm 2.4$ | 7
124 | 600–850 |  $\geq$1200 | 8–9 | 1 | $8.3^{+2.8}_{-2.1}\pm 0.1$ | $8.1\pm 1.5\pm 2.3$ | $0.31\pm 0.18\pm 0.12$ | $16.7^{+3.2}_{-2.6}\pm 2.3$ | 15
125 |  $\geq$850 | 850–1700 | 8–9 | 1 | $0.0^{+1.2}_{-0.0}\pm 0.0$ | $2.08^{+0.79}_{-0.59}\pm 0.61$ | $0.05\pm 0.04^{+0.02}_{-0.01}$ | $2.1^{+1.5}_{-0.6}\pm 0.6$ | 2
126 |  $\geq$850 |  $\geq$1700 | 8–9 | 1 | $1.0^{+1.3}_{-0.7}\pm 0.0$ | $1.35^{+0.81}_{-0.54}\pm 0.40$ | $0.02\pm 0.02^{+0.01}_{-0.00}$ | $2.4^{+1.5}_{-0.8}\pm 0.4$ | 2
127 | 300–350 | 600–1200 | 8–9 | 2 | $169\pm 11\pm 4$ | $11.0\pm 0.9\pm 4.1$ | $9.5\pm 4.9\pm 4.6$ | $190\pm 12\pm 7$ | 193
128 | 300–350 |  $\geq$1200 | 8–9 | 2 | $28.9\pm 4.4\pm 0.5$ | $5.5\pm 0.8\pm 1.9$ | $10.1\pm 5.1\pm 4.4$ | $44.6\pm 6.8\pm 4.8$ | 53
129 | 350–600 | 600–1200 | 8–9 | 2 | $146\pm 10\pm 2$ | $23.1\pm 1.3\pm 8.1$ | $4.5\pm 2.4\pm 2.1$ | $174\pm 11\pm 9$ | 158
130 | 350–600 |  $\geq$1200 | 8–9 | 2 | $42.9\pm 5.3\pm 0.9$ | $11.0\pm 1.1\pm 3.9$ | $4.1\pm 2.1\pm 1.8$ | $58.0^{+6.1}_{-5.5}\pm 4.4$ | 74
131 | 600–850 | 600–1200 | 8–9 | 2 | $3.6^{+2.4}_{-1.6}\pm 0.2$ | $2.52\pm 0.44\pm 0.89$ | $0.09\pm 0.08^{+0.04}_{-0.01}$ | $6.2^{+2.5}_{-1.6}\pm 0.9$ | 7
132 | 600–850 |  $\geq$1200 | 8–9 | 2 | $8.0^{+2.9}_{-2.2}\pm 0.3$ | $2.30\pm 0.42\pm 0.82$ | $0.08^{+0.09+0.04}_{-0.08-0.00}$ | $10.4^{+3.0}_{-2.3}\pm 0.9$ | 9
133 |  $\geq$850 | 850–1700 | 8–9 | 2 | $0.7^{+1.6}_{-0.6}\pm 0.0$ | $0.96^{+0.37}_{-0.27}\pm 0.35$ | $0.05\pm 0.04^{+0.02}_{-0.01}$ | $1.7^{+1.6}_{-0.7}\pm 0.3$ | 0
134 |  $\geq$850 |  $\geq$1700 | 8–9 | 2 | $2.5^{+3.3}_{-1.7}\pm 0.1$ | $0.40^{+0.24}_{-0.16}\pm 0.15$ | $0.02\pm 0.02^{+0.01}_{-0.00}$ | $2.9^{+3.4}_{-1.7}\pm 0.2$ | 2
135 | 300–350 | 600–1200 | 8–9 |  $\geq$3 | $46.8^{+6.1}_{-5.5}\pm 0.7$ | $3.8\pm 0.3\pm 2.3$ | $3.7\pm 2.6^{+1.8}_{-1.2}$ | $54.3\pm 6.3\pm 2.9$ | 57
136 | 300–350 |  $\geq$1200 | 8–9 |  $\geq$3 | $17.3^{+4.0}_{-3.3}\pm 0.5$ | $1.26\pm 0.17\pm 0.76$ | $3.6\pm 2.0\pm 1.5$ | $22.2^{+4.4}_{-3.8}\pm 1.8$ | 17
137 | 350–600 | 600–1200 | 8–9 |  $\geq$3 | $44.4\pm 5.6\pm 1.0$ | $7.5\pm 0.4\pm 4.6$ | $1.31\pm 0.81^{+0.63}_{-0.51}$ | $53.2\pm 5.7\pm 4.7$ | 36
138 | 350–600 |  $\geq$1200 | 8–9 |  $\geq$3 | $15.2^{+3.6}_{-2.9}\pm 0.3$ | $2.8\pm 0.3\pm 1.7$ | $1.17\pm 0.68\pm 0.50$ | $19.2\pm 3.3\pm 1.8$ | 23
139 | 600–850 | 600–1200 | 8–9 |  $\geq$3 | $0.0^{+1.7+0.0}_{-0.0-0.0}$ | $0.88^{+0.16+0.54}_{-0.14-0.53}$ | $0.04^{+0.04+0.02}_{-0.04-0.00}$ | $0.9^{+1.7+0.5}_{-0.1-0.5}$ | 2
140 | 600–850 |  $\geq$1200 | 8–9 |  $\geq$3 | $2.7^{+2.2}_{-1.3}\pm 0.1$ | $0.83\pm 0.15\pm 0.51$ | $0.05\pm 0.05^{+0.02}_{-0.00}$ | $3.6^{+2.2}_{-1.3}\pm 0.5$ | 2
141 |  $\geq$850 | 850–1700 | 8–9 |  $\geq$3 | $0.8^{+2.0}_{-0.7}\pm 0.0$ | $0.18^{+0.07}_{-0.05}\pm 0.11$ | $0.05\pm 0.04^{+0.02}_{-0.01}$ | $1.1^{+2.0}_{-0.7}\pm 0.1$ | 0
142 |  $\geq$850 |  $\geq$1700 | 8–9 |  $\geq$3 | $0.0^{+1.8}_{-0.0}\pm 0.0$ | $0.14^{+0.08}_{-0.05}\pm 0.08$ | $0.02\pm 0.02^{+0.01}_{-0.00}$ | $0.2^{+1.8}_{-0.1}\pm 0.1$ | 0

Table 5: Observed number of events and pre-fit background predictions in the
$N_{\text{jet}}\geq 10$ search bins. For the background predictions, the first
uncertainty is statistical and the second systematic.

Bin |  |  | $N_{\text{jet}}$ | $N_{{\cPqb}\text{-jet}}$ | Lost-lepton | $\cPZ\to\cPgn\cPagn$ | QCD | Total | Observed
---|---|---|---|---|---|---|---|---|---
[] | [] | background | background | background | background
143 | 300–350 | 600–1200 |  $\geq$10 | 0 | $5.7^{+2.2}_{-1.7}\pm 0.3$ | $2.9^{+1.3+0.6}_{-1.0-0.5}$ | $7.8\pm 4.5^{+3.7}_{-3.3}$ | $16.4\pm 5.0^{+3.8}_{-3.3}$ | 17
144 | 300–350 |  $\geq$1200 |  $\geq$10 | 0 | $5.7^{+2.5}_{-1.8}\pm 0.2$ | $2.5^{+1.5}_{-1.0}\pm 0.3$ | $12.6\pm 6.3\pm 5.4$ | $20.8^{+7.0}_{-6.7}\pm 5.4$ | 20
145 | 350–600 | 600–1200 |  $\geq$10 | 0 | $6.0^{+2.4}_{-1.8}\pm 0.1$ | $4.2^{+1.6}_{-1.2}\pm 0.6$ | $3.3\pm 1.8\pm 1.5$ | $13.6^{+3.4}_{-2.8}\pm 1.6$ | 12
146 | 350–600 |  $\geq$1200 |  $\geq$10 | 0 | $10.7^{+2.9}_{-2.3}\pm 0.2$ | $6.5^{+2.1}_{-1.6}\pm 0.9$ | $6.0\pm 3.1\pm 2.6$ | $23.2^{+4.7}_{-4.2}\pm 2.8$ | 21
147 | 600–850 | 600–1200 |  $\geq$10 | 0 | $0.19^{+0.44}_{-0.17}\pm 0.00$ | $0.36^{+0.84}_{-0.30}\pm 0.05$ | $0.07\pm 0.07^{+0.03}_{-0.00}$ | $0.63^{+0.95}_{-0.35}\pm 0.05$ | 2
148 | 600–850 |  $\geq$1200 |  $\geq$10 | 0 | $2.0^{+1.6}_{-1.0}\pm 0.0$ | $1.5^{+1.2}_{-0.7}\pm 0.2$ | $0.15\pm 0.13^{+0.06}_{-0.02}$ | $3.6^{+2.0}_{-1.2}\pm 0.2$ | 6
149 |  $\geq$850 | 850–1700 |  $\geq$10 | 0 | $0.0^{+2.3}_{-0.0}\pm 0.0$ | $0.00^{+0.64}_{-0.00}\pm 0.00$ | $0.05\pm 0.04^{+0.02}_{-0.01}$ | $0.0^{+2.4}_{-0.0}\pm 0.0$ | 0
150 |  $\geq$850 |  $\geq$1700 |  $\geq$10 | 0 | $0.00^{+0.91}_{-0.00}\pm 0.00$ | $0.42^{+0.96}_{-0.35}\pm 0.07$ | $0.02\pm 0.02^{+0.01}_{-0.00}$ | $0.4^{+1.3}_{-0.3}\pm 0.1$ | 2
151 | 300–350 | 600–1200 |  $\geq$10 | 1 | $15.2^{+3.3}_{-2.8}\pm 0.2$ | $1.24^{+0.56}_{-0.40}\pm 0.90$ | $4.0\pm 2.1\pm 1.9$ | $20.4^{+4.0}_{-3.5}\pm 2.1$ | 22
152 | 300–350 |  $\geq$1200 |  $\geq$10 | 1 | $11.2^{+3.2}_{-2.6}\pm 0.4$ | $1.05^{+0.63}_{-0.42}\pm 0.76$ | $6.9\pm 3.5\pm 3.0$ | $19.2^{+4.8}_{-4.4}\pm 3.1$ | 18
153 | 350–600 | 600–1200 |  $\geq$10 | 1 | $13.8^{+3.3}_{-2.7}\pm 0.3$ | $1.8^{+0.7}_{-0.5}\pm 1.3$ | $1.53\pm 0.85^{+0.74}_{-0.68}$ | $17.1^{+3.5}_{-2.9}\pm 1.5$ | 9
154 | 350–600 |  $\geq$1200 |  $\geq$10 | 1 | $16.2^{+3.4}_{-2.9}\pm 0.4$ | $2.7^{+0.9}_{-0.7}\pm 2.0$ | $2.6\pm 1.3\pm 1.1$ | $21.5^{+3.8}_{-3.2}\pm 2.3$ | 32
155 | 600–850 | 600–1200 |  $\geq$10 | 1 | $0.0^{+3.6}_{-0.0}\pm 0.0$ | $0.15^{+0.35+0.11}_{-0.13-0.09}$ | $0.04\pm 0.04^{+0.02}_{-0.00}$ | $0.2^{+3.6}_{-0.1}\pm 0.1$ | 0
156 | 600–850 |  $\geq$1200 |  $\geq$10 | 1 | $1.3^{+1.3}_{-0.7}\pm 0.0$ | $0.61^{+0.49}_{-0.29}\pm 0.44$ | $0.06\pm 0.05^{+0.03}_{-0.01}$ | $2.0^{+1.4+0.5}_{-0.8-0.4}$ | 3
157 |  $\geq$850 | 850–1700 |  $\geq$10 | 1 | $0.0^{+3.2}_{-0.0}\pm 0.0$ | $0.00^{+0.27}_{-0.00}\pm 0.00$ | $0.05\pm 0.04^{+0.02}_{-0.01}$ | $0.0^{+3.2}_{-0.0}\pm 0.0$ | 0
158 |  $\geq$850 |  $\geq$1700 |  $\geq$10 | 1 | $0.7^{+1.5}_{-0.6}\pm 0.0$ | $0.18^{+0.41+0.13}_{-0.15-0.10}$ | $0.03^{+0.04+0.01}_{-0.03-0.00}$ | $0.9^{+1.6}_{-0.6}\pm 0.1$ | 1
159 | 300–350 | 600–1200 |  $\geq$10 | 2 | $13.1^{+3.2}_{-2.6}\pm 0.3$ | $0.38^{+0.18+0.42}_{-0.13-0.36}$ | $2.1\pm 1.5^{+1.0}_{-0.6}$ | $15.5^{+3.5+1.1}_{-3.0-0.8}$ | 15
160 | 300–350 |  $\geq$1200 |  $\geq$10 | 2 | $10.8^{+3.0}_{-2.4}\pm 0.4$ | $0.33^{+0.19+0.36}_{-0.13-0.30}$ | $3.3\pm 1.7\pm 1.4$ | $14.4^{+3.5}_{-3.0}\pm 1.5$ | 11
161 | 350–600 | 600–1200 |  $\geq$10 | 2 | $18.2^{+3.8}_{-3.2}\pm 0.3$ | $0.55^{+0.21+0.60}_{-0.16-0.53}$ | $0.77\pm 0.52^{+0.37}_{-0.26}$ | $19.5\pm 3.5\pm 0.7$ | 11
162 | 350–600 |  $\geq$1200 |  $\geq$10 | 2 | $13.7^{+3.2}_{-2.6}\pm 0.3$ | $0.85^{+0.27+0.92}_{-0.21-0.82}$ | $1.15\pm 0.66\pm 0.50$ | $15.7^{+3.3}_{-2.7}\pm 1.0$ | 12
163 | 600–850 | 600–1200 |  $\geq$10 | 2 | $1.6^{+2.2}_{-1.2}\pm 0.0$ | $0.05^{+0.11+0.05}_{-0.04-0.03}$ | $0.04\pm 0.04^{+0.02}_{-0.00}$ | $1.7^{+2.2+0.1}_{-1.2-0.0}$ | 0
164 | 600–850 |  $\geq$1200 |  $\geq$10 | 2 | $0.9^{+1.2}_{-0.6}\pm 0.0$ | $0.19^{+0.15+0.21}_{-0.09-0.17}$ | $0.06\pm 0.05^{+0.03}_{-0.01}$ | $1.2^{+1.2}_{-0.6}\pm 0.2$ | 0
165 |  $\geq$850 | 850–1700 |  $\geq$10 | 2 | $0.0^{+2.4}_{-0.0}\pm 0.0$ | $0.00^{+0.08}_{-0.00}\pm 0.00$ | $0.05\pm 0.04^{+0.02}_{-0.01}$ | $0.0^{+2.4}_{-0.0}\pm 0.0$ | 0
166 |  $\geq$850 |  $\geq$1700 |  $\geq$10 | 2 | $0.0^{+1.5}_{-0.0}\pm 0.0$ | $0.05^{+0.13+0.06}_{-0.04-0.03}$ | $0.02\pm 0.02^{+0.01}_{-0.00}$ | $0.1^{+1.5+0.1}_{-0.0-0.0}$ | 0
167 | 300–350 | 600–1200 |  $\geq$10 |  $\geq$3 | $6.4^{+2.4}_{-1.8}\pm 0.1$ | $0.36^{+0.17+0.41}_{-0.12-0.34}$ | $0.46\pm 0.32^{+0.22}_{-0.14}$ | $7.2^{+2.4}_{-1.8}\pm 0.4$ | 13
168 | 300–350 |  $\geq$1200 |  $\geq$10 |  $\geq$3 | $3.8^{+2.1}_{-1.4}\pm 0.1$ | $0.31^{+0.19+0.35}_{-0.12-0.28}$ | $1.50\pm 0.87\pm 0.64$ | $5.6^{+2.3}_{-1.7}\pm 0.7$ | 5
169 | 350–600 | 600–1200 |  $\geq$10 |  $\geq$3 | $1.6^{+1.5}_{-0.9}\pm 0.0$ | $0.52^{+0.20+0.59}_{-0.15-0.50}$ | $0.11^{+0.12+0.05}_{-0.11-0.00}$ | $2.2^{+1.6+0.6}_{-0.9-0.5}$ | 3
170 | 350–600 |  $\geq$1200 |  $\geq$10 |  $\geq$3 | $4.2^{+2.1}_{-1.4}\pm 0.1$ | $0.81^{+0.26+0.90}_{-0.20-0.78}$ | $0.71\pm 0.44^{+0.31}_{-0.27}$ | $5.7^{+2.1+0.9}_{-1.5-0.8}$ | 9
171 | 600–850 | 600–1200 |  $\geq$10 |  $\geq$3 | $0.0^{+3.0}_{-0.0}\pm 0.0$ | $0.05^{+0.10+0.05}_{-0.04-0.03}$ | $0.04\pm 0.04^{+0.02}_{-0.00}$ | $0.1^{+3.0+0.1}_{-0.1-0.0}$ | 0
172 | 600–850 |  $\geq$1200 |  $\geq$10 |  $\geq$3 | $0.0^{+1.4}_{-0.0}\pm 0.0$ | $0.18^{+0.14+0.20}_{-0.09-0.16}$ | $0.04\pm 0.04^{+0.02}_{-0.00}$ | $0.2^{+1.4}_{-0.1}\pm 0.2$ | 1
173 |  $\geq$850 | 850–1700 |  $\geq$10 |  $\geq$3 | $0.0^{+2.0}_{-0.0}\pm 0.0$ | $0.00^{+0.08}_{-0.00}\pm 0.00$ | $0.05\pm 0.04^{+0.02}_{-0.01}$ | $0.0^{+2.0}_{-0.0}\pm 0.0$ | 0
174 |  $\geq$850 |  $\geq$1700 |  $\geq$10 |  $\geq$3 | $0.0^{+1.3}_{-0.0}\pm 0.0$ | $0.05^{+0.12+0.06}_{-0.04-0.03}$ | $0.02\pm 0.02^{+0.01}_{-0.00}$ | $0.1^{+1.3+0.1}_{-0.0-0.0}$ | 0

##  .12 Aggregate search bins

To simplify the results from the full set of search bins, we present in this
appendix the observed number of events and corresponding SM background
prediction in 12 aggregate search bins, obtained by summing the results from
the nominal search bins while taking correlations into account. The aggregate
bins are intended to represent 12 general topologies of interest, as indicated
in Table 6. The intervals used to define the aggregate bins are optimized
using the signal models described in this paper. The definitions of the
aggregate bins, along with the corresponding background predictions and
observed event counts, are given in Table 7. The corresponding data are
presented in Fig. 15.

Table 6: Targeted event topologies for the 12 aggregate search bins. The variable $\Delta m$ states the difference between the gluino or squark mass and the sum of the masses of the particles into which the gluino or squark decays.  Bin | Parton multiplicity | Heavy flavor | $\Delta m$
---|---|---|---
1 | Low | No | Small
2 | Low | No | Large
3 | Medium | No | Small
4 | Medium | No | Large
5 | High | No | All
6 | Low | Yes | Small
7 | Low | Yes | Large
8 | Medium | Yes | Small
9 | Medium | Yes | Large
10 | High | Yes | Small
11 | High | Yes | Large
12 | High | Yes | All
Table 7:  Selection criteria, pre-fit background predictions, and observed
number of events for the 12 aggregate search bins. For the background
predictions, the first uncertainty is statistical and the second systematic.

Bin |  |  | $N_{\text{jet}}$ | $N_{{\cPqb}\text{-jet}}$ | Lost-lepton | $\cPZ\to\cPgn\cPagn$ | QCD | Total | Observed
---|---|---|---|---|---|---|---|---|---
[] | [] | background | background | background | background
1 |  $\geq$600 |  $\geq$600 |  $\geq$2 | $0$ | $2087\pm 51\pm 28$ | $10\,210\pm 70\pm 440$ | $25.0\pm 7.0\pm 9.8$ | $12\,320\pm 80\pm 450$ | 11 281
2 |  $\geq$850 |  $\geq$1700 |  $\geq$4 | $0$ | $11.9^{+4.1}_{-2.8}\pm 0.2$ | $53.7\pm 5.0\pm 4.8$ | $0.15\pm 0.07\pm 0.04$ | $65.8^{+6.7}_{-5.4}\pm 4.9$ | 74
3 |  $\geq$600 |  $\geq$600 |  $\geq$6 | $0$ | $146\pm 10\pm 2$ | $338\pm 12\pm 18$ | $5.7\pm 1.6\pm 2.1$ | $489\pm 15\pm 18$ | 505
4 |  $\geq$600 |  $\geq$600 |  $\geq$8 |  $0$–$1$ | $17.6^{+4.6}_{-2.8}\pm 0.2$ | $35.2^{+4.6}_{-3.5}\pm 2.5$ | $1.51\pm 0.51\pm 0.56$ | $54.3^{+6.5}_{-4.5}\pm 2.5$ | 63
5 |  $\geq$850 |  $\geq$1700 |  $\geq$10 |  $0$–$1$ | $17.9^{+7.8}_{-3.5}\pm 0.2$ | $122.7^{+9.1}_{-7.9}\pm 8.8$ | $0.33\pm 0.11\pm 0.10$ | $141^{+12}_{-9}\pm 9$ | 153
6 |  $\geq$300 |  $\geq$300 |  $\geq$4 |  $\geq$2 | $7630\pm 90\pm 99$ | $2070\pm 10\pm 160$ | $390\pm 70\pm 270$ | $10\,090\pm 120\pm 330$ | 10 216
7 |  $\geq$600 |  $\geq$600 |  $\geq$2 |  $\geq$2 | $122^{+19}_{-12}\pm 2$ | $211\pm 2\pm 26$ | $2.6\pm 0.5\pm 1.6$ | $336^{+19}_{-12}\pm 26$ | 287
8 |  $\geq$350 |  $\geq$350 |  $\geq$6 |  $\geq$2 | $1362\pm 33\pm 17$ | $314\pm 4\pm 41$ | $45\pm 9\pm 16$ | $1720\pm 35\pm 47$ | 1637
9 |  $\geq$600 |  $\geq$600 |  $\geq$4 |  $\geq$2 | $105^{+16}_{-10}\pm 1$ | $123\pm 2\pm 12$ | $2.3\pm 0.5\pm 1.4$ | $230^{+16}_{-10}\pm 12$ | 224
10 |  $\geq$300 |  $\geq$300 |  $\geq$8 |  $\geq$3 | $143^{+12}_{-9}\pm 2$ | $19.6\pm 0.7\pm 9.8$ | $12.8\pm 3.5\pm 4.7$ | $176^{+13}_{-10}\pm 11$ | 168
11 |  $\geq$600 |  $\geq$600 |  $\geq$6 |  $\geq$1 | $141^{+15}_{-10}\pm 2$ | $160\pm 6\pm 16$ | $3.2\pm 0.6\pm 1.1$ | $304^{+16}_{-11}\pm 16$ | 282
12 |  $\geq$850 |  $\geq$850 |  $\geq$10 |  $\geq$3 | $0.0^{+2.4}_{-0.0}\pm 0.0$ | $0.05^{+0.14+0.06}_{-0.04-0.01}$ | $0.07\pm 0.04^{+0.03}_{-0.02}$ | $0.1^{+2.4+0.1}_{-0.1-0.0}$ | 0

Figure 15:  The observed numbers of events and pre-fit SM background
predictions in the aggregate search bins. The total background uncertainty is
shown by the hatched regions. The lower panel displays the fractional
differences between the data and the SM predictions.

##  .13 The CMS Collaboration

Yerevan Physics Institute, Yerevan, Armenia
A.M. Sirunyan${}^{\textrm{\textdagger}}$, A. Tumasyan Institut für
Hochenergiephysik, Wien, Austria
W. Adam, F. Ambrogi, T. Bergauer, J. Brandstetter, M. Dragicevic, J. Erö, A.
Escalante Del Valle, M. Flechl, R. Frühwirth1, M. Jeitler1, N. Krammer, I.
Krätschmer, D. Liko, T. Madlener, I. Mikulec, N. Rad, J. Schieck1, R.
Schöfbeck, M. Spanring, D. Spitzbart, W. Waltenberger, C.-E. Wulz1, M. Zarucki
Institute for Nuclear Problems, Minsk, Belarus
V. Drugakov, V. Mossolov, J. Suarez Gonzalez Universiteit Antwerpen,
Antwerpen, Belgium
M.R. Darwish, E.A. De Wolf, D. Di Croce, X. Janssen, A. Lelek, M. Pieters, H.
Rejeb Sfar, H. Van Haevermaet, P. Van Mechelen, S. Van Putte, N. Van Remortel
Vrije Universiteit Brussel, Brussel, Belgium
F. Blekman, E.S. Bols, S.S. Chhibra, J. D’Hondt, J. De Clercq, D. Lontkovskyi,
S. Lowette, I. Marchesini, S. Moortgat, Q. Python, K. Skovpen, S. Tavernier,
W. Van Doninck, P. Van Mulders Université Libre de Bruxelles, Bruxelles,
Belgium
D. Beghin, B. Bilin, H. Brun, B. Clerbaux, G. De Lentdecker, H. Delannoy, B.
Dorney, L. Favart, A. Grebenyuk, A.K. Kalsi, A. Popov, N. Postiau, E.
Starling, L. Thomas, C. Vander Velde, P. Vanlaer, D. Vannerom Ghent
University, Ghent, Belgium
T. Cornelis, D. Dobur, I. Khvastunov2, M. Niedziela, C. Roskas, D. Trocino, M.
Tytgat, W. Verbeke, B. Vermassen, M. Vit, N. Zaganidis Université Catholique
de Louvain, Louvain-la-Neuve, Belgium
O. Bondu, G. Bruno, C. Caputo, P. David, C. Delaere, M. Delcourt, A.
Giammanco, V. Lemaitre, A. Magitteri, J. Prisciandaro, A. Saggio, M. Vidal
Marono, P. Vischia, J. Zobec Centro Brasileiro de Pesquisas Fisicas, Rio de
Janeiro, Brazil
F.L. Alves, G.A. Alves, G. Correia Silva, C. Hensel, A. Moraes, P. Rebello
Teles Universidade do Estado do Rio de Janeiro, Rio de Janeiro, Brazil
E. Belchior Batista Das Chagas, W. Carvalho, J. Chinellato3, E. Coelho, E.M.
Da Costa, G.G. Da Silveira4, D. De Jesus Damiao, C. De Oliveira Martins, S.
Fonseca De Souza, L.M. Huertas Guativa, H. Malbouisson, J. Martins5, D. Matos
Figueiredo, M. Medina Jaime6, M. Melo De Almeida, C. Mora Herrera, L. Mundim,
H. Nogima, W.L. Prado Da Silva, L.J. Sanchez Rosas, A. Santoro, A. Sznajder,
M. Thiel, E.J. Tonelli Manganote3, F. Torres Da Silva De Araujo, A. Vilela
Pereira Universidade Estadual Paulista a, Universidade Federal do ABC b, São
Paulo, Brazil
C.A. Bernardesa, L. Calligarisa, T.R. Fernandez Perez Tomeia, E.M. Gregoresb,
D.S. Lemos, P.G. Mercadanteb, S.F. Novaesa, SandraS. Padulaa Institute for
Nuclear Research and Nuclear Energy, Bulgarian Academy of Sciences, Sofia,
Bulgaria
A. Aleksandrov, G. Antchev, R. Hadjiiska, P. Iaydjiev, M. Misheva, M. Rodozov,
M. Shopova, G. Sultanov University of Sofia, Sofia, Bulgaria
M. Bonchev, A. Dimitrov, T. Ivanov, L. Litov, B. Pavlov, P. Petkov Beihang
University, Beijing, China
W. Fang7, X. Gao7, L. Yuan Institute of High Energy Physics, Beijing, China
G.M. Chen, H.S. Chen, M. Chen, C.H. Jiang, D. Leggat, H. Liao, Z. Liu, A.
Spiezia, J. Tao, E. Yazgan, H. Zhang, S. Zhang8, J. Zhao State Key Laboratory
of Nuclear Physics and Technology, Peking University, Beijing, China
A. Agapitos, Y. Ban, G. Chen, A. Levin, J. Li, L. Li, Q. Li, Y. Mao, S.J.
Qian, D. Wang, Q. Wang Tsinghua University, Beijing, China
M. Ahmad, Z. Hu, Y. Wang Zhejiang University - Department of Physics
M. Xiao Universidad de Los Andes, Bogota, Colombia
C. Avila, A. Cabrera, C. Florez, C.F. González Hernández, M.A. Segura Delgado
Universidad de Antioquia, Medellin, Colombia
J. Mejia Guisao, J.D. Ruiz Alvarez, C.A. Salazar González, N. Vanegas Arbelaez
University of Split, Faculty of Electrical Engineering, Mechanical Engineering
and Naval Architecture, Split, Croatia