HIG-17-012

$HeadURL:svn+ssh://svn.cern.ch/reps/tdr2/papers/HIG-17-012/trunk/HIG-17-012.tex$
$Id:HIG-17-012.tex4673432018-07-0409:09:29Zcovarell$

HIG-17-012

# Search for a new scalar resonance decaying to a pair of bosons in proton-
proton collisions at $\sqrt{s}=13\TeV$

###### Abstract

A search for a new scalar resonance decaying to a pair of $\cPZ$ bosons is
performed in the mass range from 130to 3, and for various width scenarios. The
analysis is based on proton-proton collisions recorded by the CMS experiment
at the LHC in 2016, corresponding to an integrated luminosity of 35.9at a
center-of-mass energy of 13. The $\cPZ$ boson pair decays are reconstructed
using the $4\ell$, $2\ell 2\cPq$, and $2\ell 2\nu$ final states, where
$\ell=\Pe$ or . Both gluon fusion and electroweak production of the scalar
resonance are considered, with a free parameter describing their relative
cross sections. A dedicated categorization of events, based on the kinematic
properties of associated jets, and matrix element techniques are employed for
an optimal signal and background separation. A description of the interference
between signal and background amplitudes for a resonance of an arbitrary width
is included. No significant excess of events with respect to the standard
model expectation is observed and limits are set on the product of the cross
section for a new scalar boson and the branching fraction for its decay to
$\cPZ\cPZ$ for a large range of masses and widths.

##  0.1 Introduction

The standard model (SM) of particle physics postulates the existence of a
single Higgs boson as the manifestation of a scalar field responsible for
electroweak (EW) symmetry breaking [1, 2, 3, 4, 5, 6, 7]. The ATLAS and CMS
Collaborations have discovered a boson with a mass close to 125 [8, 9, 10]
with properties consistent with those expected for the SM Higgs boson [11, 12,
13, 14, 15], and no other fundamental particle that would require explanation
beyond the SM (BSM) has been discovered to date. Nonetheless, searches for BSM
physics are motivated by a number of phenomena such as the presence of dark
matter or baryon asymmetry in the universe that are not explained by the SM.
Extensions of the SM that attempt to address these questions include two-
Higgs-doublet models (2HDM) [16], of which supersymmetry is an example, or
other models predicting an extended Higgs-like EW singlet [17]. In the
following, we denote the recently discovered scalar boson as $\PH(125)$. The
search for a heavy scalar partner of the $\PH(125)$, which we will generically
denote as $\mathrm{X}$, is the subject of this paper.

The $\cPZ\cPZ$ decay has a sizable branching fraction for a SM-like Higgs
boson for masses larger than the $\cPZ$ boson pair production threshold,
$2m_{\cPZ}$, and is one of the main discovery channels for masses less than
$2m_{\cPZ}$ [8, 9, 10]. Since the mass of a new state $\mathrm{X}$ is unknown,
the search is performed over a wide range of masses from 130up to 3. Three
final states are considered: $4\ell$, $2\ell 2\cPq$, and $2\ell 2\nu$, with
$\ell=\Pe$ or . Previous searches for a new boson decaying to $\cPZ\cPZ$ or
$\PW\PW$ pairs have been reported by the CMS [18] and ATLAS [19, 20]
Collaborations at the CERN LHC, using proton-proton collisions recorded at
center-of-mass energies of 7 and 8, where no significant excess was observed.
A data set of proton-proton collisions recorded at a center-of-mass energy of
13by the CMS experiment in 2016 is used in this analysis, corresponding to an
integrated luminosity of $35.9\fbinv$.

The approach adopted in this analysis treats a new $\mathrm{X}$ boson in a
model-independent way. For any given mass $m_{\mathrm{X}}$ of the $\mathrm{X}$
boson, both its width $\Gamma_{\mathrm{X}}$ and production mechanism are
assumed to be unknown. In this analysis, $m_{\mathrm{X}}$ and
$\Gamma_{\mathrm{X}}$ refer to the mass and width of the scalar boson that
enter the propagator. No modification from the complex-pole scheme [21, 22] is
considered. The two dominant production mechanisms of a scalar boson are gluon
fusion ($\Pg\Pg\mathrm{F}$) and EW production, the latter dominated by vector
boson fusion (VBF) with a small contribution of production in association with
an EW boson $\cPZ\PH$ or $\PW\PH$ ($\mathrm{V}\PH$). We define the parameter
$f_{\mathrm{VBF}}$ as the fraction of the EW production cross section with
respect to the total cross section. The three parameters $m_{\mathrm{X}}$,
$\Gamma_{\mathrm{X}}$, and $f_{\mathrm{VBF}}$ are scanned over a wide range of
allowed phase space, and limits are set on the
$\Pp\Pp\to\mathrm{X}\to\cPZ\cPZ$ cross section.

The new state $\mathrm{X}$ can potentially have a large value
$\Gamma_{\mathrm{X}}$: in this case, there is sizable interference between the
$\mathrm{X}\to\cPZ\cPZ\to 4\textrm{f}$ amplitude and that of the SM background
process $\cPZ\cPZ/\cPZ\gamma^{*}\to 4\textrm{f}$, where f denotes any fermion.
The interference distorts both the kinematic distributions and overall yield
of the BSM contribution. The SM background includes the contribution from the
$\PH(125)\to\cPZ\cPZ\to 4\textrm{f}$ decays, which yields a nonnegligible off-
shell contribution above the $2m_{\cPZ}$ threshold [21]. The above
interference effect is present in both $\Pg\Pg\mathrm{F}$ and EW processes and
is taken into account in this analysis. The reported cross-section limits
correspond to the signal-only contribution as it would be in the absence of
interference. A novel feature in this analysis is the inclusion of all of the
above effects in a parametric way in a likelihood fit to the data. The matrix
element (ME) formalism is used both for the parameterization of the likelihood
and for the construction of the observables optimal for event categorization.

The paper is organized as follows. In Section 0.2, the CMS detector and event
reconstruction techniques are presented. Monte Carlo (MC) simulation of the
signal and background processes is described in Section 0.3. Matrix element
methods are discussed in Section 0.4. Event selection and categorization in
each channel are presented in Section 0.5. Modeling of the signal
distributions and background estimation techniques are described in Section
0.6. Systematic uncertainties are summarized in Section 0.7. In Section 0.8
results are presented, and we conclude in Section 0.9.

##  0.2 The CMS detector and event reconstruction

The CMS detector comprises a silicon pixel and strip tracker, a lead tungstate
crystal electromagnetic calorimeter (ECAL), and a brass and scintillator
hadron calorimeter (HCAL), each composed of a barrel and two endcap sections,
all within a superconducting solenoid of 6m internal diameter and providing a
magnetic field of 3.8T. Outside of the solenoid are the gas-ionization
detectors for muon measurements, which are embedded in the steel flux-return
yoke outside the solenoid. The detection layers are made using three
technologies: drift tubes, cathode strip chambers, and resistive-plate
chambers. Extensive forward calorimetry complements the coverage provided by
the barrel and endcap detectors. A more detailed description of the CMS
detector, together with a definition of the coordinate system and the relevant
kinematic variables used, can be found in Ref. [23].

The particle-flow (PF) event algorithm [24] reconstructs and identifies each
individual particle with an optimized combination of information from the
various elements of the CMS detector. The reconstructed vertex with the
largest value of summed physics-object $\pt^{2}$ is taken to be the primary
$\Pp\Pp$ interaction vertex. The physics objects are the jets, clustered using
the jet finding algorithm [25, 26] with the tracks assigned to the vertex as
inputs, and the associated missing transverse momentum, taken as the negative
vector sum of the of those jets. The energy of photons is obtained from the
ECAL measurement, corrected for zero-suppression effects. The energy of
electrons is determined from a combination of the electron momentum at the
primary interaction vertex as determined by the tracker, the energy of the
corresponding ECAL cluster, and the energy sum of all bremsstrahlung photons
spatially compatible with originating from the electron track. The momentum of
muons is obtained from the curvature of the corresponding tracks in the
tracker and the muon systems [27]. The energy of charged hadrons is determined
from a combination of their momentum measured in the tracker and the matching
ECAL and HCAL energy deposits, corrected for zero-suppression effects and for
the response function of the calorimeters to hadronic showers. Finally, the
energy of neutral hadrons is obtained from the corresponding corrected ECAL
and HCAL energy. The missing transverse momentum vector is defined as the
projection onto the plane perpendicular to the beam axis of the negative
vector sum of the momenta of all reconstructed particle-flow objects in an
event. Its magnitude is referred to as . The correction mentioned above also
applies to the determination of .

Collision events are selected by high-level trigger algorithms [28] that
require the presence of leptons passing loose identification and isolation
requirements. The main triggers for this analysis select a pair of electrons
or muons. Triggers selecting an pair are also used for the $4\ell$ channel and
in control samples for $2\ell 2\Pq$ and $2\ell 2\nu$. The minimal of the
leading electron (muon) is 23 (17), while that of the subleading lepton is 12
(8). Isolated single-electron (muon) triggers with minimal of 27 (22)are also
employed to complement the double-lepton triggers.

Electrons are measured in the ECAL in the pseudorapidity range
$\abs{\eta}<2.4$. The momentum resolution for electrons with $\pt\approx
45\GeV$ from $\cPZ\to\Pe\Pe$ decays ranges from 1.7% for nonshowering
electrons in the barrel region to 4.5% for showering electrons in the endcaps
[29]. Muons are measured in the range $\abs{\eta}<2.4$. Muons are
reconstructed by combining information from the silicon tracker and the muon
system [27]. The matching between the inner and outer tracks proceeds either
outside-in, starting from a track in the muon system, or inside-out, starting
from a track in the silicon tracker. In the latter case, tracks that match
track segments in one or two (out of four) layers of the muon system are also
considered in the analysis to collect very low muons that may not have
sufficient energy to penetrate the entire muon system. Matching muons to
tracks measured in the silicon tracker results in a relative resolution for
muons with $20<\pt<100\GeV$ of 1.3–2.0% in the barrel and better than 6% in
the endcaps. The resolution in the barrel is better than 10% for muons with up
to 1 [27].

Hadronic jets are clustered from the four-momenta of the particles in a jet
reconstructed by the PF algorithm, using the software package [26]. Jets are
clustered using the anti-algorithm [25] with a distance parameter equal either
to 0.4 (“AK4 jets”) or 0.8 (“AK8 jets”). Charged PF constituents not
associated with the primary vertex are not used in the jet clustering
procedure.

Jet energy momentum is determined as the vectorial sum of all particle four-
momenta in the jet. Jets are reconstructed in the range $\abs{\eta}<4.7$. An
offset correction is applied to jet energy momenta to account for the
contribution from additional proton proton interactions in the same or
neighboring bunch crossings (pileup). These corrections are derived from
simulation, and are confirmed with in situ measurements of the energy momentum
balance in dijet, multijet, $\gamma+\text{jet}$ and leptonically decaying
$\cPZ+\text{jets}$ events [30]. Additional selection criteria are applied to
each event to remove spurious jet like features originating from isolated
noise patterns in certain HCAL regions.

##  0.3 Monte Carlo simulation

Signal events with SM like couplings are generated at next to leading order
(NLO) in quantum chromodynamics (QCD) with 2.0 [31, 32, 33, 34, 35] for the
$\Pg\Pg\mathrm{F}$ and VBF production modes. The decays
$\mathrm{X}\to\cPZ\cPZ\to 4\ell$, $2\ell 2\cPq$, and $2\ell 2\nu$ are modeled
with JHUGen 7.0.2 [36, 37, 38, 39], including corrections for the $\cPZ\cPZ$
branching fraction, and correct modeling of the angular correlation among the
fermions. A wide range of masses $m_{\mathrm{X}}$ from 100to 3is generated
with the width $\Gamma_{\mathrm{X}}$ set according to the SM Higgs boson
expectation for $m_{\mathrm{X}}$ up to 1. For higher masses, we choose the
width $\Gamma_{\mathrm{X}}=0.5m_{\mathrm{X}}$, which approximately corresponds
to the SM Higgs boson prediction for $m_{\mathrm{X}}=1\TeV$. The samples are
used to derive a generic signal parameterization.

While NLO accuracy in QCD is used in production, no modeling of the
interference with background is included at this stage of the simulation. The
MELA matrix element package [36, 37, 38, 39], based on JHUGen for both
$\PH(125)$ and $\mathrm{X}$ signal, and on 7.0 [40, 41, 42] for the continuum
background, allows modeling of interference of a broad $\mathrm{X}$ resonance
with SM background in either $\Pg\Pg\mathrm{F}$ or EW production, the latter
including VBF and $\mathrm{V}\PH$ processes.

The loop induced production of two $\cPZ$ bosons, gg
$\to\cPZ\cPZ/\cPZ\gamma^{*}\to 4\textrm{f}$ background, including the off
shell tail of the $\PH(125)$, is modeled at leading order (LO) in QCD with .
The corresponding background from EW production,
$\Pq\Pq^{\prime}\cPZ\cPZ/\cPZ\gamma^{*}\to 4\textrm{f}\Pq\Pq^{\prime}$ is
modeled at LO in QCD with Phantom 1.2.8 [43]. For both $\Pg\Pg\mathrm{F}$ and
VBF simulation, the factorization and renormalization scales are chosen as
$m_{\cPZ\cPZ}/2$, and NNPDF3.0 parton distribution functions (PDFs) [44] are
adopted. In order to include higher order QCD corrections to gluon fusion
production, LO, NLO, and next to next to leading order (NNLO) signal cross
section calculations are performed using the and hnnlo v2 programs [45, 46,
47] for a wide range of masses using the narrow width approximation. The ratio
between the NNLO and LO, or between the NLO and LO, is used as a weight
depending on the $4\textrm{f}$ invariant mass (K factor). While this procedure
is directly applicable for the signal, it is approximate for the background.
However, an NLO calculation is available [48, 49] for the background in the
mass range $2m_{Z}<m_{4\ell}<2m_{t}$. There is a good agreement between the
NLO K factors calculated for signal and background and any differences set the
scale of systematic uncertainties in this procedure, for which we assign a 10%
uncertainty. Event yields for the $\PH(125)$ boson production are normalized
to the cross section at NNLO in QCD and NLO in EW for $\Pg\Pg\mathrm{F}$ [50]
and others taken from Ref. [51].

The MELA package is also used to reweight the /JHUGen, , or Phantom signal
samples to model various values of $m_{\mathrm{X}}$ and $\Gamma_{\mathrm{X}}$,
as well as the interference with the background component.

The background from the production of two $\cPZ$ bosons from quark antiquark
annihilation, $\cPq\overline{\cPq}\to\cPZ\cPZ/\cPZ\gamma^{*}\to 4\textrm{f}$,
is evaluated at NLO with [52] and 2.3.2 [53]. The $\PW\cPZ$ production is
generated at LO with 8.212 [54], normalized to NNLO in QCD accuracy [55]. The
$\cPZ+\text{jets}$ ( $\to\ell^{+}\ell^{-}$) simulation is made of a composite
sample comprising a set of exclusive LO samples with various associated parton
multiplicities, including a dedicated sample with associated quark production.
These samples are produced at LO with and corrected to NLO QCD accuracy with a
K factor depending on the of the dilepton pair, derived from simulation at NLO
with FxFx merging scheme [56]. The simulation of top quark antiquark pair
production, , is performed with at NLO in QCD [57].

All generated samples are interfaced with , configured with the CUETP8M1 tune
[58] for simulation of parton showers, hadronization, and underlying event
effects. All simulated events are further processed with a based description
[59] of the CMS detector and reconstructed with the same algorithms as used
for data. Supplementary minimum bias (pileup) interactions are added to the
simulated events with a multiplicity determined such as to match that observed
in data.

##  0.4 Matrix element techniques

The ME method in this study is utilized in three ways. First, it is used to
apply weights to generated events from various models to avoid having to fully
simulate the samples, as discussed in Section 0.3. Second, the ME method is
used to create a model of a broad high mass resonance $\mathrm{X}$, including
its interference with the SM background, to be used in the likelihood fit.
Finally, this method is used to create optimal discriminants for either
categorization of events according to likely production mechanism, or to
separate signal from the dominant background.

The ME calculations are performed using the MELA package, which provides the
full set of processes studied in this paper and uses JHUGen matrix elements
for the signal and matrix elements for the background. The signal includes
both the four fermion kinematic properties for the decay
$\mathrm{X}\to\cPZ\cPZ\to 4\textrm{f}$, and the kinematical properties of
associated particles in the $\mathrm{X}$ \+ 2jets, VBF, $\cPZ\PH$, $\PW\PH$
production. The background includes $\Pg\Pg$ or $\qqbar\to\cPZ\cPZ$ /
$\cPZ\gamma^{*}$ / $\gamma^{*}\gamma^{*}$ / $\cPZ\to 4\textrm{f}$ processes,
VBF production of a $\cPZ$ boson pair, the associated production of a pair
with a third vector boson, and the production of a single $\cPZ$ boson in
association with jets.

Two of the final states studied in this analysis, $\mathrm{X}\to\cPZ\cPZ\to
4\ell$ and $2\ell 2\cPq$ provide full information about the kinematic
properties of the process in both production and decay. This is illustrated in
Fig. 1, where a complete set of angles and invariant masses, denoted as
$\vec{\Omega}$, fully defines the four vectors of all involved particles in
the center of mass frame [36, 38]. The overall boost of the system depends on
QCD effects beyond LO (in the transverse plane) or PDFs (in the longitudinal
direction). Therefore, in these two channels, matrix element calculations are
used to create discriminants optimal either for categorization of the
production mechanism or to separate signal from background using production
and decay information.

Figure 1:  Illustration of an $\mathrm{X}$ boson production from
$\Pg\Pg\mathrm{F}$,
$\Pg\Pg\to\mathrm{X}\to\PZ\PZ\to(\ell^{+}\ell^{-})(f\overline{f})$ (left), and
VBF,
$\Pq{\Pq^{\prime}}\to\Pq{\Pq^{\prime}}\mathrm{X}\to\Pq{\Pq^{\prime}}\PZ\PZ$
(right). The five angles shown in blue and the invariant masses of the two
vector bosons shown in green fully characterize either the production or the
decay chain. The angles are defined in either the $\mathrm{X}$ or $\mathrm{V}$
boson rest frames [36, 38].

The discriminant sensitive to the VBF signal topology with two energetic and
forward associated jets is calculated as [18, 60]

$\displaystyle\mathcal{D}_{\textrm{2jet}}^{\textrm{VBF}}=\left[1+\frac{\mathcal{P}_{\mathrm{\mathrm{X}JJ}}(\vec{\Omega}^{\mathrm{\mathrm{X}+JJ}}|m_{\cPZ\cPZ})}{\mathcal{P}_{\mathrm{VBF}}(\vec{\Omega}^{\mathrm{\mathrm{X}+JJ}}|m_{\cPZ\cPZ})}\right]^{-1},$
(1)

where $\mathcal{P}_{\mathrm{VBF}}$ and $\mathcal{P}_{\mathrm{\mathrm{X}JJ}}$
are probabilities obtained from the JHUGen matrix elements for the VBF and
$\Pg\Pg\mathrm{F}$ production processes in association with two jets
($\mathrm{X}+2$ jets). This discriminant is equally efficient in separating
VBF from either $\Pg\Pg\to\mathrm{X}+2$ jets signal or $\Pg\Pg$ or $\qqbar\to
2\ell 2\Pq+2$ jets background because jet correlations in these processes are
distinct from the VBF process. Being independent of the type of fermions
produced in the $\cPZ$ boson decay, it is used in both the
$\mathrm{X}\to\cPZ\cPZ\to 4\ell$ and $\mathrm{X}\to\cPZ\cPZ\to 2\ell 2\cPq$
analyses.

In addition, in the $\mathrm{X}\to\cPZ\cPZ\to 4\ell$ analysis, the dominant
background originates from the $\qqbar\to\cPZ\cPZ$ / $\cPZ\gamma^{*}$ /
$\gamma^{*}\gamma^{*}\to 4\ell$ process. Therefore, the discriminant sensitive
to the $\mathrm{X}\to\cPZ\cPZ\to 4\ell$ kinematic properties and optimal for
suppression of the dominant background is defined as

$\displaystyle{\cal D}_{\mathrm{bkg}}^{\mathrm{kin}}=\left[1+\frac{{\cal
P}_{\qqbar\to 4\ell}(\vec{\Omega}^{\mathrm{X}\to 4\ell}|m_{\cPZ\cPZ})}{{\cal
P}_{\mathrm{X}\to 4\ell}(\vec{\Omega}^{\mathrm{X}\to
4\ell}|m_{\cPZ\cPZ})}\right]^{-1}\,.$ (2)

In the $\mathrm{X}\to\cPZ\cPZ\to 2\ell 2\cPq$ analysis, the dominant
background originates from the \+ 2 jets process. Therefore, the discriminant
sensitive to the $\mathrm{X}\to\cPZ\cPZ\to 2\ell 2\Pq$ kinematic properties is
calculated as

$\displaystyle\mathcal{D}_{\textrm{bkg}}^{\textrm{Zjj}}=\left[1+\frac{{\cal
P}_{\text{Zjj}}(\vec{\Omega}^{\mathrm{X}\to 2\ell 2q}|m_{\cPZ\cPZ})}{{\cal
P}_{\mathrm{X}\to 2\ell 2\Pq}(\vec{\Omega}^{\mathrm{X}\to 2\ell
2\Pq}|m_{\cPZ\cPZ})}\right]^{-1}\,.$ (3)

In Eqs. (2) and (3), ${\cal P}_{\mathrm{X}\to 4\ell}$ and ${\cal
P}_{\mathrm{X}\to 2\ell 2\Pq}$ are the probabilities for the signal, while
${\cal P}_{\qqbar\to 4\ell}$ and ${\cal P}_{\text{Zjj}}$ are the probabilities
for the dominant background processes.

##  0.5 Event selection and categorization

The searches in the three final states cover different mass ranges. The
$4\ell$ final state has the smallest backgrounds, so the search is performed
over the full range from 130to 3. The $2\ell 2\nu$ final state suffers from
large $\cPZ+\text{jets}$ background in the low mass region, and the search
range is thus restricted to be between 300and 3. For the same reason, the
$2\ell 2\Pq$ final state search is performed between 550and 3. Event
selections are optimized for the search ranges in each final state.

Leptons are reconstructed as described in Section 0.2. Electrons are also
required to pass identification criteria based on observables sensitive to the
bremsstrahlung along the electron trajectory, the geometrical and momentum
energy matching between the electron trajectory and the associated energy
cluster in the ECAL, the shape of the electromagnetic shower in the ECAL, and
variables that discriminate against electrons originating from photon
conversions. Independent selection criteria on such observables are applied in
the $2\ell 2\nu$ channel, while a multivariate discriminant based on them is
adopted in the $4\ell$ and $2\ell 2\Pq$ channel to retain high efficiency for
low leptons. Muons are selected among the reconstructed muon track candidates
by applying minimal requirements on the track in both the muon and inner
tracker system, and requiring small associated energy deposits in the
calorimeters. For muon above 200, the additional lever arm provided by the
outer muon detectors becomes a significant advantage; therefore the charge and
momentum are extracted from the combined trajectory fit for the outside in
muons, while otherwise tracks found in the silicon tracker are used.

Electrons and muons with high are required in the $2\ell 2\Pq$ ($>$24) and
$2\ell 2\nu$ ($>$25) final states, while low ($>$7for electrons and $>$5for
muons) leptons are also retained in the $4\ell$ final state to ensure high
efficiency for masses less than $2m_{Z}$. To suppress nonprompt leptons, the
impact parameter in three dimensions of the lepton track, with respect to the
primary vertex, is required to be less than 4 times its uncertainty
($\abs{\mathrm{SIP_{3D}}}<4$).

In addition, an isolation requirement of ${\cal I}^{\ell}<0.35$ is imposed to
select prompt leptons, where the isolation ${\cal I}^{\ell}$ is defined as

${\cal
I}^{\ell}\equiv\Big{(}\sum\PT^{\text{charged}}+\max\left[0,\sum\PT^{\text{neutral}}+\sum\PT^{\Pgg}-\PT^{\mathrm{PU}}(\ell)\right]\Big{)}/\PT^{\ell}.$
(4)

The three involved sums run over the of charged hadrons originating from the
primary vertex, of neutral hadrons and of photons in a cone of angular radius
$\Delta R=0.3$ around the lepton direction.

Since the isolation variable is particularly sensitive to energy deposits from
pileup interactions, a $\PT^{\text{PU}}(\ell)$ contribution is subtracted,
using two different techniques. For muons, we define
$\PT^{\mathrm{PU}}(\Pgm)\equiv 0.5\sum_{i}\PT^{\mathrm{PU},i}$, where $i$ runs
over the momenta of the charged hadron PF candidates not originating from the
primary vertex, and the factor of 0.5 accounts for the fraction of neutral
particles. For electrons, an area based subtraction technique [61, 62, 26], as
implemented in , is used, in which $\PT^{\mathrm{PU}}(\Pe)\equiv\rho
A_{\text{eff}}$, where the effective area $A_{\text{eff}}$ is the geometric
area of the isolation cone scaled by a factor that accounts for the residual
dependence of the average pileup as a function of $\eta$, and $\rho$ is the
median of the energy density distribution of neutral particles within the area
of any jet in the event.

In the $4\ell$ and $2\ell 2\Pq$ final states, an algorithm is used to recover
the final state radiation (FSR) from leptons. Photons reconstructed by the PF
algorithm within $\abs{\eta_{\Pgg}}<2.4$ are considered as FSR candidates if
they satisfy $\PT^{\Pgg}>2\GeV$ and ${\cal I}^{\ell}<1.8$ [63]. Associating
every such photon to the closest selected lepton in the event, photons that do
not satisfy $\Delta R(\cPgg,\ell)/(\PT^{\Pgg})^{2}<0.012$ and $\Delta
R(\cPgg,\ell)<0.5$ are discarded. The lowest $\Delta
R(\cPgg,\ell)/(\PT^{\Pgg})^{2}$ photon candidate for every lepton, if any, is
retained. The photons identified as FSR are excluded from any isolation
computations.

The momentum scale and resolution for electrons and muons are calibrated in
bins of $\pt^{\ell}$ and $\eta^{\ell}$ using the decay products of known
dilepton resonances. The electron momentum scale in data is corrected with a
$\cPZ\to\Pe\Pe$ sample, by adjusting the peak of the reconstructed dielectron
mass spectrum to that expected from simulation. A Gaussian smearing is applied
to electron energies in simulation such that the $\cPZ\to\Pe\Pe$ mass
resolution agrees with the one observed in data. Muon momenta are calibrated
based on a Kalman filter approach [64], using $\PJGy$ meson and $\cPZ$ boson
decays.

A “tag-and-probe” technique [65] based on inclusive samples of $\cPZ$ boson
events in data is used to correct the efficiency of the reconstruction and
selection for prompt electrons and muons in several bins of $\PT^{\ell}$ and
$\eta^{\ell}$. The difference in the efficiencies measured in simulation and
data is used to correct the selection efficiency in the simulated samples.

The jets in the three analyses must satisfy $\pt^{\text{jet}}>30\GeV$ and
$\abs{\eta^{\text{jet}}}<4.7$ and be separated from all selected leptons by
$\Delta R(\ell/\cPgg,\text{jet})>0.4$. The analyses use tagged jets of
$\abs{\eta^{\text{jet}}}<2.5$ for event categorization and selection, where a
jet is tagged using the combined secondary vertex algorithm [66, 67] based on
the impact parameter significance of the tracks associated with the jet, with
respect to the primary vertex. The loose working point is used, corresponding
to an efficiency of 80% and a mistag rate of 10% for light quark jets.

The main feature distinguishing the two dominant $\mathrm{X}$ boson production
mechanisms ($\Pg\Pg\mathrm{F}$ and VBF) is the presence of associated jets and
the kinematic correlation between such jets and the $\mathrm{X}$ boson. In
order to gain sensitivity to the production process of the $\mathrm{X}$ boson,
events are split into categories based on such kinematic correlations. In the
case of fully reconstructed final states, $\mathrm{X}\to 4\ell$ and $2\ell
2$q, a ME technique is used to categorize events based on the correlation
between the two forward jets and the $\mathrm{X}$ boson candidate, while in
the $2\ell 2\nu$ final state a simpler correlation between the two jets is
used.

Subsequent event selections differ depending on the considered final state and
are described for each final state in the following.

###  0.5.1 $\mathrm{X}\to\cPZ\cPZ\to 4\ell$

The $\mathrm{X}\to\cPZ\cPZ\to 4\ell$ analysis uses the same selection as in
the measurements of the properties of the $\PH(125)$ boson in the
$\PH\to\cPZ\cPZ\to 4\ell$ decay channel [63]. The $\cPZ$ candidates are formed
from pairs of leptons of the same flavor and opposite charge
($\Pe^{+}\Pe^{-}$, $\Pgm^{+}\Pgm^{-}$) and are required to pass the invariant
mass selection $12<m_{\ell^{+}\ell^{-}}<120\GeV$. The flavors of involved
leptons define three mutually exclusive channels: $4\Pe$, $4\Pgm$, and $2\Pe
2\Pgm$. candidates are combined into $\cPZ\cPZ$ candidates, wherein we denote
as $\cPZ_{1}$ the $\cPZ$ candidate with an invariant mass closest to the
nominal $\cPZ$ boson mass [68], and the other candidate $\cPZ_{2}$. To be
considered for the analysis, $\cPZ\cPZ$ candidates have to pass a set of
kinematic requirements. The $\cPZ_{1}$ invariant mass is required to be larger
than $40\GeV$. All leptons are separated in angular space by at least $\Delta
R(\ell_{i},\ell_{j})>0.02$. At least two leptons are required to have
$\pt>10\GeV$ and at least one is required to have $\pt>20\GeV$. In the $4\Pgm$
and $4\Pe$ channels, where an alternative $\cPZ_{a}\cPZ_{b}$ candidate can be
built out of the same four leptons, candidates with $m_{\cPZ_{b}}<12\GeV$ are
removed if $\cPZ_{a}$ is closer to the nominal $\cPZ$ boson mass than
$\cPZ_{1}$ is.

In Ref. [63], six categories are defined based on the number and types of
particles associated with the $\PH(125)$ boson. Here we follow the same
approach with some optimization specific for a high mass search. Two
categories dedicated to the production mechanisms are used: VBF jets and
inclusive; to further improve the efficiency in the electron channels at high
, a relaxed selection electron (RSE) category is added. The
$\abs{\mathrm{SIP}_{\mathrm{3}D}}<4$ requirement in the standard electron
selection removes fake electrons from photon conversions, which are not
dominant at high masses. The requirement becomes the main cause of efficiency
losses at high . The second cause of the efficiency loss, particularly at high
masses, is the opposite sign lepton charge requirement, as the charge
misidentification rate increases with lepton . Thus, a relaxed selection
removing both requirements on at most one pair of electrons is applied for
$m_{4\ell}>300$. The detailed categorization is structured as follows:

  * •

VBF-tagged requires exactly four leptons selected with regular criteria. In
addition, there must be either two or three jets among which at most one is
tagged, or at least four jets and no tagged jets, and ${\cal
D}^{\mathrm{VBF}}_{\mathrm{2jet}}$ following Eq. (1) is required to pass a
mass dependent selection;

  * •

Untagged consists of the remaining events with regularly selected leptons;

  * •

RSE contains events from the relaxed electron selection that are not in the
regular electron selection and for which $m_{4\ell}>300\GeV$.

When more than two jets pass the selection criteria, which happens in about
half of the cases, the two -leading jets are selected for matrix element
calculations.

As a result of the above categorization, events are split into eight
categories: $4\Pe$, $4\mu$, $2\Pe 2\mu$, in either the VBF-tagged or the
untagged category, or $4\Pe$ and $2\Pe 2\mu$ in the RSE category. Each event
is characterized by two observables $(m_{4\ell}$ and ${\cal
D}_{\mathrm{bkg}}^{\mathrm{kin}})$ that are shown in Fig. 2 and Fig. 3,
together with several signal hypotheses.

Figure 2:  Distributions of the four lepton invariant mass in the untagged
(upper left plot), VBF-tagged (upper right plot) and RSE (lower plot)
categories. Signal expectations including the interference effect for several
mass and width hypotheses are shown. The signals are normalized to the
expected upper limit of the cross section derived from this final state. Lower
panels show the ratio between data and background estimation in each case.
Figure 3:  Distributions of ${\cal D}_{\mathrm{bkg}}^{\mathrm{kin}}$ for all
selected events. Signal expectations including the interference effect for
several mass and width hypotheses are shown. The signals are normalized to a
total of 400 events.

###  0.5.2 $\mathrm{X}\to\cPZ\cPZ\to 2\ell 2\Pq$

In the $\mathrm{X}\to\cPZ\cPZ\to 2\ell 2\Pq$ analysis, events are selected by
combining leptonically and hadronically decaying candidates. The lepton pair
selection is similar to the four-lepton analysis: pairs of opposite sign and
same flavor electrons or muons with invariant mass between 60 and 120 are
constructed. A $\PT>\unit{40}{\GeV}$ requirement is applied on at least one of
the leptons in the pair, and a minimum dilepton of 100 is imposed to reject
Drell–Yan events with small hadronic recoil.

Hadronically decaying $\cPZ$ boson candidates ($\cPZ_{\textrm{had}}$) are
reconstructed using two distinct techniques, which are referred to as
“resolved” and “merged” in the following. In the resolved case, the two quarks
from the $\cPZ$ boson decay form two distinguishable AK4 jets, while in the
merged case a single AK8 jet with a large is taken as a $\cPZ_{\textrm{had}}$.

In the merged jet case, a pruning algorithm is applied to the AK8 jet [69,
70]. The goal of the algorithm is to recluster the jet constituents, while
applying additional requirements that eliminate soft, large angle QCD
radiation that artificially increases the jet mass relative to the nominal
$\cPZ$ boson mass. We adopt the unified nomenclature $m(\cPZ_{\textrm{had}})$
to refer to the hadronically decaying candidate mass, corresponding to the
dijet invariant mass in the resolved case and the jet pruned mass in the
merged case. The reconstructed $\cPZ_{\textrm{had}}$ is required to have an
invariant mass around the $\cPZ$ boson mass:
$40<m(\cPZ_{\textrm{had}})<\unit{180}{\GeV}$ and $\PT>\unit{100}\ (170){\GeV}$
in the resolved (merged) case. Merged jets must also be separated from all
selected leptons by $\Delta R(\ell,\text{jet})>0.8$. In addition, in the
merged jet selection we exploit substructure techniques commonly used in
searches including Lorentz boosted bosons in the final state [71]. The
$N$-subjettiness $\tau_{N}$ is defined as

$\tau_{N}=\frac{1}{d_{0}}\sum_{k}\PT{}_{,k}\min(\Delta R_{1,k},\Delta
R_{2,k},\,\ldots,\Delta R_{N,k}),$ (5)

where the index $k$ runs over the jet constituents and the distances $\Delta
R_{N,k}$ are calculated with respect to the axis of the $n^{\textrm{th}}$
subjet. The normalization factor $d_{0}$ is calculated as
$d_{0}=\sum_{k}\PT{}_{,k}R_{0}$, setting $R_{0}$ to the jet radius of the
original jet. Jets with smaller $\tau_{N}$ are more compatible with the
$N$-subjets configuration. We use the ratio of 2-subjettiness over
1-subjettiness, $\tau_{21}=\tau_{2}/\tau_{1}$, as the discriminating variable
for the jet substructure and impose a $\tau_{21}<0.6$ requirement on merged
$\cPZ_{\textrm{had}}$ candidates.

Events that pass the above selection and additionally have
$m(\cPZ_{\textrm{had}})$ in the range [70, 105]form the signal region,
covering 1–2 standard deviations dijet mass resolution. On the other hand,
events that have $m(\cPZ_{\textrm{had}})$ in the range [40, 70]or [135,
180]form the sideband regions and are retained for background estimation.

An arbitration procedure is used to rank multiple $\cPZ_{\textrm{had}}$
candidates reconstructed in a single event: merged candidates have precedence
over resolved candidates if they have $\PT>\unit{300}{\GeV}$ and the
accompanying leptonically decaying candidate has
$\PT(\ell^{+}\ell^{-})>\unit{200}{\GeV}$; resolved candidates have precedence
otherwise. Within each selection category the candidate with the largest has
priority over the others.

The hadronically and leptonically decaying $\cPZ$ boson candidates are
combined to form a resonance candidate. In order to improve the $\cPZ\cPZ$
invariant mass resolution in the resolved jet case, a kinematic fit is
performed using a mass constraint on the intermediate decay $\cPZ\to\qqbar$.
The constraint improves the signal resolution by 7–10%. When a candidate
belongs to the signal region, we reevaluate the kinematical distributions of
final state particles (here the of the two jets forming the $\cPZ$ boson of
the resonance candidate) with a constraint on the reconstructed $\cPZ$ boson
mass to follow the $\cPZ$ boson line shape. For each event, the likelihood is
maximized and the of the jets is updated. After refit, the mass of the $\cPZ$
boson candidate and $m_{\cPZ\cPZ}$ are recalculated. This procedure is not
applied to events in the sidebands, where $m(\cPZ_{\textrm{had}})$ is very
different from the nominal $\cPZ$ boson mass.

The reconstructed $\cPZ\cPZ$ candidate mass $m_{\cPZ\cPZ}$ denotes the
dilepton + dijet mass $m_{\ell\ell jj}$ in the resolved case and the dilepton
+ merged jet invariant mass $m_{\ell\ell J}$ in the merged case. A requirement
of $m_{\cPZ\cPZ}{}>\unit{500}{\GeV}$ is imposed to reduce the
$\cPZ+\text{jets}$ background.

To increase the sensitivity to the different production modes, events are
categorized into VBF and inclusive types. Furthermore, since a large fraction
of signal events is enriched with quark jets due to the presence of
$\cPZ\to\bbbar$ decays, a dedicated category is defined. The definitions are
as follows:

  * •

VBF-tagged requires two additional and forward jets besides those constituting
the hadronic $\cPZ$ boson candidate; a mass dependent selection criterion on
${\cal D}^{\mathrm{VBF}}_{\mathrm{2jet}}$ is applied;

  * •

tagged consists of the remaining events with two tagged jets (in the resolved
case) or two tagged subjets from the hadronic $\cPZ$ boson candidate;

  * •

Untagged consists of the remaining events.

As a result of this categorization, events are split into twelve categories:
$2\Pe 2\Pq$ or $2\mu 2\Pq$, either VBF-tagged, b-tagged, or untagged, and each
with either merged jets or resolved jets. Each event is characterized by the
two observables $(m_{\cPZ\cPZ},\mathcal{D}_{\textrm{bkg}}^{\textrm{Zjj}})$.
Figure 4 shows the invariant mass distribution for merged and resolved events
in each category after the selection. Figure 5 shows the
$\mathcal{D}_{\textrm{bkg}}^{\textrm{Zjj}}$and
$\mathcal{D}_{\textrm{2jet}}^{\textrm{VBF}}$distributions for resolved events
in each category together after the selection.

Figure 4: Distributions of the invariant mass $m_{\cPZ\cPZ}$ in the signal
region for the merged (left) and resolved (right) case for the different
categories in the $2{\ell}2\Pq$ channel. The points represent the data, the
stacked histograms the expected backgrounds from simulation, and the open
histograms the expected signal. The blue hatched bands refer to the sum of
background estimates derived from either simulation or control samples in
data, as described in the text. Lower panels show the ratio between data and
background estimation in each case.

Figure 5: Distributions of the
$\mathcal{D}_{\textrm{bkg}}^{\textrm{Zjj}}$(left) and
$\mathcal{D}_{\textrm{2jet}}^{\textrm{VBF}}$(right) discriminants in the
signal region for the resolved selection. The points represent the data, the
stacked histograms the expected background from simulation, and the open
histograms the expected signal.

###  0.5.3 $\mathrm{X}\to\cPZ\cPZ\to 2\ell 2\nu$

In the $\mathrm{X}\to\cPZ\cPZ\to 2\ell 2\nu$ channel, events are selected by
combining dilepton $\cPZ$ boson candidates with relatively large . Events are
selected requiring two leptons of the same flavor that have an invariant mass
within a 30window centered on the nominal $\cPZ$ boson mass. For X boson
masses considered in this analysis ($>$300), the $\cPZ$ bosons from the X
boson decay are typically produced with a large $\PT$. To suppress the bulk of
the $\cPZ+\text{jets}$ background, the $\PT$ of the dilepton system is
therefore required to be greater than 55, and a threshold of 125is imposed.
The region of large is contaminated by $\cPZ+\text{jets}$ events in which the
is largely due to mismeasurements of the jet energies. To suppress this
contribution, events are removed if the azimuthal angle between the and the
closest jet with $\pt>30\GeV$ is smaller than 0.5 radians. An additional
selection requirement $\abs{\Delta\phi(\cPZ,\ptvecmiss)}>0.5$ is placed in
order to remove events for which the instrumental is not well controlled.

Top quark decays are often associated with the production of leptons and
missing transverse momentum in the final state but are also characterized by
the presence of jets originating from quarks ( jets). The top quark background
is suppressed by applying a veto on events having a tagged jet with
$\pt>30\GeV$. To reduce the $\PW\cPZ$ background in which both bosons decay
leptonically, any event with an additional $\Pe$ ($\Pgm$) passing loose
identification and isolation criteria with $\pt>10\ (3)\GeV$ is rejected.

We select events with $\ptmiss\geq 125\GeV$ and fit the transverse mass
$m_{\mathrm{T}}$ distribution for the selected events. The requirement rejects
background processes that could lead to high $m_{\mathrm{T}}$ because of the
kinematic properties of the dilepton pair in the event. The criterion is
optimized based on expected signal significance. The significance is found to
be quite stable with the chosen requirement for masses above 400.

The transverse mass is reconstructed from the dilepton and system via the
following definition :

$m_{\mathrm{T}}^{2}=\left(\sqrt{{\PT(\ell\ell)}^{2}+{m(\ell\ell)}^{2}}+\sqrt{{\ptmiss}^{2}+m_{\cPZ}^{2}}\right)^{2}-(\ptvec(\ell\ell)+\ptvecmiss)^{2},$
(6)

where $\ptvec(\ell\ell)$ and $m(\ell\ell)$ are the transverse momentum and
invariant mass of the dilepton system, respectively. In order to maximize the
sensitivity, the search is carried out in different jet multiplicity
categories defined as follows:

  * •

VBF-tagged: in this category we require two or more jets in the forward region
with a pseudorapidity gap ($\abs{\Delta\eta}$) between the two leading jets
greater than 4, and a minimal invariant mass of those two jets of 500. The two
leptons forming the $\cPZ$ boson candidate are required to lie between these
two jets in $\eta$, while no other jets ($\PT>30\GeV$) are allowed in this
central region;

  * •

$\mathbf{\geq 1}$-jet: events with at least one reconstructed jet with
$\PT>30\GeV$, but failing the VBF selection;

  * •

0-jet: events without any reconstructed jet with $\PT>30\GeV$.

The last two categories are the most sensitive to the signal produced via
$\Pg\Pg\mathrm{F}$ but have different expected signal to background ratios. As
a result of the above selection, events are split into six categories:  $2\Pe
2\nu$ or $2\mu 2\nu$, either 0-jet, $\geq 1$-jet or VBF-tagged. Fig. 6 shows
the $m_{\mathrm{T}}$ distributions for the signal and background processes
superimposed, in the six event categories.

Figure 6:  Distributions of the transverse mass $m_{\mathrm{T}}$ in the signal
region for the different analysis categories for the 2$\ell$2$\nu$ channel, in
the (left) and $\mu\mu$ final states (right). The points represent the data
and the stacked histograms the expected background. The open histograms show
the expected gluon fusion and VBF signals for the product of cross section and
branching fraction equal to $\sigma(\Pp\Pp\to\PH\to\cPZ\cPZ)=50\unit{fb}$.
Lower panels show the ratio of data to the expected background. The shaded
areas show the systematic and total combined statistical and systematic
uncertainties in the background estimation.

##  0.6 Signal and background parameterization

The goal of the analysis is to determine if a set of $\mathrm{X}$ boson
parameters $m_{\mathrm{X}}$, $\Gamma_{\mathrm{X}}$, and
$\sigma_{i}\mathcal{B}_{X\to\cPZ\cPZ}$ is consistent with the data, where
$\sigma_{i}\mathcal{B}_{X\to\cPZ\cPZ}$ is the product of the signal production
cross section and the $\mathrm{X}\to\cPZ\cPZ$ branching fraction in each
production channel $i$ (gluon fusion or EW production). In practice, the
$\sigma_{i}\mathcal{B}$ for $i=1,2$ are expressed in terms of
$\sigma_{\mathrm{tot}}\mathcal{B}_{X\to\cPZ\cPZ}$ and $f_{\mathrm{VBF}}$,
where $\sigma_{\mathrm{tot}}$ is the sum of the cross sections in the two
production channels. The confidence intervals on
$\sigma_{\mathrm{tot}}\mathcal{B}_{X\to\cPZ\cPZ}$ are determined from profile
likelihood scans for a given set of parameters
$(m_{\mathrm{X}},\Gamma_{\mathrm{X}},f_{\mathrm{VBF}})$. The extended
likelihood function is defined for candidate events as

$\displaystyle\mathcal{L}=\exp\Big{(}-\sum_{i}n_{vv}^{i}-\sum_{i}n_{\text{bkg}}^{i}\Big{)}\prod_{k}\prod_{j}\Big{(}\sum_{i}n_{vv}^{i}\mathcal{P}^{i,k}_{vv}(\vec{x}_{j};m_{\mathrm{X}},\Gamma_{\mathrm{X}})+\sum_{i}n_{\text{bkg}}^{i}\mathcal{P}^{i,k}_{\text{bkg}}(\vec{x}_{j})\Big{)},$
(7)

where $n_{vv}^{i}$ and $n_{\text{bkg}}^{i}$ are the numbers of signal and
background events in channel $i$. The observables $\vec{x}_{j}$ are defined
for each event $j$ in category $k$ as discussed in Sections 0.5.1, 0.5.2, and
0.5.3. There are several signal and background types $i$, defined for each
production mechanism. The background processes that do not interfere with the
signal are described by the probability density functions (pdfs)
$\mathcal{P}^{i,k}_{\text{bkg}}(\vec{x}_{j})$. The $vv\to 4\textrm{f}$ process
is described by the pdf
$\mathcal{P}^{i,k}_{vv}(\vec{x}_{j};m_{\mathrm{X}},\Gamma_{\mathrm{X}})$ for
$vv=\Pg\Pg$ (gluon fusion) and $vv=$ VV (EW production). This pdf describes
the production and decay of the $\mathrm{X}$ boson signal, SM background,
including $\PH(125)$, and interference between all these contributions and is
parameterized as follows:

$\displaystyle\mathcal{P}^{i,k}_{vv}(\vec{x}_{j};m_{\mathrm{X}},\Gamma_{\mathrm{X}})=\mu_{i}\mathcal{P}^{i,k}_{vv\to\mathrm{X}\to
4\textrm{f}}(\vec{x}_{j};m_{\mathrm{X}},\Gamma_{\mathrm{X}})+\sqrt{\mu_{i}}\mathcal{P}^{i,k}_{\mathrm{int}}(\vec{x}_{j};m_{\mathrm{X}},\Gamma_{\mathrm{X}})+\mathcal{P}^{i,k}_{vv\to
4\textrm{f}}(\vec{x}_{j}),$ (8)

where $\mu_{i}$ is the relative signal strength for production type $i$
defined as the ratio of $\sigma_{i}\mathcal{B}$ with respect to a reference
value, for which normalization of the pdf is determined. The interference
contribution $\mathcal{P}^{i,k}_{\mathrm{int}}$ scales as
$\sqrt{\smash[b]{\mu_{i}}}$ and the pure signal as ${\mu_{i}}$, while both
depend on the signal parameters $m_{\mathrm{X}}$ and $\Gamma_{\mathrm{X}}$.
The likelihood defined in Eq. (7) is maximized with respect to the nuisance
parameters, which include the constrained parameters describing the systematic
uncertainties.

###  0.6.1 Signal model

The parameterization of
$\mathcal{P}^{i,k}_{vv}(\vec{x}_{j};m_{\mathrm{X}},\Gamma_{\mathrm{X}})$ is
performed using the MC simulation discussed in Section 0.3 with the ME method.
In the case of the $\mathrm{X}\to\cPZ\cPZ\to 4\ell$ or $2\ell 2\Pq$ channels,
a full reconstruction of the final state is possible. Therefore, the ideal
differential distribution prior to detector effects
$\mathcal{P}^{\mathrm{ideal}}_{vv}$, equivalent to Eq. (8), is parameterized
using ME techniques and is further corrected for detector acceptance and
resolution effects. In the case of $\mathrm{X}\to\cPZ\cPZ\to 2\ell 2\nu$, this
approach is not possible because of missing neutrinos: MC simulation is
reweighted for each hypothesis of $m_{\mathrm{X}}$, $\Gamma_{\mathrm{X}}$, and
$\sigma_{i}\mathcal{B}_{\mathrm{X}\to\cPZ\cPZ}$, leading to template
parameterization of $\mathcal{P}^{i,k}_{vv}$ for each set of signal
parameters. While ultimately the two approaches are equivalent, the former
approach is more flexible in implementation, and the latter avoids the
intermediate step of ideal pdf parameterization.

In the $\mathrm{X}\to\cPZ\cPZ\to 4\ell$ or $2\ell 2\Pq$ channels, we
parameterize the signal mass shape as follows. A pdf after detector effects
${\cal M}^{\mathrm{reco}}_{vv}(m_{\cPZ\cPZ})$ is implemented with the
multiplicative efficiency function ${\cal E}(m_{\cPZ\cPZ})$ and convolved with
a mass resolution function ${\cal
R}(m_{\cPZ\cPZ}|m^{\mathrm{Gen}}_{\cPZ\cPZ})$, both extracted from simulation
of the $\Pg\Pg\mathrm{F}$ and VBF processes:

$\displaystyle{\cal M}^{\mathrm{reco}}_{vv}(m_{\cPZ\cPZ})=\left({\cal
E}(m_{\cPZ\cPZ}^{\mathrm{Gen}}){\cal
M}_{vv}(m^{\mathrm{Gen}}_{\cPZ\cPZ}|m_{\mathrm{X}},\Gamma_{\mathrm{X}})\right)\otimes{\cal
R}(m_{\cPZ\cPZ}|m^{\mathrm{Gen}}_{\cPZ\cPZ}).$ (9)

The parameterizations of ${\cal R}(m_{\cPZ\cPZ}|m^{\mathrm{Gen}}_{\cPZ\cPZ})$
and ${\cal E}(m_{\cPZ\cPZ}^{\mathrm{Gen}})$ cover the mass range from 100to
3.5. Figure 7 shows the efficiencies in the $\mathrm{X}\to 4\ell$ and
$\mathrm{X}\to 2\ell 2\Pq$ channels in the various categories. The resolution
in the $4\ell$ final state is 1–2% and 3–5% in the $2\ell 2\Pq$ final state.
With the above ingredients, the $m_{\cPZ\cPZ}$ parameterization is shown in
Fig. 8, for a boson with $m_{\mathrm{X}}=450\GeV$,
$\Gamma_{\mathrm{X}}=10\GeV$ decaying to four leptons. The interference
contributions from $\PH(125)$ and $\Pg\Pg\to\cPZ\cPZ$ background are also
shown.

Figure 7:  The product of efficiency and acceptance for signal events to pass
the $\mathrm{X}\to\cPZ\cPZ\to 4\ell$ (upper plots) and
$\mathrm{X}\to\cPZ\cPZ\to 2\ell 2\Pq$ (lower plots) selection as a function of
the generated mass $m_{\cPZ\cPZ}^{\mathrm{Gen}}$, from $\Pg\Pg\mathrm{F}$
(left) and VBF (right) production modes.

The 2D signal distributions in the $4\ell$ and $2\ell 2\Pq$ final states are
built with the conditional template ${\cal T}(D_{\mathrm{bkg}}|m_{\cPZ\cPZ})$,
which describes the $D_{\mathrm{bkg}}$ discriminant distribution from Eq. (2)
or (3) for each value of $m_{\cPZ\cPZ}$:

$\displaystyle{\cal P}^{i,k}_{vv}(m_{\cPZ\cPZ},D_{\mathrm{bkg}})={\cal
M}^{\mathrm{reco}}_{vv}(m_{\cPZ\cPZ}){\cal T}(D_{\mathrm{bkg}}|m_{\cPZ\cPZ}).$
(10)

The template ${\cal T}(D_{\mathrm{bkg}}|m_{\cPZ\cPZ})$ parameterization
includes all detector effects affecting the $D_{\mathrm{bkg}}$ distribution. A
closure of the full model described by Eq. (10) is achieved by comparing the
model to the simulation for a number of signal parameters.

Figure 8:  Parameterizations of the four lepton invariant mass for
$\Pg\Pg\mathrm{F}$ (left) and VBF (right) production modes, for
$m_{\mathrm{X}}=450\GeV$, $\Gamma_{\mathrm{X}}=10\GeV$. The interference
contributions from $\PH(125)$ and $\Pg\Pg\to\cPZ\cPZ$ or
$\mathrm{V}\mathrm{V}\to\cPZ\cPZ$ background are also shown. The signal cross
section used corresponds to the limit obtained in the $4\ell$ final state.

###  0.6.2 Background model

Common backgrounds among the three final states include the
$\Pg\Pg(\mathrm{V}\mathrm{V})\to\cPZ\cPZ$ process, $\cPZ\cPZ$ produced via
$\qqbar$ annihilation, as well as the $\PW\cPZ$ production process. The
$\Pg\Pg\mathrm{F}$ and EW production of the
$\Pg\Pg(\mathrm{V}\mathrm{V})\to\cPZ\cPZ$ background are treated together with
the $\mathrm{X}$ boson signal and background, including interference between
the corresponding amplitudes, as discussed in detail in Section 0.6.1. Higher
order corrections are applied to these processes as discussed in Section 0.3.

The production of $\cPZ\cPZ$ via $\Pq\Paq$ annihilation is estimated using
simulation. The fully differential cross section for the
$\cPq\cPaq\to\cPZ\cPZ$ process is computed at NNLO [72], and the NNLO/NLO K
factor as a function of $m_{\cPZ\cPZ}$ is applied to the POWHEG sample. This K
factor varies from 1.0 to 1.2 and is 1.1 at $m_{\cPZ\cPZ}=125\GeV$. Additional
NLO EW corrections, which depend on the flavor of the initial state quarks and
on kinematic properties, are also applied in the region
$m_{\cPZ\cPZ}>2m_{\cPZ}$, where the corrections are computed [73, 74, 75]. The
$\PW\cPZ$ production is estimated using simulation, where photon induced EW
corrections are applied [76, 77].

The analysis specific background processes, or the ones whose contribution is
derived from control samples in data, are discussed in the following sections.

#### $\mathrm{X}\to\cPZ\cPZ\to 4\ell$

The most important background to the X signal in the $4\ell$ channel, in
addition to the irreducible arises from processes in which decays of heavy
flavor hadrons, in flight decays of light mesons within jets, or photon
conversion or decay of charged hadrons overlapping with $\pi^{0}$ decays are
misidentified as leptons. The main processes producing these backgrounds are
$\cPZ+{\mathrm{jets}}$, $\ttbar+{\mathrm{jets}}$,
$\cPZ\gamma+{\mathrm{jets}}$, $\PW\PW+{\mathrm{jets}}$, and
$\PW\cPZ+{\mathrm{jets}}$ production. Collectively, we denote these as
“reducible” backgrounds. The contribution from the reducible background is
estimated using two independent methods based on data from dedicated control
regions. The control regions are defined by a dilepton pair satisfying all the
requirements of a $\cPZ_{1}$ candidate and two additional leptons, opposite
sign (OS) or same sign (SS), satisfying more relaxed identification criteria
than the ones used for the selection and categorization for the signal events.
These four leptons are then required to pass the analysis $\cPZ\cPZ$ candidate
selection. The event yield in the signal region is obtained by weighting the
control region events by the lepton misidentification probability, defined as
the fraction of non signal leptons that are identified by the analysis
selection criteria.

The lepton misidentification probabilities are measured separately for
electrons and muons from a control sample that requires a $\cPZ_{1}$ candidate
consisting of a pair of leptons, both passing the selection requirements used
in the analysis, and exactly one additional lepton passing the relaxed
selection.

The predicted yield in the signal region of the reducible background is the
result of a combination of the two methods described above. The shape of the
$m_{4\ell}$ distribution for the reducible background is obtained by combining
the prediction from the OS and SS methods and fitting the distributions with
empirical functional forms built from Landau [78] and exponential
distributions.

#### $\mathrm{X}\to\cPZ\cPZ\to 2\ell 2\Pq$

The majority of the background ($>$90%) is composed of events from
$\cPZ+\text{jets}$ production, where jets associated to the Drell–Yan
production are misidentified as coming from a hadronic decay. Subdominant
backgrounds comprise events from production and from diboson EW production.

The $\ttbar$ background is an important source of contamination in the tagged
category. It is estimated from data using $\Pepm\PGmmp$ events passing the
same selection as for the signal. This method accounts for other small
backgrounds (such as $\PW\PW+\text{jets}$, $\cPZ\to\TT+\text{jets}$, and
single top quark production) where the lepton flavor symmetry can be used as
well. Because of the limited number of events in the $\Pepm\PGmmp$ control
region, the $m_{\cPZ\cPZ}$ shapes are taken from simulation, and the
statistical uncertainty in the control region is considered as the uncertainty
in the background estimation.

In the $\cPZ+$ jets background, the misidentified hadronic comes either from
the combinatoric background of $\cPZ+2$ jets events where the dijet system
happens to have an invariant mass in the range compatible with that of the
$\cPZ$ boson (resolved category) or from an unusual parton shower and
hadronization development for a single jet, leading to a configuration similar
to that of the boosted $\PZ\to\qqbar$ decay (merged category). In both cases,
and in each analysis category, a sideband region with a misidentified hadronic
mass close to that of the signal region can be used to estimate the
contribution of this background. To address the correlation between the
hadronic mass and $m_{\cPZ\cPZ}$ in these configurations, a correction factor
is estimated from simulation.

The alpha transfer factor $\alpha(m_{\cPZ\cPZ}{})$, defined as

$\alpha(m_{\cPZ\cPZ}{})=\frac{N_{\textrm{SIG}}^{\textrm{MC}}(m_{\cPZ\cPZ}{})}{N_{\textrm{SB}}^{\textrm{MC}}(m_{\cPZ\cPZ}{})},$
(11)

is calculated as the ratio of the $m_{\cPZ\cPZ}$ distributions in the signal
and sideband regions for $\cPZ+\text{jets}$ simulated events. The alpha
function is multiplied by the sideband $m_{\cPZ\cPZ}$ distribution to derive
the $\cPZ+\text{jets}$ contribution in the signal region. The
$\cPZ+\text{jets}$ distribution from the sideband is obtained by subtracting
the subdominant backgrounds from MC prediction. Both the shape and the yield
for the $\cPZ+\text{jets}$ background are estimated using this method.

While a binned evaluation of the product of the alpha factor and the sideband
yields would be a complete estimate of the background, low event yields from
data or simulation in specific bins or event categories could induce large
statistical fluctuations in the bins with smaller event yields, occurring at
large values of $m_{\cPZ\cPZ}$. We define a “transition” mass value
$\tilde{m}_{\cPZ\cPZ}$. For $m_{\cPZ\cPZ}<\tilde{m}_{\cPZ\cPZ}$, the binned
evaluation is used as mentioned above. For
$m_{\cPZ\cPZ}>\tilde{m}_{\cPZ\cPZ}$, in order to smooth the background
estimation, the $\cPZ+\text{jets}$ shape is then fit using a sum of two
exponential functions (a single exponential function) for the resolved jet
untagged category (the remaining categories). A binned estimation for
$m_{\cPZ\cPZ}>\tilde{m}_{\cPZ\cPZ}$ is then obtained by integrating the
smoothed estimation in the corresponding intervals. The statistical
uncertainty derived from the fit is propagated to the final result using the
full covariance matrix.

#### $\mathrm{X}\to\cPZ\cPZ\to 2\ell 2\nu$

The $\cPZ+\text{jets}$ background is modeled from a control sample of events
with a single photon produced in association with jets ($\Pgg+\text{jets}$).
This choice has the advantage of making use of a large sample, which captures
the source of instrumental from the $\cPZ$ production in all important
aspects, production mechanism, underlying event conditions, pileup scenario,
and hadronic recoil. By using the $\Pgg+\text{jets}$ expectation we avoid the
need to use the prediction from simulation for the instrumental background
arising from the mismeasurement of jets. Each $\Pgg+\text{jets}$ event must
fulfill similar requirements as the dilepton events: no tagged jets, no
additional identified leptons, and a significant transverse momentum ($\PT\geq
55\GeV$).

The kinematic properties and overall normalization of $\Pgg+\text{jets}$
events are matched to $\cPZ+\text{jets}$ in data through an event by event
reweighting as a function of the boson $\PT$ in each of the event categories
separately, to account for the dependence of the on the associated hadronic
activity. Contamination of the photon data by processes that lead to a photon
produced in association with genuine , such as $\PW(\ell\cPgn)+\Pgg$ and
$\PW(\ell\cPgn)+\text{jets}$ where the jet is mismeasured as a photon, and
$\cPZ(\cPgn\cPgn)+\Pgg$ events, are subtracted using simulation. The
simulation of the in such events is more reliable than in $\cPZ+\text{jets}$
as the is induced by a neutrino and not by detector features. After the $\PT$
reweighting and the requirement, these events represent less than 25% of the
photon sample. This procedure yields a good description of the distribution in
$\cPZ+\text{jets}$ events, as shown in Fig. 9, which compares the distribution
of the reweighted $\Pgg+\text{jets}$ events along with other backgrounds to
the distribution of the dilepton events in data.

To compute $m_{\mathrm{T}}$ for each $\Pgg+\text{jets}$ event,
$\ptvecmiss(\ell\ell)$ is defined as the photon $\ptvecmiss$ and the value of
$m(\ell\ell)$ is chosen according to a probability density function
constructed from the measured dilepton invariant mass distribution in data
(dominated by $\cPZ+\text{jets}$ events). The uncertainty in this background
estimate includes a statistical contribution from the photon control sample
and a contribution from the simulations used to subtract processes with photon
and genuine , and is found to be equal to 100% in the signal region. Another
10% contribution comes from the degree of agreement between the
$\Pgg+\text{jets}$ prediction and the distributions in a simulated dilepton
sample. Uncertainties in the production cross section of the subtracted
processes with genuine are also accounted for and are on the order of 25%.

Figure 9: Distribution of the missing transverse energy in the dilepton signal
region. The points represent the data and the stacked histograms the expected
backgrounds. The lower panel shows the ratio between data and background
estimation.

The background processes that do not involve a $\cPZ$ resonance (nonresonant
background) are estimated using a control sample of events with dileptons of
different flavor ($\Pe^{\pm}\Pgm^{\mp}$) that pass the analysis selection.
This background consists mainly of leptonic decays from $\ttbar$, $\cPqt\PW$,
and $\PW\PW$ events. Small contributions from single top quark events produced
in $s$\- and $t$-channels, $\PW+\text{jets}$ events in which the $\PW$ boson
decays leptonically and a jet is mismeasured as a lepton, and $\cPZ\cPZ$ or
$\cPZ$ events where a $\cPZ$ decays into $\Pgt$ leptons, which produce light
leptons and , are also included in this estimate. This method cannot
distinguish between the nonresonant background and the contribution from
$\PH\to\PW\PW\to 2\ell 2\cPgn$ events, which is treated as a part of the
nonresonant background estimate. The numbers of nonresonant background events
$N_{\Pgm\Pgm}$ and $N_{\Pe\Pe}$ in the $\Pep\Pem$ and $\Pgmp\Pgmm$ final
states are estimated by correcting the number of selected events $N_{\Pe\Pgm}$
in the $\Pe^{\pm}\Pgm^{\mp}$ final state. The correction factor accounts for
the difference in branching fractions, acceptance and efficiency between
unlike flavor and same flavor dilepton events, and is computed as:

$N_{\Pgm\Pgm}=\frac{N_{\Pgm\Pgm}^{\mathrm{SB}}}{N_{\Pe\Pgm}^{\mathrm{SB}}}N_{\Pe\Pgm},\qquad
N_{\Pe\Pe}=\frac{N_{\Pe\Pe}^{\mathrm{SB}}}{N_{\Pe\Pgm}^{SB}}N_{\Pe\Pgm},$ (12)

where $N_{\Pe\Pe}^{\mathrm{SB}}$, $N_{\Pgm\Pgm}^{\mathrm{SB}}$, and
$N_{\Pe\Pgm}^{\mathrm{SB}}$ are the numbers of events in a sideband control
sample of $\Pep\Pem$, $\Pgmp\Pgmm$, and $\Pe^{\pm}\Pgm^{\mp}$ final states,
respectively. The sideband selection is defined by $40<m(\ell\ell)<70\GeV$ or
$110<m(\ell\ell)<200\GeV$, $\ptmiss>70\GeV$, and at least one tagged jet. The
requirement of a tagged jet is used to provide a sample enriched in top quark
events and to suppress possible contamination from $\cPZ+\text{jet}$ events
where a jet is misidentified as a lepton. The correction factor measured in
the sideband is $0.37\pm 0.01\stat$ and $0.68\pm 0.01\stat$ for the $\Pe\Pe$
and $\Pgm\Pgm$ channels, respectively. The uncertainty in the estimate of the
nonresonant background is determined via MC closure tests using simulated
events as well as by comparing results calculated from sideband regions. The
total error is within 13%, which is assigned as the systematic uncertainty in
this method.

##  0.7 Systematic uncertainties

The three final states share common systematic uncertainties arising from the
theoretical prediction, reconstructed objects, and common backgrounds.
Theoretical uncertainties that affect both the signal and background
estimation include uncertainties from the renormalization and factorization
scales and the choice of the PDF set. The uncertainties from the
renormalization and factorization scale are determined by varying these scales
independently by factors of 0.5 and 2 with respect to their nominal values,
while keeping their ratio between 0.5 and 2. The uncertainties from the PDFs
are obtained from the root mean squares of the variations, using different
replicas of the default NNPDF set. An uncertainty of 10% in the K factor used
for the $\Pg\Pg\to\cPZ\cPZ$ prediction is applied, which is derived from
renormalization and factorization scale variations. The uncertainty in the
NNLO-to-NLO K factor for the $\cPZ\cPZ$ and $\PW\cPZ$ cross sections is about
10%. The renormalization and factorization scale and PDF uncertainties are
evaluated from simulation, and are applied to the event categorization and
overall signal and background yields. A systematic uncertainty of 2% in the
$\cPZ$ boson branching fraction value is taken into account for the signal
yields [51].

The uncertainty in the knowledge of the integrated luminosity of the data
samples (2.5%) introduces an uncertainty in the numbers of signal and
background events passing the final selection. Uncertainties in the lepton
identification and reconstruction efficiencies lead to 2.5% uncertainties in
the 4and 9% in the 4 final states for the $4\ell$ selection, 4–8% (2 and 2)
for $2\ell 2\Pq$ and 6–8% for $2\ell 2\nu$ in the normalizations of both
signal and background. The uncertainties in the lepton energy scales are
0.01–0.1% for muons and 0.3% for electrons. A 20% relative uncertainty in the
signal resolution is assigned due to per lepton energy resolution in the
$4\ell$ and $2\ell 2\Pq$ final states. The jet energy scale (JES), jet energy
resolution (JER) and jet reconstruction efficiency uncertainties affect both
signal and background yields and represent the most important uncertainties
for the $2\ell 2\Pq$ signal shapes. The systematic uncertainties that are
common among the three final states are summarized in Table 0.7.

Sources of uncertainties considered in each of the channels included in this
analysis. Uncertainties are given in percent. The numbers shown as ranges
represent the uncertainties in different final states or categories. Most
uncertainties affect the normalizations of the background estimations or
simulated event yields, and those that affect the shape of kinematic
distributions as well are labeled with (*).  Source of uncertainty [%]
$\mathrm{X}\to\cPZ\cPZ$ $\mathrm{X}\to\cPZ\cPZ$ $\mathrm{X}\to\cPZ\cPZ$ $\to
4\ell$ $\to 2\ell$2 $\to 2\ell 2\nu$ Experimental sources Integrated
luminosity 2.5 2.5 2.5 $\ell$ trigger and selection efficiency 2.5–9 4–8 6–8
$\ell$ momentum/energy scale (*) 0.04–0.3 0.1–0.3 0.01–0.3 $\ell$ resolution
(*) 20 20 JES, JER, $\ptmiss$ (*) 1–30 1–10 1–30 tagging/mistag 5–7 2–4
Background estimates $\cPZ+\text{jets}$ 36–43 10–50 20–50 top quark, $\PW\PW$
15 10 $\PW\gamma^{*}$, $\PW\cPZ$ 3–10 15 Theoretical sources Renorm./factor.
scales 3–10 3–10 5–10 PDF set 3–4 3–5 1–4 EW corrections
($\cPq\cPaq\to\cPZ\cPZ$) (*) 1 1 2 NNLO ($\Pg\Pg\to\cPZ\cPZ$) K factor 10 10
10

In addition, each final state has channel specific uncertainties, mainly from
the background estimations based on control samples in data, as well as from
merged jet reconstruction.

###  0.7.1 $\mathrm{X}\to\cPZ\cPZ\to 4\ell$

Experimental uncertainties for this channel arise mainly from the reducible
background estimation. Impacts from the limited numbers of events in the
control regions as well as in the region region where the misidentification
rates evaluated are taken into account. Additional sources of systematic
uncertainty arise from the difference in the composition of the sample from
which the misidentification rate is computed and the control regions of the
two methods where the lepton misidentification probability is applied. The
systematic uncertainty in the $m_{4\ell}$ shape is determined by taking the
envelope of differences among the shapes from the OS and SS methods in the
three different final states. The combined systematic uncertainties are
estimated to be about 36% (4) to 43% (4).

###  0.7.2 $\mathrm{X}\to\cPZ\cPZ\to 2\ell 2\Pq$

The dominant uncertainties in the signal selection efficiency for this channel
arise from uncertainties in the efficiencies to tag the hadronic jet as a in
the high mass boosted categories, and from uncertainties in the tagging
efficiency. The efficiency of the boosted boson tagging selection and its
corresponding systematic uncertainty are measured from data using a sample
enriched in $\ttbar$ events. Uncertainties in the signal efficiencies from the
jet mass scale and resolution are 1–9% and 7–13% depending on the mass.
$\tau_{21}$ selection scale factor and extrapolation lead to 8% and 2–8%
uncertainties. The tagging efficiencies and their corresponding systematic
uncertainties are measured from data enriched in $\ttbar$ events. They account
for 5–7% uncertainties in the total signal efficiencies.

For the background estimated from data, the statistical uncertainty of the
control sample is propagated to an uncertainty in the $\ttbar$+$\PW\PW$
estimation. The alpha method for the $\cPZ+\text{jets}$ background estimation
depends on the uncertainty in the extrapolation factor and on the amount of
data of the dijet mass or pruned jet mass sideband region. Jet energy scale
and resolution affect the extrapolation factor $\alpha(m_{\cPZ\cPZ})$ by 3–10%
depending on the mass. In the low mass region, the statistical uncertainties
in the simulated samples and mass sidebands in data are propagated to the
binned alpha factor estimation. In the high mass region, they are obtained by
the covariance matrix of the fit parameters of the sideband data
$m_{\cPZ\cPZ}$ distributions. Additional systematic uncertainties are derived
from comparisons between the nominal $\cPZ+\text{jets}$ MC descriptions
(exclusive LO samples with different associated parton multiplicities, and
enriched in quark production, all produced with ) and the merged simulations
at NLO. The same background estimation methods are used to derive an
alternative binned description of the $\cPZ+\text{jets}$ background, and
appropriate nuisance parameters, symmetrized around zero, describe the
variation between the nominal and alternative estimation.

For the two dimensional $\mathcal{D}_{\textrm{bkg}}^{\textrm{Zjj}}$ template
shapes, two systematic uncertainties are considered for the signal samples:
JES and JER variations, as well as comparison with identical MC samples where
[79] with EE5C tune [58] is used for parton showering and hadronization
instead of . For background templates, a conservative systematic uncertainty
from the limited size of the MC samples and the consequent smoothing procedure
is derived by using alternative templates where the content of each two
dimensional interval is replaced by the content of the preceding or following
interval in $m_{\cPZ\cPZ}$. Background systematic uncertainties are validated
in an “extended sideband region”, which includes the sideband region used in
the analysis, as well as events failing the $\tau_{21}$ selection. At masses
above 1, 1$\sigma$ differences between data and simulation in this region are
assigned as additional systematic uncertainties.

###  0.7.3 $\mathrm{X}\to\cPZ\cPZ\to 2\ell 2\nu$

Various factors contribute to the experimental uncertainties that apply to
processes derived from MC simulation. These include uncertainties in the
trigger efficiency and lepton selection efficiencies. The effects of lepton
momentum scale and JES are also taken into account and are propagated to the
evaluation of . The uncertainties in the jet veto are estimated by measuring
the tagging efficiency in data enriched in $\ttbar$ and are evaluated to be
2–4% for processes estimated from simulation, namely signal and $\PW\PW$,
$\PW\cPZ$ events. Uncertainties due to the modeling of pileup are evaluated by
varying the total inelastic cross section by $\pm 5\%$ around the nominal
value.

Uncertainties in the background estimates based on control regions in data are
estimated as described in Section 0.6.2. For the Drell–Yan background a
systematic uncertainty of $25$% is combined with a statistical uncertainty
from the size of the photon + jet control sample of 10% for the 0-jet and
$\geq$1-jet categories, and of 50% for the VBF-tagged category. For the
nonresonant background a 15% uncertainty is applied.

##  0.8 Results

The search for a scalar resonance $\mathrm{X}$ decaying to $\cPZ\cPZ$ is
performed over the mass range $130\GeV<m_{\mathrm{X}}<3$, where three final
states are combined, $\mathrm{X}\to\cPZ\cPZ\to 4\ell$, $2\ell 2\Pq$, and
$2\ell 2\nu$. Because of the different resolutions, efficiencies, and
branching fractions, each final state contributes differently depending on the
tested mass. The most sensitive final state between 130 and 500is $4\ell$ due
to its best mass resolution, whereas in the intermediate region 500–700$2\ell
2\nu$ is most sensitive, and for masses above 700$2\ell 2\Pq$ is best.

In $\mathrm{X}\to\cPZ\cPZ\to 4\ell$ and $2\ell 2\Pq$, comparisons between the
two dimensional ($m_{\cPZ\cPZ}$, $\mathcal{D}_{\textrm{bkg}}^{\textrm{Zjj}}$)
distributions observed in data and expected from the sum of background
predictions are made. We set upper limits on the production cross section of
the resonance by combining all the event categories in each analysis.

In $\mathrm{X}\to\cPZ\cPZ\to 2\ell 2\nu$, using the resulting $m_{\mathrm{T}}$
distributions, a shape based analysis is performed to extract the limits. The
shapes of the signal and $\PW\cPZ$, $\cPZ\cPZ$ backgrounds are taken from MC
simulation, those of $\cPZ+\text{jets}$ are taken from data, and for
nonresonant backgrounds, the control region is used to predict both shapes and
normalizations of the $m_{\mathrm{T}}$ distributions in the signal region, as
described in Section 0.6.2.

We follow the modified frequentist prescription described in Refs. [80, 81,
82] (CLs method), and an asymptotic approach with the profile likelihood ratio
as the test statistic is used for upper limits. Systematic uncertainties are
treated as nuisance parameters and profiled using lognormal priors.

The width of the resonance $\Gamma_{\mathrm{X}}$ is allowed to vary, starting
from the narrow width approximation (denoted as $\Gamma_{\mathrm{X}}=0$) up to
a large width. Production of the $\mathrm{X}$ resonance is considered to be
either in $\Pg\Pg\mathrm{F}$ or VBF, where ${\mathrm{V}\mathrm{X}}$ production
is included according to the relative expectation of the
${\mathrm{V}\mathrm{X}}$ and VBF cross sections. No significant excess of
events over the SM expectation is observed. Figure 10 shows upper limits at
the 95% confidence level () on the $\Pp\Pp\to\mathrm{X}\to\cPZ\cPZ$ cross
section $\sigma_{\mathrm{X}}\mathcal{B}_{{\mathrm{X}}\to\cPZ\cPZ}$ as a
function of $m_{\mathrm{X}}$ for $\Gamma_{\mathrm{X}}=$ 0, 10, and 100.

The expected and observed limits on the pure VBF production cross section are
better than the inclusive ones, because the background is smaller in the
dedicated VBF categories. In general, limits are better when assuming a narrow
width signal, since the signal over background ratio is higher. However, in
the mass region below 300, interference effects with background are more
complicated and play a role in the evolution of the limit as a function of
$\Gamma_{\mathrm{X}}$.

For $m_{{\mathrm{X}}}<2m_{\cPZ}$, while the signal events are produced on
shell around $m_{{\mathrm{X}}}$ for $\Gamma_{\mathrm{X}}\sim 0$, the majority
of the events are produced off shell in the case of
$\Gamma_{\mathrm{X}}/m_{{\mathrm{X}}}>1\%$. Thus the relevant background is
quite different when $\Gamma_{\mathrm{X}}$ varies. In the $\Pg\Pg\mathrm{F}$
dominant category, for $130<m_{{\mathrm{X}}}<140$, the signal over background
ratio is better in the relevant off shell region than in the on shell region,
where signal events partly overlap with the $\PH(125)$ peak. This makes the
sensitivity better for a wide resonance. For $150<m_{\mathrm{X}}<180\GeV$,
there is no overlap between the two on shell resonance peaks, so for a narrow
resonance the signal over background ratio is larger and the limit is better.
In the VBF category, the signal over background ratio is always smaller in the
relevant off shell region compared to the on shell region, yielding a better
sensitivity for a wide resonance. The downward fluctuation in the VBF limit
for $\Gamma_{\mathrm{X}}=10$ and 100, and $m_{\mathrm{X}}<180\GeV$, reflects
an overall deficit of events in the VBF category in the off shell region of
$m_{4\ell}>200\GeV$.

Above the 2$m_{\cPZ}$ threshold, for $180<m_{\mathrm{X}}<250\GeV$, the net
interference of the $\Pg\Pg\mathrm{F}$ signal is positive around the peak,
making the wide resonance sensitivity better. For the VBF signal, the
enhancement from interference occurs at its right hand tail, where barely any
background exists. This makes the limit for the wide VBF Higgs better in the
range $m_{\mathrm{X}}<300\GeV$. Above that, the background drops rapidly and
the limits for narrow and wide resonances are compatible.

Figure 11 shows the scan of the observed upper limits at the 95% , as a
function of $m_{\mathrm{X}}$ and $\Gamma_{\mathrm{X}}/m_{\mathrm{X}}$. The
mass is scanned from 130to 3and the relative width from 0 to 30%. The results
are provided with $f_{\mathrm{VBF}}$ profiled and fixed to unity. The excluded
product of the cross section and branching fraction ranges from 1.2fb at 3to
402.6fb at 182in the case of $f_{\mathrm{VBF}}$ profiled, and from 1.0fb at
3to 221.1fb at 134in the VBF production mode.

Figure 10:  Expected and observed upper limits at the 95% on the
$\Pp\Pp\to\mathrm{X}\to\cPZ\cPZ$ cross section as a function of
$m_{\mathrm{X}}$ and for several $\Gamma_{\mathrm{X}}$ values with
$f_{\mathrm{VBF}}$ as a free parameter (left) and fixed to 1 (right). The
results are shown for $4\ell$, $2\ell 2\Pq$, and $2\ell 2\nu$ channels
separately and combined. The reported cross section corresponds to the signal
only contribution in the absence of interference.

Figure 11:  Observed upper limits at the 95% on the
$\Pp\Pp\to\mathrm{X}\to\cPZ\cPZ$ cross section as a function of
$m_{\mathrm{X}}$ and $\Gamma_{\mathrm{X}}/m_{\mathrm{X}}$ values with
$f_{\mathrm{VBF}}$ as a free parameter (left) and fixed to 1 (right). The
results are shown for the $4\ell$, $2\ell 2\Pq$, and $2\ell 2\nu$ channels
combined. The reported cross section corresponds to the signal only
contribution in the absence of interference.

##  0.9 Summary

A search for a new scalar resonance decaying to a pair of $\cPZ$ bosons is
performed for a range of masses between 130and 3with the full data set
recorded by the CMS experiment at 13during 2016 and corresponding to an
integrated luminosity of 35.9. Three final states $\cPZ\cPZ\to 4\ell$, $2\ell
2\Pq$, and $2\ell 2\nu$ are combined in the analysis, where $\ell=\Pe$ or .
Both gluon fusion and electroweak production of the scalar resonance are
considered with a free parameter describing their relative cross sections. A
dedicated categorization of events based on the kinematic properties of the
associated jets is used to improve the sensitivity of the search. A
description of the interference between signal and background amplitudes for a
resonance of an arbitrary width is included. No significant excess of events
over the SM expectation is observed and limits are set on the product of the
cross section and the branching fraction for its decay to $\cPZ\cPZ$ for a
wide range of masses and widths, and for different production mechanisms.

###### Acknowledgements.

We thank Markus Schulze for optimizing the MCFM and JHUGen matrix element
library for this analysis. We congratulate our colleagues in the CERN
accelerator departments for the excellent performance of the LHC and thank the
technical and administrative staffs at CERN and at other CMS institutes for
their contributions to the success of the CMS effort. In addition, we
gratefully acknowledge the computing centres and personnel of the Worldwide
LHC Computing Grid 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: the Austrian Federal Ministry of Science, Research
and Economy and the Austrian Science Fund; the Belgian Fonds de la Recherche
Scientifique, and Fonds voor Wetenschappelijk Onderzoek; the Brazilian Funding
Agencies (CNPq, CAPES, FAPERJ, and FAPESP); the Bulgarian Ministry of
Education and Science; CERN; the Chinese Academy of Sciences, Ministry of
Science and Technology, and National Natural Science Foundation of China; the
Colombian Funding Agency (COLCIENCIAS); the Croatian Ministry of Science,
Education and Sport, and the Croatian Science Foundation; the Research
Promotion Foundation, Cyprus; the Secretariat for Higher Education, Science,
Technology and Innovation, Ecuador; the Ministry of Education and Research,
Estonian Research Council via IUT23-4 and IUT23-6 and European Regional
Development Fund, Estonia; the Academy of Finland, Finnish Ministry of
Education and Culture, and Helsinki Institute of Physics; the Institut
National de Physique Nucléaire et de Physique des Particules / CNRS, and
Commissariat à l’Énergie Atomique et aux Énergies Alternatives / CEA, France;
the Bundesministerium für Bildung und Forschung, Deutsche
Forschungsgemeinschaft, and Helmholtz-Gemeinschaft Deutscher
Forschungszentren, Germany; the General Secretariat for Research and
Technology, Greece; the National Scientific Research Foundation, and National
Innovation Office, Hungary; the Department of Atomic Energy and the Department
of Science and Technology, India; the Institute for Studies in Theoretical
Physics and Mathematics, Iran; the Science Foundation, Ireland; the Istituto
Nazionale di Fisica Nucleare, Italy; the Ministry of Science, ICT and Future
Planning, and National Research Foundation (NRF), Republic of Korea; the
Lithuanian Academy of Sciences; the Ministry of Education, and University of
Malaya (Malaysia); the Mexican Funding Agencies (BUAP, CINVESTAV, CONACYT,
LNS, SEP, and UASLP-FAI); the Ministry of Business, Innovation and Employment,
New Zealand; the Pakistan Atomic Energy Commission; the Ministry of Science
and Higher Education and the National Science Centre, Poland; the Fundação
para a Ciência e a Tecnologia, Portugal; JINR, Dubna; the Ministry of
Education and Science of the Russian Federation, the Federal Agency of Atomic
Energy of the Russian Federation, Russian Academy of Sciences, the Russian
Foundation for Basic Research and the Russian Competitiveness Program of NRNU
“MEPhI”; the Ministry of Education, Science and Technological Development of
Serbia; the Secretaría de Estado de Investigación, Desarrollo e Innovación,
Programa Consolider-Ingenio 2010, Plan de Ciencia, Tecnología e Innovación
2013-2017 del Principado de Asturias and Fondo Europeo de Desarrollo Regional,
Spain; the Swiss Funding Agencies (ETH Board, ETH Zurich, PSI, SNF, UniZH,
Canton Zurich, and SER); the Ministry of Science and Technology, Taipei; the
Thailand Center of Excellence in Physics, the Institute for the Promotion of
Teaching Science and Technology of Thailand, Special Task Force for Activating
Research and the National Science and Technology Development Agency of
Thailand; the Scientific and Technical Research Council of Turkey, and Turkish
Atomic Energy Authority; the National Academy of Sciences of Ukraine, and
State Fund for Fundamental Researches, Ukraine; the Science and Technology
Facilities Council, UK; the US Department of Energy, and the US National
Science Foundation. Individuals have received support from the Marie-Curie
programme and the European Research Council and Horizon 2020 Grant, contract
No. 675440 (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
Ministry of Education, Youth and Sports (MEYS) of the Czech Republic; the
Lendület (“Momentum”) Programme 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 and 125105 (Hungary);
the Council of Scientific and Industrial Research, India; the HOMING PLUS
programme of the Foundation for Polish Science, cofinanced from European
Union, Regional Development Fund, the Mobility Plus programme 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
Programa de Excelencia María de Maeztu and the Programa Severo Ochoa del
Principado de Asturias; the Thalis and Aristeia programmes 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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##  .10 The CMS Collaboration

Yerevan Physics Institute, Yerevan, Armenia
A.M. Sirunyan, A. Tumasyan Institut für Hochenergiephysik, Wien, Austria
W. Adam, F. Ambrogi, E. Asilar, T. Bergauer, J. Brandstetter, E. Brondolin, M.
Dragicevic, J. Erö, A. Escalante Del Valle, M. Flechl, M. Friedl, R.
Frühwirth1, V.M. Ghete, J. Grossmann, J. Hrubec, M. Jeitler1, A. König, N.
Krammer, I. Krätschmer, D. Liko, T. Madlener, I. Mikulec, E. Pree, N. Rad, H.
Rohringer, J. Schieck1, R. Schöfbeck, M. Spanring, D. Spitzbart, A. Taurok, W.
Waltenberger, J. Wittmann, C.-E. Wulz1, M. Zarucki Institute for Nuclear
Problems, Minsk, Belarus
V. Chekhovsky, V. Mossolov, J. Suarez Gonzalez Universiteit Antwerpen,
Antwerpen, Belgium
E.A. De Wolf, D. Di Croce, X. Janssen, J. Lauwers, M. Pieters, M. Van De
Klundert, H. Van Haevermaet, P. Van Mechelen, N. Van Remortel Vrije
Universiteit Brussel, Brussel, Belgium
S. Abu Zeid, F. Blekman, J. D’Hondt, I. De Bruyn, J. De Clercq, K. Deroover,
G. Flouris, D. Lontkovskyi, S. Lowette, I. Marchesini, S. Moortgat, L.
Moreels, Q. Python, K. Skovpen, S. Tavernier, W. Van Doninck, P. Van Mulders,
I. Van Parijs Université Libre de Bruxelles, Bruxelles, Belgium
D. Beghin, B. Bilin, H. Brun, B. Clerbaux, G. De Lentdecker, H. Delannoy, B.
Dorney, G. Fasanella, L. Favart, R. Goldouzian, A. Grebenyuk, A.K. Kalsi, T.
Lenzi, J. Luetic, N. Postiau, T. Seva, E. Starling, C. Vander Velde, P.
Vanlaer, D. Vannerom, R. Yonamine Ghent University, Ghent, Belgium
T. Cornelis, D. Dobur, A. Fagot, M. Gul, I. Khvastunov2, D. Poyraz, C. Roskas,
D. Trocino, M. Tytgat, W. Verbeke, B. Vermassen, M. Vit, N. Zaganidis
Université Catholique de Louvain, Louvain-la-Neuve, Belgium
H. Bakhshiansohi, O. Bondu, S. Brochet, G. Bruno, C. Caputo, A. Caudron, P.
David, S. De Visscher, C. Delaere, M. Delcourt, B. Francois, A. Giammanco, G.
Krintiras, V. Lemaitre, A. Magitteri, A. Mertens, M. Musich, K. Piotrzkowski,
L. Quertenmont, A. Saggio, M. Vidal Marono, S. Wertz, J. Zobec Centro
Brasileiro de Pesquisas Fisicas, Rio de Janeiro, Brazil
W.L. Aldá Júnior, F.L. Alves, G.A. Alves, L. Brito, G. Correia Silva, C.
Hensel, A. Moraes, M.E. Pol, 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, S. Fonseca De Souza, H.
Malbouisson, M. Medina Jaime5, M. Melo De Almeida, C. Mora Herrera, L. Mundim,
H. Nogima, 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
S. Ahujaa, C.A. Bernardesa, L. Calligarisa, T.R. Fernandez Perez Tomeia, E.M.
Gregoresb, P.G. Mercadanteb, S.F. Novaesa, Sandra S. Padulaa, D. Romero Abadb,
J.C. Ruiz Vargasa Institute for Nuclear Research and Nuclear Energy, Bulgarian
Academy of Sciences, Sofia, Bulgaria
A. Aleksandrov, R. Hadjiiska, P. Iaydjiev, A. Marinov, M. Misheva, M. Rodozov,
M. Shopova, G. Sultanov University of Sofia, Sofia, Bulgaria
A. Dimitrov, L. Litov, B. Pavlov, P. Petkov Beihang University, Beijing, China
W. Fang6, X. Gao6, L. Yuan Institute of High Energy Physics, Beijing, China
M. Ahmad, J.G. Bian, G.M. Chen, H.S. Chen, M. Chen, Y. Chen, C.H. Jiang, D.
Leggat, H. Liao, Z. Liu, F. Romeo, S.M. Shaheen, A. Spiezia, J. Tao, C. Wang,
Z. Wang, E. Yazgan, H. Zhang, J. Zhao State Key Laboratory of Nuclear Physics
and Technology, Peking University, Beijing, China
Y. Ban, G. Chen, J. Li, Q. Li, S. Liu, Y. Mao, S.J. Qian, D. Wang, Z. Xu
Tsinghua University, Beijing, China
Y. Wang Universidad de Los Andes, Bogota, Colombia
C. Avila, A. Cabrera, C.A. Carrillo Montoya, L.F. Chaparro Sierra, C. Florez,
C.F. González Hernández, M.A. Segura Delgado University of Split, Faculty of
Electrical Engineering, Mechanical Engineering and Naval Architecture, Split,
Croatia
B. Courbon, N. Godinovic, D. Lelas, I. Puljak, P.M. Ribeiro Cipriano, T.
Sculac University of Split, Faculty of Science, Split, Croatia
Z. Antunovic, M. Kovac Institute Rudjer Boskovic, Zagreb, Croatia
V. Brigljevic, D. Ferencek, K. Kadija, B. Mesic, A. Starodumov7, T. Susa
University of Cyprus, Nicosia, Cyprus
M.W. Ather, A. Attikis, G. Mavromanolakis, J. Mousa, C. Nicolaou, F. Ptochos,
P.A. Razis, H. Rykaczewski Charles University, Prague, Czech Republic
M. Finger8, M. Finger Jr.8 Universidad San Francisco de Quito, Quito, Ecuador
E. Carrera Jarrin Academy of Scientific Research and Technology of the Arab
Republic of Egypt, Egyptian Network of High Energy Physics, Cairo, Egypt
H. Abdalla9, E. El-khateeb10, M.A. Mahmoud11,12 National Institute of Chemical
Physics and Biophysics, Tallinn, Estonia
S. Bhowmik, R.K. Dewanjee, M. Kadastik, L. Perrini, M. Raidal, C. Veelken
Department of Physics, University of Helsinki, Helsinki, Finland
P. Eerola, H. Kirschenmann, J. Pekkanen, M. Voutilainen Helsinki Institute of
Physics, Helsinki, Finland
J. Havukainen, J.K. Heikkilä, T. Järvinen, V. Karimäki, R. Kinnunen, T.
Lampén, K. Lassila-Perini, S. Laurila, S. Lehti, T. Lindén, P. Luukka, T.
Mäenpää, H. Siikonen, E. Tuominen, J. Tuominiemi Lappeenranta University of
Technology, Lappeenranta, Finland
T. Tuuva IRFU, CEA, Université Paris-Saclay, Gif-sur-Yvette, France
M. Besancon, F. Couderc, M. Dejardin, D. Denegri, J.L. Faure, F. Ferri, S.
Ganjour, S. Ghosh, A. Givernaud, P. Gras, G. Hamel de Monchenault, P. Jarry,
C. Leloup, E. Locci, M. Machet, J. Malcles, G. Negro, J. Rander, A. Rosowsky,
M.Ö. Sahin, M. Titov Laboratoire Leprince-Ringuet, Ecole polytechnique,
CNRS/IN2P3, Université Paris-Saclay, Palaiseau, France
A. Abdulsalam13, C. Amendola, I. Antropov, S. Baffioni, F. Beaudette, P.
Busson, L. Cadamuro, C. Charlot, R. Granier de Cassagnac, M. Jo, I. Kucher, S.
Lisniak, A. Lobanov, J. Martin Blanco, M. Nguyen, C. Ochando, G. Ortona, P.
Paganini, P. Pigard, R. Salerno, J.B. Sauvan, Y. Sirois, A.G. Stahl Leiton, Y.
Yilmaz, A. Zabi, A. Zghiche Université de Strasbourg, CNRS, IPHC UMR 7178,
F-67000 Strasbourg, France
J.-L. Agram14, J. Andrea, D. Bloch, J.-M. Brom, M. Buttignol, E.C. Chabert, C.
Collard, E. Conte14, X. Coubez, F. Drouhin14, J.-C. Fontaine14, D. Gelé, U.
Goerlach, M. Jansová, P. Juillot, A.-C. Le Bihan, N. Tonon, P. Van Hove Centre
de Calcul de l’Institut National de Physique Nucleaire et de Physique des
Particules, CNRS/IN2P3, Villeurbanne, France
S. Gadrat Université de Lyon, Université Claude Bernard Lyon 1, CNRS-IN2P3,
Institut de Physique Nucléaire de Lyon, Villeurbanne, France
S. Beauceron, C. Bernet, G. Boudoul, N. Chanon, R. Chierici, D. Contardo, P.
Depasse, H. El Mamouni, J. Fay, L. Finco, S. Gascon, M. Gouzevitch, G.
Grenier, B. Ille, F. Lagarde, I.B. Laktineh, H. Lattaud, M. Lethuillier, L.
Mirabito, A.L. Pequegnot, S. Perries, A. Popov15, V. Sordini, M. Vander
Donckt, S. Viret, S. Zhang Georgian Technical University, Tbilisi, Georgia
A. Khvedelidze8 Tbilisi State University, Tbilisi, Georgia
Z. Tsamalaidze8 RWTH Aachen University, I. Physikalisches Institut, Aachen,
Germany
C. Autermann, L. Feld, M.K. Kiesel, K. Klein, M. Lipinski, M. Preuten, M.P.
Rauch, C. Schomakers, J. Schulz, M. Teroerde, B. Wittmer, V. Zhukov15 RWTH
Aachen University, III. Physikalisches Institut A, Aachen, Germany
A. Albert, D. Duchardt, M. Endres, M. Erdmann, S. Erdweg, T. Esch, R. Fischer,
A. Güth, T. Hebbeker, C. Heidemann, K. Hoepfner, S. Knutzen, M. Merschmeyer,
A. Meyer, P. Millet, S. Mukherjee, T. Pook, M. Radziej, H. Reithler, M.
Rieger, F. Scheuch, D. Teyssier, S. Thüer RWTH Aachen University, III.
Physikalisches Institut B, Aachen, Germany
G. Flügge, B. Kargoll, T. Kress, A. Künsken, T. Müller, A. Nehrkorn, A.
Nowack, C. Pistone, O. Pooth, A. Stahl16 Deutsches Elektronen-Synchrotron,
Hamburg, Germany
M. Aldaya Martin, T. Arndt, C. Asawatangtrakuldee, K. Beernaert, O. Behnke, U.
Behrens, A. Bermúdez Martínez, A.A. Bin Anuar, K. Borras17, V. Botta, A.
Campbell, P. Connor, C. Contreras-Campana, F. Costanza, V. Danilov, A. De Wit,
C. Diez Pardos, D. Domínguez Damiani, G. Eckerlin, D. Eckstein, T. Eichhorn,
E. Eren, E. Gallo18, J. Garay Garcia, A. Geiser, J.M. Grados Luyando, A.
Grohsjean, P. Gunnellini, M. Guthoff, A. Harb, J. Hauk, M. Hempel19, H. Jung,
M. Kasemann, J. Keaveney, C. Kleinwort, J. Knolle, I. Korol, D. Krücker, W.
Lange, A. Lelek, T. Lenz, K. Lipka, W. Lohmann19, R. Mankel, I.-A. Melzer-
Pellmann, A.B. Meyer, M. Meyer, M. Missiroli, G. Mittag, J. Mnich, A.
Mussgiller, D. Pitzl, A. Raspereza, M. Savitskyi, P. Saxena, R. Shevchenko, N.
Stefaniuk, H. Tholen, G.P. Van Onsem, R. Walsh, Y. Wen, K. Wichmann, C.
Wissing, O. Zenaiev University of Hamburg, Hamburg, Germany
R. Aggleton, S. Bein, V. Blobel, M. Centis Vignali, T. Dreyer, E. Garutti, D.
Gonzalez, J. Haller, A. Hinzmann, M. Hoffmann, A. Karavdina, G. Kasieczka, R.
Klanner, R. Kogler, N. Kovalchuk, S. Kurz, D. Marconi, J. Multhaup, M.
Niedziela, D. Nowatschin, T. Peiffer, A. Perieanu, A. Reimers, C. Scharf, P.
Schleper, A. Schmidt, S. Schumann, J. Schwandt, J. Sonneveld, H. Stadie, G.
Steinbrück, F.M. Stober, M. Stöver, D. Troendle, E. Usai, A. Vanhoefer, B.
Vormwald Institut für Experimentelle Teilchenphysik, Karlsruhe, Germany
M. Akbiyik, C. Barth, M. Baselga, S. Baur, E. Butz, R. Caspart, T. Chwalek, F.
Colombo, W. De Boer, A. Dierlamm, N. Faltermann, B. Freund, R. Friese, M.
Giffels, M.A. Harrendorf, F. Hartmann16, S.M. Heindl, U. Husemann, F.
Kassel16, S. Kudella, H. Mildner, M.U. Mozer, Th. Müller, M. Plagge, G. Quast,
K. Rabbertz, M. Schröder, I. Shvetsov, G. Sieber, H.J. Simonis, R. Ulrich, S.
Wayand, M. Weber, T. Weiler, S. Williamson, C. Wöhrmann, R. Wolf Institute of
Nuclear and Particle Physics (INPP), NCSR Demokritos, Aghia Paraskevi, Greece
G. Anagnostou, G. Daskalakis, T. Geralis, A. Kyriakis, D. Loukas, I. Topsis-
Giotis National and Kapodistrian University of Athens, Athens, Greece
G. Karathanasis, S. Kesisoglou, A. Panagiotou, N. Saoulidou, E. Tziaferi
National Technical University of Athens, Athens, Greece
K. Kousouris, I. Papakrivopoulos University of Ioánnina, Ioánnina, Greece
I. Evangelou, C. Foudas, P. Gianneios, P. Katsoulis, P. Kokkas, S. Mallios, N.
Manthos, I. Papadopoulos, E. Paradas, J. Strologas, F.A. Triantis, D.
Tsitsonis MTA-ELTE Lendület CMS Particle and Nuclear Physics Group, Eötvös
Loránd University, Budapest, Hungary
M. Csanad, N. Filipovic, G. Pasztor, O. Surányi, G.I. Veres20 Wigner Research
Centre for Physics, Budapest, Hungary
G. Bencze, C. Hajdu, D. Horvath21, Á. Hunyadi, F. Sikler, T.Á. Vámi, V.
Veszpremi, G. Vesztergombi20 Institute of Nuclear Research ATOMKI, Debrecen,
Hungary
N. Beni, S. Czellar, J. Karancsi22, A. Makovec, J. Molnar, Z. Szillasi
Institute of Physics, University of Debrecen, Debrecen, Hungary
M. Bartók20, P. Raics, Z.L. Trocsanyi, B. Ujvari Indian Institute of Science
(IISc), Bangalore, India
S. Choudhury, J.R. Komaragiri National Institute of Science Education and
Research, Bhubaneswar, India
S. Bahinipati23, P. Mal, K. Mandal, A. Nayak24, D.K. Sahoo23, S.K. Swain
Panjab University, Chandigarh, India
S. Bansal, S.B. Beri, V. Bhatnagar, S. Chauhan, R. Chawla, N. Dhingra, R.
Gupta, A. Kaur, M. Kaur, S. Kaur, R. Kumar, P. Kumari, M. Lohan, A. Mehta, S.
Sharma, J.B. Singh, G. Walia University of Delhi, Delhi, India
A. Bhardwaj, B.C. Choudhary, R.B. Garg, S. Keshri, A. Kumar, Ashok Kumar, S.
Malhotra, M. Naimuddin, K. Ranjan, Aashaq Shah, R. Sharma Saha Institute of
Nuclear Physics, HBNI, Kolkata, India
R. Bhardwaj25, R. Bhattacharya, S. Bhattacharya, U. Bhawandeep25, D. Bhowmik,
S. Dey, S. Dutt25, S. Dutta, S. Ghosh, N. Majumdar, K. Mondal, S.
Mukhopadhyay, S. Nandan, A. Purohit, P.K. Rout, A. Roy, S. Roy Chowdhury, S.
Sarkar, M. Sharan, B. Singh, S. Thakur25 Indian Institute of Technology
Madras, Madras, India
P.K. Behera Bhabha Atomic Research Centre, Mumbai, India
R. Chudasama, D. Dutta, V. Jha, V. Kumar, A.K. Mohanty16, P.K. Netrakanti,
L.M. Pant, P. Shukla, A. Topkar Tata Institute of Fundamental Research-A,
Mumbai, India
T. Aziz, S. Dugad, B. Mahakud, S. Mitra, G.B. Mohanty, N. Sur, B. Sutar Tata
Institute of Fundamental Research-B, Mumbai, India
S. Banerjee, S. Bhattacharya, S. Chatterjee, P. Das, M. Guchait, Sa. Jain, S.
Kumar, M. Maity26, G. Majumder, K. Mazumdar, N. Sahoo, T. Sarkar26, N.
Wickramage27 Indian Institute of Science Education and Research (IISER), Pune,
India
S. Chauhan, S. Dube, V. Hegde, A. Kapoor, K. Kothekar, S. Pandey, A. Rane, S.
Sharma Institute for Research in Fundamental Sciences (IPM), Tehran, Iran
S. Chenarani28, E. Eskandari Tadavani, S.M. Etesami28, M. Khakzad, M.
Mohammadi Najafabadi, M. Naseri, S. Paktinat Mehdiabadi29, F. Rezaei
Hosseinabadi, B. Safarzadeh30, M. Zeinali University College Dublin, Dublin,
Ireland
M. Felcini, M. Grunewald INFN Sezione di Bari a, Università di Bari b,
Politecnico di Bari c, Bari, Italy
M. Abbresciaa,b, C. Calabriaa,b, A. Colaleoa, D. Creanzaa,c, L. Cristellaa,b,
N. De Filippisa,c, M. De Palmaa,b, A. Di Florioa,b, F. Erricoa,b, L. Fiorea,
A. Gelmia,b, G. Iasellia,c, S. Lezkia,b, G. Maggia,c, M. Maggia, B.
Marangellia,b, G. Minielloa,b, S. Mya,b, S. Nuzzoa,b, A. Pompilia,b, G.
Pugliesea,c, R. Radognaa, A. Ranieria, G. Selvaggia,b, A. Sharmaa, L.
Silvestrisa,16, R. Vendittia, P. Verwilligena, G. Zitoa INFN Sezione di
Bologna a, Università di Bologna b, Bologna, Italy
G. Abbiendia, C. Battilanaa,b, D. Bonacorsia,b, L. Borgonovia,b, S. Braibant-
Giacomellia,b, R. Campaninia,b, P. Capiluppia,b, A. Castroa,b, F.R. Cavalloa,
S.S. Chhibraa,b, G. Codispotia,b, M. Cuffiania,b, G.M. Dallavallea, F.
Fabbria, A. Fanfania,b, D. Fasanellaa,b, P. Giacomellia, C. Grandia, L.
Guiduccia,b, S. Marcellinia, G. Masettia, A. Montanaria, F.L. Navarriaa,b, F.
Odoricia, A. Perrottaa, A.M. Rossia,b, T. Rovellia,b, G.P. Sirolia,b, N. Tosia
INFN Sezione di Catania a, Università di Catania b, Catania, Italy
S. Albergoa,b, S. Costaa,b, A. Di Mattiaa, F. Giordanoa,b, R. Potenzaa,b, A.
Tricomia,b, C. Tuvea,b INFN Sezione di Firenze a, Università di Firenze b,
Firenze, Italy
G. Barbaglia, K. Chatterjeea,b, V. Ciullia,b, C. Civininia, R.
D’Alessandroa,b, E. Focardia,b, G. Latino, P. Lenzia,b, M. Meschinia, S.
Paolettia, L. Russoa,31, G. Sguazzonia, D. Stroma, L. Viliania INFN Laboratori
Nazionali di Frascati, Frascati, Italy
L. Benussi, S. Bianco, F. Fabbri, D. Piccolo, F. Primavera16 INFN Sezione di
Genova a, Università di Genova b, Genova, Italy
V. Calvellia,b, F. Ferroa, F. Raveraa,b, E. Robuttia, S. Tosia,b INFN Sezione
di Milano-Bicocca a, Università di Milano-Bicocca b, Milano, Italy
A. Benagliaa, A. Beschib, L. Brianzaa,b, F. Brivioa,b, V. Cirioloa,b,16, M.E.
Dinardoa,b, S. Fiorendia,b, S. Gennaia, A. Ghezzia,b, P. Govonia,b, M.
Malbertia,b, S. Malvezzia, R.A. Manzonia,b, D. Menascea, L. Moronia, M.
Paganonia,b, K. Pauwelsa,b, D. Pedrinia, S. Pigazzinia,b,32, S. Ragazzia,b, T.
Tabarelli de Fatisa,b INFN Sezione di Napoli a, Università di Napoli ’Federico
II’ b, Napoli, Italy, Università della Basilicata c, Potenza, Italy,
Università G. Marconi d, Roma, Italy
S. Buontempoa, N. Cavalloa,c, S. Di Guidaa,d,16, F. Fabozzia,c, F. Fiengaa,b,
G. Galatia,b, A.O.M. Iorioa,b, W.A. Khana, L. Listaa, S. Meolaa,d,16, P.
Paoluccia,16, C. Sciaccaa,b, F. Thyssena, E. Voevodinaa,b INFN Sezione di
Padova a, Università di Padova b, Padova, Italy, Università di Trento c,
Trento, Italy
P. Azzia, N. Bacchettaa, L. Benatoa,b, D. Biselloa,b, A. Bolettia,b, R.
Carlina,b, A. Carvalho Antunes De Oliveiraa,b, P. Checchiaa, M. Dall’Ossoa,b,
P. De Castro Manzanoa, T. Dorigoa, U. Dossellia, F. Gasparinia,b, U.
Gasparinia,b, A. Gozzelinoa, S. Lacapraraa, P. Lujan, M. Margonia,b, A.T.
Meneguzzoa,b, N. Pozzobona,b, P. Ronchesea,b, R. Rossina,b, A. Tiko, E.
Torassaa, M. Zanettia,b, P. Zottoa,b, G. Zumerlea,b INFN Sezione di Pavia a,
Università di Pavia b, Pavia, Italy
A. Braghieria, A. Magnania, P. Montagnaa,b, S.P. Rattia,b, V. Rea, M.
Ressegottia,b, C. Riccardia,b, P. Salvinia, I. Vaia,b, P. Vituloa,b INFN
Sezione di Perugia a, Università di Perugia b, Perugia, Italy
L. Alunni Solestizia,b, M. Biasinia,b, G.M. Bileia, C. Cecchia,b, D.
Ciangottinia,b, L. Fanòa,b, P. Laricciaa,b, R. Leonardia,b, E. Manonia, G.
Mantovania,b, V. Mariania,b, M. Menichellia, A. Rossia,b, A. Santocchiaa,b, D.
Spigaa INFN Sezione di Pisa a, Università di Pisa b, Scuola Normale Superiore
di Pisa c, Pisa, Italy
K. Androsova, P. Azzurria,16, G. Bagliesia, L. Bianchinia, T. Boccalia, L.
Borrello, R. Castaldia, M.A. Cioccia,b, R. Dell’Orsoa, G. Fedia, L.
Gianninia,c, A. Giassia, M.T. Grippoa,31, F. Ligabuea,c, T. Lomtadzea, E.
Mancaa,c, G. Mandorlia,c, A. Messineoa,b, F. Pallaa, A. Rizzia,b, P.
Spagnoloa, R. Tenchinia, G. Tonellia,b, A. Venturia, P.G. Verdinia INFN
Sezione di Roma a, Sapienza Università di Roma b, Rome, Italy
L. Baronea,b, F. Cavallaria, M. Cipriania,b, N. Dacia, D. Del Rea,b, E. Di
Marcoa,b, M. Diemoza, S. Gellia,b, E. Longoa,b, B. Marzocchia,b, P.
Meridiania, G. Organtinia,b, F. Pandolfia, R. Paramattia,b, F. Preiatoa,b, S.
Rahatloua,b, C. Rovellia, F. Santanastasioa,b INFN Sezione di Torino a,
Università di Torino b, Torino, Italy, Università del Piemonte Orientale c,
Novara, Italy
N. Amapanea,b, R. Arcidiaconoa,c, S. Argiroa,b, M. Arneodoa,c, N. Bartosika,
R. Bellana,b, C. Biinoa, N. Cartigliaa, R. Castelloa,b, F. Cennaa,b, M.
Costaa,b, R. Covarellia,b, A. Deganoa,b, N. Demariaa, B. Kiania,b, C.
Mariottia, S. Masellia, E. Migliorea,b, V. Monacoa,b, E. Monteila,b, M.
Montenoa, M.M. Obertinoa,b, L. Pachera,b, N. Pastronea, M. Pelliccionia, G.L.
Pinna Angionia,b, A. Romeroa,b, M. Ruspaa,c, R. Sacchia,b, K. Shchelinaa,b, V.
Solaa, A. Solanoa,b, A. Staianoa INFN Sezione di Trieste a, Università di
Trieste b, Trieste, Italy
S. Belfortea, M. Casarsaa, F. Cossuttia, G. Della Riccaa,b, A. Zanettia
Kyungpook National University
D.H. Kim, G.N. Kim, M.S. Kim, J. Lee, S. Lee, S.W. Lee, C.S. Moon, Y.D. Oh, S.
Sekmen, D.C. Son, Y.C. Yang Chonnam National University, Institute for
Universe and Elementary Particles, Kwangju, Korea
H. Kim, D.H. Moon, G. Oh Hanyang University, Seoul, Korea
J.A. Brochero Cifuentes, J. Goh, T.J. Kim Korea University, Seoul, Korea
S. Cho, S. Choi, Y. Go, D. Gyun, S. Ha, B. Hong, Y. Jo, Y. Kim, K. Lee, K.S.
Lee, S. Lee, J. Lim, S.K. Park, Y. Roh Seoul National University, Seoul, Korea
J. Almond, J. Kim, J.S. Kim, H. Lee, K. Lee, K. Nam, S.B. Oh, B.C. Radburn-
Smith, S.h. Seo, U.K. Yang, H.D. Yoo, G.B. Yu University of Seoul, Seoul,
Korea
H. Kim, J.H. Kim, J.S.H. Lee, I.C. Park Sungkyunkwan University, Suwon, Korea
Y. Choi, C. Hwang, J. Lee, I. Yu Vilnius University, Vilnius, Lithuania
V. Dudenas, A. Juodagalvis, J. Vaitkus National Centre for Particle Physics,
Universiti Malaya, Kuala Lumpur, Malaysia
I. Ahmed, Z.A. Ibrahim, M.A.B. Md Ali33, F. Mohamad Idris34, W.A.T. Wan
Abdullah, M.N. Yusli, Z. Zolkapli Centro de Investigacion y de Estudios
Avanzados del IPN, Mexico City, Mexico
Duran-Osuna, M. C., H. Castilla-Valdez, E. De La Cruz-Burelo, Ramirez-Sanchez,
G., I. Heredia-De La Cruz35, Rabadan-Trejo, R. I., R. Lopez-Fernandez, J.
Mejia Guisao, Reyes-Almanza, R, A. Sanchez-Hernandez Universidad
Iberoamericana, Mexico City, Mexico
S. Carrillo Moreno, C. Oropeza Barrera, F. Vazquez Valencia Benemerita
Universidad Autonoma de Puebla, Puebla, Mexico
J. Eysermans, I. Pedraza, H.A. Salazar Ibarguen, C. Uribe Estrada Universidad
Autónoma de San Luis Potosí, San Luis Potosí, Mexico
A. Morelos Pineda University of Auckland, Auckland, New Zealand
D. Krofcheck University of Canterbury, Christchurch, New Zealand
S. Bheesette, P.H. Butler National Centre for Physics, Quaid-I-Azam
University, Islamabad, Pakistan
A. Ahmad, M. Ahmad, Q. Hassan, H.R. Hoorani, A. Saddique, M.A. Shah, M.
Shoaib, M. Waqas National Centre for Nuclear Research, Swierk, Poland
H. Bialkowska, M. Bluj, B. Boimska, T. Frueboes, M. Górski, M. Kazana, K.
Nawrocki, M. Szleper, P. Traczyk, P. Zalewski Institute of Experimental
Physics, Faculty of Physics, University of Warsaw, Warsaw, Poland
K. Bunkowski, A. Byszuk36, K. Doroba, A. Kalinowski, M. Konecki, J.
Krolikowski, M. Misiura, M. Olszewski, A. Pyskir, M. Walczak Laboratório de
Instrumentação e Física Experimental de Partículas, Lisboa, Portugal
P. Bargassa, C. Beirão Da Cruz E Silva, A. Di Francesco, P. Faccioli, B.
Galinhas, M. Gallinaro, J. Hollar, N. Leonardo, L. Lloret Iglesias, M.V.
Nemallapudi, J. Seixas, G. Strong, O. Toldaiev, D. Vadruccio, J. Varela Joint
Institute for Nuclear Research, Dubna, Russia
V. Alexakhin, A. Golunov, I. Golutvin, N. Gorbounov, I. Gorbunov, A. Kamenev,
V. Karjavin, A. Lanev, A. Malakhov, V. Matveev37,38, P. Moisenz, V. Palichik,
V. Perelygin, M. Savina, S. Shmatov, S. Shulha, N. Skatchkov, V. Smirnov, A.
Zarubin Petersburg Nuclear Physics Institute, Gatchina (St. Petersburg),
Russia
Y. Ivanov, V. Kim39, E. Kuznetsova40, P. Levchenko, V. Murzin, V. Oreshkin, I.
Smirnov, D. Sosnov, V. Sulimov, L. Uvarov, S. Vavilov, A. Vorobyev Institute
for Nuclear Research, Moscow, Russia
Yu. Andreev, A. Dermenev, S. Gninenko, N. Golubev, A. Karneyeu, M. Kirsanov,
N. Krasnikov, A. Pashenkov, D. Tlisov, A. Toropin Institute for Theoretical
and Experimental Physics, Moscow, Russia
V. Epshteyn, V. Gavrilov, N. Lychkovskaya, V. Popov, I. Pozdnyakov, G.
Safronov, A. Spiridonov, A. Stepennov, V. Stolin, M. Toms, E. Vlasov, A.
Zhokin Moscow Institute of Physics and Technology, Moscow, Russia
T. Aushev, A. Bylinkin38 National Research Nuclear University ’Moscow
Engineering Physics Institute’ (MEPhI), Moscow, Russia
R. Chistov41, M. Danilov41, P. Parygin, D. Philippov, S. Polikarpov, E.
Tarkovskii P.N. Lebedev Physical Institute, Moscow, Russia
V. Andreev, M. Azarkin38, I. Dremin38, M. Kirakosyan38, S.V. Rusakov, A.
Terkulov Skobeltsyn Institute of Nuclear Physics, Lomonosov Moscow State
University, Moscow, Russia
A. Baskakov, A. Belyaev, E. Boos, V. Bunichev, M. Dubinin42, L. Dudko, A.
Ershov, A. Gribushin, V. Klyukhin, O. Kodolova, I. Lokhtin, I. Miagkov, S.
Obraztsov, S. Petrushanko, V. Savrin Novosibirsk State University (NSU),
Novosibirsk, Russia
V. Blinov43, D. Shtol43, Y. Skovpen43 State Research Center of Russian
Federation, Institute for High Energy Physics of NRC &quot, Kurchatov
Institute&quot, , Protvino, Russia
I. Azhgirey, I. Bayshev, S. Bitioukov, D. Elumakhov, A. Godizov, V. Kachanov,
A. Kalinin, D. Konstantinov, P. Mandrik, V. Petrov, R. Ryutin, A. Sobol, S.
Troshin, N. Tyurin, A. Uzunian, A. Volkov National Research Tomsk Polytechnic
University, Tomsk, Russia
A. Babaev University of Belgrade, Faculty of Physics and Vinca Institute of
Nuclear Sciences, Belgrade, Serbia
P. Adzic44, P. Cirkovic, D. Devetak, M. Dordevic, J. Milosevic Centro de
Investigaciones Energéticas Medioambientales y Tecnológicas (CIEMAT), Madrid,
Spain
J. Alcaraz Maestre, A. Álvarez Fernández, I. Bachiller, M. Barrio Luna, M.
Cerrada, N. Colino, B. De La Cruz, A. Delgado Peris, C. Fernandez Bedoya, J.P.
Fernández Ramos, J. Flix, M.C. Fouz, O. Gonzalez Lopez, S. Goy Lopez, J.M.
Hernandez, M.I. Josa, D. Moran, A. Pérez-Calero Yzquierdo, J. Puerta Pelayo,
I. Redondo, L. Romero, M.S. Soares, A. Triossi Universidad Autónoma de Madrid,
Madrid, Spain
C. Albajar, J.F. de Trocóniz Universidad de Oviedo, Oviedo, Spain
J. Cuevas, C. Erice, J. Fernandez Menendez, S. Folgueras, I. Gonzalez
Caballero, J.R. González Fernández, E. Palencia Cortezon, S. Sanchez Cruz, P.
Vischia, J.M. Vizan Garcia Instituto de Física de Cantabria (IFCA), CSIC-
Universidad de Cantabria, Santander, Spain
I.J. Cabrillo, A. Calderon, B. Chazin Quero, J. Duarte Campderros, M.
Fernandez, P.J. Fernández Manteca, A. García Alonso, J. Garcia-Ferrero, G.
Gomez, A. Lopez Virto, J. Marco, C. Martinez Rivero, P. Martinez Ruiz del
Arbol, F. Matorras, J. Piedra Gomez, C. Prieels, T. Rodrigo, A. Ruiz-Jimeno,
L. Scodellaro, N. Trevisani, I. Vila, R. Vilar Cortabitarte CERN, European
Organization for Nuclear Research, Geneva, Switzerland
D. Abbaneo, B. Akgun, E. Auffray, P. Baillon, A.H. Ball, D. Barney, J.
Bendavid, M. Bianco, A. Bocci, C. Botta, T. Camporesi, M. Cepeda, G.
Cerminara, E. Chapon, Y. Chen, D. d’Enterria, A. Dabrowski, V. Daponte, A.
David, M. De Gruttola, A. De Roeck, N. Deelen, M. Dobson, T. du Pree, M.
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W. Bertl${}^{\textrm{\textdagger}}$, L. Caminada50, K. Deiters, W. Erdmann, R.
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Kuo, W. Lin, A. Pozdnyakov, S.S. Yu National Taiwan University (NTU), Taipei,
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Chulalongkorn University, Faculty of Science, Department of Physics, Bangkok,
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