SMP-20-007

SMP-20-007

[inst1]CMS experiment

# Measurement of double-parton scattering in inclusive production of four jets
with low transverse momentum in proton-proton collisions at $\sqrt{s}=13\TeV$

###### Abstract

A measurement of inclusive four-jet production in proton-proton collisions at
a center-of-mass energy of 13is presented. The transverse momenta of jets
within $\abs{\eta}<4.7$ reach down to 35, 30, 25, and 20for the first-,
second-, third-, and fourth-leading jet, respectively. Differential cross
sections are measured as functions of the jet transverse momentum, jet
pseudorapidity, and several other observables that describe the angular
correlations between the jets. The measured distributions show sensitivity to
different aspects of the underlying event, parton shower, and matrix element
calculations. In particular, the interplay between angular correlations caused
by parton shower and double-parton scattering contributions is shown to be
important. The double-parton scattering contribution is extracted by means of
a template fit to the data, using distributions for single-parton scattering
obtained from Monte Carlo event generators and a double-parton scattering
distribution constructed from inclusive single-jet events in data. The
effective double-parton scattering cross section is calculated and discussed
in view of previous measurements and of its dependence on the models used to
describe the single-parton scattering background.

##  0.1 Introduction

Quantum chromodynamics (QCD), the theory of strong interactions, provides a
good description of the production of hadron jets with large transverse
momentum () in high-energy proton-proton ($\Pp\Pp$) collisions. This is
achieved by factorizing the cross section into a perturbatively calculable
matrix element describing the scattering between partons, and parton
distribution functions (PDFs) that provide the probability to find a parton
with given properties within the proton. The PDFs cannot be perturbatively
calculated and are obtained by fitting available data. Measurements of the
cross section for the production of inclusive high-jets have been performed by
the CMS collaboration at various center-of-mass energies and show agreement
with perturbative QCD predictions at next-to-leading-order (NLO) accuracy [1,
2, 3]. However, final states with multiple jets are not as well understood,
suggesting a need for additional theoretical treatments of the strong
interaction.

Multijet final states can be produced in a single-parton scattering (SPS).
Depending on the order of the matrix element in the strong coupling, two or
more jets can be produced in SPS. Radiation before and/or after the
interaction between the partons, as described by parton shower models, can
contribute additional jets to the final state. Thus, predictions for multijet
processes in SPS provide an important test of the matching between fixed-order
matrix element calculations and the parton-shower formalism. A different
approach introduces an additional hard scattering in the $\Pp\Pp$ collision,
which also contributes a number of jets to the final state. Such processes are
in general referred to as double-parton scattering (DPS), and they represent
the simplest case of multiple-parton interactions (MPI). A schematic depiction
of inclusive four-jet production through SPS and DPS is shown in Fig. 1.

The cross section of a DPS process, $\sigma_{\mathrm{A,B}}^{\mathrm{DPS}}$,
where A and B denote two processes with their own respective cross sections
$\sigma_{\mathrm{A}}$ and $\sigma_{\mathrm{B}}$, can be expressed as:

$\sigma_{\mathrm{A,B}}^{\mathrm{DPS}}=\frac{m}{2}\frac{\sigma_{\mathrm{A}}\sigma_{\mathrm{B}}}{\sigma_{\text{eff}}}.$
(1)

The factor $m$ is a combinatorial factor, which is equal to 1 for identical
processes and 2 for nonidentical processes. The effective cross section
($\sigma_{\text{eff}}$) reflects how strongly the occurrence of A and B is
correlated [4]. For fully uncorrelated production of A and B,
$\sigma_{\text{eff}}$ tends to the total inelastic $\Pp\Pp$ cross section,
whereas a small $\sigma_{\text{eff}}$ indicates an enhanced simultaneous
occurrence of processes A and B. For multijet production, SPS processes often
exhibit strong kinematic correlations between all jets, whereas DPS processes
will manifest a distinctly different behavior. Indeed, the jets resulting from
DPS are more often produced in two independent pairs, each in a back-to-back
configuration in the transverse plane. The relevance of DPS rises with
increasing center-of-mass energy; at higher energy and for fixed of the jets,
smaller values of the momentum fraction of the protons carried by the partons
are probed, resulting in a strong increase of the gluon density and a larger
probability for DPS. A study of the extent to which DPS processes can
supplement various SPS models is therefore beneficial for a complete
description of hadronic interactions.

Figure 1: A schematic depiction of inclusive four-jet production through SPS
(left) and DPS (right). In the case of SPS, one hard scattering produces the
jets $a$ through $d$, whereas two independent hard scatterings create two jets
each in the case of DPS. Since the two jet pairs are created independently in
a DPS event, they are expected to show different kinematic correlations
compared with the four jets originating from an SPS event.

Various DPS measurements at different center-of-mass energies and for various
final states have been performed. Studies including one or two photons in the
final state have been published in Refs. [5, 6, 7, 8, 9]. Signatures involving
one or two vector bosons have been measured by the ATLAS and CMS
Collaborations [10, 11, 12, 13, 14]. Other studies have opted to include the
production of heavy flavors [15, 16, 17, 18, 19]. Earlier measurements in the
four-jet final state have been performed by the UA2 and CDF experiments [20,
21]. The ATLAS and CMS Collaborations have more recently also performed DPS
measurements with four jets [22, 23, 24, 25] at a center-of-mass energy of 7.
The CMS Collaboration additionally performed at 7 [26] a measurement of the
final state with two b-tagged jets in combination with two light-flavored
jets.

This paper presents an analysis of the inclusive production of four-jet events
in $\Pp\Pp$ collisions at a center-of-mass energy of 13. The data correspond
to an integrated luminosity of 42 and were collected with the CMS detector at
the CERN LHC in 2016 during a special data-taking period with a low
probability for several $\Pp\Pp$ interactions occurring within the same or
neighbouring bunch crossings (pileup). This avoids the confusion caused by
pilup and enables us to include jets with low pT. As a result of the low-jets,
a custom calibration of the jet energy scale is required. Data are corrected
for detector efficiency and resolution effects by means of an unfolding
procedure.

Several aspects of multijet production are studied by comparing the
distributions of DPS-sensitive observables predicted by various Monte Carlo
(MC) event generators with the distributions measured in data. These
observables all exploit differences in the kinematic correlations between the
jets expected for SPS and DPS. The DPS cross section is extracted with a
template method. A pure DPS signal template is reconstructed from data by
randomly mixing two inclusive single-jet events into one inclusive DPS four-
jet event. This is then fitted together with several SPS-only background MC
models to the distributions obtained from inclusive four-jet data. Finally,
the effective cross section is computed using Eq. (1), with
$\sigma_{\mathrm{A}}$ and $\sigma_{\mathrm{B}}$ measured from data.

Tabulated results are provided in the HEPData record for this analysis [27].

This paper is organized as follows. In Section 0.2, the observables of
interest are defined. Section 0.3 gives a brief overview of the CMS detector.
The MC models used in the comparison with data are detailed in Section 0.4,
whereas the data samples, event selection, and correction procedure are
discussed in Section 0.5. The strategy for the extraction of the DPS cross
section and $\sigma_{\text{eff}}$ is detailed in Section 0.6. Systematic
uncertainties for each of the unfolded observables are discussed in Section
0.7. Section 0.8 contains a discussion of the results, which are summarized in
Section 0.9.

##  0.2 Observables

Six observables are defined to study DPS in four-jet production processes.
Many of these variables have been used in earlier measurements [5, 6, 7, 8, 9,
10, 11, 12, 13, 15, 16, 17, 18, 19, 22, 23, 24, 25, 26] and in
phenomenological studies [28, 29, 30, 31, 32, 33]. The four leading jets are
ordered with decreasing . Based on the azimuthal angle ($\phi$),
pseudorapidity ($\eta$), and transverse momentum vector
($\vec{p}_{\mathrm{T}}$), the variables studied in this paper can be described
as follows.

  * •

The azimuthal angular difference between the two softest jets:

$\Delta\phi_{\text{Soft}}=|\phi_{3}-\phi_{4}|.$

The two softest jets are more likely to be in a back-to-back configuration
when produced by DPS since there is an increased probability that the two
softest jets are produced in an independent scattering fron the two hardest
jets and since the momentum should be conserved in the transverse plane. The
increased probability leads to an enhanced DPS contribution around
$\Delta\phi_{\text{Soft}}=\pi$.

  * •

The minimal combined azimuthal angular range of three jets:

$\Delta\phi_{\mathrm{3j}}^{\text{min}}=\min\left\\{|\phi_{i}-\phi_{j}|+|\phi_{j}-\phi_{k}|\middle|i,j,k\in[1,2,3,4],i\neq
j\neq k\right\\}.$

In DPS, at least two out of three jets are more likely to be in a back-to-back
configuration, while SPS processes have a more random distribution in their
azimuthal angular difference. Therefore, a DPS process is prone to yield
larger values of $\Delta\phi_{\mathrm{3j}}^{\text{min}}$ [33].

  * •

The maximum $\eta$ difference between two jets:

$\Delta Y=\max\left\\{|\eta_{i}-\eta_{j}|\middle|i,j\in[1,2,3,4],i\neq
j\right\\}.$

As the maximum separation in $\eta$ between two jets becomes larger, the
probability for the two jets to originate from two different parton
interactions increases.

  * •

The azimuthal angular difference between the jets with the largest $\eta$
separation:

$\phi_{ij}=|\phi_{i}-\phi_{j}|\quad\mathrm{for}\quad\Delta
Y=|\eta_{i}-\eta_{j}|$

Since the most remote jets are more likely to be produced in separate DPS
subprocesses, a decorrelation in the distribution of the azimuthal angular
difference of these jets is expected, whereas the jets will show stronger
correlations in a SPS event.

  * •

The transverse momentum balance of the two softest jets:

$\Delta
p_{\text{T,Soft}}=\frac{|\vec{p}_{\mathrm{T,3}}+\vec{p}_{\mathrm{T,4}}|}{|\vec{p}_{\mathrm{T,3}}|+|\vec{p}_{\mathrm{T,4}}|}.$

When the two softest jets originate from a DPS process, they are more likely
to be in a back-to-back configuration rendering the value for $\Delta
p_{\text{T,Soft}}$ small. In SPS processes, the two softest jets do not
necessarily balance.

  * •

The azimuthal angular difference between the hard and the soft jet pairs:

$\Delta
S=\arccos{\left(\frac{(\vec{p}_{\mathrm{T,1}}+\vec{p}_{\mathrm{T,2}})\cdot(\vec{p}_{\mathrm{T,3}}+\vec{p}_{\mathrm{T,4}})}{|\vec{p}_{\mathrm{T,1}}+\vec{p}_{\mathrm{T,2}}|\
|\vec{p}_{\mathrm{T,3}}+\vec{p}_{\mathrm{T,4}}|}\right)}.$

In a SPS process, the four jets must balance so that the $\Delta S$
distribution peaks around $\pi$, while in DPS the two jet pairs are more
likely to be independently produced, yielding a less correlated $\Delta S$
distribution. Thus we anticipate that DPS events tend toward lower values of
$\Delta S$.

##  0.3 Measuring jets with the CMS detector

The central feature of the CMS apparatus is a superconducting solenoid of 6m
internal diameter, providing a magnetic field of 3.8T. Within the solenoid
volume are a silicon pixel and strip tracker, a lead tungstate crystal
electromagnetic calorimeter (ECAL), and a brass and scintillator hadron
calorimeter (HCAL), each composed of a barrel and two endcap sections. Forward
calorimeters extend the $\eta$ coverage provided by the barrel and endcap
detectors. Muons are detected in gas-ionization chambers embedded in the steel
flux-return yoke outside the solenoid.

The silicon tracker measures charged particles within the range
$\abs{\eta}<2.5$. During the LHC running period when the data used in this
paper were recorded, the silicon tracker consisted of 1440 silicon pixel and
15 148 silicon strip detector modules.

The ECAL consists of 75 848 lead tungstate crystals, which provide coverage in
$\abs{\eta}<1.48$ in a barrel region and $1.48<\abs{\eta}<3.0$ in the two
endcap regions. Preshower detectors consisting of two planes of silicon
sensors interleaved with a total of $3X_{0}$ of lead are located in front of
each endcap detector.

In the region $\abs{\eta}<1.74$, the HCAL cells have widths of 0.087 in $\eta$
and 0.087 in azimuth ($\phi$). In the $\eta$-$\phi$ plane, and for
$\abs{\eta}<1.48$, the HCAL cells map on to $5\times 5$ arrays of ECAL
crystals to form calorimeter towers projecting radially outwards from close to
the nominal interaction point. For $\abs{\eta}>1.74$, the coverage of the
towers increases progressively to a maximum of 0.174 in $\Delta\eta$ and
$\Delta\phi$. Within each tower, the energy deposits in ECAL and HCAL cells
are summed to define the calorimeter tower energies.

The forward hadron (HF) calorimeter uses steel as an absorber and quartz
fibers as the sensitive material. The two halves of the HF are located 11.2m
from the interaction region, one on each end, and together they provide
coverage in the range $3.0<\abs{\eta}<5.2$. They also serve as luminosity
monitors.

Events of interest are selected using a two-tiered trigger system. The first
level (L1), composed of custom hardware processors, uses information from the
calorimeters and muon detectors to select events at a rate of around 100kHz
within a fixed latency of about 4 [34]. The second level, known as the high-
level trigger (HLT), consists of a farm of processors running a version of the
full event reconstruction software optimized for fast processing, and reduces
the event rate to around 1kHz before data storage [35].

A global event reconstruction (particle flow) algorithm [36] reconstructs and
identifies each individual particle in an event, with an optimized combination
of all subdetector information. Jets are clustered from these reconstructed
particles using the infrared and collinear safe anti-algorithm [37, 38] with a
distance parameter of 0.4. The jet momentum is determined as the vectorial sum
of the momenta of all particles in the jet, and is typically within 5 to 10%
of the true momentum over the whole spectrum and detector acceptance, based on
simulation. Jet-energy corrections are derived from simulation studies so that
the average measured energy of jets becomes identical to that of particle-
level jets. In situ measurements of the momentum balance in dijet, photon+jet,
Z+jet, and multijet events are used to determine any residual differences
between the jet-energy scale in data and in simulation, and appropriate
corrections are made [39]. Additional selection criteria are applied to each
jet to remove those potentially dominated by instrumental effects or
reconstruction failures. The jet-energy resolution amounts to 20–25% at 20,
10% at 100, and 5% at 1 [39].

A more detailed description of the CMS detector, together with a definition of
the coordinate system and the kinematic variables, can be found in Ref. [40].

##  0.4 Monte Carlo event generators

###  0.4.1 The 8, , and 7 models

The 8 [41], [42], and 7 [43] MC event generators use $2\to 2$ leading order
(LO) matrix elements, matched to a DGLAP evolution [44, 45, 46] at leading
logarithmic level for the simulation of the parton shower. By default, a
-ordered parton shower is implemented in 8, whereas an angular-ordered parton
shower is used in and 7 (jointly referred to as ). For hadronization, 8 uses
the Lund string model [47], whereas relies on the cluster model [48]. The
generators are interfaced with different sets of predetermined parameters (or
“tunes”) for the description of the underlying event, including MPI. These
tunes are obtained from fitting predictions to data. Off all the generated
samples, two have been passed through the detector simulation program [49].
These two samples will be used to correct the data for detector effects by
means of an unfolding procedure. The configurations used in this paper to
generate events with 8 and , are listed below.

  * •

The 8.240 generator is interfaced with three different tunes, , the CUETP8M1
tune [50, 51], the CP5 tune [52] and the CDPSTP8S1-4j tune [51].

The 8 sample, interfaced with the CUETP8M1 tune, uses the NNPDF2.3_LO PDFs
[53]. The simulation of the detector effects has been applied to these
generated events since they will be used to correct the date through an
unfolding procedure.

The 8 sample interfaced with the CP5 tune uses the NNPDF3.1 next-to-next-to-
leading order (NNLO) PDFs [53].

The CDPSTP8S1-4j tune [51] is a CMS DPS tune, based on the standard Tune 4C
[54], where parameters related to MPI and DPS have been altered to fit
predictions to the $\Delta p_{\text{T,Soft}}$ and $\Delta S$ distributions
obtained from an inclusive four-jet measurement at a center-of-mass energy of
7 [51]. This tune uses the CTEQ6L1 PDFs [55].

  * •

An additional 8.301 sample is generated with Vincia [56] activated, which
replaces the -ordered parton shower from 8 with a dipole-antenna shower. The
default parameter values of 8.301 and the NNPDF2.3_LO PDFs are used.

  * •

The 2.7.1 generator is used in combination with the CUETHS1 tune [51] and the
CTEQ6L1 PDFs. This sample is also passed through the detector simulation
program and is used in the unfolding procedure.

  * •

Two tunes are used for the 7.1.5 MC event generator.

The SoftTune is the default tune provided by the 7 authors and uses the
MMHT2014lo68cl PDFs [57].

The CH3 tune has been obtained by the CMS Collaboration from a study of
underlying event measurements [58]. It is used in combination with the
NNPDF2.3_NNLO PDF.

###  0.4.2 Multijet models

A second group of models, referred to as the multijet models, uses higher-
order matrix elements to produce more than two jets in the hard parton
scattering. These MC event generators are interfaced with , , or Cascade [59]
to include a description of the underlying event. Details of the generated
event samples are given below.

  * •

(version 2.6.5) [60] is a generator with the ability to compute tree-level and
NLO matrix elements for arbitrary processes. Two LO samples and one NLO sample
are generated, as listed below.

The LO samples combine a $2\to 2$, a $2\to 3$, and a $2\to 4$ matrix element,
referred to as $2\to 2,3,4$. An $\HT>50\GeV$ generation condition is used,
where is defined as the scalar sum of the transverse momenta of the produced
partons, and all partons must have $\abs{\eta}<5$. For one sample the
description of the underlying event, parton shower, and hadronization is
handled by 8.240, using the CP5 tune, whereas the other sample is interfaced
to 8.301 with Vincia. The former uses the NNPDF2.3_NNLO PDFs, whereas the
latter uses the NNPDF2.3_LO PDFs. The MLM scheme [61] is used to match jets
produced via matrix-element calculations with those from parton showers, using
the matching scale of 18, which was optimized by analyzing the differential
jet-rate distributions.

The $2\to 2$ NLO sample is interfaced with 8.240, using the CP5 tune with the
NNPDF2.3_NNLO PDFs and an MLM matching scheme. The two leading partons are
required to lie within $\abs{\eta}<5$ and have a above 25 and 20,
respectively.

  * •

PowhegBox version 3633 (2019.02.25) [62, 63, 64] is a framework for
implementing NLO corrections in MC event generators. Each event is constructed
by producing the Born configuration, on which the real phase space is built
afterwards. Two different samples are generated, both are interfaced with
8.240, using the CP5 tune along with the NNPDF2.3_NNLO PDFs.

A first sample is generated with a $2\to 2$ NLO matrix element [65]. The
factorization and renormalization scales are set to the of the underlying Born
configuration.

A second sample was generated with a $2\to 3$ NLO matrix element [66]. The
generator-level minimal of the underlying Born configuration is set to 10, and
the factorization and renormalization scales are set to /2.

  * •

KaTie version 23April2019 [67] is a LO parton-level event generator, based on
-factorization [68, 69, 70], allowing for on-shell and off-shell production.
In the case of the latter, the initial partons are generated with a nonzero
intrinsic , which can alter the momentum balance of the jets, yielding various
topologies and correlations between the jets compared with on-shell
production. A $2\to 4$ matrix element is used for all samples generated with
KaTie. The generator-level requirements for the of the four partons produced
by the matrix element are 35, 30, 25, and 20, and their rapidities are limited
to $|\eta|<5.0$. Since the requirements are introduced at parton level, the
effective thresholds for the resulting hadron-level jets are typically 5 to
10lower. The factorization and renormalization scales are set to /2. Two on-
shell and two off-shell samples are produced.

The two on-shell samples are interfaced with 8.240 and 7.1.5, along with the
CP5 and CH3 tunes, respectively. Both samples use the NNPDF2.3_NNLO PDFs.

For the two off-shell samples, the showering and hadronization is handled by
Cascade 3.0.01-beta1. Two different transverse-momentum-dependent (TMD) PDFs
are used: the MRW-CT10nlo TMD PDFs (MRW) [71] and the PB-NLO-
HERAI+II-2018-set2 TMD PDFs (PBTMD) [72].

###  0.4.3 SPS+DPS samples

The 8.240 and KaTie MC event generators both produce two $2\to 2$ matrix
elements per event, resulting in a pure DPS sample. In KaTie,
$\sigma_{\text{eff}}$ is a parameter that directly determines the size of the
DPS contribution relative to the SPS cross section. A value of 21.3mb for
$\sigma_{\text{eff}}$ is adopted, as in [51]. For 8, it is not possible to set
$\sigma_{\text{eff}}$, because it is determined by the underlying event
parameters, and therefore the second $2\to 2$ process is simply added with the
same kinematic requirements, without any additional scaling of the cross
section.

Four samples with an explicit DPS contribution are used in this paper.

  * •

A 8.240 sample is generated with the CP5 tune and the NNPDF2.3_NNLO PDFs. It
is the aforementioned 8 sample to which a pure DPS sample, obtained by
overlaying two $2\to 2$ matrix elements, is added.

  * •

The second 8 sample, which includes an explicit DPS contribution, is the one
already mentioned in Section 0.4.1, since the CDPSTP8S1-4j tune has been
fitted to DPS-sensitive observables.

  * •

An on-shell KaTie sample is generated with an explicit DPS contribution that
is obtained by overlaying two $2\to 2$ matrix elements, with the exact same
generation parameters as the on-shell KaTie LO sample from the multijet
models. Showering and hadronization are handled by 8.240 with the CP5 tune and
the NNPDF2.3_NNLO PDFs.

  * •

Two off-shell KaTie samples with an explicit DPS contribution are generated
using the same TMD PDFs as for the multijet samples. Since Cascade cannot
handle two $2\to 2$ matrix elements, nonperturbative corrections have been
derived from the on-shell SPS and DPS KaTie samples, and are applied to the
off-shell DPS KaTie parton level sample. The nonperturbative corrections range
from 1–4% for all observables, except for the $\Delta S$ observable for which
corrections up to 11% were found.

##  0.5 Data analysis

This analysis uses data from $\Pp\Pp$ collisions at a center-of-mass energy of
13, collected during a data taking period at low luminosity, with an average
pileup of 1.3 and an integrated luminosity of $42\,\nbinv$. The online
selection of multi-jet events was based on four single-jet triggers each
requiring the presence of at least one jet with a above 30, 50, 80, or 100,
and within $\abs{\eta}<4.7$. Because the triggers have been prescaled, they
are used in disjoint ranges. Offline requirements are imposed to ensure that
the triggers are fully efficient, except for the trigger with the lowest
threshold. In this last case, a correction as a function of the jet is applied
to the selected event, effectively altering its weight. The trigger efficiency
was determined by comparing the performance of the jet trigger with a minimum-
bias trigger serving as an unbiased reference.

Events are selected offline by requiring exactly one primary vertex, so
effects of pileup can be neglected. A systematic uncertainty due to a possible
contamination of events containing two or more $\Pp\Pp$ collisions is
nevertheless included in the results. Two phase space regions defined by
selections on jet are used. In $Region$ I, the four leading jets within
$\abs{\eta}<4.7$ are required to exceed thresholds of 35, 30, 25, and 20.
Asymmetric thresholds have been chosen over symmetric ones because the latter
tend to dampen the DPS contribution with respect to the SPS fraction,
according to higher-order calculations or calculations performed in the
-factorization framework [31, 33]. The $\Delta S$ distribution is obtained for
$Region\,{\mbox{II}}$, with thresholds of 50, 30, 30, and 30. Since there are
no jet triggers with thresholds below 30, this second set of selections is
needed to obtain the cross sections $\sigma_{\mathrm{A}}$ and
$\sigma_{\mathrm{B}}$ used in the extraction of $\sigma_{\text{eff}}$.

The measured distributions are corrected for detector effects with the TUnfold
program [73, 74], which is based on a least squares fit and Tikhonov
regularization [75]. The regularization is necessary to avoid possible
instabilities in the inversion of the matrix describing the migrations within
the phase space. Bin-to-bin migrations are kept to a minimum by choosing a bin
width that is two times larger than the resolution of the considered variable,
as obtained from a simulation study with 8. The migration matrix, as well as
the probabilities for migration into and out of the phase space, are obtained
from the 8 and MC models.

##  0.6 Extraction of the effective cross section

The DPS formula (1) allows the calculation of $\sigma_{\text{eff}}$ if the DPS
cross section, as well as the cross sections of the two Processes A and B, are
known. In the simplest case, the Processes A and B would both be dijet
production, resulting in a four-jet final state with uncorrelated jet pairs,
as depicted in Fig. 1. However, initial- and final-state radiation, and
higher-order interactions can produce final states with more than two jets,
yielding additional possibilities to form a four-jet topology.

To avoid additional model dependencies, a DPS signal template is constructed
from data, following an approach similar to the one laid out in Ref. [24]. The
Processes A and B are both defined as inclusive single-jet production.
Combining two events of Type A and B will result in a multijet final state.
Whenever at least four jets are found in the combined final state originating
from the same process, the combined event is labeled as a SPS process,
otherwise the event is labeled as a DPS process.

The lowest single-jet trigger used in this analysis has a threshold of 30, and
the jet selection of $Region$ I can therefore not be used for the extraction
of $\sigma_{\text{eff}}$ because the softest jet has a $\PT$ threshold of
20and would not fulfill the trigger requirement. Therefore,
$Region\,{\mbox{II}}$ is used and the cross sections of Processes A and B are
defined as inclusive single-jet production with

$\displaystyle\sigma_{\mathrm{A}}$
$\displaystyle=\sigma_{\mathrm{jet}}\left(p_{\mathrm{T}}\geq 50\right),$
$\displaystyle\sigma_{\mathrm{B}}$
$\displaystyle=\sigma_{\mathrm{jet}}\left(p_{\mathrm{T}}\geq 30\right).$

Combining two inclusive single-jet processes results in final states with at
least four jets in only a fraction of the cases. A “four-jet efficiency”
($\epsilon_{\mathrm{4j}}$) has been obtained from the combined sample as
detailed below.

Events that meet the online and offline analysis criteria are stored in two
disjunct datasets. Each event with at least one jet with $\PT>50\GeV$ from the
first dataset is combined with another event with at least one jet with
$\PT>30\GeV$ from the second dataset. A combined event is discarded whenever
two or more jet axes spatially coincide. This veto condition is formulated as
$R_{ij}=((\phi_{i}-\phi_{j})^{2}+(\eta_{i}-\eta_{j})^{2})^{1/2}\geq 0.4$,
where the indices $i$ and $j$ indicate jets belonging to an event from the
first and second data sample, respectively. The newly constructed combined
event sample is then subjected to the four-jet selection criteria of
$Region\,{\mbox{II}}$. The four-jet efficiency was estimated to be

$\epsilon_{\mathrm{4j}}=0.324^{+0.037}_{-0.065}\syst,$ (2)

where the statistical uncertainty is negligible and the systematic error is
detailed in the next section.

The $\Delta S$ observable is chosen for the extraction of the DPS cross
section and $\sigma_{\text{eff}}$ because it is the least affected by parton
shower effects. The signal template is taken from the combined data sample,
which is used to extract the $\Delta S$ distribution in exactly the same
manner as before, including the correction for detector effects by means of
unfolding.

The SPS MC models are taken as background templates. To avoid contamination by
MPI, additional samples are provided where an event is omitted if it contains
a generator level parton with a $\PT>20\GeV$ that originates from a MPI. This
selection ensures that no hard jets originating from MPI enter the four-jet
analysis, and will be referred to as “hard MPI removed”.

The fraction of DPS events, $f_{\mathrm{DPS}}$, is extracted by performing a
template fit to the unfolded $\Delta S$ distribution, obtained from the
original inclusive four-jet sample. The DPS signal and SPS background $\Delta
S$ distributions are both normalized to the integral of the $\Delta S$
distribution obtained from the four-jet events in data. The optimal value of
the DPS fraction $f_{\mathrm{DPS}}$ is determined with a maximum likelihood
technique using Poisson statistics [76]:

$\sigma^{\text{data}}(\Delta
S)=f_{\mathrm{DPS}}\sigma^{\text{data}}_{\mathrm{DPS}}(\Delta
S)+(1-f_{\mathrm{DPS}})\sigma^{\mathrm{MC}}_{\mathrm{SPS}}(\Delta S).$ (3)

The cross section $\sigma_{\mathrm{A,B}}^{\mathrm{DPS}}$, needed for the
extraction of $\sigma_{\text{eff}}$, is then given by the integral of the
$\Delta S$ distribution measured in data, scaled with the DPS fraction
$f_{\mathrm{DPS}}$:

$\sigma_{\mathrm{A,B}}^{\mathrm{DPS}}=f_{\mathrm{DPS}}\int\sigma^{\text{data}}(\Delta
S)\rd(\Delta S).$ (4)

Because of the overlapping ranges, the Processes A and B are not always
distinguishable and the cross section for Process B has therefore to be
rewritten as the sum of the cross section for Process A ($\sigma_{\rm A}$) and
the difference between the cross sections for Processes B and A
($\sigma_{\mathrm{B}}-\sigma_{\mathrm{A}}$). Taking into account the correct
combinatorial factor along with the four-jet efficiency, the DPS formula (1)
can be reformulated as:

$\displaystyle\sigma_{\mathrm{A,B}}^{\mathrm{DPS}}$
$\displaystyle=\frac{\epsilon_{\mathrm{4j}}}{\sigma_{\text{eff}}}\left(\frac{1}{2}\sigma_{\mathrm{A}}^{2}+\sigma_{\mathrm{A}}(\sigma_{\mathrm{B}}-\sigma_{\mathrm{A}})\right)$
(5)
$\displaystyle=\frac{\epsilon_{\mathrm{4j}}\sigma_{\mathrm{A}}\sigma_{\mathrm{B}}}{\sigma_{\text{eff}}}\left(1-\frac{1}{2}\frac{\sigma_{\mathrm{A}}}{\sigma_{\mathrm{B}}}\right).$

The cross sections $\sigma_{\mathrm{A}}$ and $\sigma_{\mathrm{B}}$ are
determined by integrating the $\eta$ spectra for jets with $\PT$ above 50 and
30in data, which are unfolded in exactly the same manner as all other
distributions.

##  0.7 Systematic uncertainties

Different sources of systematic uncertainties occurring in the data analysis
are studied. A summary is given in Tables 0.7 and 0.7.

  * Jet energy scale (JES) uncertainty:

The low-pileup, low jet-data sample used in this analysis necessitates a
dedicated JES calibration. The methods discussed in Ref. [39] are applied,
scaling the four-momentum vectors of the jets by a series of sequential
corrections. The JES uncertainty depends on jet and $\eta$ and is smaller than
10% over the whole spectrum and detector acceptance. The jet momenta are
scaled downwards and upwards by the JES uncertainty to estimate its effect on
the measured distributions. The JES uncertainty is the dominant contribution
to the total uncertainty for the observables in terms of the absolute cross
section and results in a maximal upward (downward) uncertainty of 39 (33)%. It
largely cancels in the normalized distributions, never exceeding 16%.

  * Jet energy resolution (JER) uncertainty:

The JER obtained from MC simulation differs from the one estimated for data,
which would lead to a wrong estimation of the bin-to-bin migrations. An
additional smearing of the jet at detector level is therefore applied to both
MC samples used in the unfolding. To estimate the JER uncertainty, the data-
to-simulation smearing factor is varied up and down with its own uncertainty,
resulting in migration matrices that differ from the nominal ones. The newly
obtained migration matrices are used to unfold the distributions, which are
then compared with the nominal distributions for all observables. The JER
uncertainty is less than 9%, except for the spectrum of the leading jet where
it reaches a maximum of 26%.

  * Trigger uncertainty:

An event weight as a function of jet is applied to data to correct for the
efficiency of the trigger with the lowest threshold. These weights are
obtained by fitting the trigger efficiency curve determined in data using a
least-squares minimization. Varying the fit parameters by their uncertainty
leads to a trigger uncertainty that never exceeds 1%.

  * Model uncertainty:

The data distributions are unfolded using migration matrices from the 8 and
models. The averages of the two unfolded distributions are taken as the
nominal unfolded distributions and the systematic error is estimated as half
of the difference. The model uncertainty varies between 1% and 16%, depending
on the observable.

  * Pileup:

Events with two $\Pp\Pp$ collisions in the same bunch crossing may be
reconstructed with only one vertex if the collision points are separated by
less than 0.12cm along the beam axis. Taking into account the spread of
vertices and the relative yields of events with 1 and 2 collisions, the pileup
contamination in the data sample is estimated to be 0.28%. No further
correction is applied, and a systematic uncertainty is included by reproducing
all distributions with a sample of events containing two vertices, normalizing
these to 0.28% of the nominal distributions, and estimating the effect of such
pileup correction on the data. The systematic uncertainty is smaller than 1%
in all bins for all observables.

  * Integrated luminosity uncertainty:

The uncertainty in the integrated luminosity for data collected in 2016 is
$1.2\%$ [77].

Because the four-jet efficiency is determined using uncorrected data, it has
neither JER or model systematic uncertainty. However, an additional systematic
uncertainty is included to cover a possible difference with respect to the
true efficiency to be applied on the corrected cross sections. This
uncertainty is determined by examining the four-jet efficiency obtained with 8
and at both the detector and generator levels, after a 2-dimensional
reweighting as a function of leading-jet and jet multiplicity to obtain a
better description of the data. A four-jet efficiency of $0.404$ and $0.412$
is found with 8 on detector and generator level, respectively, whereas values
of $0.403$ and $0.392$ are obtained with , with negligible statistical
uncertainty. The systematic uncertainty is therefore conservatively estimated
to be smaller than 2%.

Systematic uncertainties, along with the statistical and the total
uncertainties for the spectra, the $\eta$ spectra, and the DPS sensitive
observables, in percent. The JES uncertainty leads to asymmetric uncertainties
(an upper and a lower error), while all other systematic uncertainties, as
well as the statistical uncertainty, are symmetric.

Observable | JES | JER | Model | Trigger | Vertex | Lum. | Stat | Total
---|---|---|---|---|---|---|---|---
| Upper | Lower |  |  |  |  |  |  | Upper | Lower
Absolute cross section (%)
$p_{\mathrm{T,1}}$ | 11–39 | 9–30 | 2–26 | 0–16 | $<1$ | $<1$ | 1.2 | 1–10 | 11–51 | 10–44
$p_{\mathrm{T,2}}$ | 11–31 | 10–24 | 0–2 | 0–7 | $<1$ | $<1$ | 1.2 | 1–8 | 14–33 | 11–26
$p_{\mathrm{T,3}}$ | 1–31 | 7–24 | 1–3 | 2–7 | $<1$ | $<1$ | 1.2 | 2–15 | 13–33 | 13–25
$p_{\mathrm{T,4}}$ | 10–25 | 0–21 | 1–8 | 2–7 | $<1$ | $<1$ | 1.2 | 4–31 | 14–34 | 13–32
$\eta_{1}$ | 22–33 | 18–28 | $<1$ | 1–9 | $<1$ | $<1$ | 1.2 | 3–5 | 22–34 | 19–29
$\eta_{2}$ | 22–30 | 18–26 | $<1$ | 0–6 | $<1$ | $<1$ | 1.2 | 3–6 | 23–31 | 18–26
$\eta_{3}$ | 21–29 | 18–24 | $<1$ | 0–7 | $<1$ | $<1$ | 1.2 | 3–5 | 22–30 | 19–25
$\eta_{4}$ | 19–29 | 16–24 | $<1$ | 1–8 | $<1$ | $<1$ | 1.2 | 3–4 | 19–30 | 17–25
$\Delta\phi_{\text{Soft}}$ | 21–24 | 19–20 | $<1$ | 1–7 | $<1$ | $<1$ | 1.2 | 3–4 | 22–25 | 20–22
$\Delta\phi_{\mathrm{3j}}^{\text{min}}$ | 21–28 | 18–24 | $<1$ | 1–6 | $<1$ | $<1$ | 1.2 | 3–7 | 21–29 | 19–25
$\Delta Y$ | 22–25 | 16–33 | $<1$ | 0–6 | $<1$ | $<1$ | 1.2 | 3–6 | 23–26 | 17–34
$\phi_{ij}$ | 23–26 | 19–22 | $<1$ | 0–7 | $<1$ | $<1$ | 1.2 | 3–4 | 24–27 | 19–22
$\Delta p_{\text{T,Soft}}$ | 22–25 | 19–20 | 0–3 | 2–6 | $<1$ | $<1$ | 1.2 | 3–4 | 23–26 | 19–21
$\Delta S$ | 4–34 | 13–20 | $<1$ | 0–5 | $<1$ | $<1$ | 1.2 | 3–13 | 12–37 | 15–22
Bin-normalized cross section (%)
$\Delta\phi_{\text{Soft}}$ | 0–1 | 0–1 | $<1$ | 0–4 | $<1$ | $<1$ |  | 3–4 | 3–6 | 3–6
$\Delta\phi_{\mathrm{3j}}^{\text{min}}$ | 0–5 | 0–4 | $<1$ | 0–4 | $<1$ | $<1$ |  | 3–7 | 4–8 | 3–8
$\Delta Y$ | 0–2 | 0–18 | $<1$ | 0–5 | $<1$ | $<1$ |  | 3–6 | 3–10 | 3–21
$\phi_{ij}$ | 0–3 | 0–2 | $<1$ | 0–4 | $<1$ | $<1$ |  | 3–4 | 3–6 | 3–6
$\Delta p_{\text{T,Soft}}$ | 0–2 | 0–2 | 0–2 | 0–2 | $<1$ | $<1$ |  | 3–4 | 3–5 | 3–5
$\Delta S$ | 0–16 | 0–7 | $<1$ | 0–7 | $<1$ | $<1$ |  | 3–13 | 3–22 | 3–15

Systematic uncertainties, along with the statistical and the total
uncertainties for the cross sections of the two phase space regions, along
with the observables needed for the extraction of
$\sigma_{\mathrm{A,B}}^{\mathrm{DPS}}$, in percent. The JES uncertainty leads
to asymmetric uncertainties (an upper and a lower error): all other systematic
uncertainties, as well as the statistical uncertainty, are symmetric. An
additional uncertainty in $\epsilon_{\mathrm{4j}}$ because of possible
differences between generator- and detector-level events, is estimated to be
2%.

Observable | JES | JER | Model | Trigger | Vertex | Lum. | Stat | Total
---|---|---|---|---|---|---|---|---
| Upper | Lower |  |  |  |  |  |  | Upper | Lower
Integrated cross section (%)
$\sigma_{\text{I}}$ | 24 | 19 | $<1$ | 4 | $<1$ | $<1$ | 1.2 | 1 | 25 | 20
$\sigma_{\text{II}}$ | 17 | 13 | $<1$ | 6 | $<1$ | $<1$ | 1.2 | 2 | 20 | 16
$\sigma_{\text{eff}}$ extraction (%)
$\Delta S(\text{DPS template})$ | 7–19 | 15–24 | $<1$ | 0–3 | $<1$ | $<1$ | 1.2 | 1–2 | 7–19 | 15–25
$\sigma_{\mathrm{A}}$ | 10 | 9 | $<1$ | 4 | $<1$ | $<1$ | 1.2 | 1 | 11 | 10
$\sigma_{\mathrm{B}}$ | 7 | 9 | $<1$ | 4 | $<1$ | $<1$ | 1.2 | 1 | 9 | 10
$\epsilon_{\mathrm{4j}}$ | 11 | 20 |  |  | $<1$ | $<1$ |  | $<1$ | 11 | 20

##  0.8 Results

The total cross sections in the two phase space regions defined by thresholds
on the of the four leading jets, $Region$ I and $Region\,{\mbox{II}}$, are
obtained by integrating the differential cross section as a function of the
leading jet $\eta$ and the $\Delta S$ observable, respectively, yielding:

$\displaystyle\sigma_{\text{I}}\left(\Pp\Pp\to\mathrm{4j+X}\right)$
$\displaystyle=2.77\pm 0.02\stat\,^{+0.68}_{-0.55}\syst\,\mu\mathrm{b},$ (6)
$\displaystyle\sigma_{\text{II}}\left(\Pp\Pp\to\mathrm{4j+X}\right)$
$\displaystyle=0.61\pm 0.01\stat\,^{+0.12}_{-0.10}\syst\,\mu\mathrm{b}.$

Tables 0.8.1– 0.8.3 compares the values measured in data with the ones
obtained from MC event generators. A discussion of the total and differential
cross sections for each of the sets of models introduced in Section 0.4 is
presented below.

The cross sections of the inclusive single-jet Processes A and B are
determined by integrating the leading jet $\eta$ distribution for both
processes, and are:

$\displaystyle\sigma_{\mathrm{A}}\left(\Pp\Pp\to\mathrm{1j+X}\right)$
$\displaystyle=15.9\pm 0.1\stat\,^{+1.8}_{-1.6}\syst\,\mu\mathrm{b},$ (7)
$\displaystyle\sigma_{\mathrm{B}}\left(\Pp\Pp\to\mathrm{1j+X}\right)$
$\displaystyle=106\pm 1\stat\,^{+10}_{-11}\syst\,\mu\mathrm{b}.$

A large increase in cross section is observed when lowering the threshold from
50to 30, as expected. These cross sections will be used as input to Eq. (1)
for the determination of the DPS cross section and $\sigma_{\text{eff}}$ along
with the four-jet efficiency from Eq. (2).

###  0.8.1 The 8 and models

The models based on LO $2\to 2$ matrix elements, 8, , and 7, respectively
labeled as P8, H++, and H7 in the figures, are compared with data. Table 0.8.1
gives an overview of the event generators, tunes, and PDF sets, along with
their respective cross sections. All LO $2\to 2$ models predict cross sections
that are much larger than the measured ones; especially 8 with the
CDPSTP8S1-4j tune predicts a cross section that is roughly 2.5 times larger
than the one observed in data. Figures 2– 5 show a comparison of the data to
various MC models as a function of , $\eta$, and the DPS-sensitive
observables. Three 8 models and one 7 model are shown in direct comparison
with the data. These models employ the most recent CP5 and CH3 tunes, the
dedicated DPS tune or combine 8 with a dipole-antenna shower provided by
Vincia, while all of the models are represented in the ratio plots.

The spectra in Fig. 2, obtained for $Region$ I, show that the much larger
integrated cross section of the MC models, compared with the data, comes from
an abundance of low-jets, whereas for $\PT\gtrsim 100\GeV$ the models show
agreement within 50% of the data; for 7 it is even within the total
uncertainty. Fig. 3, the $\eta$ spectra, shows that a large part of the excess
of low-jets is located in the forward $\eta$ regions.

Cross sections obtained from data and from the 8, , and 7 models in $Region$ I
and $Region\,{\mbox{II}}$ of the phase space, where ME stands for matrix
element.  Sample ME Tune PDF $\sigma_{\text{I}}$ ($\mu\mathrm{b}$)
$\sigma_{\text{II}}$ ($\mu\mathrm{b}$) Data $2.77\pm 0.02\,^{+0.68}_{-0.55}$
$0.61$ $\pm 0.01\,^{+0.12}_{-0.10}$ 8 LO $2\to 2$ CUETP8M1 NNPDF2.3_LO 5.03
1.07 8 LO $2\to 2$ CP5 NNPDF2.3_NNLO 4.07 0.84 8 LO $2\to 2$ CDPSTP8S1-4j
CTEQ6L1 7.06 1.28 8 +Vincia LO $2\to 2$ Default NNPDF2.3_LO 4.66 0.97 LO $2\to
2$ CUETHS1 CTEQ6L1 4.35 0.83 7 LO $2\to 2$ CH3 NNPDF2.3_NNLO 4.82 0.98 7 LO
$2\to 2$ SoftTune MMHT2014lo68cl 5.34 1.07

Figure 2: Comparison of the spectra from data to different 8 (P8), (H++), and
7 (H7) tunes, for the leading (upper left), subleading (upper right), third
leading (lower left), and fourth leading (lower right) jet in $Region$ I. The
error bars represent the statistical uncertainty, and the yellow band
indicates the total (statistical+systematic) uncertainty in the measurement.

Figure 3: Comparison of the $\eta$ spectra from data to different 8 (P8),
(H++), and 7 (H7) tunes, for the leading (upper left), subleading (upper
right), third leading (lower left), and fourth leading (lower right) jet in
$Region$ I. The error bars represent the statistical uncertainty, and the
yellow band indicates the total (statistical+systematic) uncertainty in the
measurement.

The distributions in the DPS-sensitive observables are shown in Figs. 4 and 5,
for $Region\,{\mbox{II}}$ in the case of $\Delta S$ and $Region$ I for all
other observables. To make qualitative statements about the shape, the fully
corrected distributions have been normalized to one or more bins where a much
reduced DPS contribution is expected. The distribution in
$\Delta\phi_{\text{Soft}}$ is normalized to the average of the first five
bins, covering the tail of the distribution, which is determined by the jet
cone size. The distributions in $\Delta\phi_{\mathrm{3j}}^{\text{min}}$ and
$\Delta Y$ are normalized to the average of their first four bins. Normalizing
to the average of multiple bins reduces the effect of statistical
fluctuations. The distributions in $\phi_{ij}$, $\Delta p_{\text{T,Soft}}$,
and $\Delta S$ are all normalized to their last bin, since these bins already
have a small relative statistical uncertainty.

Figure 4: Comparison of the $\Delta\phi_{\text{Soft}}$,
$\Delta\phi_{\mathrm{3j}}^{\text{min}}$, $\Delta Y$, and $\phi_{ij}$
distributions from data to different 8 (P8), (H++), and 7 (H7) tunes in
$Region$ I. All distributions have been normalized to regions where a reduced
DPS contribution is expected. The error bars represent the statistical
uncertainty, and the yellow band indicates the total (statistical+systematic)
uncertainty in the measurement.

Figure 5: Comparison of the $\Delta p_{\text{T,Soft}}$ and $\Delta S$
distributions from data to different 8 (P8), (H++), and 7 (H7) tunes in
$Region$ I and $Region\,{\mbox{II}}$, respectively. All distributions have
been normalized to regions where a reduced DPS contribution is expected. The
error bars represent the statistical uncertainty, and the yellow band
indicates the total (statistical+systematic) uncertainty in the measurement.

The $\Delta\phi_{\text{Soft}}$ and $\Delta p_{\text{T,Soft}}$ distributions
are relatively well described by all LO $2\to 2$ models. Deviations from data
never exceed 20%, albeit being larger than the total uncertainty in the data
points in certain bins for some of the models. Similar results are observed
for the predictions of the $\Delta p_{\text{T,Soft}}$ observable from the DPS
tune in [14]. Deviations of 10–20% occur between a model employing a similar
DPS tune (CDPSTP8S1-WJ) and the data in the Z+jets final state.

The shape of the $\Delta Y$ distribution predicted by all the LO $2\to 2$
models differs significantly from data, and the MC-to-data ratio increases
towards higher values of $\Delta Y$. The overshoot at large $\Delta Y$ is
consistent with the excess of low-forward jets.

A distinction between two classes of models becomes apparent in the
$\Delta\phi_{\mathrm{3j}}^{\text{min}}$ and $\phi_{ij}$ distributions. The
models implementing a -ordered parton shower describe the distribution in
$\Delta\phi_{\mathrm{3j}}^{\text{min}}$ well, although yielding a distribution
in $\phi_{ij}$ that is more uncorrelated than observed in data. The slope of
the $\Delta\phi_{\mathrm{3j}}^{\text{min}}$ distribution obtained from the
models with a -ordered shower algorithm going to zero, overshoots the slope of
the distribution obtained from data. For models that use an angular-ordered or
dipole-antenna parton shower, the $\Delta\phi_{\mathrm{3j}}^{\text{min}}$
correlation is too strong. The slope of the distributions
$\Delta\phi_{\mathrm{3j}}^{\text{min}}$ distributions obtained from the models
with an angular-ordered shower overshoot the distribution obtained from data
when going to $\pi$, whereas the shape of the data is described more
accurately by $\phi_{ij}$. The 8+Vincia model confirms that the parton shower
algorithm is responsible for the different tendencies observed for the two
classes of models. This observation makes these observables less suitable to
untangle SPS and DPS contributions to the cross section.

The $\Delta S$ distribution is less affected by different parton shower
implementations. The DPS tune CDPSTP8S1-4j agrees very well with the shape of
the data, but lies slightly above the data at low values of $\Delta S$,
pointing to a potential overestimation of the DPS contribution. All other
models underestimate the data at low $\Delta S$, indicating a possible need
for more DPS to obtain a proper description of the shape of the $\Delta S$
distribution.

###  0.8.2 Multijet models

Data distributions are also compared with the multijet samples that are
obtained from models based on LO $2\to n(n\geq 2)$ and NLO $2\to 2$ and $2\to
3$ matrix elements. The group of multijet samples includes $2\to 4$ on-shell
and off-shell predictions made by KaTie, two LO samples for which $2\to 2,3,4$
matrix element are all included, a NLO $2\to 2$ sample, and two NLO samples
that use a $2\to 2$ and a $2\to 3$ matrix element. Table 0.8.2 gives a
complete overview of all models, tunes, and PDF sets, along with their
respective cross sections. In the figures, the labels KT, PW, and MG5 are used
for KaTie, , and , respectively. Figures 6– 9 show a comparison of the data to
various MC models as a function of , $\eta$, and the DPS-sensitive
observables. Four models are shown in direct comparison with the data. These
models include one of the two on- and off-shell KaTie models, the LO sample
interfaced with the CP5 tune and the NLO $2\to 2$ sample, while all of the
models are represented in the ratio plots.

Cross sections obtained from data and from KaTie, , and in region $Region$ I
and $Region\,{\mbox{II}}$ of the phase space, where ME stands for matrix
element.  Sample ME Tune PDF/TMD $\sigma_{\text{I}}$ ($\mu\mathrm{b}$)
$\sigma_{\text{II}}$ ($\mu\mathrm{b}$) Data $2.77\pm 0.02\,^{+0.68}_{-0.55}$
$0.61\pm 0.01\,^{+0.12}_{-0.10}$ KaTie on-shell + 8 LO $2\to 4$ CP5
NNPDF2.3_NNLO 4.23 2.87 KaTie on-shell + 7 LO $2\to 4$ CH3 NNPDF2.3_NNLO 3.56
2.25 KaTie off-shell + Cascade LO $2\to 4$ MRW 2.40 1.46 KaTie off-shell +
Cascade LO $2\to 4$ PBTMD 2.57 1.56 \+ 8 LO $2\to 2,3,4$ CP5 NNPDF2.3_NNLO
2.69 1.26 \+ 8+Vincia LO $2\to 2,3,4$ Default NNPDF2.3_LO 1.93 0.90 \+ 8 NLO
$2\to 2$ CP5 NNPDF2.3_NNLO 2.12 1.03 \+ 8 NLO $2\to 2$ CP5 NNPDF2.3_NNLO 3.50
1.62 \+ 8 NLO $2\to 3$ CP5 NNPDF2.3_NNLO 2.55 1.22

The predicted cross sections obtained from the on-shell KaTie samples
interfaced with 8 and 7 are larger than the cross sections obtained from data.
They sharply decrease when an off-shell matrix element is used, showing
agreement within the data uncertainty for $Region$ I. The LO samples and all
the NLO samples predict cross sections that are roughly in agreement with the
cross sections obtained from data in $Region$ I, but are larger than those
from data in $Region\,{\mbox{II}}$, as are all the KaTie cross sections in the
same region.

Fig. 6 compares the spectra of the various models with the data. The on-shell
KaTie predictions agree with the data in the first bin of each of the spectra,
but are above the data at higher . This may be explained because most jets
originate from the $2\to 4$ matrix element and not from the parton shower. The
same effect, but less pronounced, is observed for the off-shell KaTie curves.
The different PDF sets used with off-shell KaTie result in small variations. A
better description of the spectra is given by the LO sample, with a -ordered
parton shower. In this case, some jets must originate from the parton shower,
yielding a softer spectrum. The combination of the LO $2\to 2,3,4$ sample with
the dipole-antenna showering from 8+Vincia, results in a lowering of the total
cross section. All NLO models give a similar description as the sample; the
higher-order matrix element, including virtual corrections, contributes to a
lower cross section. A comparison of the multi jet data samples to the
standard 8 and curves from the previous section demonstrates that NLO
corrections and the inclusion of multi-leg matrix elements improve the
description of the spectra.

The $\eta$ spectra are shown in Fig. 7. The central region is consistently
described by all models, even the on-shell KaTie models; the overall cross
section is too large but the ratio remains flat for $|\eta|\leq 3.0$. An
excess of jets is observed in the forward region, although this is less
pronounced than in the case of the 8 and models. The excess is also strongest
for the leading jet and diminishes for the second, third and fourth leading
jet, yielding a good description of the shape for the latter.

Figure 6: Comparison of the unfolded spectra of data with different KaTie
(KT), (MG5), and (PW) models, for the leading (upper left), subleading (upper
right), third leading (lower left), and fourth leading (lower right) jet in
$Region$ I. The error bars represent the statistical uncertainty, and the
yellow band indicates the total (statistical+systematic) uncertainty in the
measurement.

Figure 7: Comparison of the unfolded $\eta$ spectra of data with different
KaTie (KT), (MG5), and (PW) models, for the leading (upper left), subleading
(upper right), third leading (lower left), and fourth leading (lower right)
jet in $Region$ I. The error bars represent the statistical uncertainty, and
the yellow band indicates the total (statistical+systematic) uncertainty in
the measurement.

Differential cross sections for all other observables are shown in Figs. 8 and
9. As before, these distributions have been normalized to a region with a much
reduced DPS contribution.

Figure 8: Comparison of the $\Delta\phi_{\text{Soft}}$,
$\Delta\phi_{\mathrm{3j}}^{\text{min}}$, $\Delta Y$, and $\phi_{ij}$
distributions from data to different KaTie (KT), (MG5), and (PW)
implementations in $Region$ I. All distributions have been normalized to
regions where a reduced DPS sensitivity is expected. The error bars represent
the statistical uncertainty, and the yellow band indicates the total
(statistical+systematic) uncertainty on the measurement.

Figure 9: Comparison of the $\Delta p_{\text{T,Soft}}$ and $\Delta S$
distributions from data to different KaTie (KT), (MG5), and (PW)
implementations in $Region$ I and $Region\,{\mbox{II}}$, respectively. All
distributions have been normalized to regions where a reduced DPS sensitivity
is expected. The error bars represent the statistical uncertainty, and the
yellow band indicates the total (statistical+systematic) uncertainty on the
measurement.

The distributions in $\Delta\phi_{\text{Soft}}$ and $\Delta p_{\text{T,Soft}}$
demonstrate that most multijet models leave room for an additional DPS
contribution in the regions where this can be expected. The exceptions are the
LO $2\to 2,3,4$ distributions that describe the shape of the distributions
from data reasonably well. This last model contains a LO $2\to 2$
contribution, and, as observed in Sec 8.1, the LO $2\to 2$ models describe the
$\Delta\phi_{\text{Soft}}$ and $\Delta p_{\text{T,Soft}}$ distributions well.

The $\Delta Y$ distributions show that some multijet models still have an
excess of jets at large rapidity separation.

The distributions in $\phi_{ij}$ confirm the strong dependence on the parton
shower implementation observed with the LO $2\to 2$ models (as shown, , the LO
$2\to 2,3,4$ predictions for $\phi_{ij}$). Angular-ordered parton showers,
reproduced by Vincia and KaTie, describe the shape of the data distributions
better. The off-shell KaTie predictions show a depletion in the region where
additional DPS is expected. The effect of the parton shower on the
$\Delta\phi_{\mathrm{3j}}^{\text{min}}$ distributions is less pronounced in
the multijet models compared to the LO $2\to 2$ models.

The $\Delta S$ distributions again show a more robust behavior with respect to
the parton shower implementation. The LO samples leave less room for an
additional DPS contribution compared with the NLO models. Due to the sole use
of a $2\to 4$ matrix element, the spectra are far too hard, resulting in a
large overestimation of the slope for all the KaTie models.

###  0.8.3 SPS+DPS Models

The last group of model predictions that are compared with data are those
including an explicit DPS contribution, as described in Section 0.4.3. The 8
CDPSTP8S1-4j predictions presented in this section are the same as in previous
sections; there is no need to add a DPS contribution explicitly, because the
underlying event parameters are specifically tuned to include a DPS
contribution. All models are labeled as before in the figures.

A comparison of the integrated cross sections obtained from the SPS+DPS
samples in Table 0.8.3 with those from pure SPS samples, shows the expected
increase. Only the values of the off-shell KaTie models agree with the
measured cross section in $Region$ I within the uncertainty. The cross
sections predicted for $Region\,{\mbox{II}}$ are all too high.

Cross sections obtained from data and from models with an explicit DPS
contribution in $Region$ I and $Region\,{\mbox{II}}$ of the phase space, where
ME stands for matrix element.  Sample ME Tune PDF/TMD $\sigma_{\text{I}}$
($\mu\mathrm{b}$) $\sigma_{\text{II}}$ ($\mu\mathrm{b}$) Data $2.77\pm
0.02\,^{+0.68}_{-0.55}$ $0.61\pm 0.01\,^{+0.12}_{-0.10}$ 8 LO $2\to 2$
CDPSTP8S1-4j CTEQ6L1 7.06 1.28 SPS+DPS 8 LO $2\to 2$ CP5 NNPDF2.3_NNLO 4.76
0.94 SPS+DPS KaTie on-shell + 8 LO $2\to 4$ CP5 NNPDF2.3_NNLO 5.04 2.14
SPS+DPS KaTie off-shell + Cascade LO $2\to 4$ MRW 3.11 0.95 SPS+DPS KaTie off-
shell + Cascade LO $2\to 4$ PBTMD 3.12 0.99

Figures 10 and 11 show the and $\eta$ spectra of the four leading jets,
respectively. A comparison with the spectra of the pure SPS samples from the
previous sections shows that the DPS samples contribute in the low-region, and
mostly in the forward regions of the $\eta$ spectra.

Figure 10: Comparison of the unfolded spectra of data with different SPS+DPS
KaTie (KT) and 8 (P8) models, for the leading (upper left), subleading (upper
right), third leading (lower left), and fourth leading (lower right) jet in
$Region$ I. The error bars represent the statistical uncertainty, and the
yellow band indicates the total (statistical+systematic) uncertainty in the
measurement.

Figure 11: Comparison of the unfolded $\eta$ spectra of data with different
SPS+DPS KaTie (KT) and 8 (P8) models, for the leading (upper left), subleading
(upper right), third leading (lower left), and fourth leading (lower right)
jet in $Region$ I. The error bars represent the statistical uncertainty, and
the yellow band indicates the total (statistical+systematic) uncertainty in
the measurement.

Normalized distributions in the DPS-sensitive observables are shown in Fig.
12. Small differences in shape, typically $\sim 5$%, occur in the DPS-
sensitive regions when comparing the SPS+DPS 8 sample, interfaced with the CP5
tune, with its pure SPS counterpart in Figs. 4 and 5. The 8 samples give a
good description of shape of the distributions in the observables
$\Delta\phi_{\text{Soft}}$, $\Delta\phi_{\mathrm{3j}}^{\text{min}}$, $\Delta
p_{\text{T,Soft}}$ and $\Delta S$, with the CDPSTP8S1-4j tune performing
slightly better than the 8 SPS+DPS sample with the CP5 tune. This might be
expected since the CDPSTP8S1-4j tune was obtained by fitting the 8 underlying
event parameters to distributions in $\Delta\phi_{\text{Soft}}$, $\Delta
p_{\text{T,Soft}}$, and $\Delta S$ measured with data at a center-of-mass
energy of 7, as detailed in [51].

The KaTie curves show a more noticeable increase where a DPS contribution is
expected, especially in the case of the off-shell samples. This is in contrast
with the performance of the SPS-only predictions (see Figs. 8 and 9) where the
off-shell KaTie models underestimate the data. This shows that a DPS
contribution is needed in the KaTie model to improve the description of the
data, but that the value of $\sigma_{\text{eff}}=21.3$mb (taken from Ref.
[51]), is too small for this model based on a $2\to 4$ matrix element.

All models fail to describe the shape of the $\Delta Y$ observable, and the
$\phi_{ij}$ observable shows the same tendencies found in the previous
sections. The LO $2\to 2$ 8 models using a -ordered parton shower show too
large a decorrelation, whereas predictions using higher-order matrix element
calculations perform better, demonstrated by the KaTie distributions.

Figure 12: Comparison of the distributions in DPS-sensitive observables
obtained from data to different SPS+DPS KaTie (KT) and 8 (P8) models. All
distributions have been determined in $Region$ I, except for the $\Delta S$
distribution which has been measured in $Region\,{\mbox{II}}$. All
distributions have been normalized to the region where a reduced DPS
contribution is expected. The error bars represent the statistical
uncertainty, and the yellow band indicates the total (statistical+systematic)
uncertainty on the measurement.

###  0.8.4 Extraction of the effective cross section

As demonstrated in the above sections, the $\Delta S$ observable exhibits the
most robust sensitivity to DPS. Other observables are either less sensitive to
DPS or suffer from large variations induced by different parton shower models.
Therefore, the $\Delta S$ distribution is used in the extraction of
$\sigma_{\text{eff}}$. The DPS cross section is determined and the effective
cross section, $\sigma_{\text{eff}}$, is extracted using different SPS MC
event samples with and without the hard MPI removed following the template
method laid out in Section 0.6. The 8 sample with the CUETP8M1 tune yields a
DPS fraction lower compared to all other tunes, while the sample with the
CUETHS1 tune gives similar results as when 7 with the CH3 tune is used, and
therefore both are omitted below. The 8 sample interfaced with the
CDPSTP8S1-4j tune without the hard MPI removed already contains a DPS
contribution, scaled with an effective cross section equal to 21.3mb [51].
Therefore, the extracted DPS fraction for this model is expected to be close
to zero. The extraction is still performed as a consistency check and to test
the performance of the tune at a center-of-mass energy of $\sqrt{s}=13\TeV$.
The multijet KaTie models are not considered; they significantly overshoot the
DPS-sensitive slope of the $\Delta S$ observable and using them would result
in a negative DPS contribution.

The mixed event sample obtained from data, as described in Section 0.6, is
used to get the $\Delta S$ distributions for pure DPS events and is corrected
by means of unfolding in the same way as the other distributions. This
corrected $\Delta S$ distribution is shown in Fig. 13, along with the $\Delta
S$ distributions obtained from the DPS component of the 8 and on-shell KaTie
generators, both interfaced with the CP5 tune. All distributions have been
normalized to unity. The distributions show a maximum at $\Delta S=\pi$
because of jet pairs with overlapping values such that the two softest and the
two hardest jets do not coincide with the jet pairs from separate events or
parton collisions. The DPS data sample exhibits a larger decorrelation as
compared to the DPS MC samples, which can be attributed to disparities in the
spectra observed in data and for MC events.

Figure 13: The $\Delta S$ distribution obtained from the mixed data sample
compared to predictions from the pure DPS sample in 8 (P8) and KaTie (KT). The
distributions are normalized to unity. The error bars represent the
statistical uncertainty, and the yellow band indicates the total
(statistical+systematic) uncertainty on the data.

The template fitter program [76] takes the SPS MC distributions along with the
DPS data sample as input, and uses the template method to determine the
fraction of DPS events, $f_{\mathrm{DPS}}$. Equations (5) and (4) are used to
determine the DPS cross sections and values for $\sigma_{\text{eff}}$ shown in
Tables 1 and 2, respectively. The results for both sets of samples (with and
without the hard MPI removed) are shown, along with the net difference between
both cross sections since this can be interpreted as the amount of DPS
inherent to the tune. An example of the template fit is presented in Fig. 14,
where the fitted distributions using the NLO $2\to 2$ model without the hard
MPI removed along with its statistical and systematic uncertainties are shown.

Figure 14: The results of the template fit for the (PW) NLO $2\to 2$ model
without the hard MPI removed. The yellow bands represent the total uncertainty
of the distribution. The ratio of the scaled MC model and of the total fitted
result over the data are shown in the bottom plot. Since the $\Delta S$
distribution obtained from the mixed data sample carries a statistical and
systematic uncertainty, so does the total fitted sample. The total uncertainty
in the ratio is shown on the plot.

The DPS cross section obtained for all models with and without the hard MPI
removed range from 14.6 to 70mb, yielding values for $\sigma_{\text{eff}}$
between 7.7 and 34.8mb. The exception is 8 with the CDPSTP8S1-4j tune without
the hard MPI removed where an excess of DPS events is found, resulting in a
negative DPS cross section. Therefore, the effective cross section for this
model has not been calculated because it would yield a nonphysical result.

In the case of the LO $2\to 2$ models, 2 final state jets originate from the
ME, and 2 additional jets stem from the parton shower. A distinction between
two groups of models using a LO $2\to 2$ matrix element can be made. On the
one hand, the 8 and 7 models using the CP5 and CH3 tunes, respectively, use
the latest underlying event tune and up-to-date PDFs. On the other hand, both
8+Vincia and 7 with the SoftTune rely on an older underlying event tune and
older PDFs. The extracted values for the DPS cross section for the former two
models are 38.5 and 38.2mb, whereas for the latter two models values of 23.3
and 29.5mb were obtained where events containing one or more hard partons
originating from MPI have been removed. The results indicate that it might be
the different underlying event tunes and the usage of older PDFs that are
responsible for the more DPS-like topology in both 8+Vincia and 7 with the
SoftTune.

Introducing higher multiplicity MEs reduces the effect of the underlying event
tune, parton showers, and the PDFs since more jets will originate from the ME.
The dominating contribution to the event sample comes from $2\to 4$ ME, where
the 4 final state jets all stem from the ME. The extracted DPS cross section
with hard MPI removed is 31mb for both 8 with the CP5 tune and 8+Vincia,
confirming that the effect of the different underlying event tunes, parton
showers, and PDFs is suppressed. In the case of 8 with the CP5 tune, the
higher multiplicity MEs reduce the need for additional DPS, whereas in the
case of 8+Vincia more room for additional DPS exists. For both models, about
half of the DPS cross section that is needed to describe the data can be
covered by the MPI that are intrinsic to the tune.

The NLO $2\to 2$ models contain a combination of exclusive NLO $2\to 2$ and LO
$2\to 3$ ME. One or more parton-shower jets are required to produce a 4-jet
final state, with a ME/parton-shower matching algorithm applied to avoid
double counting. Large DPS cross sections of up to 70mb are needed to describe
the data if events containing hard MPI partons originating from the underlying
event description, provided by the CP5 tune, are removed. Compared with the
other models, the NLO $2\to 2$ models are outliers. If events with hard MPI
partons from the underlying event description are included, they can again
account for about half of the DPS cross section needed to describe the data.

For the NLO $2\to 3$ sample, NLO $2\to 3$ and LO $2\to 4$ MEs are combined,
leaving room for zero or one additional jets from the parton shower. The
extracted DPS cross section approaches the one obtained for the models with a
LO $2\to 2,3,4$ ME. Contrary to the LO $2\to 2,3,4$ ME models, however, the
NLO $2\to 3$ models do not allow events containing hard MPI partons to
contribute as much to the DPS cross section.

Fig. 15 shows the results for $\sigma_{\text{eff}}$ extracted with the models
that are based on the recent CP5 and CH3 tunes where the hard MPI have been
removed. The extracted $\sigma_{\text{eff}}$ values show agreement with the
results from the UA2 and CDF experiments, which set a lower bound on
$\sigma_{\text{eff}}>8.3$mb [20] and found a $\sigma_{\text{eff}}$ value of
$12.1^{+10.7}_{-5.4}$mb, respectively. All results, except for the values
obtained with the NLO $2\to 2$ models, agree with the measurement performed by
the ATLAS collaboration [24] at a center-of-mass energy of 7 [21], where a
$\sigma_{\text{eff}}$ equal to $14.9^{+1.2}_{-1.0}\stat^{+5.1}_{-3.8}\syst$mb
was reported, whereas none agree with the value of $21.3^{+1.2}_{-1.6}$mb from
the CMS measurement at a center-of-mass energy of 7 [51], which is more in
line with the results obtained with some of the models based on older UE
tunes.

Figure 15: Comparison of the values for $\sigma_{\text{eff}}$ extracted from
data using different SPS models where events that have generated one or more
hard MPI partons with $\PT^{\text{parton}}\geq 20$, have been removed. The
results from four-jet measurements performed at lower center-of-mass energies
[20, 6, 24, 51] are shown alongside the newly extracted values. The error bars
in each of the values of $\sigma_{\text{eff}}$ represent the total
(statistical+systematic) uncertainties.

Two other DPS measurements have been performed at a center-of-mass energy
$\sqrt{s}=13\TeV$. A value of $\sigma_{\text{eff}}$ equal to
$12.7^{+5.0}_{-2.9}$mb has been extracted from the same-sign WW measurement in
Ref. [13]. A $\sigma_{\text{eff}}$ of $7.3\pm 0.5\stat\pm 1.0\syst$mb has been
obtained from the pair production measurement in Ref. [19]. It has been shown
that $\sigma_{\text{eff}}$ is expected to be process independent for inclusive
final states [78], therefore, it is noteworthy that the result the meson pair
production measurement shows only agreement with the NLO $2\to 2$ models. The
extracted $\sigma_{\text{eff}}$ of the same-sign WW measurement shows
agreement with all models due to the size of the errors in the measurement,
indicating that further measurements in this channel are desirable before any
further conclusions can be made.

Table 1: The values of the DPS cross section
$\sigma_{\mathrm{A,B}}^{\mathrm{DPS}}$ extracted from data using different SPS
models, along with their statistical and systematic uncertainties. The results
are shown for the model where the full tune is used, and for the same models
where the hard MPI have been removed The last column shows the net difference
between the two first columns and is interpreted as the amount of DPS inherent
to the tune.

MC Model |  Tune |  $\sigma_{\mathrm{A,B}}^{\mathrm{DPS}}\pm(\text{stat})\pm\text{(syst)}$ (nb)
---|---|---
|  | Full tune | Hard MPI removed | Inherent DPS
8 |  CP5 | $22.9\pm 0.7\,^{+5.7}_{-7.3}$ | $38.5\pm 0.9\,^{+6.5}_{-9.4}$ | $15.6\pm 1.1\,^{+6.1}_{-8.4}$
8+Vincia |  Standard 8.3 | $14.6\pm 0.6\,^{+4.4}_{-5.9}$ | $23.3\pm 0.7\,^{+4.9}_{-7.1}$ | $8.7\pm 0.9\,^{+4.7}_{-6.5}$
8 |  CDPSTP8S1-4j | $-7.9\pm 0.5\,^{+2.3}_{-2.9}$ | $18.6\pm 0.6\,^{+4.6}_{-6.5}$ | $26.5\pm 0.8\,^{+3.5}_{-4.7}$
7 |  CH3 | $22.6\pm 0.7\,^{+5.1}_{-7.3}$ | $38.2\pm 0.9\,^{+6.4}_{-9.4}$ | $15.6\pm 1.1\,^{+5.8}_{-8.4}$
7 |  SoftTune | $16.2\pm 0.6\,^{+4.6}_{-6.3}$ | $29.5\pm 0.8\,^{+5.6}_{-8.6}$ | $13.3\pm 1.0\,^{+5.1}_{-7.5}$
LO $2\to 2,3,4$, 8 |  CP5 | $15.2\pm 0.6\,^{+4.2}_{-6.1}$ | $31.2\pm 0.8\,^{+5.5}_{-8.1}$ | $16.0\pm 1.0\,^{+4.9}_{-7.1}$
LO $2\to 2,3,4$, 8+Vincia |  Standard 8.3 | $15.5\pm 0.6\,^{+4.3}_{-6.0}$ | $31.8\pm 0.8\,^{+5.3}_{-8.0}$ | $16.3\pm 1.0\,^{+4.8}_{-7.0}$
NLO $2\to 2$, 8 |  CP5 | $43.3\pm 1.0\,^{+4.5}_{-9.4}$ | $70\pm 2\,^{+8}_{-13}$ | $26.7\pm 2\,^{+6}_{-11}$
NLO $2\to 2$, 8 |  CP5 | $29.0\pm 0.9\,^{+5.3}_{-6.1}$ | $66\pm 3\,^{+7}_{-12}$ | $37.0\pm 3.1\,^{+6.2}_{-9.1}$
NLO $2\to 3$, 8 |  CP5 | $32.8\pm 0.9\,^{+5.9}_{-8.3}$ | $39.5\pm 1.0\,^{+6.3}_{-9.2}$ | $6.7\pm 1.3\,^{+6.1}_{-8.8}$

Table 2: The values of the effective cross section $\sigma_{\text{eff}}$ extracted from data using different SPS models, along with their statistical and systematic uncertainties. The results are shown for the model where the full tune is used, and for the same models where the hard MPI have been removed MC Model |  Tune |  $\sigma_{\text{eff}}\pm(\text{stat})\pm\text{(syst)}$ (mb)
---|---|---
|  | Full tune | Hard MPI removed
8 |  CP5 | $22.2\pm 0.7\,^{+1.2}_{-0.8}$ | $13.2\pm 0.3\,^{+1.6}_{-1.7}$
8+Vincia |  Standard 8.3 | $34.8\pm 1.3\,^{+0.9}_{-3.5}$ | $21.8\pm 0.7\,^{+1.9}_{-1.2}$
8 |  CDPSTP8S1-4j |  | $27.3\pm 0.9\,^{+1.5}_{-0.5}$
7 |  CH3 | $22.5\pm 0.7\,^{+1.7}_{-0.7}$ | $13.3\pm 0.3\,^{+1.7}_{-1.7}$
7 |  SoftTune | $31.4\pm 1.1\,^{+1.1}_{-2.4}$ | $17.2\pm 0.5\,^{+1.8}_{-1.5}$
LO $2\to 2,3,4$, 8 |  CP5 | $33.4\pm 1.3\,^{+1.1}_{-3.1}$ | $16.3\pm 0.5\,^{+1.9}_{-1.8}$
LO $2\to 2,3,4$, 8+Vincia |  Standard 8.3 | $32.8\pm 1.3\,^{+1.2}_{-2.1}$ | $16.0\pm 0.4\,^{+2.0}_{-1.9}$
NLO $2\to 2$, 8 |  CP5 | $11.7\pm 0.3\,^{+2.3}_{-1.9}$ | $7.3\pm 0.2\,^{+1.3}_{-1.4}$
NLO $2\to 2$, 8 |  CP5 | $17.5\pm 0.9\,^{+1.6}_{-1.7}$ | $7.7\pm 0.3\,^{+1.5}_{-1.6}$
NLO $2\to 3$, 8 |  CP5 | $15.5\pm 0.5\,^{+1.8}_{-1.8}$ | $12.9\pm 0.3\,^{+1.7}_{-1.8}$

##  0.9 Summary

A study of the inclusive production of four-jet events at low transverse
momentum has been presented based on data from proton-proton collisions
collected with the CMS detector at a center-of-mass energy of 13. Various
observables sensitive to double-parton scattering (DPS) are studied and values
for its effective cross section have been extracted.

Models based on leading order (LO) $2\to 2$ matrix elements significantly
overestimate the absolute four-jet cross section in the phase space domains
studied in this paper. This excess is related to an abundance of low-and
forward jets. The predictions of the absolute cross section generally improve
when next-to-leading order (NLO) and/or higher-multiplicity matrix elements
are used.

The azimuthal angle between the jets with the largest separation in $\eta$,
$\phi_{ij}$, has a strong discriminating power for different parton-shower
approaches and the data favor the angular-ordered and dipole-antenna parton-
shower models over those with a -ordered parton shower. The yield of jet pairs
with large rapidity separation $\Delta Y$ is, however, overestimated by all
models, although models based on NLO and/or higher-multiplicity matrix
elements are closer to the data.

The distribution of the minimal combined azimuthal angular range of three
jets, $\Delta\phi_{\mathrm{3j}}^{\text{min}}$, also exhibits sensitivity to
the parton-shower implementation, with data favoring -ordered parton showers
with the LO $2\to 2$ models for this observable. In the case of models based
on NLO and/or higher-multiplicity matrix elements the comparisons are less
conclusive.

Other observables, such as the azimuthal angle between the two softest jets,
$\Delta\phi_{\text{Soft}}$, and their transverse momentum balance, $\Delta
p_{\text{T,Soft}}$, indicate the need for a DPS contribution in the models to
various degrees, as confirmed by the extracted values of
$\sigma_{\text{eff}}$.

The distribution of the azimuthal angle between the hard and soft jet pairs,
$\Delta S$, is the least sensitive to the details of the parton-shower
modeling, and it is used for the extraction of the effective cross section,
$\sigma_{\text{eff}}$.

A dependence is observed of the extracted values of $\sigma_{\text{eff}}$ on
the model used to describe the SPS contribution. Models based on NLO $2\to 2$
matrix elements yield the smallest ($\sim$7mb) values of $\sigma_{\text{eff}}$
and need the largest DPS contribution. However, models using a $2\to 2$ matrix
element along with older underlying event descriptions and older PDFs, tend to
need the smallest DPS contribution. The sensitivity to the underlying event
description, parton showers, and the PDFs is observed to be small when
including higher-order matrix elements, since both models using the $2\to
2,3,4$ matrix elements show agreement with each other.

These results demonstrate the need for further development of models to
accurately describe final states with multiple jets in phase space regions
with large potential DPS contributions.

###### Acknowledgements.

We congratulate our colleagues in the CERN accelerator departments for the
excellent performance of the LHC and thank the technical and administrative
staffs at CERN and at other CMS institutes for their contributions to the
success of the CMS effort. In addition, we gratefully acknowledge the
computing centers and personnel of the Worldwide LHC Computing Grid and other
centers for delivering so effectively the computing infrastructure essential
to our analyses. Finally, we acknowledge the enduring support for the
construction and operation of the LHC, the CMS detector, and the supporting
computing infrastructure provided by the following funding agencies: BMBWF and
FWF (Austria); FNRS and FWO (Belgium); CNPq, CAPES, FAPERJ, FAPERGS, and
FAPESP (Brazil); MES and BNSF (Bulgaria); CERN; CAS, MoST, and NSFC (China);
MINCIENCIAS (Colombia); MSES and CSF (Croatia); RIF (Cyprus); SENESCYT
(Ecuador); MoER, ERC PUT and ERDF (Estonia); Academy of Finland, MEC, and HIP
(Finland); CEA and CNRS/IN2P3 (France); BMBF, DFG, and HGF (Germany); GSRI
(Greece); NKFIA (Hungary); DAE and DST (India); IPM (Iran); SFI (Ireland);
INFN (Italy); MSIP and NRF (Republic of Korea); MES (Latvia); LAS (Lithuania);
MOE and UM (Malaysia); BUAP, CINVESTAV, CONACYT, LNS, SEP, and UASLP-FAI
(Mexico); MOS (Montenegro); MBIE (New Zealand); PAEC (Pakistan); MSHE and NSC
(Poland); FCT (Portugal); JINR (Dubna); MON, RosAtom, RAS, RFBR, and NRC KI
(Russia); MESTD (Serbia); SEIDI, CPAN, PCTI, and FEDER (Spain); MOSTR (Sri
Lanka); Swiss Funding Agencies (Switzerland); MST (Taipei); ThEPCenter, IPST,
STAR, and NSTDA (Thailand); TUBITAK and TAEK (Turkey); NASU (Ukraine); STFC
(United Kingdom); DOE and NSF (USA). Individuals have received support from
the Marie-Curie program and the European Research Council and Horizon 2020
Grant, contract Nos. 675440, 724704, 752730, 758316, 765710, 824093, 884104,
and COST Action CA16108 (European Union); the Leventis Foundation; the Alfred
P. Sloan Foundation; the Alexander von Humboldt Foundation; the Belgian
Federal Science Policy Office; the Fonds pour la Formation à la Recherche dans
l’Industrie et dans l’Agriculture (FRIA-Belgium); the Agentschap voor
Innovatie door Wetenschap en Technologie (IWT-Belgium); the F.R.S.-FNRS and
FWO (Belgium) under the “Excellence of Science – EOS” – be.h project n.
30820817; the Beijing Municipal Science & Technology Commission, No.
Z191100007219010; the Ministry of Education, Youth and Sports (MEYS) of the
Czech Republic; the Deutsche Forschungsgemeinschaft (DFG), under Germany’s
Excellence Strategy – EXC 2121 “Quantum Universe” – 390833306, and under
project number 400140256 - GRK2497; the Lendület (“Momentum”) Program and the
János Bolyai Research Scholarship of the Hungarian Academy of Sciences, the
New National Excellence Program ÚNKP, the NKFIA research grants 123842,
123959, 124845, 124850, 125105, 128713, 128786, and 129058 (Hungary); the
Council of Science and Industrial Research, India; the Latvian Council of
Science; the Ministry of Science and Higher Education and the National Science
Center, contracts Opus 2014/15/B/ST2/03998 and 2015/19/B/ST2/02861 (Poland);
the Fundação para a Ciência e a Tecnologia, grant CEECIND/01334/2018
(Portugal); the National Priorities Research Program by Qatar National
Research Fund; the Ministry of Science and Higher Education, project no.
14.W03.31.0026 (Russia); the Programa Estatal de Fomento de la Investigación
Científica y Técnica de Excelencia María de Maeztu, grant MDM-2015-0509 and
the Programa Severo Ochoa del Principado de Asturias; the Stavros Niarchos
Foundation (Greece); the Rachadapisek Sompot Fund for Postdoctoral Fellowship,
Chulalongkorn University and the Chulalongkorn Academic into Its 2nd Century
Project Advancement Project (Thailand); the Kavli Foundation; the Nvidia
Corporation; the SuperMicro Corporation; the Welch Foundation, contract
C-1845; and the Weston Havens Foundation (USA).

## References

  * [1] CMS Collaboration, “Measurement of the ratio of inclusive jet cross sections using the anti-algorithm with radius parameters R = 0.5 and 0.7 in pp collisions at $\sqrt{s}=7$ TeV”,  Phys. Rev. D 90 (2014) 072006, 10.1103/PhysRevD.90.072006, arXiv:1406.0324.
  * [2] CMS Collaboration, “Measurement and QCD analysis of double-differential inclusive jet cross sections in pp collisions at $\sqrt{s}=8$ and cross section ratios to 2.76 and 7 TeV”,  JHEP 03 (2017) 156, 10.1007/JHEP03(2017)156, arXiv:1609.05331.
  * [3] CMS Collaboration, “Measurement of the double-differential inclusive jet cross section in proton-proton collisions at $\sqrt{s}=13\,\text{TeV}$”,  Eur. Phys. J. C. 76 (2016) 451, 10.1140/epjc/s10052-016-4286-3, arXiv:1605.04436.
  * [4] M. Diehl, D. Ostermeier, and A. Schafer, “Elements of a theory for multiparton interactions in QCD”,  JHEP 03 (2012) 089, 10.1007/JHEP03(2012)089, arXiv:1111.0910. [Erratum: JHEP 03, 001 (2016)].
  * [5] CDF Collaboration, “Measurement of double parton scattering in $\mathrm{\overline{p}p}$ collisions at $\sqrt{\mathit{s}}\phantom{\rule{0.0pt}{0.0pt}}=\phantom{\rule{0.0pt}{0.0pt}}1.8~{}\mathrm{TeV}$”,  Phys. Rev. Lett. 79 (1997) 584, 10.1103/PhysRevLett.79.584.
  * [6] CDF Collaboration, “Double parton scattering in $\mathrm{\overline{p}p}$ collisions at $\sqrt{s}=1.8~{}\mathrm{TeV}$”,  Phys. Rev. D 56 (1997) 3811, 10.1103/PhysRevD.56.3811.
  * [7] D0 Collaboration, “Double parton interactions in $\gamma+3$ jet events in $\mathrm{p\overline{p}}$ collisions at $\sqrt{s}=1.96\text{ }\text{ }\mathrm{TeV}$”,  Phys. Rev. D 81 (2010) 052012, 10.1103/PhysRevD.81.052012, arXiv:0912.5104.
  * [8] D0 Collaboration, “Double parton interactions in $\gamma+3$ jet and $\gamma+\mathrm{b/c~{}jet}+2$ jet events in $\mathrm{p\bar{p}}$ collisions at $\sqrt{s}=1.96$ TeV”,  Phys. Rev. D 89 (2014) 072006, 10.1103/PhysRevD.89.072006, arXiv:1402.1550.
  * [9] D0 Collaboration, “Study of double parton interactions in diphoton + dijet events in $\mathrm{p\bar{p}}$ collisions at $\sqrt{s}=1.96$ TeV”,  Phys. Rev. D 93 (2016) 052008, 10.1103/PhysRevD.93.052008, arXiv:1512.05291.
  * [10] ATLAS Collaboration, “Measurement of hard double-parton interactions in $\mathrm{W}(\to\mathrm{l}\nu)$\+ 2 jet events at $\sqrt{s}$ = 7with the ATLAS detector”,  New J. Phys. 15 (2013) 033038, 10.1088/1367-2630/15/3/033038, arXiv:1301.6872.
  * [11] CMS Collaboration, “Study of double parton scattering using W + 2-jet events in proton-proton collisions at $\sqrt{s}$ = 7 TeV”,  JHEP 03 (2014) 032, 10.1007/JHEP03(2014)032, arXiv:1312.5729.
  * [12] CMS Collaboration, “Constraints on the double-parton scattering cross section from same-sign W boson pair production in proton-proton collisions at $\sqrt{s}=8$ TeV”,  JHEP 02 (2018) 032, 10.1007/JHEP02(2018)032, arXiv:1712.02280.
  * [13] CMS Collaboration, “Evidence for WW production from double-parton interactions in proton-proton collisions at $\sqrt{s}=$ 13 TeV”,  Eur. Phys. J. C 80 (2020) 41, 10.1140/epjc/s10052-019-7541-6, arXiv:1909.06265.
  * [14] CMS Collaboration, “Measurements of Z bosons plus jets using variables sensitive to double parton scattering in pp collisions at 13 TeV”, 2021. arXiv:2105.14511. Submitted to JHEP.
  * [15] LHCb Collaboration, “Observation of double charm production involving open charm in pp collisions at $\sqrt{s}$ = 7 TeV”,  JHEP 06 (2012) 141, 10.1007/JHEP06(2012)141, arXiv:1205.0975. [Addendum: JHEP03,108(2014)].
  * [16] LHCb Collaboration, “Observation of associated production of a Z boson with a D meson in the forward region”,  JHEP 04 (2014) 091, 10.1007/JHEP04(2014)091, arXiv:1401.3245.
  * [17] D0 Collaboration, “Observation and studies of double $\mathrm{J}/\psi$ production at the Tevatron”,  Phys. Rev. D 90 (2014) 111101, 10.1103/PhysRevD.90.111101.
  * [18] LHCb Collaboration, “Production of associated Y and open charm hadrons in pp collisions at $\sqrt{s}=7$ and 8via double parton scattering”,  JHEP 07 (2016) 052, 10.1007/JHEP07(2016)052, arXiv:1510.05949.
  * [19] LHCb Collaboration, “Measurement of the J/$\psi$ pair production cross-section in pp collisions at $\sqrt{s}=13$ TeV”,  JHEP 06 (2017) 047, 10.1007/JHEP06(2017)047, arXiv:1612.07451. [Erratum: JHEP 10, 068 (2017)].
  * [20] UA2 Collaboration, “A study of multi-jet events at the CERN pp collider and a search for double parton scattering”,  Phys. Lett. B 268 (1991) 145, 10.1016/0370-2693(91)90937-L.
  * [21] CDF Collaboration, “Study of four-jet events and evidence for double parton interactions in $\mathrm{p\bar{p}}$ collisions at $\sqrt{s}=1.8$ TeV”,  Phys. Rev. D 47 (1993) 4857, 10.1103/PhysRevD.47.4857.
  * [22] ATLAS Collaboration, “Measurement of four-jet differential cross sections in $\sqrt{s}=8\TeV$ proton-proton collisions using the ATLAS detector”,  JHEP 12 (2015) 105, 10.1007/JHEP12(2015)105, arXiv:1509.07335.
  * [23] I. Sadeh, “Double parton scattering in four-jet events in pp collisions at 7 TeV with the ATLAS experiment at the LHC”.  PhD thesis, Tel Aviv U., 2013.  arXiv:1308.0587.
  * [24] ATLAS Collaboration, “Study of hard double-parton scattering in four-jet events in pp collisions at $\sqrt{s}=7$ with the ATLAS experiment”,  JHEP 11 (2016) 110, 10.1007/JHEP11(2016)110, arXiv:1608.01857.
  * [25] CMS Collaboration, “Measurement of four-jet production in proton-proton collisions at $\sqrt{s}=7$ TeV”,  Phys. Rev. D 89 (2014) 092010, 10.1103/PhysRevD.89.092010, arXiv:1312.6440.
  * [26] CMS Collaboration, “Studies of inclusive four-jet production with two $\mathrm{b}$-tagged jets in proton-proton collisions at 7 TeV”,  Phys. Rev. D 94 (2016) 112005, 10.1103/PhysRevD.94.112005, arXiv:1609.03489.
  * [27] “HEPData record for this analysis”, 2021.  10.17182/hepdata.102460.
  * [28] S. Domdey, H.-J. Pirner, and U. A. Wiedemann, “Testing the scale dependence of the scale factor $\sigma_{\mathrm{eff}}$ in double dijet production at the LHC”,  Eur. Phys. J. C 65 (2010) 153, 10.1140/epjc/s10052-009-1198-5, arXiv:0906.4335.
  * [29] E. L. Berger, C. B. Jackson, and G. Shaughnessy, “Characteristics and estimates of double parton scattering at the Large Hadron Collider”,  Phys. Rev. D 81 (2010) 014014, 10.1103/PhysRevD.81.014014, arXiv:0911.5348.
  * [30] R. Maciuła and A. Szczurek, “Searching for and exploring double-parton scattering effects in four-jet production at the LHC”,  Phys. Lett. B 749 (2015) 57, 10.1016/j.physletb.2015.07.035, arXiv:1503.08022.
  * [31] K. Kutak et al., “Four-jet production in single- and double-parton scattering within high-energy factorization”,  JHEP 04 (2016) 175, 10.1007/JHEP04(2016)175, arXiv:1602.06814.
  * [32] K. Kutak, “Four-jet production in single- and double-parton scattering within high-energy factorization”,  PoS ICHEP2016 (2016) 610, 10.22323/1.282.0610, arXiv:1701.00410.
  * [33] K. Kutak et al., “Search for optimal conditions for exploring double-parton scattering in four-jet production: -factorization approach”,  Phys. Rev. D 94 (2016) 014019, 10.1103/PhysRevD.94.014019, arXiv:1605.08240.
  * [34] CMS Collaboration, “Performance of the CMS Level-1 trigger in proton-proton collisions at $\sqrt{s}=13$ TeV”,  JINST 15 (2020) P10017, 10.1088/1748-0221/15/10/P10017, arXiv:2006.10165.
  * [35] CMS Collaboration, “The CMS trigger system”,  JINST 12 (2017) P01020, 10.1088/1748-0221/12/01/P01020, arXiv:1609.02366.
  * [36] CMS Collaboration, “Particle-flow reconstruction and global event description with the CMS detector”,  JINST 12 (2017) P10003, 10.1088/1748-0221/12/10/P10003, arXiv:1706.04965.
  * [37] M. Cacciari, G. P. Salam, and G. Soyez, “The anti-jet clustering algorithm”,  JHEP 04 (2008) 063, 10.1088/1126-6708/2008/04/063, arXiv:0802.1189.
  * [38] M. Cacciari, G. P. Salam, and G. Soyez, “FastJet user manual”,  Eur. Phys. J. C 72 (2012) 1896, 10.1140/epjc/s10052-012-1896-2, arXiv:1111.6097.
  * [39] CMS Collaboration, “Jet energy scale and resolution in the CMS experiment in pp collisions at 8 TeV”,  JINST 12 (2017) P02014, 10.1088/1748-0221/12/02/P02014, arXiv:1607.03663.
  * [40] CMS Collaboration, “The CMS experiment at the CERN LHC”,  JINST 3 (2008) S08004, 10.1088/1748-0221/3/08/S08004.
  * [41] T. Sjöstrand et al., “An introduction to PYTHIA 8.2”,  Comput. Phys. Commun. 191 (2015) 159, 10.1016/j.cpc.2015.01.024, arXiv:1410.3012.
  * [42] M. Bähr et al., “Herwig++ physics and manual”,  Eur. Phys. J. C 58 (2008) 639, 10.1140/epjc/s10052-008-0798-9, arXiv:0803.0883.
  * [43] J. Bellm et al., “Herwig 7.0 / Herwig++ 3.0 release note”,  Eur. Phys. J. C 76 (2015) 196, 10.1140/epjc/s10052-016-4018-8, arXiv:1512.0117.
  * [44] V. N. Gribov and L. N. Lipatov, “Deep inelastic e p scattering in perturbation theory”,  Sov. J. Nucl. Phys. 15 (1972) 438.
  * [45] Y. L. Dokshitzer, “Calculation of the structure functions for deep inelastic scattering and e+ e- annihilation by perturbation theory in quantum chromodynamics.”,  Sov. Phys. JETP 46 (1977) 641\.
  * [46] G. Altarelli and G. Parisi, “Asymptotic freedom in parton language”,  Nuclear Physics B 126 (1977) 298, 10.1016/0550-3213(77)90384-4.
  * [47] B. Andersson, G. Gustafson, G. Ingelman, and T. Sjöstrand, “Parton fragmentation and string dynamics”,  Phys. Rep. 97 (1983) 31, 10.1016/0370-1573(83)90080-7.
  * [48] D. Amati and G. Veneziano, “Preconfinement as a property of perturbative QCD”,  Phys. Lett. B 83 (1979) 87, 10.1016/0370-2693(79)90896-7.
  * [49] GEANT4 Collaboration, “—a simulation toolkit”,  Nucl. Instrum. Meth. A 506 (2003) 250, 10.1016/S0168-9002(03)01368-8.
  * [50] P. Skands, S. Carrazza, and J. Rojo, “Tuning PYTHIA 8.1: the Monash 2013 tune”,  Eur. Phys. J. C 74 (2014) 3024, 10.1140/epjc/s10052-014-3024-y, arXiv:1404.5630.
  * [51] CMS Collaboration, “Event generator tunes obtained from underlying event and multiparton scattering measurements”,  Eur. Phys. J. C 76 (2016) 155, 10.1140/epjc/s10052-016-3988-x, arXiv:1512.00815.
  * [52] CMS Collaboration, “Extraction and validation of a new set of CMS PYTHIA8 tunes from underlying-event measurements”,  Eur. Phys. J. C 80 (2020) 4, 10.1140/epjc/s10052-019-7499-4, arXiv:1903.12179.
  * [53] NNPDF Collaboration, “Parton distributions from high-precision collider data”,  Eur. Phys. J. C 77 (2017) 663, 10.1140/epjc/s10052-017-5199-5, arXiv:1706.00428.
  * [54] R. Corke and T. Sjöstrand, “Interleaved parton showers and tuning prospects”,  JHEP 03 (2011) 032, 10.1007/JHEP03(2011)032, arXiv:1011.1759.
  * [55] J. Pumplin et al., “New generation of parton distributions with uncertainties from global QCD analysis”,  JHEP 07 (2002) 012, 10.1088/1126-6708/2002/07/012, arXiv:hep-ph/0201195.
  * [56] N. Fischer, S. Prestel, M. Ritzmann, and P. Skands, “VINCIA for hadron colliders”,  Eur. Phys. J. C 76 (2016) 589, 10.1140/epjc/s10052-016-4429-6, arXiv:1605.06142.
  * [57] L. A. Harland-Lang, A. D. Martin, P. Motylinski, and R. S. Thorne, “Parton distributions in the LHC era: MMHT 2014 PDFs”,  Eur. Phys. J. C 75 (2015) 204, 10.1140/epjc/s10052-015-3397-6, arXiv:1412.3989.
  * [58] CMS Collaboration, “Development and validation of HERWIG 7 tunes from CMS underlying-event measurements”,  Eur. Phys. J. C 81 (2021) 312, 10.1140/epjc/s10052-021-08949-5, arXiv:2011.03422.
  * [59] H. Jung et al., “The CCFM Monte Carlo generator CASCADE version 2.2.03”,  Eur. Phys. J. C 70 (2010) 1237, 10.1140/epjc/s10052-010-1507-z, arXiv:1008.0152.
  * [60] J. Alwall et al., “The automated computation of tree-level and next-to-leading order differential cross sections, and their matching to parton shower simulations”,  JHEP 07 (2014) 079, 10.1007/JHEP07(2014)079, arXiv:1405.0301.
  * [61] J. Alwall et al., “Comparative study of various algorithms for the merging of parton showers and matrix elements in hadronic collisions”,  Eur. Phys. J. C 53 (2008) 473, 10.1140/epjc/s10052-007-0490-5, arXiv:0706.2569.
  * [62] P. Nason, “A new method for combining NLO QCD with shower Monte Carlo algorithms”,  JHEP 11 (2004) 040, 10.1088/1126-6708/2004/11/040, arXiv:hep-ph/0409146.
  * [63] S. Frixione, P. Nason, and C. Oleari, “Matching NLO QCD computations with parton shower simulations: the POWHEG method”,  JHEP 11 (2007) 070, 10.1088/1126-6708/2007/11/070, arXiv:0709.2092.
  * [64] S. Alioli, P. Nason, C. Oleari, and E. Re, “A general framework for implementing NLO calculations in shower Monte Carlo programs: the POWHEG BOX”,  JHEP 06 (2010) 043, 10.1007/JHEP06(2010)043, arXiv:1002.2581.
  * [65] S. Alioli et al., “Jet pair production in POWHEG”,  JHEP 04 (2011) 081, 10.1007/JHEP04(2011)081, arXiv:1012.3380.
  * [66] A. Kardos, P. Nason, and C. Oleari, “Three-jet production in POWHEG”,  JHEP 04 (2014) 043, 10.1007/JHEP04(2014)043, arXiv:1402.4001.
  * [67] A. van Hameren, “KaTie : For parton-level event generation with -dependent initial states”,  Comput. Phys. Commun. 224 (2018) 371, 10.1016/j.cpc.2017.11.005, arXiv:1611.00680.
  * [68] S. Catani and F. Hautmann, “High-energy factorization and small-x deep inelastic scattering beyond leading order”,  Nucl. Phys. B 427 (1994) 475, 10.1016/0550-3213(94)90636-X, arXiv:hep-ph/9405388.
  * [69] M. Deak, F. Hautmann, H. Jung, and K. Kutak, “Forward jet production at the Large Hadron Collider”,  JHEP 09 (2009) 121, 10.1088/1126-6708/2009/09/121, arXiv:0908.0538.
  * [70] S. Sapeta, “QCD and jets at hadron colliders”,  Prog. Part. Nucl. Phys. 89 (2016) 1, 10.1016/j.ppnp.2016.02.002, arXiv:1511.09336.
  * [71] M. Bury et al., “Calculations with off-shell matrix elements, TMD parton densities and TMD parton showers”,  Eur. Phys. J. C 78 (2018) 137, 10.1140/epjc/s10052-018-5642-2, arXiv:1712.05932.
  * [72] A. Bermudez Martinez et al., “Collinear and TMD parton densities from fits to precision DIS measurements in the parton branching method”,  Phys. Rev. D 99 (2019) 074008, 10.1103/PhysRevD.99.074008, arXiv:1804.11152.
  * [73] S. Schmitt, “TUnfold, an algorithm for correcting migration effects in high energy physics”,  JINST 7 (2012) T10003, 10.1088/1748-0221/7/10/T10003, arXiv:1205.6201.
  * [74] S. Schmitt, “Data unfolding methods in high energy physics”,  EPJ Web Conf. 137 (2017) 11008, 10.1051/epjconf/201713711008, arXiv:1611.01927.
  * [75] A. N. Tikhonov, “Solution of incorrectly formulated problems and the regularization method”,  Soviet Math. Dokl. 4 (1963) 1035.
  * [76] R. Brun and F. Rademakers, “ROOT- An object oriented data analysis framework”,  Nucl. Instrum. Meth. A 389 (1997) 81, 10.1016/S0168-9002(97)00048-X.
  * [77] CMS Collaboration, “Precision luminosity measurement in proton-proton collisions at $\sqrt{s}=$ 13 TeV in 2015 and 2016 at CMS”,  Eur. Phys. J. C 81 (2021) 800, 10.1140/epjc/s10052-021-09538-2, arXiv:2104.01927.
  * [78] M. H. Seymour and A. Siodmok, “Extracting $\sigma_{\mathrm{effective}}$ from the LHCb double-charm measurement”, 2013. arXiv:1308.6749.

##  .10 The CMS Collaboration

Yerevan Physics Institute, Yerevan, Armenia
A. Tumasyan Institut für Hochenergiephysik, Vienna, Austria
W. Adam, J.W. Andrejkovic, T. Bergauer, S. Chatterjee, M. Dragicevic, A.
Escalante Del Valle, R. Frühwirth1, M. Jeitler1, N. Krammer, L. Lechner, D.
Liko, I. Mikulec, P. Paulitsch, F.M. Pitters, J. Schieck1, R. Schöfbeck, M.
Spanring, S. Templ, W. Waltenberger, C.-E. Wulz1 Institute for Nuclear
Problems, Minsk, Belarus
V. Chekhovsky, A. Litomin, V. Makarenko Universiteit Antwerpen, Antwerpen,
Belgium
M.R. Darwish2, E.A. De Wolf, X. Janssen, T. Kello3, A. Lelek, M. Pieters, H.
Rejeb Sfar, H. Van Haevermaet, P. Van Mechelen, S. Van Putte, N. Van Remortel
Vrije Universiteit Brussel, Brussel, Belgium
F. Blekman, E.S. Bols, J. D’Hondt, J. De Clercq, M. Delcourt, H. El Faham, S.
Lowette, S. Moortgat, A. Morton, D. Müller, A.R. Sahasransu, S. Tavernier, W.
Van Doninck, P. Van Mulders Université Libre de Bruxelles, Bruxelles, Belgium
D. Beghin, B. Bilin, B. Clerbaux, G. De Lentdecker, L. Favart, A. Grebenyuk,
A.K. Kalsi, K. Lee, M. Mahdavikhorrami, I. Makarenko, L. Moureaux, L. Pétré,
A. Popov, N. Postiau, E. Starling, L. Thomas, M. Vanden Bemden, C. Vander
Velde, P. Vanlaer, D. Vannerom, L. Wezenbeek Ghent University, Ghent, Belgium
T. Cornelis, D. Dobur, J. Knolle, L. Lambrecht, G. Mestdach, M. Niedziela, C.
Roskas, A. Samalan, K. Skovpen, M. Tytgat, W. Verbeke, B. Vermassen, M. Vit
Université Catholique de Louvain, Louvain-la-Neuve, Belgium
A. Bethani, G. Bruno, F. Bury, C. Caputo, P. David, C. Delaere, I.S. Donertas,
A. Giammanco, K. Jaffel, Sa. Jain, V. Lemaitre, K. Mondal, J. Prisciandaro, A.
Taliercio, M. Teklishyn, T.T. Tran, P. Vischia, S. Wertz, S. Wuyckens Centro
Brasileiro de Pesquisas Fisicas, Rio de Janeiro, Brazil
G.A. Alves, C. Hensel, A. Moraes Universidade do Estado do Rio de Janeiro, Rio
de Janeiro, Brazil
W.L. Aldá Júnior, M. Alves Gallo Pereira, M. Barroso Ferreira Filho, H.
BRANDAO MALBOUISSON, W. Carvalho, J. Chinellato4, E.M. Da Costa, G.G. Da
Silveira5, D. De Jesus Damiao, S. Fonseca De Souza, D. Matos Figueiredo, C.
Mora Herrera, K. Mota Amarilo, L. Mundim, H. Nogima, P. Rebello Teles, A.
Santoro, S.M. Silva Do Amaral, A. Sznajder, M. Thiel, F. Torres Da Silva De
Araujo, A. Vilela Pereira Universidade Estadual Paulista a, Universidade
Federal do ABC b, São Paulo, Brazil
C.A. Bernardesa,a, L. Calligarisa, T.R. Fernandez Perez Tomeia, E.M.
Gregoresa,b, D.S. Lemosa, P.G. Mercadantea,b, S.F. Novaesa, Sandra S. Padulaa
Institute for Nuclear Research and Nuclear Energy, Bulgarian Academy of
Sciences, Sofia, Bulgaria
A. Aleksandrov, G. Antchev, R. Hadjiiska, P. Iaydjiev, M. Misheva, M. Rodozov,
M. Shopova, G. Sultanov University of Sofia, Sofia, Bulgaria
A. Dimitrov, T. Ivanov, L. Litov, B. Pavlov, P. Petkov, A. Petrov Beihang
University, Beijing, China
T. Cheng, W. Fang3, Q. Guo, T. Javaid6, M. Mittal, H. Wang, L. Yuan Department
of Physics, Tsinghua University
M. Ahmad, G. Bauer, C. Dozen7, Z. Hu, J. Martins8, Y. Wang, K. Yi9,10
Institute of High Energy Physics, Beijing, China
E. Chapon, G.M. Chen6, H.S. Chen6, M. Chen, F. Iemmi, A. Kapoor, D. Leggat, H.
Liao, Z.-A. LIU6, V. Milosevic, F. Monti, R. Sharma, J. Tao, J. Thomas-
wilsker, J. Wang, H. Zhang, S. Zhang6, J. Zhao State Key Laboratory of Nuclear
Physics and Technology, Peking University, Beijing, China
A. Agapitos, Y. Ban, C. Chen, Q. Huang, A. Levin, Q. Li, X. Lyu, Y. Mao, S.J.
Qian, D. Wang, Q. Wang, J. Xiao Sun Yat-Sen University, Guangzhou, China
M. Lu, Z. You Institute of Modern Physics and Key Laboratory of Nuclear
Physics and Ion-beam Application (MOE) - Fudan University, Shanghai, China
X. Gao3, H. Okawa Zhejiang University, Hangzhou, China
Z. Lin, M. Xiao Universidad de Los Andes, Bogota, Colombia
C. Avila, A. Cabrera, C. Florez, J. Fraga, A. Sarkar, M.A. Segura Delgado
Universidad de Antioquia, Medellin, Colombia
J. Mejia Guisao, F. Ramirez, J.D. Ruiz Alvarez, C.A. Salazar González
University of Split, Faculty of Electrical Engineering, Mechanical Engineering
and Naval Architecture, Split, Croatia
D. Giljanovic, N. Godinovic, D. Lelas, I. Puljak University of Split, Faculty
of Science, Split, Croatia
Z. Antunovic, M. Kovac, T. Sculac Institute Rudjer Boskovic, Zagreb, Croatia
V. Brigljevic, D. Ferencek, D. Majumder, M. Roguljic, A. Starodumov11, T. Susa
University of Cyprus, Nicosia, Cyprus
A. Attikis, K. Christoforou, E. Erodotou, A. Ioannou, G. Kole, M. Kolosova, S.
Konstantinou, J. Mousa, C. Nicolaou, F. Ptochos, P.A. Razis, H. Rykaczewski,
H. Saka Charles University, Prague, Czech Republic
M. Finger12, M. Finger Jr.12, A. Kveton Escuela Politecnica Nacional, Quito,
Ecuador
E. Ayala 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
A.A. Abdelalim13,14, S. Elgammal15 Center for High Energy Physics (CHEP-FU),
Fayoum University, El-Fayoum, Egypt
A. Lotfy, M.A. Mahmoud National Institute of Chemical Physics and Biophysics,
Tallinn, Estonia
S. Bhowmik, A. Carvalho Antunes De Oliveira, R.K. Dewanjee, K. Ehataht, M.
Kadastik, S. Nandan, C. Nielsen, J. Pata, M. Raidal, L. Tani, C. Veelken
Department of Physics, University of Helsinki, Helsinki, Finland
P. Eerola, L. Forthomme, H. Kirschenmann, K. Osterberg, M. Voutilainen
Helsinki Institute of Physics, Helsinki, Finland
S. Bharthuar, E. Brücken, F. Garcia, J. Havukainen, M.S. Kim, R. Kinnunen, T.
Lampén, K. Lassila-Perini, S. Lehti, T. Lindén, M. Lotti, L. Martikainen, J.
Ott, H. Siikonen, E. Tuominen, J. Tuominiemi Lappeenranta University of
Technology, Lappeenranta, Finland
P. Luukka, H. Petrow, T. Tuuva IRFU, CEA, Université Paris-Saclay, Gif-sur-
Yvette, France
C. Amendola, M. Besancon, F. Couderc, M. Dejardin, D. Denegri, J.L. Faure, F.
Ferri, S. Ganjour, A. Givernaud, P. Gras, G. Hamel de Monchenault, P. Jarry,
B. Lenzi, E. Locci, J. Malcles, J. Rander, A. Rosowsky, M.Ö. Sahin, A. Savoy-
Navarro16, M. Titov, G.B. Yu Laboratoire Leprince-Ringuet, CNRS/IN2P3, Ecole
Polytechnique, Institut Polytechnique de Paris, Palaiseau, France
S. Ahuja, F. Beaudette, M. Bonanomi, A. Buchot Perraguin, P. Busson, A.
Cappati, C. Charlot, O. Davignon, B. Diab, G. Falmagne, S. Ghosh, R. Granier
de Cassagnac, A. Hakimi, I. Kucher, M. Nguyen, C. Ochando, P. Paganini, J.
Rembser, R. Salerno, J.B. Sauvan, Y. Sirois, A. Zabi, A. Zghiche Université de
Strasbourg, CNRS, IPHC UMR 7178, Strasbourg, France
J.-L. Agram17, J. Andrea, D. Apparu, D. Bloch, G. Bourgatte, J.-M. Brom, E.C.
Chabert, C. Collard, D. Darej, J.-C. Fontaine17, U. Goerlach, C. Grimault,
A.-C. Le Bihan, E. Nibigira, P. Van Hove Institut de Physique des 2 Infinis de
Lyon (IP2I ), Villeurbanne, France
E. Asilar, S. Beauceron, C. Bernet, G. Boudoul, C. Camen, A. Carle, N. Chanon,
D. Contardo, P. Depasse, H. El Mamouni, J. Fay, S. Gascon, M. Gouzevitch, B.
Ille, I.B. Laktineh, H. Lattaud, A. Lesauvage, M. Lethuillier, L. Mirabito, S.
Perries, K. Shchablo, V. Sordini, L. Torterotot, G. Touquet, M. Vander Donckt,
S. Viret Georgian Technical University, Tbilisi, Georgia
I. Lomidze, T. Toriashvili18, Z. Tsamalaidze12 RWTH Aachen University, I.
Physikalisches Institut, Aachen, Germany
L. Feld, K. Klein, M. Lipinski, D. Meuser, A. Pauls, M.P. Rauch, N. Röwert, J.
Schulz, M. Teroerde RWTH Aachen University, III. Physikalisches Institut A,
Aachen, Germany
A. Dodonova, D. Eliseev, M. Erdmann, P. Fackeldey, B. Fischer, S. Ghosh, T.
Hebbeker, K. Hoepfner, F. Ivone, H. Keller, L. Mastrolorenzo, M. Merschmeyer,
A. Meyer, G. Mocellin, S. Mondal, S. Mukherjee, D. Noll, A. Novak, T. Pook, A.
Pozdnyakov, Y. Rath, H. Reithler, J. Roemer, A. Schmidt, S.C. Schuler, A.
Sharma, S. Wiedenbeck, S. Zaleski RWTH Aachen University, III. Physikalisches
Institut B, Aachen, Germany
C. Dziwok, G. Flügge, W. Haj Ahmad19, O. Hlushchenko, T. Kress, A. Nowack, C.
Pistone, O. Pooth, D. Roy, H. Sert, A. Stahl20, T. Ziemons Deutsches
Elektronen-Synchrotron, Hamburg, Germany
H. Aarup Petersen, M. Aldaya Martin, P. Asmuss, I. Babounikau, S. Baxter, O.
Behnke, A. Bermúdez Martínez, S. Bhattacharya, A.A. Bin Anuar, K. Borras21, V.
Botta, D. Brunner, A. Campbell, A. Cardini, C. Cheng, F. Colombina, S.
Consuegra Rodríguez, G. Correia Silva, V. Danilov, L. Didukh, G. Eckerlin, D.
Eckstein, L.I. Estevez Banos, O. Filatov, E. Gallo22, A. Geiser, A. Giraldi,
A. Grohsjean, M. Guthoff, A. Jafari23, N.Z. Jomhari, H. Jung, A. Kasem21, M.
Kasemann, H. Kaveh, C. Kleinwort, D. Krücker, W. Lange, J. Lidrych, K. Lipka,
W. Lohmann24, R. Mankel, I.-A. Melzer-Pellmann, J. Metwally, A.B. Meyer, M.
Meyer, J. Mnich, A. Mussgiller, Y. Otarid, D. Pérez Adán, D. Pitzl, A.
Raspereza, B. Ribeiro Lopes, J. Rübenach, A. Saggio, A. Saibel, M. Savitskyi,
M. Scham, V. Scheurer, C. Schwanenberger22, A. Singh, R.E. Sosa Ricardo, D.
Stafford, N. Tonon, O. Turkot, M. Van De Klundert, R. Walsh, D. Walter, Y.
Wen, K. Wichmann, L. Wiens, C. Wissing, S. Wuchterl University of Hamburg,
Hamburg, Germany
R. Aggleton, S. Albrecht, S. Bein, L. Benato, A. Benecke, P. Connor, K. De
Leo, M. Eich, F. Feindt, A. Fröhlich, C. Garbers, E. Garutti, P. Gunnellini,
J. Haller, A. Hinzmann, G. Kasieczka, R. Klanner, R. Kogler, T. Kramer, V.
Kutzner, J. Lange, T. Lange, A. Lobanov, A. Malara, A. Nigamova, K.J. Pena
Rodriguez, O. Rieger, P. Schleper, M. Schröder, J. Schwandt, D. Schwarz, J.
Sonneveld, H. Stadie, G. Steinbrück, A. Tews, B. Vormwald, I. Zoi Karlsruher
Institut fuer Technologie, Karlsruhe, Germany
J. Bechtel, T. Berger, E. Butz, R. Caspart, T. Chwalek, W. De
Boer${}^{\textrm{\textdagger}}$, A. Dierlamm, A. Droll, K. El Morabit, N.
Faltermann, M. Giffels, J.o. Gosewisch, A. Gottmann, F. Hartmann20, C.
Heidecker, U. Husemann, I. Katkov25, P. Keicher, R. Koppenhöfer, S. Maier, M.
Metzler, S. Mitra, Th. Müller, M. Neukum, A. Nürnberg, G. Quast, K. Rabbertz,
J. Rauser, D. Savoiu, M. Schnepf, D. Seith, I. Shvetsov, H.J. Simonis, R.
Ulrich, J. Van Der Linden, R.F. Von Cube, M. Wassmer, M. Weber, S. Wieland, R.
Wolf, S. Wozniewski, S. Wunsch Institute of Nuclear and Particle Physics
(INPP), NCSR Demokritos, Aghia Paraskevi, Greece
G. Anagnostou, P. Asenov, G. Daskalakis, T. Geralis, A. Kyriakis, D. Loukas,
A. Stakia National and Kapodistrian University of Athens, Athens, Greece
M. Diamantopoulou, D. Karasavvas, G. Karathanasis, P. Kontaxakis, C.K. Koraka,
A. Manousakis-katsikakis, A. Panagiotou, I. Papavergou, N. Saoulidou, K.
Theofilatos, E. Tziaferi, K. Vellidis, E. Vourliotis National Technical
University of Athens, Athens, Greece
G. Bakas, K. Kousouris, I. Papakrivopoulos, G. Tsipolitis, A. Zacharopoulou
University of Ioánnina, Ioánnina, Greece
I. Evangelou, C. Foudas, P. Gianneios, P. Katsoulis, P. Kokkas, N. Manthos, I.
Papadopoulos, J. Strologas MTA-ELTE Lendület CMS Particle and Nuclear Physics
Group, Eötvös Loránd University
M. Csanad, K. Farkas, M.M.A. Gadallah26, S. Lökös27, P. Major, K. Mandal, A.
Mehta, G. Pasztor, A.J. Rádl, O. Surányi, G.I. Veres Wigner Research Centre
for Physics, Budapest, Hungary
M. Bartók28, G. Bencze, C. Hajdu, D. Horvath29, F. Sikler, V. Veszpremi, G.
Vesztergombi${}^{\textrm{\textdagger}}$ Institute of Nuclear Research ATOMKI,
Debrecen, Hungary
S. Czellar, J. Karancsi28, J. Molnar, Z. Szillasi, D. Teyssier Institute of
Physics, University of Debrecen
P. Raics, Z.L. Trocsanyi30, B. Ujvari Karoly Robert Campus, MATE Institute of
Technology
T. Csorgo31, F. Nemes31, T. Novak Indian Institute of Science (IISc),
Bangalore, India
J.R. Komaragiri, D. Kumar, L. Panwar, P.C. Tiwari National Institute of
Science Education and Research, HBNI, Bhubaneswar, India
S. Bahinipati32, D. Dash, C. Kar, P. Mal, T. Mishra, V.K. Muraleedharan Nair
Bindhu33, A. Nayak33, P. Saha, N. Sur, S.K. Swain, D. Vats33 Panjab
University, Chandigarh, India
S. Bansal, S.B. Beri, V. Bhatnagar, G. Chaudhary, S. Chauhan, N. Dhingra34, R.
Gupta, A. Kaur, M. Kaur, S. Kaur, P. Kumari, M. Meena, K. Sandeep, J.B. Singh,
A.K. Virdi University of Delhi, Delhi, India
A. Ahmed, A. Bhardwaj, B.C. Choudhary, M. Gola, S. Keshri, A. Kumar, M.
Naimuddin, P. Priyanka, K. Ranjan, A. Shah Saha Institute of Nuclear Physics,
HBNI, Kolkata, India
M. Bharti35, R. Bhattacharya, S. Bhattacharya, D. Bhowmik, S. Dutta, S. Dutta,
B. Gomber36, M. Maity37, P. Palit, P.K. Rout, G. Saha, B. Sahu, S. Sarkar, M.
Sharan, B. Singh35, S. Thakur35 Indian Institute of Technology Madras, Madras,
India
P.K. Behera, S.C. Behera, P. Kalbhor, A. Muhammad, R. Pradhan, P.R. Pujahari,
A. Sharma, A.K. Sikdar Bhabha Atomic Research Centre, Mumbai, India
D. Dutta, V. Jha, V. Kumar, D.K. Mishra, K. Naskar38, P.K. Netrakanti, L.M.
Pant, P. Shukla Tata Institute of Fundamental Research-A, Mumbai, India
T. Aziz, S. Dugad, M. Kumar, U. Sarkar Tata Institute of Fundamental
Research-B, Mumbai, India
S. Banerjee, R. Chudasama, M. Guchait, S. Karmakar, S. Kumar, G. Majumder, K.
Mazumdar, S. Mukherjee Indian Institute of Science Education and Research
(IISER), Pune, India
K. Alpana, S. Dube, B. Kansal, A. Laha, S. Pandey, A. Rane, A. Rastogi, S.
Sharma Isfahan University of Technology, Isfahan, Iran
H. Bakhshiansohi39, M. Zeinali40 Institute for Research in Fundamental
Sciences (IPM), Tehran, Iran
S. Chenarani41, S.M. Etesami, M. Khakzad, M. Mohammadi Najafabadi University
College Dublin, Dublin, Ireland
M. Grunewald INFN Sezione di Bari a, Università di Bari b, Politecnico di Bari
c, Bari, Italy
M. Abbresciaa,b, R. Alya,b,42, C. Arutaa,b, A. Colaleoa, D. Creanzaa,c, N. De
Filippisa,c, M. De Palmaa,b, A. Di Florioa,b, A. Di Pilatoa,b, W.
Elmetenaweea,b, L. Fiorea, A. Gelmia,b, M. Gula, G. Iasellia,c, M. Incea,b, S.
Lezkia,b, G. Maggia,c, M. Maggia, I. Margjekaa,b, V. Mastrapasquaa,b, J.A.
Merlina, S. Mya,b, S. Nuzzoa,b, A. Pellecchiaa,b, A. Pompilia,b, G.
Pugliesea,c, A. Ranieria, G. Selvaggia,b, L. Silvestrisa, F.M. Simonea,b, R.
Vendittia, P. Verwilligena INFN Sezione di Bologna a, Università di Bologna b,
Bologna, Italy
G. Abbiendia, C. Battilanaa,b, D. Bonacorsia,b, L. Borgonovia, L.
Brigliadoria, R. Campaninia,b, P. Capiluppia,b, A. Castroa,b, F.R. Cavalloa,
M. Cuffiania,b, G.M. Dallavallea, T. Diotalevia,b, F. Fabbria, A. Fanfania,b,
P. Giacomellia, L. Giommia,b, C. Grandia, L. Guiduccia,b, S. Lo Meoa,43, L.
Lunertia,b, S. Marcellinia, G. Masettia, F.L. Navarriaa,b, A. Perrottaa, F.
Primaveraa,b, A.M. Rossia,b, T. Rovellia,b, G.P. Sirolia,b INFN Sezione di
Catania a, Università di Catania b, Catania, Italy
S. Albergoa,b,44, S. Costaa,b,44, A. Di Mattiaa, R. Potenzaa,b, A.
Tricomia,b,44, C. Tuvea,b INFN Sezione di Firenze a, Università di Firenze b,
Firenze, Italy
G. Barbaglia, A. Cassesea, R. Ceccarellia,b, V. Ciullia,b, C. Civininia, R.
D’Alessandroa,b, E. Focardia,b, G. Latinoa,b, P. Lenzia,b, M. Lizzoa,b, M.
Meschinia, S. Paolettia, R. Seiditaa,b, G. Sguazzonia, L. Viliania INFN
Laboratori Nazionali di Frascati, Frascati, Italy
L. Benussi, S. Bianco, D. Piccolo INFN Sezione di Genova a, Università di
Genova b, Genova, Italy
M. Bozzoa,b, F. Ferroa, R. Mulargiaa,b, E. Robuttia, S. Tosia,b INFN Sezione
di Milano-Bicocca a, Università di Milano-Bicocca b, Milano, Italy
A. Benagliaa, F. Brivioa,b, F. Cetorellia,b, V. Cirioloa,b,20, F. De Guioa,b,
M.E. Dinardoa,b, P. Dinia, S. Gennaia, A. Ghezzia,b, P. Govonia,b, L.
Guzzia,b, M. Malbertia, S. Malvezzia, A. Massironia, D. Menascea, L. Moronia,
M. Paganonia,b, D. Pedrinia, S. Ragazzia,b, N. Redaellia, T. Tabarelli de
Fatisa,b, D. Valsecchia,b,20, D. Zuoloa,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, F. Carnevalia,b, N. Cavalloa,c, A. De Iorioa,b, F. Fabozzia,c,
A.O.M. Iorioa,b, L. Listaa,b, S. Meolaa,d,20, P. Paoluccia,20, B. Rossia, C.
Sciaccaa,b INFN Sezione di Padova a, Università di Padova b, Padova, Italy,
Università di Trento c, Trento, Italy
P. Azzia, N. Bacchettaa, D. Biselloa,b, P. Bortignona, A. Bragagnoloa,b, R.
Carlina,b, P. Checchiaa, T. Dorigoa, U. Dossellia, F. Gasparinia,b, U.
Gasparinia,b, S.Y. Hoha,b, L. Layera,45, M. Margonia,b, A.T. Meneguzzoa,b, J.
Pazzinia,b, M. Presillaa,b, P. Ronchesea,b, R. Rossina,b, F. Simonettoa,b, G.
Stronga, M. Tosia,b, H. YARARa,b, M. Zanettia,b, P. Zottoa,b, A. Zucchettaa,b,
G. Zumerlea,b INFN Sezione di Pavia a, Università di Pavia b
C. Aime‘a,b, A. Braghieria, S. Calzaferria,b, D. Fiorinaa,b, P. Montagnaa,b,
S.P. Rattia,b, V. Rea, C. Riccardia,b, P. Salvinia, I. Vaia, P. Vituloa,b INFN
Sezione di Perugia a, Università di Perugia b, Perugia, Italy
G.M. Bileia, D. Ciangottinia,b, L. Fanòa,b, P. Laricciaa,b, M. Magherinib, G.
Mantovania,b, V. Mariania,b, M. Menichellia, F. Moscatellia, A. Piccinellia,b,
A. Rossia,b, A. Santocchiaa,b, D. Spigaa, T. Tedeschia,b INFN Sezione di Pisa
a, Università di Pisa b, Scuola Normale Superiore di Pisa c, Pisa Italy,
Università di Siena d, Siena, Italy
P. Azzurria, G. Bagliesia, V. Bertacchia,c, L. Bianchinia, T. Boccalia, E.
Bossinia,b, R. Castaldia, M.A. Cioccia,b, R. Dell’Orsoa, M.R. Di Domenicoa,d,
S. Donatoa, A. Giassia, M.T. Grippoa, F. Ligabuea,c, E. Mancaa,c, G.
Mandorlia,c, A. Messineoa,b, F. Pallaa, S. Paroliaa,b, G. Ramirez-Sancheza,c,
A. Rizzia,b, G. Rolandia,c, S. Roy Chowdhurya,c, A. Scribanoa, N. Shafieia,b,
P. Spagnoloa, R. Tenchinia, G. Tonellia,b, N. Turinia,d, A. Venturia, P.G.
Verdinia INFN Sezione di Roma a, Sapienza Università di Roma b, Rome, Italy
M. Campanaa,b, F. Cavallaria, M. Cipriania,b, D. Del Rea,b, E. Di Marcoa, M.
Diemoza, E. Longoa,b, P. Meridiania, G. Organtinia,b, F. Pandolfia, R.
Paramattia,b, C. Quarantaa,b, S. Rahatloua,b, C. Rovellia, F.
Santanastasioa,b, L. Soffia, R. Tramontanoa,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, A. Belloraa,b, J. Berenguer Antequeraa,b, C. Biinoa, N.
Cartigliaa, S. Comettia, M. Costaa,b, R. Covarellia,b, N. Demariaa, B.
Kiania,b, F. Leggera, C. Mariottia, S. Masellia, E. Migliorea,b, E.
Monteila,b, M. Montenoa, M.M. Obertinoa,b, G. Ortonaa, L. Pachera,b, N.
Pastronea, M. Pelliccionia, G.L. Pinna Angionia,b, M. Ruspaa,c, K.
Shchelinaa,b, F. Sivieroa,b, V. Solaa, A. Solanoa,b, D. Soldia,b, A. Staianoa,
M. Tornagoa,b, D. Trocinoa,b, A. Vagnerini INFN Sezione di Trieste a,
Università di Trieste b, Trieste, Italy
S. Belfortea, V. Candelisea,b, M. Casarsaa, F. Cossuttia, A. Da Rolda,b, G.
Della Riccaa,b, G. Sorrentinoa,b, F. Vazzolera,b Kyungpook National
University, Daegu, Korea
S. Dogra, C. Huh, B. Kim, D.H. Kim, G.N. Kim, J. Kim, J. Lee, S.W. Lee, C.S.
Moon, Y.D. Oh, S.I. Pak, B.C. Radburn-Smith, S. Sekmen, Y.C. Yang Chonnam
National University, Institute for Universe and Elementary Particles, Kwangju,
Korea
H. Kim, D.H. Moon Hanyang University, Seoul, Korea
B. Francois, T.J. Kim, J. Park Korea University, Seoul, Korea
S. Cho, S. Choi, Y. Go, B. Hong, K. Lee, K.S. Lee, J. Lim, J. Park, S.K. Park,
J. Yoo Kyung Hee University, Department of Physics, Seoul, Republic of Korea
J. Goh, A. Gurtu Sejong University, Seoul, Korea
H.S. Kim, Y. Kim Seoul National University, Seoul, Korea
J. Almond, J.H. Bhyun, J. Choi, S. Jeon, J. Kim, J.S. Kim, S. Ko, H. Kwon, H.
Lee, S. Lee, B.H. Oh, M. Oh, S.B. Oh, H. Seo, U.K. Yang, I. Yoon University of
Seoul, Seoul, Korea
W. Jang, D. Jeon, D.Y. Kang, Y. Kang, J.H. Kim, S. Kim, B. Ko, J.S.H. Lee, Y.
Lee, I.C. Park, Y. Roh, M.S. Ryu, D. Song, I.J. Watson, S. Yang Yonsei
University, Department of Physics, Seoul, Korea
S. Ha, H.D. Yoo Sungkyunkwan University, Suwon, Korea
Y. Jeong, H. Lee, Y. Lee, I. Yu College of Engineering and Technology,
American University of the Middle East (AUM), Egaila, Kuwait
T. Beyrouthy, Y. Maghrbi Riga Technical University
T. Torims, V. Veckalns46 Vilnius University, Vilnius, Lithuania
M. Ambrozas, A. Juodagalvis, A. Rinkevicius, G. Tamulaitis, A. Vaitkevicius
National Centre for Particle Physics, Universiti Malaya, Kuala Lumpur,
Malaysia
N. Bin Norjoharuddeen, W.A.T. Wan Abdullah, M.N. Yusli, Z. Zolkapli
Universidad de Sonora (UNISON), Hermosillo, Mexico
J.F. Benitez, A. Castaneda Hernandez, M. León Coello, J.A. Murillo Quijada, A.
Sehrawat, L. Valencia Palomo Centro de Investigacion y de Estudios Avanzados
del IPN, Mexico City, Mexico
G. Ayala, H. Castilla-Valdez, I. Heredia-De La Cruz47, R. Lopez-Fernandez,
C.A. Mondragon Herrera, D.A. Perez Navarro, A. Sanchez-Hernandez Universidad
Iberoamericana, Mexico City, Mexico
S. Carrillo Moreno, C. Oropeza Barrera, M. Ramirez-Garcia, F. Vazquez Valencia
Benemerita Universidad Autonoma de Puebla, Puebla, Mexico
I. Pedraza, H.A. Salazar Ibarguen, C. Uribe Estrada University of Montenegro,
Podgorica, Montenegro
J. Mijuskovic48, N. Raicevic 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.I. Asghar, A. Awais, M.I.M. Awan, H.R. Hoorani, W.A. Khan, M.A.
Shah, M. Shoaib, M. Waqas AGH University of Science and Technology Faculty of
Computer Science, Electronics and Telecommunications, Krakow, Poland
V. Avati, L. Grzanka, M. Malawski National Centre for Nuclear Research,
Swierk, Poland
H. Bialkowska, M. Bluj, B. Boimska, M. Górski, M. Kazana, M. Szleper, P.
Zalewski Institute of Experimental Physics, Faculty of Physics, University of
Warsaw, Warsaw, Poland
K. Bunkowski, K. Doroba, A. Kalinowski, M. Konecki, J. Krolikowski, M. Walczak
Laboratório de Instrumentação e Física Experimental de Partículas, Lisboa,
Portugal
M. Araujo, P. Bargassa, D. Bastos, A. Boletti, P. Faccioli, M. Gallinaro, J.
Hollar, N. Leonardo, T. Niknejad, M. Pisano, J. Seixas, O. Toldaiev, J. Varela
Joint Institute for Nuclear Research, Dubna, Russia
S. Afanasiev, D. Budkouski, I. Golutvin, I. Gorbunov, V. Karjavine, V.
Korenkov, A. Lanev, A. Malakhov, V. Matveev49,50, V. Palichik, V. Perelygin,
M. Savina, D. Seitova, V. Shalaev, S. Shmatov, S. Shulha, V. Smirnov, O.
Teryaev, N. Voytishin, B.S. Yuldashev51, A. Zarubin, I. Zhizhin Petersburg
Nuclear Physics Institute, Gatchina (St. Petersburg), Russia
G. Gavrilov, V. Golovtcov, Y. Ivanov, V. Kim52, E. Kuznetsova53, V. Murzin, V.
Oreshkin, I. Smirnov, D. Sosnov, V. Sulimov, L. Uvarov, S. Volkov, A. Vorobyev
Institute for Nuclear Research, Moscow, Russia
Yu. Andreev, A. Dermenev, S. Gninenko, N. Golubev, A. Karneyeu, D.
Kirpichnikov, M. Kirsanov, N. Krasnikov, A. Pashenkov, G. Pivovarov, D.
Tlisov${}^{\textrm{\textdagger}}$, A. Toropin Institute for Theoretical and
Experimental Physics named by A.I. Alikhanov of NRC ‘Kurchatov Institute’,
Moscow, Russia
V. Epshteyn, V. Gavrilov, N. Lychkovskaya, A. Nikitenko54, V. Popov, A.
Spiridonov, A. Stepennov, M. Toms, E. Vlasov, A. Zhokin Moscow Institute of
Physics and Technology, Moscow, Russia
T. Aushev National Research Nuclear University ’Moscow Engineering Physics
Institute’ (MEPhI), Moscow, Russia
M. Chadeeva55, A. Oskin, P. Parygin, E. Popova, V. Rusinov P.N. Lebedev
Physical Institute, Moscow, Russia
V. Andreev, M. Azarkin, I. Dremin, M. Kirakosyan, A. Terkulov Skobeltsyn
Institute of Nuclear Physics, Lomonosov Moscow State University, Moscow,
Russia
A. Belyaev, E. Boos, M. Dubinin56, L. Dudko, A. Ershov, A. Gribushin, V.
Klyukhin, O. Kodolova, I. Lokhtin, S. Obraztsov, S. Petrushanko, V. Savrin, A.
Snigirev Novosibirsk State University (NSU), Novosibirsk, Russia
V. Blinov57, T. Dimova57, L. Kardapoltsev57, A. Kozyrev57, I. Ovtin57, Y.
Skovpen57 Institute for High Energy Physics of National Research Centre
‘Kurchatov Institute’, Protvino, Russia
I. Azhgirey, I. Bayshev, D. Elumakhov, V. Kachanov, D. Konstantinov, P.
Mandrik, V. Petrov, R. Ryutin, S. Slabospitskii, A. Sobol, S. Troshin, N.
Tyurin, A. Uzunian, A. Volkov National Research Tomsk Polytechnic University,
Tomsk, Russia
A. Babaev, V. Okhotnikov Tomsk State University, Tomsk, Russia
V. Borchsh, V. Ivanchenko, E. Tcherniaev University of Belgrade: Faculty of
Physics and VINCA Institute of Nuclear Sciences, Belgrade, Serbia
P. Adzic58, M. Dordevic, P. Milenovic, J. Milosevic Centro de Investigaciones
Energéticas Medioambientales y Tecnológicas (CIEMAT), Madrid, Spain
M. Aguilar-Benitez, J. Alcaraz Maestre, A. Álvarez Fernández, I. Bachiller, M.
Barrio Luna, Cristina F. Bedoya, C.A. Carrillo Montoya, M. Cepeda, M. Cerrada,
N. Colino, B. De La Cruz, A. Delgado Peris, J.P. Fernández Ramos, J. Flix,
M.C. Fouz, O. Gonzalez Lopez, S. Goy Lopez, J.M. Hernandez, M.I. Josa, J. León
Holgado, D. Moran, Á. Navarro Tobar, A. Pérez-Calero Yzquierdo, J. Puerta
Pelayo, I. Redondo, L. Romero, S. Sánchez Navas, L. Urda Gómez, C. Willmott
Universidad Autónoma de Madrid, Madrid, Spain
J.F. de Trocóniz, R. Reyes-Almanza Universidad de Oviedo, Instituto
Universitario de Ciencias y Tecnologías Espaciales de Asturias (ICTEA),
Oviedo, Spain
B. Alvarez Gonzalez, J. Cuevas, C. Erice, J. Fernandez Menendez, S. Folgueras,
I. Gonzalez Caballero, E. Palencia Cortezon, C. Ramón Álvarez, J. Ripoll Sau,
V. Rodríguez Bouza, A. Trapote, N. Trevisani Instituto de Física de Cantabria
(IFCA), CSIC-Universidad de Cantabria, Santander, Spain
J.A. Brochero Cifuentes, I.J. Cabrillo, A. Calderon, J. Duarte Campderros, M.
Fernandez, C. Fernandez Madrazo, P.J. Fernández Manteca, A. García Alonso, G.
Gomez, C. Martinez Rivero, P. Martinez Ruiz del Arbol, F. Matorras, P.
Matorras Cuevas, J. Piedra Gomez, C. Prieels, T. Rodrigo, A. Ruiz-Jimeno, L.
Scodellaro, I. Vila, J.M. Vizan Garcia University of Colombo, Colombo, Sri
Lanka
MK Jayananda, B. Kailasapathy59, D.U.J. Sonnadara, DDC Wickramarathna
University of Ruhuna, Department of Physics, Matara, Sri Lanka
W.G.D. Dharmaratna, K. Liyanage, N. Perera, N. Wickramage CERN, European
Organization for Nuclear Research, Geneva, Switzerland
T.K. Aarrestad, D. Abbaneo, J. Alimena, E. Auffray, G. Auzinger, J. Baechler,
P. Baillon${}^{\textrm{\textdagger}}$, D. Barney, J. Bendavid, M. Bianco, A.
Bocci, T. Camporesi, M. Capeans Garrido, G. Cerminara, S.S. Chhibra, L.
Cristella, D. d’Enterria, A. Dabrowski, N. Daci, A. David, A. De Roeck, M.M.
Defranchis, M. Deile, M. Dobson, M. Dünser, N. Dupont, A. Elliott-Peisert, N.
Emriskova, F. Fallavollita60, D. Fasanella, S. Fiorendi, A. Florent, G.
Franzoni, W. Funk, S. Giani, D. Gigi, K. Gill, F. Glege, L. Gouskos, M.
Haranko, J. Hegeman, Y. Iiyama, V. Innocente, T. James, P. Janot, J. Kaspar,
J. Kieseler, M. Komm, N. Kratochwil, C. Lange, S. Laurila, P. Lecoq, K. Long,
C. Lourenço, L. Malgeri, S. Mallios, M. Mannelli, A.C. Marini, F. Meijers, S.
Mersi, E. Meschi, F. Moortgat, M. Mulders, S. Orfanelli, L. Orsini, F.
Pantaleo, L. Pape, E. Perez, M. Peruzzi, A. Petrilli, G. Petrucciani, A.
Pfeiffer, M. Pierini, D. Piparo, M. Pitt, H. Qu, T. Quast, D. Rabady, A. Racz,
G. Reales Gutiérrez, M. Rieger, M. Rovere, H. Sakulin, J. Salfeld-Nebgen, S.
Scarfi, C. Schäfer, C. Schwick, M. Selvaggi, A. Sharma, P. Silva, W. Snoeys,
P. Sphicas61, S. Summers, V.R. Tavolaro, D. Treille, A. Tsirou, G.P. Van
Onsem, M. Verzetti, J. Wanczyk62, K.A. Wozniak, W.D. Zeuner Paul Scherrer
Institut, Villigen, Switzerland
L. Caminada63, A. Ebrahimi, W. Erdmann, R. Horisberger, Q. Ingram, H.C.
Kaestli, D. Kotlinski, U. Langenegger, M. Missiroli, T. Rohe ETH Zurich -
Institute for Particle Physics and Astrophysics (IPA), Zurich, Switzerland
K. Androsov62, M. Backhaus, P. Berger, A. Calandri, N. Chernyavskaya, A. De
Cosa, G. Dissertori, M. Dittmar, M. Donegà, C. Dorfer, F. Eble, T.A. Gómez
Espinosa, C. Grab, D. Hits, W. Lustermann, A.-M. Lyon, R.A. Manzoni, C. Martin
Perez, M.T. Meinhard, F. Micheli, F. Nessi-Tedaldi, J. Niedziela, F. Pauss, V.
Perovic, G. Perrin, S. Pigazzini, M.G. Ratti, M. Reichmann, C. Reissel, T.
Reitenspiess, B. Ristic, D. Ruini, D.A. Sanz Becerra, M. Schönenberger, V.
Stampf, J. Steggemann62, R. Wallny, D.H. Zhu Universität Zürich, Zurich,
Switzerland
C. Amsler64, P. Bärtschi, C. Botta, D. Brzhechko, M.F. Canelli, K. Cormier, A.
De Wit, R. Del Burgo, J.K. Heikkilä, M. Huwiler, A. Jofrehei, B. Kilminster,
S. Leontsinis, A. Macchiolo, P. Meiring, V.M. Mikuni, U. Molinatti, I.
Neutelings, A. Reimers, P. Robmann, S. Sanchez Cruz, K. Schweiger, Y.
Takahashi National Central University, Chung-Li, Taiwan
C. Adloff65, C.M. Kuo, W. Lin, A. Roy, T. Sarkar37, S.S. Yu National Taiwan
University (NTU), Taipei, Taiwan
L. Ceard, Y. Chao, K.F. Chen, P.H. Chen, W.-S. Hou, Y.y. Li, R.-S. Lu, E.
Paganis, A. Psallidas, A. Steen, H.y. Wu, E. Yazgan, P.r. Yu Chulalongkorn
University, Faculty of Science, Department of Physics, Bangkok, Thailand
B. Asavapibhop, C. Asawatangtrakuldee, N. Srimanobhas Çukurova University,
Physics Department, Science and Art Faculty, Adana, Turkey
F. Boran, S. Damarseckin66, Z.S. Demiroglu, F. Dolek, I. Dumanoglu67, E.
Eskut, Y. Guler, E. Gurpinar Guler68, I. Hos69, C. Isik, O. Kara, A. Kayis
Topaksu, U. Kiminsu, G. Onengut, K. Ozdemir70, A. Polatoz, A.E. Simsek, B.
Tali71, U.G. Tok, S. Turkcapar, I.S. Zorbakir, C. Zorbilmez Middle East
Technical University, Physics Department, Ankara, Turkey
B. Isildak72, G. Karapinar73, K. Ocalan74, M. Yalvac75 Bogazici University,
Istanbul, Turkey
B. Akgun, I.O. Atakisi, E. Gülmez, M. Kaya76, O. Kaya77, Ö. Özçelik, S.
Tekten78, E.A. Yetkin79 Istanbul Technical University, Istanbul, Turkey
A. Cakir, K. Cankocak67, Y. Komurcu, S. Sen80 Istanbul University, Istanbul,
Turkey
S. Cerci71, B. Kaynak, S. Ozkorucuklu, D. Sunar Cerci71 Institute for
Scintillation Materials of National Academy of Science of Ukraine, Kharkov,
Ukraine
B. Grynyov National Scientific Center, Kharkov Institute of Physics and
Technology, Kharkov, Ukraine
L. Levchuk University of Bristol, Bristol, United Kingdom
D. Anthony, E. Bhal, S. Bologna, J.J. Brooke, A. Bundock, E. Clement, D.
Cussans, H. Flacher, J. Goldstein, G.P. Heath, H.F. Heath, L. Kreczko, B.
Krikler, S. Paramesvaran, S. Seif El Nasr-Storey, V.J. Smith, N. Stylianou81,
R. White Rutherford Appleton Laboratory, Didcot, United Kingdom
K.W. Bell, A. Belyaev82, C. Brew, R.M. Brown, D.J.A. Cockerill, K.V. Ellis, K.
Harder, S. Harper, J. Linacre, K. Manolopoulos, D.M. Newbold, E. Olaiya, D.
Petyt, T. Reis, T. Schuh, C.H. Shepherd-Themistocleous, I.R. Tomalin, T.
Williams Imperial College, London, United Kingdom
R. Bainbridge, P. Bloch, S. Bonomally, J. Borg, S. Breeze, O. Buchmuller, V.
Cepaitis, G.S. Chahal83, D. Colling, P. Dauncey, G. Davies, M. Della Negra, S.
Fayer, G. Fedi, G. Hall, M.H. Hassanshahi, G. Iles, J. Langford, L. Lyons,
A.-M. Magnan, S. Malik, A. Martelli, J. Nash84, M. Pesaresi, D.M. Raymond, A.
Richards, A. Rose, E. Scott, C. Seez, A. Shtipliyski, A. Tapper, K. Uchida, T.
Virdee20, N. Wardle, S.N. Webb, D. Winterbottom, A.G. Zecchinelli Brunel
University, Uxbridge, United Kingdom
K. Coldham, J.E. Cole, A. Khan, P. Kyberd, I.D. Reid, L. Teodorescu, S. Zahid
Baylor University, Waco, USA
S. Abdullin, A. Brinkerhoff, B. Caraway, J. Dittmann, K. Hatakeyama, A.R.
Kanuganti, B. McMaster, N. Pastika, S. Sawant, C. Sutantawibul, J. Wilson
Catholic University of America, Washington, DC, USA
R. Bartek, A. Dominguez, R. Uniyal, A.M. Vargas Hernandez The University of
Alabama, Tuscaloosa, USA
A. Buccilli, S.I. Cooper, D. Di Croce, S.V. Gleyzer, C. Henderson, C.U. Perez,
P. Rumerio85, C. West Boston University, Boston, USA
A. Akpinar, A. Albert, D. Arcaro, C. Cosby, Z. Demiragli, E. Fontanesi, D.
Gastler, J. Rohlf, K. Salyer, D. Sperka, D. Spitzbart, I. Suarez, A. Tsatsos,
S. Yuan, D. Zou Brown University, Providence, USA
G. Benelli, B. Burkle, X. Coubez21, D. Cutts, M. Hadley, U. Heintz, J.M.
Hogan86, G. Landsberg, K.T. Lau, M. Lukasik, J. Luo, M. Narain, S. Sagir87, E.
Usai, W.Y. Wong, X. Yan, D. Yu, W. Zhang University of California, Davis,
Davis, USA
J. Bonilla, C. Brainerd, R. Breedon, M. Calderon De La Barca Sanchez, M.
Chertok, J. Conway, P.T. Cox, R. Erbacher, G. Haza, F. Jensen, O. Kukral, R.
Lander, M. Mulhearn, D. Pellett, B. Regnery, D. Taylor, Y. Yao, F. Zhang
University of California, Los Angeles, USA