SMP-22-007

SMP-22-007

# Measurement of the primary Lund jet plane density in proton-proton
collisions at $\sqrt{s}=13\TeV$

###### Abstract

A measurement is presented of the primary Lund jet plane (LJP) density in
inclusive jet production in proton-proton collisions. The analysis uses 138of
data collected by the CMS experiment at $\sqrt{s}=13\TeV$. The LJP, a
representation of the phase space of emissions inside jets, is constructed
using iterative jet declustering. The transverse momentum and the splitting
angle $\Delta R$ of an emission relative to its emitter are measured at each
step of the jet declustering process. The average density of emissions as
function of $\ln(\kt/\GeV)$ and $\ln(R/\Delta R)$ is measured for jets with
distance parameters $R=0.4$ or 0.8, transverse momentum $\pt>700\GeV$, and
rapidity $\abs{y}<1.7$. The jet substructure is measured using the charged-
particle tracks of the jet. The measured distributions, unfolded to the level
of stable particles, are compared with theoretical predictions from
simulations and with perturbative quantum chromodynamics calculations. Due to
the ability of the LJP to factorize physical effects, these measurements can
be used to improve different aspects of the physics modeling in event
generators.

##  0.1 Introduction

The production of jets, collimated sprays of particles that result from the
fragmentation of energetic quarks and gluons, is one of the primary processes
studied to deepen our understanding of the strong force, described by quantum
chromodynamics (QCD). In recent years, it has become clear that valuable
information about the formation of jets is contained in their substructure [1,
2, 3, 4]. The phenomenological description of the substructure of jets
requires an understanding of the cascade of partons produced by highly
energetic quarks and gluons, a self-similar branching process referred to as
parton showering, and the strongly coupled transition of partons into hadrons,
known as hadronization. In a given hadronic collision, secondary parton-parton
scatterings and beam-beam remnant interactions, collectively known as the
underlying-event (UE) activity, also contribute to the substructure of jets.
The separation of these effects in the jet substructure is challenging, since
jet substructure observables are necessarily constructed using only the final-
state hadrons, whose exact origin cannot be traced back easily. The modeling
of jet formation in Monte Carlo (MC) event generators has a direct impact on
the theoretical and experimental uncertainties associated with precision
measurements of fundamental parameters of the standard model, such as the
strong coupling and the mass of elementary particles, like the top quark.
Thus, dedicated substructure measurements are beneficial, preferably with
observables where the various physical effects contributing to the jet
substructure can be separated in a transparent way.

One way of representing radiation in QCD is via the Lund plane [5], which is a
two-dimensional representation of the phase space of $1\to 2$ partonic
splittings (Fig. 1). The kinematics of a splitting can be described with two
degrees of freedom: the splitting angle of the branching $\Delta R$, and the
transverse momentum of the emission relative to its emitter. The logarithm of
and the logarithm of $1/\Delta R$ are used for the vertical and horizontal
axes of the Lund plane, respectively. This choice is based on the scaling
given by the soft and collinear divergences of QCD, which is such that partons
are emitted uniformly as a function of $\ln(\kt/\GeV)$ and $\ln(1/\Delta R)$.
Historically, the Lund plane has been used for the development of parton
showering algorithms and for calculations with resummation at all orders in .

References [6, 7] proposed to use iterative jet declustering using the
Cambridge–Aachen (CA) algorithm [8, 9] to represent the internal structure of
the jet in the Lund plane. The CA algorithm clusters the pair of particles
(and pairs of subjets thereafter) with the smallest separation in rapidity and
azimuthal angle first, and the pair of subjets with the largest separation
last. The strict angular ordering of the CA clustering algorithm resembles the
angular ordering of $1\to 2$ splittings in QCD due to color coherence effects
[8, 9] and at the same time it favors the collinear divergences of QCD. The
different branches of the jet clustering tree can be used as proxies for
emissions whose kinematics are mapped onto the Lund plane. This representation
of the phase space of emissions is known as the Lund jet plane (LJP).

Figure 1: Left: schematic diagram of the Cambridge–Aachen primary declustering
tree of a jet. The black lines represent the branch that follows the harder
subjet at each step of the declustering tree. The softer subjet at each node
is used as a proxy for an emission in the primary LJP. Right: schematic
diagram of the primary emissions of a jet in the LJP, which is filled from
left to right corresponding to emissions ordered from large to small angles.
The numbers represent the order of appearance in the declustering tree. The
dashed diagonal line represents the kinematical limit.

The constituents of a jet are reclustered using the CA algorithm, following
the prescription in Ref. [7]. Then, the CA pairwise clustering history is
followed in reverse, as shown schematically in Fig. 1. Starting with the
reclustered jet ${j}$, the last step of the CA clustering is undone, such that
the original jet is declustered into the two subjets of the previous
clustering step $j\to j_{1}+j_{2}$, where $j_{1}$ and $j_{2}$ are the harder
and softer subjets in the branching, respectively. The notation of $j$,
$j_{1}$, and $j_{2}$ is used for subjets in the declustering process. The
properties of the branching are recorded,

$\Delta
R=\sqrt{\smash[b]{(y^{j_{1}}-y^{j_{2}})^{2}+(\phi^{j_{1}}-\phi^{j_{2}})^{2}}},\hskip
28.45274pt\kt=\pt^{j_{2}}\Delta R$ (1)

where $y^{j_{1,2}}$ and $\phi^{j_{1,2}}$ represent the rapidity and azimuthal
angle of the harder and softer subjets and $\pt^{j_{2}}$ the transverse
momentum of the softer subjet relative to the beam axis. The radiation pattern
of the jet can be explored in numerous ways depending on which branch is being
followed in the CA declustering tree. The focus of this paper is specifically
the primary LJP [7], which is corresponds to the LJP of emissions obtained by
declustering the harder subjet at each step of the declustering process, as
shown schematically in Fig. 1 (left). The harder subjet is the one with the
highest at a given step of the CA declustering. The softer subjet is treated
as an emission in the LJP. A given jet is then represented as a sequence of
angular-ordered points in the LJP, as illustrated in Fig. 1 (right). Due to
the strict angular ordering of the CA clustering algorithm, the emissions in
the primary LJP are always filled from large to small $\Delta R$, from left to
right on the LJP. The jet is declustered iteratively until the hardest subjet
is composed of a single particle. The primary LJP contains a significant
amount of information about the radiation pattern of the jet while allowing
for a transparent physical interpretation.

The observable measured in this paper is the average density of emissions in
the primary LJP [10],

$\rho(\kt,\Delta
R)\equiv\frac{1}{N_{\text{jets}}}\frac{\rd^{2}N_{\text{emissions}}}{\rd\ln(\kt/\GeV)\rd\ln(R/\Delta
R)},$ (2)

where $N_{\text{jets}}$ represents the total number of jets in a given
fiducial region, $N_{\text{emissions}}$ the total number of emissions of such
jets, and $R$ is the jet distance parameter under consideration. The per-jet
normalization renders the observable insensitive to the inclusive jet cross
section. The density is expressed double-differentially in $\ln(\kt/\GeV)$ and
$\ln(R/\Delta R)$, since this is the approximate momentum and angular scaling
behavior of QCD radiation. Indeed, for independent emissions in the soft and
collinear limit of perturbative QCD (pQCD), the LJP density is directly
proportional to ,

$\rho(\kt,\Delta R)\approx\frac{2}{\pi}C_{\mathrm{R}}\alpS(\kt),$ (3)

where $C_{\mathrm{R}}$ is the appropriate color factor of the emission, for
instance $C_{\mathrm{F}}=4/3$ for gluon emissions from quarks and
$C_{\mathrm{A}}=3$ for gluon emissions from gluons. Equation 3 does not
account for parton flavor changes in the declustering history. The hard scale
used in the evolution of is given by the of an emission [7]. The fact that the
LJP density scales with $\alpS(\kt)$ means that the emission density is
expected to be approximately uniform for large values and to grow rapidly at
small following the running of $\alpS\propto
1/\ln(\kt/\Lambda_{\mathrm{QCD}})$, where $\Lambda_{\mathrm{QCD}}$ is the
energy scale where the theory becomes strongly coupled. For values of about 1,
there is a transition towards the nonperturbative regime, dominated by
hadronization effects.

Figure 2: Schematic diagram of the mechanisms affecting different regions of
the primary LJP in a given proton-proton collision. Initial-state radiation
(ISR), the underlying event (UE) activity, and multiple-parton interactions
(MPI) affect wide-angle radiation at $\Delta R\sim R$, close to the boundary
of the jet. In an experimental context, pileup contributes to the same region
as the UE. Hadronization affects the low $\ln(\kt/\GeV)$ region (below
$\kt\sim 1\GeV$) at all angles. Soft and hard collinear parton splittings
affect the rest of the LJP. The diagonal line represents the kinematical limit
of the primary LJP, which corresponds to $\pt^{j_{1}}=\pt^{j_{2}}$.

The primary LJP density provides detailed information about the radiation
pattern of the jet, which branches out to numerous applications in high-energy
physics. For instance, measurements of the primary LJP density can be used to
improve the parton shower, hadronization, and UE activity modeling, since
their effects approximately factorize in the LJP [7], as illustrated in Fig.
2. Precision measurements of the primary LJP density can be used to benchmark
the next generation of general purpose parton showers with resummation at
next-to-leading-logarithmic (NLL) accuracy [11, 12, 13, 14, 15, 16, 17, 18].
The LJP has been used to obtain the first direct evidence of the dead-cone
effect in heavy-flavor jets [19]. Highly boosted color-singlet particles have
unique signatures in the LJP, which can be exploited for jet flavor tagging
[7, 20, 21]. The LJP can provide an effective space-time picture of the quark-
gluon plasma created in ultrarelativistic heavy-ion collisions [6].

The primary LJP density can be calculated analytically in the framework of
perturbation theory [10]. The most recent calculations include corrections at
next-to-leading order (NLO) in for the fixed-order matrix element matched to
an NLL resummation to all-orders in [10]. Substructure observables obtained
with grooming techniques [1, 2, 3, 4], such as the groomed jet radius or
groomed momentum fraction obtained with the soft-drop grooming algorithm [22,
23], effectively select a subset of emissions of the primary LJP. Measurements
of groomed jet observables based on jet clustering have been reported in Refs.
[24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36].

The primary LJP has been measured by the ATLAS Collaboration [37] using jets
initially clustered with the anti-algorithm [38, 39] with a distance parameter
$R=0.4$. The two highest jets in the event were selected, where the leading
and subleading jet have $\pt^{\text{jet1}}>675\GeV$ and
$\pt^{\text{jet2}}>\frac{2}{3}\pt^{\text{jet1}}$. They reported the LJP
density as a function of the momentum fraction shared between the softer and
harder subjets $z=\pt^{j2}/(\pt^{j_{1}}+\pt^{j_{2}})$ and as a function of
$\ln(R/\Delta R)$. The variable is related to $z$ via $\kt=z\Delta R\pt^{j}$,
where $\pt^{j}$ is the transverse momentum of the parent subjet of the
splitting. The broad features of the LJP density, such as the running of and
the separation of physical mechanisms, are also exposed in this representation
of the primary LJP.

In this paper, a measurement of the primary LJP density using the CMS detector
is presented. The analysis uses anti-jets with $\pt^{\text{jet}}>700\GeV$ and
$\abs{y}<1.7$ using proton-proton ($\Pp\Pp$) data collected at
$\sqrt{s}=13\TeV$ during Run 2 (2016–2018), corresponding to an integrated
luminosity of 138. The charged particles of the anti-jet are reclustered with
the CA algorithm to construct the LJP. The present measurement is reported for
two distance parameters: $R=0.4$ and $R=0.8$. The value of 0.4 is the default
choice in most measurements at 13at the LHC, whereas the 0.8 value, which has
not been used in previous measurements of the LJP, allows us to extend the
available phase space for wide-angle, hard emissions. Large $R$ jets are
typically used to search for highly-boosted particles that decay hadronically.
Identification algorithms, which are optimized using MC-simulated events, are
used to distinguish such boosted particles from the QCD background. Thus,
precision jet substructure measurements of large $R$ jets can help to improve
the physics modeling in the simulation and reduce possible biases in the
performance of such algorithms. For this measurement, the $\ln(\kt/\GeV)$
versus $\ln(R/\Delta R)$ representation of the primary LJP proposed in Ref.
[7] is used. The choice of has the advantage that one can unambiguously
identify the absolute momentum scale of the emissions in the LJP, which in
turn enables a clean separation of the mechanisms contributing to the strongly
and weakly coupled regions of phase space.

The measurement is performed using data recorded by the CMS detector, whose
components are described in Section 0.2, which also describes the algorithms
used to reconstruct events are described. Section 0.3 contains details of the
measured and simulated samples. Details of the extraction of the LJP density
from the measurement are detailed in Section 0.4. The strategy for the
corrections to stable-particle level is discussed in Section 0.5. The
systematic uncertainties in the corrected distributions are described in
Section 0.6. The results on the corrected LJP density and their comparison
with theoretical calculations are covered in Section 0.7. A summary of the
measurement is presented in Section 0.8.

Tabulated results are provided in the HEPData record for this analysis [40].

##  0.2 The CMS detector and event reconstruction

The central feature of the CMS apparatus is a superconducting solenoid of 6m
internal diameter, providing a magnetic field of 3.8T. Within the magnetic
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 pseudorapidity coverage provided by the barrel and
endcap detectors. Muons are measured in gas-ionization detectors embedded in
the steel flux-return yoke outside the solenoid. A more detailed description
of the CMS detector, together with a definition of the coordinate system used
and the relevant kinematic variables, is presented in Ref. [41].

The silicon tracker used in 2016 measured charged particles within the
pseudorapidity range $\abs{\eta}<2.5$. For nonisolated particles of
$1<\pt<10\GeV$ and $\abs{\eta}<1.4$, the track resolutions were typically 1.5%
in and 25–90 (45–150)in the transverse (longitudinal) impact parameter [42].
At the start of 2017, a new pixel detector was installed [43]; the upgraded
tracker measured particles up to $\abs{\eta}<3.0$ with typical resolutions of
1.5% in and 20–75in the transverse impact parameter [44] for nonisolated
particles of $1<\pt<10\GeV$.

The primary vertex (PV) is taken to be the vertex corresponding to the hardest
scattering in the event, evaluated using tracking information alone, as
described in Section 9.4.1 of Ref. [45]. The physics objects are jets,
clustered using the anti-jet finding algorithm [38, 39] with the tracks
assigned to a candidate vertex as inputs, and the associated missing
transverse momentum, which is the negative vector sum of those jets.

The particle-flow algorithm [46] aims to reconstruct and identify each
individual particle in an event, with an optimized combination of information
from the various elements of the CMS detector. The energy of photons is
obtained from the ECAL measurement. The energy of electrons is determined from
a combination of the electron momentum at the primary interaction vertex as
determined by the tracker, the energy of the corresponding ECAL cluster, and
the energy sum of all bremsstrahlung photons spatially compatible with
originating from the electron track. The energy of muons is obtained from the
curvature of the corresponding track. The energy of charged hadrons is
determined from a combination of their momentum measured in the tracker and
the matching ECAL and HCAL energy deposits, corrected for the response
function of the calorimeters to hadronic showers. Finally, the energy of
neutral hadrons is obtained from the corrected ECAL and HCAL energies.

For each event, hadronic jets are clustered from these reconstructed particles
using the anti-algorithm with $R=0.4$ and 0.8, referred to as AK4 and AK8 jets
in the following. Jet momentum is determined as the vectorial sum of all
particle momenta in the jet. It is found from simulation to be, on average,
within 5–10% of the true momentum over the whole spectrum and detector
acceptance. Additional $\Pp\Pp$ interactions within the same or nearby bunch
crossings (pileup) can contribute additional tracks and calorimetric energy
depositions to the jet momentum. To mitigate this effect, charged particles
identified to be originating from pileup vertices are discarded and an offset
correction is applied to correct for remaining contributions for both AK4 and
AK8 jets, as described in Ref. [46]. Jet energy corrections are derived from
simulation to bring the measured response of jets to that of particle-level
jets on average. In situ measurements of the momentum balance in dijet,
photon$+$jet, $\PZ+$jet, and multijet events are used to account for any
residual differences in the jet energy scale between data and simulation [47].
The jet energy resolution amounts typically to 5% at 1 [47]. Additional
selection criteria are applied to each jet to remove jets potentially
dominated by anomalous contributions from various subdetector components or
reconstruction failures [47]. For the charged-particle tracks used for the jet
substructure extraction, further selection requirements are applied for the
mitigation of residual pileup particles and to reject badly reconstructed
objects, such as artifacts from detector noise [48]. If there are charged-
particle tracks in the jet that do not belong to any vertex, they are used for
the jet substructure observable only if their distance of closest approach to
the primary vertex along the beam axis is smaller than 0.3 [48].

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 4 [49]. 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 [50].

##  0.3 Data and simulated samples

The analysis uses $\Pp\Pp$ collision data collected by the CMS experiment in
2016–2018 at a center-of-mass energy of $\sqrt{s}=13\TeV$, corresponding to an
integrated luminosity of 138 [51, 52, 53]. Events with high-jets are collected
with triggers requiring at least one AK4 or AK8 jet. The minimum jet of
700considered in this analysis is well beyond the turn-on region of the
trigger efficiency curve. The residual inefficiency is smaller than 1% and is
negligible in comparison with the statistical uncertainties of the
measurement. No corrections are applied to account for residual trigger
inefficiencies.

The main processes of interest in this analysis are events composed of jets
produced through the strong interaction. Their simulation is performed with
two main combinations of MC event generators to correct for the detector
response and to derive systematic uncertainties for the measurement. A sample
of jet events is generated at leading order (LO) with 8.240 [54], which
implements a -ordered shower and where the hadronization of quarks and gluons
into stable hadrons is described by the Lund string model [55, 56]. The 8
parameters for the UE are set according to the CP5 tune [57]. A second sample
is generated at LO with 7.1.4 [58] with the CH3 tune [59] to assess systematic
uncertainties related to the modeling of the parton shower and hadronization.
In 7, the parton shower follows angular-ordered radiation [60], and the
hadronization is described by the cluster fragmentation model [61]. The next-
to-NLO (NNLO) NNPDF 3.1 [58] parton distribution functions (PDFs) with
$\alpS(m_{\PZ})=0.118$ are used for both MC generators, where $m_{\PZ}$ is the
boson mass. We verified that the contribution of processes beyond those
produced purely by the strong interaction is negligible within the precision
of the measurement.

The 8 CP5 and 7 CH3 generated samples are passed through a detailed simulation
of the CMS detector using [62]. To simulate the effect of pileup, multiple
inelastic events are generated using 8 and are superimposed on each primary
interaction event. The MC simulated events are reweighed to reproduce the
observed pileup activity in data.

Additional particle-level predictions are compared with the corrected
distributions. Predictions are computed at LO with 8.303 with CP2, CUEP8M1,
and Monash tunes [63, 64, 57]. The Monash tune [63] is used as a baseline for
the 8 tunes developed by the CMS Collaboration, which was tuned mostly to data
at LEP and SLD, to $\Pp\PAp$ data at the SPS and Tevatron, and to $\Pp\Pp$
data from Run 1 at the LHC. The comparison with the predictions from the
CUEP8M1 tune [64], which was widely used in $\sqrt{s}=7$ and 8analyses by CMS,
illustrates the effects of including 13data in the development of the CP tunes
of 8. In the context of this analysis, the main difference of the CP5 tune
with respect to the other tunes of 8 is the value of for final-state radiation
(FSR), $\alpS^{\mathrm{FSR}}(m_{\PZ})$, which is
$\alpS^{\mathrm{FSR}}(m_{\PZ})=0.118,0.130,0.1365$, and 0.1365 for the CP5,
CP2, CUEP8M1, and Monash tunes. Additional 8.303 predictions calculated using
the dire [65] and vincia [66] parton showers are presented. The dire shower
implements a -ordered color dipole shower, where the radiator-spectator
particle pairs evolve simultaneously, and it includes higher-order
corrections, such as triple-collinear or double-soft parton emissions. The
version of vincia in 8.303 uses the antenna sector shower formalism [67, 66,
68]. The branching kernels, known as antenna functions, treat coherent sums of
parton pairs without requiring a separation into radiators and spectators.
Both vincia and dire have their respective set of tuning parameters in 8. We
also present predictions calculated with 7.2.0 [69, 70] using a dipole parton
shower, which is an alternative to the standard angular-ordered shower of 7.
The dipole parton shower available in 7 uses the Catani–Seymour dipole
factorization formalism [71]. In addition to 7 and 8, we also present
predictions generated with 2.2.10 [72, 73, 74]. The parton shower in 2 is also
based on the Catani–Seymour dipole factorization approach [75], and hadrons
are formed by a modified cluster hadronization model [76].

We also consider particle-level predictions of 7.2.0 with different choices of
the ordering scale variable in its angular-ordered shower [70, 77]. This
choice determines which quantity is preserved for subsequent emissions, which
affects both the momentum recoil assignment in the parton shower as well as
its logarithmic accuracy. Depending on the recoil scheme, they can reach NLL
accuracy for certain classes of global observables, such as event shapes and
jet-resolution variables [78]. In 7, there are four different options for the
recoil scheme. The transverse momentum preserving scheme (scheme) ensures the
independence of successive soft-collinear emissions that are well separated in
rapidity, but it can produce an excessive amount of hard radiation in phase
space regions with no logarithmic enhancements. The virtuality-preserving
scheme ($q^{2}$ scheme) avoids overpopulating such region of phase space, but
breaks the independence of successive emissions. The dot-product-preserving
scheme ($q_{1}\cdot q_{2}$ scheme) retains features of both and $q^{2}$
schemes, although to some extent the $q_{1}\cdot q_{2}$ scheme can
overpopulate the nonlogarithmically-enhanced phase space region. Thus, a
recoil scheme with a phase space veto that suppresses events with large-
virtuality partons was introduced ($q_{1}\cdot q_{2}+\text{veto}$ scheme). For
the 7 CH3 sample used for the corrections to particle level, the $q^{2}$
scheme is used, which was the default setting of 7.1.4 when the CH3 tune was
developed.

The 8 and 2 generators apply a model where multiple-parton interactions (MPI)
are interleaved with the parton shower [79], whereas the 7 generator models
the spatial overlap between the colliding protons through a Fourier transform
of the electromagnetic form factor of the proton, which plays the role of an
effective inverse proton radius [80, 81, 82, 83]. The MPI parameters of the
generators are tuned to measurements in $\Pp\Pp$ collisions at the LHC [64].
The NNLO NNPDF 3.1 PDFs with $\alpS(m_{\PZ})=0.118$ are used for all MC event
generator predictions.

##  0.4 Event selection and jet substructure extraction

Jets with $\pt>700\GeV$ and $\abs{y}<1.7$ are selected for the measurement. As
motivated in Refs. [7, 10], a high-jet selection yields a larger phase space
for hard radiation inside the jet in a region where nonperturbative effects
are small. The maximum at a particular $\Delta R$ is given by
$\kt^{\text{max}}=\frac{1}{2}\pt^{\text{jet}}\Delta R$, which corresponds to a
diagonal line in the LJP. Due to the inclusive jet selection, all emissions
share the same minimum kinematical limit. Both AK4 and AK8 jets are contained
within the tracker acceptance with the jet rapidity selection.

We follow the prescription described in Section 0.1. The anti-jet constituents
are reclustered using the CA algorithm to construct the primary LJP. We use
the anti-clustering algorithm for the initial clustering of the jet, since
these are the jets for which the jet energy scale and resolution are
determined in data collected in high pileup conditions at the LHC. The use of
another algorithm for the initial clustering affects mostly the $\Delta
R\approx R$ region, whereas it leaves the collinear region mostly unaffected
[7, 10]. Although the original anti-jet is clustered using neutral and charged
particle-flow candidates, the primary LJP is calculated using only its
charged-particle constituents. This allows us to resolve hard collinear
emissions and mitigate pileup better. Due to the approximate isospin symmetry
of the strong force, the radiation pattern of the jet does not depend on the
electric charge of the final-state particles. Although the charged-particle
jet substructure is not infrared and collinear safe, this choice does not
affect the comparison to theoretical calculations of the primary LJP density,
since it can be incorporated as part of the nonperturbative corrections [10].
The measured charged-particle constituents are required to have $\pt>1\GeV$ to
further suppress the contributions of residual pileup particles and to avoid
the decrease in track reconstruction efficiency below 1. The measurement is
reported for splitting angles as small as $\Delta R\approx 0.005$, which is a
$\Delta R$ separation where pixel cluster merging effects can efficiently be
mitigated with the dedicated cluster splitting algorithms of CMS [84]. The
largest splitting angle reported in the measurement is $\Delta R=0.8$, which
is the distance parameter of AK8 jets. The range reported in the measurement
spans 0.4 to 720. The largest value of is accessed only with $R=0.8$ jets.
Figure 3 shows different slices of the primary LJP density measured in data.
The detector-level predictions of 7 CH3 and 8 CP5 are shown in the same plots.
Throughout the paper, four different regions of the LJP are presented, each
probing different aspects of the radiation pattern of the jet. The vertical
slice at large $\Delta R$ shows the density of emissions in a wide range of
values, and is mostly sensitive to the parton cascade evolution in the jet. A
vertical slice at small $\Delta R$ shows the behavior of the density of
emissions for collinear emissions. A horizontal slice at low shows a region of
the LJP dominated by hadronization effects and the underlying event activity
as a function of $\Delta R$, whereas a horizontal slice at high shows the
density of emissions for hard emissions and is less sensitive to hadronization
effects.

Figure 3: Detector-level distributions of measured and MC-simulated events
generated with 8 CP5 and 7 CH3 for four different slices of the LJP, as
indicated by the triangular diagrams in the plots. The lower panels in the
plots show the ratio of the predictions with respect to the data. Only
statistical uncertainties are included here. The comparison shows that neither
7 CH3 nor 8 CP5 are able to describe the data well in various regions of the
LJP. The vertical bars represent the statistical uncertainties, which are
smaller than the markers for most of the bins.

##  0.5 Unfolding

Figure 4: Event displays of a simulated AK4 jet at detector level (solid
triangles) and particle level (open triangles). The right-hand side plot
represents the $\eta$ and $\phi$ coordinates of the emissions in the CMS
coordinate system to illustrate the geometrical matching used for the
corrections in the measurement. The center of the particle-level anti-jet is
represented by the solid circular marker. The circular line with radius
$R=0.4$ serves as a proxy for the anti-distance parameter used to cluster the
AK4 jet. The Lund plane on the left plot is associated with the same jet, and
is filled with the primary emissions from the CA declustering from left to
right (from large to small angles). The numbers in both plots represent the
order of the emission of the primary CA tree declustering sequence.

The measured detector-level distributions are corrected to particle level
using corrections derived from simulation. The particle level is defined by
the set of all particles that have a lifetime longer than $10^{-8}$s as given
by the MC event generator. The corrections to particle level are applied
sequentially in three steps. First, a set of bin-by-bin corrections is applied
to the detector-level distribution to account for the background (purity
corrections). In this measurement, the background consists of detector-level
emissions that are not paired with particle-level emissions. Then, a
correction for bin-to-bin migration effects due to detector effects a
multidimensional unfolding of the LJP emissions is applied. After the
correction for bin-to-bin migration effects, a set of bin-by-bin corrections
to account for particle-level emissions that are not reconstructed at detector
level (efficiency corrections) is applied. At particle level, jets are
clustered without a requirement on the particles used for the jet clustering.
The particle- and detector-level distributions have the same binning in the
fiducial region. The particle-level distributions have additional underflow
and overflow bins to account for phase space migrations, which are removed
after the full chain of corrections.

To derive the corrections, a mapping between the detector- and particle-level
emissions is necessary. The response matrix is determined from simulation for
geometrically matched emissions, which is described in the following. To match
the detector- and particle-level emissions, for a given detector-level
emission, we iterate through the list of particle-level emissions and
calculate their distance relative to the detector-level emission in
$\eta$–$\phi$. The particle-level emission that is closest to the detector-
level emission is the candidate for the particle-level matched emission. Then,
a similar iteration is done for a given particle-level emission, and iterating
through the detector-level emissions. We only consider a pair of emissions to
be matched if the same pair of emissions is found when iterating through the
list of detector- and particle-level list of emissions. As a result, no
detector- (particle-)level emission is assigned to two different particle-
(detector-)level emissions. The corrections are derived using 8 CP5 and 7 CH3
simulated events. Neither of the detector-level predictions of 8 CP5 and 7 CH3
are able to describe the data in the entire LJP. The nominal set of
corrections is derived using the sample of 8 CP5 simulated events, since we
can use its parton shower event weights to propagate uncertainties related to
the renormalization scale choice for FSR and initial-state radiation (ISR), as
described in Section 0.6. The sample of 7 CH3 simulated events is used to
estimate biases in the unfolding corrections and to compute the systematic
uncertainties associated with the parton shower and hadronization model used
for the corrections, as described in Section 0.6.

The purity corrections have values smaller than 5% in most of the LJP, except
in the region of wide-angle, soft emissions, where it has values of the order
of 20%. This region is dominated by UE activity particles and residual pileup
particles. The efficiencies are above 90% throughout most of the LJP. The
efficiency drops to 70% in the large $\Delta R$ and low region and decreases
with decreasing $\Delta R$ down to 40–50%. The phase space region of low and
large $\Delta R$ is affected by the charged-particle $\pt>1\GeV$ requirement
that is applied at detector level, resulting in a higher number of splittings
at particle level than at detector level, which leads to a reduction in the
reconstruction efficiency. In the small $\Delta R$ region, particle-level
subjets can be lost in the reconstruction due to pixel cluster merging effects
that are not effectively mitigated by the cluster splitting algorithm [84] and
the aforementioned $\pt>1\GeV$ requirement that reduces the particle
multiplicity in subjets and leads to a reduction in the reconstruction
efficiency. The purity and efficiency corrections calculated with the 7 CH3
and 8 CP5 samples are consistent with each other within 1 to 7% throughout
most of the LJP.

An example of the correspondence of the detector- and particle-level emissions
in a simulated jet is shown in Fig. 4. For most simulated jets, there is a
close correspondence in the $\eta$–$\phi$ coordinate system, with smearing
effects and particle losses affecting the reconstruction of in the LJP, and
angular resolution smearing at small $\Delta R$. The correspondence between
the respective primary LJP emissions might be lost due to detector effects.
This can occur when a different branch of the jet tree of primary emissions is
followed at detector level relative to the one followed at particle level. The
presence of these mismatches is mitigated with the aforementioned requirement
of using unique geometrically matched emissions for the corrections, and they
are accounted for using the bin-by-bin purity and efficiency corrections. The
residual amount of mismatches represents less than a few percent of the total
number of matched emissions in simulation. The residual mismatches include
cases where the particle-level emissions are merged or fragmented at detector
level, or cases where the harder (softer) subjet becomes the softer (harder)
subjet due to momentum smearing effects, which becomes harder to mitigate in
the collinear region. These mismatches are observed in both 7 CH3 and 8 CP5
simulated events.

A multidimensional unfolding of the number of emissions $N_{\text{emissions}}$
is performed to correct for the bin-to-bin migrations caused by detector
effects. The dimensions that are considered in the correction are the anti-jet
, and the and $\Delta R$ of the emissions. The number of jets
$N_{\text{jets}}$, which is used to calculate the per-jet average LJP density,
is also corrected to account for migration effects in the anti-jet . The
response matrix used for the unfolding is calculated using events simulated
with 8 CP5. To assess if the deconvolution problem is sensitive to small
perturbations in the input distribution, we calculate the condition number of
the probability matrix, which is defined as the ratio of its largest to
smallest nonzero eigenvalues. The probability matrix is obtained by
normalizing the response matrix such that the probability of reconstruction in
the different detector-level bins adds up to 1 for each particle-level bin. A
condition number of order unity suggests that the probability matrix is well-
conditioned. The condition number of the probability matrix used in the
unfolding of the LJP of emissions is much larger than unity, suggesting that
the deconvolution problem is ill-conditioned, and that regularized unfolding
is required. For the present measurement, we perform the regularized matrix
inversion using iterative D’Agostini unfolding with early stopping [85]. We
use its implementation in the RooUnfold package [86]. Regularized unfolding
introduces a bias towards an input particle-level spectrum (8 CP5 or 7 CH3 in
this analysis) in order to control the sensitivity to small perturbations in
the input distribution. The particle-level spectrum that is used in
regularized unfolding is referred to as the “prior distribution.” There is
model dependence in the response matrix as well; the detector response for
subjets simulated with 7 CH3 is different from the response of subjets
simulated with 8 CP5. These two components of model dependence are included in
the systematic uncertainties described in Section 0.6.

Since there are multiple entries in the LJP histogram for a given jet, the
detector-level bins are statistically correlated. These statistical
correlations manifest as off-diagonal elements in the covariance matrix built
from statistical uncertainties. We find statistical bin-to-bin correlations of
5–10%. The hard, wide-angle emissions have weak correlations with the rest of
the LJP. Emissions at low and large $\Delta R$ have the largest correlations
with the rest of the LJP. In this region of phase space, the contribution from
the UE and residual pileup particles is important. The covariance matrix of
statistical uncertainties is used as an input for the unfolding procedure.

The number of iterations, which plays the role of the regularization parameter
in iterative D’Agostini unfolding, is optimized based on $\chi^{2}$ goodness-
of-fits tests at detector level. At each iteration, the detector-level
distribution associated with the unfolded distribution is calculated by
multiplying the unfolded distribution by the migration matrix. We call this
“forward folding,” and the detector-level distribution obtained after matrix
multiplication as the “forward-folded distribution.” To quantify the
compatibility between the forward-folded distribution and the input measured
distribution, the $\chi^{2}$ of the forward-folded distribution and the
measured detector-level distribution is calculated at a given iteration. In
D’Agostini unfolding, the agreement between the input distribution and the
forward-folded distributions improves monotonically at each iteration. To
avoid overfitting the unfolded distributions to the statistical fluctuations
present in the measured distributions, the algorithm is stopped at the
iteration at which the corresponding $p$-value is above 0.05. The covariance
matrix of statistical uncertainties measured at detector level is used for
these goodness-of-fit tests at each iteration.

Figure 5: Detector-level (open symbols) and particle-level (closed symbols)
distributions for the data and MC simulated events of 8 CP5. Only statistical
uncertainties are included in these plots, which are smaller than the markers
for most of the bins. The lower panels in the plot show the ratio of the
particle-level to the respective detector-level distributions, which is used
as a metric for the effective modifications of the LJP density because of the
detector effects. The size of the corrections can be inferred from the ratio
of the particle-level to the detector-level distributions, which are larger
closer to the kinematical edge of the LJP.

To illustrate the effective modifications of the particle-level LJP density
because of the detector effects, which are corrected with the unfolding
procedure, Figure 5 shows the distributions of four different slices of the
LJP density measured in data using AK4 jets at both the detector and particle
(unfolded) levels. The 8 CP5 predictions are used as a reference in Fig. 5 at
both the detector and particle levels. Due to the finite tracking efficiency,
the detector-level of a subjet is on average lower than its corresponding
particle-level . This effect accumulates with increasing (on average, subjets
with higher have larger particle multiplicities), which explains the
difference between the detector- and particle-level LJP densities at high in
Fig. 5. At low and large $\Delta R$, the modification of the LJP density at
detector level relative to particle level is due to the presence of residual
pileup particles that populate that region of phase space as well as the
$\pt>1\GeV$ threshold used at detector level.

##  0.6 Systematic uncertainties

Theoretical and experimental uncertainties are propagated by repeating the
unfolding procedure with variations of the response matrix, prior
distribution, purity, and efficiency corrections. The following systematic
uncertainties are considered:

Shower and hadronization modeling uncertainty: This uncertainty is estimated
by repeating the unfolding procedure with uncorrelated variations of the prior
distribution used for regularization and the response matrix. For the prior
bias variation, the distribution of 7 CH3 is assumed instead of the one of 8
CP5, while keeping the response matrix calculated with 8 CP5 events. For the
response matrix variation, the 7 CH3 response matrix is used, while keeping
the 8 CP5 spectrum for the prior distribution. The difference of each
variation with respect to the nominal results, which are calculated with 8 CP5
for both the prior distribution and response matrix, is used to calculate the
corresponding systematic uncertainty. The two components are symmetrized and
treated as uncorrelated between each other. The prior bias and response matrix
components have similar contributions in the bulk of the LJP (the region away
from the kinematical edge) at large $\Delta R$, whereas the component
associated with the response matrix is dominant at small $\Delta R$. The total
systematic uncertainty is of the order of 2–7% across the bulk of the
distribution, increasing to about 10% close to the kinematical edge of the
LJP.

Parton shower scale uncertainties: To estimate the theoretical uncertainty due
to missing higher-order corrections in the perturbative calculation of the
parton shower of 8 CP5, we consider variations of the renormalization scale
for FSR and ISR, denoted symbolically with
($\mu^{\mathrm{FSR}},\mu^{\mathrm{ISR}}$). We repeat the unfolding procedure
for six different variations of the renormalization scale by factors of
($\frac{1}{2}$, $\frac{1}{2}$), ($\frac{1}{2}$,1), (1,$\frac{1}{2}$), (2,2),
(2,1), and (1,2) [87, 88]. The corresponding uncertainties of the unfolded
distributions are of the order of 0.5–3.0%. Generally, the variations by
factors of 2 and 1/2 have symmetric effects on the LJP density and in the
associated systematic uncertainties. The effect of the variations of the ISR
renormalization scale are smaller than the ones from FSR. The
($\frac{1}{2}$,1) and (2,1) variations are referred to as FSR down and up,
respectively, and likewise for ISR down and up.

Tracking efficiency uncertainties: To account for the mismodeling of track
reconstruction in the simulation in high-density environments, such as in the
vicinity of the jet core, we propagate a track reconstruction efficiency
uncertainty through the unfolding procedure. This is done by randomly removing
3% of the tracks in simulation. This value covers the residual differences
observed in data and simulation for tracking in the jet core in the context of
jet energy scale determination [47]. The unfolding is repeated with this
variation, and the symmetrized difference of the unfolded distributions with
this variation relative to the nominal unfolded distributions is taken as a
systematic uncertainty. Since there was a new pixel detector installed in 2017
[43], the tracking efficiency uncertainty of 2016 is decorrelated from the one
of 2017–2018. The symmetrized difference of the unfolding with these
variations relative to the nominal unfolded distributions is taken as a
systematic uncertainty. The uncertainty is about 1–2% in the bulk of the
primary LJP and increases up to about 15–25% in the kinematical edge of the
LJP. This is because the density of emissions falls rapidly at the edge of the
LJP and because the average number of subjet constituents is larger in that
region; emissions close to the edge of the LJP behave more jet-like than those
in the bulk of the LJP. On average, the detector-level is lower than the
corresponding particle-level . The track reconstruction efficiency affects
such correspondence between the detector-level and the particle-level for a
given pair of matched emissions.

Response matrix statistical uncertainties:  The statistical uncertainties of
the simulated sample that is used to derive the migration matrix are
propagated through the unfolding procedure, which results in a contribution to
the covariance matrix.

Pileup modeling: We vary the value of the inelastic cross section used to
generate the number of pileup interactions in the simulation. The distribution
of pileup interactions in the simulation is reweighed with $\pm 4.6$%
variations of the $\Pp\Pp$ inelastic cross section at 13relative to the
nominal value of 69.2mb. The resulting systematic uncertainty is less than 1%
in most of the LJP and increases to about 2% at the kinematical edge of the
LJP.

Jet energy scale and resolution: The jet energy scale uncertainty is
propagated through the unfolding by shifting the jet at detector level in the
simulation according to the $\eta$-dependent jet energy scale uncertainties
[47]. This uncertainty has an effect through the $\pt>700\GeV$ selection
requirement. The uncertainty is smaller than 1% throughout the unfolded LJP
density. We also consider the uncertainties in the jet energy resolution
measurement [47]. The jet is further smeared at detector level in simulation
in order to better reproduce the jet energy resolution measured in data [47].
Such a smearing procedure comes with an associated systematic uncertainty,
which is propagated through the unfolding procedure. The respective
uncertainty is at the per-mille level in the corrected primary LJP density.

The various sources of uncertainty are considered to be independent and their
effects are added in quadrature in a given bin. The total experimental
uncertainties range from 2–7% in the bulk of the LJP. The systematic
uncertainties can go up to about 25% at the edge of the LJP, which is the
region where the smearing effects are stronger and where the LJP density drops
faster. The uncertainties of each source are considered as bin-to-bin fully
correlated, with the exception of the systematic uncertainty related to the
response matrix statistical uncertainties.

Figures 6 and 7 show the different contributions of the systematic
uncertainties in four different slices of the LJP for AK4 jets. The parton
shower and hadronization uncertainties are the leading systematic
uncertainties in the bulk of the LJP, which have typical values of 2–7%
throughout the LJP, reaching up to 20% in certain bins close to the
kinematical edge of the LJP. This systematic uncertainty reflects the
difference in the detector response at the subjet level between 7 CH3 and 8
CP5. The tracking efficiency uncertainty becomes more prominent as one
approaches the LJP kinematical edge, reaching values of up to 25%. Other
contributions to the experimental uncertainties, which are due to the modeling
of event-level properties in simulation or jet-level corrections and
reconstruction, are less significant and typically below 1% in the bulk of the
LJP. Luminosity calibration uncertainties and PDF set uncertainties have a
negligible effect for this measurement because of cancellations in the per-jet
normalization of the average density of emissions.

Figure 6: Different components of the systematic uncertainties for AK4 jets
for two different vertical slices of the LJP density. The upper plot is for
large angles $0.205<\Delta R<0.287$, and the lower plot is for small angles
$0.039<\Delta R<0.054$. The total experimental uncertainty is represented by
the filled area. The statistical uncertainties in the data are represented by
the hashed band.

Figure 7: Different components of the systematic uncertainties for AK4 jets
for different horizontal slices of the LJP density. The upper plot is for low
of $1.09<\kt<1.79\GeV$, and the lower plot is for higher of
$8.03<\kt<13.25\GeV$. The total experimental uncertainty is represented by the
filled area. The statistical uncertainties in the data are represented by the
hashed band.

##  0.7 Results

Figure 8: Two-dimensional distributions of the primary LJP densities corrected
to particle level for AK4 jets (upper plot) and AK8 jets (lower plot). The
diagonal line in both plots represents the kinematical limit of the emissions
for a jet with $\pt^{\text{jet}}=700\GeV$.

Figure 9: Four slices of the primary LJP density of AK4 jets compared with
predictions by 8 CP5 and 7 CH3. Variations of the ISR and FSR scales for 8 CP5
predictions are shown as well. The band represents the total experimental
uncertainty. The upper two plots correspond to vertical slices for fixed
$\ln(R/\Delta R)$ (large angles on upper-left, small angles on upper-right).
The lower two plots correspond to two different horizontal slices for fixed
$\ln(\kt/\GeV)$: the lower-left plot contains low-splittings, whereas the
lower-right plot contains high-splittings, which populate mostly wide-angle
radiation.

Figure 10: Four slices of the primary LJP density of AK8 jets compared with
predictions by 8 CP5 and 7 CH3. Variations of the ISR and FSR scales for 8 CP5
predictions are shown as well. The band represents the total experimental
uncertainty. The upper two plots correspond to vertical slices for fixed
$\ln(R/\Delta R)$ (large angles on upper-left, small angles on upper-right).
The lower two plots correspond to two different horizontal slices for fixed
$\ln(\kt/\GeV)$: the lower-left plot corresponds to low-splittings and spans
the full range in $\ln(R/\Delta R)$, whereas the lower-right plot corresponds
to high-splittings, which populate mostly wide-angle radiation.

Figure 11: Four different slices of the primary LJP density of AK8 jets
compared with predictions generated with 8 using tunes CP2, CP5, Monash, and
CUEP8M1. The most important difference between the tunes is the value of
$\alpS^{\mathrm{FSR}}(m_{\PZ})$, as described in the text. The band represents
the total experimental uncertainty. The upper two plots correspond to vertical
slices of the LJP for fixed $\ln(R/\Delta R)$ (large angles on upper-left,
small angles on upper-right). The lower two plots correspond to two different
horizontal slices for fixed $\ln(\kt/\GeV)$: the lower-left plot corresponds
to low-splittings and spans the full range in $\ln(R/\Delta R)$, whereas the
lower-right plot corresponds to high-splittings, which populate mostly wide-
angle radiation. Statistical uncertainties in data and MC-simulated events are
represented by vertical bars, which are smaller than the markers in most of
the bins.

Figure 12: Four different slices of the primary LJP density of AK8 jets
compared with predictions by 8+vincia, 8+dire, 7 with dipole shower, and 2.
The band represents the total experimental uncertainty. The upper two plots
correspond to vertical slices of the LJP for fixed $\ln(R/\Delta R)$ (large
angles on upper-left, small angles on upper-right). The lower two plots
correspond to two different horizontal slices for fixed $\ln(\kt/\GeV)$: the
lower-left plot corresponds to low-splittings and spans the full range in
$\ln(R/\Delta R)$, whereas the lower-right plot corresponds to high-
splittings, which populate mostly wide-angle radiation. Statistical
uncertainties in data and MC-simulated events are represented by vertical
bars, which are smaller than the markers in most of the bins.

The primary LJP densities corrected to stable particle level are presented in
Fig. 8 for AK4 and AK8 jets. The primary LJP of AK8 jets give access to
emissions at large $\Delta R$ and high . In these two-dimensional plots, one
can readily see the plateauing of the emission density at high , as well as
the fast growth of emissions at low , as expected from the dependence of the
density of emissions with . The angular region, where the density of emissions
plateaus, is much broader for AK8 jets (starting at about $\Delta R<0.4$),
since clustering effects are mitigated due to the larger distance parameter
$R$ [10].

In Figs. 9 and 10, we project the primary LJP density distribution onto the
$\ln(\kt/\GeV)$ axis in a window of large-angle splittings (upper-left plot)
and in a window of small-angle splittings (upper-right plot). We also project
the LJP onto the $\ln(R/\Delta R)$ axis in a window of low-splittings (lower-
left plot) and in a window of high-splittings (lower-right plot). The low-
splittings populate a wide range in $\Delta R$, whereas the hard splittings
populate mostly the wide-angle radiation region. The shapes of the
distributions are similar for AK4 and AK8 jets except that the soft and large-
angle splittings are more abundant for AK8, which is because of the larger
contribution of the UE due to the larger $\Delta R$ interval for the first bin
in $\ln(R/\Delta R)$.

The unfolded distributions are compared with a number of MC event generator
predictions at particle level. The MC generator predictions differ in their
implementation of color coherence in the parton showers as well as their
logarithmic accuracy in different regions of the LJP. There are differences
also in the modeling of the UE activity and hadronization effects. First, we
discuss the comparison with the predictions based on events generated with 7
CH3 and 8 CP5, including the FSR scale variations of the latter. Figure 9
(lower-left) shows that 8 CP5 overestimates the number of emissions relative
to data by approximately 15–20%, whereas 7 CH3 is in better agreement with the
data within 5–10%. For 8 CP5, we show also the predictions for different
renormalization scale variations. The FSR up and down scale variations
generate a theoretical uncertainty band of about 10% for emissions in the
perturbative region. The sensitivity of the distributions to variations of the
renormalization scale in the FSR shower can be understood from the linear
dependence of the LJP density on $\alpS^{\mathrm{FSR}}(m_{\PZ})$. This
uncertainty band shrinks monotonically at low , where nonperturbative effects
are more important and are effectively decoupled from the hard perturbative
shower. In the region dominated by the parton shower, the predictions with the
FSR down variation are in better agreement with the measured data. This is
equivalent to choosing a larger value of $\alpS^{\mathrm{FSR}}(m_{\PZ})$. The
improvement in the description of jet substructure data with a larger value of
$\alpS^{\mathrm{FSR}}(m_{\PZ})$ has been observed in other jet substructure
measurements [35, 89]. The correlated variations of the FSR and ISR scales
have the same effect as the variations of the FSR scales alone. The
predictions using the ISR up and down variations are consistent with the
predictions calculated with the nominal scale values.

The predictions based on 8 with the Monash, CUEP8M1, and CP2 tunes shown in
Fig. 11 are in better agreement with the data than the predictions from 8 CP5
in the bulk of the LJP. The main difference of these tunes with respect to the
CP5 tune is the larger value of $\alpS^{\mathrm{FSR}}(m_{\PZ})$
($\alpS^{\mathrm{FSR}}(m_{\PZ})=0.1365$ for the Monash and CUEP8M1 tune and
0.130 for CP2). This is consistent with the better description of 8 CP5 with
the FSR down variation mentioned in the previous paragraph. The CP5 tune was
introduced to have an improved description of data with high jet
multiplicities relative to the other 8 CP tunes while potentially compromising
the mismodeling of some jet substructure observables [57]. The difference
between the predictions generated with the CP tunes of 8 and the previous
CUEP8M1 and Monash tunes highlight the complementarity of jet substructure
data relative to the minimum bias data that is typically used for tuning. The
predictions of 8 using the vincia or dire showers in Fig. 12 are in agreement
with the measured LJP within 1–10% in the bulk of the distribution. Both
8+vincia and 8+dire overestimate the density of emissions at low , as observed
also for the 8 predictions calculated with its standard shower. This suggests
that it is likely related to the hadronization model. The predictions by 2 and
7 with dipole showers, shown in Fig. 12, describe the data within 5–10% across
a broad region of the LJP density. The 7 dipole shower overestimates the
density of emissions at large angles and of about 10.

Figure 13 compares the measured LJP density with predictions generated with 7
using different choices of the recoil scheme of its angular-ordered shower.
The recoil scheme, related to the momentum recoil redistribution of the parton
shower, affects the logarithmic accuracy of the parton shower, and it can
reach NLL accuracy for certain classes of global observables [77]. The $q^{2}$
scheme has the largest discrepancy with data, particularly in the high tails.
The scheme has a better agreement with the data than the predictions based on
the $q^{2}$ scheme. This was noted in Ref. [77] for other jet-based
observables at the LHC. The $q_{1}\cdot q_{2}$ scheme has a better description
of the data than the $q^{2}$ or schemes. However, the best global description
among the four schemes is given by the $q_{1}\cdot q_{2}+\text{veto}$ scheme.
Similar trends are observed in measurements of hadronic event shape variables
in $\EE$ collisions at $\sqrt{s}=91.2\GeV$ at LEP, where the $q_{1}\cdot
q_{2}+\text{veto}$ scheme provides a better global description of the data
[77, 70]. The LJP density can be used as a complementary handle at the LHC to
benchmark the choice of the recoil scheme in angular-ordered parton showers in
a region where both quark and gluon fragmentation play an important role.

Another difference between the 7, 2, and 8 generators is the cutoff value used
to terminate the FSR evolution and initiate hadronization. For 8 with the
tunes used in this paper, the cutoff for FSR is at 0.5. For 7 and 2, the
cutoff is at 1. A perturbative cascade evolving to very low momentum followed
by hadronization effects might lead to a larger amount of emissions in the LJP
at low . Figure 14 shows a variation of 8 Monash predictions with two
different values of the FSR cutoff, $\kt^{\text{FSR\,cutoff}}=1.0$ and 1.5;
the latter yields a better agreement with the data. These variations do not
have a strong effect for emissions with $\kt\gtrsim 5\GeV$, further confirming
the ability of the LJP to factorize effects. This indicates that the effect of
the $\kt^{\text{FSR\,cutoff}}$ can be effectively decoupled in the primary LJP
for event generator tuning.

Figure 13: Four different slices of the primary LJP density of AK8 jets
compared with predictions based on different choices of the recoil scheme of
the angular-ordered shower of 7. Each recoil scheme achieves a different
degree of logarithmic accuracy, up to NLL for certain observables, as
described in the text. The band represents the total experimental uncertainty.
The upper two plots correspond to vertical slices of the LJP for fixed
$\ln(R/\Delta R)$ (large angles on upper-left, small angles on upper-right).
The lower two plots correspond to two different horizontal slices for fixed
interval: the lower-left plot corresponds to low-splittings and spans the full
range in $\ln(R/\Delta R)$, whereas the lower-right plot corresponds to high-
splittings, which populate mostly wide-angle radiation. Statistical
uncertainties in data and MC-simulated events are represented by vertical
bars, which are smaller than the markers in most of the bins.

Figure 14: Four different slices of the primary LJP density of AK8 jets
compared with predictions based on different values of the transverse momentum
cutoff used for FSR ($\kt^{\text{FSR\,cutoff}}$) in 8 with the Monash tune.
The larger $\kt^{\text{FSR\,cutoff}}$ value yields a better agreement with the
data at low . The lower two plots correspond to two different horizontal
slices for fixed interval: the lower-left plot corresponds to low-splittings
and spans the full range in $\ln(R/\Delta R)$, whereas the lower-right plot
corresponds to high-splittings, which populate mostly wide-angle radiation.
Statistical uncertainties in data and MC-simulated events are represented by
vertical bars, which are smaller than the markers in most of the bins. Figure
15: Measured LJP distribution for AK8 jets, compared with the leading-order
perturbative-QCD asymptotic prediction in the soft and collinear limit. The
grey boxes represent the total experimental uncertainty from the measured
data. For the prediction, an effective color factor of
$C_{\mathrm{R}}^{\text{eff}}~{}=~{}0.59~{}C_{\mathrm{F}}+0.41~{}C_{\mathrm{A}}\approx
2$ is assumed, as described in the text. The strong coupling evolves with
using the one-loop $\beta$ function with $\alpS(m_{\PZ})=0.118$. The
theoretical uncertainty band is calculated with variations of the
renormalization scale up and down by factors of 2. The discontinuity is due to
the change of the number of active flavors when reaches the mass of the bottom
quark, which is assumed to be 4.2.

It is instructive to analyze the LJP density in terms of the simplest
analytical prediction in perturbation theory to illustrate explicitly the
effect of the running of in the substructure of the jet. In Fig. 15, we
display a slice of the LJP density for AK8 jets and compare it to the soft and
collinear limit prediction using the one-loop $\beta$ function for the running
of . The quark jet (0.59) and gluon jet (0.41) fractions from 8 CP5 simulated
events are determined using the jet flavor definition from Ref. [90]. Based on
this, an effective color factor of
$C_{\mathrm{R}}^{\text{eff}}~{}=~{}0.59~{}C_{\mathrm{F}}+0.41~{}C_{\mathrm{A}}\approx
2$ is assumed. This asymptotic expression does not take into account parton
flavor changes in the jet clustering history, gluon to quark-antiquark
splitting. We assume a value of $\alpS(m_{\PZ})=0.118$, close to the world-
average value [91]. The soft and collinear limit prediction with these basic
assumptions qualitatively describes the shape and normalization of the
unfolded distribution in the collinear region, consistent with the expectation
that the dominant mechanism responsible for the rise of the LJP density at low
is due to the running of in the jet shower, with as the characteristic energy
scale used in the evolution of .

Figure 16: Four different slices of the primary LJP density of AK8 jets
compared with perturbation theory calculations by A. Lifson, G. P. Salam, G.
Soyez [10]. The calculations include all-orders resummation at next-to-leading
logarithmic (NLL) accuracy matched to a next-to-leading order (NLO) fixed-
order calculation, and supplemented with nonperturbative (NP) corrections, as
described in the text. The band around the theory prediction represents the
uncertainty from variations of the renormalization scale uncertainty in the
perturbative calculation as well as uncertainties in the NP corrections. The
gray band represents the total experimental uncertainty. The upper two plots
correspond to vertical slices of the LJP for fixed $\ln(R/\Delta R)$ (large
angles on upper-left, small angles on upper-right). The lower two plots
correspond to two different horizontal slices for fixed interval: the lower-
left plot corresponds to low-splittings and spans the full range in
$\ln(R/\Delta R)$, whereas the lower-right plot corresponds to high-
splittings, which populate mostly wide-angle radiation.

Although the asymptotic formula captures the broad features of the LJP density
in terms of the running of for collinear emissions, higher-order corrections
are necessary to better describe the radiation pattern of the jet. Thus, we
also present a comparison of the unfolded distributions with the theoretical
calculations of the primary LJP density by A. Lifson, G. P. Salam, and G.
Soyez using the setup described in Ref. [10]. The calculations are adapted to
match the particle-level definition of the jets and their substructure
presented in this analysis. The calculations include several pieces associated
with the resummation of single-logarithmically enhanced terms in the
perturbative expansion in . The largest contribution comes from the
resummation of logarithmic terms from the running of , which is accounted for
using a two-loop $\beta$ function. A value of $\alpS(m_{\PZ})=0.118$ is used
for the pQCD pieces of the calculation. A resummation at NLL accuracy includes
contributions that can change the and the flavor of the leading parton. The
calculation also includes a resummation of nonglobal logarithms associated to
multiple soft-gluon emissions and a resummation of boundary logarithms to
account for the fact that the jet is initially clustered with the anti-
algorithm and reclustered with the CA algorithm. These pieces modify the LJP
density mostly at large $\Delta R$. The all-orders resummation is matched to a
fixed-order NLO pQCD calculation for jet production. The parton-level
calculations are corrected to the hadron level using bin-by-bin corrections
derived from MC simulated events. Since the substructure is calculated using
the charged particles in the jet, the is scaled by a factor of 0.62 to account
for the average charged fraction in a jet. The nonperturbative corrections
affect mostly the $\kt<5\GeV$ region. The resulting theoretical uncertainties
include uncertainties from the perturbative calculation, derived from scale
variations, and uncertainties in the nonperturbative corrections [10]. Four
different slices of the primary LJP density of AK8 jets are shown in Fig. 16.
For the vertical slices in $\Delta R$, one can distinguish the effects from
the resummation in . For the horizontal slices in , one can see the net effect
from the nonglobal logarithms, which is an increase in the density of
emissions at large $\Delta R$. The predictions and the unfolded data are
consistent with each other within the theoretical and experimental
uncertainties, meaning that a first-principles understanding of the radiation
pattern of the jet in terms of the primary LJP is achieved.

##  0.8 Summary

We have presented a measurement of the primary Lund jet plane (LJP) density in
inclusive jet production in proton-proton collisions at $\sqrt{s}=13\TeV$
using data, corresponding to an integrated luminosity of 138, collected in Run
2 (2016–2018) with the CMS experiment. The LJP is a two-dimensional
representation of the phase space of emissions inside a jet constructed using
iterative Cambridge–Aachen declustering. The logarithm of the relative
transverse momentum of the emission and the logarithm of the opening angle of
the branching $\Delta R$ are used for the vertical and horizontal axes of the
LJP. We analyzed the substructure of jets initially clustered with the anti-
algorithm with transverse momentum $\pt>700\GeV$ and rapidity $\abs{y}<1.7$
clustered with distance parameters $R=0.4$ or 0.8. The smaller $R=0.4$ is the
standard $R$ for Run 2 analyses. The larger $R=0.8$, used for the first time
in a measurement of the primary LJP density, enables the exploration of a
broader kinematical region of the LJP that is inaccessible with the $R=0.4$
parameter value, particularly for wide-angle, hard radiation. Clustering
effects associated with the initial anti-clustering have a less strong effect
in the collinear region with the larger $R$ value; hence the angular region
where the emission density plateaus is wider for $R=0.8$ jets. The corrected
distributions have an experimental uncertainty in a range of 2–7% in the
region away from the kinematical LJP edge and about 15–25% close to the LJP
edge.

We compared the corrected primary LJP density with various particle-level
predictions from Monte Carlo (MC) simulated events. The predictions use
different implementations of parton showers as well as different models for
the underlying-event (UE) activity, beam-beam remnants, hadronization, and
color reconnection effects. The aforementioned mechanisms can be effectively
factorized in the primary LJP density, which allows for strong constraints in
terms of the substructure of jets. At leading-logarithmic (LL) accuracy, the
primary LJP density is proportional to the strong coupling $\alpS(\kt)$, so it
can be used to tune the value of evaluated at the boson mass used for final-
state radiation (FSR) in MC event generators, $\alpS^{\mathrm{FSR}}(m_{\PZ})$.

Predictions generated with the CP5 tune of the 8 generator underestimate the
measured density of emissions in the perturbative region ($\kt>5\GeV$) by
about 15% because of the small value of $\alpS^{\mathrm{FSR}}(m_{\PZ})$ used
for this tune. Other 8 tunes or parton shower options tested in the
measurement are in better agreement with the data.

The predictions generated with the angular-ordered shower of the 7.2.0
generator are in better agreement with the data than those generated with its
alternative dipole shower. The data were also compared with different recoil
schemes of the angular-ordered shower of 7, which allow the parton shower to
reach up to next-to-LL (NLL) accuracy for certain global observables. The 7
predictions with the dot-product preserving recoil scheme, together with a
veto on high-virtuality partons, have the best global agreement with the data
among the generators tested in the measurement.

The low-region is dominated by hadronization effects in a wide range of
$\Delta R$ values, with additional contributions from the UE at large $\Delta
R\approx R$. The predictions based on cluster fragmentation models, such as
those generated with 7 or 2 generators, are in better agreement with the data
at low for a wide range of $\Delta R$ values than those of 8. The 8
predictions, where hadronization is described with the Lund string
fragmentation model, overestimate the LJP density by about 15–20% for at the
scale for a wide range of $\Delta R$ values. One possibility to improve the
description of the low region is to include the FSR cutoff as a free parameter
in future event generator tuning; a larger FSR cutoff value decreases the
density of emissions at low in the LJP without affecting the high-region that
is dominated by the parton shower.

Finally, the data are also compared with a perturbative QCD calculation with a
resummation at NLL accuracy, which is matched to a fixed-order next-to-leading
order calculation [10]. To compare with the measured LJP at hadron level,
nonperturbative corrections are supplemented to the calculation. The
predictions are in agreement with the data within the theoretical and
experimental uncertainties. For collinear emissions, the data can be
qualitatively described with the running of with .

These measurements highlight the different aspects of the physics modeling of
event generators that should be improved, ranging from the modeling of
hadronization and up to the logarithmic accuracy of parton showering
algorithms.

###### Acknowledgements.

We thank Andrew Lifson, Gavin P. Salam, and Gregory Soyez for their
theoretical calculations of the primary Lund jet plane density adapted with
the selection requirements used in this paper. 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: SC (Armenia), 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); SRNSF (Georgia); BMBF, DFG, and HGF (Germany); GSRI (Greece); NKFIH
(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); MES and NSC (Poland); FCT
(Portugal); MESTD (Serbia); MCIN/AEI and PCTI (Spain); MOSTR (Sri Lanka);
Swiss Funding Agencies (Switzerland); MST (Taipei); MHESI and NSTDA
(Thailand); TUBITAK and TENMAK (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, and COST Action
CA16108 (European Union); the Leventis Foundation; the Alfred P. Sloan
Foundation; the Alexander von Humboldt Foundation; the Science Committee,
project no. 22rl-037 (Armenia); 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 and Fundamental Research Funds for
the Central Universities (China); the Ministry of Education, Youth and Sports
(MEYS) of the Czech Republic; the Shota Rustaveli National Science Foundation,
grant FR-22-985 (Georgia); the Deutsche Forschungsgemeinschaft (DFG), under
Germany’s Excellence Strategy – EXC 2121 “Quantum Universe” – 390833306, and
under project number 400140256 - GRK2497; the Hellenic Foundation for Research
and Innovation (HFRI), Project Number 2288 (Greece); the Hungarian Academy of
Sciences, the New National Excellence Program - ÚNKP, the NKFIH research
grants K 124845, K 124850, K 128713, K 128786, K 129058, K 131991, K 133046, K
138136, K 143460, K 143477, 2020-2.2.1-ED-2021-00181, and TKP2021-NKTA-64
(Hungary); the Council of Science and Industrial Research, India; ICSC –
National Research Center for High Performance Computing, Big Data and Quantum
Computing, funded by the EU NexGeneration program (Italy); the Latvian Council
of Science; the Ministry of Education and Science, project no. 2022/WK/14, and
the National Science Center, contracts Opus 2021/41/B/ST2/01369 and
2021/43/B/ST2/01552 (Poland); the Fundação para a Ciência e a Tecnologia,
grant CEECIND/01334/2018 (Portugal); the National Priorities Research Program
by Qatar National Research Fund; MCIN/AEI/10.13039/501100011033, ERDF “a way
of making Europe”, and the Programa Estatal de Fomento de la Investigación
Científica y Técnica de Excelencia María de Maeztu, grant MDM-2017-0765 and
Programa Severo Ochoa del Principado de Asturias (Spain); the Chulalongkorn
Academic into Its 2nd Century Project Advancement Project, and the National
Science, Research and Innovation Fund via the Program Management Unit for
Human Resources & Institutional Development, Research and Innovation, grant
B37G660013 (Thailand); the Kavli Foundation; the Nvidia Corporation; the
SuperMicro Corporation; the Welch Foundation, contract C-1845; and the Weston
Havens Foundation (USA).

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##  .9 The CMS Collaboration

Yerevan Physics Institute, Yerevan, Armenia A. Hayrapetyan, A.
Tumasyan10009-0000-0684-6742

Institut für Hochenergiephysik, Vienna, Austria W. Adam0000-0001-9099-4341,
J.W. Andrejkovic, T. Bergauer0000-0002-5786-0293, S.
Chatterjee0000-0003-2660-0349, K. Damanakis0000-0001-5389-2872, M.
Dragicevic0000-0003-1967-6783, A. Escalante Del Valle0000-0002-9702-6359, P.S.
Hussain0000-0002-4825-5278, M. Jeitler20000-0002-5141-9560, N.
Krammer0000-0002-0548-0985, D. Liko0000-0002-3380-473X, I.
Mikulec0000-0003-0385-2746, J. Schieck20000-0002-1058-8093, R.
Schöfbeck0000-0002-2332-8784, D. Schwarz0000-0002-3821-7331, M.
Sonawane0000-0003-0510-7010, S. Templ0000-0003-3137-5692, W.
Waltenberger0000-0002-6215-7228, C.-E. Wulz20000-0001-9226-5812

Universiteit Antwerpen, Antwerpen, Belgium M.R. Darwish30000-0003-2894-2377,
T. Janssen0000-0002-3998-4081, P. Van Mechelen0000-0002-8731-9051

Vrije Universiteit Brussel, Brussel, Belgium E.S. Bols0000-0002-8564-8732, J.
D’Hondt0000-0002-9598-6241, S. Dansana0000-0002-7752-7471, A. De
Moor0000-0001-5964-1935, M. Delcourt0000-0001-8206-1787, H. El
Faham0000-0001-8894-2390, S. Lowette0000-0003-3984-9987, I.
Makarenko0000-0002-8553-4508, D. Müller0000-0002-1752-4527, A.R.
Sahasransu0000-0003-1505-1743, S. Tavernier0000-0002-6792-9522, M.
Tytgat40000-0002-3990-2074, S. Van Putte0000-0003-1559-3606, D.
Vannerom0000-0002-2747-5095

Université Libre de Bruxelles, Bruxelles, Belgium B.
Clerbaux0000-0001-8547-8211, G. De Lentdecker0000-0001-5124-7693, L.
Favart0000-0003-1645-7454, D. Hohov0000-0002-4760-1597, J.
Jaramillo0000-0003-3885-6608, A. Khalilzadeh, K. Lee0000-0003-0808-4184, M.
Mahdavikhorrami0000-0002-8265-3595, A. Malara0000-0001-8645-9282, S.
Paredes0000-0001-8487-9603, L. Pétré0009-0000-7979-5771, N. Postiau, L.
Thomas0000-0002-2756-3853, M. Vanden Bemden0009-0000-7725-7945, C. Vander
Velde0000-0003-3392-7294, P. Vanlaer0000-0002-7931-4496

Ghent University, Ghent, Belgium M. De Coen0000-0002-5854-7442, D.
Dobur0000-0003-0012-4866, Y. Hong0000-0003-4752-2458, J.
Knolle0000-0002-4781-5704, L. Lambrecht0000-0001-9108-1560, G. Mestdach, C.
Rendón, A. Samalan, K. Skovpen0000-0002-1160-0621, N. Van Den
Bossche0000-0003-2973-4991, L. Wezenbeek0000-0001-6952-891X

Université Catholique de Louvain, Louvain-la-Neuve, Belgium A.
Benecke0000-0003-0252-3609, G. Bruno0000-0001-8857-8197, C.
Caputo0000-0001-7522-4808, C. Delaere0000-0001-8707-6021, I.S.
Donertas0000-0001-7485-412X, A. Giammanco0000-0001-9640-8294, K.
Jaffel0000-0001-7419-4248, Sa. Jain0000-0001-5078-3689, V. Lemaitre, J.
Lidrych0000-0003-1439-0196, P. Mastrapasqua0000-0002-2043-2367, K.
Mondal0000-0001-5967-1245, T.T. Tran0000-0003-3060-350X, S.
Wertz0000-0002-8645-3670

Centro Brasileiro de Pesquisas Fisicas, Rio de Janeiro, Brazil G.A.
Alves0000-0002-8369-1446, E. Coelho0000-0001-6114-9907, C.
Hensel0000-0001-8874-7624, T. Menezes De Oliveira, A.
Moraes0000-0002-5157-5686, P. Rebello Teles0000-0001-9029-8506, M. Soeiro

Universidade do Estado do Rio de Janeiro, Rio de Janeiro, Brazil W.L. Aldá
Júnior0000-0001-5855-9817, M. Alves Gallo Pereira0000-0003-4296-7028, M.
Barroso Ferreira Filho0000-0003-3904-0571, H. Brandao
Malbouisson0000-0002-1326-318X, W. Carvalho0000-0003-0738-6615, J.
Chinellato5, E.M. Da Costa0000-0002-5016-6434, G.G. Da
Silveira60000-0003-3514-7056, D. De Jesus Damiao0000-0002-3769-1680, S.
Fonseca De Souza0000-0001-7830-0837, J. Martins70000-0002-2120-2782, C. Mora
Herrera0000-0003-3915-3170, K. Mota Amarilo0000-0003-1707-3348, L.
Mundim0000-0001-9964-7805, H. Nogima0000-0001-7705-1066, A.
Santoro0000-0002-0568-665X, S.M. Silva Do Amaral0000-0002-0209-9687, A.
Sznajder0000-0001-6998-1108, M. Thiel0000-0001-7139-7963, A. Vilela
Pereira0000-0003-3177-4626

Universidade Estadual Paulista, Universidade Federal do ABC, São Paulo, Brazil
C.A. Bernardes60000-0001-5790-9563, L. Calligaris0000-0002-9951-9448, T.R.
Fernandez Perez Tomei0000-0002-1809-5226, E.M. Gregores0000-0003-0205-1672,
P.G. Mercadante0000-0001-8333-4302, S.F. Novaes0000-0003-0471-8549, B.
Orzari0000-0003-4232-4743, Sandra S. Padula0000-0003-3071-0559

Institute for Nuclear Research and Nuclear Energy, Bulgarian Academy of
Sciences, Sofia, Bulgaria A. Aleksandrov0000-0001-6934-2541, G.
Antchev0000-0003-3210-5037, R. Hadjiiska0000-0003-1824-1737, P.
Iaydjiev0000-0001-6330-0607, M. Misheva0000-0003-4854-5301, M.
Shopova0000-0001-6664-2493, G. Sultanov0000-0002-8030-3866

University of Sofia, Sofia, Bulgaria A. Dimitrov0000-0003-2899-701X, T.
Ivanov0000-0003-0489-9191, L. Litov0000-0002-8511-6883, B.
Pavlov0000-0003-3635-0646, P. Petkov0000-0002-0420-9480, A.
Petrov0009-0003-8899-1514, E. Shumka0000-0002-0104-2574

Instituto De Alta Investigación, Universidad de Tarapacá, Casilla 7 D, Arica,
Chile S. Keshri0000-0003-3280-2350, S. Thakur0000-0002-1647-0360

Beihang University, Beijing, China T. Cheng0000-0003-2954-9315, Q. Guo, T.
Javaid0009-0007-2757-4054, M. Mittal0000-0002-6833-8521, L.
Yuan0000-0002-6719-5397

Department of Physics, Tsinghua University, Beijing, China G. Bauer8,9, Z.
Hu0000-0001-8209-4343, K. Yi8,100000-0002-2459-1824

Institute of High Energy Physics, Beijing, China G.M.
Chen110000-0002-2629-5420, H.S. Chen110000-0001-8672-8227, M.
Chen110000-0003-0489-9669, F. Iemmi0000-0001-5911-4051, C.H. Jiang, A.
Kapoor120000-0002-1844-1504, H. Liao0000-0002-0124-6999, Z.-A.
Liu130000-0002-2896-1386, F. Monti0000-0001-5846-3655, M.A. Shahzad11, R.
Sharma140000-0003-1181-1426, J.N. Song13, J. Tao0000-0003-2006-3490, C.
Wang11, J. Wang0000-0002-3103-1083, Z. Wang11, H. Zhang0000-0001-8843-5209

State Key Laboratory of Nuclear Physics and Technology, Peking University,
Beijing, China A. Agapitos0000-0002-8953-1232, Y. Ban0000-0002-1912-0374, A.
Levin0000-0001-9565-4186, C. Li0000-0002-6339-8154, Q. Li0000-0002-8290-0517,
X. Lyu, Y. Mao, S.J. Qian0000-0002-0630-481X, X. Sun0000-0003-4409-4574, D.
Wang0000-0002-9013-1199, H. Yang, C. Zhou0000-0001-5904-7258

Sun Yat-Sen University, Guangzhou, China Z. You0000-0001-8324-3291

University of Science and Technology of China, Hefei, China N.
Lu0000-0002-2631-6770

Institute of Modern Physics and Key Laboratory of Nuclear Physics and Ion-beam
Application (MOE) - Fudan University, Shanghai, China X.
Gao150000-0001-7205-2318, D. Leggat, H. Okawa0000-0002-2548-6567, Y.
Zhang0000-0002-4554-2554

Zhejiang University, Hangzhou, Zhejiang, China Z. Lin0000-0003-1812-3474, C.
Lu0000-0002-7421-0313, M. Xiao0000-0001-9628-9336

Universidad de Los Andes, Bogota, Colombia C. Avila0000-0002-5610-2693, D.A.
Barbosa Trujillo, A. Cabrera0000-0002-0486-6296, C. Florez0000-0002-3222-0249,
J. Fraga0000-0002-5137-8543, J.A. Reyes Vega

Universidad de Antioquia, Medellin, Colombia J. Mejia
Guisao0000-0002-1153-816X, F. Ramirez0000-0002-7178-0484, M.
Rodriguez0000-0002-9480-213X, J.D. Ruiz Alvarez0000-0002-3306-0363

University of Split, Faculty of Electrical Engineering, Mechanical Engineering
and Naval Architecture, Split, Croatia D. Giljanovic0009-0005-6792-6881, N.
Godinovic0000-0002-4674-9450, D. Lelas0000-0002-8269-5760, A.
Sculac0000-0001-7938-7559

University of Split, Faculty of Science, Split, Croatia M.
Kovac0000-0002-2391-4599, T. Sculac0000-0002-9578-4105

Institute Rudjer Boskovic, Zagreb, Croatia P. Bargassa0000-0001-8612-3332, V.
Brigljevic0000-0001-5847-0062, B.K. Chitroda0000-0002-0220-8441, D.
Ferencek0000-0001-9116-1202, S. Mishra0000-0002-3510-4833, A.
Starodumov160000-0001-9570-9255, T. Susa0000-0001-7430-2552

University of Cyprus, Nicosia, Cyprus A. Attikis0000-0002-4443-3794, K.
Christoforou0000-0003-2205-1100, S. Konstantinou0000-0003-0408-7636, J.
Mousa0000-0002-2978-2718, C. Nicolaou, F. Ptochos0000-0002-3432-3452, P.A.
Razis0000-0002-4855-0162, H. Rykaczewski, H. Saka0000-0001-7616-2573, A.
Stepennov0000-0001-7747-6582

Charles University, Prague, Czech Republic M. Finger0000-0002-7828-9970, M.
Finger Jr.0000-0003-3155-2484, A. Kveton0000-0001-8197-1914

Escuela Politecnica Nacional, Quito, Ecuador E. Ayala0000-0002-0363-9198

Universidad San Francisco de Quito, Quito, Ecuador E. Carrera
Jarrin0000-0002-0857-8507

Academy of Scientific Research and Technology of the Arab Republic of Egypt,
Egyptian Network of High Energy Physics, Cairo, Egypt S. Elgammal17, A.
Ellithi Kamel18

Center for High Energy Physics (CHEP-FU), Fayoum University, El-Fayoum, Egypt
M.A. Mahmoud0000-0001-8692-5458, Y. Mohammed0000-0001-8399-3017

National Institute of Chemical Physics and Biophysics, Tallinn, Estonia R.K.
Dewanjee190000-0001-6645-6244, K. Ehataht0000-0002-2387-4777, M. Kadastik, T.
Lange0000-0001-6242-7331, S. Nandan0000-0002-9380-8919, C.
Nielsen0000-0002-3532-8132, J. Pata0000-0002-5191-5759, M.
Raidal0000-0001-7040-9491, L. Tani0000-0002-6552-7255, C.
Veelken0000-0002-3364-916X

Department of Physics, University of Helsinki, Helsinki, Finland H.
Kirschenmann0000-0001-7369-2536, K. Osterberg0000-0003-4807-0414, M.
Voutilainen0000-0002-5200-6477

Helsinki Institute of Physics, Helsinki, Finland S.
Bharthuar0000-0001-5871-9622, E. Brücken0000-0001-6066-8756, F.
Garcia0000-0002-4023-7964, J. Havukainen0000-0003-2898-6900, K.T.S.
Kallonen0000-0001-9769-7163, M.S. Kim0000-0003-0392-8691, R. Kinnunen, T.
Lampén0000-0002-8398-4249, K. Lassila-Perini0000-0002-5502-1795, S.
Lehti0000-0003-1370-5598, T. Lindén0009-0002-4847-8882, M. Lotti, L.
Martikainen0000-0003-1609-3515, M. Myllymäki0000-0003-0510-3810, M.m.
Rantanen0000-0002-6764-0016, H. Siikonen0000-0003-2039-5874, E.
Tuominen0000-0002-7073-7767, J. Tuominiemi0000-0003-0386-8633

Lappeenranta-Lahti University of Technology, Lappeenranta, Finland P.
Luukka0000-0003-2340-4641, H. Petrow0000-0002-1133-5485, T.
Tuuva${}^{\textrm{\textdagger}}$

IRFU, CEA, Université Paris-Saclay, Gif-sur-Yvette, France M.
Besancon0000-0003-3278-3671, F. Couderc0000-0003-2040-4099, M.
Dejardin0009-0008-2784-615X, D. Denegri, J.L. Faure, F.
Ferri0000-0002-9860-101X, S. Ganjour0000-0003-3090-9744, P.
Gras0000-0002-3932-5967, G. Hamel de Monchenault0000-0002-3872-3592, V.
Lohezic0009-0008-7976-851X, J. Malcles0000-0002-5388-5565, J. Rander, A.
Rosowsky0000-0001-7803-6650, M.Ö. Sahin0000-0001-6402-4050, A. Savoy-
Navarro200000-0002-9481-5168, P. Simkina0000-0002-9813-372X, M.
Titov0000-0002-1119-6614

Laboratoire Leprince-Ringuet, CNRS/IN2P3, Ecole Polytechnique, Institut
Polytechnique de Paris, Palaiseau, France C. Baldenegro
Barrera0000-0002-6033-8885, F. Beaudette0000-0002-1194-8556, A. Buchot
Perraguin0000-0002-8597-647X, P. Busson0000-0001-6027-4511, A.
Cappati0000-0003-4386-0564, C. Charlot0000-0002-4087-8155, F.
Damas0000-0001-6793-4359, O. Davignon0000-0001-8710-992X, A. De
Wit0000-0002-5291-1661, G. Falmagne0000-0002-6762-3937, B.A. Fontana Santos
Alves0000-0001-9752-0624, S. Ghosh0009-0006-5692-5688, A.
Gilbert0000-0001-7560-5790, R. Granier de Cassagnac0000-0002-1275-7292, A.
Hakimi0009-0008-2093-8131, B. Harikrishnan0000-0003-0174-4020, L.
Kalipoliti0000-0002-5705-5059, G. Liu0000-0001-7002-0937, J.
Motta0000-0003-0985-913X, M. Nguyen0000-0001-7305-7102, C.
Ochando0000-0002-3836-1173, L. Portales0000-0002-9860-9185, R.
Salerno0000-0003-3735-2707, U. Sarkar0000-0002-9892-4601, J.B.
Sauvan0000-0001-5187-3571, Y. Sirois0000-0001-5381-4807, A.
Tarabini0000-0001-7098-5317, E. Vernazza0000-0003-4957-2782, A.
Zabi0000-0002-7214-0673, A. Zghiche0000-0002-1178-1450

Université de Strasbourg, CNRS, IPHC UMR 7178, Strasbourg, France J.-L.
Agram210000-0001-7476-0158, J. Andrea0000-0002-8298-7560, D.
Apparu0009-0004-1837-0496, D. Bloch0000-0002-4535-5273, J.-M.
Brom0000-0003-0249-3622, E.C. Chabert0000-0003-2797-7690, C.
Collard0000-0002-5230-8387, S. Falke0000-0002-0264-1632, U.
Goerlach0000-0001-8955-1666, C. Grimault, R. Haeberle0009-0007-5007-6723,
A.-C. Le Bihan0000-0002-8545-0187, M.A. Sessini0000-0003-2097-7065, P. Van
Hove0000-0002-2431-3381

Institut de Physique des 2 Infinis de Lyon (IP2I ), Villeurbanne, France S.
Beauceron0000-0002-8036-9267, B. Blancon0000-0001-9022-1509, G.
Boudoul0009-0002-9897-8439, N. Chanon0000-0002-2939-5646, J.
Choi0000-0002-6024-0992, D. Contardo0000-0001-6768-7466, P.
Depasse0000-0001-7556-2743, C. Dozen220000-0002-4301-634X, H. El Mamouni, J.
Fay0000-0001-5790-1780, S. Gascon0000-0002-7204-1624, M.
Gouzevitch0000-0002-5524-880X, C. Greenberg, G. Grenier0000-0002-1976-5877, B.
Ille0000-0002-8679-3878, I.B. Laktineh, M. Lethuillier0000-0001-6185-2045, L.
Mirabito, S. Perries, M. Vander Donckt0000-0002-9253-8611, P.
Verdier0000-0003-3090-2948, J. Xiao0000-0002-7860-3958

Georgian Technical University, Tbilisi, Georgia D.
Chokheli0000-0001-7535-4186, I. Lomidze0009-0002-3901-2765, Z.
Tsamalaidze160000-0001-5377-3558

RWTH Aachen University, I. Physikalisches Institut, Aachen, Germany V.
Botta0000-0003-1661-9513, L. Feld0000-0001-9813-8646, K.
Klein0000-0002-1546-7880, M. Lipinski0000-0002-6839-0063, D.
Meuser0000-0002-2722-7526, A. Pauls0000-0002-8117-5376, N.
Röwert0000-0002-4745-5470, M. Teroerde0000-0002-5892-1377

RWTH Aachen University, III. Physikalisches Institut A, Aachen, Germany S.
Diekmann0009-0004-8867-0881, A. Dodonova0000-0002-5115-8487, N.
Eich0000-0001-9494-4317, D. Eliseev0000-0001-5844-8156, F.
Engelke0000-0002-9288-8144, M. Erdmann0000-0002-1653-1303, P.
Fackeldey0000-0003-4932-7162, B. Fischer0000-0002-3900-3482, T.
Hebbeker0000-0002-9736-266X, K. Hoepfner0000-0002-2008-8148, F.
Ivone0000-0002-2388-5548, A. Jung0000-0002-2511-1490, M.y.
Lee0000-0002-4430-1695, L. Mastrolorenzo, M. Merschmeyer0000-0003-2081-7141,
A. Meyer0000-0001-9598-6623, S. Mukherjee0000-0001-6341-9982, D.
Noll0000-0002-0176-2360, A. Novak0000-0002-0389-5896, F. Nowotny, A.
Pozdnyakov0000-0003-3478-9081, Y. Rath, W. Redjeb0000-0001-9794-8292, F. Rehm,
H. Reithler0000-0003-4409-702X, V. Sarkisovi0000-0001-9430-5419, A.
Schmidt0000-0003-2711-8984, S.C. Schuler, A. Sharma0000-0002-5295-1460, A.
Stein0000-0003-0713-811X, F. Torres Da Silva De Araujo230000-0002-4785-3057,
L. Vigilante, S. Wiedenbeck0000-0002-4692-9304, S. Zaleski

RWTH Aachen University, III. Physikalisches Institut B, Aachen, Germany C.
Dziwok0000-0001-9806-0244, G. Flügge0000-0003-3681-9272, W. Haj
Ahmad240000-0003-1491-0446, T. Kress0000-0002-2702-8201, A.
Nowack0000-0002-3522-5926, O. Pooth0000-0001-6445-6160, A.
Stahl0000-0002-8369-7506, T. Ziemons0000-0003-1697-2130, A.
Zotz0000-0002-1320-1712

Deutsches Elektronen-Synchrotron, Hamburg, Germany H. Aarup
Petersen0009-0005-6482-7466, M. Aldaya Martin0000-0003-1533-0945, J.
Alimena0000-0001-6030-3191, S. Amoroso, Y. An0000-0003-1299-1879, S.
Baxter0009-0008-4191-6716, M. Bayatmakou0009-0002-9905-0667, H. Becerril
Gonzalez0000-0001-5387-712X, O. Behnke0000-0002-4238-0991, A.
Belvedere0000-0002-2802-8203, S. Bhattacharya0000-0002-3197-0048, F.
Blekman250000-0002-7366-7098, K. Borras260000-0003-1111-249X, D.
Brunner0000-0001-9518-0435, A. Campbell0000-0003-4439-5748, A.
Cardini0000-0003-1803-0999, C. Cheng, F. Colombina0009-0008-7130-100X, S.
Consuegra Rodríguez0000-0002-1383-1837, G. Correia Silva0000-0001-6232-3591,
M. De Silva0000-0002-5804-6226, G. Eckerlin, D. Eckstein0000-0002-7366-6562,
L.I. Estevez Banos0000-0001-6195-3102, O. Filatov0000-0001-9850-6170, E.
Gallo250000-0001-7200-5175, A. Geiser0000-0003-0355-102X, A.
Giraldi0000-0003-4423-2631, G. Greau, V. Guglielmi0000-0003-3240-7393, M.
Guthoff0000-0002-3974-589X, A. Hinzmann0000-0002-2633-4696, A.
Jafari270000-0001-7327-1870, L. Jeppe0000-0002-1029-0318, N.Z.
Jomhari0000-0001-9127-7408, B. Kaech0000-0002-1194-2306, M.
Kasemann0000-0002-0429-2448, H. Kaveh0000-0002-3273-5859, C.
Kleinwort0000-0002-9017-9504, R. Kogler0000-0002-5336-4399, M.
Komm0000-0002-7669-4294, D. Krücker0000-0003-1610-8844, W. Lange, D. Leyva
Pernia0009-0009-8755-3698, K. Lipka280000-0002-8427-3748, W.
Lohmann290000-0002-8705-0857, R. Mankel0000-0003-2375-1563, I.-A. Melzer-
Pellmann0000-0001-7707-919X, M. Mendizabal Morentin0000-0002-6506-5177, J.
Metwally, A.B. Meyer0000-0001-8532-2356, G. Milella0000-0002-2047-951X, A.
Mussgiller0000-0002-8331-8166, A. Nürnberg0000-0002-7876-3134, Y. Otarid, D.
Pérez Adán0000-0003-3416-0726, E. Ranken0000-0001-7472-5029, A.
Raspereza0000-0003-2167-498X, B. Ribeiro Lopes0000-0003-0823-447X, J.
Rübenach, A. Saggio0000-0002-7385-3317, M. Scham30,260000-0001-9494-2151, V.
Scheurer, S. Schnake260000-0003-3409-6584, P. Schütze0000-0003-4802-6990, C.
Schwanenberger250000-0001-6699-6662, D. Selivanova0000-0002-7031-9434, M.
Shchedrolosiev0000-0003-3510-2093, R.E. Sosa Ricardo0000-0002-2240-6699, L.P.
Sreelatha Pramod0000-0002-2351-9265, D. Stafford, F.
Vazzoler0000-0001-8111-9318, A. Ventura Barroso0000-0003-3233-6636, R.
Walsh0000-0002-3872-4114, Q. Wang0000-0003-1014-8677, Y.
Wen0000-0002-8724-9604, K. Wichmann, L. Wiens260000-0002-4423-4461, C.
Wissing0000-0002-5090-8004, S. Wuchterl0000-0001-9955-9258, Y.
Yang0009-0009-3430-0558, A. Zimermmane Castro Santos0000-0001-9302-3102

University of Hamburg, Hamburg, Germany A. Albrecht0000-0001-6004-6180, S.
Albrecht0000-0002-5960-6803, M. Antonello0000-0001-9094-482X, S.
Bein0000-0001-9387-7407, L. Benato0000-0001-5135-7489, M.
Bonanomi0000-0003-3629-6264, P. Connor0000-0003-2500-1061, M. Eich, K. El
Morabit0000-0001-5886-220X, Y. Fischer0000-0002-3184-1457, A. Fröhlich, C.
Garbers0000-0001-5094-2256, E. Garutti0000-0003-0634-5539, A.
Grohsjean0000-0003-0748-8494, M. Hajheidari, J. Haller0000-0001-9347-7657,
H.R. Jabusch0000-0003-2444-1014, G. Kasieczka0000-0003-3457-2755, P. Keicher,
R. Klanner0000-0002-7004-9227, W. Korcari0000-0001-8017-5502, T.
Kramer0000-0002-7004-0214, V. Kutzner0000-0003-1985-3807, F.
Labe0000-0002-1870-9443, J. Lange0000-0001-7513-6330, A.
Lobanov0000-0002-5376-0877, C. Matthies0000-0001-7379-4540, A.
Mehta0000-0002-0433-4484, L. Moureaux0000-0002-2310-9266, M. Mrowietz, A.
Nigamova0000-0002-8522-8500, Y. Nissan, A. Paasch0000-0002-2208-5178, K.J.
Pena Rodriguez0000-0002-2877-9744, T. Quadfasel0000-0003-2360-351X, B.
Raciti0009-0005-5995-6685, M. Rieger0000-0003-0797-2606, D.
Savoiu0000-0001-6794-7475, J. Schindler0009-0006-6551-0660, P.
Schleper0000-0001-5628-6827, M. Schröder0000-0001-8058-9828, J.
Schwandt0000-0002-0052-597X, M. Sommerhalder0000-0001-5746-7371, H.
Stadie0000-0002-0513-8119, G. Steinbrück0000-0002-8355-2761, A. Tews, M.
Wolf0000-0003-3002-2430

Karlsruher Institut fuer Technologie, Karlsruhe, Germany S.
Brommer0000-0001-8988-2035, M. Burkart, E. Butz0000-0002-2403-5801, T.
Chwalek0000-0002-8009-3723, A. Dierlamm0000-0001-7804-9902, A. Droll, N.
Faltermann0000-0001-6506-3107, M. Giffels0000-0003-0193-3032, A.
Gottmann0000-0001-6696-349X, F. Hartmann310000-0001-8989-8387, R.
Hofsaess0009-0008-4575-5729, M. Horzela0000-0002-3190-7962, U.
Husemann0000-0002-6198-8388, M. Klute0000-0002-0869-5631, R.
Koppenhöfer0000-0002-6256-5715, M. Link, A. Lintuluoto0000-0002-0726-1452, S.
Maier0000-0001-9828-9778, S. Mitra0000-0002-3060-2278, M.
Mormile0000-0003-0456-7250, Th. Müller0000-0003-4337-0098, M. Neukum, M.
Oh0000-0003-2618-9203, G. Quast0000-0002-4021-4260, K.
Rabbertz0000-0001-7040-9846, B. Regnery0000-0003-1539-923X, N.
Shadskiy0000-0001-9894-2095, I. Shvetsov0000-0002-7069-9019, H.J.
Simonis0000-0002-7467-2980, N. Trevisani0000-0002-5223-9342, R.
Ulrich0000-0002-2535-402X, J. van der Linden0000-0002-7174-781X, R.F. Von
Cube0000-0002-6237-5209, M. Wassmer0000-0002-0408-2811, S.
Wieland0000-0003-3887-5358, F. Wittig, R. Wolf0000-0001-9456-383X, S. Wunsch,
X. Zuo0000-0002-0029-493X

Institute of Nuclear and Particle Physics (INPP), NCSR Demokritos, Aghia
Paraskevi, Greece G. Anagnostou, P. Assiouras0000-0002-5152-9006, G.
Daskalakis0000-0001-6070-7698, A. Kyriakis, A. Papadopoulos31, A.
Stakia0000-0001-6277-7171

National and Kapodistrian University of Athens, Athens, Greece D. Karasavvas,
P. Kontaxakis0000-0002-4860-5979, G. Melachroinos, A. Panagiotou, I.
Papavergou0000-0002-7992-2686, I. Paraskevas0000-0002-2375-5401, N.
Saoulidou0000-0001-6958-4196, K. Theofilatos0000-0001-8448-883X, E.
Tziaferi0000-0003-4958-0408, K. Vellidis0000-0001-5680-8357, I.
Zisopoulos0000-0001-5212-4353

National Technical University of Athens, Athens, Greece G.
Bakas0000-0003-0287-1937, T. Chatzistavrou, G. Karapostoli0000-0002-4280-2541,
K. Kousouris0000-0002-6360-0869, I. Papakrivopoulos0000-0002-8440-0487, E.
Siamarkou, G. Tsipolitis, A. Zacharopoulou

University of Ioánnina, Ioánnina, Greece K. Adamidis, I. Bestintzanos, I.
Evangelou0000-0002-5903-5481, C. Foudas, P. Gianneios0009-0003-7233-0738, C.
Kamtsikis, P. Katsoulis, P. Kokkas0009-0009-3752-6253, P.G. Kosmoglou
Kioseoglou0000-0002-7440-4396, N. Manthos0000-0003-3247-8909, I.
Papadopoulos0000-0002-9937-3063, J. Strologas0000-0002-2225-7160

HUN-REN Wigner Research Centre for Physics, Budapest, Hungary M.
Bartók320000-0002-4440-2701, C. Hajdu0000-0002-7193-800X, D.
Horvath33,340000-0003-0091-477X, F. Sikler0000-0001-9608-3901, V.
Veszpremi0000-0001-9783-0315

MTA-ELTE Lendület CMS Particle and Nuclear Physics Group, Eötvös Loránd
University, Budapest, Hungary M. Csanád0000-0002-3154-6925, K.
Farkas0000-0003-1740-6974, M.M.A. Gadallah350000-0002-8305-6661, Á.
Kadlecsik0000-0001-5559-0106, P. Major0000-0002-5476-0414, K.
Mandal0000-0002-3966-7182, G. Pásztor0000-0003-0707-9762, A.J.
Rádl360000-0001-8810-0388, G.I. Veres0000-0002-5440-4356

Faculty of Informatics, University of Debrecen, Debrecen, Hungary P. Raics, B.
Ujvari370000-0003-0498-4265, G. Zilizi0000-0002-0480-0000

Institute of Nuclear Research ATOMKI, Debrecen, Hungary G. Bencze, S. Czellar,
J. Karancsi320000-0003-0802-7665, J. Molnar, Z. Szillasi

Karoly Robert Campus, MATE Institute of Technology, Gyongyos, Hungary T.
Csorgo360000-0002-9110-9663, F. Nemes360000-0002-1451-6484, T.
Novak0000-0001-6253-4356

Panjab University, Chandigarh, India J. Babbar0000-0002-4080-4156, S.
Bansal0000-0003-1992-0336, S.B. Beri, V. Bhatnagar0000-0002-8392-9610, G.
Chaudhary0000-0003-0168-3336, S. Chauhan0000-0001-6974-4129, N.
Dhingra380000-0002-7200-6204, R. Gupta, A. Kaur0000-0002-1640-9180, A.
Kaur0000-0003-3609-4777, H. Kaur0000-0002-8659-7092, M.
Kaur0000-0002-3440-2767, S. Kumar0000-0001-9212-9108, P.
Kumari0000-0002-6623-8586, M. Meena0000-0003-4536-3967, K.
Sandeep0000-0002-3220-3668, T. Sheokand, J.B. Singh0000-0001-9029-2462, A.
Singla0000-0003-2550-139X

University of Delhi, Delhi, India A. Ahmed0000-0002-4500-8853, A.
Bhardwaj0000-0002-7544-3258, A. Chhetri0000-0001-7495-1923, B.C.
Choudhary0000-0001-5029-1887, A. Kumar0000-0003-3407-4094, M.
Naimuddin0000-0003-4542-386X, K. Ranjan0000-0002-5540-3750, S.
Saumya0000-0001-7842-9518

Saha Institute of Nuclear Physics, HBNI, Kolkata, India S.
Acharya390009-0001-2997-7523, S. Baradia0000-0001-9860-7262, S.
Barman400000-0001-8891-1674, S. Bhattacharya0000-0002-8110-4957, D. Bhowmik,
S. Dutta0000-0001-9650-8121, S. Dutta, B. Gomber390000-0002-4446-0258, P.
Palit0000-0002-1948-029X, G. Saha0000-0002-6125-1941, B.
Sahu390000-0002-8073-5140, S. Sarkar

Indian Institute of Technology Madras, Madras, India M.M.
Ameen0000-0002-1909-9843, P.K. Behera0000-0002-1527-2266, S.C.
Behera0000-0002-0798-2727, S. Chatterjee0000-0003-0185-9872, P.
Jana0000-0001-5310-5170, P. Kalbhor0000-0002-5892-3743, J.R.
Komaragiri410000-0002-9344-6655, D. Kumar410000-0002-6636-5331, L.
Panwar410000-0003-2461-4907, R. Pradhan0000-0001-7000-6510, P.R.
Pujahari0000-0002-0994-7212, N.R. Saha0000-0002-7954-7898, A.
Sharma0000-0002-0688-923X, A.K. Sikdar0000-0002-5437-5217, S.
Verma0000-0003-1163-6955

Tata Institute of Fundamental Research-A, Mumbai, India T. Aziz, I.
Das0000-0002-5437-2067, S. Dugad, M. Kumar0000-0003-0312-057X, G.B.
Mohanty0000-0001-6850-7666, P. Suryadevara

Tata Institute of Fundamental Research-B, Mumbai, India A.
Bala0000-0003-2565-1718, S. Banerjee0000-0002-7953-4683, R.M. Chatterjee, M.
Guchait0009-0004-0928-7922, S. Karmakar0000-0001-9715-5663, S.
Kumar0000-0002-2405-915X, G. Majumder0000-0002-3815-5222, K.
Mazumdar0000-0003-3136-1653, S. Mukherjee0000-0003-3122-0594, A.
Thachayath0000-0001-6545-0350

National Institute of Science Education and Research, An OCC of Homi Bhabha
National Institute, Bhubaneswar, Odisha, India S.
Bahinipati420000-0002-3744-5332, A.K. Das, C. Kar0000-0002-6407-6974, D.
Maity430000-0002-1989-6703, P. Mal0000-0002-0870-8420, T.
Mishra0000-0002-2121-3932, V.K. Muraleedharan Nair
Bindhu430000-0003-4671-815X, K. Naskar430000-0003-0638-4378, A.
Nayak430000-0002-7716-4981, P. Sadangi, P. Saha0000-0002-7013-8094, S.K.
Swain0000-0001-6871-3937, S. Varghese430009-0000-1318-8266, D.
Vats430009-0007-8224-4664

Indian Institute of Science Education and Research (IISER), Pune, India A.
Alpana0000-0003-3294-2345, S. Dube0000-0002-5145-3777, B.
Kansal0000-0002-6604-1011, A. Laha0000-0001-9440-7028, A.
Rastogi0000-0003-1245-6710, S. Sharma0000-0001-6886-0726

Isfahan University of Technology, Isfahan, Iran H.
Bakhshiansohi440000-0001-5741-3357, E. Khazaie450000-0001-9810-7743, M.
Zeinali460000-0001-8367-6257

Institute for Research in Fundamental Sciences (IPM), Tehran, Iran S.
Chenarani470000-0002-1425-076X, S.M. Etesami0000-0001-6501-4137, M.
Khakzad0000-0002-2212-5715, M. Mohammadi Najafabadi0000-0001-6131-5987

University College Dublin, Dublin, Ireland M. Grunewald0000-0002-5754-0388

INFN Sezione di Baria, Università di Barib, Politecnico di Baric, Bari, Italy
M. Abbresciaa,b0000-0001-8727-7544, R. Alya,c,480000-0001-6808-1335, A.
Colaleoa,b0000-0002-0711-6319, D. Creanzaa,c0000-0001-6153-3044, B.
D’Anzia,b0000-0002-9361-3142, N. De Filippisa,c0000-0002-0625-6811, M. De
Palmaa,b0000-0001-8240-1913, A. Di Florioa,c0000-0003-3719-8041, W.
Elmetenaweea,b,480000-0001-7069-0252, L. Fiorea0000-0002-9470-1320, G.
Iasellia,c0000-0003-2546-5341, G. Maggia,c0000-0001-5391-7689, M.
Maggia0000-0002-8431-3922, I. Margjekaa,b0000-0002-3198-3025, V.
Mastrapasquaa,b0000-0002-9082-5924, S. Mya,b0000-0002-9938-2680, S.
Nuzzoa,b0000-0003-1089-6317, A. Pellecchiaa,b0000-0003-3279-6114, A.
Pompilia,b0000-0003-1291-4005, G. Pugliesea,c0000-0001-5460-2638, R.
Radognaa0000-0002-1094-5038, G. Ramirez-Sancheza,c0000-0001-7804-5514, D.
Ramosa0000-0002-7165-1017, A. Ranieria0000-0001-7912-4062, L.
Silvestrisa0000-0002-8985-4891, F.M. Simonea,b0000-0002-1924-983X, Ü.
Sözbilira0000-0001-6833-3758, A. Stamerraa0000-0003-1434-1968, R.
Vendittia0000-0001-6925-8649, P. Verwilligena0000-0002-9285-8631, A.
Zazaa,b0000-0002-0969-7284

INFN Sezione di Bolognaa, Università di Bolognab, Bologna, Italy G.
Abbiendia0000-0003-4499-7562, C. Battilanaa,b0000-0002-3753-3068, D.
Bonacorsia,b0000-0002-0835-9574, L. Borgonovia0000-0001-8679-4443, R.
Campaninia,b0000-0002-2744-0597, P. Capiluppia,b0000-0003-4485-1897, A.
Castroa,b0000-0003-2527-0456, F.R. Cavalloa0000-0002-0326-7515, M.
Cuffiania,b0000-0003-2510-5039, G.M. Dallavallea0000-0002-8614-0420, T.
Diotalevia,b0000-0003-0780-8785, F. Fabbria0000-0002-8446-9660, A.
Fanfania,b0000-0003-2256-4117, D. Fasanellaa,b0000-0002-2926-2691, P.
Giacomellia0000-0002-6368-7220, L. Giommia,b0000-0003-3539-4313, C.
Grandia0000-0001-5998-3070, L. Guiduccia,b0000-0002-6013-8293, S. Lo
Meoa,490000-0003-3249-9208, L. Lunertia,b0000-0002-8932-0283, S.
Marcellinia0000-0002-1233-8100, G. Masettia0000-0002-6377-800X, F.L.
Navarriaa,b0000-0001-7961-4889, A. Perrottaa0000-0002-7996-7139, F.
Primaveraa,b0000-0001-6253-8656, A.M. Rossia,b0000-0002-5973-1305, G.P.
Sirolia,b0000-0002-3528-4125

INFN Sezione di Cataniaa, Università di Cataniab, Catania, Italy S.
Costaa,b,500000-0001-9919-0569, A. Di Mattiaa0000-0002-9964-015X, R.
Potenzaa,b, A. Tricomia,b,500000-0002-5071-5501, C. Tuvea,b0000-0003-0739-3153

INFN Sezione di Firenzea, Università di Firenzeb, Firenze, Italy G.
Barbaglia0000-0002-1738-8676, G. Bardellia,b0000-0002-4662-3305, B.
Camaiania,b0000-0002-6396-622X, A. Cassesea0000-0003-3010-4516, R.
Ceccarellia0000-0003-3232-9380, V. Ciullia,b0000-0003-1947-3396, C.
Civininia0000-0002-4952-3799, R. D’Alessandroa,b0000-0001-7997-0306, E.
Focardia,b0000-0002-3763-5267, T. Kelloa, G. Latinoa,b0000-0002-4098-3502, P.
Lenzia,b0000-0002-6927-8807, M. Lizzoa0000-0001-7297-2624, M.
Meschinia0000-0002-9161-3990, S. Paolettia0000-0003-3592-9509, A.
Papanastassioua,b, G. Sguazzonia0000-0002-0791-3350, L.
Viliania0000-0002-1909-6343

INFN Laboratori Nazionali di Frascati, Frascati, Italy L.
Benussi0000-0002-2363-8889, S. Bianco0000-0002-8300-4124, S.
Meola510000-0002-8233-7277, D. Piccolo0000-0001-5404-543X

INFN Sezione di Genovaa, Università di Genovab, Genova, Italy P.
Chatagnona0000-0002-4705-9582, F. Ferroa0000-0002-7663-0805, E.
Robuttia0000-0001-9038-4500, S. Tosia,b0000-0002-7275-9193

INFN Sezione di Milano-Bicoccaa, Università di Milano-Bicoccab, Milano, Italy
A. Benagliaa0000-0003-1124-8450, G. Boldrinia0000-0001-5490-605X, F.
Brivioa0000-0001-9523-6451, F. Cetorellia0000-0002-3061-1553, F. De
Guioa,b0000-0001-5927-8865, M.E. Dinardoa,b0000-0002-8575-7250, P.
Dinia0000-0001-7375-4899, S. Gennaia0000-0001-5269-8517, A.
Ghezzia,b0000-0002-8184-7953, P. Govonia,b0000-0002-0227-1301, L.
Guzzia0000-0002-3086-8260, M.T. Lucchinia,b0000-0002-7497-7450, M.
Malbertia0000-0001-6794-8419, S. Malvezzia0000-0002-0218-4910, A.
Massironia0000-0002-0782-0883, D. Menascea0000-0002-9918-1686, L.
Moronia0000-0002-8387-762X, M. Paganonia,b0000-0003-2461-275X, D.
Pedrinia0000-0003-2414-4175, B.S. Pinolinia, S. Ragazzia,b0000-0001-8219-2074,
N. Redaellia0000-0002-0098-2716, T. Tabarelli de Fatisa,b0000-0001-6262-4685,
D. Zuoloa0000-0003-3072-1020

INFN Sezione di Napolia, Università di Napoli ’Federico II’b, Napoli, Italy;
Università della Basilicatac, Potenza, Italy; Scuola Superiore Meridionale
(SSM)d, Napoli, Italy S. Buontempoa0000-0001-9526-556X, A.
Cagnottaa,b0000-0002-8801-9894, F. Carnevalia,b, N.
Cavalloa,c0000-0003-1327-9058, A. De Iorioa,b0000-0002-9258-1345, F.
Fabozzia,c0000-0001-9821-4151, A.O.M. Iorioa,b0000-0002-3798-1135, L.
Listaa,b,520000-0001-6471-5492, P. Paoluccia,310000-0002-8773-4781, B.
Rossia0000-0002-0807-8772, C. Sciaccaa,b0000-0002-8412-4072

INFN Sezione di Padovaa, Università di Padovab, Padova, Italy; Università di
Trentoc, Trento, Italy R. Ardinoa0000-0001-8348-2962, P.
Azzia0000-0002-3129-828X, N. Bacchettaa,530000-0002-2205-5737, D.
Biselloa,b0000-0002-2359-8477, P. Bortignona0000-0002-5360-1454, A.
Bragagnoloa,b0000-0003-3474-2099, R. Carlina,b0000-0001-7915-1650, T.
Dorigoa0000-0002-1659-8727, F. Gasparinia,b0000-0002-1315-563X, U.
Gasparinia,b0000-0002-7253-2669, A. Gozzelinoa0000-0002-6284-1126, G. Grossoa,
M. Gulminia,540000-0003-4198-4336, L. Layera,55, E.
Lusiania0000-0001-8791-7978, M. Margonia,b0000-0003-1797-4330, A.T.
Meneguzzoa,b0000-0002-5861-8140, M. Migliorinia,b0000-0002-5441-7755, J.
Pazzinia,b0000-0002-1118-6205, P. Ronchesea,b0000-0001-7002-2051, R.
Rossina,b0000-0003-3466-7500, F. Simonettoa,b0000-0002-8279-2464, G.
Stronga0000-0002-4640-6108, M. Tosia,b0000-0003-4050-1769, A.
Triossia,b0000-0001-5140-9154, H. Yarara,b, M. Zanettia,b0000-0003-4281-4582,
P. Zottoa,b0000-0003-3953-5996, A. Zucchettaa,b0000-0003-0380-1172, G.
Zumerlea,b0000-0003-3075-2679

INFN Sezione di Paviaa, Università di Paviab, Pavia, Italy S. Abu
Zeida,560000-0002-0820-0483, C. Aimèa,b0000-0003-0449-4717, A.
Braghieria0000-0002-9606-5604, S. Calzaferria,b0000-0002-1162-2505, D.
Fiorinaa,b0000-0002-7104-257X, P. Montagnaa,b0000-0001-9647-9420, V.
Rea0000-0003-0697-3420, C. Riccardia,b0000-0003-0165-3962, P.
Salvinia0000-0001-9207-7256, I. Vaia,b0000-0003-0037-5032, P.
Vituloa,b0000-0001-9247-7778

INFN Sezione di Perugiaa, Università di Perugiab, Perugia, Italy S.
Ajmala,b0000-0002-2726-2858, P. Asenova,570000-0003-2379-9903, G.M.
Bileia0000-0002-4159-9123, D. Ciangottinia,b0000-0002-0843-4108, L.
Fanòa,b0000-0002-9007-629X, M. Magherinia,b0000-0003-4108-3925, G.
Mantovania,b, V. Mariania,b0000-0001-7108-8116, M.
Menichellia0000-0002-9004-735X, F. Moscatellia,570000-0002-7676-3106, A.
Piccinellia,b0000-0003-0386-0527, M. Presillaa,b0000-0003-2808-7315, A.
Rossia,b0000-0002-2031-2955, A. Santocchiaa,b0000-0002-9770-2249, D.
Spigaa0000-0002-2991-6384, T. Tedeschia,b0000-0002-7125-2905

INFN Sezione di Pisaa, Università di Pisab, Scuola Normale Superiore di Pisac,
Pisa, Italy; Università di Sienad, Siena, Italy P.
Azzurria0000-0002-1717-5654, G. Bagliesia0000-0003-4298-1620, R.
Bhattacharyaa0000-0002-7575-8639, L. Bianchinia,b0000-0002-6598-6865, T.
Boccalia0000-0002-9930-9299, E. Bossinia0000-0002-2303-2588, D.
Bruschinia,c0000-0001-7248-2967, R. Castaldia0000-0003-0146-845X, M.A.
Cioccia,b0000-0003-0002-5462, M. Cipriania,b0000-0002-0151-4439, V.
D’Amantea,d0000-0002-7342-2592, R. Dell’Orsoa0000-0003-1414-9343, S.
Donatoa0000-0001-7646-4977, A. Giassia0000-0001-9428-2296, F.
Ligabuea,c0000-0002-1549-7107, D. Matos Figueiredoa0000-0003-2514-6930, A.
Messineoa,b0000-0001-7551-5613, M. Musicha,b0000-0001-7938-5684, F.
Pallaa0000-0002-6361-438X, S. Paroliaa0000-0002-9566-2490, A.
Rizzia,b0000-0002-4543-2718, G. Rolandia,c0000-0002-0635-274X, S. Roy
Chowdhurya0000-0001-5742-5593, T. Sarkara0000-0003-0582-4167, A.
Scribanoa0000-0002-4338-6332, P. Spagnoloa0000-0001-7962-5203, R.
Tenchinia0000-0003-2574-4383, G. Tonellia,b0000-0003-2606-9156, N.
Turinia,d0000-0002-9395-5230, A. Venturia0000-0002-0249-4142, P.G.
Verdinia0000-0002-0042-9507

INFN Sezione di Romaa, Sapienza Università di Romab, Roma, Italy P.
Barriaa0000-0002-3924-7380, M. Campanaa,b0000-0001-5425-723X, F.
Cavallaria0000-0002-1061-3877, L. Cunqueiro Mendeza,b0000-0001-6764-5370, D.
Del Rea,b0000-0003-0870-5796, E. Di Marcoa0000-0002-5920-2438, M.
Diemoza0000-0002-3810-8530, F. Erricoa,b0000-0001-8199-370X, E.
Longoa,b0000-0001-6238-6787, P. Meridiania0000-0002-8480-2259, J.
Mijuskovica,b0009-0009-1589-9980, G. Organtinia,b0000-0002-3229-0781, F.
Pandolfia0000-0001-8713-3874, R. Paramattia,b0000-0002-0080-9550, C.
Quarantaa,b0000-0002-0042-6891, S. Rahatloua,b0000-0001-9794-3360, C.
Rovellia0000-0003-2173-7530, F. Santanastasioa,b0000-0003-2505-8359, L.
Soffia0000-0003-2532-9876, R. Tramontanoa,b0000-0001-5979-5299

INFN Sezione di Torinoa, Università di Torinob, Torino, Italy; Università del
Piemonte Orientalec, Novara, Italy N. Amapanea,b0000-0001-9449-2509, R.