2022 011 24 January

Charged-particle jets in pp collisions at $\sqrt{s}=13\,\mathrm{TeV}$

ALICE Collaboration††thanks: See Appendix B for the list of collaboration
members ALICE Collaboration

The multiplicity dependence of jet production in pp collisions at the centre-
of-mass energy of $\sqrt{s}=13\ \mathrm{TeV}$ is studied for the first time.
Jets are reconstructed from charged particles using the anti-$k_{\mathrm{T}}$
algorithm with resolution parameters $R$ varying from $0.2$ to $0.7$. The jets
are measured in the pseudorapidity range $|\eta_{\rm jet}|<0.9-R$ and in the
transverse momentum range $5<p_{\mathrm{T,jet}}^{\rm ch}<140\ \mathrm{GeV}/c$.
The multiplicity intervals are categorised by the ALICE forward detector V0.
The $p_{\mathrm{T}}$ differential cross section of charged-particle jets are
compared to leading order (LO) and next-to-leading order (NLO) perturbative
quantum chromodynamics (pQCD) calculations. It is found that the data are
better described by the NLO calculation, although the NLO prediction
overestimates the jet cross section below $20\ \mathrm{GeV}/c$. The cross
section ratios for different $R$ are also measured and compared to model
calculations. These measurements provide insights into the angular dependence
of jet fragmentation. The jet yield increases with increasing self-normalised
charged-particle multiplicity. This increase shows only a weak dependence on
jet transverse momentum and resolution parameter at the highest multiplicity.
While such behaviour is qualitatively described by the present version of
PYTHIA, quantitative description may require implementing new mechanisms for
multi-particle production in hadronic collisions.

##  1 Introduction

Jets, as sprays of collimated hadrons resulting from fragmentation of high-
energy partons produced in hard scatterings, are multipurpose tools to explore
various properties of the strong interaction, via measurements of the strong
coupling constant [1, 2], heavy-flavour production [3], and the global fit
analysis of Parton Distribution Functions (PDF) [4]. Jet processes are also
pivotal to address fundamental questions such as the validity of factorisation
theorems [5, 6, 7], or existence of gluon saturation due to nonlinear QCD
dynamics [8]. Jets, produced abundantly at LHC energies due to the large
centre-of-mass energy and high luminosity, provide high precision tests of QCD
[9, 10, 11, 12]. Moreover, measuring the “jet quenching” phenomenon [13]
observed for jets produced in heavy-ion collisions offers an insight into how
high-momentum partons interact with the medium created in the collisions.
Through this interaction one probes QCD at high energy densities and
temperatures, where the strongly-interacting matter enters the guark–gluon
plasma (QGP) phase. The observed properties of this matter are consistent with
a strongly-coupled, low-viscosity fluid of quarks and gluons [14, 15].

Recent measurements in high-multiplicity pp and pA collisions [16] exhibit
several collective effects qualitatively similar to the ones observed in AA
collisions for various observables. Such collective behaviour encompasses
long-range ($\lvert\Delta\eta\rvert>2$) near-side
($\lvert\Delta\varphi\rvert\approx 0$) two-particle angular correlations,
known as the “ridge” [17, 18, 19, 20, 21]; enhanced yield of charged- or
identified-particle production in high-multiplicity events with respect to the
reference using minimum-bias (MB) charged- or pion-particle production [22,
23, 24, 25, 26]; elliptic flow of heavy-flavour hadrons [27]; and enhanced
baryon production at intermediate transverse momentum ($p_{\mathrm{T}}\sim 3\
\mathrm{GeV}/c$) [28]. With the lack of experimental observations of jet
quenching effect with present accuracy in small collision systems [29, 30],
the measurements aforementioned raise the difficult but intriguing question of
whether these observations arise similarly to heavy-ion collisions, namely
from the formation of a hot and dense fluid-like medium, or rather involve
other physical mechanisms [31, 32]. Several theoretical approaches and models
have been put forward to explain these QGP-like effects in small systems while
accounting for the absence of jet quenching [33, 34, 35, 36, 37], such as
multiple parton interactions (MPI) [38], string shoving [39], or rope
hadronisation [40]. However, these models cannot explain the measured non-zero
elliptic flow at high $p_{\mathrm{T}}$ from two-particle correlations [19],
which is usually attributed to in-medium path-length dependent energy loss
[41, 42, 43].

To deepen our understanding of the mechanisms that are at play in high-
multiplicity collisions of small systems, the multiplicity dependence of the
charged-jet production has been studied in pp collisions at a centre-of-mass
energy $\sqrt{s}=13\ \mathrm{TeV}$ by ALICE. Charged-particle jets are
reconstructed from tracks measured at midrapidity using the
anti-$k_{\mathrm{T}}$ clustering algorithm [44] with jet resolution parameters
$R$ ranging from $0.2$ to $0.7$. The measured inclusive jet cross sections are
compared to model calculations, allowing us to test the relative importance of
various mechanisms at play in particular hadronisation and MPI to which the
lowest transverse momentum jets are most sensitive.

The event activity is quantified by the charged-particle multiplicity measured
by the ALICE V0 detector at forward rapidity, in order to minimise the
autocorrelations between the event selection and the measured observable. By
taking advantage of the largest integrated luminosity collected so far by the
ALICE experiment, this work extends previous measurements [12, 45, 9] to
higher collision energy, broader jet kinematic range, larger jet radii (up to
$R=0.7$), and higher event activities. A complementary insight is thereby
provided to similar CMS [46] and ALICE measurements focusing on the soft
sector based on transverse spherocity [47] and two-particle correlations [48].
Thanks to these new measurements, stronger constraints are placed on models
that describe fundamental mechanisms of particle production in hadronic
collisions.

The results presented in this article test whether the seemingly universal
pattern of the self-normalised production of hard probes as a function of
event activity, emerging from the ALICE measurements of $\mathrm{J/\psi}$ [49,
50, 51], $\rm D$ [52], and $\rm B$-meson production [53], holds also for jets.
While this self-normalised hard probe production pattern could be ascribed to
mere collision geometry up to a certain multiplicity, a new regime of high-
density gluon configurations is expected to set in at the highest
multiplicities [54].

The article is organised as follows: Sec. 2 describes the ALICE detectors, the
experimental data samples, and Monte-Carlo simulations used for this analysis;
Sec. 3 discusses the multiplicity selection and the jet reconstruction
methods; Sec. 4 outlines the unfolding corrections and the estimation of the
systematic uncertainties; Sec. 5 presents the results; and finally, Sec. 6
gives a summary and outlook.

##  2 Experimental setup and data sample

ALICE is the dedicated heavy-ion experiment at the LHC. A detailed description
of the ALICE apparatus can be found in Ref. [55]. In the following, only the
detector components used in the data analysis presented in this article are
described.

The ALICE apparatus comprises a central barrel (pseudorapidity coverage
$|\eta|<0.9$ over the full azimuth) situated in a uniform $0.5\ \mathrm{T}$
magnetic field along the beam axis ($z$), which is supplied by the large L3
solenoid magnet [56]. The central barrel contains a set of tracking detectors:
a six-layer silicon Inner Tracking System (ITS) surrounding the beam pipe, and
a large-volume ($5\ \mathrm{m}$ length, $0.85\ \mathrm{m}$ inner radius and
$2.8\ \mathrm{m}$ outer radius) cylindrical Time Projection Chamber (TPC). The
first two layers of the ITS are instrumented with high-granularity Silicon
Pixel Detectors (SPD), followed by two layers composed of Silicon Drift
Detectors (SDD), and finally, the two outer layers are made of double-sided
Silicon micro-Strip Detectors (SSD). In the forward and backward rapidity
regions, a pair of plastic scintillator counters called V0A and V0C are
positioned on each side of the interaction point, covering pseudorapidity
ranges ${2.8<\eta<5.1}$ and ${-3.7<\eta<-1.7}$, respectively. The V0 system
provides the interaction trigger for the whole experiment, and is further used
to suppress machine-induced background events [57].

The measurement was based on the data from pp collisions at a centre-of-mass
energy of $\sqrt{s}=13~{}\,\mathrm{TeV}$ collected between 2016 and 2018.
During this period, MB events were selected online using the high purity
V0-based MB trigger [58], which required a charged-particle signal coincidence
in the V0A and V0C arrays. The visible cross section satisfying the MB trigger
requirement was determined in a van der Meer scan [59, 60]. The integrated
luminosity of the used sample, measured with V0, is $8.12\pm 0.16~{}\rm
nb^{-1}$ for 2016, $10.67\pm 0.29~{}\rm nb^{-1}$ for 2017, and $13.14\pm
0.27~{}\rm nb^{-1}$ for 2018, respectively. The luminosity uncertainty was
evaluated to be 1.6 % by taking into account the correlations during the
combination of the samples [61]. For the offline analysis, further event
selection was made by requiring a primary vertex position within $\pm 10\
\mathrm{cm}$ in the longitudinal direction around the nominal interaction
point to ensure full geometrical acceptance in the ITS for ${|\eta|<0.9}$.
Pile up, i.e. the average number of simultaneous interactions per bunch
crossing, was maintained well below unity through beam separation in the
horizontal plane. Residual pile-up events were rejected based on a multiple
vertex finding algorithm using tracking information from the SPD. The final
corresponding data sample consists of $2.2\times 10^{9}$ events after the
trigger and offline selection.

Reconstructed tracks with transverse momenta larger than $0.15\
\mathrm{GeV}/c$ were selected in the analysis. The track selection criteria
was optimised for good momentum resolution and minimal contamination from
secondary particles, as described in Refs. [12, 11]. To ensure a uniform
$(\eta,\varphi)$ distribution in the regions where the SPD was inactive,
tracks with no hit in either of the two SPD layers were constrained to the
primary vertex. The tracking efficiency estimated from a full detector
simulation amounts to $80\%$ for $p_{\mathrm{T}}>0.4\ \mathrm{GeV}/c$,
decreasing to $60\%$ at $0.15\ \mathrm{GeV}/c$. The transverse momentum
resolution is better than $3\%$ for tracks with $p_{\mathrm{T}}$ below $1\
\mathrm{GeV}/c$, and increases linearly up to $10\%$ at $p_{\mathrm{T}}=100\
\mathrm{GeV}/c$.

The response of the ALICE detector to produced particles was evaluated using
GEANT3 [62]. Based on this response, measured distributions were corrected for
instrumental effects, see Sec. 4.1. In this paper, the default Monte Carlo
(MC) event generator used for comparison with measurements is the PYTHIA 8.125
general-purpose Leading Order (LO) MC generator (hereafter referred to as
PYTHIA8) with the Monash-2013 set of tuned parameters (tune) [63] for the
underlying event (UE) and NNPDF2.3 LO PDF set [64], while MPI and Colour
Reconnection (CR) models being enabled. Furthermore, in order to reduce the
large theoretical uncertainties affecting the computations at LO in
perturbative QCD, like the residual dependence of the unphysical factorisation
and renormalisation scales, jet production at Next-to-Leading Order (NLO)
accuracy was obtained within the POWHEG framework [65]. Unlike pure fixed
order calculations, POWHEG interfaces NLO calculations with PYTHIA8 parton
showers to generate exclusive final states. The particle level outputs of such
simulations were then directly compared with the experimental data, which were
corrected for instrumental effects.

##  3 Multiplicity selection and jet reconstruction

###  3.1 Multiplicity selection

In order to study the multiplicity dependence of inclusive charged-particle
jet production, the MB sample was divided into event classes based on the “V0M
amplitude” that is proportional to the total number of charged particles
passing through the V0A and V0C detectors. The distribution of the self-
normalised V0M amplitude from data and the PYTHIA8 event generator is shown in
Fig. 1. The distribution is normalised to its average value, $\left\langle\rm
V0M~{}amplitude\right\rangle$, to reduce the sensitivity of the multiplicity
percentile determination on the amplitude. PYTHIA8 MC does not reproduce the
measured multiplicity distribution, as was already reported in Ref. [66]. To
reduce the potential model-dependent bias, corrections of the multiplicity
dependent jet yields were done using a data-driven method instead of pure MC
samples, which is discussed in Sec. 4.1.

Figure 1: Scaled V0M distribution which is used to determine the forward
multiplicity classes in pp collisions at $\sqrt{s}$ = 13 TeV. The colour
shaded areas represent V0M multiplicity classes obtained from real data. The
PYTHIA8 distribution is shown with the open black markers.

The event classes used in the analysis and the corresponding midrapidity
charged-particle densities for experimental data are summarised in Table 1.
The multiplicity classes were defined in terms of percentile intervals of
experimental V0M amplitude
$/\left\langle\mathrm{V0M~{}amplitude}\right\rangle$ as shown in Fig. 1. The
average charged-particle multiplicity densities in MB pp collisions and for
events of a given multiplicity class were obtained by integrating the
corresponding fully corrected $p_{\mathrm{T}}$ spectra given in Ref. [66].
When comparing the data to MC predictions, the multiplicity percentile was
calculated from data and MC using their respective self-normalised
distribution accordingly in order to minimise the difference observed in the
V0M amplitude distribution. The 0 – 1% range corresponds to the highest
multiplicity class (1), while the 60 – 100% interval corresponds to the lowest
multiplicity class (8).

Table 1: Average charged-particle pseudorapidity densities at midrapidity $\left\langle\mathrm{d}N_{\rm ch}/\mathrm{d}\eta\right\rangle$ from data for inclusive events and different V0M multiplicity classes [66]. Class | V0M percentile | V0M amplitude $/\left\langle\mathrm{V0M~{}amplitude}\right\rangle$ | $\left\langle\mathrm{d}N_{\rm ch}/\mathrm{d}\eta\right\rangle_{\left|\eta\right|<1}$
---|---|---|---
MB | 0–100% |  |  $6.93$ $\pm$ $0.09$
1 | 0–1% | $\geq 3.66$ |  $26.01$ $\pm$ $0.34$
2 | 1–5% | 2.68–3.66 |  $19.99$ $\pm$ $0.24$
3 | 5–10% | 2.15–2.68 |  $16.18$ $\pm$ $0.20$
4 | 10–15% | 1.84–2.15 |  $13.78$ $\pm$ $0.18$
5 | 15–20% | 1.59–1.84 |  $12.01$ $\pm$ $0.16$
6 | 20–40% | 0.97–1.59 |  $9.18$ $\pm$ $0.10$
7 | 40–60% | 0.59–0.97 |  $5.78$ $\pm$ $0.06$
8 | 60–100% | 0–0.59 |  $2.94$ $\pm$ $0.03$

###  3.2 Jet reconstruction

Jets were reconstructed from tracks with $p_{\rm T,track}>0.15\
\mathrm{GeV}/c$ and $\left|\eta_{\rm track}\right|<0.9$, using the
anti-$k_{\rm T}$ sequential recombination algorithm [44] from the FastJet
package [67]. The jet transverse momenta were calculated using boost-invariant
$p_{\rm T}$ recombination scheme as a scalar sum of their constituent
transverse momenta. Jet resolution parameters were varied in the range from
$R=0.2$ to $0.7$. The pseudorapidity of the reconstructed jets was limited to
$\left|\eta_{\rm jet}\right|<0.9-R$ to ensure they remain in the fiducial
acceptance [68]. The transverse momentum range of the inclusive charged-
particle jet spectra spans from $5$ to $140\ \mathrm{GeV}/c$. The spectra
measured in V0M multiplicity classes have the upper limit $100\
\mathrm{GeV}/c$. The cross section of inclusive jet production was measured as
a function of $p_{\mathrm{T}}$ considering the van der Meer minimum bias
visible cross section mentioned in Sec. 2. For the multiplicity dependence
study, the per-event jet yield was measured as a function of multiplicity
classes defined by the V0M percentile intervals. In addition, the integrated
jet yield was calculated as a function of the charged-particle density
$\mathrm{d}N_{\rm ch}/\mathrm{d}\eta$, self-normalised similarly to other
ALICE measurements [49, 50, 51, 52, 53].

The measured jets are inevitably affected by the UE activity originating from
MPI, fragmentation of beam remnants, as well as initial- and final-state
radiation [69]. In pp collisions, the UE effect on jet measurements is rather
limited [12]. However, since the UE contribution depends on event
multiplicity, the measured jets were not affected in the same way for events
falling in different multiplicity classes. In order to perform fair
comparisons between different multiplicity intervals, the results presented in
this paper include the UE subtraction.

The UE contribution to the charged-particle jet $p_{\mathrm{T}}$ was estimated
event-by-event using the same approach as in previous measurements in pp [70]
and p–Pb collisions [29, 30]. The background density $\rho_{\rm ch}$ was
determined using the $k_{\rm T}$ algorithm [71] with a fixed radius of 0.2,
taking into account only jets containing at least one physical particle, while
removing the two $k_{\rm T}$ clusters of highest transverse momentum to limit
the impact of the jet signal on the underlying event estimation. The
background density $\rho_{\rm ch}$ is then used to subtract the average
background from each jet in the same event: $p_{\rm T}^{\rm corr}=p_{\rm
T}^{\rm raw}-\rho_{\rm ch}\cdot A$, where $A$ is the jet area.

During the subtraction of the average UE background of each jet, the local
background fluctuations smear the reconstructed jet transverse momentum. To
study jet-by-jet fluctuations of the background, the Random Cone (RC) method
was used [72]. In this method, cones of radius $R$ positioned at random
($\eta,\varphi$) coordinates within the detector acceptance (fiducial region)
were generated in each event. The sum of the charged-particle $p_{\rm T}$ in a
given cone was then compared to the expected average background obtained from
$\rho_{\rm ch}$ as follows:

$\delta p_{\rm T}^{\rm RC}=\sum^{\rm RC}p_{\rm T,track}-\rho_{\rm ch}\pi
R^{2},$ (1)

where the sum runs over track $p_{\rm T}$ inside the random cone, and $\pi
R^{2}$ is the area of the random cone. The width of $\delta p_{\rm T}^{\rm
RC}$ is a measure of the momentum smearing due to local background
fluctuations [73]. To minimise the influence of signal jets on the $\delta
p_{\rm T}^{\rm RC}$ distribution, a minimum distance from the random cone to
the two highest momentum jets (leading jets) in the event was required. The
$\delta p_{\rm T}^{\rm RC}$ distribution, obtained for different cone radii
$R$ in events with excluded leading jets, are shown in Fig. 2 a). It clearly
shows stronger background fluctuations with increasing jet radius, as expected
due to the larger number of particles within the jet cone.

An alternative embedding method was used to quantify the background
fluctuations. In this procedure, a probe track was embedded into an event
[74]. The azimuthal angle of the probe track was required to be perpendicular
to the jet ($\varphi_{\rm track}^{\rm emb}=\varphi_{\rm ch\,jet}+\pi/2$) while
retaining its $\eta$ value ($\eta_{\rm track}^{\rm emb}=\eta_{\rm ch\,jet}$).
The transverse momentum of the probe track ($p_{\rm T}^{\rm emb}$) was
uniformly chosen between $0$ and $100\ \mathrm{GeV}/c$. After embedding the
probe track into the event, the jet finding algorithm was relaunched with the
same background subtraction method as described above. The embedded $\delta
p_{\rm T}^{\rm emb}$ was evaluated in a similar way to Eq. 1 after removing
the momentum of the embedded probe track:

$\delta p_{\rm T}^{\rm emb}=p_{\rm T,ch\,jet}^{\rm raw,emb}-\rho_{\rm
ch}A_{\rm ch\,jet}^{\rm emb}-p_{\rm T}^{\rm emb},$ (2)

where $p_{\rm T,ch\,jet}^{\rm raw,emb}$ and $A_{\rm ch\,jet}^{\rm emb}$ are
the transverse momentum and area of the reconstructed jet with the embedded
probe track.

The background fluctuations determined by the random cone and the track
embedding method are presented in Fig. 2 b). While the distributions obtained
from the different methods show very similar negative tails, the tail on the
right-hand side of the distribution caused by real jets is much less
pronounced when a minimum distance to two leading jets is required. Therefore,
the $\delta p_{\rm T}$ distribution from the RC method without two leading
jets was used as default to build up the background fluctuation response,
while the track embedding method was used for the assessment of the systematic
uncertainty on the background fluctuation estimate. Figure 2 c) compares the
$\delta p_{\rm T}$ distribution in different multiplicity intervals with the
RC method when avoiding that the cone overlaps with the two leading jets. The
figure suggests that the magnitude of local background fluctuations grows with
imposed multiplicity bias, as expected.

Figure 2: a) Comparison of the $\delta p_{\rm T}$ distribution obtained for
different random cone radii ($R=0.2,0.4,0.7$). b) Comparison of the $\delta
p_{\rm T}$ distribution with the RC method (including and excluding two
leading jets) and the track embedding approach for $R=0.4$. c) Comparison of
measured $\delta p_{\rm T}$ distribution using RC method without leading jets
for $R=0.4$ in different multiplicity classes .

##  4 Corrections and systematic uncertainties

The differential charged-particle jet cross section after UE subtraction was
corrected for jet energy scale smearing due to local background fluctuations
and detector effects. The resulting cross section unfolded to charged particle
level allows for a direct comparison with the theoretical predictions. These
unfolding correction approaches are explained in Sec. 4.1. The corresponding
systematic uncertainties are presented in Sec. 4.2.

###  4.1 Unfolding corrections

The measured jet momentum is affected by background fluctuations and a variety
of instrumental effects, including finite momentum resolution and track
reconstruction efficiency. The jet spectrum was corrected for these effects to
obtain the particle-level jet spectrum through an unfolding procedure [72].
First, the particle-level true jets were constructed from the PYTHIA8 (Monash
2013) event generator [63], by selecting only those stable charged particles
defined as all particles with a mean proper lifetime larger than $1\
\mathrm{cm}/c$, and excluding the decay products of these particles [75].
Next, jets were reconstructed at detector level from tracks coming from MC
particles propagated through the GEANT3 model of the ALICE setup. The
corresponding jet energy scale residual and resolution were estimated to be
about $20$% for jet transverse momentum larger than $10~{}\mathrm{GeV}/c$ with
jet resolution parameter $R=0.4$.

Based on the geometrical matching between the corresponding jets at the
particle level and detector level, the detector level response matrix was
constructed. The response matrix employed in the unfolding procedure was a
combination of the detector response matrix and the background fluctuation
response matrix. The background fluctuation response matrix utilises the
$\delta p_{\rm T}$ distribution obtained from data, based on distributions
shown in Fig. 2. This data-driven approach ensures that the response matrix
used for unfolding reflects the accurate multiplicity dependence. Finally, the
measured jet spectrum was unfolded using the combined response matrix which
corrects for background fluctuations as well as detector effects.

In this analysis, the default unfolding method was based on the Singular Value
Decomposition (SVD) approach as implemented in the RooUnfold package [76]. The
regularisation parameter $k$, which suppresses high-frequency variations in
the unfolded result, was selected by examining the $d$-vector distribution
[77]. In addition to the SVD unfolding, Bayesian unfolding [78] was also used
for systematic uncertainty evaluation. Consistent results were obtained
between both unfolding methods. To validate the unfolding process and identify
potential biases, closure tests that compare the unfolded distributions to the
particle-level true distributions were performed. The consistency of the
unfolding procedure was also checked by folding the solution to detector level
and comparing it to the measured raw spectrum. In both cases, no significant
difference was found.

###  4.2 Systematic uncertainties

The sources of systematic uncertainty that affect the jet measurement were
divided into the following categories: tracking efficiency and $p_{\rm T}$
resolution, unfolding corrections, background fluctuations, contamination from
secondary particles and normalisation. Additionally, in the case of
multiplicity dependent measurements, a systematic uncertainty due to
multiplicity estimation was also considered. All uncertainties from these
sources were considered as uncorrelated, except the uncertainties of the
unfolding corrections that come from several correlated sources. Therefore,
the uncertainty of the unfolding category is calculated by varying each source
and calculating the RMS of all variations. Then, all systematic uncertainty
categories were treated separately and their respective contributions we added
in quadrature.

Table 2 summarises the contributions to the systematic uncertainties for the
inclusive jet cross section in a few selected jet $p_{\rm T}$ and $R$ bins.
Table 3 summarises the systematic uncertainties for multiplicity-dependent jet
production in a few selected jet $p_{\rm T}$ and multiplicity intervals for a
jet reconstruction resolution parameter of $R=0.4$.

The total systematic uncertainty increases with jet $p_{\rm T}$ and $R$, and
its evolution is similar for all jet radii and multiplicity intervals that are
not listed here. In the following, the individual sources of systematic
uncertainties listed in Table 2 and Table 3 are briefly described.

Table 2: Summary of systematic uncertainties on inclusive jet cross section
for three selected jet transverse momentum bins with different resolution
parameters.

Resolution parameter |  Jet $p_{\mathrm{T}}$ bin (GeV/$c$) |  Tracking efficiency (%) |  Track $p_{\rm T}$ resolution (%) |  Unfolding (%) |  Background fluctuation (%) |  Normalisation (%) |  Secondaries (%) |  Total (%)
---|---|---|---|---|---|---|---|---
$R=0.2$ |  5–6 |  2.6 |  0.2 |  0.3 |  2.1 |  1.6 |  2.2 |  4.5
|  30–40 |  5.7 |  0.3 |  1.7 |  0.3 |  1.6 |  2.2 |  6.6
|  85–100 |  6.9 |  1.0 |  2.6 |  0.2 |  1.6 |  2.5 |  8.1
$R=0.4$ |  5–6 |  4.2 |  0.4 |  0.2 |  5.2 |  1.6 |  1.7 |  7.2
|  30–40 |  7.4 |  0.4 |  3.4 |  2.5 |  1.6 |  2.3 |  9.1
|  85–100 |  8.2 |  0.7 |  4.5 |  1.1 |  1.6 |  2.6 |  10.0
$R=0.7$ |  5–6 |  3.9 |  0.7 |  0.5 |  3.1 |  1.6 |  2.7 |  6.1
|  30–40 |  9.8 |  1.0 |  3.7 |  1.1 |  1.6 |  2.8 |  11.2
|  85–100 |  10.6 |  1.4 |  5.8 |  0.4 |  1.6 |  2.9 |  12.7

Table 3: Summary of systematic uncertainties on jet production for three jet
transverse momentum bins with different multiplicity percentile intervals for
jets with resolution parameter $R=0.4$.

Multiplicity percentile |  Jet $p_{\mathrm{T}}$ bin (GeV/$c$) |  Tracking efficiency (%) |  Track $p_{\rm T}$ resolution (%) |  Unfolding (%) |  Background fluctuation (%) |  Multiplicity determination (%) |  Secondaries (%) |  Total (%)
---|---|---|---|---|---|---|---|---
0–1% |  5–6 |  3.9 |  0.1 |  2.3 |  5.2 |  5.7 |  1.4 |  9.1
|  30–40 |  7.4 |  1.7 |  3.0 |  2.1 |  1.7 |  2.2 |  8.8
|  85–100 |  8.2 |  1.9 |  6.0 |  0.8 |  0.3 |  2.5 |  10.7
10–15% |  5–6 |  4.2 |  0.1 |  1.0 |  5.2 |  5.5 |  1.8 |  8.9
|  30–40 |  7.4 |  1.6 |  4.0 |  1.9 |  0.8 |  2.2 |  9.1
|  85–100 |  8.2 |  1.6 |  5.2 |  0.9 |  0.3 |  2.5 |  10.2
60–100% |  5–6 |  4.5 |  0.1 |  1.0 |  3.2 |  1.9 |  2.0 |  6.3
|  30–40 |  7.6 |  1.3 |  3.6 |  0.6 |  1.6 |  2.4 |  9.0
|  85–100 |  8.2 |  1.3 |  4.9 |  0.2 |  0.4 |  2.6 |  10.0

The dominant source of systematic uncertainty comes from track reconstruction
efficiency since it directly affects the jet energy scale and resolution. The
systematic uncertainty on tracking efficiency was estimated to be 3% based on
variations of the criteria used in the track selection [12]. To evaluate the
effect of this uncertainty on the measured jet spectra, a new detector
response matrix was computed by generating a PYTHIA simulation that accounts
for a 3% reduction of tracking efficiency, and then used in the unfolding
procedure. The difference between the spectra corrected with the default
response matrix and with the response matrix obtained with the decreased
tracking efficiency was taken as a systematic uncertainty. The relative
uncertainty on the jet spectra caused by tracking efficiency increases slowly
with increasing jet $p_{\rm T}$ and has a weak multiplicity dependence.

The relative systematic uncertainty on track momentum resolution was estimated
from the study of the invariant mass distributions of $\Lambda$ and
$\mathrm{K^{0}_{s}}$ as a function of $p_{\mathrm{T}}$ and amounts to 20%
[79]. This track $p_{\mathrm{T}}$ resolution uncertainty was then propagated
to the corrected jet spectra with a similar method as used for the tracking
efficiency uncertainty evaluation. The resulting uncertainty from track
$p_{\mathrm{T}}$ resolution is about 2%.

In order to assign the uncertainty arising from the unfolding corrections,
several variations are considered. By default, the reconstructed jet spectra
were unfolded using a detector response matrix and prior spectrum obtained
based on events generated by the PYTHIA8 generator with the Monash 2013 tune
[63]. The prior spectrum is used as initial guess of the true spectrum. The
dependence on MC event generator was quantified by comparing the spectra
unfolded using the response matrix and prior from the default generator with
those unfolded with response from the EPOS generator with LHC tune [80]. The
resulting uncertainty is of the order of 3%. Second, the SVD unfolding method
[77], as the default approach used in this paper, was regularised by the
choice of parameter $k$ for each cone radius parameter. To estimate the
related systematic uncertainty, the regularisation parameter was varied by
$\pm 2$ around the optimised value. The unfolded results were stable against
regularisation parameter variations, and the corresponding systematic
uncertainty is negligible. To validate the unfolding procedure, the SVD
unfolded spectra were compared with the results obtained with the Bayesian
unfolding method and the remaining differences were taken as an uncertainty.
In addition to the above variations, the bin boundary migration uncertainty
was also evaluated by changing the boundaries of the input spectra and the
response matrix during the unfolding process. The uncertainties discussed
above were then with the RMS calculated for all variations and referred to as
the unfolding systematic uncertainty in Table 2 and Table 3.

The systematic uncertainty due to the background fluctuation estimation was
quantified by comparing unfolded spectra obtained with $\delta p_{\rm T}$
distributions using the method of RC without two leading jets (default) and
the track embedding method as discussed in Sec. 3.2.

The difference between both corrected jet spectra was assigned as background
fluctuation uncertainty. A systematic uncertainty on the background density
$\rho_{\rm ch}$ measurement was estimated to be 5%, resulting in a 2%
uncertainty on the UE-subtracted jet cross section at $p_{\mathrm{T}}=5\
\mathrm{GeV}/c$, and smaller for higher jet transverse momentum. This
uncertainty is highest at low $p_{\mathrm{T,jet}}$ in high multiplicity
events.

By default the multiplicity percentiles were determined from the measured
distribution of V0M amplitude in data as listed in Table 1. As shown in Fig.
1, PYTHIA8 MC cannot reproduce such multiplicity distribution, which is mainly
attributed to a limited description of the UE [81, 70, 69] and inaccurate
description of secondary particles and magnetic field during particle
transport in the detector simulation. To prevent such multiplicity differences
from being propagated as multiplicity dependent results, the unfolding
corrections use the data-driven approach with the background fluctuation
response matrices taken from the corresponding event multiplicity class based
on data directly, see Fig. 2. This matrix was multiplied with the instrumental
matrix obtained from PYTHIA minimum bias events. To account for the
multiplicity estimation uncertainty, a response matrix obtained from pure MC
simulation was also used, where the multiplicity intervals and the background
fluctuations were both extracted from PYTHIA8 generator. The systematic
uncertainty was assigned based on the comparison of the unfolded spectra
obtained from the default analysis and this variation. Such uncertainty
reaches 5.7% for low-$p_{\mathrm{T}}$ jets in the highest multiplicity class,
and decreases in the lower multiplicity percentile intervals. The uncertainty
is independent of the jet $R$ since the multiplicity estimation is at the
event level, and the ratio of jet yields of different $R$ is independent of
multiplicity.

Secondary charged particles are mostly produced by weak decays of strange
particles ($\mathrm{K^{0}_{s}}$, $\Lambda$, etc.), photon conversions,
hadronic interactions in the detector material, and decays of charged pions.
Contamination from such secondary charged particles was significantly reduced
by a requirement on the maximum distance of closest approach (DCA) of the
tracks to the primary vertex. Therefore, the systematic uncertainties due to
secondaries were estimated by varying the DCA threshold of track selection,
resulting in a jet $p_{\mathrm{T}}$ scale uncertainty of 0.5% [9, 45], which
turns into a jet cross section uncertainty of about 3%.

A systematic uncertainty on the integrated luminosity measurement of 2% [61]
was assigned to the inclusive jet cross section measurement as a normalisation
uncertainty which consequently does not affect the ratios of the measured
cross section spectra.

When calculating the systematic uncertainties on the ratios of jet spectra,
each uncertainty source was varied simultaneously both for numerator and
denominator, and the ratio was calculated using the varied spectra. The
resulting difference between the varied spectra and the nominal one is taken
as the uncertainty on the ratio for that given uncertainty source. This
results in a significant reduction of the correlated uncertainties from the
cancellation between the numerator and the denominator [82]. The remaining
relative difference from each source was added in quadrature.

The statistical uncertainties on the jet production ratio were also treated
carefully between numerator and denominator. To avoid the statistical
correlations, the total event sample was divided into two parts for the
calculation of the numerator and denominator, respectively. The resulting
statistical uncertainty on the ratio remains smaller than the systematic
uncertainty.

##  5 Results

###  5.1 Inclusive jet cross section measurements

The fully-corrected inclusive charged-particle jet cross sections after UE
subtraction in pp collisions at $\sqrt{s}=13~{}\mathrm{TeV}$ are shown in Fig.
3 as a function of jet $p_{\mathrm{T}}$ for jet resolution parameters ranging
from $R=0.2$ to $R=0.7$ and pseudorapidity ranges $|\eta_{\rm jet}|<0.9-R$.
The choice of $R$ changes the relative strength of perturbative and non-
perturbative (hadronisation and UE) effects on the jet transverse momentum
distribution [83]. To be consistent with the multiplicity dependent results,
all figures presented hereafter are obtained with UE subtraction, while the
same measurements without UE subtraction are listed in Appendix A.1.

Figure 3: Inclusive charged-particle jet cross sections in pp collisions at
$\sqrt{s}=13$ TeV using the anti-$k_{\rm T}$ algorithm for different jet
resolution parameters $R$ from $0.2$ to $0.7$, with UE subtraction.
Statistical uncertainties are displayed as vertical error bars. The total
systematic uncertainties are shown as solid boxes around the data points.

Figure 4 compares the inclusive charged-particle jet cross sections with
predictions from the PYTHIA8 and POWHEG MC event generators after UE
subtraction, with the same selections and background subtraction procedure
applied. The ratios of the MC simulations to ALICE data are shown in the
bottom panels of Fig. 4. The POWHEG MC provides a better description of the
data within uncertainties for $p_{\mathrm{T,jet}}^{\rm ch}\gtrsim 20\
\mathrm{GeV}/c$. Nevertheless, large deviations occur for jet transverse
momenta below $20\ \mathrm{GeV}/c$ where POWHEG overestimates the data. Such
deviation increases with the jet $R$. A similar enhancement of POWHEG with
respect to the data is also observed at 7 TeV [9], where the implementation of
MPI in PYTHIA shows a significant effect on the low $p_{\mathrm{T}}$ jet yield
when coupled with POWHEG.

Figure 4: Inclusive charged-particle jet cross sections in pp collisions at
$\sqrt{s}=13$ TeV with UE subtraction. Data for different jet resolution
parameters $R$ varied from $0.2$ to $0.7$ are compared to LO and NLO MC
predictions. The statistical uncertainties are displayed as vertical error
bars. The systematic uncertainties on the data are indicated by shaded boxes
in the top panels and shaded bands drawn around unity in the bottom panels.
The red lines in the ratio correspond to unity.

Figure 5 shows the inclusive jet cross section ratios for jets reconstructed
with a resolution parameter of $R=0.2$ to other resolution parameters $R=0.3$
to $0.7$. The observable defined by the ratio of inclusive jet cross sections
relates directly to the relative difference between jet $p_{\mathrm{T}}$
distributions when using different resolution parameters and therefore
provides insights into the angular dependence of jet fragmentation.

Figure 5: Ratio of charged-particle jet cross section for resolution parameter
$R=0.2$ to other radii $R=X$, with $X$ ranging from $0.3$ to $0.7$, after UE
subtraction. Data are compared with LO (PYTHIA) and NLO (POWHEG+PYTHIA8)
predictions as shown in the bottom panels. The systematic uncertainties of the
cross section ratios from data are indicated by solid boxes around data points
in the upper panel and shaded bands around unity in the mid and lower panels.
No uncertainties are shown for theoretical predictions for better visibility.

This observable is also less sensitive to experimental systematic
uncertainties since the correlated uncertainty on the numerator and
denominator spectra are largely cancelled in the ratio. Consequently, the
comparisons between data and model predictions provide better precision than
those for inclusive spectra. In order to compare the ratios within the same
jet pseudorapidity range, the ratios were studied for jet $|\eta_{\rm
jet}|<0.2$, which coincides with the fiducial jet acceptance for the largest
resolution parameter studied ($R=0.7$). Statistical correlations between the
numerator and denominator of the jet cross section ratios were removed by
using exclusive subsets events for their respective assessments. The measured
ratios were compared with PYTHIA and POWHEG calculations in Fig. 5. Both
predictions give a reasonable description of the data for
high-$p_{\mathrm{T}}$ jets within 10%, although they fail to describe the
low-$p_{\mathrm{T}}$ region, especially for large resolution parameters, where
non-perturbative and UE contributions become large. Even though PYTHIA8
overestimates the jet yields (see Fig. 4), the jet production ratio can still
be well described by PYTHIA8 MC.

Figure 6 shows the ratio of the charged-particle jet cross section with
different $R$ values for a) $R=0.2/R=0.4$ and b) $R=0.2/R=0.6$ in pp
collisions at $\sqrt{s}=5.02$ [12], $7$ [45], $13$ $\mathrm{TeV}$, and p–Pb
collisions at $\sqrt{s_{\mathrm{NN}}}=5.02\ \mathrm{TeV}$ [29]. These results,
which are in good agreement within uncertainties, show a similar increase of
the jet cross section ratio as a function of jet $p_{\mathrm{T}}$, as expected
from the stronger collimation of high-$p_{\mathrm{T}}$ jets. No significant
energy nor collision species dependence is observed within uncertainties.

Figure 6: Comparison of charged-particle jet cross section ratio with UE
subtraction in pp collisions at $\sqrt{s}=5.02$ [12], $7$ [45], and $13$
$\mathrm{TeV}$ and in p–Pb collisions at $\sqrt{s_{\mathrm{NN}}}=5.02\
\mathrm{TeV}$ [29]. Results are a) $\sigma(R=0.2)/\sigma(R=0.4)$ , and b)
$\sigma(R=0.2)/\sigma(R=0.6)$.

###  5.2 Multiplicity dependence of jet production

The jet production yields measured in different V0M multiplicity intervals as
a function of jet $p_{\mathrm{T}}$ for different resolution parameters $R$
varied from $0.2$ to $0.7$ in pp collisions at $\sqrt{s}=13\ \mathrm{TeV}$ are
shown in Fig. 7. A higher (lower) jet yield is observed in higher (lower)
multiplicity classes. To better investigate this multiplicity dependence, the
ratios of jet spectra from multiplicity classes and with MB events (Fig. 3)
are presented in Fig. 8.

Figure 7: Charged-particle jet yields in different V0M multiplicity percentile
intervals for resolution parameters $R$ varied from $0.2$ to $0.7$ in pp
collisions at $\sqrt{s}=13\ \mathrm{TeV}$. Statistical and total systematic
uncertainties are shown as vertical error bars and boxes around the data
points, respectively. Figure 8: Ratio of charged-particle jet yield measured
in different multiplicity classes with respect to that in MB events as a
function of $p_{\rm T}$ for different resolution parameters $R$ from $0.2$ to
$0.7$. Statistical and total systematic uncertainties are shown as vertical
error bars and boxes around the data points, respectively.

The charged-particle jet yield ratio in the highest event multiplicity class
(0–1%) is about 10 times higher than in the MB case, independent of the jet
resolution parameter $R$, while in the lowest event class (60–100%), it
amounts to only about 10% of the MB yield. Furthermore, such ratio has a weak
$p_{\mathrm{T}}$ dependence, except for the very low $p_{\mathrm{T}}$ region.
This indicates that jet production changes with event activity, but the slope
of the spectrum stays similar to the one measured in MB events.

Figure 9 shows the ratios of the $R=0.2$ jet spectrum to other radii for
different multiplicity classes. To better understand the multiplicity
dependence of the jet spectra ratios, Fig. 10 compares these ratios observed
in three selected multiplicity intervals (0–1%, 10–15% and 60–100%) to the
ones measured in MB events for a) $R=0.2/0.3$, b) $0.2/0.5$, and c) $0.2/0.7$.
The ratios are consistent with the ones obtained in the MB case (Fig. 5) for
small jet radii. At larger jet radii, a hint of ordering of the jet production
ratios with event multiplicity is observed. It is more pronounced for large
radii ($R=0.2/0.7$) and low $p_{\rm T}$. However, with the current systematic
uncertainty on data, it is difficult to draw final conclusions on such
dependence. Similar behaviour is observed in MC simulations as shown in Fig.
11. The MC predictions tend to underestimate the data and this discrepancy
increases with jet radius. However, within the current experimental systematic
uncertainties, there is no clear indication of multiplicity dependence for jet
yield ratios.

Figure 9: Ratios of charged-particle jet spectra with $R=0.2$ to that with
other jet resolution parameters $R$ from $0.3$ to $0.7$, shown in different
V0M multiplicity classes. Statistical and systematic uncertainties are shown
as vertical error bars and boxes around the data points, respectively. Figure
10: Comparison of jet spectra ratios of $R=0.2$ to other radii $R=$ a) $0.3$,
b) $0.5$, c) $0.7$ in MB events and in three multiplicity intervals (0–1%,
10–15% and 60–100%). Statistical and systematic uncertainties are shown as
vertical error bars and boxes around the data points, respectively. Results
for other radii can be found in Appendix Fig. 19. Figure 11: Comparison of jet
spectra ratios of $R=0.2$ to $R=$ a) $0.3$, b) $0.5$, c) $0.7$ in three
multiplicity intervals (0–1%, 10–15% and 60–100%) and compared with PYTHIA8
simulations. Statistical and systematic uncertainties are shown as vertical
error bars and boxes around the data points, respectively. Results for other
radii can be found in Appendix Fig. 20.

The $p_{\mathrm{T}}$-integrated ($5\leq p_{\rm T}<100\ \mathrm{GeV}/c$) jet
yields and the average transverse momentum of charged-particle jets as a
function of the self-normalised charged-particle multiplicity are shown in
Fig. 12 for different resolution parameters $R$ from $0.2$ to $0.7$. Both jet
yields and the average jet $p_{\rm T}$ increase with multiplicity, the
increase is more evident at larger $R$. Jets with $R=0.2$ exhibit very weak
dependence of their $\left\langle p_{\mathrm{T}}\right\rangle$ on
multiplicity, indicating that jets reconstructed with small radii are
dominated by the leading particle inside in the jet.

Figure 12: a) Integrated jet yields, and b) $\left\langle p_{\rm
T}\right\rangle$ of jets with $5\leq p_{\rm T,jet}^{\rm ch}<100\ {\rm GeV}/c$
as a function of self-normalised charged-particle multiplicity for different
resolution parameters $R$ varied from $0.2$ to $0.7$, with the charged-
particle multiplicities provided in Ref. [66]. Statistical and systematic
uncertainties are shown as vertical error bars and boxes around the data
points, respectively.

Fig. 13 presents the jet yield ratios in different multiplicity percentiles
with respect to MB events as a function of self-normalised charged-particle
multiplicity. The ratios are shown for four selected jet $p_{\mathrm{T}}$ bins
($5\leq p_{\rm T,jet}^{\rm ch}<7\ {\rm GeV}/c$, $9\leq p_{\rm T,jet}^{\rm
ch}<12\ {\rm GeV}/c$, $30\leq p_{\rm T,jet}^{\rm ch}<50\ {\rm GeV}/c$, and
$70\leq p_{\rm T,jet}^{\rm ch}<100\ {\rm GeV}/c$), and for resolution
parameters $R=0.2$ – $0.7$. The jet yield ratios increase with multiplicity
for all resolution parameters and $p_{\mathrm{T}}$ intervals. No significant
dependence of the jet yields with the jet resolution parameter $R$ is seen.

Figure 13: Self-normalised jet yields as a function of the self-normalised
charged-particle multiplicity for different resolution parameters $R$ varied
from $0.2$ to $0.7$ in different jet $p_{\rm T}$ intervals: a) $5\leq p_{\rm
T,jet}^{\rm ch}<7\ {\rm GeV}/c$, b) $9\leq p_{\rm T,jet}^{\rm ch}<12\ {\rm
GeV}/c$, c) $30\leq p_{\rm T,jet}^{\rm ch}<50\ {\rm GeV}/c$, and d) $70\leq
p_{\rm T,jet}^{\rm ch}<100\ {\rm GeV}/c$. The charged-particle multiplicities
are taken from Ref. [66]. Statistical and systematic uncertainties are shown
as vertical error bars and boxes around the data points, respectively.

To explore the $p_{\mathrm{T}}$ dependence of the normalised jet production as
a function of self-normalised charged-particle multiplicity, Fig. 14 shows the
self-normalised jet yields as a function of the self-normalised multiplicity
in four selected jet $p_{\mathrm{T}}$ intervals for resolution parameter
$R=0.3$, $0.5$ and $0.7$. The PYTHIA8 predictions are also compared against
data.

Figure 14: Comparison of self-normalised jet yields as a function of the self-
normalised charged-particle multiplicity in four selected jet $p_{\mathrm{T}}$
intervals ($5\leq p_{\rm T,jet}^{\rm ch}<7\ {\rm GeV}/c$, $9\leq p_{\rm
T,jet}^{\rm ch}<12\ {\rm GeV}/c$, $30\leq p_{\rm T,jet}^{\rm ch}<50\ {\rm
GeV}/c$, and $70\leq p_{\rm T,jet}^{\rm ch}<100\ {\rm GeV}/c$) for a given jet
radii: a) $R=0.3$, b) $R=0.5$, c) $R=0.7$ between data and PYTHIA8
predictions, with the charged-particle multiplicities provided in Ref. [66].
Statistical and systematic uncertainties are shown as vertical error bars and
boxes around the data points, respectively. Results for other radii can be
found in Appendix Fig. 21.

The jet production ratios measured at midrapidity increase with multiplicity
in a similar way to the results presented in earlier publications for
identified particles when using forward multiplicity V0 estimator [49, 50,
51]. The increase is weaker for the lowest jet $p_{\mathrm{T}}$ in the highest
multiplicity interval. In general, PYTHIA8 simulations predict the overall
increasing trend, however, the absolute magnitude is overestimated by the
PYTHIA8 MC, especially in the highest multiplicity interval.

##  6 Summary

The inclusive charged-particle jet production cross sections measured with
transverse momentum from $5\ \mathrm{GeV}/c$ to $140\ \mathrm{GeV}/c$ in pp
collisions at $\sqrt{s}=13\ \mathrm{TeV}$ have been reported. The measurements
were performed using the anti-$k_{\mathrm{T}}$ jet finding algorithm with
different resolution parameters $R$ varied from $0.2$ to $0.7$ and the
pseudorapidity range $|\eta_{\rm jet}|<0.9-R$. The inclusive charged-particle
jet cross sections were compared to LO PYTHIA and NLO POWHEG pQCD
calculations. As expected, a better agreement between data and MC is observed
for the NLO predictions, although the NLO prediction overestimates the jet
yield below $20\ \mathrm{GeV}/c$. The cross section ratios for different
resolution parameters were also studied. These ratios increase with jet
$p_{\mathrm{T}}$ and saturate at the high end of the jet $p_{\mathrm{T}}$
range, indicating a stronger collimation for high-momentum jets.

The multiplicity dependence of jet production using different resolution
parameters has also been studied. A higher (lower) jet yield is observed in
higher (lower) multiplicity classes. Jet production in different multiplicity
intervals compared to MB has a weak $p_{\mathrm{T}}$ and jet resolution
parameter dependence. Furthermore, the self-normalised jet production yields
and average jet $p_{\mathrm{T}}$ as a function of the self-normalised charged-
particle multiplicity have been measured. The integrated jet yields and
$\left\langle p_{\mathrm{T}}\right\rangle$ in the integrated $p_{\mathrm{T}}$
interval between 5 and 100 ${\rm GeV}/c$ increase with the self-normalised
charged-particle multiplicity. No strong dependence of jet $p_{\mathrm{T}}$
and the resolution parameter $R$ are observed except at low transverse
momentum in the highest multiplicity percentile interval. A similar
multiplicity dependence has also been reported for prompt D mesons in p–Pb
collisions at $\sqrt{s_{\rm NN}}=5.02\ \mathrm{TeV}$ and non-prompt J/$\psi$
(from B hadron decays) production in pp collisions at $\sqrt{s}=7\
\mathrm{TeV}$ when using a forward multiplicity estimator. Current MC event
generators can only predict the rising trend but cannot describe the absolute
yields, especially in the highest multiplicity class.

The measurements presented in this paper provide further insight into the
interplay between soft particle production and hard processes. Detailed
comparisons of models with data will help to elucidate the relationship
between jet production mechanisms and high-multiplicity events in small
systems, particularly at LHC energies.

## Acknowledgements

The ALICE Collaboration would like to thank all its engineers and technicians for their invaluable contributions to the construction of the experiment and the CERN accelerator teams for the outstanding performance of the LHC complex. The ALICE Collaboration gratefully acknowledges the resources and support provided by all Grid centres and the Worldwide LHC Computing Grid (WLCG) collaboration. The ALICE Collaboration acknowledges the following funding agencies for their support in building and running the ALICE detector: A. I. Alikhanyan National Science Laboratory (Yerevan Physics Institute) Foundation (ANSL), State Committee of Science and World Federation of Scientists (WFS), Armenia; Austrian Academy of Sciences, Austrian Science Fund (FWF): [M 2467-N36] and Nationalstiftung für Forschung, Technologie und Entwicklung, Austria; Ministry of Communications and High Technologies, National Nuclear Research Center, Azerbaijan; Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq), Financiadora de Estudos e Projetos (Finep), Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) and Universidade Federal do Rio Grande do Sul (UFRGS), Brazil; Ministry of Education of China (MOEC) , Ministry of Science & Technology of China (MSTC) and National Natural Science Foundation of China (NSFC), China; Ministry of Science and Education and Croatian Science Foundation, Croatia; Centro de Aplicaciones Tecnológicas y Desarrollo Nuclear (CEADEN), Cubaenergía, Cuba; Ministry of Education, Youth and Sports of the Czech Republic, Czech Republic; The Danish Council for Independent Research | Natural Sciences, the VILLUM FONDEN and Danish National Research Foundation (DNRF), Denmark; Helsinki Institute of Physics (HIP), Finland; Commissariat à l’Energie Atomique (CEA) and Institut National de Physique Nucléaire et de Physique des Particules (IN2P3) and Centre National de la Recherche Scientifique (CNRS), France; Bundesministerium für Bildung und Forschung (BMBF) and GSI Helmholtzzentrum für Schwerionenforschung GmbH, Germany; General Secretariat for Research and Technology, Ministry of Education, Research and Religions, Greece; National Research, Development and Innovation Office, Hungary; Department of Atomic Energy Government of India (DAE), Department of Science and Technology, Government of India (DST), University Grants Commission, Government of India (UGC) and Council of Scientific and Industrial Research (CSIR), India; Indonesian Institute of Science, Indonesia; Istituto Nazionale di Fisica Nucleare (INFN), Italy; Japanese Ministry of Education, Culture, Sports, Science and Technology (MEXT) and Japan Society for the Promotion of Science (JSPS) KAKENHI, Japan; Consejo Nacional de Ciencia (CONACYT) y Tecnología, through Fondo de Cooperación Internacional en Ciencia y Tecnología (FONCICYT) and Dirección General de Asuntos del Personal Academico (DGAPA), Mexico; Nederlandse Organisatie voor Wetenschappelijk Onderzoek (NWO), Netherlands; The Research Council of Norway, Norway; Commission on Science and Technology for Sustainable Development in the South (COMSATS), Pakistan; Pontificia Universidad Católica del Perú, Peru; Ministry of Education and Science, National Science Centre and WUT ID-UB, Poland; Korea Institute of Science and Technology Information and National Research Foundation of Korea (NRF), Republic of Korea; Ministry of Education and Scientific Research, Institute of Atomic Physics, Ministry of Research and Innovation and Institute of Atomic Physics and University Politehnica of Bucharest, Romania; Joint Institute for Nuclear Research (JINR), Ministry of Education and Science of the Russian Federation, National Research Centre Kurchatov Institute, Russian Science Foundation and Russian Foundation for Basic Research, Russia; Ministry of Education, Science, Research and Sport of the Slovak Republic, Slovakia; National Research Foundation of South Africa, South Africa; Swedish Research Council (VR) and Knut & Alice Wallenberg Foundation (KAW), Sweden; European Organization for Nuclear Research, Switzerland; Suranaree University of Technology (SUT), National Science and Technology Development Agency (NSDTA), Suranaree University of Technology (SUT), Thailand Science Research and Innovation (TSRI) and National Science, Research and Innovation Fund (NSRF), Thailand; Turkish Energy, Nuclear and Mineral Research Agency (TENMAK), Turkey; National Academy of Sciences of Ukraine, Ukraine; Science and Technology Facilities Council (STFC), United Kingdom; National Science Foundation of the United States of America (NSF) and United States Department of Energy, Office of Nuclear Physics (DOE NP), United States of America.

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##  Appendix A Appendix

###  A.1 Charged-particle jet cross section and ratios without UE subtraction

The fully corrected inclusive charged-particle jet cross sections and cross
section ratios without UE corrections in pp collisions at $\sqrt{s}=13\
\mathrm{TeV}$ are presented in this section. Figure 15 shows the jet cross
section for different resolution parameters $R$ varied from $0.2$ to $0.7$
without UE subtraction. The comparisons with LO and NLO theoretical
calculations are shown in Fig. 16. Figure 17 and 18 show the jet cross section
ratios without UE subtraction, in addition to comparison with theoretical
calculations between different collision energies, respectively.

Figure 15: Inclusive charged-particle jet cross sections in pp collisions at
$\sqrt{s}=$ 13 TeV using the anti-$k_{\rm T}$ algorithm for different
resolution parameters $R$ varied from $0.2$ to $0.7$, without UE subtraction.
Statistical uncertainties are displayed as vertical error bars. The total
systematic uncertainties are shown as solid boxes around the data points.

Figure 16: Inclusive charged-particle jet cross sections in pp collisions at
$\sqrt{s}=13$ TeV without UE subtraction and compared to LO and NLO MC
predictions with different resolution parameters $R$ varied from $0.2$ to
$0.7$. The statistical uncertainties are displayed as vertical error bars. The
systematic uncertainties on the data are indicated by shaded boxes in the top
panels and shaded bands drawn around unity in the bottom panels. The red
dashed lines in the ratio correspond to unity. Figure 17: Ratio of charged-
particle jet cross section for resolution parameter $R=0.2$ to other radii
$R=X$, with $X$ ranging from $0.3$ to $0.7$, without UE subtraction, and the
comparison of calculations from LO (PYTHIA) and NLO event generators
(POWHEG+PYTHIA8). The systematic uncertainties of the cross section ratios
from data are indicated by solid boxes around data points in the upper panels,
and shaded bands around unity in the lower panels. No uncertainties are shown
for theoretical predictions for better visibility. Figure 18: Comparison of
charged-particle jet cross section ratios for $\sigma(R=0.2)/\sigma(R=0.4)$
and $\sigma(R=0.2)/\sigma(R=0.6)$ without UE subtraction in pp collisions at
$\sqrt{s}=13$ and $5.02$ $\mathrm{TeV}$ [12].

###  A.2 Multiplicity dependence of jet production

Figure 19 selects three multiplicity intervals (0–1%, 10–15% and 60–100%) and
compares the jet production ratio for a) $R=0.2/0.4$ and b) $0.2/0.6$. Then
Fig. 20 compares the jet production ratio in three multiplicity classes for a)
$R=0.2/0.4$ and b) $0.2/0.6$ between data and PYTHIA MC, with the ratio
between MC and data shown in the bottom panels. Figure 21 shows the jet
production ratio as a function of the self-normalised charged-particle
multiplicity in four selected jet transverse momentum intervals for jet
resolution parameters a) $R=0.2$, b) $R=0.4$, and c) $R=0.6$.

Figure 19: Comparison of jet production ratios of $R=0.2$ to a) $R=0.4$, b)
$R=0.6$ in three multiplicity intervals (0–1%, 10–15% and 60–100%) and
compared with PYTHIA simulations. Statistical and systematic uncertainties are
shown as vertical error bars and boxes around the data points, respectively.
Figure 20: Comparison of jet production ratios of $R=0.2$ to a) $R=0.4$, b)
$R=0.6$ in three different multiplicity classes and compared with PYTHIA MC
simulations. Statistical and the total systematic uncertainties are shown as
vertical error bars and boxes around the data points, respectively. Figure 21:
Comparison of self-normalised jet yields as a function of the self-normalised
charged-particle multiplicity in four selected jet $p_{\mathrm{T}}$ intervals
($5\leq p_{\rm T,jet}^{\rm ch}<7\ {\rm GeV}/c$, $9\leq p_{\rm T,jet}^{\rm
ch}<12\ {\rm GeV}/c$, $30\leq p_{\rm T,jet}^{\rm ch}<50\ {\rm GeV}/c$, and
$70\leq p_{\rm T,jet}^{\rm ch}<100\ {\rm GeV}/c$) for a given jet radii: a)
$R=0.2$, b) $R=0.4$, c) $R=0.6$ between data and PYTHIA8 predictions. The
charged-particle multiplicities are taken from Ref. [66]. Statistical and
systematic uncertainties are shown as vertical error bars and boxes around the
data points, respectively.

##  Appendix B The ALICE Collaboration

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Ilyas14, M. Inaba134, G.M. Innocenti34, M. Ippolitov89, A. Isakov96, T.
Isidori127, M.S. Islam110, M. Ivanov108, V. Ivanov99, V. Izucheev92, M.
Jablonski2, B. Jacak80, N. Jacazio34, P.M. Jacobs80, S. Jadlovska117, J.
Jadlovsky117, S. Jaelani62, C. Jahnke122,121, M.J. Jakubowska143, A.
Jalotra102, M.A. Janik143, T. Janson74, M. Jercic100, O. Jevons111, A.A.P.
Jimenez69, F. Jonas97,145, P.G. Jones111, J.M. Jowett 34,108, J. Jung68, M.
Jung68, A. Junique34, A. Jusko111, M.J. Kabus143, J. Kaewjai116, P. Kalinak64,
A.S. Kalteyer108, A. Kalweit34, V. Kaplin94, A. Karasu Uysal77, D.
Karatovic100, O. Karavichev63, T. Karavicheva63, P. Karczmarczyk143, E.
Karpechev63, V. Kashyap87, A. Kazantsev89, U. Kebschull74, R. Keidel47, D.L.D.
Keijdener62, M. Keil34, B. Ketzer43, A.M. Khan7, S. Khan16, A. Khanzadeev99,
Y. Kharlov92,82, A. Khatun16, A. Khuntia118, B. Kileng36, B. Kim17,61, C.
Kim17, D.J. Kim126, E.J. Kim73, J. Kim148, J.S. Kim41, J. Kim105, J. Kim73, M.
Kim105, S. Kim18, T. Kim148, S. Kirsch68, I. Kisel39, S. Kiselev93, A.
Kisiel143, J.P. Kitowski2, J.L. Klay6, J. Klein34, S. Klein80, C. Klein-
Bösing145, M. Kleiner68, T. Klemenz106, A. Kluge34, A.G. Knospe125, C.
Kobdaj116, T. Kollegger108, A. Kondratyev75, N. Kondratyeva94, E.
Kondratyuk92, J. Konig68, S.A. Konigstorfer106, P.J. Konopka34, G.
Kornakov143, S.D. Koryciak2, A. Kotliarov96, O. Kovalenko86, V. Kovalenko113,
M. Kowalski118, I. Králik64, A. Kravčáková38, L. Kreis108, M. Krivda111,64, F.
Krizek96, K. Krizkova Gajdosova37, M. Kroesen105, M. Krüger68, D.M. Krupova37,
E. Kryshen99, M. Krzewicki39, V. Kučera34, C. Kuhn138, P.G. Kuijer91, T.
Kumaoka134, D. Kumar142, L. Kumar101, N. Kumar101, S. Kundu34, P.
Kurashvili86, A. Kurepin63, A.B. Kurepin63, A. Kuryakin109, S. Kushpil96, J.
Kvapil111, M.J. Kweon61, J.Y. Kwon61, Y. Kwon148, S.L. La Pointe39, P. La
Rocca26, Y.S. Lai80, A. Lakrathok116, M. Lamanna34, R. Langoy130, P.
Larionov34,52, E. Laudi34, L. Lautner34,106, R. Lavicka114,37, T. Lazareva113,
R. Lea141,58, J. Lehrbach39, R.C. Lemmon95, I. León Monzón120, M.M. Lesch106,
E.D. Lesser19, M. Lettrich34,106, P. Lévai146, X. Li11, X.L. Li7, J. Lien130,
R. Lietava111, B. Lim17, S.H. Lim17, V. Lindenstruth39, A. Lindner48, C.
Lippmann108, A. Liu19, D.H. Liu7, J. Liu128, I.M. Lofnes21, V. Loginov94, C.
Loizides97, P. Loncar35, J.A. Lopez105, X. Lopez136, E. López Torres8, J.R.
Luhder145, M. Lunardon27, G. Luparello60, Y.G. Ma40, A. Maevskaya63, M.
Mager34, T. Mahmoud43, A. Maire138, M. Malaev99, N.M. Malik102, Q.W. Malik20,
S.K. Malik102, L. MalininaIV,75, D. Mal’Kevich93, D. Mallick87, N. Mallick50,
G. Mandaglio32,56, V. Manko89, F. Manso136, V. Manzari53, Y. Mao7, G.V.
Margagliotti23, A. Margotti54, A. Marín108, C. Markert119, M. Marquard68, N.A.
Martin105, P. Martinengo34, J.L. Martinez125, M.I. Martínez45, G. Martínez
García115, S. Masciocchi108, M. Masera24, A. Masoni55, L. Massacrier78, A.
Mastroserio140,53, A.M. Mathis106, O. Matonoha81, P.F.T. Matuoka121, A.
Matyja118, C. Mayer118, A.L. Mazuecos34, F. Mazzaschi24, M. Mazzilli34, J.E.
Mdhluli132, A.F. Mechler68, Y. Melikyan63, A. Menchaca-Rocha71, E.
Meninno114,29, A.S. Menon125, M. Meres13, S. Mhlanga124,72, Y. Miake134, L.
Micheletti59, L.C. Migliorin137, D.L. Mihaylov106, K. Mikhaylov75,93, A.N.
Mishra146, D. Miśkowiec108, A. Modak4, A.P. Mohanty62, B. Mohanty87, M.
Mohisin KhanV,16, M.A. Molander44, Z. Moravcova90, C. Mordasini106, D.A.
Moreira De Godoy145, I. Morozov63, A. Morsch34, T. Mrnjavac34, V. Muccifora52,
E. Mudnic35, D. Mühlheim145, S. Muhuri142, J.D. Mulligan80, A. Mulliri22, M.G.
Munhoz121, R.H. Munzer68, H. Murakami133, S. Murray124, L. Musa34, J.
Musinsky64, J.W. Myrcha143, B. Naik132, R. Nair86, B.K. Nandi49, R. Nania54,
E. Nappi53, A.F. Nassirpour81, A. Nath105, C. Nattrass131, A. Neagu20, A.
Negru135, L. Nellen69, S.V. Nesbo36, G. Neskovic39, D. Nesterov113, B.S.
Nielsen90, E.G. Nielsen90, S. Nikolaev89, S. Nikulin89, V. Nikulin99, F.
Noferini54, S. Noh12, P. Nomokonov75, J. Norman128, N. Novitzky134, P.
Nowakowski143, A. Nyanin89, J. Nystrand21, M. Ogino83, A. Ohlson81, V.A.
Okorokov94, J. Oleniacz143, A.C. Oliveira Da Silva131, M.H. Oliver147, A.
Onnerstad126, C. Oppedisano59, A. Ortiz Velasquez69, T. Osako46, A.
Oskarsson81, J. Otwinowski118, M. Oya46, K. Oyama83, Y. Pachmayer105, S.
Padhan49, D. Pagano141,58, G. Paić69, A. Palasciano53, S. Panebianco139, J.
Park61, J.E. Parkkila126, S.P. Pathak125, R.N. Patra102,34, B. Paul22, H.
Pei7, T. Peitzmann62, X. Peng7, L.G. Pereira70, H. Pereira Da Costa139, D.
Peresunko89,82, G.M. Perez8, S. Perrin139, Y. Pestov5, V. Petráček37, V.
Petrov113, M. Petrovici48, R.P. Pezzi115,70, S. Piano60, M. Pikna13, P.
Pillot115, O. Pinazza54,34, L. Pinsky125, C. Pinto26, S. Pisano52, M.
Płoskoń80, M. Planinic100, F. Pliquett68, M.G. Poghosyan97, B. Polichtchouk92,
S. Politano30, N. Poljak100, A. Pop48, S. Porteboeuf-Houssais136, J. Porter80,
V. Pozdniakov75, S.K. Prasad4, R. Preghenella54, F. Prino59, C.A. Pruneau144,
I. Pshenichnov63, M. Puccio34, S. Qiu91, L. Quaglia24, R.E. Quishpe125, S.
Ragoni111, A. Rakotozafindrabe139, L. Ramello31, F. Rami138, S.A.R. Ramirez45,
T.A. Rancien79, R. Raniwala103, S. Raniwala103, S.S. Räsänen44, R. Rath50, I.
Ravasenga91, K.F. Read97,131, A.R. Redelbach39, K. RedlichVI,86, A. Rehman21,
P. Reichelt68, F. Reidt34, H.A. Reme-ness36, Z. Rescakova38, K. Reygers105, A.
Riabov99, V. Riabov99, T. Richert81, M. Richter20, W. Riegler34, F. Riggi26,
C. Ristea67, M. Rodríguez Cahuantzi45, K. Røed20, R. Rogalev92, E.
Rogochaya75, T.S. Rogoschinski68, D. Rohr34, D. Röhrich21, P.F. Rojas45, S.
Rojas Torres37, P.S. Rokita143, F. Ronchetti52, A. Rosano32,56, E.D. Rosas69,
A. Rossi57, A. Roy50, P. Roy110, S. Roy49, N. Rubini25, O.V. Rueda81, D.
Ruggiano143, R. Rui23, B. Rumyantsev75, P.G. Russek2, R. Russo91, A.
Rustamov88, E. Ryabinkin89, Y. Ryabov99, A. Rybicki118, H. Rytkonen126, W.
Rzesa143, O.A.M. Saarimaki44, R. Sadek115, S. Sadovsky92, J. Saetre21, K.
Šafařík37, S.K. Saha142, S. Saha87, B. Sahoo49, P. Sahoo49, R. Sahoo50, S.
Sahoo65, D. Sahu50, P.K. Sahu65, J. Saini142, S. Sakai134, M.P. Salvan108, S.
Sambyal102, T.B. Saramela121, D. Sarkar144, N. Sarkar142, P. Sarma42, V.M.
Sarti106, M.H.P. Sas147, J. Schambach97, H.S. Scheid68, C. Schiaua48, R.
Schicker105, A. Schmah105, C. Schmidt108, H.R. Schmidt104, M.O. Schmidt34,105,
M. Schmidt104, N.V. Schmidt97,68, A.R. Schmier131, R. Schotter138, J.
Schukraft34, K. Schwarz108, K. Schweda108, G. Scioli25, E. Scomparin59, J.E.
Seger15, Y. Sekiguchi133, D. Sekihata133, I. Selyuzhenkov108,94, S.
Senyukov138, J.J. Seo61, D. Serebryakov63, L. Šerkšnytė106, A. Sevcenco67,
T.J. Shaba72, A. Shabanov63, A. Shabetai115, R. Shahoyan34, W. Shaikh110, A.
Shangaraev92, A. Sharma101, D. Sharma49, H. Sharma118, M. Sharma102, N.
Sharma101, S. Sharma102, U. Sharma102, A. Shatat78, O. Sheibani125, K.
Shigaki46, M. Shimomura84, S. Shirinkin93, Q. Shou40, Y. Sibiriak89, S.
Siddhanta55, T. Siemiarczuk86, T.F. Silva121, D. Silvermyr81, T.
Simantathammakul116, G. Simonetti34, B. Singh106, R. Singh87, R. Singh102, R.
Singh50, V.K. Singh142, V. Singhal142, T. Sinha110, B. Sitar13, M. Sitta31,
T.B. Skaali20, G. Skorodumovs105, M. Slupecki44, N. Smirnov147, R.J.M.
Snellings62, C. Soncco112, J. Song125, A. Songmoolnak116, F. Soramel27, S.
Sorensen131, I. Sputowska118, J. Stachel105, I. Stan67, P.J. Steffanic131,
S.F. Stiefelmaier105, D. Stocco115, I. Storehaug20, M.M. Storetvedt36, P.
Stratmann145, S. Strazzi25, C.P. Stylianidis91, A.A.P. Suaide121, C. Suire78,
M. Sukhanov63, M. Suljic34, R. Sultanov93, V. Sumberia102, S. Sumowidagdo51,
S. Swain65, A. Szabo13, I. Szarka13, U. Tabassam14, S.F. Taghavi106, G.
Taillepied108,136, J. Takahashi122, G.J. Tambave21, S. Tang136,7, Z. Tang129,
J.D. Tapia TakakiVII,127, N. Tapus135, M.G. Tarzila48, A. Tauro34, G. Tejeda
Muñoz45, A. Telesca34, L. Terlizzi24, C. Terrevoli125, G. Tersimonov3, S.
Thakur142, D. Thomas119, R. Tieulent137, A. Tikhonov63, A.R. Timmins125, M.
Tkacik117, A. Toia68, N. Topilskaya63, M. Toppi52, F. Torales-Acosta19, T.
Tork78, A.G. Torres Ramos33, A. Trifiró32,56, A.S. Triolo32, S. Tripathy54,69,
T. Tripathy49, S. Trogolo34,27, V. Trubnikov3, W.H. Trzaska126, T.P.
Trzcinski143, A. Tumkin109, R. Turrisi57, T.S. Tveter20, K. Ullaland21, A.
Uras137, M. Urioni58,141, G.L. Usai22, M. Vala38, N. Valle28, S. Vallero59,
L.V.R. van Doremalen62, M. van Leeuwen91, R.J.G. van Weelden91, P. Vande
Vyvre34, D. Varga146, Z. Varga146, M. Varga-Kofarago146, M. Vasileiou85, A.
Vasiliev89, O. Vázquez Doce52,106, V. Vechernin113, A. Velure21, E.
Vercellin24, S. Vergara Limón45, L. Vermunt62, R. Vértesi146, M. Verweij62, L.
Vickovic35, Z. Vilakazi132, O. Villalobos Baillie111, G. Vino53, A.
Vinogradov89, T. Virgili29, V. Vislavicius90, A. Vodopyanov75, B.
Volkel34,105, M.A. Völkl105, K. Voloshin93, S.A. Voloshin144, G. Volpe33, B.
von Haller34, I. Vorobyev106, N. Vozniuk63, J. Vrláková38, B. Wagner21, C.
Wang40, D. Wang40, M. Weber114, A. Wegrzynek34, S.C. Wenzel34, J.P.
Wessels145, S.L. Weyhmiller147, J. Wiechula68, J. Wikne20, G. Wilk86, J.
Wilkinson108, G.A. Willems145, B. Windelband105, M. Winn139, W.E. Witt131,
J.R. Wright119, W. Wu40, Y. Wu129, R. Xu7, A.K. Yadav142, S. Yalcin77, Y.
Yamaguchi46, K. Yamakawa46, S. Yang21, S. Yano46, Z. Yin7, I.-K. Yoo17, J.H.
Yoon61, S. Yuan21, A. Yuncu105, V. Zaccolo23, C. Zampolli34, H.J.C. Zanoli62,
F. Zanone105, N. Zardoshti34, A. Zarochentsev113, P. Závada66, N.
Zaviyalov109, M. Zhalov99, B. Zhang7, S. Zhang40, X. Zhang7, Y. Zhang129, V.
Zherebchevskii113, Y. Zhi11, N. Zhigareva93, D. Zhou7, Y. Zhou90, J. Zhu108,7,
Y. Zhu7, G. ZinovjevI,3, N. Zurlo141,58

## Affiliation Notes

I Deceased
II Also at: Italian National Agency for New Technologies, Energy and
Sustainable Economic Development (ENEA), Bologna, Italy
III Also at: Dipartimento DET del Politecnico di Torino, Turin, Italy
IV Also at: M.V. Lomonosov Moscow State University, D.V. Skobeltsyn Institute
of Nuclear, Physics, Moscow, Russia
V Also at: Department of Applied Physics, Aligarh Muslim University, Aligarh,
India
VI Also at: Institute of Theoretical Physics, University of Wroclaw, Poland
VII Also at: University of Kansas, Lawrence, Kansas, United States

## Collaboration Institutes

1 A.I. Alikhanyan National Science Laboratory (Yerevan Physics Institute)
Foundation, Yerevan, Armenia
2 AGH University of Science and Technology, Cracow, Poland
3 Bogolyubov Institute for Theoretical Physics, National Academy of Sciences
of Ukraine, Kiev, Ukraine
4 Bose Institute, Department of Physics and Centre for Astroparticle Physics
and Space Science (CAPSS), Kolkata, India
5 Budker Institute for Nuclear Physics, Novosibirsk, Russia
6 California Polytechnic State University, San Luis Obispo, California, United
States
7 Central China Normal University, Wuhan, China
8 Centro de Aplicaciones Tecnológicas y Desarrollo Nuclear (CEADEN), Havana,
Cuba
9 Centro de Investigación y de Estudios Avanzados (CINVESTAV), Mexico City and
Mérida, Mexico
10 Chicago State University, Chicago, Illinois, United States
11 China Institute of Atomic Energy, Beijing, China
12 Chungbuk National University, Cheongju, Republic of Korea
13 Comenius University Bratislava, Faculty of Mathematics, Physics and
Informatics, Bratislava, Slovakia
14 COMSATS University Islamabad, Islamabad, Pakistan
15 Creighton University, Omaha, Nebraska, United States
16 Department of Physics, Aligarh Muslim University, Aligarh, India
17 Department of Physics, Pusan National University, Pusan, Republic of Korea
18 Department of Physics, Sejong University, Seoul, Republic of Korea
19 Department of Physics, University of California, Berkeley, California,
United States
20 Department of Physics, University of Oslo, Oslo, Norway
21 Department of Physics and Technology, University of Bergen, Bergen, Norway
22 Dipartimento di Fisica dell’Università and Sezione INFN, Cagliari, Italy
23 Dipartimento di Fisica dell’Università and Sezione INFN, Trieste, Italy
24 Dipartimento di Fisica dell’Università and Sezione INFN, Turin, Italy
25 Dipartimento di Fisica e Astronomia dell’Università and Sezione INFN,
Bologna, Italy
26 Dipartimento di Fisica e Astronomia dell’Università and Sezione INFN,
Catania, Italy
27 Dipartimento di Fisica e Astronomia dell’Università and Sezione INFN,
Padova, Italy
28 Dipartimento di Fisica e Nucleare e Teorica, Università di Pavia, Pavia,
Italy
29 Dipartimento di Fisica ‘E.R. Caianiello’ dell’Università and Gruppo
Collegato INFN, Salerno, Italy
30 Dipartimento DISAT del Politecnico and Sezione INFN, Turin, Italy
31 Dipartimento di Scienze e Innovazione Tecnologica dell’Università del
Piemonte Orientale and INFN Sezione di Torino, Alessandria, Italy
32 Dipartimento di Scienze MIFT, Università di Messina, Messina, Italy
33 Dipartimento Interateneo di Fisica ‘M. Merlin’ and Sezione INFN, Bari,
Italy
34 European Organization for Nuclear Research (CERN), Geneva, Switzerland
35 Faculty of Electrical Engineering, Mechanical Engineering and Naval
Architecture, University of Split, Split, Croatia
36 Faculty of Engineering and Science, Western Norway University of Applied
Sciences, Bergen, Norway
37 Faculty of Nuclear Sciences and Physical Engineering, Czech Technical
University in Prague, Prague, Czech Republic
38 Faculty of Science, P.J. Šafárik University, Košice, Slovakia
39 Frankfurt Institute for Advanced Studies, Johann Wolfgang Goethe-
Universität Frankfurt, Frankfurt, Germany
40 Fudan University, Shanghai, China
41 Gangneung-Wonju National University, Gangneung, Republic of Korea
42 Gauhati University, Department of Physics, Guwahati, India
43 Helmholtz-Institut für Strahlen- und Kernphysik, Rheinische Friedrich-
Wilhelms-Universität Bonn, Bonn, Germany
44 Helsinki Institute of Physics (HIP), Helsinki, Finland
45 High Energy Physics Group, Universidad Autónoma de Puebla, Puebla, Mexico
46 Hiroshima University, Hiroshima, Japan
47 Hochschule Worms, Zentrum für Technologietransfer und Telekommunikation
(ZTT), Worms, Germany
48 Horia Hulubei National Institute of Physics and Nuclear Engineering,
Bucharest, Romania
49 Indian Institute of Technology Bombay (IIT), Mumbai, India
50 Indian Institute of Technology Indore, Indore, India
51 Indonesian Institute of Sciences, Jakarta, Indonesia
52 INFN, Laboratori Nazionali di Frascati, Frascati, Italy
53 INFN, Sezione di Bari, Bari, Italy
54 INFN, Sezione di Bologna, Bologna, Italy
55 INFN, Sezione di Cagliari, Cagliari, Italy
56 INFN, Sezione di Catania, Catania, Italy
57 INFN, Sezione di Padova, Padova, Italy
58 INFN, Sezione di Pavia, Pavia, Italy
59 INFN, Sezione di Torino, Turin, Italy
60 INFN, Sezione di Trieste, Trieste, Italy
61 Inha University, Incheon, Republic of Korea
62 Institute for Gravitational and Subatomic Physics (GRASP), Utrecht
University/Nikhef, Utrecht, Netherlands
63 Institute for Nuclear Research, Academy of Sciences, Moscow, Russia
64 Institute of Experimental Physics, Slovak Academy of Sciences, Košice,
Slovakia
65 Institute of Physics, Homi Bhabha National Institute, Bhubaneswar, India
66 Institute of Physics of the Czech Academy of Sciences, Prague, Czech
Republic
67 Institute of Space Science (ISS), Bucharest, Romania
68 Institut für Kernphysik, Johann Wolfgang Goethe-Universität Frankfurt,
Frankfurt, Germany
69 Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México,
Mexico City, Mexico
70 Instituto de Física, Universidade Federal do Rio Grande do Sul (UFRGS),
Porto Alegre, Brazil
71 Instituto de Física, Universidad Nacional Autónoma de México, Mexico City,
Mexico
72 iThemba LABS, National Research Foundation, Somerset West, South Africa
73 Jeonbuk National University, Jeonju, Republic of Korea
74 Johann-Wolfgang-Goethe Universität Frankfurt Institut für Informatik,
Fachbereich Informatik und Mathematik, Frankfurt, Germany
75 Joint Institute for Nuclear Research (JINR), Dubna, Russia
76 Korea Institute of Science and Technology Information, Daejeon, Republic of
Korea
77 KTO Karatay University, Konya, Turkey
78 Laboratoire de Physique des 2 Infinis, Irène Joliot-Curie, Orsay, France
79 Laboratoire de Physique Subatomique et de Cosmologie, Université Grenoble-
Alpes, CNRS-IN2P3, Grenoble, France
80 Lawrence Berkeley National Laboratory, Berkeley, California, United States
81 Lund University Department of Physics, Division of Particle Physics, Lund,
Sweden
82 Moscow Institute for Physics and Technology, Moscow, Russia
83 Nagasaki Institute of Applied Science, Nagasaki, Japan
84 Nara Women’s University (NWU), Nara, Japan
85 National and Kapodistrian University of Athens, School of Science,
Department of Physics , Athens, Greece
86 National Centre for Nuclear Research, Warsaw, Poland
87 National Institute of Science Education and Research, Homi Bhabha National
Institute, Jatni, India
88 National Nuclear Research Center, Baku, Azerbaijan
89 National Research Centre Kurchatov Institute, Moscow, Russia
90 Niels Bohr Institute, University of Copenhagen, Copenhagen, Denmark
91 Nikhef, National institute for subatomic physics, Amsterdam, Netherlands
92 NRC Kurchatov Institute IHEP, Protvino, Russia
93 NRC «Kurchatov»Institute - ITEP, Moscow, Russia
94 NRNU Moscow Engineering Physics Institute, Moscow, Russia
95 Nuclear Physics Group, STFC Daresbury Laboratory, Daresbury, United Kingdom
96 Nuclear Physics Institute of the Czech Academy of Sciences, Řež u Prahy,
Czech Republic
97 Oak Ridge National Laboratory, Oak Ridge, Tennessee, United States
98 Ohio State University, Columbus, Ohio, United States
99 Petersburg Nuclear Physics Institute, Gatchina, Russia
100 Physics department, Faculty of science, University of Zagreb, Zagreb,
Croatia
101 Physics Department, Panjab University, Chandigarh, India
102 Physics Department, University of Jammu, Jammu, India
103 Physics Department, University of Rajasthan, Jaipur, India
104 Physikalisches Institut, Eberhard-Karls-Universität Tübingen, Tübingen,
Germany
105 Physikalisches Institut, Ruprecht-Karls-Universität Heidelberg,
Heidelberg, Germany
106 Physik Department, Technische Universität München, Munich, Germany
107 Politecnico di Bari and Sezione INFN, Bari, Italy
108 Research Division and ExtreMe Matter Institute EMMI, GSI Helmholtzzentrum
für Schwerionenforschung GmbH, Darmstadt, Germany
109 Russian Federal Nuclear Center (VNIIEF), Sarov, Russia
110 Saha Institute of Nuclear Physics, Homi Bhabha National Institute,
Kolkata, India
111 School of Physics and Astronomy, University of Birmingham, Birmingham,
United Kingdom
112 Sección Física, Departamento de Ciencias, Pontificia Universidad Católica
del Perú, Lima, Peru
113 St. Petersburg State University, St. Petersburg, Russia
114 Stefan Meyer Institut für Subatomare Physik (SMI), Vienna, Austria
115 SUBATECH, IMT Atlantique, Université de Nantes, CNRS-IN2P3, Nantes, France
116 Suranaree University of Technology, Nakhon Ratchasima, Thailand
117 Technical University of Košice, Košice, Slovakia
118 The Henryk Niewodniczanski Institute of Nuclear Physics, Polish Academy of
Sciences, Cracow, Poland
119 The University of Texas at Austin, Austin, Texas, United States
120 Universidad Autónoma de Sinaloa, Culiacán, Mexico
121 Universidade de São Paulo (USP), São Paulo, Brazil
122 Universidade Estadual de Campinas (UNICAMP), Campinas, Brazil
123 Universidade Federal do ABC, Santo Andre, Brazil
124 University of Cape Town, Cape Town, South Africa
125 University of Houston, Houston, Texas, United States
126 University of Jyväskylä, Jyväskylä, Finland
127 University of Kansas, Lawrence, Kansas, United States
128 University of Liverpool, Liverpool, United Kingdom
129 University of Science and Technology of China, Hefei, China
130 University of South-Eastern Norway, Tonsberg, Norway
131 University of Tennessee, Knoxville, Tennessee, United States
132 University of the Witwatersrand, Johannesburg, South Africa
133 University of Tokyo, Tokyo, Japan
134 University of Tsukuba, Tsukuba, Japan
135 University Politehnica of Bucharest, Bucharest, Romania
136 Université Clermont Auvergne, CNRS/IN2P3, LPC, Clermont-Ferrand, France
137 Université de Lyon, CNRS/IN2P3, Institut de Physique des 2 Infinis de
Lyon, Lyon, France
138 Université de Strasbourg, CNRS, IPHC UMR 7178, F-67000 Strasbourg, France,
Strasbourg, France
139 Université Paris-Saclay Centre d’Etudes de Saclay (CEA), IRFU, Départment
de Physique Nucléaire (DPhN), Saclay, France
140 Università degli Studi di Foggia, Foggia, Italy
141 Università di Brescia, Brescia, Italy
142 Variable Energy Cyclotron Centre, Homi Bhabha National Institute, Kolkata,
India
143 Warsaw University of Technology, Warsaw, Poland
144 Wayne State University, Detroit, Michigan, United States
145 Westfälische Wilhelms-Universität Münster, Institut für Kernphysik,
Münster, Germany
146 Wigner Research Centre for Physics, Budapest, Hungary
147 Yale University, New Haven, Connecticut, United States
148 Yonsei University, Seoul, Republic of Korea