2019 094 7 May

Particle production as a function of multiplicity and spherocity in pp
collisions

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

We present a study of the inclusive charged-particle transverse momentum
($p_{\rm T}$) spectra as a function of charged-particle multiplicity density
at mid-pseudorapidity, ${\rm d}N_{\rm ch}/{\rm d}\eta$, in pp collisions at
$\sqrt{s}=5.02$ and 13 TeV covering the kinematic range $|\eta|<0.8$ and
$0.15<p_{\rm T}<20$ GeV/$c$. The results are presented for events with at
least one charged particle in $|\eta|<1$ (INEL$\,>0$). The $p_{\rm T}$ spectra
are reported for two multiplicity estimators covering different pseudorapidity
regions. The $p_{\rm T}$ spectra normalized to that for INEL$\,>0$ show little
energy dependence. Moreover, the high-$p_{\rm T}$ yields of charged particles
increase faster than the charged-particle multiplicity density. The average
$\it{p}_{\rm T}$ as a function of multiplicity and transverse spherocity is
reported for pp collisions at $\sqrt{s}=13$ TeV. For low- (high-) spherocity
events, corresponding to jet-like (isotropic) events, the average $p_{\rm T}$
is higher (smaller) than that measured in INEL$\,>0$ pp collisions. Within
uncertainties, the functional form of $\langle p_{\rm T}\rangle(N_{\rm ch})$
is not affected by the spherocity selection. While EPOS LHC gives a good
description of many features of data, PYTHIA overestimates the average $p_{\rm
T}$ in jet-like events.

##  1 Introduction

Proton-proton collisions at the Large Hadron Collider (LHC) energies have
unveiled features very similar to the ones observed in heavy-ion collisions
[1]. The previous consensus of the heavy-ion community was that the partonic
system created in nuclear collisions needs a large volume to thermalize and to
lead to phenomena like collective flow. However, radial [2, 3, 4] and
anisotropic flow [5], as well as strangeness enhancement [6], are also
observed in pp and p-A collisions when they are studied as a function of event
multiplicity. Surprisingly, with the same level of precision, microscopic and
macroscopic approaches describe qualitatively well the observed features in pp
collisions. While macroscopic models incorporate hydrodynamical evolution of
the system [7], the others include overlapping strings [8], string percolation
[9], multi-parton interactions and color reconnection [10, 11]. The multiphase
transport model [12], as well as the fragmentation of saturated gluon states
[13, 14], is able to describe some features of data.

The inclusive transverse momentum ($p_{\rm T}$) spectrum of charged particles
carries information of the dynamics of soft and hard interactions. On one
hand, the high-$p_{\rm T}$ ($p_{\rm T}>10$ GeV/$c$) particle production is
quantitatively well described by perturbative QCD (pQCD) calculations; on the
other hand, the understanding of particle production at low-$p_{\rm T}$ has to
resort to phenomenological QCD inspired models. Most of the new effects
discovered in pp collisions have been unveiled in the low- ($p_{\rm T}<2$
GeV/$c$) and intermediate- ($2\leq p_{\rm T}<10$ GeV/$c$) $p_{\rm T}$ domains
[2, 3, 4, 5, 6]. The present paper reports a novel multi-differential analysis
aimed at understanding charged-particle production associated to partonic
scatterings with large momentum transfer and their possible correlations with
soft particle production.

The transverse momentum distributions are reported for two multiplicity
estimators which cover different pseudorapidity regions. The estimators are
based on either the total charge deposited in the forward detector (covering
the pseudorapidity regions $2.8<\eta<5.1$ and $-3.7<\eta<-1.7$) or on the
number of tracks in the pseudorapidity region $|\eta|<0.8$. The forward
multiplicity estimator is commonly used by the ALICE collaboration to minimize
the possible autocorrelations induced by the use of the mid-pseudorapidity
estimator. One such examples is the “fragmentation bias” [15], which is the
correlation between jet fragments and event multiplicity arising when the
particle’s $p_{\rm T}$ and event multiplicity are both measured within the
same pseudorapidity interval [16]. For each estimator, we defined different
multiplicity classes based on either the number of tracks at mid-
pseudorapidity ($|\eta|<0.8$) or the signal in the forward detectors. It is
worth mentioning that a similar study has been performed by ALICE using p-Pb
data; the results showed different modifications of the spectral shapes
depending on the multiplicity estimators which were used [17]. To disentangle
the energy and multiplicity dependence, for a given multiplicity class, the
$p_{\rm T}$ distributions are measured for pp collisions at $\sqrt{s}=5.02$
and 13 TeV. Particle production from intermediate to high $p_{\rm T}$ ($>4$
GeV/$c$) is studied by fitting a power-law function to the invariant yield,
and studying the multiplicity and energy dependence of the exponent. This has
been proposed in Ref. [18] as a way to characterize the high-$p_{\rm T}$ tails
of different systems and energies in a convenient way that may make the
comparison for the different systems more straightforward.

Finally, we explore a new approach, which has been proposed to study multi-
parton interaction effects in pp collisions. Transverse spherocity [19],
hereinafter referred to as spherocity, has been proven to be a valuable tool
to discriminate between jet-like and isotropic events [20] associated with an
underlying event activity which is either suppressed or enhanced. The previous
measurement of average transverse momentum of inclusive charged particles as a
function of event multiplicity [21] is now explored adding a new dimension:
the event shape characterized by spherocity. The aim of this study is to
investigate the importance of jets in high-multiplicity pp collisions and
their contribution to charged-particle production at low $p_{\rm T}$.

The paper is organized as follows: Section 2 describes the run conditions
during the data taking and the main detectors used in the present analysis.
Section 3 outlines the analysis details for the event and track selection, as
well as the definitions of the different event classes. The correction
procedures and the estimation of the systematic uncertainties are summarized
in Sections 4 and 5, respectively. Results and discussions are presented in
Section 6. Finally, our summary and conclusions are reported in Section 7.

##  2 The ALICE apparatus

The main detectors used in the present work are the Inner Tracking System
(ITS), the Time Projection Chamber (TPC) and the V0 detector. The ITS and TPC
detectors are both used for primary vertex and track reconstruction. The V0
detector is used for triggering and for background rejection. More details
concerning the full ALICE detector system can be found in Ref. [22].

The central barrel covers the pseudorapidity region $|\eta|<0.8$ for full-
length tracks. The main central-barrel tracking devices are the ITS and the
TPC, which are located inside a solenoid magnet providing a 0.5 T magnetic
field allowing the tracking of particles from 0.15 GeV/$c$. The ITS is
composed of six cylindrical layers of high-resolution silicon tracking
detectors. The innermost layers consist of two arrays of hybrid Silicon Pixel
Detectors (SPD) located at an average radial distance ($r$) of 3.9 and 7.6 cm
from the beam axis and covering $|\eta|<2$ and $|\eta|<1.4$, respectively. The
SPD is also used to reconstruct tracklets, which are track segments built
using the position of the reconstructed primary vertex and two hits, one on
each SPD layer. The number of tracklets gives an excellent estimate of the
charged-particle multiplicity at mid-pseudorapidity ($N_{\rm ch}$). The outer
layers of the ITS are composed of silicon strip and drift detectors, with the
outermost layer sitting at $r=43$ cm. The TPC is a large cylindrical drift
detector of radial and longitudinal size of about $85<r<250$ cm and
$-250<z<250$ cm, respectively. It is segmented in radial “pad rows”, providing
up to 159 tracking points. The measurement of charged particles is based on
“global tracks”, reconstructed using the combined ITS and TPC information. The
V0 detector consists of two forward scintillator arrays (V0-A and V0-C)
employed for triggering, background suppression, and event-class
determination. They are placed on either side of the interaction region at
$z=3.3$ m and $z=-0.9$ m, covering the pseudorapidity regions $2.8<\eta<5.1$
and $-3.7<\eta<-1.7$, respectively.

The data were collected using a minimum-bias trigger which required coincident
signals in both V0-A and V0-C detectors . The events were recorded in
coincidence with signals from two beam pick-up counters each positioned on
either side of the interaction region to tag the arrival of proton bunches
from both directions. Control triggers taken for various combinations of beam
and empty buckets were used to measure beam-induced and accidental
backgrounds. The contamination from background events was removed offline by
using the timing information from the V0 detector, which has a time resolution
better than 1 ns. Background events were also rejected by exploiting the
correlation between the number of clusters of pixel hits and the number of
tracklets in the SPD.

##  3 Analysis

The results presented here were obtained from the analysis of about 105 and 60
million minimum-bias pp events at $\sqrt{s}=5.02$ and 13 TeV, respectively.
The interaction probability per single bunch crossing ranges between 2% and
14% for pp collisions at 13 TeV and from 0.3% to 6% for pp collisions at 5.02
TeV. The measurements have been obtained for events having at least one
charged particle produced in the pseudorapidity interval $|\eta|<1$
(INEL$\,>0$). For the analysis, the events were furthermore required to have a
reconstructed vertex located within $|z|<10$ cm, where $z$ is the position of
the vertex along the beam axis, and $z=0$ cm corresponds to the nominal center
of the detector [22]. Events containing more than one distinct vertex were
tagged as pileup and discarded from the analysis. The systematic uncertainty
associated to pileup is between 3 – 4% and is not the dominant source of
uncertainty for the $p_{\rm T}$ spectra reported here. The corrections are
calculated using Monte Carlo events from the PYTHIA 6 [23] (tune Perugia 2011
[24]) event generator with particle transport performed via a GEANT 3 [25]
simulation of the ALICE detector.

Only primary charged particles in the kinematic range $|\eta|<0.8$ and
$0.15<p_{\rm T}<20$ GeV/$c$ are considered in the transverse momentum
analysis. A primary charged particle is defined as a charged particle with a
mean proper lifetime $\tau$ larger than 1 cm$/c$, which is either produced
directly in the interaction or from decays of particles with $\tau$ smaller
than 1 cm$/c$, excluding particles produced in interactions with the detector
material [26].

#### Transverse momentum distributions.

The measurement of the $p_{\rm T}$ spectra follows the standard procedure
already employed in several ALICE publications [27, 28, 29]. Tracks
reconstructed using the information from the ITS and TPC detectors are used.
The track selection criteria have been optimised for best track quality and
minimal contamination from secondary particles. Tracks are required to have at
least two hits in the ITS detector, of which at least one is in either of the
two innermost SPD layers. The geometrical track length $L$ (in cm) is
calculated in the TPC readout plane, excluding the information from the pads
at the sector boundaries ($\sim$3 cm from the sector edges). The number of
crossed TPC rows has to be larger than 0.85$L$. The number of TPC clusters has
to be larger than 0.7$L$. The fit quality for the ITS and TPC track points
must satisfy $\chi^{2}_{\rm ITS}/N_{\rm hits}<36$ and $\chi^{2}_{\rm
TPC}/N_{\rm clusters}<4$, respectively, where $N_{\rm hits}$ and $N_{\rm
clusters}$ are the numbers of hits in the ITS and the number of clusters in
the TPC, respectively. Tracking information from the combined ITS and TPC
track reconstruction algorithm is compared to that derived only from the TPC
and constrained by the interaction vertex point. Then, the quantity
$\chi^{2}_{\rm TPC-ITS}$ is derived as described in Ref. [30]. Only tracks
with $\chi^{2}_{\rm TPC-ITS}<36$ are included in the analysis in order to
improve the purity of primary track reconstruction at high $p_{\rm T}$. Tracks
are rejected if their distance of closest approach to the reconstructed vertex
in longitudinal and radial direction, $d_{z}$ and $d_{xy}$, respectively,
satisfies $d_{z}>2$ cm or $d_{xy}>0.018$ cm $+$ $0.035$ cm $\times p_{\rm
T}^{-1.01}$, with $p_{\rm T}$ in GeV/$c$.

#### Multiplicity estimators.

In order to study the multiplicity dependence of the inclusive charged
particle $p_{\rm T}$ distributions, the INEL$\,>0$ sample is divided into
event classes based on the total charge deposited in the V0 detector (V0M
amplitude) and on the number of SPD tracklets ($N_{\rm SPD\,tracklets}$) in
the pseudorapidity region $|\eta|<0.8$. The event classes used in the analysis
and the corresponding mid-pseudorapidity charged particle densities are
summarized in Tables 1 and 2. The average charged-particle multiplicity
densities for INEL$\,>0$ collisions and for the multiplicity classes are
obtained by integrating the corresponding fully corrected $p_{\rm T}$ spectra
(measured using ITS and TPC information). To this end, the $p_{\rm T}$ spectra
were extrapolated to $p_{\rm T}=0$ with a Hagedorn function [31]. Different
functions were used and the differences with respect to the reference values
were considered in the systematic uncertainties. For INEL$\,>0$ pp collisions
at $\sqrt{s}=5.02$ TeV the mid-pseudorapidity ($|\eta|<0.8$) charged-particle
density is $\langle{\rm d}N_{\rm ch}/{\rm d}\eta\rangle=5.91\pm 0.45$, while
for $\sqrt{s}=13$ TeV the corresponding value is $7.60\pm 0.50$. The
comparison of results obtained with these estimators allows to understand
potential biases from measuring the multiplicity and $p_{\rm T}$ distributions
in overlapping $\eta$ regions.

Table 1: V0M event multiplicity classes, their corresponding experimental
definition and their corresponding $\langle{\rm d}N_{\rm ch}/{\rm
d}\eta\rangle$ in $|\eta|<0.8$. The uncertainties are the quadratic sum of
statistical and systematic contributions. Statistical uncertainties are
negligible compared to the systematic ones. pp collisions at $\sqrt{s}=13$ TeV
---
Class name |  I |  II |  III |  IV |  V
V0M percentile |  0 – 1% |  1 – 5% |  5 – 10% |  10 – 15% |  15 – 20%
$\langle{\rm d}N_{\rm ch}/{\rm d}\eta\rangle$ |  26.6$\pm$1.1 |  20.5$\pm$0.8 |  16.7$\pm$0.7 |  14.3$\pm$0.6 |  12.6$\pm$0.5
Class name |  VI |  VII |  VIII |  IX |  X
V0M percentile |  20 – 30% |  30 – 40% |  40 – 50% |  50 – 70% |  70 – 100%
$\langle{\rm d}N_{\rm ch}/{\rm d}\eta\rangle$ |  10.6$\pm$0.5 |  8.46$\pm$0.40 |  6.82$\pm$0.34 |  4.94$\pm$0.28 |  2.54$\pm$0.26
pp collisions at $\sqrt{s}=5.02$ TeV
Class name |  I |  II |  III |  IV |  V
V0M percentile |  0 – 1% |  1 – 5% |  5 – 10% |  10 – 15% |  15 – 20%
$\langle{\rm d}N_{\rm ch}/{\rm d}\eta\rangle$ |  19.2$\pm$0.9 |  15.1$\pm$0.7 |  12.4$\pm$0.6 |  10.7$\pm$0.5 |  9.47$\pm$0.47
Class name |  VI |  VII |  VIII |  IX |  X
V0M percentile |  20 – 30% |  30 – 40% |  40 – 50% |  50 – 70% |  70 – 100%
$\langle{\rm d}N_{\rm ch}/{\rm d}\eta\rangle$ |  8.04$\pm$0.42 |  6.56$\pm$0.37 |  5.39$\pm$0.32 |  4.05$\pm$0.27 |  2.27$\pm$0.27
Table 2: Event multiplicity classes based on the number of tracklets ($N_{\rm
SPD\,tracklets}$) within $|\eta|<0.8$, their corresponding experimental
definition and their corresponding $\langle{\rm d}N_{\rm ch}/{\rm
d}\eta\rangle$ in $|\eta|<0.8$. The uncertainties are the quadratic sum of
statistical and systematic contributions. pp collisions at $\sqrt{s}=13$ TeV
---
Class name (percentile) |  I′ 0–0.006% |  II′ 0.006–0.058% |  III′ 0.058–0.177% |  IV′ 0.177–0.513% |  V′ 0.513–1.419%
$N_{\rm SPD\,tracklets}$ |  $\geq$ 51 |  41 – 50 |  36 – 40 |  31 – 35 |  26 – 30
$\langle{\rm d}N_{\rm ch}/{\rm d}\eta\rangle$ |  54.1$\pm$2.7 |  44.6$\pm$2.2 |  38.9$\pm$1.9 |  34.1$\pm$1.7 |  29.3$\pm$1.5
Class name percentile |  VI′ 1.419–3.699% |  VII′ 3.699–9.059% |  VIII′ 9.059–20.77% |  IX′ 20.77–45.25% |  X′ 45.25–100.0%
$N_{\rm SPD\,tracklets}$ |  21 – 25 |  16 – 20 |  11 – 15 |  6 – 10 |  0 – 5
$\langle{\rm d}N_{\rm ch}/{\rm d}\eta\rangle$ |  24.5$\pm$1.3 |  19.5$\pm$1.2 |  14.4$\pm$0.9 |  9.03$\pm$0.58 |  2.91$\pm$0.29
pp collisions at $\sqrt{s}=5.02$ TeV
Class name (percentile) |  - |  II′ 0.009–0.088% |  III′ 0.088–0.253% |  IV′ 0.253–0.700% |  V′ 0.700–1.840%
$N_{\rm SPD\,tracklets}$ |  - |  41 – 50 |  36 – 40 |  31 – 35 |  26 – 30
$\langle{\rm d}N_{\rm ch}/{\rm d}\eta\rangle$ |  - |  34.6$\pm$1.8 |  29.9$\pm$1.5 |  26.2$\pm$1.3 |  22.4$\pm$1.1
Class name (percentile) |  VI′ 1.840–4.573% |  VII′ 4.57–10.69% |  VIII′ 10.69–23.50% |  IX′ 23.50–49.48% |  X′ 49.48–100.0%
$N_{\rm SPD\,tracklets}$ |  21 – 25 |  16 – 20 |  11 – 15 |  6 – 10 |  0 – 5
$\langle{\rm d}N_{\rm ch}/{\rm d}\eta\rangle$ |  18.5$\pm$1.0 |  14.6$\pm$0.9 |  10.6$\pm$0.7 |  6.58$\pm$0.43 |  2.21$\pm$0.24

#### Spherocity.

For the data analysis we followed a strategy similar to that already reported
in Ref. [32]. Spherocity, $S_{0}$, originally proposed here [33] is defined
for a unit vector $\mathbf{\hat{\rm\mathbf{n}}_{\rm\mathbf{s}}}$ which
minimizes the ratio:

$S_{\rm
0}\equiv\frac{\pi^{2}}{4}\underset{\bf\hat{n}_{\rm\bf{s}}}{\text{min}}\left(\frac{\sum_{i}|{\vec{p}}_{{\rm
T},i}\times{\bf\hat{n}_{\rm\bf{s}}}|}{\sum_{i}p_{{\rm T},i}}\right)^{2},$ (1)

where the sum runs over all reconstructed ITS-TPC tracks. At least three
tracks are required within $|\eta|<0.8$ and $p_{\rm T}>0.15$ GeV/$c$ in order
to achieve a good spherocity resolution. The spherocity resolution improves
with the track-reconstruction efficiency, therefore the restrictions on the
purity of primary charged particles can be relaxed. For spherocity we
considered all tracks with at least 50 clusters in the TPC, which satisfy:
$d_{\rm xy}<2.4$ cm, $d_{z}<3.2$ cm, and $\chi^{2}_{\rm TPC}/N_{\rm
clusters}<4$. The exclusion of the ITS requirements guarantees a homogeneous
azimuthal track-reconstruction efficiency.

It is worth mentioning some important features of spherocity:

  * •

The vector products are linear in particle momenta, therefore spherocity is a
collinear safe quantity in pQCD.

  * •

The lower limit of spherocity ($S_{0}\rightarrow 0$) corresponds to event
topologies where all transverse momentum vectors are (anti)parallel or the sum
of the $p_{\rm T}$ is dominated by a single track.

  * •

The upper limit of spherocity ($S_{0}\rightarrow 1$) corresponds to event
topologies where transverse momentum vectors are “isotropically” distributed.
$S_{0}=1$ can only be reached in the limit of an infinite amount of particles.

Since the goal of the present study is to separate jet events from isotropic
ones, we study different spherocity classes for a given multiplicity value.
The multiplicity is measured by counting the number of tracks within
$|\eta|<0.8$. As explained later, we adopted the procedure used in the
analysis of average $p_{\rm T}$ as a function of multiplicity to correct the
number of tracks for detector effects [21]. The detector response is
represented by a two-dimensional distribution: reconstructed spherocity as a
function of generated spherocity, each bin of generated spherocity is
normalized to unity. In this representation, the two-dimensional distribution
gives the normalized response matrix $R^{\prime}(S_{0},S_{\rm m})$, which
contains the probability that an event with spherocity $S_{0}$ is
reconstructed with spherocity $S_{\rm m}$. Figure 1 shows the spherocity
response matrices for two track multiplicity ($N_{\rm m}$). Tracking
efficiency effects on the spherocity resolution are relevant only for low-
multiplicity events, therefore, the $S_{0}$ resolution improves with
increasing multiplicity.

Figure 1:  The detector response for spherocity for two track multiplicity
classes: $\langle{\rm d}N_{\rm m}/{\rm d}\eta\rangle=3.12$ (left) and
$\langle{\rm d}N_{\rm m}/{\rm d}\eta\rangle=25$ (right). Proton-proton
collisions were simulated using PYTHIA 6. The simulations include the particle
transport performed via a GEANT 3 simulation of the ALICE detector. The
markers (boxes around the points) indicate the average (RMS) of the measured
spherocity distributions for each bin of spherocity at generator level. The
spherocity binning varies with ${\rm d}N_{\rm m}/{\rm d}\eta$, because in this
way, it allows the analysis of ten event sub-classes of equal size. The
probability that an event with spherocity $S_{0}$ be reconstructed with
spherocity $S_{\rm m}$ is represented by ${\rm P}(S_{\rm m})$.

In order to study the spherocity dependence of the particle production for a
given track multiplicity value, the sample is divided into ten event sub-
classes of equal size (percentiles), based on the measured spherocity
distribution. From now on, the most jet-like and isotropic events will be
referred to as 0 – 10% and 90 – 100% spherocity event class, respectively.

It has been reported that the evolution of several observables as a function
of center-of-mass energy can be factored out to be due to the changes in
charged-particle multiplicities which in turn depend on the energy. For
example, the particle production sensitive to the underlying event for
different $\sqrt{s}$ exhibits approximate scaling properties connected to
changes in $\langle N_{\rm ch}\rangle$ [34]. Moreover, within uncertainties,
the average $p_{\rm T}$ as a function of multiplicity exhibits a small energy
dependence [21]. Therefore, the spherocity dependent average $p_{\rm T}$ as a
function of charged-particle multiplicity is only presented for pp collisions
at $\sqrt{s}=13$ TeV. The physics message is valid for other center-of-mass
energies, this was verified using data from pp collisions at $\sqrt{s}=5.02$
TeV.

##  4 Corrections

All the measurements presented in this paper are fully corrected for
acceptance and tracking efficiency, contamination from secondary particles,
event and signal loss, as well as multiplicity and spherocity resolution.
Details of these corrections are presented below.

###  4.1 Transverse momentum distributions as a function of particle
multiplicity

The transverse momentum spectrum for a specific event class is obtained by
correcting the track yields $N^{\rm rec}$ reconstructed in each
$(\Delta\eta,\Delta p_{\rm T})$ interval for all detector effects that either
influence the event reconstruction or the track reconstruction. The transverse
momentum distribution is obtained as follows:

$\frac{1}{N_{\rm ev}}\frac{{\rm d}^{2}N_{\rm ch}}{{\rm d}\eta{\rm d}p_{\rm
T}}\equiv\frac{N^{\rm rec}(\eta,p_{\rm T})C(\eta,p_{\rm T})}{N_{\rm ev}^{\rm
rec}\Delta\eta\Delta p_{\rm T}}\epsilon_{\rm ev.\,class}\epsilon_{\rm vz}.$
(2)

The event selection (for a specific event class) and vertex reconstruction
efficiencies are represented by $\epsilon_{\rm ev.\,class}$ and $\epsilon_{\rm
vz}$, respectively. The number of events of a given event class is represented
by $N_{\rm ev}^{\rm rec}$. For the lowest multiplicity class selected using
the V0M amplitude and for $\sqrt{s}=5.02$ TeV ($\sqrt{s}=13$ TeV) they reach
66% and 95% (75% and 95%), respectively, while for the highest multiplicity
class the detector is fully efficient. The track-level correction factors,
$C(\Delta\eta,\Delta p_{\rm T})$, are obtained for events which satisfy the
selection criteria; they include acceptance, efficiency, purity, and $p_{\rm
T}$ resolution. The estimation of the four terms will be explained in detail
in the following.

A data-driven method has been developed to reduce the systematic uncertainty
related to incorrect description of the particle composition in Monte Carlo.
The tracking efficiency is determined using the re-weighting procedure which
is discussed for the first time in Ref. [29] and which is employed also in the
present paper. The method uses the knowledge of the particle composition at
LHC energies, i.e. the abundances of the different particle species within a
specific interval of $p_{\rm T}$ and for a specific event class.

To correct the distributions for secondary-particle contamination, i.e. the
products of weak decays of kaons and $\Lambda$ baryons, and the particles
originating from interactions in the detector material, we used the $d_{\rm
xy}$ distributions of particles in data and Monte Carlo simulations.
Exploiting the differences of the $d_{\rm xy}$ distributions between primary
and secondary particles, especially in the tails, the measured distributions
were fitted by a linear combination of $d_{\rm xy}$ distributions (templates)
for primary and secondary particles obtained from Monte Carlo simulations in
different $p_{\rm T}$ bins. For INEL$\,>0$ pp collisions at $\sqrt{s}=13$ TeV
the contamination ranges from 8.5% at $p_{\rm T}=0.2$ GeV/$c$ to 1% for
$p_{\rm T}>2$ GeV/$c$. The contamination exhibits a small multiplicity
dependence, which is below 2%. For pp collisions at $\sqrt{s}=5.02$ TeV, the
correction factors reach similar values.

The transverse momentum spectra are also corrected for $p_{\rm T}$ resolution;
the correction factor is calculated using the covariance matrix of the Kalman
fit [35]. The $p_{\rm T}$ (multiplicity) dependence of the correction factor
is negligible [29] (below 1%).

Finally, the $p_{\rm T}$ spectra are corrected for the amount of signal which
is missing from the yield due to the event selection (signal loss). This
correction is negligible for high-multiplicity events and reaches 13% (4%) at
$p_{\rm T}=0.2$ ($p_{\rm T}=1$) GeV/$c$ for the lowest multiplicity class
based on $N_{\rm SPD\,tracklets}$.

###  4.2 Spherocity studies

The measurement of the average transverse momentum as a function of charged-
particle multiplicity and spherocity is performed following a strategy close
to that used in earlier publications [36, 21]. The transverse momentum spectra
for different multiplicity and spherocity classes are fully corrected as
described in the previous section. The average transverse momentum is then
calculated from the corrected spectra as the arithmetic mean in the kinematic
range $0.15<p_{\rm T}<10$ GeV/$c$ and $|\eta|<0.8$.

To extract the correlation between $\langle p_{\rm T}\rangle$ and the number
of primary charged particles ($N_{\rm ch}$) in $|\eta|~{}<~{}0.8$ and for the
spherocity class $S_{0}$, the following re-weighting procedure is applied to
account for the experimental resolution of the measured event multiplicity
($N_{\rm m}$) and spherocity ($S_{\rm m}$):

$\langle p_{\rm T}\rangle(N_{\rm ch},S_{0})=\sum_{N_{\rm m}}\sum_{S_{\rm
m}}R(N_{\rm ch},N_{\rm m})\langle p_{\rm T}\rangle(N_{\rm m},S_{\rm
m})R^{\prime}(S_{0},S_{\rm m}).$ (3)

This method is an extension to the one developed for the previous $\langle
p_{\rm T}\rangle$ analysis [36]. It exploits the normalized response matrices
$R$ and $R^{\prime}$ which encode the multiplicity, and spherocity detector
resolutions, respectively. The average $p_{\rm T}$ for the $S_{0}$ event class
is encoded inside the inner sum, where the weights $R^{\prime}(S_{0},S_{\rm
m})$ are explicitly applied to $\langle p_{\rm T}\rangle$ values. The
resulting $\langle p_{\rm T}\rangle(N_{\rm m},S_{0})$ is then corrected for
multiplicity resolution. It is worth mentioning that the spherocity-integrated
class (0 – 100%) only requires the multiplicity correction. The Monte Carlo
non-closure, discussed in the next section, is assigned as systematic
uncertainty.

##  5 Systematic uncertainties

###  5.1 Transverse momentum spectra

The relative systematic uncertainties on the $p_{\rm T}$ spectra are
summarized in Table 3. They include the effect of the event selection based on
the vertex position, which is studied by comparing the fully corrected $p_{\rm
T}$ spectra obtained with alternative vertex selections: $|z|<5$ cm and
$|z|<20$ cm. The corrections due to trigger and vertex selection were
determined using the EPOS LHC [37] event generator and the deviations with
respect to the nominal values, i.e. those obtained with PYTHIA 6, were
assigned as systematic uncertainties. The same procedure was employed for the
estimation of the systematic uncertainty associated to the signal loss
correction. The systematic uncertainty related to the track selection was
studied by varying the track cuts for which we used the variation intervals
described in Ref. [29]. We also studied the systematic effects related to the
uncertainty on the primary particle composition which is assumed for the
efficiency correction. This uncertainty takes into account the extrapolation
of the spectra to low $p_{\rm T}$, the relative particle abundances at high
$p_{\rm T}$, the uncertainties of the measured particle spectra, and the Monte
Carlo assumptions on the $\Sigma^{\pm}/\Lambda$ spectra ratios. The systematic
uncertainties of the correction for secondaries contamination is estimated by
varying the fit model using two templates, i.e. for primaries and secondaries,
or three templates, i.e. primaries, secondaries from interactions in the
detector material, and secondaries from weak decays, as well as varying the
fit momentum ranges. Since we are using the same event selection and track
cuts as those used in Ref. [29], the systematic uncertainties associated with
matching efficiency, $p_{\rm T}$ resolution and material budget, are
identical.

Table 3: Main sources and values of the relative systematic uncertainties of
transverse momentum spectra for pp collisions at $\sqrt{s}=5.02$ TeV. The
maximum values of the uncertainties, among all the multiplicity classes, are
reported for low-, intermediate-, and high-$p_{\rm T}$ intervals. Systematic
uncertainties for pp collisions at $\sqrt{s}=13$ TeV are shown inside the
parentheses. The systematic uncertainty due to trigger and event selection is
$p_{\rm T}$ independent and therefore it is not included in the table. It
reaches $\sim 7.6$% ($\sim 6.3$%) for the lowest multiplicity class in pp
collisions at $\sqrt{s}=5.02$ TeV ($\sqrt{s}=13$ TeV), and it is smaller than
0.5% for the other multiplicity classes. pp collisions at $\sqrt{s}=5.02$ TeV
($\sqrt{s}=13$ TeV)
---
$p_{\rm T}$ (GeV/$c$) |  0.15 |  3.0 |  10
Pileup |  3.5% (3.5%) |  4.5% (4.5%) |  4.5% (4.5%)
Vertex selection |  0.5% (0.5%) |  0.5% (0.5%) |  0.5% (0.5%)
Signal loss |  2.3% (1.1%) |  1.2%(0.5%) |  0.4% (0.7%)
Track selection |  1.6% (1.7%) |  3.1% (1.7%) |  4.0% (4.0%)
Secondary particles |  1.3% (1.4%) |  1.0% (1.0%) |  1.0% (1.0%)
Particle composition |  2.0% (2.0%) |  2.5% (2.5%) |  2.0% (2.0%)
Tracking efficiency |  1.0% (1.0%) |  4.2% (4.2%) |  4.2% (4.2%)
$p_{\rm T}$ resolution |  0.0% (0.0%) |  0.0% (0.0%) |  0.1% (0.1%)
Material budget |  1.5% (1.5%) |  0.5% (0.5%) |  0.2% (0.2%)
Total |  5.4% (5.1%) |  7.5% (7.0%) |  7.7% (7.7%)
Total ($N_{\rm ch}$-dependent) |  4.1% (3.5%) |  5.8% (5.5%) |  5.9% (6.5%)

###  5.2 Average transverse momentum

A summary of the systematic uncertainties for three multiplicity values and
for different spherocity classes is shown in Table 4. In order to estimate the
systematic uncertainties of $\langle p_{\rm T}\rangle$, the results of the
data analysis and of the evaluation of the corrections from Monte Carlo
simulations were studied considering cut variations and Monte Carlo
assumptions, within reasonable limits. The effect of the track cuts on
$\langle p_{\rm T}\rangle$ was found to be spherocity independent and of the
order of 1%. The efficiency correction is another spherocity independent
contribution and it is found to be $\sim$1%. This contribution takes into
account the different particle composition in data and models, as well as the
multiplicity dependence of the correction. We also studied the multiplicity
dependence of the purity correction; the effect was found to be smaller than
0.5%. The most relevant spherocity independent contribution is related to the
re-weighting procedure to correct for the detector multiplicity resolution.
This was quantified from the Monte Carlo non-closure, it amounts to
$\sim$1.36%, $\sim$0.86% and $\sim$1.26% for ${\rm d}N_{\rm ch}/{\rm
d}\eta=1.88$, 6.25, 25.00, respectively.

The set of track cuts used to measure spherocity was also varied compared to
those used for the $p_{\rm T}$ spectra analysis. The effect on the results
amounted to 1%. The most relevant contribution to the systematic uncertainties
originates from the re-weighting procedure method which is used to correct for
the spherocity resolution. The Monte Carlo non-closure is assigned as a
systematic uncertainty. For the lowest multiplicity value, ${\rm d}N_{\rm
ch}/{\rm d}\eta$=1.88, the uncertainty reaches 3.23%, 4.55%, and 7.06% for the
0 – 10%, 40 – 50%, and 90 – 100% spherocity classes, respectively. For higher
multiplicities, e.g. ${\rm d}N_{\rm ch}/{\rm d}\eta$=25.0, the Monte Carlo
non-closure amounts to 0.57%, 1.07%, and 2.01% for the 0 – 10%, 40 – 50%, and
90 – 100% spherocity classes, respectively. As expected from the detector
response, the most relevant effects are observed for low-multiplicity events
in particular for the isotropic classes. As will be seen later, in Monte Carlo
jet-like events, the average $p_{\rm T}$ shows a strong change with
multiplicity at ${\rm d}N_{\rm ch}/{\rm d}\eta\sim 7$. This effect increases
the size of the uncertainty (Monte Carlo non-closure) in that multiplicity
interval. This is the dominant contribution to the systematic uncertainties
and covers the largest variations observed between data and PYTHIA 8 (version
8.212) [10] (tune Monash 2013 [38]).

The model dependence is also checked by using events simulated with PYTHIA 8
and EPOS LHC which include the particle transport through the detector. The
corrections were calculated using these simulations and the maximum variation
with respect to the nominal values (using PYTHIA 6 simulations) are below 1%.

Table 4: Main sources and values of the relative systematic uncertainties on
the average $p_{\rm T}$ for different spherocity classes. The three quoted
values (for each contribution) correspond to ${\rm d}N_{\rm ch}/{\rm
d}\eta=1.88$, 6.25, and 25.0, respectively. Spherocity-dependent contributions
---
Spherocity class |  0 – 100% |  0 – 10% |  40 – 50% |  90 – 100%
Model dep. (%) |  0.5, 0.7, 0.2 |  0.4, 0.4, 0.6 |  0.6, 0.5, 0.3 |  0.9, 0.8, 0.2
Sec. particles (%) |  0.2, 0.3, 1.2 |  1.0, 1.5, 1.9 |  0.3, 0.3, 1.1 |  0.6, 0.3, 0.9
Ev. selection (%) |  2.2, 0.0, 0.0 |  1.9, 1.4, 0.4 |  1.3, 0.4, 0.0 |  1.3, 0.1, 0.00
$S_{\rm o}$ res. corr. (%) | na |  3.2, 5.4, 0.6 |  4.6, 2.4, 1.1 |  7.1, 3.7, 2.0
$S_{\rm o}$ track cuts (%) | 1.00
Spherocity-independent contributions
$N_{\rm ch}$ res. corr (%) | 1.4, 0.9, 1.3
$p_{\rm T}$ track cuts (%) | 0.8, 0.9, 1.2
Efficiency corr. (%) | 0.4, 0.2, 0.2
Particle composition (%) | 1.0, 1.0, 1.0
$N_{\rm ch}$ dep. eff. corr. (%) | 0.5, 0.7, 0.9
$N_{\rm ch}$ dep. sec. corr. (%) | 0.2, 0.1, 0.1
$S_{\rm o}$-dep. total (%) |  2.2, 0.8, 1.2 |  4.0, 5.8, 2.3 |  4.9, 2.7, 1.9 |  7.3, 3.9, 2.4
$S_{\rm o}$-indep. total (%) | 2.0, 1.8, 2.2
Total (%) |  3.0, 2.0, 2.5 |  4.5, 6.1, 3.2 |  5.3, 3.2, 3.0 |  7.6, 4.3, 3.3

Figure 2: Transverse momentum distributions of charged particles for
multiplicity classes selected using SPD tracklets in $|\eta|<0.8$. Results for
pp collisions at $\sqrt{s}=5.02$ and 13 TeV are shown in the left and right
panels, respectively. Statistical and total systematic uncertainties are shown
as error bars and boxes around the data points, respectively. In the middle
panels, ratios of multiplicity dependent spectra to INEL$\,>0$ are shown in
logarithmic scale. In the bottom panels we show the ratios in a linear scale
to illustrate the dramatic behavior of the ratios. The systematic
uncertainties on the ratios are obtained by considering only contributions
uncorrelated across multiplicity. The spectra are scaled to improve the
visibility.

Figure 3: Transverse momentum distributions of charged particles for different
V0M multiplicity classes. Results for pp collisions at $\sqrt{s}=5.02$ and 13
TeV are shown in the left and right panels, respectively. Statistical and
total systematic uncertainties are shown as error bars and boxes around the
data points, respectively. In the middle panels, ratios of multiplicity
dependent spectra to INEL$\,>0$ are shown in logarithmic scale. The systematic
uncertainties on the ratios are obtained by considering only contributions
uncorrelated across multiplicity. The spectra are scaled to improve the
visibility.

Figure 4: Transverse momentum distributions of charged particles for high-
multiplicity ($\langle{\rm d}N_{\rm ch}/{\rm d}\eta\rangle\approx 20$) pp
collisions at $\sqrt{s}=5.02$ (empty markers) and 13 TeV (full markers).
Results for V0-based (squares) and SPD-based (circles) multiplicity estimators
are shown. The bottom panel shows the $p_{\rm T}$ spectrum obtained using the
V0-based multiplicity estimator normalized to that using the SPD-based
multiplicity estimator. Only statistical uncertainties are shown as error
bars.

Figure 5: Evolution of the spectral shape of the transverse momentum
distribution as a function of charged-particle multiplicity. The spectral
shape is characterized by the exponent of the power-law function which fits
the high-$p_{\rm T}$ part ($p_{\rm T}>6$ GeV/$c$) of the invariant yields.
Results for pp collisions at $\sqrt{s}=13$ TeV are shown. A comparison of the
two multiplicity estimators discussed in this paper is shown in the left
panel. Comparisons with Monte Carlo generators predictions are shown in the
middle and right panels. Statistical and total systematic uncertainties are
shown as error bars and boxes around the data points, respectively.

##  6 Results

###  6.1 Transverse momentum spectra as a function of charged-particle
multiplicity

The $p_{\rm T}$ distributions of charged particles, measured in $|\eta|<0.8$
for pp collisions at $\sqrt{s}=5.02$ and 13 TeV, are shown in Fig. 2 for the
different multiplicity classes selected using the estimator based on $N_{\rm
SPD\,tracklets}$. The bottom panels depict the ratios to the $p_{\rm T}$
distribution of the INEL$\,>0$ event class. The features of the spectra, i.e.
the change of the spectral shape going from low- to high-multiplicity values,
are qualitatively the same for both energies. The only significant difference
is the multiplicity reach which is higher at 13 TeV than that at 5.02 TeV. In
the following we discuss the results for pp collisions at the highest energy.
As shown in Fig. 2, the $p_{\rm T}$ spectra become harder as the multiplicity
increases, which contributes to the increase of the average transverse
momentum with multiplicity. The ratios to the INEL$>0$ $p_{\rm T}$
distribution exhibit two distinct behavior. While at low $p_{\rm T}$ ($<0.5$
GeV/$c$) the ratios exhibit a modest $p_{\rm T}$ dependence, for $p_{\rm
T}>0.5$ GeV/$c$ they strongly depend on multiplicity and $p_{\rm T}$.

Figure 6: Self-normalized yields of charged particles integrated over
different $p_{\rm T}$ intervals: $2<p_{\rm T}<4$ GeV/$c$, $4<p_{\rm T}<6$
GeV/$c$, and $6<p_{\rm T}<10$ GeV/$c$. The integrated yields for pp collisions
at $\sqrt{s}=13$ TeV are shown as a function of charged-particle density at
mid-pseudorapidity. Statistical and uncorrelated (across multiplicity)
systematic uncertainties are shown as error bars and boxes around the data
points, respectively. Statistical uncertainties are negligible compared to
systematic uncertainties. Data are compared with PYTHIA 8 (dashed lines) and
EPOS LHC (solid lines). The dotted line is drawn to see the differences
between data and the linear dependence. Deviations of data from the linear
trend are shown in the bottom panel.

Figure 3 shows the multiplicity dependent $p_{\rm T}$ spectra using a
multiplicity selection based on the V0M amplitude. Results for pp collisions
at $\sqrt{s}=5.02$ and 13 TeV are shown. The average multiplicity values are
significantly smaller than those reached with the mid-pseudorapidity estimator
(based on $N_{\rm SPD\,tracklets}$). For example, in pp collisions at
$\sqrt{s}=13$ TeV, while the average charged-particle multiplicity density
amounts to 56.55 for the highest $N_{\rm SPD\,tracklets}$ class, it only
reaches 27.61 for the highest V0M multiplicity class. We note that for similar
average particle densities, e.g. the multiplicity classes II (V0M) and VII’
(SPD tracklets) in pp collisions at $\sqrt{s}=13$ TeV, the ratios measured
using the V0M amplitude and the $N_{\rm SPD\,tracklets}$ are similar. The
comparison of the $p_{\rm T}$ spectra for these multiplicity classes is shown
in Fig. 4. We observe that for transverse momentum below 0.5 GeV/$c$, the
spectra exhibit the same shape. For transverse momenta within 0.5–3 GeV/$c$
the spectra for the multiplicity class II is harder than that for the VII”
class. At higher $p_{\rm T}$, the spectral shapes are the same, but the yield
of the class II is $\sim$15% higher than that for the VII’ class. Similar
results are obtained if we compare the multiplicity classes I and VI’ for pp
collisions at 5.02 TeV.

Commonly, the particle production is characterized by quantities like
integrated yields, or any fit parameter of the curve extracted from fits to
the data, for example, the so-called inverse slope parameter reported by ALICE
in Ref. [39]. This facilitates the visualization of the evolution of the
particle production as a function of multiplicity and the comparison among
different colliding systems. Several publications have adopted this strategy
for soft ($p_{\rm T}<2$ GeV/$c$) [2, 6, 21] physics and others to describe the
particle production for intermediate and high $p_{\rm T}$ ($2\leq p_{\rm
T}<20$ GeV/$c$) [40]. It is interesting and important to define a common
quantity to compare the shape of the high-$p_{\rm T}$ part of the spectra of
different particle species and collision systems. The natural choice is
fitting a power-law function ($\alpha\times p_{\rm T}^{-n}$) to the invariant
yield and studying the multiplicity dependence of the exponent ($n$) extracted
from the fit. Figure 5 illustrates the results considering particles with
transverse momentum within 6–20 GeV/$c$ for pp at $\sqrt{s}=13$ TeV. It is
worth mentioning that within uncertainties the power-law function describes
rather well the data in that $p_{\rm T}$ interval. Similarly, the $p_{\rm T}$
spectra simulated with the different generators are well described (within 2%)
by the power-law function.

Within uncertainties, going from low to high multiplicity $n$ decreases taking
values from 6 to 5, respectively. A similar behavior has been reported for
heavy-ion collisions [41]. Moreover, the results using the two multiplicity
estimators are consistent within the overlapping multiplicity interval. This
result is consistent with that shown in Fig. 4. PYTHIA 6 and 8 simulations
describe the trends very well, but a strong deviation between EPOS LHC and
data is observed. In PYTHIA 8, it has been shown that the number of
high-$p_{\rm T}$ jets increases with event multiplicity. Moreover, for a given
event multiplicity and fixed jet $p_{\rm T}$, the high-$p_{\rm T}$ tails of
the charged-particle spectra are very similar in low- and high-multiplicity
events [16]. Therefore, based on PYTHIA 8 studies, the reduction of the power-
law exponent with increasing multiplicity can be attributed to an increasing
number of high-$p_{\rm T}$ jets.

As pointed out above, the ratios to the INEL$\,>0$ $p_{\rm T}$ distributions
for $\langle{\rm d}N_{\rm ch}/{\rm d}\eta\rangle\lesssim 25$ exhibit a weak
$p_{\rm T}$-dependence for $p_{\rm T}>4$ GeV/$c$. This applies to both
energies and to all multiplicity estimators. To illustrate better the
behaviour of the yields at high momenta, we adopted a representation
previously used for heavy-flavour hadrons [42] to point out to the
similarities between the two results. The trend at high-$p_{\rm T}$ is
highlighted in Fig. 6, which shows the integrated yields for three transverse
momentum intervals ($2<p_{\rm T}<10$ GeV/$c$, $4<p_{\rm T}<10$ GeV/$c$, and
$6<p_{\rm T}<10$ GeV/$c$) as a function of the average mid-pseudorapidity
multiplicity. Both the charged-particle yields and the average multiplicity
are self-normalized, i.e. they are divided by their average value for the
INEL$\,>0$ sample. The high-$p_{\rm T}$ ($>4$ GeV/$c$) yields of charged
particles increase faster than the charged-particle multiplicity, while the
increase is smaller when we consider lower-$p_{\rm T}$ particles. The trend of
the data is qualitatively well reproduced by PYTHIA 8, but for $p_{\rm T}>6$
GeV/$c$ the model significantly overestimates the ratio by a factor larger
than 1.5. Although the shapes of the spectra (characterized by $n$) are not
well reproduced by EPOS LHC, the model gives the best description of the self-
normalized yields. Despite the large uncertainties, it is clear the data show
a non-linear increase.

###  6.2  Double-differential study of the average transverse momentum

The spherocity-integrated average $p_{\rm T}$ as a function of ${\rm d}N_{\rm
ch}/{\rm d}\eta$ for pp collisions at $\sqrt{s}=13$ TeV is shown in Fig. 7. In
accordance with measurements at lower energies [21], the $\langle p_{\rm
T}\rangle$ increases with ${\rm d}N_{\rm ch}/{\rm d}\eta$. In PYTHIA 8 the
effect is enhanced by color reconnection, which allows the interaction among
partons originating from multiple semi-hard scatterings via color strings. The
minimum-bias data are compared with analogous measurements for the most jet-
like structure (0 – 10%) and isotropic (90 – 100%) event classes. Studying
observables as a function of spherocity reveals interesting features. On one
hand, for isotropic events the average $p_{\rm T}$ stays systematically below
the spherocity-integrated $\langle p_{\rm T}\rangle$ over the full
multiplicity range; on the other hand, for jet-like events the $\langle p_{\rm
T}\rangle$ is higher than that for spherocity-integrated events. Moreover,
within uncertainties the overall shape of the correlation, i.e. a steep linear
rise below ${\rm d}N_{\rm ch}/{\rm d}\eta=10$ followed by a less steep but
still linear rise above, is not spherocity-dependent.

Figure 8 shows that within uncertainties, PYTHIA 8 with color reconnection
gives an adequate description of the spherocity-integrated event class. It is
worth mentioning that color reconnection was originally introduced to explain
the rise of $\langle p_{\rm T}\rangle$ with multiplicity [43]. However, PYTHIA
6 shows a steeper rise of $\langle p_{\rm T}\rangle$ with ${\rm d}N_{\rm
ch}/{\rm d}\eta$ than that seen in data. The Perugia 2011 tune relies on
Tevatron and SPS minimum-bias data, while the Monash tune was constrained
using the early LHC measurements [38]. The comparison of data with EPOS LHC is
also shown. Clearly, the quantitative agreement is as good as that achieved by
PYTHIA 8. The EPOS LHC model uses a different approach in order to simulate
the hadronic interactions. Namely, the model considers a collective
hadronization which depends only on the geometry and the density [37].

Figure 7: Average transverse momentum as a function of event multiplicity in
pp collisions at $\sqrt{s}=13$ TeV. Results for the spherocity-integrated case
(0 – 100%) are contrasted with the measurements for the most jet-like (0 –
10%) and isotropic (90 – 100%) events. Statistical uncertainties (error bars)
are negligible compared to systematic uncertainties (boxes around the data
points).

Figure 8: Average transverse momentum as a function of event multiplicity in
pp collisions at $\sqrt{s}=13$ TeV. Results for the spherocity-integrated case
(0 – 100%), the most jet-like (0 – 10%) and isotropic (90 – 100%) events are
compared with Monte Carlo predictions. Predictions of PYTHIA 8 with and
without (null reconnection range, $\rm{rr}=0$) color reconnection, as well as
PYTHIA 6 and EPOS LHC are displayed. Statistical uncertainties (error bars)
are negligible compared to systematic uncertainties (shaded area around the
data points). Data to model ratios are shown in the bottom panel. The color
band around unity represents the systematic uncertainty.

For the 0 – 10% and 90 – 100% spherocity classes, Fig. 8 also shows
comparisons between data and Monte Carlo generators (PYTHIA 6, PYTHIA 8 and
EPOS LHC). It is worth mentioning that we also used spherocity percentiles in
all the Monte Carlo event generators reported in this paper because their
spherocity distributions do not differ much from those measured in data. For
further Monte Carlo comparisons the spherocity binning which was used in the
analysis is provided as HEP data. In low-multiplicity events (${\rm d}N_{\rm
ch}/{\rm d}\eta<10$), the deviations between data and PYTHIA 8 (without color
reconnection) are smaller and larger respectively for the 0 – 10% and 90 –
100% spherocity classes than those seen for the 0 – 100% spherocity class. The
effect could be a consequence of the reduction of color reconnection
contribution in events containing jets surrounded by a small underlying event
activity. For isotropic events the three models quantitatively describe the
correlation. Even for PYTHIA 6, the size of the discrepancy which was pointed
out for the spherocity-integrated event class is reduced. On the contrary, for
jet-like events both PYTHIA 6 and 8 exhibit a larger disagreement with the
data. These models produce three distinct multiplicity regions, for ${\rm
d}N_{\rm ch}/{\rm d}\eta\lesssim 7$ the models give a steeper rise of $\langle
p_{\rm T}\rangle$ than data. Within the intermediate multiplicity interval
($7\lesssim{\rm d}N_{\rm ch}/{\rm d}\eta\lesssim 25$), the slope of $\langle
p_{\rm T}\rangle$ given by models is more compatible with that seen in data,
although the models overestimate the average $p_{\rm T}$. While in data the
average $p_{\rm T}$ increases at a constant rate with multiplicity for ${\rm
d}N_{\rm ch}/{\rm d}\eta\gtrsim 7$, PYTHIA 6 and 8 shows a third change of the
slope of $\langle p_{\rm T}\rangle$, observed for ${\rm d}N_{\rm ch}/{\rm
d}\eta\gtrsim 25$. The data to model ratio indicates a discrepancy larger than
10%, which is larger than the systematic uncertainties associated to $\langle
p_{\rm T}\rangle$ in that multiplicity interval.

In order to study the details of the changes of the functional form of
$\langle p_{\rm T}\rangle(N_{\rm ch})$ due to the spherocity selection, Fig. 9
shows the average $p_{\rm T}$ of jet-like and isotropic events normalized to
that for the spherocity-integrated event class. For jet-like events, the data
exhibit a hint of a modest peak at ${\rm d}N_{\rm ch}/d\eta\sim 7$, which is
not significant if we consider the size of the systematic uncertainties.
Moreover, within uncertainties the ratio remains constant for ${\rm d}N_{\rm
ch}/{\rm d}\eta\gtrsim 25$. EPOS LHC describes rather well the high-
multiplicity behavior, however, it overestimates the peak. PYTHIA 6 and 8 show
the worst agreement with the data. In this representation, the three distinct
regions, which were described before are highlighted. In PYTHIA 8, the peak
(at ${\rm d}N_{\rm ch}/d\eta\sim 7$) in jet-like events is caused by particles
with transverse momentum above 2 GeV/$c$. The size of the peak is determined
by particles with $p_{\rm T}>5-6$ GeV/$c$. In contrast, data do not show a
significant peak structure for any specific transverse momentum interval. We
also varied the upper $p_{\rm T}$ ($0.15<p_{\rm T}<p_{\rm T}^{\rm max}$) limit
($p_{\rm T}^{\rm max}=10$ GeV/$c$ is the default) and studied the effect on
the extracted $\langle p_{\rm T}\rangle$. The $\langle p_{\rm T}\rangle$
remains constant within uncertainties for $4<p_{\rm T}^{\rm max}<10$ GeV/$c$
in data and for $6<p_{\rm T}^{\rm max}<10$ GeV/$c$ in PYTHIA 8. For $p_{\rm
T}^{\rm max}=2$ GeV/c the $\langle p_{\rm T}\rangle$ decreases by 23% (29%) in
data (PYTHIA 8) compared to $p_{\rm T}^{\rm max}=10$ GeV/$c$. The relative
difference of $\langle p_{\rm T}\rangle$ between data and PYTHIA 8 amounts to
9% (4%) for $p_{\rm T}^{\rm max}=2$ GeV/$c$ ($p_{\rm T}^{\rm max}=10$
GeV/$c$). The results suggest that the power-law tail produces a smaller
impact on data than in PYTHIA 8. A similar ratio for isotropic events shows a
smaller structure at ${\rm d}N_{\rm ch}/d\eta\sim 7$. This effect is well
reproduced by all models.

Finally, we also examined the evolution of $\langle p_{\rm T}\rangle(N_{\rm
ch})$ going from the most jet-like to the most isotropic event classes. Figure
10 shows the spherocity-dependent $\langle p_{\rm T}\rangle(N_{\rm ch})$ in
data and models, the data to model ratios are displayed in Fig. 11. The
difference between the 0 – 10% and 10 – 20% spherocity classes is smaller for
data and EPOS LHC than for PYTHIA 6 and 8. Moreover, within uncertainties
PYTHIA 8 describes rather well the data for the 10 – 20% spherocity class.
This contrasts with the disagreement between the model and data for the 0 –
10% spherocity class. Other features in PYTHIA 6 and 8 are the reduction of
the bump at ${\rm d}N_{\rm ch}/d\eta\sim 7$ and the disappearance of a third
rise of the $\langle p_{\rm T}\rangle$ for ${\rm d}N_{\rm ch}/d\eta\gtrsim 25$
when one goes from the 0 – 10% to the 10 – 20% spherocity classes. The
agreement among models and data for the 20 – 100% spherocity classes is
similar to that observed for the 10 – 20% spherocity class. Within
uncertainties, PYTHIA 8 and EPOS LHC qualitatively describe the data for ${\rm
d}N_{\rm ch}/{\rm d}\eta\gtrsim 10$, while PYTHIA 6 overestimates the average
$p_{\rm T}$.

From previous LHC studies we know that the production cross section of jets in
high-multiplicity pp collisions is smaller in data than predicted from the
Monte Carlo generators [32, 44, 45]. Therefore, a possible interpretation is
that the low-momentum partons, color connected with higher momentum ones
(jets), would produce an overall increase of the hadron transverse momentum.
This would affect more the low-$p_{\rm T}$ part of the spectrum associated
with jet-enriched samples, which are achieved by requiring low-spherocity
values. The incorporation of these new observables into the PYTHIA 8 tuning
could be a challenge because, on one hand, the color reconnection has to be
reduced to describe the low-$S_{0}$ data; on the other hand, the variation
should not be too large because the good description of the spherocity-
integrated and isotropic classes could be affected.

Figure 9: Average $p_{\rm T}$ of jet-like (circles) and isotropic (triangles)
events normalized to that for the spherocity-integrated event class. The
measurements are compared with different Monte Carlo generators. Statistical
uncertainties (error bars) are negligible compared to systematic uncertainties
(boxes around the data points).

Figure 10: Average transverse momentum as a function of event multiplicity in
pp collisions at $\sqrt{s}=13$ TeV. Results for nine spherocity classes are
compared with Monte Carlo predictions. Statistical uncertainties (error bars)
are negligible compared to systematic uncertainties (shaded area around the
data points).

Figure 11: Data to model ratios as a function of event multiplicity in pp
collisions at $\sqrt{s}=13$ TeV. Results for nine spherocity classes are
shown. Systematic uncertainties are displayed as shaded areas around unity.

##  7 Summary and conclusions

In this paper, we have reported the transverse momentum spectra of inclusive
charged particles in pp collisions at $\sqrt{s}=5.02$ and 13 TeV. The
measurements were performed in the kinematic range of $|\eta|<0.8$ and $p_{\rm
T}>0.15$ GeV/$c$. The particle production was studied as a function of event
multiplicity quantified by two estimators, one based on the number of SPD
tracklets within $|\eta|<0.8$, and the second one based on the multiplicity in
the V0 forward detector (V0M amplitude). For similar average charged-particle
densities, the particle production above $p_{\rm T}=1$ GeV/$c$ is higher in pp
collisions at $\sqrt{s}=13$ TeV than at $\sqrt{s}=5.02$ TeV. For a fixed
center-of-mass energy, particle production above $p_{\rm T}=0.5$ GeV/$c$
exhibits a remarkable multiplicity dependence. Namely, for transverse momenta
below 0.5 GeV/$c$, the ratio of the multiplicity dependent spectra to those
for INEL$\,>0$ pp collisions is rather constant, and for higher momenta, it
shows a significant $p_{\rm T}$ dependence. The behavior observed for each of
the two multiplicity estimators are consistent within the $\langle{\rm
d}N_{\rm ch}/{\rm d}\eta\rangle$ interval defined by the V0M multiplicity
estimator, which gives a $\langle{\rm d}N_{\rm ch}/{\rm d}\eta\rangle$ reach
of $\sim$25\. For the highest V0M multiplicity class, the ratio increases
going from $p_{\rm T}=0.5$ GeV/$c$ up to $p_{\rm T}\approx 4$ GeV/$c$, then
for higher $p_{\rm T}$, it shows a smaller increase.

The particle production at high transverse momenta is characterized by the
exponent of a power-law function which is fitted to the invariant yield
considering particles with $6<p_{\rm T}<20$ GeV/$c$. Within that $p_{\rm T}$
interval, the power-law function describes rather well the $p_{\rm T}$
spectra. In concordance to the ratios discussed above, within uncertainties,
the functional form of $n$ as a function of $\langle{\rm d}N_{\rm ch}/{\rm
d}\eta\rangle$ is the same for the two multiplicity estimators used in this
analysis. Moreover, $n$ is found to decrease with $\langle{\rm d}N_{\rm
ch}/{\rm d}\eta\rangle$. Within uncertainties, PYTHIA 8 (tune Monash 2013) and
PYTHIA 6 (tune Perugia 2011) quantitatively reproduce the behavior of data,
while EPOS LHC overestimates the value of the exponent. Nevertheless, all
models quantitative describe the $p_{\rm T}$ integrated yields. The use of
power-law exponents facilitates the study of the particle production at high
$p_{\rm T}$ for different collision systems.

Finally, the measurement of the average transverse momentum as a function of
event multiplicity at mid-pseudorapidity was presented. The results for the
spherocity-integrated class (nearly identical to INEL$\,>0$ pp collisions) at
$\sqrt{s}=13$ TeV are consistent with previous measurements at lower energies.
The increase of the average $p_{\rm T}$ with increasing multiplicity is well
captured by PYTHIA 8 and EPOS LHC. In order to get a better insight into the
particle production mechanisms, the spherocity-integrated sample was separated
into different sub-classes characterized by the event structure in the
transverse plane. Jet-like and isotropic events were selected based on the
spherocity of the events. Isotropic events are well described by the three
models which were considered in this work. Interestingly, PYTHIA 6 reproduces
these event classes better than the INEL$\,>0$ sample. For jet-like events,
the average $p_{\rm T}$ is overestimated by PYTHIA 6 and 8 models in the full
multiplicity interval reported. However, EPOS LHC gives the best description
of the jet-like event subsample.

The results presented in this paper illustrate the difficulties for the models
to describe different observables once they are differentially analyzed as a
function of several variables. The measurements are important to better
understand the similarities between heavy-ion and small collision systems, as
well as for Monte Carlo tuning purposes.

## 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), Universidade Federal do Rio Grande do Sul (UFRGS),
Financiadora de Estudos e Projetos (Finep) and Fundação de Amparo à Pesquisa
do Estado de São Paulo (FAPESP), Brazil; Ministry of Science & Technology of
China (MSTC), National Natural Science Foundation of China (NSFC) and Ministry
of Education of China (MOEC) , China; Croatian Science Foundation and Ministry
of Science and Education, 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 Carlsberg Foundation and Danish
National Research Foundation (DNRF), Denmark; Helsinki Institute of Physics
(HIP), Finland; Commissariat à l’Energie Atomique (CEA), Institut National de
Physique Nucléaire et de Physique des Particules (IN2P3) and Centre National
de la Recherche Scientifique (CNRS) and Région des Pays de la Loire, 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; Centro Fermi - Museo Storico della
Fisica e Centro Studi e Ricerche Enrico Fermi and Istituto Nazionale di Fisica
Nucleare (INFN), Italy; Institute for Innovative Science and Technology ,
Nagasaki Institute of Applied Science (IIST), Japan Society for the Promotion
of Science (JSPS) KAKENHI and Japanese Ministry of Education, Culture, Sports,
Science and Technology (MEXT), 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 Science and Higher
Education and National Science Centre, 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 and Ministry of Research and Innovation and Institute of Atomic
Physics, 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; National Science and Technology Development Agency (NSDTA),
Suranaree University of Technology (SUT) and Office of the Higher Education
Commission under NRU project of Thailand, Thailand; Turkish Atomic Energy
Agency (TAEK), 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.

## References

  * [1] C. Loizides, “Experimental overview on small collision systems at the LHC,” Nucl. Phys. A956 (2016) 200–207, arXiv:1602.09138 [nucl-ex].
  * [2] ALICE Collaboration, B. Abelev et al., “Multiplicity Dependence of Pion, Kaon, Proton and Lambda Production in p-Pb Collisions at $\sqrt{s_{NN}}$ = 5.02 TeV,” Phys. Lett. B728 (2014) 25–38, arXiv:1307.6796 [nucl-ex].
  * [3] ALICE Collaboration, J. Adam et al., “Multiplicity dependence of charged pion, kaon, and (anti)proton production at large transverse momentum in p-Pb collisions at $\mathbf{\sqrt{{\textit{s}}_{\rm NN}}}$ = 5.02 TeV,” Phys. Lett. B760 (2016) 720–735, arXiv:1601.03658 [nucl-ex].
  * [4] ALICE Collaboration, S. Acharya et al., “Multiplicity dependence of light-flavor hadron production in pp collisions at $\sqrt{s}$ = 7 TeV,” arXiv:1807.11321 [nucl-ex].
  * [5] CMS Collaboration, V. Khachatryan et al., “Evidence for collectivity in pp collisions at the LHC,” Phys. Lett. B765 (2017) 193–220, arXiv:1606.06198 [nucl-ex].
  * [6] ALICE Collaboration, J. Adam et al., “Enhanced production of multi-strange hadrons in high-multiplicity proton-proton collisions,” Nature Phys. 13 (2017) 535–539, arXiv:1606.07424 [nucl-ex].
  * [7] K. Werner, M. Bleicher, B. Guiot, I. Karpenko, and T. Pierog, “Evidence for Flow from Hydrodynamic Simulations of $p$-Pb Collisions at 5.02 TeV from $\nu_{2}$ Mass Splitting,” Phys. Rev. Lett. 112 no. 23, (2014) 232301, arXiv:1307.4379 [nucl-th].
  * [8] C. Bierlich, G. Gustafson, L. Lönnblad, and A. Tarasov, “Effects of Overlapping Strings in pp Collisions,” JHEP 1503 (2015) 148, arXiv:1412.6259 [hep-ph].
  * [9] I. Bautista, A. F. Téllez, and P. Ghosh, “Indication of change of phase in high-multiplicity proton-proton events at LHC in String Percolation Model,” Phys. Rev. D92 no. 7, (2015) 071504, arXiv:1509.02278 [nucl-th].
  * [10] T. Sjöstrand, S. Ask, J. R. Christiansen, R. Corke, N. Desai, et al., “An Introduction to PYTHIA 8.2,” Comput. Phys. Commun. 191 (2015) 159–177, arXiv:1410.3012 [hep-ph].
  * [11] A. Ortiz, P. Christiansen, E. Cuautle, I. A. Maldonado, and G. Paić, “Color reconnection and flowlike patterns in $pp$ collisions,” Phys. Rev. Lett. 111 (Jul, 2013) 042001. http://link.aps.org/doi/10.1103/PhysRevLett.111.042001.
  * [12] J. D. Orjuela Koop, A. Adare, D. McGlinchey, and J. L. Nagle, “Azimuthal anisotropy relative to the participant plane from a multiphase transport model in central $p+\mathrm{Au}$, $d+\mathrm{Au}$, and ${}^{3}\mathrm{He}+\phantom{\rule{4.0pt}{0.0pt}}\mathrm{Au}$ collisions at $\sqrt{{s}_{NN}}=200$ gev,” Phys. Rev. C 92 (Nov, 2015) 054903. https://link.aps.org/doi/10.1103/PhysRevC.92.054903.
  * [13] S. Schlichting and P. Tribedy, “Collectivity in Small Collision Systems: An Initial-State Perspective,” Adv. High Energy Phys. 2016 (2016) 8460349, arXiv:1611.00329 [hep-ph].
  * [14] B. Schenke, S. Schlichting, P. Tribedy, and R. Venugopalan, “Mass ordering of spectra from fragmentation of saturated gluon states in high multiplicity proton-proton collisions,” Phys. Rev. Lett. 117 no. 16, (2016) 162301, arXiv:1607.02496 [hep-ph].
  * [15] ALICE Collaboration, B. Abelev et al., “Multiplicity dependence of two-particle azimuthal correlations in pp collisions at the LHC,” JHEP 09 (2013) 049, arXiv:1307.1249 [nucl-ex].
  * [16] A. Ortiz, G. Bencedi, and H. Bello, “Revealing the source of the radial flow patterns in proton-proton collisions using hard probes,” J. Phys. G44 no. 6, (2017) 065001, arXiv:1608.04784 [hep-ph].
  * [17] ALICE Collaboration, J. Adam et al., “Centrality dependence of particle production in p-Pb collisions at $\sqrt{s_{\rm NN}}$= 5.02 TeV,” Phys. Rev. C91 no. 6, (2015) 064905, arXiv:1412.6828 [nucl-ex].
  * [18] F. Arleo, S. J. Brodsky, D. S. Hwang, and A. M. Sickles, “Higher-Twist Dynamics in Large Transverse Momentum Hadron Production,” Phys. Rev. Lett. 105 (2010) 062002, arXiv:0911.4604 [hep-ph].
  * [19] A. Ortiz, G. Paić, and E. Cuautle, “Mid-rapidity charged hadron transverse spherocity in pp collisions simulated with Pythia,” Nucl. Phys. A941 (2015) 78–86, arXiv:1503.03129 [hep-ph].
  * [20] A. Ortiz, “Experimental results on event shapes at hadron colliders,” Adv. Ser. Direct. High Energy Phys. 29 (2018) 343–357, arXiv:1705.02056 [hep-ex].
  * [21] ALICE Collaboration, B. Abelev et al., “Multiplicity dependence of the average transverse momentum in pp, p-Pb, and Pb-Pb collisions at the LHC,” Phys. Lett. B727 (2013) 371–380, arXiv:1307.1094 [nucl-ex].
  * [22] ALICE Collaboration, B. Abelev et al., “Performance of the ALICE Experiment at the CERN LHC,” Int. J. Mod. Phys. A29 (2014) 1430044, arXiv:1402.4476 [nucl-ex].
  * [23] T. Sjöstrand, S. Mrenna, and P. Z. Skands, “PYTHIA 6.4 Physics and Manual,” JHEP 05 (2006) 026, arXiv:hep-ph/0603175 [hep-ph].
  * [24] P. Z. Skands, “Tuning Monte Carlo Generators: The Perugia Tunes,” Phys. Rev. D82 (2010) 074018, arXiv:1005.3457 [hep-ph].
  * [25] R. Brun, F. Bruyant, F. Carminati, S. Giani, M. Maire, A. McPherson, G. Patrick, and L. Urban, “GEANT Detector Description and Simulation Tool,”.
  * [26] ALICE Collaboration Collaboration, “The ALICE definition of primary particles,”. https://cds.cern.ch/record/2270008.
  * [27] ALICE Collaboration, B. Abelev et al., “Energy Dependence of the Transverse Momentum Distributions of Charged Particles in pp Collisions Measured by ALICE,” Eur. Phys. J. C73 no. 12, (2013) 2662, arXiv:1307.1093 [nucl-ex].
  * [28] ALICE Collaboration, J. Adam et al., “Pseudorapidity and transverse-momentum distributions of charged particles in proton-proton collisions at $\sqrt{s}=$ 13 TeV,” Phys. Lett. B753 (2016) 319–329, arXiv:1509.08734 [nucl-ex].
  * [29] ALICE Collaboration, S. Acharya et al., “Transverse momentum spectra and nuclear modification factors of charged particles in pp, p-Pb and Pb-Pb collisions at the LHC,” arXiv:1802.09145 [nucl-ex].
  * [30] ALICE Collaboration, B. Abelev et al., “Centrality Dependence of Charged Particle Production at Large Transverse Momentum in Pb–Pb Collisions at $\sqrt{s_{\rm{NN}}}=2.76$ TeV,” Phys. Lett. B720 (2013) 52–62, arXiv:1208.2711 [hep-ex].
  * [31] R. Hagedorn Riv. Nuovo Cim. 6 (1983) 1.
  * [32] ALICE Collaboration, B. Abelev et al., “Transverse sphericity of primary charged particles in minimum bias proton-proton collisions at $\sqrt{s}=0.9$, 2.76 and 7 TeV,” Eur. Phys. J. C72 (2012) 2124, arXiv:1205.3963 [hep-ex].
  * [33] A. Banfi, G. P. Salam, and G. Zanderighi, “Phenomenology of event shapes at hadron colliders,” JHEP 06 (2010) 038.
  * [34] A. Ortiz and L. Valencia Palomo, “Universality of the underlying event in pp collisions,” Phys. Rev. D96 no. 11, (2017) 114019, arXiv:1710.04741 [hep-ex].
  * [35] R. E. Kalman, “A new approach to linear filtering and prediction problems,” Transactions of the ASME–Journal of Basic Engineering 82 no. Series D, (1960) 35–45.
  * [36] ALICE Collaboration, K. Aamodt et al., “Transverse momentum spectra of charged particles in proton-proton collisions at $\sqrt{s}=900$ GeV with ALICE at the LHC,” Phys. Lett. B693 (2010) 53–68, arXiv:1007.0719 [hep-ex].
  * [37] T. Pierog, I. Karpenko, J. M. Katzy, E. Yatsenko, and K. Werner, “EPOS LHC: Test of collective hadronization with data measured at the CERN Large Hadron Collider,” Phys. Rev. C92 no. 3, (2015) 034906, arXiv:1306.0121 [hep-ph].
  * [38] P. Skands, S. Carrazza, and J. Rojo, “Tuning PYTHIA 8.1: the Monash 2013 Tune,” Eur. Phys. J. C74 no. 8, (2014) 3024, arXiv:1404.5630 [hep-ph].
  * [39] ALICE Collaboration, B. Abelev et al., “Centrality dependence of $\pi$, K, p production in Pb-Pb collisions at $\sqrt{s_{NN}}$ = 2.76 TeV,” Phys. Rev. C88 (2013) 044910, arXiv:1303.0737 [hep-ex].
  * [40] ALICE Collaboration, B. Abelev et al., “Neutral pion and $\eta$ meson production in proton-proton collisions at $\sqrt{s}=0.9$ TeV and $\sqrt{s}=7$ TeV,” Phys. Lett. B717 (2012) 162–172, arXiv:1205.5724 [hep-ex].
  * [41] A. N. Mishra, A. Ortiz, and G. Paic, “Intriguing similarities of high-$p_{T}$ particle production between $pp$ and $A-A$ collisions,” Phys. Rev. C99 no. 3, (2019) 034911, arXiv:1805.04572 [hep-ph].
  * [42] ALICE Collaboration, J. Adam et al., “Measurement of charm and beauty production at central rapidity versus charged-particle multiplicity in proton-proton collisions at $\sqrt{s}=7$ TeV,” JHEP 09 (2015) 148, arXiv:1505.00664 [nucl-ex].
  * [43] T. Sjöstrand and M. van Zijl, “A Multiple Interaction Model for the Event Structure in Hadron Collisions,” Phys. Rev. D36 (1987) 2019.
  * [44] CMS Collaboration, S. Chatrchyan et al., “Jet and underlying event properties as a function of charged-particle multiplicity in proton-proton collisions at $\sqrt{s}$ = 7 TeV,” Eur. Phys. J. C73 no. 12, (2013) 2674, arXiv:1310.4554 [hep-ex].
  * [45] ATLAS Collaboration, G. Aad et al., “Measurement of charged-particle event shape variables in $\sqrt{s}=7$ TeV proton-proton interactions with the ATLAS detector,” Phys. Rev. D88 no. 3, (2013) 032004, arXiv:1207.6915 [hep-ex].

##  Appendix A The ALICE Collaboration

S. Acharyaorg141&D. Adamováorg93&S.P. Adhyaorg141&A. Adlerorg74&J.
Adolfssonorg80&M.M. Aggarwalorg98&G. Aglieri Rinellaorg34&M. Agnelloorg31&N.
Agrawalorg10&Z. Ahammedorg141&S. Ahmadorg17&S.U. Ahnorg76&S. Aiolaorg146&A.
Akindinovorg64&M. Al-Turanyorg105&S.N. Alamorg141&D.S.D. Albuquerqueorg122&D.
Aleksandrovorg87&B. Alessandroorg58&H.M. Alfandaorg6&R. Alfaro Molinaorg72&B.
Aliorg17&Y. Aliorg15&A. Aliciorg10,org53,org27&A. Alkinorg2&J. Almeorg22&T.
Altorg69&L. Altenkamperorg22&I. Altsybeevorg112&M.N. Anaamorg6&C.
Andreiorg47&D. Andreouorg34&H.A. Andrewsorg109&A. Andronicorg144&M.
Angelettiorg34&V. Anguelovorg102&C. Ansonorg16&T. Antičićorg106&F.
Antinoriorg56&P. Antonioliorg53&R. Anwarorg126&N. Apadulaorg79&L.
Aphecetcheorg114&H. Appelshäuserorg69&S. Arcelliorg27&R. Arnaldiorg58&M.
Arratiaorg79&I.C. Arseneorg21&M. Arslandokorg102&A. Augustinusorg34&R.
Averbeckorg105&S. Azizorg61&M.D. Azmiorg17&A. Badalàorg55&Y.W. Baekorg40&S.
Bagnascoorg58&X. Baiorg105&R. Bailhacheorg69&R. Balaorg99&A.
Baldisseriorg137&M. Ballorg42&R.C. Baralorg85&R. Barberaorg28&L.
Barioglioorg26&G.G. Barnaföldiorg145&L.S. Barnbyorg92&V. Barretorg134&P.
Bartaliniorg6&K. Barthorg34&E. Bartschorg69&F. Baruffaldiorg29&N.
Bastidorg134&S. Basuorg143&G. Batigneorg114&B. Batyunyaorg75&P.C.
Batzingorg21&D. Bauriorg48&J.L. Bazo Albaorg110&I.G. Beardenorg88&C.
Beddaorg63&N.K. Beheraorg60&I. Belikovorg136&F. Belliniorg34&R.
Bellwiedorg126&V. Belyaevorg91&G. Bencediorg145&S. Beoleorg26&A.
Bercuciorg47&Y. Berdnikovorg96&D. Berenyiorg145&R.A. Bertensorg130&D.
Berzanoorg58&M.G. Besoiuorg68&L. Betevorg34&A. Bhasinorg99&I.R. Bhatorg99&H.
Bhattorg48&B. Bhattacharjeeorg41&A. Bianchiorg26&L. Bianchiorg126,org26&N.
Bianchiorg51&J. Bielčíkorg37&J. Bielčíkováorg93&A. Bilandzicorg117,org103&G.
Biroorg145&R. Biswasorg3&S. Biswasorg3&J.T. Blairorg119&D. Blauorg87&C.
Blumeorg69&G. Bocaorg139&F. Bockorg94,org34&A. Bogdanovorg91&L.
Boldizsárorg145&A. Bolozdynyaorg91&M. Bombaraorg38&G. Bonomiorg140&H.
Borelorg137&A. Borissovorg144,org91&M. Borriorg128&H. Bossiorg146&E.
Bottaorg26&C. Bourjauorg88&L. Bratrudorg69&P. Braun-Munzingerorg105&M.
Bregantorg121&T.A. Brokerorg69&M. Brozorg37&E.J. Bruckenorg43&E.
Brunaorg58&G.E. Brunoorg33,org104&M.D. Bucklandorg128&D. Budnikovorg107&H.
Bueschingorg69&S. Bufalinoorg31&O. Bugnonorg114&P. Buhlerorg113&P.
Buncicorg34&Z. Butheleziorg73&J.B. Buttorg15&J.T. Buxtonorg95&D.
Caffarriorg89&A. Calivaorg105&E. Calvo Villarorg110&R.S. Camachoorg44&P.
Cameriniorg25&A.A. Caponorg113&F. Carnesecchiorg10&J. Castillo
Castellanosorg137&A.J. Castroorg130&E.A.R. Casulaorg54&F. Catalanoorg31&C.
Ceballos Sanchezorg52&P. Chakrabortyorg48&S. Chandraorg141&B. Changorg127&W.
Changorg6&S. Chapelandorg34&M. Chartierorg128&S. Chattopadhyayorg141&S.
Chattopadhyayorg108&A. Chauvinorg24&C. Cheshkovorg135&B. Cheynisorg135&V.
Chibante Barrosoorg34&D.D. Chinellatoorg122&S. Choorg60&P. Chochulaorg34&T.
Chowdhuryorg134&P. Christakoglouorg89&C.H. Christensenorg88&P.
Christiansenorg80&T. Chujoorg133&C. Cicaloorg54&L. Cifarelliorg10,org27&F.
Cindoloorg53&J. Cleymansorg125&F. Colamariaorg52&D. Colellaorg52&A.
Colluorg79&M. Colocciorg27&M. Concasorg58orgI&G. Conesa Balbastreorg78&Z.
Conesa del Valleorg61&G. Continorg59,org128&J.G. Contrerasorg37&T.M.
Cormierorg94&Y. Corrales Moralesorg58,org26&P. Corteseorg32&M.R.
Cosentinoorg123&F. Costaorg34&S. Costanzaorg139&J. Crkovskáorg61&P.
Crochetorg134&E. Cuautleorg70&L. Cunqueiroorg94&D. Dabrowskiorg142&T.
Dahmsorg117,org103&A. Daineseorg56&F.P.A. Damasorg137,org114&S. Daniorg66&M.C.
Danischorg102&A. Danuorg68&D. Dasorg108&I. Dasorg108&S. Dasorg3&A.
Dashorg85&S. Dashorg48&A. Dashiorg103&S. Deorg49,org85&A. De Caroorg30&G. de
Cataldoorg52&C. de Contiorg121&J. de Cuvelandorg39&A. De Falcoorg24&D. De
Gruttolaorg10&N. De Marcoorg58&S. De Pasqualeorg30&R.D. De Souzaorg122&S.
Deborg49&H.F. Degenhardtorg121&K.R. Dejaorg142&A. Delofforg84&S.
Delsantoorg131,org26&P. Dhankherorg48&D. Di Bariorg33&A. Di Mauroorg34&R.A.
Diazorg8&T. Dietelorg125&P. Dillensegerorg69&Y. Dingorg6&R. Diviàorg34&Ø.
Djuvslandorg22&U. Dmitrievaorg62&A. Dobrinorg34,org68&B. Dönigusorg69&O.
Dordicorg21&A.K. Dubeyorg141&A. Dublaorg105&S. Dudiorg98&M. Dukhishyamorg85&P.
Dupieuxorg134&R.J. Ehlersorg146&D. Eliaorg52&H. Engelorg74&E. Eppleorg146&B.
Erazmusorg114&F. Erhardtorg97&A. Erokhinorg112&M.R. Ersdalorg22&B.
Espagnonorg61&G. Eulisseorg34&J. Eumorg18&D. Evansorg109&S. Evdokimovorg90&L.
Fabbiettiorg117,org103&M. Fagginorg29&J. Faivreorg78&A. Fantoniorg51&M.
Faselorg94&P. Fecchioorg31&L. Feldkamporg144&A. Felicielloorg58&G.
Feofilovorg112&A. Fernández Téllezorg44&A. Ferreroorg137&A. Ferrettiorg26&A.
Festantiorg34&V.J.G. Feuillardorg102&J. Figielorg118&S. Filchaginorg107&D.
Finogeevorg62&F.M. Fiondaorg22&G. Fiorenzaorg52&F. Flororg126&S.
Foertschorg73&P. Fokaorg105&S. Fokinorg87&E. Fragiacomoorg59&U.
Frankenfeldorg105&G.G. Fronzeorg26&U. Fuchsorg34&C. Furgetorg78&A.
Fursorg62&M. Fusco Girardorg30&J.J. Gaardhøjeorg88&M. Gagliardiorg26&A.M.
Gagoorg110&A. Galorg136&C.D. Galvanorg120&P. Ganotiorg83&C. Garabatosorg105&E.
Garcia-Solisorg11&K. Gargorg28&C. Gargiuloorg34&K. Garnerorg144&P.
Gasikorg103,org117&E.F. Gaugerorg119&M.B. Gay Ducatiorg71&M. Germainorg114&J.
Ghoshorg108&P. Ghoshorg141&S.K. Ghoshorg3&P. Gianottiorg51&P.
Giubellinoorg105,org58&P. Giubilatoorg29&P. Glässelorg102&D.M. Goméz
Coralorg72&A. Gomez Ramirezorg74&V. Gonzalezorg105&P. González-Zamoraorg44&S.
Gorbunovorg39&L. Görlichorg118&S. Gotovacorg35&V. Grabskiorg72&L.K.
Graczykowskiorg142&K.L. Grahamorg109&L. Greinerorg79&A. Grelliorg63&C.
Grigorasorg34&V. Grigorievorg91&A. Grigoryanorg1&S. Grigoryanorg75&O.S.
Groettvikorg22&J.M. Gronefeldorg105&F. Grosaorg31&J.F. Grosse-
Oetringhausorg34&R. Grossoorg105&R. Guernaneorg78&B. Guerzoniorg27&M.
Guittiereorg114&K. Gulbrandsenorg88&T. Gunjiorg132&A. Guptaorg99&R.
Guptaorg99&I.B. Guzmanorg44&R. Haakeorg34,org146&M.K. Habiborg105&C.
Hadjidakisorg61&H. Hamagakiorg81&G. Hamarorg145&M. Hamidorg6&R.
Hanniganorg119&M.R. Haqueorg63&A. Harlenderovaorg105&J.W. Harrisorg146&A.
Hartonorg11&J.A. Hasenbichlerorg34&H. Hassanorg78&D.
Hatzifotiadouorg10,org53&P. Hauerorg42&S. Hayashiorg132&S.T. Heckelorg69&E.
Hellbärorg69&H. Helstruporg36&A. Herghelegiuorg47&E.G. Hernandezorg44&G.
Herrera Corralorg9&F. Herrmannorg144&K.F. Hetlandorg36&T.E. Hildenorg43&H.
Hillemannsorg34&C. Hillsorg128&B. Hippolyteorg136&B. Hohlwegerorg103&D.
Horakorg37&S. Hornungorg105&R. Hosokawaorg133&P. Hristovorg34&C. Huangorg61&C.
Hughesorg130&P. Huhnorg69&T.J. Humanicorg95&H. Hushnudorg108&L.A.
Husovaorg144&N. Hussainorg41&S.A. Hussainorg15&T. Hussainorg17&D.
Hutterorg39&D.S. Hwangorg19&J.P. Iddonorg128,org34&R. Ilkaevorg107&M.
Inabaorg133&M. Ippolitovorg87&M.S. Islamorg108&M. Ivanovorg105&V.
Ivanovorg96&V. Izucheevorg90&B. Jacakorg79&N. Jacazioorg27&P.M.
Jacobsorg79&M.B. Jadhavorg48&S. Jadlovskaorg116&J. Jadlovskyorg116&S.
Jaelaniorg63&C. Jahnkeorg121&M.J. Jakubowskaorg142&M.A. Janikorg142&M.
Jercicorg97&O. Jevonsorg109&R.T. Jimenez Bustamanteorg105&M. Jinorg126&F.
Jonasorg144,org94&P.G. Jonesorg109&A. Juskoorg109&P. Kalinakorg65&A.
Kalweitorg34&J.H. Kangorg147&V. Kaplinorg91&S. Karorg6&A. Karasu Uysalorg77&O.
Karavichevorg62&T. Karavichevaorg62&P. Karczmarczykorg34&E. Karpechevorg62&U.
Kebschullorg74&R. Keidelorg46&M. Keilorg34&B. Ketzerorg42&Z.
Khabanovaorg89&A.M. Khanorg6&S. Khanorg17&S.A. Khanorg141&A.
Khanzadeevorg96&Y. Kharlovorg90&A. Khatunorg17&A. Khuntiaorg118,org49&B.
Kilengorg36&B. Kimorg60&B. Kimorg133&D. Kimorg147&D.J. Kimorg127&E.J.
Kimorg13&H. Kimorg147&J. Kimorg147&J.S. Kimorg40&J. Kimorg102&J. Kimorg147&J.
Kimorg13&M. Kimorg102&S. Kimorg19&T. Kimorg147&T. Kimorg147&S. Kirschorg39&I.
Kiselorg39&S. Kiselevorg64&A. Kisielorg142&J.L. Klayorg5&C. Kleinorg69&J.
Kleinorg58&S. Kleinorg79&C. Klein-Bösingorg144&S. Klewinorg102&A.
Klugeorg34&M.L. Knichelorg34&A.G. Knospeorg126&C. Kobdajorg115&M.K.
Köhlerorg102&T. Kolleggerorg105&A. Kondratyevorg75&N. Kondratyevaorg91&E.
Kondratyukorg90&P.J. Konopkaorg34&L. Koskaorg116&O. Kovalenkoorg84&V.
Kovalenkoorg112&M. Kowalskiorg118&I. Králikorg65&A. Kravčákováorg38&L.
Kreisorg105&M. Krivdaorg109,org65&F. Krizekorg93&K. Krizkova Gajdosovaorg37&M.
Krügerorg69&E. Kryshenorg96&M. Krzewickiorg39&A.M. Kuberaorg95&V.
Kučeraorg60&C. Kuhnorg136&P.G. Kuijerorg89&L. Kumarorg98&S. Kumarorg48&S.
Kunduorg85&P. Kurashviliorg84&A. Kurepinorg62&A.B. Kurepinorg62&S.
Kushpilorg93&J. Kvapilorg109&M.J. Kweonorg60&J.Y. Kwonorg60&Y. Kwonorg147&S.L.
La Pointeorg39&P. La Roccaorg28&Y.S. Laiorg79&R. Langoyorg124&K.
Lapidusorg34,org146&A. Lardeuxorg21&P. Larionovorg51&E. Laudiorg34&R.
Lavickaorg37&T. Lazarevaorg112&R. Leaorg25&L. Leardiniorg102&S. Leeorg147&F.
Lehasorg89&S. Lehnerorg113&J. Lehrbachorg39&R.C. Lemmonorg92&I. León
Monzónorg120&E.D. Lesserorg20&M. Lettrichorg34&P. Lévaiorg145&X. Liorg12&X.L.
Liorg6&J. Lienorg124&R. Lietavaorg109&B. Limorg18&S. Lindalorg21&V.
Lindenstruthorg39&S.W. Lindsayorg128&C. Lippmannorg105&M.A. Lisaorg95&V.
Litichevskyiorg43&A. Liuorg79&S. Liuorg95&W.J. Llopeorg143&I.M. Lofnesorg22&V.
Loginovorg91&C. Loizidesorg94&P. Loncarorg35&X. Lopezorg134&E. López
Torresorg8&P. Luettigorg69&J.R. Luhderorg144&M. Lunardonorg29&G.
Luparelloorg59&M. Lupiorg74&A. Maevskayaorg62&M. Magerorg34&S.M.
Mahmoodorg21&T. Mahmoudorg42&A. Maireorg136&R.D. Majkaorg146&M.
Malaevorg96&Q.W. Malikorg21&L. Malininaorg75orgII&D. Mal’Kevichorg64&P.
Malzacherorg105&A. Mamonovorg107&V. Mankoorg87&F. Mansoorg134&V.
Manzariorg52&Y. Maoorg6&M. Marchisoneorg135&J. Marešorg67&G.V.
Margagliottiorg25&A. Margottiorg53&J. Marguttiorg63&A. Marínorg105&C.
Markertorg119&M. Marquardorg69&N.A. Martinorg102&P. Martinengoorg34&J.L.
Martinezorg126&M.I. Martínezorg44&G. Martínez Garcíaorg114&M. Martinez
Pedreiraorg34&S. Masciocchiorg105&M. Maseraorg26&A. Masoniorg54&L.
Massacrierorg61&E. Massonorg114&A. Mastroserioorg52,org138&A.M.
Mathisorg103,org117&P.F.T. Matuokaorg121&A. Matyjaorg118&C. Mayerorg118&M.
Mazzilliorg33&M.A. Mazzoniorg57&A.F. Mechlerorg69&F. Meddiorg23&Y.
Melikyanorg91&A. Menchaca-Rochaorg72&E. Meninnoorg30&M. Meresorg14&S.
Mhlangaorg125&Y. Miakeorg133&L. Michelettiorg26&M.M. Mieskolainenorg43&D.L.
Mihaylovorg103&K. Mikhaylovorg64,org75&A. Mischkeorg63org*&A.N. Mishraorg70&D.
Miśkowiecorg105&C.M. Mituorg68&N. Mohammadiorg34&A.P. Mohantyorg63&B.
Mohantyorg85&M. Mohisin Khanorg17orgIII&M. Mondalorg141&M.M. Mondalorg66&C.
Mordasiniorg103&D.A. Moreira De Godoyorg144&L.A.P. Morenoorg44&S.
Morettoorg29&A. Morrealeorg114&A. Morschorg34&T. Mrnjavacorg34&V.
Mucciforaorg51&E. Mudnicorg35&D. Mühlheimorg144&S. Muhuriorg141&J.D.
Mulliganorg79,org146&M.G. Munhozorg121&K. Münningorg42&R.H. Munzerorg69&H.
Murakamiorg132&S. Murrayorg73&L. Musaorg34&J. Musinskyorg65&C.J.
Myersorg126&J.W. Myrchaorg142&B. Naikorg48&R. Nairorg84&B.K. Nandiorg48&R.
Naniaorg53,org10&E. Nappiorg52&M.U. Naruorg15&A.F. Nassirpourorg80&H. Natal da
Luzorg121&C. Nattrassorg130&R. Nayakorg48&T.K. Nayakorg141,org85&S.
Nazarenkoorg107&R.A. Negrao De Oliveiraorg69&L. Nellenorg70&S.V. Nesboorg36&G.
Neskovicorg39&B.S. Nielsenorg88&S. Nikolaevorg87&S. Nikulinorg87&V.
Nikulinorg96&F. Noferiniorg10,org53&P. Nomokonovorg75&G. Noorenorg63&J.
Normanorg78&P. Nowakowskiorg142&A. Nyaninorg87&J. Nystrandorg22&M.
Oginoorg81&A. Ohlsonorg102&J. Oleniaczorg142&A.C. Oliveira Da Silvaorg121&M.H.
Oliverorg146&C. Oppedisanoorg58&R. Oravaorg43&A. Ortiz Velasquezorg70&A.
Oskarssonorg80&J. Otwinowskiorg118&K. Oyamaorg81&Y. Pachmayerorg102&V.
Pacikorg88&D. Paganoorg140&G. Paićorg70&P. Palniorg6&J. Panorg143&A.K.
Pandeyorg48&S. Panebiancoorg137&V. Papikyanorg1&P. Pareekorg49&J.
Parkorg60&J.E. Parkkilaorg127&S. Parmarorg98&A. Passfeldorg144&S.P.
Pathakorg126&R.N. Patraorg141&B. Paulorg24,org58&H. Peiorg6&T.
Peitzmannorg63&X. Pengorg6&L.G. Pereiraorg71&H. Pereira Da Costaorg137&D.
Peresunkoorg87&G.M. Perezorg8&E. Perez Lezamaorg69&V. Peskovorg69&Y.
Pestovorg4&V. Petráčekorg37&M. Petroviciorg47&R.P. Pezziorg71&S. Pianoorg59&M.
Piknaorg14&P. Pillotorg114&L.O.D.L. Pimentelorg88&O. Pinazzaorg53,org34&L.
Pinskyorg126&S. Pisanoorg51&D.B. Piyarathnaorg126&M. Płoskońorg79&M.
Planinicorg97&F. Pliquettorg69&J. Plutaorg142&S. Pochybovaorg145&M.G.
Poghosyanorg94&B. Polichtchoukorg90&N. Poljakorg97&W. Poonsawatorg115&A.
Poporg47&H. Poppenborgorg144&S. Porteboeuf-Houssaisorg134&V.
Pozdniakovorg75&S.K. Prasadorg3&R. Preghenellaorg53&F. Prinoorg58&C.A.
Pruneauorg143&I. Pshenichnovorg62&M. Puccioorg34,org26&V. Puninorg107&K.
Puranapandaorg141&J. Putschkeorg143&R.E. Quishpeorg126&S. Ragoniorg109&S.
Rahaorg3&S. Rajputorg99&J. Rakorg127&A. Rakotozafindrabeorg137&L.
Ramelloorg32&F. Ramiorg136&R. Raniwalaorg100&S. Raniwalaorg100&S.S.
Räsänenorg43&B.T. Rascanuorg69&R. Rathorg49&V. Ratzaorg42&I.
Ravasengaorg31&K.F. Readorg130,org94&K. Redlichorg84orgIV&A. Rehmanorg22&P.
Reicheltorg69&F. Reidtorg34&X. Renorg6&R. Renfordtorg69&A. Reshetinorg62&J.-P.
Revolorg10&K. Reygersorg102&V. Riabovorg96&T. Richertorg80,org88&M.
Richterorg21&P. Riedlerorg34&W. Rieglerorg34&F. Riggiorg28&C. Risteaorg68&S.P.
Rodeorg49&M. Rodríguez Cahuantziorg44&K. Røedorg21&R. Rogalevorg90&E.
Rogochayaorg75&D. Rohrorg34&D. Röhrichorg22&P.S. Rokitaorg142&F.
Ronchettiorg51&E.D. Rosasorg70&K. Roslonorg142&P. Rosnetorg134&A.
Rossiorg29&A. Rotondiorg139&F. Roukoutakisorg83&A. Royorg49&P. Royorg108&O.V.
Ruedaorg80&R. Ruiorg25&B. Rumyantsevorg75&A. Rustamovorg86&E.
Ryabinkinorg87&Y. Ryabovorg96&A. Rybickiorg118&H. Rytkonenorg127&S.
Saarinenorg43&S. Sadhuorg141&S. Sadovskyorg90&K. Šafaříkorg37,org34&S.K.
Sahaorg141&B. Sahooorg48&P. Sahooorg49&R. Sahooorg49&S. Sahooorg66&P.K.
Sahuorg66&J. Sainiorg141&S. Sakaiorg133&S. Sambyalorg99&V.
Samsonovorg96,org91&A. Sandovalorg72&A. Sarkarorg73&D. Sarkarorg141,org143&N.
Sarkarorg141&P. Sarmaorg41&V.M. Sartiorg103&M.H.P. Sasorg63&E.
Scapparoneorg53&B. Schaeferorg94&J. Schambachorg119&H.S. Scheidorg69&C.
Schiauaorg47&R. Schickerorg102&A. Schmahorg102&C. Schmidtorg105&H.R.
Schmidtorg101&M.O. Schmidtorg102&M. Schmidtorg101&N.V. Schmidtorg94,org69&A.R.
Schmierorg130&J. Schukraftorg34,org88&Y. Schutzorg34,org136&K.
Schwarzorg105&K. Schwedaorg105&G. Scioliorg27&E. Scomparinorg58&M.
Šefčíkorg38&J.E. Segerorg16&Y. Sekiguchiorg132&D. Sekihataorg45&I.
Selyuzhenkovorg105,org91&S. Senyukovorg136&D. Serebryakovorg62&E.
Serradillaorg72&P. Settorg48&A. Sevcencoorg68&A. Shabanovorg62&A.
Shabetaiorg114&R. Shahoyanorg34&W. Shaikhorg108&A. Shangaraevorg90&A.
Sharmaorg98&A. Sharmaorg99&M. Sharmaorg99&N. Sharmaorg98&A.I. Sheikhorg141&K.
Shigakiorg45&M. Shimomuraorg82&S. Shirinkinorg64&Q. Shouorg111&Y.
Sibiriakorg87&S. Siddhantaorg54&T. Siemiarczukorg84&D. Silvermyrorg80&C.
Silvestreorg78&G. Simatovicorg89&G. Simonettiorg103,org34&R. Singhorg85&R.
Singhorg99&V.K. Singhorg141&V. Singhalorg141&T. Sinhaorg108&B. Sitarorg14&M.
Sittaorg32&T.B. Skaaliorg21&M. Slupeckiorg127&N. Smirnovorg146&R.J.M.
Snellingsorg63&T.W. Snellmanorg127&J. Sochanorg116&C. Sonccoorg110&J.
Songorg60,org126&A. Songmoolnakorg115&F. Soramelorg29&S. Sorensenorg130&I.
Sputowskaorg118&J. Stachelorg102&I. Stanorg68&P. Stankusorg94&P.J.
Steffanicorg130&E. Stenlundorg80&D. Stoccoorg114&M.M. Storetvedtorg36&P.
Strmenorg14&A.A.P. Suaideorg121&T. Sugitateorg45&C. Suireorg61&M.
Suleymanovorg15&M. Suljicorg34&R. Sultanovorg64&M. Šumberaorg93&S.
Sumowidagdoorg50&K. Suzukiorg113&S. Swainorg66&A. Szaboorg14&I. Szarkaorg14&U.
Tabassamorg15&G. Taillepiedorg134&J. Takahashiorg122&G.J. Tambaveorg22&S.
Tangorg134,org6&M. Tarhiniorg114&M.G. Tarzilaorg47&A. Tauroorg34&G. Tejeda
Muñozorg44&A. Telescaorg34&C. Terrevoliorg126,org29&D. Thakurorg49&S.
Thakurorg141&D. Thomasorg119&F. Thoresenorg88&R. Tieulentorg135&A.
Tikhonovorg62&A.R. Timminsorg126&A. Toiaorg69&N. Topilskayaorg62&M.
Toppiorg51&F. Torales-Acostaorg20&S.R. Torresorg120&S. Tripathyorg49&T.
Tripathyorg48&S. Trogoloorg26,org29&G. Trombettaorg33&L. Tropporg38&V.
Trubnikovorg2&W.H. Trzaskaorg127&T.P. Trzcinskiorg142&B.A. Trzeciakorg63&T.
Tsujiorg132&A. Tumkinorg107&R. Turrisiorg56&T.S. Tveterorg21&K.
Ullalandorg22&E.N. Umakaorg126&A. Urasorg135&G.L. Usaiorg24&A.
Utrobicicorg97&M. Valaorg116,org38&N. Valleorg139&S. Valleroorg58&N. van der
Kolkorg63&L.V.R. van Doremalenorg63&M. van Leeuwenorg63&P. Vande Vyvreorg34&D.
Vargaorg145&M. Varga-Kofaragoorg145&A. Vargasorg44&M. Vargyasorg127&R.
Varmaorg48&M. Vasileiouorg83&A. Vasilievorg87&O. Vázquez Doceorg117,org103&V.
Vecherninorg112&A.M. Veenorg63&E. Vercellinorg26&S. Vergara Limónorg44&L.
Vermuntorg63&R. Vernetorg7&R. Vértesiorg145&L. Vickovicorg35&J.
Viinikainenorg127&Z. Vilakaziorg131&O. Villalobos Baillieorg109&A. Villatoro
Telloorg44&G. Vinoorg52&A. Vinogradovorg87&T. Virgiliorg30&V.
Vislaviciusorg88&A. Vodopyanovorg75&B. Volkelorg34&M.A. Völklorg101&K.
Voloshinorg64&S.A. Voloshinorg143&G. Volpeorg33&B. von Hallerorg34&I.
Vorobyevorg103,org117&D. Voscekorg116&J. Vrlákováorg38&B. Wagnerorg22&Y.
Watanabeorg133&M. Weberorg113&S.G. Weberorg105&A. Wegrzynekorg34&D.F.
Weiserorg102&S.C. Wenzelorg34&J.P. Wesselsorg144&E. Widmannorg113&J.
Wiechulaorg69&J. Wikneorg21&G. Wilkorg84&J. Wilkinsonorg53&G.A.
Willemsorg34&E. Willsherorg109&B. Windelbandorg102&W.E. Wittorg130&Y.
Wuorg129&R. Xuorg6&S. Yalcinorg77&K. Yamakawaorg45&S. Yangorg22&S.
Yanoorg137&Z. Yinorg6&H. Yokoyamaorg63&I.-K. Yooorg18&J.H. Yoonorg60&S.
Yuanorg22&A. Yuncuorg102&V. Yurchenkoorg2&V. Zaccoloorg58,org25&A.
Zamanorg15&C. Zampolliorg34&H.J.C. Zanoliorg121&N. Zardoshtiorg34&A.
Zarochentsevorg112&P. Závadaorg67&N. Zaviyalovorg107&H. Zbroszczykorg142&M.
Zhalovorg96&X. Zhangorg6&Z. Zhangorg6,org134&C. Zhaoorg21&V.
Zherebchevskiiorg112&N. Zhigarevaorg64&D. Zhouorg6&Y. Zhouorg88&Z.
Zhouorg22&J. Zhuorg6&Y. Zhuorg6&A. Zichichiorg27,org10&M.B. Zimmermannorg34&G.
Zinovjevorg2&N. Zurloorg140&

## Affiliation notes

org*Deceased

orgIDipartimento DET del Politecnico di Torino, Turin, Italy

orgIIM.V. Lomonosov Moscow State University, D.V. Skobeltsyn Institute of
Nuclear, Physics, Moscow, Russia

orgIIIDepartment of Applied Physics, Aligarh Muslim University, Aligarh, India

orgIVInstitute of Theoretical Physics, University of Wroclaw, Poland

## Collaboration Institutes

org1A.I. Alikhanyan National Science Laboratory (Yerevan Physics Institute)
Foundation, Yerevan, Armenia

org2Bogolyubov Institute for Theoretical Physics, National Academy of Sciences
of Ukraine, Kiev, Ukraine

org3Bose Institute, Department of Physics and Centre for Astroparticle Physics
and Space Science (CAPSS), Kolkata, India

org4Budker Institute for Nuclear Physics, Novosibirsk, Russia

org5California Polytechnic State University, San Luis Obispo, California,
United States

org6Central China Normal University, Wuhan, China

org7Centre de Calcul de l’IN2P3, Villeurbanne, Lyon, France

org8Centro de Aplicaciones Tecnológicas y Desarrollo Nuclear (CEADEN), Havana,
Cuba

org9Centro de Investigación y de Estudios Avanzados (CINVESTAV), Mexico City
and Mérida, Mexico

org10Centro Fermi - Museo Storico della Fisica e Centro Studi e Ricerche
“Enrico Fermi’, Rome, Italy

org11Chicago State University, Chicago, Illinois, United States

org12China Institute of Atomic Energy, Beijing, China

org13Chonbuk National University, Jeonju, Republic of Korea

org14Comenius University Bratislava, Faculty of Mathematics, Physics and
Informatics, Bratislava, Slovakia

org15COMSATS University Islamabad, Islamabad, Pakistan

org16Creighton University, Omaha, Nebraska, United States

org17Department of Physics, Aligarh Muslim University, Aligarh, India

org18Department of Physics, Pusan National University, Pusan, Republic of
Korea

org19Department of Physics, Sejong University, Seoul, Republic of Korea

org20Department of Physics, University of California, Berkeley, California,
United States

org21Department of Physics, University of Oslo, Oslo, Norway

org22Department of Physics and Technology, University of Bergen, Bergen,
Norway

org23Dipartimento di Fisica dell’Università ’La Sapienza’ and Sezione INFN,
Rome, Italy

org24Dipartimento di Fisica dell’Università and Sezione INFN, Cagliari, Italy

org25Dipartimento di Fisica dell’Università and Sezione INFN, Trieste, Italy

org26Dipartimento di Fisica dell’Università and Sezione INFN, Turin, Italy

org27Dipartimento di Fisica e Astronomia dell’Università and Sezione INFN,
Bologna, Italy

org28Dipartimento di Fisica e Astronomia dell’Università and Sezione INFN,
Catania, Italy

org29Dipartimento di Fisica e Astronomia dell’Università and Sezione INFN,
Padova, Italy

org30Dipartimento di Fisica ‘E.R. Caianiello’ dell’Università and Gruppo
Collegato INFN, Salerno, Italy

org31Dipartimento DISAT del Politecnico and Sezione INFN, Turin, Italy

org32Dipartimento di Scienze e Innovazione Tecnologica dell’Università del
Piemonte Orientale and INFN Sezione di Torino, Alessandria, Italy

org33Dipartimento Interateneo di Fisica ‘M. Merlin’ and Sezione INFN, Bari,
Italy

org34European Organization for Nuclear Research (CERN), Geneva, Switzerland

org35Faculty of Electrical Engineering, Mechanical Engineering and Naval
Architecture, University of Split, Split, Croatia

org36Faculty of Engineering and Science, Western Norway University of Applied
Sciences, Bergen, Norway

org37Faculty of Nuclear Sciences and Physical Engineering, Czech Technical
University in Prague, Prague, Czech Republic

org38Faculty of Science, P.J. Šafárik University, Košice, Slovakia

org39Frankfurt Institute for Advanced Studies, Johann Wolfgang Goethe-
Universität Frankfurt, Frankfurt, Germany

org40Gangneung-Wonju National University, Gangneung, Republic of Korea

org41Gauhati University, Department of Physics, Guwahati, India

org42Helmholtz-Institut für Strahlen- und Kernphysik, Rheinische Friedrich-
Wilhelms-Universität Bonn, Bonn, Germany

org43Helsinki Institute of Physics (HIP), Helsinki, Finland

org44High Energy Physics Group, Universidad Autónoma de Puebla, Puebla, Mexico

org45Hiroshima University, Hiroshima, Japan

org46Hochschule Worms, Zentrum für Technologietransfer und Telekommunikation
(ZTT), Worms, Germany

org47Horia Hulubei National Institute of Physics and Nuclear Engineering,
Bucharest, Romania

org48Indian Institute of Technology Bombay (IIT), Mumbai, India

org49Indian Institute of Technology Indore, Indore, India

org50Indonesian Institute of Sciences, Jakarta, Indonesia

org51INFN, Laboratori Nazionali di Frascati, Frascati, Italy

org52INFN, Sezione di Bari, Bari, Italy

org53INFN, Sezione di Bologna, Bologna, Italy

org54INFN, Sezione di Cagliari, Cagliari, Italy

org55INFN, Sezione di Catania, Catania, Italy

org56INFN, Sezione di Padova, Padova, Italy

org57INFN, Sezione di Roma, Rome, Italy

org58INFN, Sezione di Torino, Turin, Italy

org59INFN, Sezione di Trieste, Trieste, Italy

org60Inha University, Incheon, Republic of Korea

org61Institut de Physique Nucléaire d’Orsay (IPNO), Institut National de
Physique Nucléaire et de Physique des Particules (IN2P3/CNRS), Université de
Paris-Sud, Université Paris-Saclay, Orsay, France

org62Institute for Nuclear Research, Academy of Sciences, Moscow, Russia

org63Institute for Subatomic Physics, Utrecht University/Nikhef, Utrecht,
Netherlands

org64Institute for Theoretical and Experimental Physics, Moscow, Russia

org65Institute of Experimental Physics, Slovak Academy of Sciences, Košice,
Slovakia

org66Institute of Physics, Homi Bhabha National Institute, Bhubaneswar, India

org67Institute of Physics of the Czech Academy of Sciences, Prague, Czech
Republic

org68Institute of Space Science (ISS), Bucharest, Romania

org69Institut für Kernphysik, Johann Wolfgang Goethe-Universität Frankfurt,
Frankfurt, Germany

org70Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México,
Mexico City, Mexico

org71Instituto de Física, Universidade Federal do Rio Grande do Sul (UFRGS),
Porto Alegre, Brazil

org72Instituto de Física, Universidad Nacional Autónoma de México, Mexico
City, Mexico

org73iThemba LABS, National Research Foundation, Somerset West, South Africa

org74Johann-Wolfgang-Goethe Universität Frankfurt Institut für Informatik,
Fachbereich Informatik und Mathematik, Frankfurt, Germany

org75Joint Institute for Nuclear Research (JINR), Dubna, Russia

org76Korea Institute of Science and Technology Information, Daejeon, Republic
of Korea

org77KTO Karatay University, Konya, Turkey

org78Laboratoire de Physique Subatomique et de Cosmologie, Université
Grenoble-Alpes, CNRS-IN2P3, Grenoble, France

org79Lawrence Berkeley National Laboratory, Berkeley, California, United
States

org80Lund University Department of Physics, Division of Particle Physics,
Lund, Sweden

org81Nagasaki Institute of Applied Science, Nagasaki, Japan

org82Nara Women’s University (NWU), Nara, Japan

org83National and Kapodistrian University of Athens, School of Science,
Department of Physics , Athens, Greece

org84National Centre for Nuclear Research, Warsaw, Poland

org85National Institute of Science Education and Research, Homi Bhabha
National Institute, Jatni, India

org86National Nuclear Research Center, Baku, Azerbaijan

org87National Research Centre Kurchatov Institute, Moscow, Russia

org88Niels Bohr Institute, University of Copenhagen, Copenhagen, Denmark

org89Nikhef, National institute for subatomic physics, Amsterdam, Netherlands

org90NRC Kurchatov Institute IHEP, Protvino, Russia

org91NRNU Moscow Engineering Physics Institute, Moscow, Russia

org92Nuclear Physics Group, STFC Daresbury Laboratory, Daresbury, United
Kingdom

org93Nuclear Physics Institute of the Czech Academy of Sciences, Řež u Prahy,
Czech Republic

org94Oak Ridge National Laboratory, Oak Ridge, Tennessee, United States

org95Ohio State University, Columbus, Ohio, United States

org96Petersburg Nuclear Physics Institute, Gatchina, Russia

org97Physics department, Faculty of science, University of Zagreb, Zagreb,
Croatia

org98Physics Department, Panjab University, Chandigarh, India

org99Physics Department, University of Jammu, Jammu, India

org100Physics Department, University of Rajasthan, Jaipur, India

org101Physikalisches Institut, Eberhard-Karls-Universität Tübingen, Tübingen,
Germany

org102Physikalisches Institut, Ruprecht-Karls-Universität Heidelberg,
Heidelberg, Germany

org103Physik Department, Technische Universität München, Munich, Germany

org104Politecnico di Bari, Bari, Italy

org105Research Division and ExtreMe Matter Institute EMMI, GSI
Helmholtzzentrum für Schwerionenforschung GmbH, Darmstadt, Germany

org106Rudjer Bošković Institute, Zagreb, Croatia

org107Russian Federal Nuclear Center (VNIIEF), Sarov, Russia

org108Saha Institute of Nuclear Physics, Homi Bhabha National Institute,
Kolkata, India

org109School of Physics and Astronomy, University of Birmingham, Birmingham,
United Kingdom

org110Sección Física, Departamento de Ciencias, Pontificia Universidad
Católica del Perú, Lima, Peru

org111Shanghai Institute of Applied Physics, Shanghai, China

org112St. Petersburg State University, St. Petersburg, Russia

org113Stefan Meyer Institut für Subatomare Physik (SMI), Vienna, Austria

org114SUBATECH, IMT Atlantique, Université de Nantes, CNRS-IN2P3, Nantes,
France

org115Suranaree University of Technology, Nakhon Ratchasima, Thailand

org116Technical University of Košice, Košice, Slovakia

org117Technische Universität München, Excellence Cluster ’Universe’, Munich,
Germany

org118The Henryk Niewodniczanski Institute of Nuclear Physics, Polish Academy
of Sciences, Cracow, Poland

org119The University of Texas at Austin, Austin, Texas, United States

org120Universidad Autónoma de Sinaloa, Culiacán, Mexico

org121Universidade de São Paulo (USP), São Paulo, Brazil

org122Universidade Estadual de Campinas (UNICAMP), Campinas, Brazil

org123Universidade Federal do ABC, Santo Andre, Brazil

org124University College of Southeast Norway, Tonsberg, Norway

org125University of Cape Town, Cape Town, South Africa

org126University of Houston, Houston, Texas, United States

org127University of Jyväskylä, Jyväskylä, Finland

org128University of Liverpool, Liverpool, United Kingdom

org129University of Science and Techonology of China, Hefei, China

org130University of Tennessee, Knoxville, Tennessee, United States

org131University of the Witwatersrand, Johannesburg, South Africa

org132University of Tokyo, Tokyo, Japan

org133University of Tsukuba, Tsukuba, Japan

org134Université Clermont Auvergne, CNRS/IN2P3, LPC, Clermont-Ferrand, France

org135Université de Lyon, Université Lyon 1, CNRS/IN2P3, IPN-Lyon,
Villeurbanne, Lyon, France

org136Université de Strasbourg, CNRS, IPHC UMR 7178, F-67000 Strasbourg,
France, Strasbourg, France

org137Université Paris-Saclay Centre d’Etudes de Saclay (CEA), IRFU,
Départment de Physique Nucléaire (DPhN), Saclay, France

org138Università degli Studi di Foggia, Foggia, Italy

org139Università degli Studi di Pavia, Pavia, Italy

org140Università di Brescia, Brescia, Italy

org141Variable Energy Cyclotron Centre, Homi Bhabha National Institute,
Kolkata, India

org142Warsaw University of Technology, Warsaw, Poland

org143Wayne State University, Detroit, Michigan, United States

org144Westfälische Wilhelms-Universität Münster, Institut für Kernphysik,
Münster, Germany

org145Wigner Research Centre for Physics, Hungarian Academy of Sciences,
Budapest, Hungary

org146Yale University, New Haven, Connecticut, United States

org147Yonsei University, Seoul, Republic of Korea