2020 024 03 March

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

This paper presents the measurements of $\pi^{\pm}$, $\mathrm{K}^{\pm}$, p and
$\rm\overline{p}$ transverse momentum ($p_{\textrm{T}}$) spectra as a function
of charged-particle multiplicity density in proton-proton (pp) collisions at
$\sqrt{s}\ =\ 13\ \textrm{TeV}$ with the ALICE detector at the LHC. Such study
allows us to isolate the center-of-mass energy dependence of light-flavour
particle production. The measurements reported here cover a $p_{\textrm{T}}$
range from 0.1 $\textrm{GeV}/c$ to 20 $\textrm{GeV}/c$ and are done in the
rapidity interval $|y|<0.5$. The $p_{\textrm{T}}$-differential particle ratios
exhibit an evolution with multiplicity, similar to that observed in pp
collisions at $\sqrt{s}\ =\ 7\ \textrm{TeV}$, which is qualitatively described
by some of the hydrodynamical and pQCD-inspired models discussed in this
paper. Furthermore, the $p_{\textrm{T}}$-integrated hadron-to-pion yield
ratios measured in pp collisions at two different center-of-mass energies are
consistent when compared at similar multiplicities. This also extends to
strange and multi-strange hadrons, suggesting that, at LHC energies, particle
hadrochemistry scales with particle multiplicity the same way under different
collision energies and colliding systems.

##  1 Introduction

The unprecedented energies available at the Large Hadron Collider (LHC)
provide unique opportunities to investigate the properties of strongly-
interacting matter. Particle production at large transverse momenta
($p_{\textrm{T}}$) is well-described by perturbative Quantum Chromodynamics
(pQCD). The soft regime ($p_{\textrm{T}}$ $\lesssim$ 2 GeV/$c$), in which
several collective phenomena are observed in proton-proton (pp), proton-lead
(p–Pb), and heavy-ion (A–A) collisions, is not calculable from first
principles of QCD. Instead, in order to describe bulk particle production in
A–A collisions, one usually relies on hydrodynamic and thermodynamic
modelling, which assumes the system to be in kinetic and chemical equilibrium
[1, 2]. On the other hand, the description of low-$p_{\textrm{T}}$ particle
spectra in smaller systems such as pp collisions is often based on
phenomenological modelling of multi-partonic interactions (MPI) and color
reconnection (CR) [3, 4] or overlapping strings [5].

Recent reports on the enhancement of (multi-)strange hadrons [6], double-ridge
structure [7, 8], non-zero $v_{\textrm{2}}$ coefficients [9], mass ordering in
hadron $p_{\textrm{T}}$ spectra, and characteristic modifications of baryon-
to-meson ratios [10] suggest that collective phenomena are present at the LHC
energies also in p–Pb collisions. This is further extended to even smaller
systems, such as pp collisions at $\sqrt{s}\ =\ 7\ \textrm{TeV}$, where
similar observations have been reported in high multiplicity events,
indicating that the collective effects are not characteristic of heavy-ion
collisions only. Furthermore, a continuous transition of light-flavor hadron
to pion ratios as a function of charged-particle multiplicity density
$\textrm{d}N_{\textrm{ch}}/\textrm{d}\eta$ from pp to p–Pb and then to Pb–Pb
collisions was found [11, 12, 13]. The observed similarities suggest the
existence of a common underlying mechanism determining the chemical
composition of particles produced in these three collision systems.

Results from pp [11] and p–Pb [10] collisions indicate that particle
production scales with $\textrm{d}N_{\textrm{ch}}/\textrm{d}\eta$ despite the
colliding system. However, measurements reported in previous multiplicity-
dependent studies have considered different colliding systems, each at a
different center-of-mass energy. In this work, we extend the existing
observations by performing a detailed study of pp collisions at $\sqrt{s}\ =\
13\ \textrm{TeV}$. Thanks to the availability of Run 2 data from the LHC, for
the first time, in pp collisions, we can disentangle the effect of center-of-
mass energy from the multiplicity dependence of $\pi^{\pm}$,
$\mathrm{K}^{\pm}$and $\rm p$ ($\rm\overline{p}$) production.

In this paper, we report on the multiplicity dependence of the production of
primary $\pi^{\pm}$, $\mathrm{K}^{\pm}$and p ($\rm\overline{p}$) at $\sqrt{s}\
=\ 13\ \textrm{TeV}$. Particles are considered as primary if they are created
in the collision (including products of strong and electromagnetic decays),
but not from a weak decay of other light-flavor hadrons or muons [14]. The
reported particle spectra are measured in the rapidity region $|y|<0.5$ with
the ALICE detector [15], which offers excellent tracking and particle
identification capabilities from $p_{\textrm{T}}=0.1$ $\textrm{GeV}/c$ to
several tens of $\textrm{GeV}/c$ [16]. As particles and anti-particles are
produced in equal amounts at LHC energies [17], we adopt a notation where
$\pi$, K, and p refer to $(\pi^{+}+\pi^{-})$,
$(\mathrm{K}^{+}+\mathrm{K}^{-})$, and $(\textrm{p}$ \+ $\rm\overline{p}$)
unless stated otherwise. This paper is organized as follows. In Sec. 2, the
details on particle identification techniques, systematic uncertainties,
spectra corrections and normalization are provided. The results are presented
and discussed in Sec. 3, together with comparisons to Monte Carlo model
predictions. Finally, the most important findings are summarized in Sec. 4.

##  2 Data set and experimental setup

The dataset used for this study was recorded by the ALICE Experiment during
the 2016 LHC pp data taking period. Overall $\sim$143M events have been
analysed, corresponding to an integrated luminosity of $2.47\textrm{\
nb}^{-1}$ considering the visible cross-section measured with the V0 detector
[18]. A detailed description of the ALICE detector and its performance is
provided in [15, 16]. Measurements of identified particle spectra have been
performed by using the central barrel detectors: the Inner Tracking System
(ITS) (Sec. 3.1 of [15]), the Time Projection Chamber (TPC) [19] and the Time-
of-Flight detector (TOF) [20]. The charged-particle multiplicity estimation is
done by the V0 detector (Sec. 5.4 of [15]), which consists of two arrays of 32
scintillators each, positioned in the forward (V0A, $2.8<\eta<5.1$) and
backward (V0C, $-3.7<\eta<-1.7$) rapidity regions. In addition, the V0 is also
used for triggering purposes as well as background rejection. The
determination of the event collision time [21] is performed by the T0 detector
as well as the TOF detector. The former consists of two arrays of Cherenkov
counters, positioned on both sides of the interaction region, and covering a
pseudorapidity range of $-3.3<\eta<-2.9$ (T0-C) and $4.5<\eta<5$ (T0-A). The
central barrel detectors are placed inside a solenoidal magnet, which provides
a field strength of 0.5 T.

The ITS is the innermost detector and consists of six concentric cylindrical
layers of high-resolution silicon detectors based on different technologies,
covering pseudorapidity region $|\eta|<0.9$. The two innermost layers form the
Silicon Pixel Detector (SPD), which features binary readout and is also used
as a trigger detector. The Silicon Drift Detector (SDD) and the Silicon Strip
Detector (SSD), which form the four outer layers of the ITS, provide the
amplitude of the charge signal, which is used for particle identification
through the measurement of specific energy loss at low transverse momenta
($p_{\textrm{T}}\gtrsim 100$ MeV/c).

The TPC, which is the main tracking detector of the ALICE central barrel, is
based on a cylindrical gaseous chamber with radial and longitudinal dimensions
of $85{\rm\,cm}<r<247{\rm\,cm}$ and $-250{\rm\,cm}<z<250{\rm\,cm}$,
respectively. The TPC is read out by multi-wire proportional chambers (MWPC)
with cathode pad readout, located at its endplates. With the measurement of
drift time, the TPC provides three-dimensional space-point information for
each charged track in pseudorapidity range $|\eta|<0.8$ with up to 159 samples
per track. In the TPC, the identification of charged particles is based on the
measurement of the specific energy loss, which in pp collisions is performed
with a resolution of $5.2\%$ [16].

The TOF is a large-area array of multigap resistive plate chambers (MRPC),
formed into a $\sim 4$ m radius cylinder around the interaction point and
covering the pseudorapidity region $|\eta|<0.9$ with full-azimuth coverage.
The time-of-flight is measured as the difference between the particle arrival
time and the event collision time, enabling particle identification at
intermediate transverse momenta, $0.5\lesssim p_{\textrm{T}}\lesssim 4$
$\textrm{GeV}/c$. The arrival time is measured by the MRPCs with an intrinsic
time resolution of 50 ps, while the event collision time is determined by
combining the T0 detector measurement with the estimate using the particle
arrival times at the TOF [21].

###  2.1 Event selection, classification and normalization

The analysed data were recorded using a minimum-bias trigger requiring signals
in both V0A and V0C scintillators in coincidence with the arrival of the
proton bunches from both directions. The background events produced outside
the interaction region are rejected using the correlation between the SPD
clusters and the tracklets reconstructed in SPD. The out-of-bunch pileup was
rejected offline using the timing information from the V0 counter. The primary
vertex was reconstructed either using global tracks (reconstructed using ITS
and TPC information) or SPD tracklets (reconstructed using only the SPD
information) with $|z_{\textrm{vtx}}|<10$ cm along the beam axis. Events with
in-bunch pileup were removed if a second vertex was reconstructed within
$8{\rm\,mm}$ of the primary vertex in the beam direction. The typical
interaction rate of pp collisions in the 2016 data taking periods was around
120 kHz while beam-gas interactions occurred at a rate of 1.2 kHz.

In the analysis presented in this paper, we consider the event class INEL$>$0
with at least one charged particle produced in the pseudorapidity region
$|\eta|<1$, which corresponds to $\sim 75\%$ of the total inelastic scattering
cross-section [22]. To avoid auto-correlation biases [11, 22], the events are
classified using the total charge collected in the V0 detector (V0M
amplitude), which scales linearly with the total number of the corresponding
charged particles in its acceptance. For each event class, the corresponding
mean charged-particle multiplicity density
$\langle\textrm{d}N_{\textrm{ch}}/\textrm{d}\eta\rangle$ is measured at mid-
rapidity $(|\eta|<0.5)$ as summarised in Table 1.

Table 1: Mean charged-particle multiplicity density $\langle\textrm{d}N_{\textrm{ch}}/\textrm{d}\eta\rangle$ measured in different event multiplicity classes. V0M mult. class | I | II | III | IV | V
---|---|---|---|---|---
$\sigma$/$\sigma_{\rm INEL>0}$ (%) | 0–0.92 | 0.92–4.6 | 4.6–9.2 | 9.2–13.8 | 13.8–18.4
$\langle\textrm{d}N_{\textrm{ch}}/\textrm{d}\eta\rangle$ | $26.02\pm 0.35$ | $20.02\pm 0.27$ | $16.17\pm 0.22$ | $13.77\pm 0.19$ | $12.04\pm 0.17$
V0M mult. class | VI | VII | VIII | IX | X
$\sigma$/$\sigma_{\rm INEL>0}$ (%) | 18.4–27.6 | 27.6–36.8 | 36.8–46.0 | 46.0–64.5 | 64.5–100
$\langle\textrm{d}N_{\textrm{ch}}/\textrm{d}\eta\rangle$ | $10.02\pm 0.14$ | $7.95\pm 0.11$ | $6.32\pm 0.09$ | $4.50\pm 0.07$ | $2.55\pm 0.04$
Table 2: Different $p_{\textrm{T}}$ ranges used for the identification of pions, kaons and protons. The final $p_{\textrm{T}}$ spectra have been obtained by combining the results of the various PID techniques. Analysis |  PID Technique |  $p_{\textrm{T}}$ ranges ($\textrm{GeV}/c$) |  (pseudo)rapidity
---|---|---|---
| $\pi^{\pm}$ | $\mathrm{K}^{\pm}$ |  $\rm p$ ($\rm\overline{p}$) |  range
ITSsa |  n$\sigma$ integral | 0.1$-$0.7 | 0.2$-$0.6 | 0.3$-$0.65 |  $|y|<$0.5
TPC-TOF fits |  | n$\sigma$ fits to TPC,
---
$\beta$ fits to TOF
0.25$-$3.0 | 0.3$-$3.0 | 0.45$-$3.0 |  |  $|y|<$0.5 (TPC)
---
$|\eta|<$0.4 (TOF)
TOF template fits |  | Statistical
---
unfolding of $\Delta t$
0.7$-$4.0 | 0.6$-$3.0 | 0.9$-$4.0 |  $|y|<$0.5
Kinks |  Kink topology | $-$ | 0.35$-$6.0 | $-$ |  $|y|<$0.5
rTPC |  TPC dE/dx fits | 2$-$20 | 3$-$20 | 3$-$20 |  $|\eta|<$0.8

###  2.2 Identification of charged pions, kaons and protons

In order to measure particle spectra in a wide $p_{\textrm{T}}$ range, several
sub-analyses employing different detectors and particle identification (PID)
techniques were performed and combined. As a result, the combined spectra
cover transverse momenta ranges from 0.1/0.2/0.3 $\textrm{GeV}/c$ to 20
$\textrm{GeV}/c$ for $\pi$/K/p. The $p_{\textrm{T}}$ and (pseudo)rapidity
ranges covered by each analysis for different particle species are summarized
in Table 2.

At low $p_{\textrm{T}}$, hadron spectra were measured by the ITS stand-alone
(ITSsa) analysis. The dynamic range of the analogue readout of SDD and SSD
allows for $\textrm{d}E/\textrm{d}x$ measurements of highly ionizing
particles, which otherwise do not reach the outer detectors. Hadron
identification in the ITS is carried out by calculating the truncated mean of
$\textrm{d}E/\textrm{d}x$ and comparing it to the expected energy loss under
different mass hypotheses. The difference between measured and expected
$\textrm{d}E/\textrm{d}x$ is then estimated in terms of the standard deviation
$\sigma$ and the particle mass hypothesis with the lowest score is assigned.
This is feasible even for pp collisions with the highest multiplicities, as
the number of charge clusters wrongly assigned to the reconstructed tracks is
negligible. A detailed description of the method is provided in [11].

Hadrons at intermediate $p_{\textrm{T}}$ enter the fiducial volume of the TPC
where they can be identified by measuring the charge generated in the gas. The
truncated mean of $\textrm{d}E/\textrm{d}x$ is calculated for the global
tracks and compared to the expected energy loss under a given mass hypothesis.
At low transverse momenta where the separation between different species is
sufficiently large, tracks within three standard deviations from the expected
$\textrm{d}E/\textrm{d}x$ are assigned to a given hypothesis. In the regions
where signals from several species overlap
($p_{\textrm{T}}<0.4~{}\textrm{GeV}/c$ for $\pi$,
$p_{\textrm{T}}>0.45~{}\textrm{GeV}/c$ for K, and
$p_{\textrm{T}}>0.6~{}\textrm{GeV}/c$ for p), statistical unfolding techniques
are used to remove the background contributions [11].

In the $p_{\textrm{T}}$ region where the statistical unfolding of the TPC
signal becomes unfeasible, particle identification is performed using the
time-of-flight measurements. The results presented in this paper were obtained
by combining the particle spectra estimated with two separate TOF analyses,
taking into account the non-common part of the respective systematic
uncertainties. In the “TOF template fits”, the PID is based on a statistical
unfolding method, where the distribution of the difference between measured
and expected time-of-flight (i.e. $\Delta t$) is fitted with templates for
pions, kaons and protons in each $p_{\textrm{T}}$ and multiplicity bin [23].
An additional template is needed to take into account the background due to
wrongly associated tracks with hits in the TOF detector. The template for each
particle is built from data, considering the measured TOF time response
function (Gaussian with an additional exponential tail for larger arrival
times). The fits are repeated separately for each particle hypothesis in
$|y|<0.5$. In contrast to this, in the “TOF fits” analysis, the velocity
$\beta$ distribution is simultaneously fitted for all three particle types.
For this purpose, four analytic functions, three for $\pi$, K and p, and one
for mismatches, are employed. The analysis is performed in two narrow
pseudorapidity slices ($|\eta|<0.2$ and $0.2<|\eta|<0.4$) and in momentum
bins, which are then unfolded to transverse momenta. The corresponding
rapidity interval is determined under the assumption of a flat
$\textrm{d}N_{\textrm{ch}}/\textrm{d}\eta$ distribution in the aforementioned
pseudorapidity bins [24].

Charged kaons can also be identified via the kink decay topology, where a
charged particle decays into a charged and a neutral daughter
($K^{\pm}\rightarrow\mu^{\pm}\nu_{\mu}$ or
$K^{\pm}\rightarrow\pi^{\pm}\pi^{0}$). This secondary vertex where both
decaying particle and the charged decay product have the same charge is
reconstructed inside the ALICE TPC detector. This technique extends the
charged kaon identification up to 6 GeV/$c$ on a track-by-track basis. The
algorithm for selecting kaons via their kink decay is used in a fiducial
volume inside the TPC corresponding to a radial distance of $120<R<210$ cm.
This selection allows for an adequate number of TPC clusters to be associated
with the decaying particle and its products. The track of the decaying
particle is required to fulfil all the criteria of the global tracks except
for the minimum number of clusters, which in this case is 30.

The topological selection of the kaon candidates and their separation from the
pion decays ($\pi^{\pm}\rightarrow\mu^{\pm}\nu_{\mu}$) is based on the two-
body decay kinematics. The transverse momentum of the decay product with
respect to the decaying particle’s direction ($q_{\rm T}$) has an upper limit
of 236 MeV/$c$ for kaons and 30 MeV/$c$ for pions for the two-body decay to
$\mu^{\pm}\nu_{\mu}$. Similarly, for kaons decaying to pions, this limit is
205 MeV/$c$. Thus, a selection of $q_{\textrm{T}}<120{\rm\ \textrm{MeV}/c}$
rejects the majority (85%) of pion decays. In addition, the angle between the
mother and the daughter tracks is selected to be above the maximum allowed
decay angle for pions and below the maximum allowed decay angle for kaons
[25]. The invariant mass for the decay $\mu^{\pm}\nu_{\mu}$, $M_{\mu\nu}$ is
calculated by assuming the daughter track to be a muon and the undetected
track to be a neutrino. These selection criteria lead to a kaon sample with a
purity of $97\%$.

The strategy employed to measure particle production in the region of the
relativistic rise of the TPC was reported in [26]. The
$\textrm{d}E/\textrm{d}x$ signal in the relativistic rise
$(3<\beta\gamma\left(=\frac{p}{m}\right)<1000)$ follows the functional form
$\ln(\beta\gamma)$. In addition to the logarithmic growth, the separation in
number of standard deviations between pions and protons, pions and kaons, and
kaons and protons as a function of momentum is nearly constant, which allows
identification of charged pions, kaons, and (anti)protons with a statistical
deconvolution approach from $p_{\rm T}\approx 2-3~{}{\rm GeV}/c$ up to $p_{\rm
T}=20~{}{\rm GeV}/c$. In order to describe the TPC response in the
relativistic rise, clean external samples of secondary particles were used to
parametrize the Bethe-Bloch and resolution curves. These correspond to pions
(protons) from weak decays: ${\rm
K}^{0}_{S}\rightarrow\pi^{+}+\pi^{-}(\Lambda\rightarrow\rm{p}+\pi^{-})$ and
electrons from photon conversion. Moreover, primary pions measured with the
TOF detector were used. The parametrization is done in four different
pseudorapidity intervals. For short (long) tracks, i.e tracks within
$|\eta|<0.2\,(0.6<|\eta|<0.8)$, the resolution for protons is $\approx
6.2\%(\approx 5.4\%)$, while for pions it is $\approx 5.4\%(\approx 5.0\%)$.
To extract the fraction of charged pions, kaons, and protons in the four
different pseudorapidity intervals a 4-Gaussian fit (three for $\pi$, K, p and
one to remove the unwanted electron contribution) to the
$\textrm{d}E/\textrm{d}x$ distribution in momentum bins is performed. The only
free parameter in each of the Gaussian functions is the normalization, while
the $\langle{\rm d}E/{\rm d}x\rangle$ and $\sigma_{\langle{\rm d}E/{\rm
d}x\rangle}$ are obtained and fixed using the Bethe-Bloch and resolution
parametrizations, respectively. A weighted average of the four different
measurements is calculated to obtain the particle fractions in $|\eta|<0.8$.
The yields are obtained by multiplying the particle fractions by the measured
unidentified charged particle spectrum.

###  2.3 Corrections and normalization

The raw particle distributions are normalized to the total number of events
analysed111Events that passed all the selection criteria. in each multiplicity
class. To obtain the $p_{\textrm{T}}$ distributions of primary $\pi$, K, and
p, the raw particle distributions obtained from the different PID approaches
need to be also corrected for the detector efficiency and acceptance, the ITS-
TPC, and TPC-TOF matching efficiency, the PID efficiency, the trigger
efficiency and the contamination from secondary particles.
Secondary particles are either produced in weak decays or from the interaction
of particles with the detector material. The estimation of secondary particle
contribution is based on the Monte Carlo (MC) templates of the distance of
closest approach of the track to the primary vertex in the transverse plane
with respect to the beam axis (DCAxy), as carried out in previous works [23,
11]. The DCAxy distributions of the tracks in data are fitted with three MC
templates corresponding to the expected shapes of primary particles,
secondaries from material and secondaries from weak decays to obtain the
correct fraction of primary particles in the data. This procedure is repeated
in each $p_{\textrm{T}}$ and multiplicity bin and thus takes into account the
possible differences in the feed-down corrections due to the change in the
abundances and spectral shapes of the weakly decaying particles. The
contamination is different in each PID analysis due to different track
selection criteria and PID techniques and hence it is estimated separately for
each analysis. The contribution of secondary particles was found to be
significant for $\pi$ (up to 2%) and p (up to 15%) whereas the contribution
for K is negligible.
The spectra are corrected for the detector acceptance and track reconstruction
efficiencies based on a simulation using the P  YTHIA 8 (Monash-2013 tune)
Monte Carlo event generator [27] and particle propagation through the full
ALICE geometry using GEANT3 [28]. In this simulation, tracks are reconstructed
using the same algorithms as for the data. The detector acceptance and
reconstruction efficiencies are found to be independent of charged-particle
multiplicity and thus the multiplicity-integrated values are used in all
multiplicity classes. As GEANT3 does not fully describe the interaction of
low-momentum $\rm\overline{p}$ and $\mathrm{K}^{-}$ with the detector
material, an additional correction factor to the efficiency for these two
particles is estimated with GEANT4 [29] and FLUKA [30], respectively, where
the interaction processes are known to be better reproduced [23]. Additional
corrections to the efficiency are applied when TPC or TOF information is used
to take into account the track matching between ITS and TPC, and between TPC
and TOF.
Signal losses due to the trigger selection are extracted from P  YTHIA 8
(Monash-2013 tune) MC simulation as performed in [22]. The correction is found
to be 17–18% at low $p_{\textrm{T}}$ in the V0M class X (the lowest
multiplicity), and reduces to $\sim$5%, $\sim$2% in classes IX and VIII,
respectively. The correction is negligible in higher multiplicity pp
collisions and for $p_{\textrm{T}}$ $\gtrsim$ 4 GeV/$c$ in all multiplicity
bins except in class X. In the latter, the correction reaches $\sim$2% at
$p_{\textrm{T}}$ = 7 GeV/$c$. Finally, an additional correction is applied to
pass from triggered INEL$>$0 to true INEL$>0$ events, i.e. events with at
least one primary charged particle in $|\eta^{\rm true}|$ $<$ 1 and with the
primary vertex in the region $|V^{\rm true}_{\rm z}|$ $<$ 10 cm. The
correction is independent of particle species and is found to be negligible
from V0M I (the highest multiplicity) to V0M VI, while it ranges from 1% in
class VII to 11% in class X. The correction is about 8% for multiplicity-
integrated INEL$>0$ events.

###  2.4 Systematic uncertainties

The systematic uncertainties are divided into two categories, those common to
all analyses and those which are analysis specific. The common systematic
uncertainties are those due to tracking, which includes track quality criteria
and the $p_{\textrm{T}}$-dependent ITS-TPC matching efficiency (except for the
ITSsa analysis), the TPC-TOF matching efficiency (for TPC-TOF and TOF
analyses), and the signal loss correction. In addition, the systematic source
related to the effect of the material budget on the global tracking
($p_{\textrm{T}}$ dependent) is also added. The uncertainties on global
tracking and TPC-TOF matching due to material budget are calculated by varying
the material budget in the simulation by $\pm$ 5%. The uncertainty related to
the hadronic interaction cross section in the detector material is estimated
using GEANT4 [29] and FLUKA [30] transport codes. Finally, an additional
systematic uncertainty of 2% is added to account for possible multiplicity
dependence of track reconstruction efficiency and signal loss correction
calculated from a MC simulation. All common sources of systematic
uncertainties are summarised in Table 3. In the same table, the individual
analysis systematic uncertainties are also listed for each particle species.

The estimation of the systematic uncertainties for the ITSsa analysis is
described in detail in [23, 11]. The ITSsa tracking uncertainties are
estimated by varying the main criteria for the track selection, namely those
on the DCAxy, on the $\chi^{2}$ of the track, and on the number of clusters
required in the ITS layers. The uncertainty related to the particle
identification is calculated by using a Bayesian technique and comparing the
results obtained with the standard n$\sigma$ method as already performed in
[31]. Due to the Lorentz force, the positions of ITS clusters are shifted
depending on the magnetic field polarity, giving rise to a 3% uncertainty.
Finally, the energy-independent uncertainty related to the ITS material budget
is estimated with a simulation of pp collisions at $\sqrt{\rm s}$ = 900 GeV by
varying the material budget of the ITS by $\pm$7.5% [32]. For the TPC-TOF fits
analysis at low $p_{\textrm{T}}$ (below 500, 600, and 800 $\textrm{MeV}/c$ for
$\pi$, K, and p, respectively), the systematic uncertainty associated with the
PID technique is calculated by integrating the measured
$\textrm{d}E/\textrm{d}x$ of charged tracks in the ranges of $\pm 3.5\sigma$
and $\pm 2.5\sigma$, where $\sigma$ represents one standard deviation from the
$\langle\textrm{d}E/\textrm{d}x\rangle$ under given mass hypothesis. At higher
$p_{\textrm{T}}$ values, where only the time-of-flight information is used,
the associated uncertainties are calculated by simultaneously varying the
width and tail parameters by 10%. An additional uncertainty is calculated by
fixing the central values of the fit functions to the $\beta$ calculated for
each particle species in a given momentum range. This was found to be the
dominant source of systematic uncertainty for $\pi$ and K at the highest
$p_{\textrm{T}}$ values ($\gtrsim 2.5~{}\textrm{GeV}/c$). For the TOF template
fits analysis, PID uncertainties are estimated by simultaneously varying the
spread and tail slope of each $\Delta t$ template by 10%. In addition to this,
for both the TPC-TOF and TOF template fits analyses, systematic uncertainties
associated with tracking are calculated by varying the track selection
criteria: the number of crossed rows in the TPC, the distance of closest
approach in beam and transverse directions, and the quality of the global
track fit $\chi^{2}$. For the kink analysis the sources of systematic
uncertainties are: the kink vertex finding efficiency (3% constant in
$p_{\textrm{T}}$), the kink PID efficiency (calculated by taking into account
the position of the kink vertex), the number of TPC clusters of the decaying
particle track and the $q_{\rm T}$ of the decay product, and the uncertainty
related to the purity of the selected sample. The contamination due to the
random association of tracks wrongly attributed to kaon decays is of the order
of 2.3% at low transverse momenta and reaches the value of 3.4% above 4
GeV/$c$. The largest component of the systematic uncertainties in the analysis
of the relativistic rise of the TPC arises from the imprecise parametrization
of both the Bethe-Bloch and resolution curves. To quantify this uncertainty,
the variations of the Bethe-Bloch resolution parametrizations with respect to
the measured $\langle{\rm d}E/{\rm d}x\rangle(\sigma_{\langle{\rm d}E/{\rm
d}x\rangle})$ are used to vary the values of the mean and $\sigma$ in the
4-Gaussian fit [26]. The largest relative deviation between the nominal
particle ratios and the ones obtained after the variations are assigned as a
systematic uncertainty.

Table 3: Sources of the relative systematic uncertainties of the $p_{\textrm{T}}$-differential yields of $\pi$, K, and p. The uncertainties are split into two categories, the common and the individual-analysis specific for low, intermediate and high $p_{\textrm{T}}$. Numbers in parenthesis in the p column refer to $\rm\overline{p}$ uncertainties. In the last rows, the maximum (among multiplicity classes) total systematic uncertainty is reported. | Uncertainty (%)
---|---
Common source | $\pi$ | K |  p ($\rm\overline{p}$)
$p_{\textrm{T}}$ ($\textrm{GeV}/c$) |  0.1 |  3.0 |  20.0 |  0.2 |  2.5 |  20.0 |  0.3 |  4.0 |  20.0
Correction for secondaries |  1 |  1 | 1 | negl. |  4 |  1 |  1
Hadronic interactions |  2 |  2.4 |  2.4 |  2.7 |  1.8 |  1.8 |  1 (3.6) |  1 (3.6) |  1 (3.6)
ITS-TPC matching efficiency |  0.7 |  1.5 |  2.9 |  0.7 |  1.5 |  2.9 |  0.7 |  1.5 |  2.9
Global tracking efficiency | 0.7 | 0.5 | 1.5
TOF matching efficiency
(TPC-TOF fits,TOF template fits) | 3 | 6 | 4
Signal-loss correction | 0.2 | 1 | 3.3
$p_{\textrm{T}}$ ($\textrm{GeV}/c$) |  0.3 |  3.0 |  20.0 |  0.3 |  2.5 |  20.0 |  0.4 |  4.0 |  20.0
Material budget
(TPC-TOF) |  0.5 |  1.0 |  0.2 |  1.5 |  1.0 |  0.4 |  2.9 |  1.7 |  0.1
Specific source | $\pi$ | K |  p ($\rm\overline{p}$)
ITSsa, $p_{\textrm{T}}$ ($\textrm{GeV}/c$) |  0.10 |  |  0.70 |  0.20 |  |  0.60 |  0.30 |  |  0.65
Tracking |  1.4 |  |  1.4 |  1.5 |  |  1.5 |  1.1 |  |  1.1
Material budget |  4.8 |  |  0.3 |  2.3 |  |  0.6 |  5.0 |  |  0.9
$E\times B$ effect |  |  3.0 |  |  |  3.0 |  |  |  3.0 |
PID |  0.4 |  |  0.4 |  3.9 |  |  3.9 |  4.2 |  |  4.2
TOF templates, $p_{\textrm{T}}$ ($\textrm{GeV}/c$) |  0.7 |  |  4.0 |  0.6 |  |  3.0 |  0.9 |  |  4.0
PID |  1 |  |  9.4 |  1 |  |  12 |  1 |  |  21
TPC-TOF fits, $p_{\textrm{T}}$ ($\textrm{GeV}/c$) |  0.3 |  |  3 |  0.3 |  |  3 |  0.4 |  |  3
PID |  1.4 |  |  7 |  3 |  |  16 |  1 |  |  4.3
rTPC, $p_{\textrm{T}}$ ($\textrm{GeV}/c$) |  2.0 |  |  20.0 |  2.0 |  |  20.0 |  2.0 |  |  20.0
Bethe–Bloch parameterization |  8.1 |  |  4 |  14.8 |  |  8.0 |  14 |  |  6.0
Feed-Down |  0.5 |  |  0.5 |  - |  |  - |  2.4 |  |  2.0
Kinks, $p_{\textrm{T}}$ ($\textrm{GeV}/c$) |  0.6 |  |  6.0 |  0.6 |  |  6.0 |  0.6 |  |  6.0
PID |  - |  |  - |  0.75 |  |  5.3 |  - |  |  -
Kink vertex finding efficiency |  - |  |  - |  3 |  |  3 |  - |  |  -
Contamination |  - |  |  - |  2.3 |  |  3.4 |  - |  |  -
Total | $\pi$ | K |  p ($\rm\overline{p}$)
$p_{\textrm{T}}$ ($\textrm{GeV}/c$) |  0.3 |  3.0 |  20.0 |  0.3 |  3.0 |  20.0 |  0.3 |  3.0 |  20.0
Total |  6.6 |  5.1 |  4.3 |  6.6 |  6.8 |  7.8 |  9.6 |  9.7 |  12.4
Particle ratios | K/$\pi$ | p/$\pi$ |  |  |
$p_{\textrm{T}}$ ($\textrm{GeV}/c$) |  0.2 |  3.0 |  20.0 |  0.3 |  3.0 |  20.0 |  |  |
Total |  7.2 |  14.6 |  7.7 |  10.2 |  12.2 |  11.5 |  |  |

##  3 Results and discussion

The $p_{\textrm{T}}$-differential spectra of $\pi$, K, and p measured as a
function of the charged-particle multiplicity density in pp collisions at
$\sqrt{s}\ =\ 13\ \textrm{TeV}$ are shown in Fig. 1. For each V0M class,
charged-particle multiplicity density has been measured in the central region
($|\eta|<0.5$), as summarized in Table 1. The bottom panels in Fig. 1 show
spectral ratios to the INEL$>$0 (sum of all V0M classes) class. We observe
that the measured $p_{\textrm{T}}$ spectra become harder with increasing
$\langle\textrm{d}N_{\textrm{ch}}/\textrm{d}\eta\rangle$, and the effect is
more pronounced for protons. The hardening of the inclusive charged-hadron
spectra with $\langle\textrm{d}N_{\textrm{ch}}/\textrm{d}\eta\rangle$ has been
also recently reported in [33], where different MPI models were shown to
describe such effect. On the other hand, the mass dependence of spectral shape
modifications is also observed in Pb–Pb collisions at $\sqrt{s_{\rm NN}}\ =\
2.76\ \textrm{TeV}$ [26], where it is usually associated with the
hydrodynamical evolution of the system. At higher $p_{\textrm{T}}$ ($\gtrsim
8\ \textrm{GeV}/c$), we find that slopes of particle spectra become
independent of the multiplicity class considered, as expected from pQCD
calculations [34].

Figure 1: Transverse momentum spectra of $\pi$, K, and p for different
multiplicity event classes. Spectra are scaled by powers of 2 in order to
improve visibility. The corresponding ratios to INEL$>$0 spectra are shown in
the bottom panels.

The $p_{\textrm{T}}$-differential K/$\pi$ and p/$\pi$ ratios as a function of
$\langle\textrm{d}N_{\textrm{ch}}/\textrm{d}\eta\rangle$ measured at low and
intermediate transverse momenta are shown in Fig. 2 together with those
measured in pp collisions at $\sqrt{s}\ =\ 7\ \textrm{TeV}$ [11] and
predictions from several MC generators for pp collisions at $\sqrt{s}\ =\ 13\
\textrm{TeV}$. The measured K/$\pi$ ratio shows no evident sign of evolution
with multiplicity in all $p_{\textrm{T}}$ ranges considered, while the p/$\pi$
ratio shows depletion at low $p_{\textrm{T}}$, an increase at intermediate
$p_{\textrm{T}}$, and constant behavior at high $p_{\textrm{T}}$. In addition,
the measured K/$\pi$ and p/$\pi$ ratios are consistent between the two center-
of-mass energies [11].

For MC predictions, the event classification is based on the number of charged
tracks simulated at forward and backward pseudorapidities covered by the V0
detector, in a way similar to the way the event classification is done for the
data. The mean charged-particle multiplicity density is then calculated in the
central pseudorapidity region, $|\eta|<0.5$. HERWIG 7 [35, 36], where a
clustering approach is used for hadronization, provides a good description of
the evolution of the K/$\pi$ and p/$\pi$ ratios with
$\langle\textrm{d}N_{\textrm{ch}}/\textrm{d}\eta\rangle$ in the low and
intermediate $p_{\textrm{T}}$ ranges and is consistent with the measured
ratios within 1-2 standard deviations. P  YTHIA 8 [37] without color
reconnection (CR) predicts no evolution of K/$\pi$ and p/$\pi$ ratios. The CR
scheme, which has been shown to capture the modifications of the baryon-to-
meson ratios [3], provides only a qualitative description of the evolution of
the p/$\pi$ ratio with
$\langle\textrm{d}N_{\textrm{ch}}/\textrm{d}\eta\rangle$ and overestimates the
absolute values of the ratio at low and high $p_{\textrm{T}}$. The
implementation of color ropes [38, 5, 39] in P  YTHIA 8, which results in
higher effective string tension and thus enhances strange- and di-quark
production, provides a qualitative description K/$\pi$ (p/$\pi$) ratio only at
low (intermediate) $p_{\textrm{T}}$ and overestimates the p/$\pi$ ratio at low
$p_{\textrm{T}}$. This could be understood considering that larger effective
string tension is mostly translated to hadronic mass and thus feeds down the
low $p_{\textrm{T}}$ part of the spectrum.

In large collision systems such as Pb–Pb, multiplicity-dependent modifications
of hadron $p_{\textrm{T}}$ spectra can be interpreted as the hydrodynamical
radial expansion of the system and studied in the context of the Boltzmann-
Gibbs Blast-Wave model [40]. In this model, a thermalized medium expands
radially and undergoes an instantaneous kinematic freeze-out. The average
expansion velocity $\langle\beta_{\textrm{T}}\rangle$, the kinetic freeze-out
temperature $T_{\textrm{kin}}$, and the velocity profile exponent $n$ can be
extracted from simultaneous model fits to hadron spectra. As the trends
observed in the evolution of particle spectra measured in pp collisions are
highly reminiscent to those in p–Pb and Pb–Pb, it is interesting to check
whether the Blast-Wave model can be extended to describe pp collisions. Such
study has been previously reported in [11], where pp, p–Pb, and Pb–Pb
collisions at $\sqrt{s_{\rm NN}}\ =\ \textrm{7, 5.02, and 2.76}\ \textrm{TeV}$
were considered. Now, for the first time, we can study the evolution of
$\langle\beta_{\textrm{T}}\rangle$, $T_{\textrm{kin}}$ and $n$ in pp
collisions as a function of the collision energy.

Figure 2: Multiplicity dependence of $p_{\textrm{T}}$-differential K/$\pi$
(upper panels) and p/$\pi$ (lower panels) ratios measured in pp collisions at
$\sqrt{s}$ = 7 TeV [11] and 13 TeV (blue and red, respectively). Lines
represent different MC generator predictions for pp collisions at $\sqrt{s}\
=\ 13\ \textrm{TeV}$. Left to right: low-, intermediate-, and high-transverse
momenta. Vertical bars, open, and shaded bands represent statistical, total
systematic, and multiplicity uncorrelated systematic uncertainties,
respectively.

At low transverse momenta ($p_{\textrm{T}}\lesssim 500~{}\textrm{MeV}/c$), the
dominant mechanism of $\pi$ production is from resonance decays. To account
for this in the Blast-Wave model fits, spectral measurements of all strongly
decaying hadrons are required. Alternatively, one can choose to omit the
low-$p_{\textrm{T}}$ pions. Noting that there is a strong dependence of Blast-
Wave parameters on the fitting range [23], it is important to consider the
same $p_{\textrm{T}}$ range in the fitting procedure in order to obtain a
consistent comparison between different colliding systems. The comparison of
the $\langle\beta_{\textrm{T}}\rangle$-$T_{\textrm{kin}}$ correlations
measured in different systems and center-of-mass energies is shown in Fig. 3.
In this paper we consider three different approaches to the Blast-Wave model
fits to particle spectra measured in pp collisions at $\sqrt{s}\ =\ 13\
\textrm{TeV}$: a) traditional fits as done in [23, 10, 11], where $\pi$, K,
and p spectra are fitted and resonance feed-down is neglected (represented by
markers in Fig. 3), b) simultaneously fitting K, p, and $\Lambda$ spectra [22]
noting that $\Lambda$ are not significantly affected by resonance decays
(represented by a solid line in Fig. 3), and c) a method proposed in [41, 42],
where the resonance feed-down is calculated before the Cooper–Frye freeze-out
using a statistical hadronization model (represented by a dashed line in Fig.
3). We find that the $T_{\textrm{kin}}$-$\langle\beta_{\textrm{T}}\rangle$
correlation in pp collisions at $\sqrt{s}\ =\ 13\ \textrm{TeV}$ follows
similar trends as seen at lower energies. When $\Lambda$’s are considered
instead of pions, the trends seen in
$\langle\beta_{\textrm{T}}\rangle$-$T_{\textrm{kin}}$ correlation do not
change significantly and only at highest multiplicities we find a larger
$T_{\textrm{kin}}$. On the other hand, when a proper treatment of resonance
decays is used, we find a significantly lower $T_{\textrm{kin}}$ of around 135
MeV at the lowest multiplicities, which then grows with increasing
$\langle\textrm{d}N_{\textrm{ch}}/\textrm{d}\eta\rangle$ and approaches the
pseudocritical QCD temperature $T_{\rm c}=156\pm 1.5~{}\mathrm{MeV}$ [43] at
the highest multiplicity pp collisions. In addition, the evolution of
$\langle\beta_{\textrm{T}}\rangle$, $T_{\textrm{kin}}$, and $n$ with
$\langle\textrm{d}N_{\textrm{ch}}/\textrm{d}\eta\rangle$ is shown in Fig. 4
for different colliding systems. From the lowest multiplicities,
$T_{\textrm{kin}}$ grows with $\langle\beta_{\textrm{T}}\rangle$ until it
saturates at around 180 MeV. At larger multiplicities
($\langle\textrm{d}N_{\textrm{ch}}/\textrm{d}\eta\rangle\gtrsim 16$),
$T_{\textrm{kin}}$ decreases and becomes similar to that measured in p–Pb
collisions at $\sqrt{s}\ =\ 5.02\ \textrm{TeV}$, suggesting that the system
decouples at lower temperature and thus is longer-lived. The average expansion
velocity $\langle\beta_{\textrm{T}}\rangle$ increases with
$\langle\textrm{d}N_{\textrm{ch}}/\textrm{d}\eta\rangle$ and its values are
consistent for pp collisions at different $\sqrt{s}$ as well as with the
corresponding values for p–Pb collisions, indicating that small systems become
more explosive at larger multiplicities. In contrast to this,
$\langle\beta_{\textrm{T}}\rangle$ measured in Pb–Pb collisions is lower than
that in smaller systems for the common
$\langle\textrm{d}N_{\textrm{ch}}/\textrm{d}\eta\rangle$ range, see Fig. 4.
This indicates that the size of the colliding system might have significant
effects on the final state particle dynamics. This is also reflected in the
expansion velocity profile power $n$ shown in Fig. 4: in pp and p–Pb
collisions, large $n$ suggests high pressure gradients which lead to larger
$\langle\beta_{\textrm{T}}\rangle$, while in Pb–Pb collisions, $n\sim 1$ could
be interpreted as lower pressure gradient and thus smaller expansion velocity
[44].

Figure 3: Correlation of kinetic freeze-out temperature $T_{\textrm{kin}}$ and
average expansion velocity $\langle\beta_{\textrm{T}}\rangle$, extracted from
simultaneous Blast-Wave fits to $\pi$, K, and p spectra measured in pp, p–Pb,
and Pb–Pb collisions. Contours represent 1$\sigma$ uncertainty. The shaded
ellipses represent the $T_{\textrm{kin}}$-$\langle\beta_{\textrm{T}}\rangle$
correlation calculated from Blast-Wave fit to K, p, and $\Lambda$ spectra [22]
measured in pp collisions at $\sqrt{s}\ =\ 13\ \textrm{TeV}$. The empty
circles represent Blast-Wave fits with resonance decays [42]. References from
[10, 11, 42, 12].

Figure 4: Evolution of $\langle\beta_{\textrm{T}}\rangle$, $T_{\textrm{kin}}$,
and $n$ with $\langle\textrm{d}N_{\textrm{ch}}/\textrm{d}\eta\rangle$.
$\langle\beta_{\textrm{T}}\rangle$, $T_{\textrm{kin}}$ and $n$ are extracted
from Blast-Wave fits to $\pi$, K, and p $p_{\textrm{T}}$ spectra measured in
pp, p–Pb, and Pb–Pb collisions at different $\sqrt{s}$.

Previous studies on hadron production as a function of multiplicity have
reported the factorization of $p_{\textrm{T}}$-integrated particle yields with
$\langle\textrm{d}N_{\textrm{ch}}/\textrm{d}\eta\rangle$ [11], which extends
across different colliding systems and collision energies. Now for the first
time we can isolate the center-of-mass energy dependence of this scaling for
$\pi$, K, and p in pp collisions. The $p_{\textrm{T}}$-integrated particle
yields ($\textrm{d}N/\textrm{d}y$) and average transverse momenta ($\langle
p_{\textrm{T}}\rangle$) are calculated by integrating the measured transverse
momentum spectra and using the Lévy-Tsallis parametrization [45, 46, 47] to
extrapolate to the low $p_{\textrm{T}}$ regions not covered by the
measurements. The extrapolated fractions of the yields at low $p_{\textrm{T}}$
are 8% (10%) for $\pi$, 6% (13%) for K, and 7% (20%) for p for the highest
(lowest) multiplicities. For systematic uncertainties on the extrapolation,
Bylinkin, Bose-Einstein, Fermi-Dirac, $m_{\rm T}$-exponential and Hagedorn
functions are used to fit particle spectra. The statistical uncertainties of
$\textrm{d}N/\textrm{d}y$ and $\langle p_{\textrm{T}}\rangle$ are calculated
by coherently shifting the central values of each spectra point by a fraction
of its statistical uncertainty. The fraction is randomly drawn from Gaussian
distribution and new values of integrated yields and mean transverse momenta
are calculated. The procedure is repeated 1000 times to calculate the standard
deviations of $\textrm{d}N/\textrm{d}y$ and $\langle p_{\textrm{T}}\rangle$,
which are then used as the statistical uncertainties. To estimate the
systematic uncertainty on the integrated yields, the spectra points are moved
to maximal/minimal values allowed by their respective systematic uncertainties
before repeating the fit procedure. For $\langle p_{\textrm{T}}\rangle$, each
point of the spectra is shifted to the upper/lower edge of the corresponding
$p_{\textrm{T}}$ bin to obtain the hardest/softest particle distribution. The
largest differences to the nominal yield and $\langle p_{\textrm{T}}\rangle$
values are combined with the extrapolation uncertainties to calculate the
total systematic uncertainties. The kaon- and proton-to-pion integrated yield
ratios measured in pp collisions at $\sqrt{s}\ =\ 13\ \textrm{TeV}$ are found
to be in a good agreement within systematic uncertainties with those measured
in pp, p–Pb, and Pb–Pb collisions at $\sqrt{s_{\rm NN}}\ =\ \textrm{7, 5.02,
and 2.76}\ \textrm{TeV}$, respectively, as shown in Fig. 5. This indicates
that hadrochemistry at LHC energies scales with charged-particle multiplicity
density in a uniform way, despite the colliding system or collision energy.

The description of hadron-to-pion ratio factorization with multiplicity at
lower center-of-mass energies in MC generators has been previously shown to be
qualitative at best [11]. In fact, both P  YTHIA 8 with color reconnection and
HERWIG 7 [35, 36] predict no evolution of the ratios with
$\langle\textrm{d}N_{\textrm{ch}}/\textrm{d}\eta\rangle$. In this paper, we
consider more recent versions of the two MC generators. In particular, the
hadronization in P  YTHIA 8 now considers overlapping color strings, which
form color ropes with a larger effective string tension and are then allowed
to interact with each other [39]. On the other hand, hadronization in HERWIG 7
now includes baryonic ropes – a reconnection scheme that enhances the
probability of partons forming a baryon [35]. We find that both P  YTHIA 8 and
HERWIG 7 predict the enhancement of strange baryons which is more pronounced
for hadrons with a larger strangeness content. The largest quantitative
differences are seen for $\Omega$/$\pi$ ratio at the lowest multiplicity in pp
collisions. This might point to the need of a further refinement of MC
generator tuning, as similar discrepancies are already observed for e+e- data
[48]. The integrated K/$\pi$ yield ratio shown in Fig. 5 at high multiplicity
pp collisions are captured by P  YTHIA 8 ropes and HERWIG 7, but the latter
predicts a peak-like structure at low
$\langle\textrm{d}N_{\textrm{ch}}/\textrm{d}\eta\rangle$ which is not observed
in the data. The predictions from P  YTHIA 8 Monash tune are inconsistent with
the measured K/$\pi$ ratios in pp collisions at $\sqrt{s}\ =\ 13\
\textrm{TeV}$, whether color reconnection is considered or not. The
quantitative description of p/$\pi$ ratio is given only by HERWIG 7, while all
considered versions of P  YTHIA 8 overpredict the data. Moreover, P  YTHIA 8
with color ropes predicts an increase of the p/$\pi$ ratio with
$\langle\textrm{d}N_{\textrm{ch}}/\textrm{d}\eta\rangle$, which could be
attributed to the enhanced production of strange- and di-quark in the rope
fragmentation. Overall, we conclude that none of the models considered provide
a consistent description of the data.

The average transverse momenta of identified particles are found to increase
with multiplicity in pp collisions at $\sqrt{s}\ =\ \textrm{7 and 13}\
\textrm{TeV}$ as shown in Fig. 7. A clear mass ordering is observed among the
particle species considered, where protons have the largest $\langle
p_{\textrm{T}}\rangle$. Similar observations have been previously reported in
pp [49] and p–Pb [10] collisions at lower energies and for strange hadrons in
pp collisions at $\sqrt{s}\ =\ 13\ \textrm{TeV}$ [22]. The solid red line in
Fig. 7 represents a fit of the form
$a-b/(c-\langle\textrm{d}N_{\textrm{ch}}/\textrm{d}\eta\rangle)$ to the
$\sqrt{s}\ =\ 13\ \textrm{TeV}$ data, which is then used for a better
comparison of $\langle p_{\textrm{T}}\rangle$ between the two center-of-mass
energies, see lower panels of the same figure. We find a small hint of an
increase with $\sqrt{s}$ for similar multiplicities for $\pi$, while the
$\langle p_{\textrm{T}}\rangle$ of protons is similar at the two center-of-
mass energies. Note that similar observations have been already reported in
[22], where spectra of K${}^{0}_{\rm s}$ were found to become harder with
$\sqrt{s}$ at similar multiplicities. In addition, we find that P  YTHIA 8
Monash tune with color reconnection, HERWIG 7, and P  YTHIA 8 with ropes give
a very good description of $\pi$ $\langle p_{\textrm{T}}\rangle$ evolution
with $\langle\textrm{d}N_{\textrm{ch}}/\textrm{d}\eta\rangle$. This is
expected as pions are the most abundant particles produced in collisions, and
the three generators are tuned to explicitly to describe the $\langle
p_{\textrm{T}}\rangle$ of charged-particles. On the other hand, we observe
that the $\langle p_{\textrm{T}}\rangle$ of K and p are well described only by
HERWIG 7, while P  YTHIA 8 with rope implementation underestimates the
$\langle p_{\textrm{T}}\rangle$ in the whole
$\langle\textrm{d}N_{\textrm{ch}}/\textrm{d}\eta\rangle$ range considered.
This could be understood considering that the additional energy available
during the rope fragmentation predominantly enhances the production of heavier
hadrons at low $p_{\textrm{T}}$.

Figure 5: Integrated K/$\pi$ (top) and p/$\pi$ (bottom) yield ratios as a
function of charged-particle multiplicity density measured in pp, p–Pb, and
Pb–Pb collisions at different center-of-mass energies. Empty (shaded) boxes
represent total (multiplicity uncorrelated) systematic uncertainties. Black
lines represent predictions from different MC generators for pp collisions at
$\sqrt{s}\ =\ 13\ \textrm{TeV}$. References from [11, 31, 23, 50]. Figure 6:
Integrated strange hadron-to-pion ratios as a function of
$\langle\textrm{d}N_{\textrm{ch}}/\textrm{d}\eta\rangle$ measured in pp, p–Pb,
and Pb–Pb collisions. The open (shaded) boxes around markers represent full
(multiplicity uncorrelated) systematic uncertainties. Different lines
represent predictions from different MC generators for pp collisions at
$\sqrt{s}\ =\ 13\ \textrm{TeV}$. References from [6, 12, 11, 22]. Figure 7:
Upper panels: average transverse momenta of $\pi$, K, and p as a function of
charged-particle multiplicity density measured in pp collisions at $\sqrt{s}\
=\ \textrm{7 and 13}\ \textrm{TeV}$. The red solid line represents
$a-b(c-\langle\textrm{d}N_{\textrm{ch}}/\textrm{d}\eta\rangle)^{-1}$ fit to
the 13 TeV data to guide the eye. Open (shaded) boxes represent total
(multiplicity uncorrelated) systematic uncertainties. Black lines represent
predictions from different MC generators for pp collisions at $\sqrt{s}\ =\
13\ \textrm{TeV}$. Bottom panels: ratios of $\langle p_{\textrm{T}}\rangle$ to
the fits. Data at $\sqrt{s}\ =\ 7\ \textrm{TeV}$ are from [11].

##  4 Summary

We have studied $\pi$, K, and p production as a function of multiplicity in pp
collisions at $\sqrt{s}\ =\ 13\ \textrm{TeV}$. To avoid auto-correlation
biases, the event classification has been based on multiplicity measurements
at forward (backward) pseudorapidity, while event activity
$\langle\textrm{d}N_{\textrm{ch}}/\textrm{d}\eta\rangle$ has been
correspondingly estimated at central pseudorapidities, $|\eta|<0.5$. We find
that hadron $p_{\textrm{T}}$ spectra become harder with multiplicity, and the
effect is more pronounced for heavier particles. The hardening of the spectra
is predicted by P  YTHIA 8 with rope hadronization, P  YTHIA 8 Monash with
color reconnection, and HERWIG7 MC generators. In addition, all three
generators provide a quantitative description of $\pi$ $\langle
p_{\textrm{T}}\rangle$, while K and p are described qualitatively only by
HERWIG7. At high $p_{\textrm{T}}$ $(\gtrsim 8\,\textrm{GeV}/c)$ we find that
spectral shapes become independent of
$\langle\textrm{d}N_{\textrm{ch}}/\textrm{d}\eta\rangle$ as predicted by pQCD
calculations [34].

The measured $p_{\textrm{T}}$-differential K/$\pi$ ratios show no evolution
with multiplicity in the $p_{\textrm{T}}$ range considered. In contrast to
this, a depletion (enhancement, saturation) is visible for the p/$\pi$ ratios
at low (intermediate, high) $p_{\textrm{T}}$. In addition, we find that the
ratios measured in pp collisions at $\sqrt{s}\ =\ 13\ \textrm{TeV}$ are
consistent with those measured at $\sqrt{s}\ =\ 7\ \textrm{TeV}$. While some
of the most common MC generators capture the trends seen in the
$p_{\textrm{T}}$-differential K/$\pi$ and p/$\pi$ ratios, none of them
provides a consistent description of the data.

The saturation at high $p_{\textrm{T}}$ is captured by P  YTHIA 8 Monash
tunes, while HERWIG 7 and P  YTHIA 8 with color ropes show signs of
enhancement. However, it is interesting to see that none of the generators can
predict the absolute values of the K/$\pi$ and p/$\pi$ ratios at high
$p_{\textrm{T}}$.

The study of hadron $p_{\textrm{T}}$ spectra in the context of the Blast-Wave
model reveals that the kinetic freeze-out temperature $T_{\textrm{kin}}$,
average expansion velocity $\langle\beta_{\textrm{T}}\rangle$, and the
velocity profile exponent $n$ show little or no dependence on the center-of-
mass energy and are consistent within uncertainties with those extracted from
particle spectra measured in pp collisions at $\sqrt{s}\ =\ 7\ \textrm{TeV}$
[11]. On the other hand, we observe a strong dependence of the extracted
parameters on $\langle\textrm{d}N_{\textrm{ch}}/\textrm{d}\eta\rangle$.

The $p_{\textrm{T}}$-integrated hadron-to-pion ratios as a function of
multiplicity show no center-of-mass dependence and the measurement in pp
collisions at $\sqrt{s}\ =\ 13\ \textrm{TeV}$ are compatible to those in pp,
p–Pb, and Pb–Pb collisions at $\sqrt{s_{\rm NN}}\ =\ \textrm{7, 5.02, and
2.76}\ \textrm{TeV}$, respectively. This suggests that, at the LHC energies,
the chemical composition of primary hadrons scales with charged-particle
multiplicity density in a uniform way, despite the colliding system and
collision energy. Comparisons of the integrated hadron-to-pion ratios to the
predictions from MC generators show that P  YTHIA 8 with color ropes provides
the best description of (multi)strange hadrons, but overestimates the measured
p/$\pi$ ratio. HERWIG7 also captures the evolution of the ratios with
$\langle\textrm{d}N_{\textrm{ch}}/\textrm{d}\eta\rangle$, but underestimates
the absolute values of $\Xi$/$\pi$ and $\Omega$/$\pi$. Overall, none of the
generators are able to provide a consistent quantitative description of the
measured hadron-to-pion ratios.

## Acknowledgements

The ALICE Collaboration would like to thank all its engineers and technicians for their invaluable contributions to the construction of the experiment and the CERN accelerator teams for the outstanding performance of the LHC complex. The ALICE Collaboration gratefully acknowledges the resources and support provided by all Grid centres and the Worldwide LHC Computing Grid (WLCG) collaboration. The ALICE Collaboration acknowledges the following funding agencies for their support in building and running the ALICE detector: A. I. Alikhanyan National Science Laboratory (Yerevan Physics Institute) Foundation (ANSL), State Committee of Science and World Federation of Scientists (WFS), Armenia; Austrian Academy of Sciences, Austrian Science Fund (FWF): [M 2467-N36] and Nationalstiftung für Forschung, Technologie und Entwicklung, Austria; Ministry of Communications and High Technologies, National Nuclear Research Center, Azerbaijan; Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq), Financiadora de Estudos e Projetos (Finep), Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) and Universidade Federal do Rio Grande do Sul (UFRGS), Brazil; Ministry of Education of China (MOEC) , Ministry of Science & Technology of China (MSTC) and National Natural Science Foundation of China (NSFC), China; Ministry of Science and Education and Croatian Science Foundation, Croatia; Centro de Aplicaciones Tecnológicas y Desarrollo Nuclear (CEADEN), Cubaenergía, Cuba; Ministry of Education, Youth and Sports of the Czech Republic, Czech Republic; The Danish Council for Independent Research | Natural Sciences, the VILLUM FONDEN and Danish National Research Foundation (DNRF), Denmark; Helsinki Institute of Physics (HIP), Finland; Commissariat à l’Energie Atomique (CEA), 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), Japanese Ministry of Education, Culture, Sports, Science and Technology (MEXT) and Japan Society for the Promotion of Science (JSPS) KAKENHI, Japan; Consejo Nacional de Ciencia (CONACYT) y Tecnología, through Fondo de Cooperación Internacional en Ciencia y Tecnología (FONCICYT) and Dirección General de Asuntos del Personal Academico (DGAPA), Mexico; Nederlandse Organisatie voor Wetenschappelijk Onderzoek (NWO), Netherlands; The Research Council of Norway, Norway; Commission on Science and Technology for Sustainable Development in the South (COMSATS), Pakistan; Pontificia Universidad Católica del Perú, Peru; Ministry of 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; Suranaree University of Technology (SUT), National Science and Technology Development Agency (NSDTA) 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] R. Derradi de Souza, T. Koide, and T. Kodama, “Hydrodynamic Approaches in Relativistic Heavy Ion Reactions,” Prog. Part. Nucl. Phys. 86 (2016) 35–85, arXiv:1506.03863 [nucl-th].
  * [2] A. Andronic, P. Braun-Munzinger, K. Redlich, and J. Stachel, “Decoding the phase structure of QCD via particle production at high energy,” Nature 561 no. 7723, (2018) 321–330, arXiv:1710.09425 [nucl-th].
  * [3] A. Ortiz Velasquez, P. Christiansen, E. Cuautle Flores, I. Maldonado Cervantes, and G. Paić, “Color Reconnection and Flowlike Patterns in pp Collisions,” Phys. Rev. Lett. 111 no. 4, (2013) 042001, arXiv:1303.6326 [hep-ph].
  * [4] T. Sjöstrand, S. Ask, J. R. Christiansen, R. Corke, N. Desai, P. Ilten, S. Mrenna, S. Prestel, C. O. Rasmussen, and P. Z. Skands, “An Introduction to PYTHIA 8.2,” Comput. Phys. Commun. 191 (2015) 159–177, arXiv:1410.3012 [hep-ph].
  * [5] C. Bierlich, G. Gustafson, L. Lönnblad, and A. Tarasov, “Effects of Overlapping Strings in pp Collisions,” JHEP 03 (2015) 148, arXiv:1412.6259 [hep-ph].
  * [6] ALICE Collaboration, J. Adam et al., “Multi-strange baryon production in p–Pb collisions at $\sqrt{s_{NN}}=5.02$ TeV,” Phys. Lett. B758 (2016) 389–401, arXiv:1512.07227 [nucl-ex].
  * [7] CMS Collaboration, S. Chatrchyan et al., “Observation of long-range near-side angular correlations in proton-lead collisions at the LHC,” Phys. Lett. B718 (2013) 795–814, arXiv:1210.5482 [nucl-ex].
  * [8] ALICE Collaboration, B. Abelev et al., “Long-range angular correlations on the near and away side in p–Pb collisions at $\sqrt{s_{NN}}=5.02$ TeV,” Phys. Lett. B719 (2013) 29–41, arXiv:1212.2001 [nucl-ex].
  * [9] ALICE Collaboration, B. Abelev et al., “Multiparticle azimuthal correlations in p–Pb and Pb–Pb collisions at the CERN Large Hadron Collider,” Phys. Rev. C90 no. 5, (2014) 054901, arXiv:1406.2474 [nucl-ex].
  * [10] 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].
  * [11] ALICE Collaboration, S. Acharya et al., “Multiplicity dependence of light-flavor hadron production in pp collisions at $\sqrt{s}$ = 7 TeV,” Phys. Rev. C99 no. 2, (2019) 024906, arXiv:1807.11321 [nucl-ex].
  * [12] 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].
  * [13] ATLAS Collaboration, G. Aad et al., “Observation of Long-Range Elliptic Azimuthal Anisotropies in $\sqrt{s}=$13 and 2.76 TeV pp Collisions with the ATLAS Detector,” Phys. Rev. Lett. 116 no. 17, (2016) 172301, arXiv:1509.04776 [hep-ex].
  * [14] ALICE Collaboration, “The ALICE definition of primary particles,”. https://cds.cern.ch/record/2270008.
  * [15] ALICE Collaboration, K. Aamodt et al., “The ALICE experiment at the CERN LHC,” JINST 3 (2008) S08002.
  * [16] 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].
  * [17] ALICE Collaboration, E. Abbas et al., “Mid-rapidity anti-baryon to baryon ratios in pp collisions at $\sqrt{s}$ = 0.9, 2.76 and 7 TeV measured by ALICE,” Eur. Phys. J. C73 (2013) 2496, arXiv:1305.1562 [nucl-ex].
  * [18] ALICE Collaboration, “ALICE luminosity determination for pp collisions at $\sqrt{s}=13$ TeV,”. http://cds.cern.ch/record/2160174.
  * [19] J. Alme et al., “The ALICE TPC, a large 3-dimensional tracking device with fast readout for ultra-high multiplicity events,” Nucl. Instrum. Meth. A622 (2010) 316–367, arXiv:1001.1950 [physics.ins-det].
  * [20] ALICE Collaboration, D. De Gruttola, “Particle IDentification with the ALICE Time-Of-Flight detector at the LHC,” JINST 9 no. 10, (2014) C10019.
  * [21] ALICE Collaboration, J. Adam et al., “Determination of the event collision time with the ALICE detector at the LHC,” Eur. Phys. J. Plus 132 no. 2, (2017) 99, arXiv:1610.03055 [physics.ins-det].
  * [22] ALICE Collaboration, S. Acharya et al., “Multiplicity dependence of (multi-)strange hadron production in proton-proton collisions at $\sqrt{s}$ = 13 TeV,” arXiv:1908.01861 [nucl-ex].
  * [23] 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].
  * [24] ALICE Collaboration, J. Adam et al., “Charged-particle multiplicities in proton–proton collisions at $\sqrt{s}=0.9$ to 8 TeV,” Eur. Phys. J. C77 no. 1, (2017) 33, arXiv:1509.07541 [nucl-ex].
  * [25] ALICE Collaboration, J. Adam et al., “Measurement of pion, kaon and proton production in proton–proton collisions at $\sqrt{s}=7$ TeV,” Eur. Phys. J. C75 no. 5, (2015) 226, arXiv:1504.00024 [nucl-ex].
  * [26] ALICE Collaboration, J. Adam et al., “Centrality dependence of the nuclear modification factor of charged pions, kaons, and protons in Pb–Pb collisions at $\sqrt{s_{\rm NN}}=2.76$ TeV,” Phys. Rev. C93 no. 3, (2016) 034913, arXiv:1506.07287 [nucl-ex].
  * [27] 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].
  * [28] R. Brun, F. Bruyant, M. Maire, A. C. McPherson, and P. Zanarini, GEANT 3: user’s guide Geant 3.10, Geant 3.11; rev. version.  CERN, Geneva, 1987.  https://cds.cern.ch/record/1119728.
  * [29] GEANT4 Collaboration, S. Agostinelli et al., “GEANT4: A Simulation toolkit,” Nucl. Instrum. Meth. A506 (2003) 250–303.
  * [30] A. Ferrari, P. R. Sala, A. Fasso, and J. Ranft, “FLUKA: A multi-particle transport code (Program version 2005),”.
  * [31] 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].
  * [32] ALICE Collaboration, K. Aamodt et al., “Production of pions, kaons and protons in pp collisions at $\sqrt{s}=900$ GeV with ALICE at the LHC,” Eur. Phys. J. C71 (2011) 1655, arXiv:1101.4110 [hep-ex].
  * [33] ALICE Collaboration, S. Acharya et al., “Charged-particle production as a function of multiplicity and transverse spherocity in pp collisions at $\sqrt{s}=5.02$ and 13 TeV,” arXiv:1905.07208 [nucl-ex].
  * [34] S. Kretzer, “Fragmentation functions from flavour inclusive and flavour tagged e+e- annihilations,” Phys. Rev. D62 (2000) 054001, arXiv:hep-ph/0003177 [hep-ph].
  * [35] J. Bellm et al., “Herwig 7.0/Herwig++ 3.0 release note,” Eur. Phys. J. C76 no. 4, (2016) 196, arXiv:1512.01178 [hep-ph].
  * [36] M. Bahr et al., “Herwig++ Physics and Manual,” Eur. Phys. J. C58 (2008) 639–707, arXiv:0803.0883 [hep-ph].
  * [37] T. Sjostrand, S. Mrenna, and P. Z. Skands, “A Brief Introduction to PYTHIA 8.1,” Comput. Phys. Commun. 178 (2008) 852–867, arXiv:0710.3820 [hep-ph].
  * [38] C. Flensburg, G. Gustafson, and L. Lönnblad, “Inclusive and Exclusive Observables from Dipoles in High Energy Collisions,” JHEP 08 (2011) 103, arXiv:1103.4321 [hep-ph].
  * [39] C. Bierlich, G. Gustafson, L. Lönnblad, and H. Shah, “The Angantyr model for Heavy-Ion Collisions in PYTHIA8,” JHEP 10 (2018) 134, arXiv:1806.10820 [hep-ph].
  * [40] E. Schnedermann, J. Sollfrank, and U. W. Heinz, “Thermal phenomenology of hadrons from 200-AGeV S+S collisions,” Phys. Rev. C48 (1993) 2462–2475, arXiv:nucl-th/9307020 [nucl-th].
  * [41] A. Mazeliauskas, S. Floerchinger, E. Grossi, and D. Teaney, “Fast resonance decays in nuclear collisions,” arXiv:1809.11049 [nucl-th].
  * [42] A. Mazeliauskas and V. Vislavicius, “Temperature and fluid velocity on the freeze-out surface from $\pi$, $K$, $p$ spectra in pp, p–Pb and Pb–Pb collisions,” arXiv:1907.11059 [hep-ph].
  * [43] HotQCD Collaboration, A. Bazavov et al., “Chiral crossover in QCD at zero and non-zero chemical potentials,” Phys. Lett. B795 (2019) 15–21, arXiv:1812.08235 [hep-lat].
  * [44] E. Shuryak and I. Zahed, “High-multiplicity pp and pA collisions: Hydrodynamics at its edge,” Phys. Rev. C88 no. 4, (2013) 044915, arXiv:1301.4470 [hep-ph].
  * [45] C. Tsallis, “Possible Generalization of Boltzmann-Gibbs Statistics,” J. Statist. Phys. 52 (1988) 479–487.
  * [46] G. Wilk and Z. Wlodarczyk, “On the interpretation of nonextensive parameter q in Tsallis statistics and Levy distributions,” Phys. Rev. Lett. 84 (2000) 2770, arXiv:hep-ph/9908459 [hep-ph].
  * [47] STAR Collaboration, J. Adams et al., “K(892)* resonance production in Au+Au and p+p collisions at $\sqrt{s_{\rm NN}}=200{\rm\ GeV}$ at STAR,” Phys. Rev. C71 (2005) 064902, arXiv:nucl-ex/0412019 [nucl-ex].
  * [48] C. Bierlich and J. R. Christiansen, “Effects of color reconnection on hadron flavor observables,” Phys. Rev. D92 no. 9, (2015) 094010, arXiv:1507.02091 [hep-ph].
  * [49] CMS Collaboration, S. Chatrchyan et al., “Study of the inclusive production of charged pions, kaons, and protons in pp collisions at $\sqrt{s}=0.9$, 2.76, and 7 TeV,” Eur. Phys. J. C72 (2012) 2164, arXiv:1207.4724 [hep-ex].
  * [50] ALICE Collaboration, S. Acharya et al., “Production of charged pions, kaons and (anti-)protons in Pb-Pb and inelastic pp collisions at $\sqrt{s_{\rm{NN}}}$ = 5.02 TeV,” arXiv:1910.07678 [nucl-ex].

##  Appendix A The ALICE Collaboration

S. Acharyaorg141&D. Adamováorg94&A. Adlerorg74&J. Adolfssonorg80&M.M.
Aggarwalorg99&G. Aglieri Rinellaorg33&M. Agnelloorg30&N. Agrawalorg10,org53&Z.
Ahammedorg141&S. Ahmadorg16&S.U. Ahnorg76&A. Akindinovorg91&M. Al-
Turanyorg106&S.N. Alamorg141&D.S.D. Albuquerqueorg122&D. Aleksandrovorg87&B.
Alessandroorg58&H.M. Alfandaorg6&R. Alfaro Molinaorg71&B. Aliorg16&Y.
Aliorg14&A. Aliciorg10,org26,org53&A. Alkinorg2&J. Almeorg21&T. Altorg68&L.
Altenkamperorg21&I. Altsybeevorg112&M.N. Anaamorg6&C. Andreiorg47&D.
Andreouorg33&H.A. Andrewsorg110&A. Andronicorg144&M. Angelettiorg33&V.
Anguelovorg103&C. Ansonorg15&T. Antičićorg107&F. Antinoriorg56&P.
Antonioliorg53&N. Apadulaorg79&L. Aphecetcheorg114&H. Appelshäuserorg68&S.
Arcelliorg26&R. Arnaldiorg58&M. Arratiaorg79&I.C. Arseneorg20&M.
Arslandokorg103&A. Augustinusorg33&R. Averbeckorg106&S. Azizorg61&M.D.
Azmiorg16&A. Badalàorg55&Y.W. Baekorg40&S. Bagnascoorg58&X. Baiorg106&R.
Bailhacheorg68&R. Balaorg100&A. Balbinoorg30&A. Baldisseriorg137&M.
Ballorg42&S. Balouzaorg104&D. Banerjeeorg3&R. Barberaorg27&L.
Barioglioorg25&G.G. Barnaföldiorg145&L.S. Barnbyorg93&V. Barretorg134&P.
Bartaliniorg6&K. Barthorg33&E. Bartschorg68&F. Baruffaldiorg28&N.
Bastidorg134&S. Basuorg143&G. Batigneorg114&B. Batyunyaorg75&D.
Bauriorg48&J.L. Bazo Albaorg111&I.G. Beardenorg88&C. Beattieorg146&C.
Beddaorg63&N.K. Beheraorg60&I. Belikovorg136&A.D.C. Bell Hechavarriaorg144&F.
Belliniorg33&R. Bellwiedorg125&V. Belyaevorg92&G. Bencediorg145&S.
Beoleorg25&A. Bercuciorg47&Y. Berdnikovorg97&D. Berenyiorg145&R.A.
Bertensorg130&D. Berzanoorg58&M.G. Besoiuorg67&L. Betevorg33&A.
Bhasinorg100&I.R. Bhatorg100&M.A. Bhatorg3&H. Bhattorg48&B.
Bhattacharjeeorg41&A. Bianchiorg25&L. Bianchiorg25&N. Bianchiorg51&J.
Bielčíkorg36&J. Bielčíkováorg94&A. Bilandzicorg104,org117&G. Biroorg145&R.
Biswasorg3&S. Biswasorg3&J.T. Blairorg119&D. Blauorg87&C. Blumeorg68&G.
Bocaorg139&F. Bockorg33,org95&A. Bogdanovorg92&S. Boiorg23&L.
Boldizsárorg145&A. Bolozdynyaorg92&M. Bombaraorg37&G. Bonomiorg140&H.
Borelorg137&A. Borissovorg92&H. Bossiorg146&E. Bottaorg25&L. Bratrudorg68&P.
Braun-Munzingerorg106&M. Bregantorg121&M. Brozorg36&E. Brunaorg58&G.E.
Brunoorg105&M.D. Bucklandorg127&D. Budnikovorg108&H. Bueschingorg68&S.
Bufalinoorg30&O. Bugnonorg114&P. Buhlerorg113&P. Buncicorg33&Z.
Butheleziorg72,org131&J.B. Buttorg14&J.T. Buxtonorg96&S.A. Bysiakorg118&D.
Caffarriorg89&A. Calivaorg106&E. Calvo Villarorg111&R.S. Camachoorg44&P.
Cameriniorg24&A.A. Caponorg113&F. Carnesecchiorg10,org26&R. Caronorg137&J.
Castillo Castellanosorg137&A.J. Castroorg130&E.A.R. Casulaorg54&F.
Catalanoorg30&C. Ceballos Sanchezorg52&P. Chakrabortyorg48&S. Chandraorg141&W.
Changorg6&S. Chapelandorg33&M. Chartierorg127&S. Chattopadhyayorg141&S.
Chattopadhyayorg109&A. Chauvinorg23&C. Cheshkovorg135&B. Cheynisorg135&V.
Chibante Barrosoorg33&D.D. Chinellatoorg122&S. Choorg60&P. Chochulaorg33&T.
Chowdhuryorg134&P. Christakoglouorg89&C.H. Christensenorg88&P.
Christiansenorg80&T. Chujoorg133&C. Cicaloorg54&L. Cifarelliorg10,org26&F.
Cindoloorg53&G. Claiorg53orgI&J. Cleymansorg124&F. Colamariaorg52&D.
Colellaorg52&A. Colluorg79&M. Colocciorg26&M. Concasorg58orgII&G. Conesa
Balbastreorg78&Z. Conesa del Valleorg61&G. Continorg24,org59&J.G.
Contrerasorg36&T.M. Cormierorg95&Y. Corrales Moralesorg25&P. Corteseorg31&M.R.
Cosentinoorg123&F. Costaorg33&S. Costanzaorg139&P. Crochetorg134&E.
Cuautleorg69&P. Cuiorg6&L. Cunqueiroorg95&D. Dabrowskiorg142&T.
Dahmsorg104,org117&A. Daineseorg56&F.P.A. Damasorg114,org137&M.C.
Danischorg103&A. Danuorg67&D. Dasorg109&I. Dasorg109&P. Dasorg85&P. Dasorg3&S.
Dasorg3&A. Dashorg85&S. Dashorg48&S. Deorg85&A. De Caroorg29&G. de
Cataldoorg52&J. de Cuvelandorg38&A. De Falcoorg23&D. De Gruttolaorg10&N. De
Marcoorg58&S. De Pasqualeorg29&S. Deborg49&H.F. Degenhardtorg121&K.R.
Dejaorg142&A. Delofforg84&S. Delsantoorg25,org131&W. Dengorg6&D.
Devetakorg106&P. Dhankherorg48&D. Di Bariorg32&A. Di Mauroorg33&R.A.
Diazorg8&T. Dietelorg124&P. Dillensegerorg68&Y. Dingorg6&R. Diviàorg33&D.U.
Dixitorg19&Ø. Djuvslandorg21&U. Dmitrievaorg62&A. Dobrinorg67&B.
Dönigusorg68&O. Dordicorg20&A.K. Dubeyorg141&A. Dublaorg106&S. Dudiorg99&M.
Dukhishyamorg85&P. Dupieuxorg134&R.J. Ehlersorg95,org146&V.N. Eikelandorg21&D.
Eliaorg52&E. Eppleorg146&B. Erazmusorg114&F. Erhardtorg98&A.
Erokhinorg112&M.R. Ersdalorg21&B. Espagnonorg61&G. Eulisseorg33&D.
Evansorg110&S. Evdokimovorg90&L. Fabbiettiorg104,org117&M. Fagginorg28&J.
Faivreorg78&F. Fanorg6&A. Fantoniorg51&M. Faselorg95&P. Fecchioorg30&A.
Felicielloorg58&G. Feofilovorg112&A. Fernández Téllezorg44&A. Ferreroorg137&A.
Ferrettiorg25&A. Festantiorg33&V.J.G. Feuillardorg103&J. Figielorg118&S.
Filchaginorg108&D. Finogeevorg62&F.M. Fiondaorg21&G. Fiorenzaorg52&F.
Flororg125&S. Foertschorg72&P. Fokaorg106&S. Fokinorg87&E. Fragiacomoorg59&U.
Frankenfeldorg106&U. Fuchsorg33&C. Furgetorg78&A. Fursorg62&M. Fusco
Girardorg29&J.J. Gaardhøjeorg88&M. Gagliardiorg25&A.M. Gagoorg111&A.
Galorg136&C.D. Galvanorg120&P. Ganotiorg83&C. Garabatosorg106&E. Garcia-
Solisorg11&K. Gargorg114&C. Gargiuloorg33&A. Garibliorg86&K. Garnerorg144&P.
Gasikorg104,org117&E.F. Gaugerorg119&M.B. Gay Ducatiorg70&M. Germainorg114&J.
Ghoshorg109&P. Ghoshorg141&S.K. Ghoshorg3&M. Giacaloneorg26&P.
Gianottiorg51&P. Giubellinoorg58,org106&P. Giubilatoorg28&P. Glässelorg103&A.
Gomez Ramirezorg74&V. Gonzalezorg106&L.H. González-Truebaorg71&S.
Gorbunovorg38&L. Görlichorg118&A. Goswamiorg48&S. Gotovacorg34&V.
Grabskiorg71&L.K. Graczykowskiorg142&K.L. Grahamorg110&L. Greinerorg79&A.
Grelliorg63&C. Grigorasorg33&V. Grigorievorg92&A. Grigoryanorg1&S.
Grigoryanorg75&O.S. Groettvikorg21&F. Grosaorg30&J.F. Grosse-
Oetringhausorg33&R. Grossoorg106&R. Guernaneorg78&M. Guittiereorg114&K.
Gulbrandsenorg88&T. Gunjiorg132&A. Guptaorg100&R. Guptaorg100&I.B.
Guzmanorg44&R. Haakeorg146&M.K. Habiborg106&C. Hadjidakisorg61&H.
Hamagakiorg81&G. Hamarorg145&M. Hamidorg6&R. Hanniganorg119&M.R.
Haqueorg63,org85&A. Harlenderovaorg106&J.W. Harrisorg146&A. Hartonorg11&J.A.
Hasenbichlerorg33&H. Hassanorg95&D. Hatzifotiadouorg10,org53&P. Hauerorg42&S.
Hayashiorg132&S.T. Heckelorg68,org104&E. Hellbärorg68&H. Helstruporg35&A.
Herghelegiuorg47&T. Hermanorg36&E.G. Hernandezorg44&G. Herrera Corralorg9&F.
Herrmannorg144&K.F. Hetlandorg35&H. Hillemannsorg33&C. Hillsorg127&B.
Hippolyteorg136&B. Hohlwegerorg104&J. Honermannorg144&D. Horakorg36&A.
Hornungorg68&S. Hornungorg106&R. Hosokawaorg15&P. Hristovorg33&C.
Huangorg61&C. Hughesorg130&P. Huhnorg68&T.J. Humanicorg96&H.
Hushnudorg109&L.A. Husovaorg144&N. Hussainorg41&S.A. Hussainorg14&D.
Hutterorg38&J.P. Iddonorg33,org127&R. Ilkaevorg108&H. Ilyasorg14&M.
Inabaorg133&G.M. Innocentiorg33&M. Ippolitovorg87&A. Isakovorg94&M.S.
Islamorg109&M. Ivanovorg106&V. Ivanovorg97&V. Izucheevorg90&B. Jacakorg79&N.
Jacazioorg33&P.M. Jacobsorg79&S. Jadlovskaorg116&J. Jadlovskyorg116&S.
Jaelaniorg63&C. Jahnkeorg121&M.J. Jakubowskaorg142&M.A. Janikorg142&T.
Jansonorg74&M. Jercicorg98&O. Jevonsorg110&M. Jinorg125&F.
Jonasorg95,org144&P.G. Jonesorg110&J. Jungorg68&M. Jungorg68&A. Juskoorg110&P.
Kalinakorg64&A. Kalweitorg33&V. Kaplinorg92&S. Karorg6&A. Karasu Uysalorg77&O.
Karavichevorg62&T. Karavichevaorg62&P. Karczmarczykorg33&E. Karpechevorg62&U.
Kebschullorg74&R. Keidelorg46&M. Keilorg33&B. Ketzerorg42&Z.
Khabanovaorg89&A.M. Khanorg6&S. Khanorg16&S.A. Khanorg141&A.
Khanzadeevorg97&Y. Kharlovorg90&A. Khatunorg16&A. Khuntiaorg118&B.
Kilengorg35&B. Kimorg60&B. Kimorg133&D. Kimorg147&D.J. Kimorg126&E.J.
Kimorg73&H. Kimorg17,org147&J. Kimorg147&J.S. Kimorg40&J. Kimorg103&J.
Kimorg147&J. Kimorg73&M. Kimorg103&S. Kimorg18&T. Kimorg147&T. Kimorg147&S.
Kirschorg38,org68&I. Kiselorg38&S. Kiselevorg91&A. Kisielorg142&J.L.
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Bösingorg144&M. Kleinerorg68&A. Klugeorg33&M.L. Knichelorg33&A.G.
Knospeorg125&C. Kobdajorg115&M.K. Köhlerorg103&T. Kolleggerorg106&A.
Kondratyevorg75&N. Kondratyevaorg92&E. Kondratyukorg90&J. Konigorg68&P.J.
Konopkaorg33&L. Koskaorg116&O. Kovalenkoorg84&V. Kovalenkoorg112&M.
Kowalskiorg118&I. Králikorg64&A. Kravčákováorg37&L. Kreisorg106&M.
Krivdaorg64,org110&F. Krizekorg94&K. Krizkova Gajdosovaorg36&M. Krügerorg68&E.
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Kuhnorg136&P.G. Kuijerorg89&L. Kumarorg99&S. Kunduorg85&P. Kurashviliorg84&A.
Kurepinorg62&A.B. Kurepinorg62&A. Kuryakinorg108&S. Kushpilorg94&J.
Kvapilorg110&M.J. Kweonorg60&J.Y. Kwonorg60&Y. Kwonorg147&S.L. La
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Nikulinorg87&V. Nikulinorg97&F. Noferiniorg10,org53&P. Nomokonovorg75&J.
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Pianoorg59&M. Piknaorg13&P. Pillotorg114&O. Pinazzaorg33,org53&L.
Pinskyorg125&C. Pintoorg27&S. Pisanoorg10,org51&D. Pistoneorg55&M.
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Rahaorg3&S. Rajputorg100&J. Rakorg126&A. Rakotozafindrabeorg137&L.
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Richertorg80,org88&M. Richterorg20&P. Riedlerorg33&W. Rieglerorg33&F.
Riggiorg27&C. Risteaorg67&S.P. Rodeorg49&M. Rodríguez Cahuantziorg44&K.
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Shabanovorg62&A. Shabetaiorg114&R. Shahoyanorg33&W. Shaikhorg109&A.
Shangaraevorg90&A. Sharmaorg99&A. Sharmaorg100&H. Sharmaorg118&M.
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Shigakiorg45&M. Shimomuraorg82&S. Shirinkinorg91&Q. Shouorg39&Y.
Sibiriakorg87&S. Siddhantaorg54&T. Siemiarczukorg84&D. Silvermyrorg80&G.
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Sitarorg13&M. Sittaorg31&T.B. Skaaliorg20&M. Slupeckiorg126&N.
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Songmoolnakorg115&F. Soramelorg28&S. Sorensenorg130&I. Sputowskaorg118&J.
Stachelorg103&I. Stanorg67&P. Stankusorg95&P.J. Steffanicorg130&E.
Stenlundorg80&D. Stoccoorg114&M.M. Storetvedtorg35&L.D. Strittoorg29&A.A.P.
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Tambaveorg21&S. Tangorg6,org134&M. Tarhiniorg114&M.G. Tarzilaorg47&A.
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Závadaorg66&N. Zaviyalovorg108&H. Zbroszczykorg142&M. Zhalovorg97&S.
Zhangorg39&X. Zhangorg6&Z. Zhangorg6&V. Zherebchevskiiorg112&D. Zhouorg6&Y.
Zhouorg88&Z. Zhouorg21&J. Zhuorg6,org106&Y. Zhuorg6&A. Zichichiorg10,org26&G.
Zinovjevorg2&N. Zurloorg140&

## Affiliation notes

org*Deceased

orgIItalian National Agency for New Technologies, Energy and Sustainable
Economic Development (ENEA), Bologna, Italy

orgIIDipartimento DET del Politecnico di Torino, Turin, Italy

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

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

orgVInstitute 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

org13Comenius University Bratislava, Faculty of Mathematics, Physics and
Informatics, Bratislava, Slovakia

org14COMSATS University Islamabad, Islamabad, Pakistan

org15Creighton University, Omaha, Nebraska, United States

org16Department of Physics, Aligarh Muslim University, Aligarh, India

org17Department of Physics, Pusan National University, Pusan, Republic of
Korea

org18Department of Physics, Sejong University, Seoul, Republic of Korea

org19Department of Physics, University of California, Berkeley, California,
United States

org20Department of Physics, University of Oslo, Oslo, Norway

org21Department of Physics and Technology, University of Bergen, Bergen,
Norway

org22Dipartimento di Fisica dell’Università ’La Sapienza’ and Sezione INFN,
Rome, Italy

org23Dipartimento di Fisica dell’Università and Sezione INFN, Cagliari, Italy

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

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

org26Dipartimento di Fisica e Astronomia dell’Università and Sezione INFN,
Bologna, Italy

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

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

org29Dipartimento di Fisica ‘E.R. Caianiello’ dell’Università and Gruppo
Collegato INFN, Salerno, Italy

org30Dipartimento DISAT del Politecnico and Sezione INFN, Turin, Italy

org31Dipartimento di Scienze e Innovazione Tecnologica dell’Università del
Piemonte Orientale and INFN Sezione di Torino, Alessandria, Italy

org32Dipartimento Interateneo di Fisica ‘M. Merlin’ and Sezione INFN, Bari,
Italy

org33European Organization for Nuclear Research (CERN), Geneva, Switzerland

org34Faculty of Electrical Engineering, Mechanical Engineering and Naval
Architecture, University of Split, Split, Croatia

org35Faculty of Engineering and Science, Western Norway University of Applied
Sciences, Bergen, Norway

org36Faculty of Nuclear Sciences and Physical Engineering, Czech Technical
University in Prague, Prague, Czech Republic

org37Faculty of Science, P.J. Šafárik University, Košice, Slovakia

org38Frankfurt Institute for Advanced Studies, Johann Wolfgang Goethe-
Universität Frankfurt, Frankfurt, Germany

org39Fudan University, Shanghai, China

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

org65Institute of Physics, Homi Bhabha National Institute, Bhubaneswar, India

org66Institute of Physics of the Czech Academy of Sciences, Prague, Czech
Republic

org67Institute of Space Science (ISS), Bucharest, Romania

org68Institut für Kernphysik, Johann Wolfgang Goethe-Universität Frankfurt,
Frankfurt, Germany

org69Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México,
Mexico City, Mexico

org70Instituto de Física, Universidade Federal do Rio Grande do Sul (UFRGS),
Porto Alegre, Brazil

org71Instituto de Física, Universidad Nacional Autónoma de México, Mexico
City, Mexico

org72iThemba LABS, National Research Foundation, Somerset West, South Africa

org73Jeonbuk National University, Jeonju, Republic of Korea

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

org91NRC «Kurchatov Institute» - ITEP, Moscow, Russia

org92NRNU Moscow Engineering Physics Institute, Moscow, Russia

org93Nuclear Physics Group, STFC Daresbury Laboratory, Daresbury, United
Kingdom

org94Nuclear Physics Institute of the Czech Academy of Sciences, Řež u Prahy,
Czech Republic

org95Oak Ridge National Laboratory, Oak Ridge, Tennessee, United States

org96Ohio State University, Columbus, Ohio, United States

org97Petersburg Nuclear Physics Institute, Gatchina, Russia

org98Physics department, Faculty of science, University of Zagreb, Zagreb,
Croatia

org99Physics Department, Panjab University, Chandigarh, India

org100Physics Department, University of Jammu, Jammu, India

org101Physics Department, University of Rajasthan, Jaipur, India

org102Physikalisches Institut, Eberhard-Karls-Universität Tübingen, Tübingen,
Germany

org103Physikalisches Institut, Ruprecht-Karls-Universität Heidelberg,
Heidelberg, Germany

org104Physik Department, Technische Universität München, Munich, Germany

org105Politecnico di Bari, Bari, Italy

org106Research Division and ExtreMe Matter Institute EMMI, GSI
Helmholtzzentrum für Schwerionenforschung GmbH, Darmstadt, Germany

org107Rudjer Bošković Institute, Zagreb, Croatia

org108Russian Federal Nuclear Center (VNIIEF), Sarov, Russia

org109Saha Institute of Nuclear Physics, Homi Bhabha National Institute,
Kolkata, India

org110School of Physics and Astronomy, University of Birmingham, Birmingham,
United Kingdom

org111Sección Física, Departamento de Ciencias, Pontificia Universidad
Católica del Perú, Lima, Peru

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 of Cape Town, Cape Town, South Africa

org125University of Houston, Houston, Texas, United States

org126University of Jyväskylä, Jyväskylä, Finland

org127University of Liverpool, Liverpool, United Kingdom

org128University of Science and Technology of China, Hefei, China

org129University of South-Eastern Norway, Tonsberg, Norway

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, Budapest, Hungary

org146Yale University, New Haven, Connecticut, United States

org147Yonsei University, Seoul, Republic of Korea