2018 025 16 Feb

Charged-particle spectra and nuclear modification factors

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

We report the measured transverse momentum ($p_{\mathrm{T}}$) spectra of
primary charged particles from pp, p–Pb and Pb–Pb collisions at a center-of-
mass energy $\sqrt{s_{\mathrm{NN}}}$ = 5.02 TeV in the kinematic range of
$0.15<p_{\mathrm{T}}<50$ GeV/$c$ and $|\eta|<0.8$. A significant improvement
of systematic uncertainties motivated the reanalysis of data in pp and Pb–Pb
collisions at $\sqrt{s_{\mathrm{NN}}}$ = 2.76 TeV, as well as in p–Pb
collisions at $\sqrt{s_{\mathrm{NN}}}$ = 5.02 TeV, which is also presented.
Spectra from Pb–Pb collisions are presented in nine centrality intervals and
are compared to a reference spectrum from pp collisions scaled by the number
of binary nucleon-nucleon collisions. For central collisions, the
$p_{\mathrm{T}}$ spectra are suppressed by more than a factor of 7 around 6–7
GeV/$c$ with a significant reduction in suppression towards higher momenta up
to 30 GeV/$c$. The nuclear modification factor $R_{\mathrm{pPb}}$, constructed
from the pp and p–Pb spectra measured at the same collision energy, is
consistent with unity above 8 GeV/$c$. While the spectra in both pp and Pb–Pb
collisions are substantially harder at $\sqrt{s_{\mathrm{NN}}}=5.02$ TeV
compared to 2.76 TeV, the nuclear modification factors show no significant
collision energy dependence. The obtained results should provide further
constraints on the parton energy loss calculations to determine the transport
properties of the hot and dense QCD matter.

##  1 Introduction

The properties of hot and dense deconfined QCD matter, the Quark-Gluon Plasma
(QGP), which is formed in high-energy heavy-ion collisions, can be
characterized by the measurement of high transverse momentum particles
produced by hadronisation of hard scattered partons in the early stage of the
collision. It is expected that these partons lose energy by interactions with
the hot and dense QCD matter, which leads to jet quenching [1]. Manifested
also as a suppression of high-$p_{\mathrm{T}}$ particles, jet quenching
enables the extraction of the properties of the deconfined medium, in
particular its transport coefficient $\hat{q}$ [2].

The modification of high-$p_{\mathrm{T}}$ particle production is quantified
with the nuclear modification factor $R_{\mathrm{AA}}$, defined as the ratio
of the charged-particle $p_{\mathrm{T}}$ spectrum in A–A collisions to that in
pp collisions scaled by the average number of binary nucleon–nucleon
collisions $\langle N_{\mathrm{coll}}\rangle$ for a given centrality class of
A–A collisions,

$R_{\mathrm{AA}}=\frac{{\rm d}N^{{\rm AA}}/{\rm d}p_{\mathrm{T}}}{\langle
N_{\mathrm{coll}}\rangle{\rm d}N^{{\rm pp}}/{\rm d}p_{\mathrm{T}}}=\frac{{\rm
d}N^{{\rm AA}}/{\rm d}p_{\mathrm{T}}}{\langle T_{\mathrm{AA}}\rangle{\rm
d}\sigma^{{\rm pp}}/{\rm d}p_{\mathrm{T}}},$ (1)

where $N^{{\rm AA}}$ and $N^{{\rm pp}}$ are the charged-particle yields in A–A
and pp collisions and $\sigma^{{\rm pp}}$ is the production cross section in
pp collisions, respectively. The average nuclear overlap function, $\langle
T_{\mathrm{AA}}\rangle=\langle N_{\mathrm{coll}}\rangle/\sigma^{\rm NN}_{\rm
inel}$, which depends on the collision centrality, is determined from the
Glauber model of the nuclear collision geometry [3], where $\sigma^{\rm
NN}_{\rm inel}$ is the total inelastic nucleon-nucleon cross section. Over the
years, a number of results on $R_{\mathrm{AA}}$ have been reported by
experiments at the Relativistic Heavy-Ion Collider (RHIC) and at the Large
Hadron Collider (LHC). At RHIC, the yields of charged hadrons [4, 5] or
neutral pions [6] measured in the central Au–Au collisions at
$\sqrt{s_{\mathrm{NN}}}=130$ and 200 GeV were found to be suppressed by a
factor of about 5 in the $p_{\mathrm{T}}$ range of 5–25 GeV/$c$, indicating
for the first time strong medium effects on hadron production. The first
$R_{\mathrm{AA}}$ measurements for charged particles at the LHC [7, 8, 9, 10]
have shown that in central Pb–Pb collisions at $\sqrt{s_{\mathrm{NN}}}=2.76$
TeV the yields are suppressed by a factor of up to 7 for $p_{\mathrm{T}}=6$–7
GeV/$c$. For larger $p_{\mathrm{T}}$, the suppression decreases, but remains
significant (a factor of about 2) in the range of 30–150 GeV/$c$.

The first Pb–Pb collisions at $\sqrt{s_{\mathrm{NN}}}=5.02$ TeV were delivered
by the LHC in 2015. Data in pp collisions at the same energy were also
collected by the LHC experiments, allowing for a direct comparison of particle
production in pp, p–Pb and Pb–Pb collisions. The first results on charged-
particle $R_{\mathrm{AA}}$ at $\sqrt{s_{\mathrm{NN}}}=5.02$ TeV have recently
become available from the CMS Collaboration [11], showing that in central
Pb–Pb collisions charged-particle production is suppressed by a factor of 7–8
for $p_{\mathrm{T}}=6$–9 GeV/$c$. The suppression continues up to the highest
$p_{\mathrm{T}}$ measured and approaches unity in the vicinity of
$p_{\mathrm{T}}$ = 200 GeV/$c$.

Measurements of p–Pb collisions at the LHC were performed to establish whether
the initial state of the colliding nuclei plays a role in the observed
suppression of high-$p_{\mathrm{T}}$ hadron production in Pb–Pb collisions.
The $R_{\mathrm{pPb}}$ was found to be consistent with unity for
$p_{\mathrm{T}}$ up to a few tens of GeV/$c$, indicating that in this domain
initial state effects do not influence particle production [12, 13, 14, 15].

In this paper, we report the measurement of transverse momentum spectra of
charged particles in pp and Pb–Pb collisions at $\sqrt{s_{\mathrm{NN}}}=5.02$
TeV. The resulting $p_{\mathrm{T}}$ spectra are used to determine the nuclear
modification factors in Pb–Pb collisions at the highest energy currently
accessible at the LHC. The $p_{\mathrm{T}}$ spectrum measured in pp collisions
at the same collision energy as p–Pb is also used as the reference to
calculate $R_{\mathrm{pPb}}$. These measurements allow us to compare the
particle production in pp, p–Pb and Pb–Pb collisions at the same
$\sqrt{s_{\mathrm{NN}}}$, for the first time with ALICE at the LHC. In
addition, we report a reanalysis of data collected in pp and Pb–Pb collisions
at $\sqrt{s_{\mathrm{NN}}}=2.76$ TeV, and in p–Pb collisions at
$\sqrt{s_{\mathrm{NN}}}=5.02$ TeV. The reanalysis is warranted by significant
improvements in track selection and efficiency corrections, which benefit from
the experience accumulated in the past years as well as better knowledge of
the particle production at the LHC energies. This leads to significantly-
reduced systematic uncertainties by a factor of about 2 as compared to
previously published results [8, 16, 13], which the current analysis
supersedes. The increase in $\sqrt{s_{\mathrm{NN}}}$ from 2.76 TeV to 5.02 TeV
for Pb–Pb collisions leads to $\sim 20\%$ increase in the particle
multiplicity [17] indicating that the larger medium density is reached at the
higher collision energy. We characterize this medium by comparing the
$p_{\mathrm{T}}$ spectra and nuclear modification factors measured at the two
energies.

##  2 Experiment and data analysis

The data in Pb–Pb and pp collisions at $\sqrt{s_{\mathrm{NN}}}$ = 2.76 TeV and
in p–Pb collisions at $\sqrt{s_{\mathrm{NN}}}$ = 5.02 TeV were collected with
the ALICE apparatus [18] in 2010, 2011 and 2013, respectively. Details on the
ALICE experimental conditions and the detector performance are given in [19].
The data in Pb–Pb and pp collisions at $\sqrt{s_{\mathrm{NN}}}$ = 5.02 TeV
were recorded in 2015.

###  2.1 Trigger and event selection

The analysis is based on tracking information from the Inner Tracking System
(ITS) [20] and the Time Projection Chamber (TPC) [21], both are located in the
central barrel of the experiment and embedded in a solenoidal magnetic field
of 0.5 T parallel to its axis.

The minimum-bias (MB) interaction trigger was based on signals from the
forward scintillator arrays (V0A and V0C) and the two innermost layers of the
ITS, the Silicon Pixel Detector (SPD), in coincidence with two beam bunches
crossing in the ALICE interaction region. The pp collisions at $\sqrt{s}$ =
2.76 TeV were selected requiring a signal in either one of the V0A or the V0C
detectors or in the SPD. The Pb–Pb collisions at $\sqrt{s_{\mathrm{NN}}}$ =
2.76 TeV were selected based on different combinations of hits in the SPD and
either V0A or V0C detector. The efficiency for hadronic interactions is
approximately 100% in the 0–80% centrality range considered in this analysis,
see details in [19]. For measurements of pp, p–Pb and Pb–Pb collisions at
$\sqrt{s_{\mathrm{NN}}}$ = 5.02 TeV the trigger required a signal in both V0A
and V0C detectors.

The offline event selection was optimized to reject beam-induced background in
all collision systems. The background events were efficiently rejected by
exploiting the timing signals in the two V0 detectors. In Pb-Pb collisions
background was also rejected exploiting the correlation between the arrival
times measured in each neutron Zero Degree Calorimeter (ZDC), positioned on
both sides of the interaction point at 114.0 m for pp and Pb–Pb data at
$\sqrt{s_{\mathrm{NN}}}$ = 2.76 TeV and at 112.5 m for the rest data sets. The
contamination from electromagnetic interactions in Pb–Pb collisions was
strongly suppressed using signals from the ZDCs (see [19] for details).

The primary event vertex is determined with tracks from the central barrel.
For the analysis of pp collisions, if no vertex is found using tracks, the
vertex reconstruction is performed using SPD tracklets; track segments
reconstructed based on the information from the two innermost layers of the
ITS. To ensure a uniform acceptance and reconstruction efficiency in the
pseudorapidity region $|\eta|<0.8$, only events with a reconstructed vertex
within $\pm$10 cm from the center of the detector along the beam direction are
used. It corresponds to around 2 standard deviations from the mean of the
interaction region distribution (Gaussian shape) determined for all collisions
systems and energies.

In Pb–Pb collisions, the centrality quantifies the fraction of the geometrical
cross-section of the colliding nuclei, and it is related to their geometrical
overlap region. It is determined using the sum of the amplitudes of the V0A
and V0C signals [22]. The analysis is limited to the 0–80% most central
events, to ensure that effects of trigger inefficiency and contamination by
electromagnetic processes [23], as well as possible biases in the selection of
more peripheral events [24], are negligible. The average quantities
characterizing a centrality class, such as the mean number of participants
$\langle N_{\mathrm{part}}\rangle$, the mean number of binary collisions
$\langle N_{\mathrm{coll}}\rangle$ or the average nuclear overlap function
$\langle T_{\mathrm{AA}}\rangle$ were obtained [22] by fitting the
experimental distributions with a Glauber Monte Carlo model [3], coupled to
the model of particle production with $f\cdot N_{\mathrm{part}}+(1-f)\cdot
N_{\mathrm{coll}}$ particle sources, each source producing particles according
to a Negative Binomial Distribution (NBD). This approach is inspired by two-
component models [25, 26], which decompose nucleus-nucleus collisions into
soft and hard interactions, where the soft interactions produce particles with
an average multiplicity proportional to $N_{\mathrm{part}}$, and the
probability for hard interactions to occur is proportional to
$N_{\mathrm{coll}}$. The fit parameter $f$ represents the contribution of soft
processes to the particle production and amounts to about $0.8$ for the two
energies. In this calculations, we used an inelastic nucleon–nucleon cross-
section $\sigma_{{\rm NN}}=(67.6\pm 0.6)$ mb for $\sqrt{s_{\mathrm{NN}}}$ =
5.02 TeV and $\sigma_{{\rm NN}}=(61.8\pm 0.9)$ mb for $\sqrt{s_{\mathrm{NN}}}$
= 2.76 TeV, obtained by interpolation [3] of the existing world data.

In p–Pb collisions, the average quantities $\langle N_{\mathrm{part}}\rangle$,
$\langle N_{\mathrm{coll}}\rangle$ and $\langle T_{\mathrm{pPb}}\rangle$ were
determined [22] following the procedure described in [27], with the updated
inelastic nucleon–nucleon cross-section $\sigma_{{\rm NN}}=(67.6\pm 0.6)$ mb
at $\sqrt{s_{\mathrm{NN}}}$ = 5.02 TeV and nuclear density function. In order
to omit potential biases on the $p_{\mathrm{T}}$ spectra related to p–Pb
collision centrality determination [27], only p–Pb events in the 0–100%
centrality interval were used in the presented analysis.

The number of events satisfying the trigger and offline selection criteria for
various collision systems and energies are listed in Table 1.

collision system |  $\sqrt{s_{\mathrm{NN}}}$ = 2.76 TeV |  $\sqrt{s_{\mathrm{NN}}}$ = 5.02 TeV
---|---|---
pp | 52 M | 109 M
p–Pb | - | 107 M
Pb–Pb (0–80%) | 13 M | 20 M
Table 1:  Number of events used in the analysis for various systems and
energies. The analysis of Pb–Pb events was performed for the 0–80% centrality
range.

###  2.2 Track selection

Primary charged particles are measured in the kinematic range $|\eta|<0.8$ and
$0.15<p_{\mathrm{T}}<50$ GeV/$c$. A primary charged particle is defined [28]
to be 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. The track-selection criteria were
identical for all data sets and were optimized for best track quality and
minimal contamination from secondary particles. Each track is required to
have:

  * •

at least 2 hits in the ITS detector, of which at least one hit is in the two
innermost (SPD) layers;

  * •

the length $L$ (in cm) of its projection curve calculated in the TPC readout
plane, excluding the information from the pads at the sector boundaries ($\sim
3$ cm from the sector edges), larger than $A-B\cdot p_{\mathrm{T}}^{C}$, with
$A=130$ cm, $B=1.0~{}{\rm cm}\cdot({\rm GeV}/c)^{-C}$, $C=-1.5$ and
$p_{\mathrm{T}}$ in units of GeV/$c$;

  * •

the number of crossed TPC pad rows larger than $0.85\cdot L$ (the height of
pad rows varies from 7.5 mm to 15 mm [21]); a TPC readout pad row is
considered crossed if there is a cluster in this row and in any of its
neighboring 2 rows;

  * •

the number of TPC clusters (one cluster per pad row) larger than $0.7\cdot L$;

  * •

the ratio of crossed TPC pad rows to the number of findable TPC clusters
(maximum number of clusters which can be assigned to a track in the TPC
fiducial volume, excluding the information from the pads at the sector
boundaries) larger than 0.8;

  * •

the fraction of TPC clusters shared with another track lower than 0.4;

  * •

the fit quality for the ITS and TPC track points satisfying $\chi_{{\rm
ITS}}^{2}/{N_{\rm hits}}<36$ and $\chi_{{\rm TPC}}^{2}/{N_{\rm clusters}}<4$,
respectively;

  * •

$\chi^{2}_{\rm TPC-ITS}<36$, where $\chi^{2}_{\rm TPC-ITS}$ is calculated
comparing the track parameters of the helix fit from the combined ITS+TPC
track reconstruction to that derived only from the TPC and constrained by the
interaction point, see details in [8];

  * •

the distance of closest approach to the primary vertex in the transverse plane
$|{\rm DCA}_{{\rm xy}}|<A+B\cdot p_{\mathrm{T}}^{C}$, with $A=0.0182$ cm,
$B=0.035~{}{\rm cm}\cdot({\rm GeV}/c)^{-C}$, $C=-1.0$ and $p_{\mathrm{T}}$ in
units of GeV/$c$; and along the beam axis $|{\rm DCA}_{{\rm z}}|<2$ cm.

###  2.3 Corrections

The data are presented as differential cross sections for inelastic (INEL) pp
collisions

$\frac{{\rm d}^{2}\sigma}{{\rm d}\eta{\rm
d}p_{\mathrm{T}}}=\sigma_{\rm{MB}}^{\rm{pp}}\cdot\frac{1}{N_{{\rm ev}}^{{\rm
MB}}}\frac{{\rm d}^{2}N}{{\rm d}\eta{\rm
d}p_{\mathrm{T}}}\equiv\sigma_{\rm{MB}}^{\rm{pp}}\cdot\frac{N^{\rm{rec}}(\Delta\eta,\Delta
p_{\mathrm{T}})\cdot C(\Delta\eta,\Delta p_{\mathrm{T}})}{N_{\rm{ev}}^{{\rm
rec}}\cdot\Delta\eta\Delta p_{\mathrm{T}}}\cdot\epsilon_{\rm{VZ}},$ (2)

and transverse momentum spectra for non-single diffractive (NSD) p–Pb and
centrality-selected INEL Pb–Pb collisions

$\frac{1}{N_{{\rm ev}}}\frac{{\rm d}^{2}N}{{\rm d}\eta{\rm
d}p_{\mathrm{T}}}\equiv\frac{N^{\rm{rec}}(\Delta\eta,\Delta
p_{\mathrm{T}})\cdot C(\Delta\eta,\Delta p_{\mathrm{T}})}{N_{\rm{ev}}^{{\rm
rec}}\cdot\Delta\eta\Delta
p_{\mathrm{T}}}\cdot\epsilon_{\rm{MB}}\cdot\epsilon_{\rm{VZ}},$ (3)

which are obtained by correcting the charged particle yields $N^{\rm{rec}}$
reconstructed in the $(\Delta\eta,\Delta p_{\mathrm{T}})$ intervals for all
detector effects that either influence the event reconstruction, and thus are
relevant only for the overall normalization (event-level corrections), or
influence the track reconstruction and are relevant for both the spectral
shape and normalization (track-level corrections). The $\epsilon_{{\rm MB}}$
and $\epsilon_{{\rm VZ}}$ denote the MB trigger and event vertex
reconstruction efficiencies, and $C(\Delta\eta,\Delta p_{\mathrm{T}})$ are
track-level correction factors. One should note that the $\epsilon_{{\rm VZ}}$
is calculated for the triggered events. In general, both the $\epsilon_{{\rm
MB}}$ and $\epsilon_{{\rm VZ}}$ are multiplicity dependent. Details of the
correction procedure and variables are described in the following.

####  2.3.1 Event-level corrections

In Eq. 2 the minimum-bias cross section $\sigma_{\rm MB}^{\rm pp}$ in
triggered pp collisions is determined by the van-der-Meer scans and depends on
the trigger settings, it was measured to be $55.4\pm 1.0$ mb at $\sqrt{s}$ =
2.76 TeV [29] and $51.2\pm 1.2$ mb at $\sqrt{s}$ = 5.02 TeV [30], with the MB
trigger OR (V0A or V0C or SPD) and AND (V0A and V0C), respectively. The
differential charged-particle yields ${\rm d}^{2}N/{\rm d}\eta{\rm
d}p_{\mathrm{T}}$ were calculated for the MB event class
$\left({N_{\rm{ev}}^{\rm{MB}}}\right)$ by normalizing to the number of
reconstructed events ${N_{\rm{ev}}^{\rm{rec}}}$, which have a reconstructed
event vertex within $\pm$10 cm from of the center of the detector and
correcting for the event vertex reconstruction efficiency
$\epsilon_{\rm{VZ}}$.

For INEL pp collisions, the $\epsilon_{\rm{VZ}}$ was estimated using the
PYTHIA 8 (Monash 2013 tune) event generator [31, 32] and GEANT3 [33] detector
response model. The resulting values $\epsilon_{\rm{VZ}}=88.3\%(97.7\%)$ at
$\sqrt{s}=2.76$ (5.02) TeV were used for corrections.

For NSD p–Pb collisions, the efficiency of the trigger ($\epsilon_{\rm MB}$)
and event vertex reconstruction ($\epsilon_{\rm VZ}$), as in Eq. 3, were
estimated using GEANT3 detector simulation with a combination of event
generators as described in [12]. The obtained values $\epsilon_{\rm
MB}=99.2\%$ and $\epsilon_{\rm VZ}=98.6\%$ were used for corrections.

For Pb–Pb collisions, the trigger and event vertex reconstruction is fully
efficient for the centrality intervals considered in this work, as estimated
using Monte Carlo simulations with GEANT3 and HIJING [34] as event generator.

Figure 1: Left: Combined tracking efficiency and acceptance as a function of
$p_{\mathrm{T}}$ for different particle species and the sum of all, obtained
in Monte Carlo simulations of pp collisions at $\sqrt{s}=5.02$ TeV with PYTHIA
8 (Monash 2013 tune). For $p_{\mathrm{T}}>1$ GeV/$c$ parameterizations are
shown. The relative systematic uncertainties on parameterizations are small
($<0.2\%$) and are not shown. The statistical uncertainties for
$p_{\mathrm{T}}<1$ GeV/$c$ are smaller than the symbol size ($<0.5\%$). Right:
The relative particle abundances as a function of $p_{\mathrm{T}}$ in Monte
Carlo (open symbols, for $\sqrt{s}=5.02$ TeV) and in data (full symbols, for
$\sqrt{s}=7$ TeV) [35, 36, 37]. The data are extrapolated beyond the range of
the measurements (see description in the text). The statistical and systematic
uncertainties (combined $<1.6\%$) are not shown.

####  2.3.2 Track-level corrections

The differential charged-particle yields ${\rm d}^{2}N/{\rm d}\eta{\rm
d}p_{\mathrm{T}}$ (Eqs 2 and 3) are obtained from the reconstructed yields of
tracks $N^{\rm{rec}}(\Delta\eta,\Delta p_{\mathrm{T}})$ corrected using
correction factors $C(\Delta\eta,\Delta p_{\mathrm{T}})$, which are products
of acceptance, efficiency, purity and $p_{\mathrm{T}}$ resolution.

The efficiency and purity of the primary charged particle reconstruction as
well as acceptance correction for the pp, p–Pb and Pb–Pb data are calculated
using Monte Carlo event generators with GEANT3 detector modeling combined with
data-driven corrections, which are discussed in detail in the following
sections.

##### Tracking efficiency

The efficiency of the primary charged particle reconstruction is shown in Fig.
1 (left). While the low efficiency at low $p_{\mathrm{T}}$ is related to the
strong track curvature caused by the magnetic field and to the energy loss in
the detector material, the characteristic shape around $p_{\mathrm{T}}$ of 1
GeV/$c$ is caused primarily by the track length requirement. Tracks in this
momentum range are more likely to cross the TPC sector boundaries and are thus
reconstructed with lower efficiencies. The asymptotic value reached at high
$p_{\mathrm{T}}$ reflects the acceptance limitations (detector boundaries and
active channels) of the measurement.

The tracking efficiency depends on particle species, as can be seen in Fig. 1
(left), and was calculated using a detector simulation with the PYTHIA 8
(Monash 2013 tune) event generator and the GEANT3 transport code. The
efficiency is particularly species-dependent at low $p_{\mathrm{T}}$ (below
0.5 GeV/$c$) due to differences in ionization energy loss in the detector
material, hadronic interaction cross-section or decay probability.

A particular case is that of charged hyperons, for which the reconstruction
efficiency is very low and essentially negligible below 10 GeV/$c$, due to the
fact that they decay before any significant interaction with the detector. For
higher $p_{\mathrm{T}}$, they reach the detector and can be observed with
increasing efficiency. One should note that the reconstruction efficiency is
different for the $\Sigma^{+}$ and $\Sigma^{-}$ hyperons in the
$p_{\mathrm{T}}$ range considered, because of their different lifetimes. The
tracking efficiency for other primary charged particle species, including
electrons, muons and $\Xi$ and $\Omega$ hyperons (denoted as ”Rest”) is also
shown.

In order to reduce statistical fluctuations at high $p_{\mathrm{T}}$, we
parameterized the efficiency above $p_{\mathrm{T}}=1$ GeV/$c$ for each
particle species. Each parameterization is a combination of the universal
(independent of particle species) function $f(p_{\mathrm{T}})=a\left(1-b\cdot
e^{-cp_{\mathrm{T}}}\right)$ and the survival probability
$P(p_{\mathrm{T}})=e^{-d\cdot m/p_{\mathrm{T}}\cdot\tau}$ that a particle with
the mass $m$ and a mean proper lifetime $\tau$ survives a minimal distance $d$
before decaying. The fitting parameters ($a$, $b$ and $c$) are determined from
the fit to the efficiency calculated as an average of efficiencies for stable
particles. The calculations were performed for $d=200$ cm, corresponding to
the minimum track length in the ITS and the TPC required in the analysis.

The parametrized efficiencies shown in Fig. 1 (left) were used to determine
data-driven correction factors in the efficiency rewieghting procedure, which
is discussed below.

Figure 2: Left: Combined tracking efficiency and acceptance as a function of
$p_{\mathrm{T}}$ for pp, p–Pb, central (0-5%) and peripheral (70–80%) Pb–Pb
collisions determined using Monte Carlo simulations and a reweighting method
(see text for details). For better visibility, the curves for p–Pb and Pb–Pb
are offset by the indicated values. The effect of the reweighting on the
efficiency corrections is shown in the bottom panel. The systematic
uncertainties of the reweighting ($<2.4\%$) are not shown. Right:
Contamination from secondary particles estimated from Monte Carlo simulations
and from the impact parameter fits in data (see text for details). The effect
of the reweighting of secondary particles is shown in the bottom panel. The
systematic uncertainties on the scaling factors ($<20\%$) are not shown.

##### Reweighting with measured particle composition

The experimental knowledge of the primary particle composition has
significantly improved recently at the LHC [35, 36, 37, 38, 39, 40, 41, 42,
43, 44], which allows for a precise determination of the tracking efficiency.
For the first time, we determined the tracking efficiency by reweighting the
primary particle composition based on data driven method.

In the right panel of Fig. 1, the relative particle abundances measured by
ALICE in pp collisions at $\sqrt{s}=7$ TeV are compared to those from Monte
Carlo simulations with the PYTHIA 8 (Monash 2013 tune) event generator for
$\sqrt{s}=5.02$ TeV. Charged pions, kaons and protons were measured from
$p_{\mathrm{T}}$ = 0.15, 0.2, and 0.3 GeV/$c$ to 20 GeV/$c$ [35, 36],
respectively. It is known that Monte Carlo event generators underestimate
hyperon production substantially [38, 39]. In particular, the
$\Sigma^{+}(1385)$ and $\Sigma^{-}(1385)$ hyperons and their antiparticles are
underestimated by a factor of 2–3 in the recent PYTHIA 8 tunes. The
$p_{\mathrm{T}}$ spectra of $\Sigma^{\pm}$ hyperons have not been measured.
Therefore, the $p_{\mathrm{T}}$ spectra of $\Sigma^{\pm}$ are approximated
using the measured spectrum of $\Lambda$ hyperons [37] scaled by the ratio of
$\Sigma^{\pm}$ to $\Lambda$ hyperons from the Monte Carlo generator.

Relative particle abundances measured in pp collisions at $\sqrt{s}=7$ TeV are
used to reweight the tracking efficiency determined for $\sqrt{s}=2.76$ and
5.02 TeV collision energies, based on the experimental knowledge that their
energy dependence is weak [37]. The relative abundance of other particle
species containing electrons, muons and $\Xi$ and $\Omega$ hyperons (denoted
“Rest” in Fig. 1) is taken from simulations without further modification and
has only a small influence on the final result ($<1\%$). The measured
$p_{\mathrm{T}}$ spectra of kaons, protons and $\Lambda$ are extrapolated down
to $p_{\mathrm{T}}=0.15$ GeV/$c$ using a parameterization proposed by Bylinkin
and Rostovtsev [45]. For high $p_{\mathrm{T}}$, beyond the reach of the
identified particle measurement, the relative abundances are assumed to be
independent of $p_{\mathrm{T}}$, as motivated by pQCD [46].

The reweighting of the efficiency has also been applied in the analysis of
p–Pb and Pb–Pb data. The relative particle abundances obtained from Monte
Carlo simulations with DPMJET (p–Pb) [47] and HIJING (Pb–Pb) event generators
are reweighted using ALICE measurements of identified particle species (pions,
kaons, protons and $\Lambda$ hyperons) for p–Pb collisions at
$\sqrt{s_{\mathrm{NN}}}$ = 5 TeV [40, 36] and Pb–Pb collisions at
$\sqrt{s_{\mathrm{NN}}}$ = 2.76 TeV [41, 42, 43, 44]. The relative particle
abundances at low $p_{\mathrm{T}}$ are determined by extrapolating the
measured $p_{\mathrm{T}}$ spectra of kaons, protons and $\Lambda$ hyperons
down to $p_{\mathrm{T}}=0.15$ GeV/$c$ using a blast-wave parameterization
[48]. As in the pp case, for $p_{\mathrm{T}}$ beyond the reach of these
measurements, the relative abundances are assumed to be independent of
$p_{\mathrm{T}}$.

In the left panel of Fig. 2 the combined tracking efficiency and acceptance
obtained from MC simulations (open symbols) and after reweighting (full
symbols) is shown as a function of $p_{\mathrm{T}}$ for pp, p–Pb, and central
(0-5%) and peripheral (70-80%) Pb–Pb collisions. The effect of the reweighting
on the efficiency corrections is shown in the bottom panel. It amounts to a
difference of about 7% at $p_{\mathrm{T}}$ around 3 GeV/c for the most central
Pb–Pb collisions, and is lower in peripheral Pb–Pb collisions, p–Pb and pp
collisions. When comparing central to peripheral Pb–Pb collisions, the
importance of an increasing radial flow that shifts the heavy $\Sigma^{\pm}$
baryons to larger momenta becomes apparent.

##### Purity

The contribution from secondary particles, i.e. products of weak decays of
kaons, $\Lambda$ hyperons and muons, and particles arising from interactions
in the detector material, was estimated using the transverse impact parameter
$d_{xy}$ distributions of particles in data and Monte Carlo simulations.
Exploiting the differences, especially in the tails, of the $d_{xy}$
distributions between primary and secondary particles, the measured
distributions were fitted by a linear combination of $d_{xy}$ distributions
(templates) for primary and secondary particles obtained from the Monte Carlo
simulations in different $p_{\mathrm{T}}$ bins (as described in more detail in
[41]). The effect of this data-driven correction, shown in the bottom panel of
Fig. 2 (right), depends on $p_{\mathrm{T}}$ and is different for pp, p–Pb and
Pb–Pb collisions. The resulting contamination with secondary particles, i.e.
the fraction of secondary particles in the sample of selected particles,
ranges from 8.5% in pp to 20% in central Pb–Pb collisions at
$p_{\mathrm{T}}=0.15$ GeV/$c$ and decreases to around 1.0% for
$p_{\mathrm{T}}>5$ GeV/$c$, as shown in the upper panel of Fig. 2 (right).

Source of Uncertainty | pp | p–Pb | Pb–Pb
---|---|---|---
| 2.76 TeV | 5.02 TeV | 5.02 TeV | 2.76 TeV | 5.02 TeV
Event selection | 0.9 | 0.5 | 0.1 | 1.5 | 0.14
Track selection | 0.4–3.8 | 0.6–3.5 | 0.6–3.8 | 1.0–2.0 | 0.6–4.9
Secondary particles | 0.5–5.1 | 0.0–2.8 | 0.0–2.1 | 0.0–4.0 | 0.0–4.5
Particle composition | 0.1–1.6 | 0.2–2.4 | 0.4–2.2 | 0.0–2.0 | 0.2–2.0
Matching efficiency | 1.0–4.0 | 0.0–1.1 | 0.3–3.2 | 0.2–2.0 | 0.2–1.2
Trigger and vertex selection | 0.0–0.5 | 0.0–1.2 | – | – | –
$p_{\mathrm{T}}$ resolution | 0.0–3.0 | 0.0–1.4 | 0.0–3.0 | 0.0–2.7 | 0.0–1.0
Interaction rate | – | 0.0 | – | – | 1.0
Material budget | 0.1–0.9 | 0.1–0.9 | 0.1–0.9 | 0.1–0.9 | 0.1–0.9
Acceptance | – | – | 0.0–0.2 | – | –
Combined Uncertainty | 3.5–6.2 | 1.3–4.3 | 1.7–5.1 | 1.9–5.2 | 1.0–7.5
Normalization | 1.9 | 2.3 | 3.1 | – | –
Centrality | – | – | – | 0.1–3.6 | 0.1–3.5
Table 2: Contributions to the relative systematic uncertainty for
$p_{\mathrm{T}}$ spectra in pp, p–Pb, and Pb–Pb collisions. The ranges
correspond to the maximal variation within the considered $p_{\mathrm{T}}$
range of 0.15–50 GeV/$c$, as well as Pb–Pb centrality intervals. The
$p_{\mathrm{T}}$-dependent contributions are assumed to be independent and are
summed in quadrature, resulting in the combined uncertainty. All values are in
%.

##### Transverse momentum resolution

The transverse momentum of charged particles is reconstructed from the track
curvature measured in the ITS and the TPC (see [19] for details). The
modification of the spectra arising from the finite momentum resolution is
estimated from the error obtained from the corresponding covariance matrix
element of the Kalman fit. The relative $p_{\mathrm{T}}$ resolution,
$\sigma(p_{\mathrm{T}})/p_{\mathrm{T}}$, depends on momentum and is
approximately 3–4% at $p_{\mathrm{T}}=0.15$ GeV/$c$, has a minimum of 1.0% at
$p_{\mathrm{T}}=1.0$ GeV/$c$, and increases linearly for larger
$p_{\mathrm{T}}$, approaching 3–10% at 50 GeV/$c$, depending on collision
energy, system or Pb–Pb centrality interval. The $p_{\mathrm{T}}$ resolution
has been verified by studying the widths of the invariant mass distributions
of $K^{{\rm 0}}_{{\rm s}}$ reconstructed from their decays to two charged
pions.

To account for the finite $p_{\mathrm{T}}$ resolution, correction factors to
the spectra were determined based on the Bayesian unfolding approach [49]
implemented in the RooUnfold package [50]. This unfolding is based on the
response matrix, ${\bf R}^{\rm det}_{\rm m,t}$, which relates the measured
spectrum ${\bf M}_{\rm m}$ and the true spectrum ${\bf T}_{\rm t}$, ${\bf
M}_{\rm m}={\bf R}^{\rm det}_{\rm m,t}\cdot{\bf T}_{\rm t}$, where $m$ and $t$
are indices indicating the bin number. The response matrix was generated for
each data set and Pb–Pb collision centrality using GEANT3 detector simulations
with different Monte-Carlo generators. For $p_{\mathrm{T}}>10$ GeV/$c$,
another unfolding procedure similar to what was done in previous work [16] was
also used.

The correction factors depend on the collision energy and system as well as on
the collision centrality, due the change of the spectral shape. For momenta
below 10 GeV/$c$, the corrections are significant only in the first momentum
bin $p_{\mathrm{T}}=0.15$–0.2 GeV/$c$, and reach 3%(2.5%) for pp(Pb–Pb) at
$\sqrt{s_{\mathrm{NN}}}=2.76$ TeV, 3% for p–Pb at
$\sqrt{s_{\mathrm{NN}}}=5.02$ TeV and around 1% for pp(Pb–Pb) at
$\sqrt{s_{\mathrm{NN}}}=5.02$ TeV. At low $p_{\mathrm{T}}$, these corrections
are independent of Pb–Pb collision centrality. For $p_{\mathrm{T}}>10$
GeV/$c$, both unfolding methods yield almost identical correction factors. For
$\sqrt{s_{\mathrm{NN}}}=5.02$ TeV, the correction factors reach 5%, 1.5% and
3% (4%) at $p_{\mathrm{T}}=50$ GeV/$c$ for pp, p–Pb and 0-5%(70–80%) central
Pb–Pb collisions, respectively. For $\sqrt{s_{\mathrm{NN}}}=2.76$ TeV, they
amount to 4% for pp and 4% (8%) for 0-5%(70–80%) central Pb–Pb collisions at
the highest $p_{\mathrm{T}}$. The resulting $p_{\mathrm{T}}$-dependent
correction factors are applied (bin-by-bin) to the measured $p_{\mathrm{T}}$
spectra.

##### Trigger and vertex selection

The event selection (trigger and vertex) introduces a small
$p_{\mathrm{T}}$-dependence in the correction on the $p_{\mathrm{T}}$ spectra
in pp collisions. This is due to the fact that the low-multiplicity pp events,
which are also characterized by a softer spectrum, are mostly rejected by the
trigger and vertex selection criteria. The effect on the $p_{\mathrm{T}}$
spectra was calculated from simulations with the PYTHIA 8 (Monash 2013 tune)
and the PYTHIA 6 (Perugia2011 tune) event generators and was estimated to be
around 0.4–0.6% (2.2–2.6%) for $p_{\mathrm{T}}<1$ GeV/$c$ at $\sqrt{s}$ = 2.76
(5.02) TeV. The spectra are corrected by the average bias of these two
generators, resulting in 0.5% (2.4%) corrections to the spectra.

##### Acceptance correction for the p–Pb data

The two-in-one magnet design of the LHC imposes the same magnetic rigidity of
the beams in the two rings. The configuration for p–Pb collisions with protons
at 4 TeV energy colliding with ${}^{208}_{82}$Pb ions at 82$\times$4 TeV
results in a shift in the rapidity of the nucleon–nucleon center-of-mass
system by $\Delta y_{\text{NN}}$ = 0.465 in the direction of the proton beam
(negative $z$-direction). Therefore the detector coverage
$|\eta_{\text{lab}}|<0.8$ corresponds to roughly $-0.3<\eta_{\text{cms}}<1.3$.
For massless or high $p_{\mathrm{T}}$ particles,
$\eta_{\text{cms}}=\eta_{\text{lab}}+y_{\text{NN}}$ but the differential yield
of non-massless particles at low $p_{\mathrm{T}}$ suffers from a distortion,
which is estimated and corrected for based on the HIJING event generator
weighted by the measured relative particle abundances [40, 36]. For
$p_{\mathrm{T}}$ = 0.5 GeV/$c$ the correction is 2% for
$-0.3<\eta_{\text{cms}}<1.3$.

###  2.4 Systematic uncertainty

The relative systematic uncertainties on the $p_{\mathrm{T}}$ spectra are
summarized in Table 2.

  * •

The effect of the selection of events based on the vertex position is studied
by comparing the fully corrected $p_{\mathrm{T}}$ spectra obtained with
alternative vertex selections corresponding to $\pm$5 and $\pm$20 cm.

  * •

The systematic uncertainties related to the track selection criteria (listed
above) were studied by varying the track quality cuts. In particular, we
varied the upper limits of the track fit quality parameters in the ITS
($\chi_{{\rm ITS}}^{2}/{N_{\rm hits}}$) and the TPC ($\chi_{{\rm
TPC}}^{2}/{N_{\rm clusters}}$) in the ranges of 25–49 and 3–5, respectively.
The systematic uncertainties related to high-$p_{\mathrm{T}}$ fake tracks [8]
were estimated by modifying the upper limits of the track matching criteria
given by the $\chi^{2}_{\rm TPC-ITS}$ in the range of 25–49. The resulting
uncertainty dominates at high $p_{\mathrm{T}}$ for all collision systems.

  * •

The systematic uncertainty on the secondary-particle contamination (Fig. 2,
right) includes contributions from the template fits to the measured impact
parameter distributions. We have varied the fit model using templates with two
(primaries, secondaries) or three (primaries, secondaries from material,
secondaries from weak decays of $K^{0}_{{\rm s}}$ and $\Lambda$) components,
as well as the fit ranges. The maximum difference between the data and the 2
component-template fit is summed in quadrature with the difference between
results obtained from the 2 and the 3 component-template fits and result is
assigned as the systematic uncertainty on the contamination. This contribution
dominates for the lowest $p_{\mathrm{T}}$ independently of the collision
system.

  * •

The systematic uncertainty on the primary particle composition consists of
several contributions, including the extrapolation of the spectra to low
$p_{\mathrm{T}}$, the approximation of the relative particle abundances at
high $p_{\mathrm{T}}$, the efficiency parameterization at high
$p_{\mathrm{T}}$, the uncertainties of the measured particle spectra and the
MC assumptions on the $\Sigma^{\pm}/\Lambda$ spectra ratios. For the
extrapolation to low $p_{\mathrm{T}}$, we have studied different
parameterizations (Bylinkin and Rostovtsev, modified Hagedorn [51], Blast-
Wave) and fit ranges. We have varied the $p_{\mathrm{T}}$ thresholds for the
approximation of the relative particle abundances as well as the efficiency
parameterization at high $p_{\mathrm{T}}$. The measured particle spectra were
varied within systematic uncertainties (one particle species at a time), and
the resulting differences to the nominal spectra were added in quadrature to
the systematic uncertainties. We have also assigned an additional uncertainty
related to the different spectral shape of $\Sigma^{\pm}$ and $\Lambda$ from
the MC generators.

  * •

To account for the imperfect description of the experimental setup in
simulations, we compared the track matching between the TPC and the ITS
information in data and Monte Carlo after scaling of the fraction of secondary
particles obtained from the fits to the $d_{xy}$ distributions. After
rescaling the fraction of secondary particles, the agreement between data and
Monte Carlo is within 4%. This value is assigned as an additional systematic
uncertainty.

  * •

The systematic uncertainty on the $p_{\mathrm{T}}$ resolution at low
$p_{\mathrm{T}}$ (only first $p_{\mathrm{T}}$ bin) was estimated by changing
Monte-Carlo generators in the unfolding procedure. The pp collisions were
simulated with PYTHIA and PHOJET, p–Pb collisions with HIJING and DPMJET, and
Pb–Pb collisions with HIJING and AMPT [52]. The average correction factor of
two generators was assigned as systematic uncertainty. At low
$p_{\mathrm{T}}$, we observe a weak dependence of correction factors on the
considered Monte-Carlo generators. The resulting uncertainties amount to
3%(2.5%) for pp(Pb–Pb) collisions at $\sqrt{s_{\mathrm{NN}}}=2.76$ TeV, to 3%
for p–Pb collisions at $\sqrt{s_{\mathrm{NN}}}=5.02$ TeV, and to 1% for pp and
Pb–Pb collisions at $\sqrt{s_{\mathrm{NN}}}=5.02$ TeV. The systematic
uncertainty on the $p_{\mathrm{T}}$ resolution at high $p_{\mathrm{T}}$ ($>10$
GeV/$c$) was estimated using the azimuthal angle dependence of the
$1/p_{\mathrm{T}}$ spectra for positively and negatively charged particles.
The relative shift of the spectra for oppositely charged particles along
$1/p_{\mathrm{T}}$ determines the size of uncertainty for a given angle. We
used the RMS of the 1/$p_{\mathrm{T}}$ shift distribution for the full azimuth
as additional smearing of the $p_{\mathrm{T}}$ resolution. We checked that
these shifts are due to detector effects (such as ${\bf E}\times{\bf B}$
effect) and are not related to the physics of hadronic interaction in GEANT3.
To take into account the decrease in the $p_{\mathrm{T}}$ resolution with
increasing interaction rate, we have studied the systematic uncertainty for
the pp and Pb–Pb data sets at $\sqrt{s_{\mathrm{NN}}}$ = 5.02 TeV, obtained
from the difference of the spectra at high and low interaction rate. The
uncertainty is negligible for pp collisions, and is about 1% for Pb–Pb
collisions.

  * •

For the correction due to the trigger and vertex selection, calculated as the
average bias of two generators, half of the value is assigned as systematic
uncertainty.

  * •

The systematic uncertainty for the acceptance correction on the p–Pb data was
estimated by varying the relative particle abundances within their measured
uncertainties and by changing the fit function for the low-$p_{\mathrm{T}}$
extrapolation. The uncertainty is sizable only at low $p_{\mathrm{T}}$ where
it reaches 0.2%.

  * •

The material budget in the simulation was varied by $\pm$4.5% [19], resulting
in the systematic uncertainty in the range of 0.1–0.9%.

  * •

The normalization uncertainty on the spectra in pp collisions was propagated
from the cross section measurements.

  * •

The systematic uncertainties related to centrality selection were estimated by
a comparison of the $p_{\mathrm{T}}$ spectra when the limits of the centrality
classes are shifted due to an uncertainty of $\pm$ 0.5% in the fraction of the
hadronic cross section used in the analysis and by a comparison of results
obtained using the SPD detector to estimate centrality as opposed to the V0A
and V0C.

For the evaluation of the total systematic uncertainty all contributions are
considered to be uncorrelated and they are summed in quadrature. The improved
reconstruction and track selection in the reanalysis of pp and Pb–Pb data at
$\sqrt{s_{\mathrm{NN}}}=2.76$ TeV and p–Pb data at
$\sqrt{s_{\mathrm{NN}}}=5.02$ TeV lead to significantly reduced systematic
uncertainties by a factor of about 2 as compared to previously published
results [8, 16, 13].

##  3 Results and discussion

###  3.1 Spectra

The fully corrected $p_{\mathrm{T}}$ spectra of primary charged particles
measured in INEL pp and Pb–Pb collisions at $\sqrt{s_{\mathrm{NN}}}=2.76$ TeV
and 5.02 TeV and in NSD p–Pb collisions at $\sqrt{s_{\mathrm{NN}}}=5.02$ are
shown in Fig. 3. The Pb–Pb spectra are presented in nine centrality classes.
For pp collisions, the $p_{\mathrm{T}}$-differential cross sections are
divided by the corresponding inelastic nucleon-nucleon cross section at
$\sqrt{s}=2.76$ (61.8 mb) and 5.02 TeV (67.6 mb) [3], respectively. The
relative systematic uncertainties for the various datasets are shown in the
bottom panels. Substantial improvements in track selection and efficiency
corrections have been achieved. However the uncertainty on the pp data at
$\sqrt{s_{\mathrm{NN}}}=2.76$ TeV is still larger than for the data at
$\sqrt{s_{\mathrm{NN}}}$ = 5.02 TeV due to larger number of inactive channels
in the SPD [19], which affects the track reconstruction and the determination
of the secondary particle contribution.

Figure 3:  Transverse momentum distributions of primary charged particles in
$|\eta|<0.8$ in nine centrality intervals in Pb–Pb collisions at
$\sqrt{s_{\mathrm{NN}}}$ = 2.76 (left) and 5.02 TeV (right) (scale factors as
indicated are used for better visibility). The data for pp collisions,
obtained scaling the cross section by $\sigma^{\rm NN}_{\rm inel}$, and NSD
p–Pb at $\sqrt{s_{\mathrm{NN}}}~{}=~{}5.02$ TeV are also shown. The relative
systematic uncertainties are shown in the lower panels for various datasets;
these do not contain the normalization uncertainty.

In Pb–Pb collisions the shape of the $p_{\mathrm{T}}$ spectrum varies strongly
with collision centrality. For peripheral collisions, the spectral shape is
similar to that measured in pp collisions as well as to the spectrum in p–Pb
collisions. With increasing collision centrality, a marked depletion of the
Pb–Pb spectra develops for $p_{\mathrm{T}}>5$ GeV/$c$. These measurements
supersede our previous results [8, 16, 13], which allows for a better
discrimination between jet quenching scenarios.

Figure 4 compares the measured $p_{\mathrm{T}}$ spectra in pp collisions with
results from PYTHIA 8 (Monash-2013 tune), including colour reconnection, and
EPOS LHC [53], which incorporates collective (flow-like) effects. These event
generators show a similar description of the $p_{\mathrm{T}}$ spectra at both
energies. They reproduce the spectral shape within 20%.

Figure 4:  Comparison of the charged-particle transverse momentum spectra
measured in pp collisions to PYTHIA 8 (Monash-2013 tune) [31, 32] and EPOS
[53] model calculations at $\sqrt{s}$ = 2.76 (top) and 5.02 TeV (bottom). The
statistical uncertainties of the data and model calculations are added in
quadrature. The boxes represent systematic uncertainties of the data.

Figure 5:  Ratio of transverse momentum spectra at $\sqrt{s_{\mathrm{NN}}}$ =
5.02 and $\sqrt{s_{\mathrm{NN}}}$ = 2.76 TeV for Pb–Pb collisions, for nine
centrality classes, and in pp collisions (repeated in each panel). The
relative normalization uncertainties due to the centrality determination are
indicated for each centrality class. For the pp spectrum, the relative
normalization uncertainty is $\pm 3\%$.

Figure 5 shows the ratios of $p_{\mathrm{T}}$ spectra measured at
$\sqrt{s_{\mathrm{NN}}}$ = 5.02 and $\sqrt{s_{\mathrm{NN}}}$ = 2.76 TeV in
Pb–Pb and pp collisions. The ratios for Pb–Pb collisions are determined in
nine centrality classes ranging from 0–5% (top-left) to the 70–80% (bottom-
right). As indicated by the ratios, the $p_{\mathrm{T}}$ spectra measured at
higher collision energy are significantly harder for both Pb–Pb and pp
collision systems. One can see that there is a similar energy dependence of
the ratio for peripheral (70–80%) Pb–Pb and in pp collisions, while towards
central Pb–Pb collisions a gradual reduction of the ratio is apparent.

Figure 6:  The transverse momentum dependence of the nuclear modification
factor measured in Pb–Pb collisions, for nine centrality classes. The new data
at $\sqrt{s_{\mathrm{NN}}}$ = 5.02 (full symbols) are compared to the
reanalyzed data at $\sqrt{s_{\mathrm{NN}}}$ = 2.76 TeV (open symbols). The
normalization uncertainties are shown as boxes around unity.

###  3.2 Nuclear modification factors

In order to quantify in-medium modification of charged-particle transverse
momentum spectrum, the nuclear modification factors are determined. Figure 6
shows the $R_{\mathrm{AA}}$ for Pb–Pb collisions measured at
$\sqrt{s_{\mathrm{NN}}}$ = 2.76 and 5.02 TeV. The nuclear modification factor
has a strong centrality dependence, and is very similar in magnitude for the
two collision energies.

Given that the $p_{\mathrm{T}}$ spectra are harder at the higher
$\sqrt{s_{\mathrm{NN}}}$ (see Fig. 5) and that the medium density increases
with $\sqrt{s_{\mathrm{NN}}}$ by $\sim 20\%$ [17], this similarity of the
$R_{\mathrm{AA}}$ may indicate a larger parton energy loss in the
hotter/denser and longer-lived deconfined medium produced at the higher
center-of-mass energy. Assuming that the initial parton $p_{\mathrm{T}}$
spectrum, parton distribution and fragmentation functions are not
significantly modified by the energy increase, and that the parton energy loss
in expanding medium is sublinear to the medium density increase, we would
expect larger energy loss at $\sqrt{s_{\mathrm{NN}}}=5.02$ TeV than at
$\sqrt{s_{\mathrm{NN}}}=2.76$ TeV, but no more than 20%.

In 0–5% central collisions the yield is suppressed by a factor of about 8
($R_{\mathrm{AA}}\approx 0.13$) at $p_{\mathrm{T}}=6$–7 GeV/$c$. Above
$p_{\mathrm{T}}=7$ GeV/$c$, there is a significant rise of the nuclear
modification factor, which reaches a value of about 0.4 for our highest
$p_{\mathrm{T}}$ bin, 30–50 GeV/$c$. In peripheral collisions (70–80%), the
suppression is 30% for intermediate momenta and approaches unity for the
highest $p_{\mathrm{T}}$ bin. The normalization uncertainties for
$R_{\mathrm{AA}}$ originate from the pp measurement and centrality
determination and were added in quadrature.

Figure 7:  Left: Nuclear modification factors measured by ALICE in central
(0–5%) and peripheral (70–80%) Pb–Pb collisions and in p–Pb collisions at
$\sqrt{s_{\mathrm{NN}}}=5.02$ TeV. Right: A comparison of the nuclear
modification factors for central (0-5%) Pb–Pb and p–Pb collisions measured by
ALICE and CMS [14, 11]. In both figures, the $p_{\mathrm{T}}$-dependent
systematic uncertainties are shown as boxes around data points. The
normalization uncertainties are shown as boxes around unity.

Figure 7 (left) shows the $R_{\mathrm{pPb}}$ factor compared to
$R_{\mathrm{AA}}$ measured in the 0–5% and 70–80% centrality classes for Pb–Pb
collisions at $\sqrt{s_{\mathrm{NN}}}=5.02$. The $R_{\mathrm{pPb}}$ factor
exhibits a maximum for the intermediate $p_{\mathrm{T}}$ range,
$2<p_{\mathrm{T}}<6$ GeV/$c$, a feature generically called the Cronin effect
[54]. A study on its dependence on the particle species [40] suggested that
protons are responsible for the observed maximum. The maximum occurs at values
of $p_{\mathrm{T}}$ (3–5 GeV/$c$) larger than the maximum of $R_{\mathrm{AA}}$
seen in the $p_{\mathrm{T}}$ range 1.5–3 GeV/$c$. The $R_{\mathrm{pPb}}$
factor is consistent with unity for $p_{\mathrm{T}}\gtrsim 8$ GeV/$c$,
demonstrating that the strong suppression observed in central Pb–Pb collisions
is not related to initial state effects but rather to the formation of hot and
dense QCD matter. The ALICE results for $R_{\mathrm{AA}}$ and
$R_{\mathrm{pPb}}$ measured at $\sqrt{s_{\mathrm{NN}}}=5.02$ TeV are compared
to measurements by CMS [14] in Fig. 7 (right). Agreement within $1.5\sigma$ is
observed for both $R_{\mathrm{AA}}$ and $R_{\mathrm{pPb}}$ taking into account
the current uncertainties.

Figure 8:  The charged-particle nuclear modification factor measured in the
0–5% most central Pb–Pb collisions at $\sqrt{s_{\mathrm{NN}}}=5.02$ TeV in
comparison to model predictions [55, 56, 57, 58] (lower panel) and [59, 60,
61, 62] (upper panel). The red boxes around data points represent
$p_{\mathrm{T}}$ dependent systematic uncertainties. The normalization
uncertainty of the data ($\pm 2.7\%$) is not part of the uncertainties of the
plotted data points.

###  3.3 Comparison with theoretical models

In Fig. 8 the measured $R_{\mathrm{AA}}$ for 0-5% central collisions at
$\sqrt{s_{\mathrm{NN}}}$ = 5.02 TeV is compared to model predictions. All
presented models are based on the pQCD factorization, where the entire effect
of energy loss is encoded in the medium-modified parton fragmentation
function. All models include radiative energy loss based on different
approaches. The model by Djordjevic et al. [57, 58] and CUJET 3.0 [60, 61]
include in addition collisional energy loss. The energy loss is calculated in
dynamically expanding medium in all models except that of Vitev et al. [55,
56], in which the medium is composed of static scattering centers. In the
following, the models are discussed in more detail.

The calculations by Vitev et al. are based on the SCETG model [55, 56], which
uses an extended soft-collinear effective theory to describe inclusive
particle production and suppression in the heavy-ion environment. This
theoretical framework provides an analytic connection between generalized
DGLAP evolution equations for the fragmentation functions in dense strongly-
interacting matter and parton energy loss for hard processes. The calculations
employ the pQCD-based hard cross section and QGP medium evolved parton-to-
hadron fragmentation functions, combined with initial-state cold nuclear
matter (CNM) effects, which include dynamical nuclear shadowing, the Cronin
effect and initial-state parton energy loss (see [56] and references therein
for details). The two upper and lower curves represent calculations for the
nuclear modification factor with variations of the coupling strength $g=1.9\pm
0.1$ between the jet and the medium, which is a free parameter in the
calculations. Djordjevic et al. [57, 58] use a dynamical energy loss formalism
based on pQCD calculations in a finite size dynamical QCD medium. While the
initial $p_{\mathrm{T}}$ spectrum is the same as that used in the SCETG model,
the dynamical description of the medium provides a consistent treatment of
both radiative and collisional energy loss, including a finite magnetic
screening mass, which modifies the gluon self energy and therefore changes the
energy loss, as well as a running coupling constant for the strongly-
interacting medium. The two curves correspond to different electric-to-
magnetic screening mass ratios in the range $0.4<\mu_{{\rm M}}/\mu_{{\rm
E}}<0.6$. The model of Bianchi et al. [59] uses the pQCD factorization scheme
with a pQCD-based radiative energy loss in a hydrodynamically expanding
medium. In this framework, high $p_{\mathrm{T}}$ hadrons arise from
fragmentation of hard partons, which lose energy prior to hadronization via
interactions with the medium. The amount of energy loss is regulated by the
medium transport coefficient $\hat{q}$, which varies with the temperature-
dependent entropy density of the medium as well as with the energy scale of
jets propagating in the medium. The CUJET 3.0 model [60, 61] is an extension
of the perturbative-QCD-based CUJET 2.0 model, with the two complementary non-
perturbative features of the QCD cross-over phase transition: the suppression
of quark and gluon degrees of freedom and the emergence of chromomagnetic
monopoles. The calculations were performed varying the value of the QCD
running coupling $\alpha_{{\rm c}}$ from 0.95 to 1.33 for $Q<T_{{\rm C}}$, and
the ratio of electric to magnetic screening scales $c_{{\rm m}}=g_{\rm
s}\mu_{{\rm E}}/\mu_{M}$ ($c_{{\rm m}}=0,0.3,0.4$), where $g_{\rm s}$ is the
strong coupling constant. The value of $\alpha_{\rm c}$ was fixed for each
$c_{{\rm m}}$ value by fitting a single reference datum,
$R_{\mathrm{AA}}(p_{\mathrm{T}}=12~{}{\rm GeV}/c)\approx 0.3$, for charged
hadrons in 20–30% central Pb–Pb collisions at the LHC. The calculations by
Andrés et al. [62] use the jet quenching formalism of quenching weights. This
approach consists of fitting a $K$ factor, defined as
$K\equiv\hat{q}/2\epsilon^{3/4}$, that quantifies departure of this parameter
from the perturbative estimate, $\hat{q}_{\rm ideal}\sim 2\epsilon^{3/4}$
[63], where the local energy density $\epsilon$ is taken from a hydrodynamical
model of the medium. The $K$ factor is the only free parameter in the fit of
nuclear modification factors. Without including new data at
$\sqrt{s_{\mathrm{NN}}}=5.02$ TeV in the fit procedure, they predict a $\sim
15\%$ larger suppression at $\sqrt{s_{\mathrm{NN}}}=5.02$ TeV as compared to
$\sqrt{s_{\mathrm{NN}}}=2.76$ TeV, assuming the same value of K as the one
obtained from the fit to the data at the lower energy.

All models presented here describe the main features of the data. The models
by Vitev et al., Djordjevic et al. and CUJET 3.0 give quantitatively good
description of the data. The model by Bianchi et al. is consistent with data
within $1.5\sigma$ while that by Andrés et al. underestimates the data at high
$p_{\mathrm{T}}$. However, one should note that this comparison is made
between unbinned theory calculations and binned data in relatively large
$p_{\mathrm{T}}$ bins, which might introduce additional uncertainty.

##  4 Summary

In summary, we measured the primary charged particle $p_{\mathrm{T}}$ spectra
in pp and Pb–Pb collisions at $\sqrt{s_{\mathrm{NN}}}=5.02$ TeV. We also
reanalyzed the data collected in pp and Pb–Pb collisions at
$\sqrt{s_{\mathrm{NN}}}=2.76$ TeV as well as in p–Pb collisions at
$\sqrt{s_{\mathrm{NN}}}=5.02$ TeV with the revised techniques. Thanks to an
improved reconstruction, track selection and data-driven efficiency correction
procedure we were able to reduce the systematic uncertainties by a factor of
$\sim 2$ as compared to previously published ALICE results. The measured
spectra were used to determine the nuclear modification factors
$R_{\mathrm{pPb}}$ and $R_{\mathrm{AA}}$. The nuclear modification factor in
p–Pb collisions is consistent with unity at high $p_{\mathrm{T}}$, showing
that the strong suppression observed in Pb–Pb is not due to CNM effects but
rather due to final state partonic energy loss in the hot and dense QGP
created in Pb–Pb collisions. This suppression is weak in peripheral collisions
and increases with centrality reaching a value of $R_{\mathrm{AA}}=0.13$ at
$p_{\mathrm{T}}$ = 6–7 GeV, indicating an increasing parton energy loss with
centrality. This suppression is found to be similar at
$\sqrt{s_{\mathrm{NN}}}=2.76$ and 5.02 TeV, despite the much harder
$p_{\mathrm{T}}$ spectrum at the top energy, which may indicate a stronger
parton energy loss and a larger energy density of the medium at the higher
energy. All models presented here describe the main features of the data with
Vitev et al., Djordjevic et al. and CUJET 3.0 being compatible with data
within uncertainties. However, further precision in the theoretical
calculations is needed to extract the transport properties of the hot and
dense deconfined QCD matter.

## 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 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;
Ministry of Science, Education and Sport and Croatian Science Foundation,
Croatia; 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) and Institut National de Physique Nucléaire et de Physique des
Particules (IN2P3) and Centre National de la Recherche Scientifique (CNRS),
France; Bundesministerium für Bildung, Wissenschaft, Forschung und Technologie
(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 Romanian National Agency for Science, Technology and Innovation,
Romania; Joint Institute for Nuclear Research (JINR), Ministry of Education
and Science of the Russian Federation and National Research Centre Kurchatov
Institute, Russia; Ministry of Education, Science, Research and Sport of the
Slovak Republic, Slovakia; National Research Foundation of South Africa, South
Africa; Centro de Aplicaciones Tecnológicas y Desarrollo Nuclear (CEADEN),
Cubaenergía, Cuba and Centro de Investigaciones Energéticas, Medioambientales
y Tecnológicas (CIEMAT), Spain; 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.

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##  Appendix A The ALICE Collaboration

S. Acharyaorg139&F.T.-. Acostaorg22&D. Adamováorg94&J. Adolfssonorg81&M.M.
Aggarwalorg98&G. Aglieri Rinellaorg36&M. Agnelloorg33&N. Agrawalorg48&Z.
Ahammedorg139&S.U. Ahnorg77&S. Aiolaorg144&A. Akindinovorg64&M. Al-
Turanyorg104&S.N. Alamorg139&D.S.D. Albuquerqueorg120&D. Aleksandrovorg88&B.
Alessandroorg58&R. Alfaro Molinaorg72&Y. Aliorg16&A. Aliciorg11,org53,org29&A.
Alkinorg3&J. Almeorg24&T. Altorg69&L. Altenkamperorg24&I. Altsybeevorg138&C.
Andreiorg47&D. Andreouorg36&H.A. Andrewsorg108&A. Andronicorg104&M.
Angelettiorg36&V. Anguelovorg102&C. Ansonorg17&T. Antičićorg105&F.
Antinoriorg56&P. Antonioliorg53&N. Apadulaorg80&L. Aphecetcheorg112&H.
Appelshäuserorg69&S. Arcelliorg29&R. Arnaldiorg58&O.W.
Arnoldorg103,org115&I.C. Arseneorg23&M. Arslandokorg102&B. Audurierorg112&A.
Augustinusorg36&R. Averbeckorg104&M.D. Azmiorg18&A. Badalàorg55&Y.W.
Baekorg60,org76&S. Bagnascoorg58&R. Bailhacheorg69&R. Balaorg99&A.
Baldisseriorg135&M. Ballorg43&R.C. Baralorg86&A.M. Barbanoorg28&R.
Barberaorg30&F. Barileorg52&L. Barioglioorg28&G.G. Barnaföldiorg143&L.S.
Barnbyorg93&V. Barretorg132&P. Bartaliniorg7&K. Barthorg36&E. Bartschorg69&N.
Bastidorg132&S. Basuorg141&G. Batigneorg112&B. Batyunyaorg75&P.C.
Batzingorg23&J.L. Bazo Albaorg109&I.G. Beardenorg89&H. Beckorg102&C.
Beddaorg63&N.K. Beheraorg60&I. Belikovorg134&F. Belliniorg29,org36&H. Bello
Martinezorg2&R. Bellwiedorg124&L.G.E. Beltranorg118&V. Belyaevorg92&G.
Bencediorg143&S. Beoleorg28&A. Bercuciorg47&Y. Berdnikovorg96&D.
Berenyiorg143&R.A. Bertensorg128&D. Berzanoorg36,org58&L. Betevorg36&P.P.
Bhaduriorg139&A. Bhasinorg99&I.R. Bhatorg99&B. Bhattacharjeeorg42&J.
Bhomorg116&A. Bianchiorg28&L. Bianchiorg124&N. Bianchiorg51&J. Bielčíkorg38&J.
Bielčíkováorg94&A. Bilandzicorg103,org115&G. Biroorg143&R. Biswasorg4&S.
Biswasorg4&J.T. Blairorg117&D. Blauorg88&C. Blumeorg69&G. Bocaorg136&F.
Bockorg36&A. Bogdanovorg92&L. Boldizsárorg143&M. Bombaraorg39&G.
Bonomiorg137&M. Bonoraorg36&H. Borelorg135&A. Borissovorg20&M. Borriorg126&E.
Bottaorg28&C. Bourjauorg89&L. Bratrudorg69&P. Braun-Munzingerorg104&M.
Bregantorg119&T.A. Brokerorg69&M. Brozorg38&E.J. Bruckenorg44&E.
Brunaorg58&G.E. Brunoorg36,org35&D. Budnikovorg106&H. Bueschingorg69&S.
Bufalinoorg33&P. Buhlerorg111&P. Buncicorg36&O. Buschorg131&Z.
Butheleziorg73&J.B. Buttorg16&J.T. Buxtonorg19&J. Cabalaorg114&D.
Caffarriorg36,org90&H. Cainesorg144&A. Calivaorg104&E. Calvo Villarorg109&R.S.
Camachoorg2&P. Cameriniorg27&A.A. Caponorg111&F. Carenaorg36&W. Carenaorg36&F.
Carnesecchiorg11,org29&J. Castillo Castellanosorg135&A.J. Castroorg128&E.A.R.
Casulaorg54&C. Ceballos Sanchezorg9&S. Chandraorg139&B. Changorg125&W.
Changorg7&S. Chapelandorg36&M. Chartierorg126&S. Chattopadhyayorg139&S.
Chattopadhyayorg107&A. Chauvinorg115,org103&C. Cheshkovorg133&B.
Cheynisorg133&V. Chibante Barrosoorg36&D.D. Chinellatoorg120&S. Choorg60&P.
Chochulaorg36&S. Choudhuryorg139&T. Chowdhuryorg132&P. Christakoglouorg90&C.H.
Christensenorg89&P. Christiansenorg81&T. Chujoorg131&S.U. Chungorg20&C.
Cicaloorg54&L. Cifarelliorg11,org29&F. Cindoloorg53&J. Cleymansorg123&F.
Colamariaorg52,org35&D. Colellaorg36,org52,org65&A. Colluorg80&M.
Colocciorg29&M. Concasorg58orgI&G. Conesa Balbastreorg79&Z. Conesa del
Valleorg61&J.G. Contrerasorg38&T.M. Cormierorg95&Y. Corrales Moralesorg58&I.
Cortés Maldonadoorg2&P. Corteseorg34&M.R. Cosentinoorg121&F. Costaorg36&S.
Costanzaorg136&J. Crkovskáorg61&P. Crochetorg132&E. Cuautleorg70&L.
Cunqueiroorg95,org142&T. Dahmsorg115,org103&A. Daineseorg56&M.C.
Danischorg102&A. Danuorg68&D. Dasorg107&I. Dasorg107&S. Dasorg4&A.
Dashorg86&S. Dashorg48&S. Deorg49&A. De Caroorg32&G. de Cataldoorg52&C. de
Contiorg119&J. de Cuvelandorg40&A. De Falcoorg26&D. De Gruttolaorg32,org11&N.
De Marcoorg58&S. De Pasqualeorg32&R.D. De Souzaorg120&H.F. Degenhardtorg119&A.
Deistingorg104,org102&A. Delofforg85&S. Delsantoorg28&C. Deplanoorg90&P.
Dhankherorg48&D. Di Bariorg35&A. Di Mauroorg36&B. Di Ruzzaorg56&R.A.
Diazorg9&T. Dietelorg123&P. Dillensegerorg69&Y. Dingorg7&R. Diviàorg36&Ø.
Djuvslandorg24&A. Dobrinorg36&D. Domenicis Gimenezorg119&B. Dönigusorg69&O.
Dordicorg23&L.V.R. Doremalenorg63&A.K. Dubeyorg139&A. Dublaorg104&L.
Ducrouxorg133&S. Dudiorg98&A.K. Duggalorg98&M. Dukhishyamorg86&P.
Dupieuxorg132&R.J. Ehlersorg144&D. Eliaorg52&E. Endressorg109&H. Engelorg74&E.
Eppleorg144&B. Erazmusorg112&F. Erhardtorg97&M.R. Ersdalorg24&B.
Espagnonorg61&G. Eulisseorg36&J. Eumorg20&D. Evansorg108&S. Evdokimovorg91&L.
Fabbiettiorg103,org115&M. Fagginorg31&J. Faivreorg79&A. Fantoniorg51&M.
Faselorg95&L. Feldkamporg142&A. Felicielloorg58&G. Feofilovorg138&A. Fernández
Téllezorg2&A. Ferrettiorg28&A. Festantiorg31,org36&V.J.G.
Feuillardorg135,org132&J. Figielorg116&M.A.S. Figueredoorg119&S.
Filchaginorg106&D. Finogeevorg62&F.M. Fiondaorg24,org26&M. Florisorg36&S.
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Francesconorg36&A. Franciscoorg112&U. Frankenfeldorg104&G.G. Fronzeorg28&U.
Fuchsorg36&C. Furgetorg79&A. Fursorg62&M. Fusco Girardorg32&J.J.
Gaardhøjeorg89&M. Gagliardiorg28&A.M. Gagoorg109&K. Gajdosovaorg89&M.
Gallioorg28&C.D. Galvanorg118&P. Ganotiorg84&C. Garabatosorg104&E. Garcia-
Solisorg12&K. Gargorg30&C. Gargiuloorg36&P. Gasikorg115,org103&E.F.
Gaugerorg117&M.B. Gay Ducatiorg71&M. Germainorg112&J. Ghoshorg107&P.
Ghoshorg139&S.K. Ghoshorg4&P. Gianottiorg51&P. Giubellinoorg104,org58&P.
Giubilatoorg31&P. Glässelorg102&D.M. Goméz Coralorg72&A. Gomez Ramirezorg74&V.
Gonzalezorg104&P. González-Zamoraorg2&S. Gorbunovorg40&L. Görlichorg116&S.
Gotovacorg127&V. Grabskiorg72&L.K. Graczykowskiorg140&K.L. Grahamorg108&L.
Greinerorg80&A. Grelliorg63&C. Grigorasorg36&V. Grigorievorg92&A.
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Hadjidakisorg61&H. Hamagakiorg82&G. Hamarorg143&J.C. Hamonorg134&M.R.
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Herrmannorg142&K.F. Hetlandorg37&T.E. Hildenorg44&H. Hillemannsorg36&C.
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Hussainorg18&D. Hutterorg40&D.S. Hwangorg21&J.P. Iddonorg126&S.A. Iga
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Islamorg107&M. Ivanovorg104&V. Ivanovorg96&V. Izucheevorg91&B. Jacakorg80&N.
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Karorg7,org139&A. Karasu Uysalorg78&O. Karavichevorg62&T. Karavichevaorg62&L.
Karayanorg104,org102&P. Karczmarczykorg36&E. Karpechevorg62&U.
Kebschullorg74&R. Keidelorg46&D.L.D. Keijdenerorg63&M. Keilorg36&B.
Ketzerorg43&Z. Khabanovaorg90&S. Khanorg18&S.A. Khanorg139&A.
Khanzadeevorg96&Y. Kharlovorg91&A. Khatunorg18&A. Khuntiaorg49&M.M.
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Lindenstruthorg40&S.W. Lindsayorg126&C. Lippmannorg104&M.A. Lisaorg19&V.
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Pinskyorg124&S. Pisanoorg51&D.B. Piyarathnaorg124&M. Płoskońorg80&M.
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Podesta-Lermaorg118&M.G. Poghosyanorg95&B. Polichtchoukorg91&N. Poljakorg97&W.
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## 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

org2Benemérita Universidad Autónoma de Puebla, Puebla, Mexico

org3Bogolyubov Institute for Theoretical Physics, National Academy of Sciences
of Ukraine, Kiev, Ukraine

org4Bose Institute, Department of Physics and Centre for Astroparticle Physics
and Space Science (CAPSS), Kolkata, India

org5Budker Institute for Nuclear Physics, Novosibirsk, Russia

org6California Polytechnic State University, San Luis Obispo, California,
United States

org7Central China Normal University, Wuhan, China

org8Centre de Calcul de l’IN2P3, Villeurbanne, Lyon, France

org9Centro de Aplicaciones Tecnológicas y Desarrollo Nuclear (CEADEN), Havana,
Cuba

org10Centro de Investigación y de Estudios Avanzados (CINVESTAV), Mexico City
and Mérida, Mexico

org11Centro Fermi - Museo Storico della Fisica e Centro Studi e Ricerche
“Enrico Fermi’, Rome, Italy

org12Chicago State University, Chicago, Illinois, United States

org13China Institute of Atomic Energy, Beijing, China

org14Chonbuk National University, Jeonju, Republic of Korea

org15Comenius University Bratislava, Faculty of Mathematics, Physics and
Informatics, Bratislava, Slovakia

org16COMSATS Institute of Information Technology (CIIT), Islamabad, Pakistan

org17Creighton University, Omaha, Nebraska, United States

org18Department of Physics, Aligarh Muslim University, Aligarh, India

org19Department of Physics, Ohio State University, Columbus, Ohio, United
States

org20Department of Physics, Pusan National University, Pusan, Republic of
Korea

org21Department of Physics, Sejong University, Seoul, Republic of Korea

org22Department of Physics, University of California, Berkeley, California,
United States

org23Department of Physics, University of Oslo, Oslo, Norway

org24Department of Physics and Technology, University of Bergen, Bergen,
Norway

org25Dipartimento di Fisica dell’Università ’La Sapienza’ and Sezione INFN,
Rome, Italy

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

org27Dipartimento di Fisica dell’Università and Sezione INFN, Trieste, Italy

org28Dipartimento di Fisica dell’Università and Sezione INFN, Turin, Italy

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

org30Dipartimento di Fisica e Astronomia dell’Università and Sezione INFN,
Catania, Italy

org31Dipartimento di Fisica e Astronomia dell’Università and Sezione INFN,
Padova, Italy

org32Dipartimento di Fisica ‘E.R. Caianiello’ dell’Università and Gruppo
Collegato INFN, Salerno, Italy

org33Dipartimento DISAT del Politecnico and Sezione INFN, Turin, Italy

org34Dipartimento di Scienze e Innovazione Tecnologica dell’Università del
Piemonte Orientale and INFN Sezione di Torino, Alessandria, Italy

org35Dipartimento Interateneo di Fisica ‘M. Merlin’ and Sezione INFN, Bari,
Italy

org36European Organization for Nuclear Research (CERN), Geneva, Switzerland

org37Faculty of Engineering and Science, Western Norway University of Applied
Sciences, Bergen, Norway

org38Faculty of Nuclear Sciences and Physical Engineering, Czech Technical
University in Prague, Prague, Czech Republic

org39Faculty of Science, P.J. Šafárik University, Košice, Slovakia

org40Frankfurt Institute for Advanced Studies, Johann Wolfgang Goethe-
Universität Frankfurt, Frankfurt, Germany

org41Gangneung-Wonju National University, Gangneung, Republic of Korea

org42Gauhati University, Department of Physics, Guwahati, India

org43Helmholtz-Institut für Strahlen- und Kernphysik, Rheinische Friedrich-
Wilhelms-Universität Bonn, Bonn, Germany

org44Helsinki Institute of Physics (HIP), Helsinki, Finland

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, 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

org76Konkuk University, Seoul, Republic of Korea

org77Korea Institute of Science and Technology Information, Daejeon, Republic
of Korea

org78KTO Karatay University, Konya, Turkey

org79Laboratoire de Physique Subatomique et de Cosmologie, Université
Grenoble-Alpes, CNRS-IN2P3, Grenoble, France

org80Lawrence Berkeley National Laboratory, Berkeley, California, United
States

org81Lund University Department of Physics, Division of Particle Physics,
Lund, Sweden

org82Nagasaki Institute of Applied Science, Nagasaki, Japan

org83Nara Women’s University (NWU), Nara, Japan

org84National and Kapodistrian University of Athens, School of Science,
Department of Physics , Athens, Greece

org85National Centre for Nuclear Research, Warsaw, Poland

org86National Institute of Science Education and Research, HBNI, Jatni, India

org87National Nuclear Research Center, Baku, Azerbaijan

org88National Research Centre Kurchatov Institute, Moscow, Russia

org89Niels Bohr Institute, University of Copenhagen, Copenhagen, Denmark

org90Nikhef, National institute for subatomic physics, Amsterdam, Netherlands

org91NRC ¿Kurchatov Institute¿ ¿ IHEP , Protvino, 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

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

org104Research Division and ExtreMe Matter Institute EMMI, GSI
Helmholtzzentrum für Schwerionenforschung GmbH, Darmstadt, Germany

org105Rudjer Bošković Institute, Zagreb, Croatia

org106Russian Federal Nuclear Center (VNIIEF), Sarov, Russia

org107Saha Institute of Nuclear Physics, Kolkata, India

org108School of Physics and Astronomy, University of Birmingham, Birmingham,
United Kingdom

org109Sección Física, Departamento de Ciencias, Pontificia Universidad
Católica del Perú, Lima, Peru

org110Shanghai Institute of Applied Physics, Shanghai, China

org111Stefan Meyer Institut für Subatomare Physik (SMI), Vienna, Austria

org112SUBATECH, IMT Atlantique, Université de Nantes, CNRS-IN2P3, Nantes,
France

org113Suranaree University of Technology, Nakhon Ratchasima, Thailand

org114Technical University of Košice, Košice, Slovakia

org115Technische Universität München, Excellence Cluster ’Universe’, Munich,
Germany

org116The Henryk Niewodniczanski Institute of Nuclear Physics, Polish Academy
of Sciences, Cracow, Poland

org117The University of Texas at Austin, Austin, Texas, United States

org118Universidad Autónoma de Sinaloa, Culiacán, Mexico

org119Universidade de São Paulo (USP), São Paulo, Brazil

org120Universidade Estadual de Campinas (UNICAMP), Campinas, Brazil

org121Universidade Federal do ABC, Santo Andre, Brazil

org122University College of Southeast Norway, Tonsberg, Norway

org123University of Cape Town, Cape Town, South Africa

org124University of Houston, Houston, Texas, United States

org125University of Jyväskylä, Jyväskylä, Finland

org126University of Liverpool, Liverpool, United Kingdom

org127University of Split, Faculty of Electrical Engineering, Mechanical
Engineering and Naval Architecture, Split, Croatia

org128University of Tennessee, Knoxville, Tennessee, United States

org129University of the Witwatersrand, Johannesburg, South Africa

org130University of Tokyo, Tokyo, Japan

org131University of Tsukuba, Tsukuba, Japan

org132Université Clermont Auvergne, CNRS/IN2P3, LPC, Clermont-Ferrand, France

org133Université de Lyon, Université Lyon 1, CNRS/IN2P3, IPN-Lyon,
Villeurbanne, Lyon, France

org134Université de Strasbourg, CNRS, IPHC UMR 7178, F-67000 Strasbourg,
France, Strasbourg, France

org135 Université Paris-Saclay Centre d¿Études de Saclay (CEA), IRFU,
Department de Physique Nucléaire (DPhN), Saclay, France

org136Università degli Studi di Pavia, Pavia, Italy

org137Università di Brescia, Brescia, Italy

org138V. Fock Institute for Physics, St. Petersburg State University, St.
Petersburg, Russia

org139Variable Energy Cyclotron Centre, Kolkata, India

org140Warsaw University of Technology, Warsaw, Poland

org141Wayne State University, Detroit, Michigan, United States

org142Westfälische Wilhelms-Universität Münster, Institut für Kernphysik,
Münster, Germany

org143Wigner Research Centre for Physics, Hungarian Academy of Sciences,
Budapest, Hungary

org144Yale University, New Haven, Connecticut, United States

org145Yonsei University, Seoul, Republic of Korea