2015 140 11 June

Centrality dependence of pion freeze-out radii in Pb–Pb collisions

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

We report on the measurement of freeze-out radii for pairs of identical-charge
pions measured in Pb–Pb collisions at $\sqrt{s_{\mathrm{NN}}}$=2.76 TeV as a
function of collision centrality and the average transverse momentum of the
pair $k_{\rm T}$. Three-dimensional sizes of the system (femtoscopic radii),
as well as direction-averaged one-dimensional radii are extracted. The radii
decrease with $k_{\rm T}$, following a power-law behavior. This is
qualitatively consistent with expectations from a collectively expanding
system, produced in hydrodynamic calculations. The radii also scale linearly
with $\left<\mathrm{d}N_{\rm ch}/\mathrm{d}\eta\right>^{1/3}$. This behaviour
is compared to world data on femtoscopic radii in heavy-ion collisions. While
the dependence is qualitatively similar to results at smaller
$\sqrt{s_{\mathrm{NN}}}$, a decrease in the $R_{\rm out}/R_{\rm side}$ ratio
is seen, which is in qualitative agreement with a specific prediction from
hydrodynamic models: a change from inside-out to outside-in freezeout
configuration. The results provide further evidence for the production of a
collective, strongly coupled system in heavy-ion collisions at the LHC.

##  1 Introduction

Collisions of lead ions at $\sqrt{s_{\mathrm{NN}}}$=2.76 TeV have been
recorded by A Large Ion Collider Experiment (ALICE) at the Large Hadron
Collider (LHC) at CERN. In this energy regime, Quantum Chromodynamics (QCD)
predicts the existence of a new state of strongly interacting matter, the
quark-gluon plasma (QGP) in which quarks and gluons are no longer confined to
individual nucleons. Experimental evidence for the existence of such matter
has been found both at the Relativistic Heavy-Ion Collider (RHIC) [1, 2, 3, 4]
as well as at the LHC [5, 6, 7, 8, 9, 10]. The QGP behaves like a fluid with
small viscosity and undergoes an explosive expansion. The study of the space-
time structure and dynamics of this process may reveal important information
about the matter properties, such as its equation of state and the nature of
the phase transition between deconfined and ordinary hadronic matter [11, 12].

Two-pion correlations at low relative momentum were first shown to be
sensitive to the interaction volume of the emitting source in $\bar{{\rm
p}}+{\rm p}$ collisions by G. Goldhaber et al. 50 years ago [13]. Since then,
they were studied in ${\rm e}^{+}+{\rm e}^{-}$ [14], hadron- and lepton-hadron
[15], and heavy-ion [16, 17, 18, 19, 20, 21, 22, 23, 24, 25] collisions.
Especially in the heavy-ion case, two-particle femtoscopy has been developed
into a precision tool to probe the dynamically-generated spatial structure of
the emitting system. In particular, a sharp phase transition between the
color-deconfined and confined states was excluded by the observation of short
timescales. Moreover, femtoscopic measurement, together with other
observations related to bulk collective flow, provide evidence that a strongly
interacting system was created in the collision [26, 27, 12].

Femtoscopy in heavy-ion collisions is understood in some detail; for example
see the experimental overview in [20] and model calculations in [28, 27, 29,
30]. The dependence of the system size extracted from the data is investigated
as a function of collision centrality and average transverse momentum of the
pair $k_{\rm T}=|\vec{p}_{1,\rm T}+\vec{p}_{2,\rm T}|/2$. As the initial size
of the system grows with increasing multiplicity (decreasing centrality), so
does the apparent system size at freeze-out, measured by femtoscopy. Such
increase is naturally produced in a hydrodynamic calculation. Strong
hydrodynamic collective flow in the longitudinal and transverse directions
results in the decrease of the apparent size of the system with increasing
$k_{\rm T}$. This is because longitudinal and transverse velocity boosts cause
particles emitted from spatially separated parts of the collision region to
move away from one another. Such particles cannot have a small momentum
difference, and so correlation functions of boosted particles are sensitive to
only part of the collision region. This part is referred to as the
”homogeneity length” [31]. The decrease of the size with $k_{\mathrm{T}}$ is
observed in experimental data from heavy-ion collisions at all centralities,
various collision energies and colliding system types, and is well described
quantitatively in hydrodynamic models [11, 30] and qualitatively in hadronic
rescattering codes [32].

Taking into account the successful description of the femtoscopic scales at
lower energies, the hydrodynamic modelling has been extrapolated to collision
energies of the LHC [33, 34, 30, 35]. The expected increase in initial energy
density (temperature) leads to larger evolution times, which in turn produce
larger overall system size and stronger transverse and longitudinal flows. At
the same time the freeze-out hypersurface evolves to have significant positive
space-time correlation. This influences the radii of the system in the plane
perpendicular to the beam axis. In particular the radius along the pair
transverse momentum (called $R_{\rm out}$) is decreased by the correlation
with respect to the other transverse radius (called $R_{\rm side}$), which
decreases the $R_{\rm out}/R_{\rm side}$ ratio All of those effects have been
observed in the first measurement for central (0–5%) collisions at the LHC
[36]. This work extends this measurement to other centralities and compares
the obtained radii to recent hydrodynamic calculations, in order to check
their validity in a large range of event multiplicities. A measurement of one-
dimensional radii was also performed using the two-pion and three-pion
cumulants [37]. This work extends the two-pion measurement to several ranges
of pair transverse momentum.

The paper is organized as follows. In Section 2 the data taking conditions and
data treatment is described. In Section 3 we give the details of the analysis
of the correlation function. In Section 4 the extracted radii are presented
and compared to model expectations, while Section 5 summarizes our findings.

##  2 Data taking and track reconstruction

This work reports on the analysis of Pb–Pb collisions produced by the LHC
during the 2010 datataking period. They were recorded by the ALICE experiment;
the detailed description of the detector and the performance of all of its
subsystems is given in [38, 39]. Here we only briefly describe the specific
detectors used in this analysis. The ALICE Time Projection Chamber (TPC) [40]
is a large volume gaseous ionization chamber detector, which was used both for
tracking at mid-rapidity as well as for particle identification via the
measurement of the specific ionization energy loss associated with each track.
In addition to the TPC, the information from the ALICE Inner Tracker System
(ITS) was used. The ITS consists of six cylindrical layers, two Silicon Pixel
Detectors closest to the beam pipe, two Silicon Drift Detector layers in the
middle, and two Silicon Strip Detectors on the outside. The information from
ITS was used for tracking and primary particle selection, as well as for
triggering. However the main triggering detector was the V0. It is a small
angle detector consisting of two arrays of 32 scintillating counters. The
first (V0A) is located 330 cm away from the vertex and covers $2.8<\eta<5.1$,
the second (V0C) is fixed at the front of the hadronic absorber of the muon
arm and covers $-3.7<\eta<-1.7$. The tracking detectors are located inside the
solenoidal ALICE magnet, which provides a uniform magnetic field of $0.5$ T
along the beam direction. The T0 detector [41] was a main luminometer in the
heavy-ion run. It consists of two arrays of 12 Cherenkov counters, covering
$-3.28<\eta-2.97$ and $4.61<\eta<4.92$. It has a time resolution of 40 ps.

The minimum-bias trigger required a signal in both V0 detectors, which was
consistent with the collision occurring at the center of the ALICE apparatus.
A total sample of approximately four million Pb–Pb events was used for this
analysis. For the centrality range considered in this work the trigger
efficiency was 100%. The centrality was determined by analyzing the signal
from the V0 detector with the procedure described in details in [5]. This
ensured that the centrality determination was obtained using particles at
significantly different rapidities than the ones used for the pion correlation
analysis. This work presents results for seven centrality ranges: 0–5%, 5–10%,
10–20%, 20–30%, 30–40%, 40–50%, and 50–60% of the total hadronic cross
section. The position $V_{z}$ of the event vertex in the beam direction with
respect to the center of the ALICE apparatus was determined for each event. In
order to ensure uniform pseudorapidity acceptance, only events with
$|V_{z}|<8$ cm were used in the analysis.

For each event, a list of tracks identified as primary pions was created,
separately for positive and negative particles. Each track was required to
leave a signal both in the TPC and the ITS and the two parts of the track had
to match. The TPC is divided by the central electrode into two halves, each of
them is composed of 18 sectors (covering the full azimuthal angle) with 159
padrows placed radially in each sector. A track signal in the TPC consists of
space points (clusters), each of which is reconstructed in one of the padrows.
A track was required to be composed out of at least 80 such clusters. The
parameters of the track are determined by performing a Kalman fit to a set of
clusters. The quality of the fit is judged by the value of $\chi^{2}$, which
was required to be better than 4 per cluster (each cluster has two d.o.f.).
The transverse momentum of each track was determined from its curvature in the
uniform magnetic field. Two opposite field polarities were used through the
data-taking period, for a check of systematic tracking effects. The momentum
from this fit in the TPC was used in the analysis. Tracks which had a kink in
the trajectory in the TPC were rejected. Trajectories closer than $3.2$ cm in
the longitudinal direction and $2.4$ cm in the transverse direction to the
primary vertex were selected to reduce the number of secondaries. The
kinematic range for accepted particles was $(0.14,2.0)$ GeV/$c$ in transverse
momentum and $(-0.8,0.8)$ in pseudorapidity. Based on the specific ionization
energy loss in the TPC gas $\mathrm{d}E/\mathrm{d}x$, a probability for each
track to be a pion, kaon, proton, and electron was determined after comparing
with the corresponding Bethe-Bloch curve. Particles for which the pion
probability was the largest were used in this analysis. This resulted in an
overall purity above 95%, with small contamination from electrons in the
region where the $\mathrm{d}E/\mathrm{d}x$ curves for the two particle types
intersect.

The accepted particles from each event are combined into same-charge pairs.
The two-particle detector acceptance effects must be taken into account in
this procedure. Two main effects are present: track splitting and track
merging. Track splitting occurs when a single trajectory is mistakenly
reconstructed as two tracks. The tracking algorithm has been specifically
designed to suppress such cases. In a rare event when splitting happens, two
tracks are reconstructed mostly from the same clusters in the TPC. Therefore,
pairs which share more than 5% of clusters are removed from the sample.
Together with the anti-merging cut described below this eliminates the
influence of the split pairs.

Two-particle correlated efficiency and separation power is affected by track
merging. In the TPC, two tracks cannot be distinguished if their trajectories
stay close to each other through a significant part of the TPC volume.
Although this happens rarely, such pairs by definition have low relative
momentum and therefore their absence distorts the correlation function in the
signal region. The effect of track merging has been studied in central
collisions in the previous work [36]. In this work we have used a similar
procedure to correct for the merging effects, through dedicated two-particle
selection criteria. More details are given in Sec. 3.3.

##  3 Correlation function analysis

The two-particle distribution for same-event pion pairs depends on several
factors, including trivial single-particle acceptance effects. To extract only
the relevant two-particle correlation effects, the correlation function
formalism, described below, is applied.

###  3.1 Correlation function construction

The femtoscopic correlation function $C$ is constructed experimentally as

$C(\vec{q})=\frac{A(\vec{q})}{B(\vec{q})},$ (1)

where $\vec{q}=\vec{p_{1}}-\vec{p_{2}}$ is the pair relative momentum (due to
fixed masses of the particles only three components are independent). The
magnitude of this vector is referred to as $q_{\rm inv}$. For a detailed
description of the formalism, see e.g. [42]. The signal distribution $A$ is
composed of pairs of particles where both come from the same event. The
background distribution $B$ is constructed with the “mixing” method, in which
the two particles come from different events, which must have similar
characteristics, so that their single-particle efficiency and distribution are
as close as possible. To form a “mixed” pair, particles must come from two
events, for which the centralities differ by no more than 2.5% and vertex
positions differ by no more than $4$ cm. The correlation function is
normalized with the ratio of the number of pairs in the $B$ and $A$ samples in
the full $q$ range used ($0-0.25$ GeV/$c$), so that $C$ at unity means no
correlation. The dependence on pair momentum sum is investigated by doing the
analysis for various ranges of $k_{\rm T}$, namely: 0.2–0.3, 0.3–0.4, 0.4–0.5,
0.5–0.6, 0.6–0.7, 0.7–0.8, and 0.8–1.0 GeV/$c$. The ranges were the same for
each centrality range, which overall resulted in 49 independent correlation
functions per pair charge combination.

Figure 1: Projections of the Cartesian representation of the three-dimensional
two-pion correlation functions along the $out$ (a), $side$ (b) and $long$ (c)
axes. The centrality and pair momentum ranges for the three functions are
given on the plot. In each case the other components are projected over $\pm$
20 MeV/$c$ around 0 in the other $q$ directions for central collisions at low
$k_{\mathrm{T}}$ and $\pm$ 33 MeV/$c$ in the other two cases. Lines represent
the corresponding projections of the fit to the experimental correlation
functions with formula from Eq. (3.2).

The momentum difference $\vec{q}$ is calculated in the Longitudinally Co-
Moving System (LCMS), in which the pair total longitudinal momentum vanishes:
$p_{1,L}+p_{2,L}=0$. The three coordinates of $\vec{q}$ in LCMS are defined as
follows: $long$ \- along the beam axis, $out$ \- along the pair transverse
momentum, and $side$ \- perpendicular to the other two. In Fig. 1 the
projections of three example correlation functions along these axes are shown.
A significant, approximately Gaussian enhancement at low relative momentum is
seen in all projections. The width of the correlation grows with increasing
centrality (lowering multiplicity) as well as with increasing $k_{\rm T}$.

The pair distributions for identical particles have specific symmetries, which
are naturally represented in a spherical harmonic (SH) decomposition [43, 44].
In particular for identical particles all odd-$l$ and odd-$m$ components of a
correlation function representation vanish. The gross features of the
correlation function which are relevant for femtoscopy are fully captured by
the low-$l$ components of the decomposition. The $l=0,m=0$ component is
sensitive to the overall size of the pion source. The $l=2,m=0$ component is
sensitive to the difference between longitudinal and transverse size, and the
$l=2,m=2$ component reflects the difference between sideward and outward
component of the transverse radius. Therefore, those three components of the
SH representation contain the same information as the Cartesian one for the
purpose of the femtoscopic analysis. In particular both representations allow
for fitting of the correlation function with the same theoretical formula. The
next non-vanishing components are for $l=4$. Their analysis is beyond the
scope of this paper, which focuses on the overall width (variance) of the
distribution in three directions.

Figure 2: First three non-vanishing components of the SH representation of the
two-pion correlation functions, $l=0,m=0$ in (a), $l=2,m=0$ in (b) and
$l=2,m=2$ in (c). The centrality and pair momentum ranges for the three
functions are given on the plot. The lines show the corresponding SH
components of the fit with formula from Eq. (3.2).

In Fig. 2 we show the first three non-vanishing components of the spherical
harmonics representation of three example correlation functions, the same as
in Fig. 1. In the $(0,0)$ component the enhancement at low-$q$ is clearly
visible and its width is increasing with centrality and $k_{\rm T}$. In this
representation the low-$q$ dip coming from Coulomb repulsion is visible better
than in the Cartesian one. For large $k_{\rm T}$, there is a lack of low-$q$
pairs, as a result of track merging (see below). Nevertheless, the correlation
clearly extends well beyond the region with low statistics. The other two
components: $(2,0)$ and $(2,2)$, show a non-trivial correlation structure
deviating from zero, indicating that the shape is not spherical, but rather
ellipsoidal in LCMS. The width of these structures is consistent with the
width of the correlation enhancement in the $(0,0)$ component, which means
that all three reflect the properties of the femtoscopic signal. The analysis
of the shape of these structures is the main focus of the next section.

If the available statistics is limited, as is sometimes the case for lower
collision energies or particles heavier than pions, the analysis is performed
only as a function of magnitude of relative momentum $q_{\rm inv}$, most
naturally calculated in the Pair Rest Frame (PRF). In this work we present
results in this variable for completeness. Data was analyzed in the same
centrality and pair $k_{\mathrm{T}}$ ranges as the ones used in the three-
dimensional analysis.

###  3.2 Fitting the correlation function

The space-time characteristics of the source are reflected in the correlation
function. They are connected via the Koonin-Pratt equation

$C(\vec{q})=\int S({\mathbb{r}},\vec{q})|\Psi(\vec{q},\mathbb{r})|^{2}d^{4}r,$
(2)

where $\mathbb{r}$ is the pair space-time separation four-vector. $S$ is the
source emission function, interpreted as a probability to emit a pair of
particles with a given relative momentum and space-time separation. $\Psi$ is
the two-particle interaction kernel. In the simplest case of non-interacting
particles (e.g. photons) it is the modulus of the pair wave-function. If the
Coulomb or strong interaction between the particles (called Final State
Interaction - FSI) needs to be taken into account, then $\Psi$ becomes the
Bethe-Salpeter amplitude corresponding to the solution of the relevant quantum
scattering problem, taken with the inverse time direction [45].

Previous studies at RHIC [16, 17, 18, 46, 47, 22, 23] and at the LHC [36] have
approximated the source by a Gaussian, treating any difference between the
real data and a Gaussian as a correction. This procedure was also universally
used in all past pion femtoscopic analyses of heavy-ion collisions. Therefore,
we also use it here by writing

$S(\mathbb{r},\vec{q})\approx\exp\left(-\frac{r^{2}_{\rm out}}{4R^{2}_{\rm
out}}-\frac{r^{2}_{\rm side}}{4R^{2}_{\rm side}}-\frac{r^{2}_{\rm
long}}{4R^{2}_{\rm long}}\right)$ (3)

where $r_{\rm out}$, $r_{\rm side}$, and $r_{\rm long}$ are components of the
relative separation $\mathbf{r}$. This static form of $S$ is expressed in
LCMS, with $R_{\rm out}$, $R_{\rm side}$, and $R_{\rm long}$ being the single-
particle source sizes of the system later referred to as “femtoscopic radii”,
or simply “radii”. They quantify the lengths of homogeneity of the system in
the $outwards$, $sidewards$, and $longitudinal$ direction, respectively.

For like-sign pions the strong interaction contribution is small for the
source sizes expected here (a few fm) [42], so it is neglected. The remaining
$\Psi$ is a convolution of the Coulomb interaction and wave-function
symmetrization. As an approximation, the Coulomb part is factorized out and
integrated separately in the procedure known as the Bowler-Sinyukov fitting
[48, 49]. It is well tested and is applicable for pions and for large source
sizes expected in this analysis. In this approximation the integration of Eq.
(2) with $S$ given by Eq. (3) gives the following fit form for the correlation
function

$\displaystyle C(\vec{q})$ $\displaystyle=$ $\displaystyle N(1-\lambda)$
$\displaystyle+$ $\displaystyle N\lambda K_{\mathrm{C}}(q_{\rm
inv})\left[1+\exp\left(-R_{\rm out}^{2}q_{\rm out}^{2}-R_{\rm side}^{2}q_{\rm
side}^{2}-R_{\rm long}^{2}q_{\rm long}^{2}\right)\right],$

where N is the overall normalization factor. The function
$K_{\mathrm{C}}(q_{\rm inv})$ is the Coulomb part of the two-pion wave-
function integrated over the spherical Gaussian source with a given radius.
For each correlation function it is set to the value from the one-dimensional
analysis (see Section 4.3), to reflect the decrease of the source size with
multiplicity and $k_{\rm T}$. Its variation is a source of systematic
uncertainty. The dilution parameter $\lambda$ is introduced to account for the
fact that not all measured pion pairs are correlated, and that the real
emission function may deviate from a Gaussian form.

The fit is performed with the log-likelihood method for the three dimensional
correlation function in Cartesian representation, resulting usually in several
thousand degrees of freedom. Examples are shown in Fig. 1. The Gaussian fit is
able to reproduce the overall width of the correlation in all cases. Some
details of the behavior at low-$q$ may not be perfectly described, which can
be attributed to the limitations of the Bowler-Sinyukov formula as well as to
the non-Gaussian, long-range tails which may be present in the source. Some
deviations from the Gaussian ellipsoid shape for the higher centrality can
also be seen for the $long$ direction. We leave the detailed investigation of
these effects for future work. Nevertheless, the overall sizes $R$ of the
system, which are mostly sensitive to the width of the correlation are well
estimated. The deviation of the correlation function from the pure Gaussian
shape is smaller than a similar deviation in pp collisions [50].

An equivalent fit is also performed for the SH representation of the
correlation. Eq. (3.2) is numerically integrated on a $\varphi-\theta$ sphere
for each $q_{\rm LCMS}$ bin, with proper $Y_{l}^{m}$ weights, to produce the 3
components of the SH decomposition. Statistical uncertainties on each
component are taken into account, as well as the covariance matrix between
components. Examples are shown in Fig. 2. The fit describes the general
direction-averaged width of the correlation function, shown in the upper
panel. Small deviations can be seen in the shape and the behavior of the fit
at small $q$, as discussed earlier for the Cartesian fit. The deviations from
zero in the $(2,0)$ and $(2,2)$ components are small but statistically
significant for a large number of multiplicity/$k_{\mathrm{T}}$ ranges,
indicating that the source size is slightly different in all three directions.

For the one-dimensional correlation functions constructed as a function of
$q_{\rm inv}$, the fit was performed with a simplified version of Eq. (3.2)

$\displaystyle C(\vec{q})$ $\displaystyle=$ $\displaystyle(1-\lambda)$
$\displaystyle+$ $\displaystyle\lambda K_{C}\left[1+\exp(-R_{\rm
inv}^{2}q_{\rm inv}^{2})\right]$

where the only radius parameter is $R_{\rm inv}$ – the one-dimensional
direction-averaged femtoscopic radius in the PRF.

###  3.3 Systematic uncertainties of the radii

Uncertainty source |  ${\it R}_{\rm out}$ [%] |  ${\it R}_{\rm side}$ [%] |  ${\it R}_{\rm long}$ [%]
---|---|---|---
CF representation | 0.5–5 | 0.5–4 | 0.5–8
Dataset comparison | $<1.5$ | $<1.5$ | $<2$
Fit-range dependence | 0.5–4 | 0.5–3 | 1–5
Two-track cut variation | 3–10 | 2–12 | 2–13
Coulomb correction | 3 | 1 | 1
Momentum resolution correction | 2 | 2 | 2
Centrality estimation | 1 | 1 | 1
Total | 6–14 | 4–13 | 4–17
Table 1: List of contributions to the systematic uncertainty of the extracted
femtoscopic radii (ranges given).

Table 1 lists the systematic uncertainty contributions. The range of values is
given to provide a general estimate of the importance of each contribution,
however the systematic uncertainty is estimated for each point individually.
Separate analyses were performed for positive and negative pions, as well as
for two datasets collected with opposite polarities of the magnetic field
inside ALICE. This results in four independent data samples for which certain
systematic effects, most notably the single-track inefficiencies, are
different. Correlation functions for all four samples for all centrality and
pair momentum ranges are statistically consistent, after all corrections are
applied; this is an important systematic cross-check of the methodology. In
the following discussion the central values are statistical averages of the
fit values obtained for the four samples. The systematic uncertainty arising
from differences among the data sample is between 1 and 2% for all radii. The
other systematic uncertainties are analyzed for each sample separately; their
final value is the convolution of the uncertainties for each sample.

Two correlation function representations are used in this work: the Cartesian
and spherical harmonics. They are mathematically equivalent, the fitting
procedure used the same functional form for both. However the implementation
of the fitting procedure is quite different: log-likelihood vs. regular
$\chi^{2}$ fit, three-dimensional Cartesian histogram vs. three one-
dimensional histograms, fitting range as three-dimensional cube in $q_{\rm
out},q_{\rm side},q_{\rm long}$ or a three-dimensional sphere with constant
$q_{\rm LCMS}$ radius among others. Therefore, the fits to the two
representations differ systematically upon variation of the fitting procedure
(fit ranges, Bowler-Sinyukov approximation, etc.). The difference between the
values for the two fits is taken as a part of the systematic uncertainty. It
usually ranges from 1% to 3% and grows with pair $k_{\mathrm{T}}$ and
multiplicity.

Variation of single particle cuts around the default value results in
modifications of single particle acceptances and purities. However the
correlation function shape should be to the first order insensitive to those
effects. We have checked that for a reasonable variation of the single
particle cuts, the resulting radii are consistent within statistical
uncertainties.

The measurement of the average event multiplicity for a given centrality range
has a known uncertainty of 3–4% for all centrality classes [5]. The
femtoscopic radii in heavy-ion collsions were observed to scale linearly with
$\left<\mathrm{d}N_{\rm ch}/\mathrm{d}\eta\right>^{1/3}$at lower collision
energies [20]. Such trend is also predicted by hydrodynamical models and is
expected to hold at LHC. Therefore the systematic uncertainty coming from the
multiplicity estimation is about 1%.

The dominant systematic effect on the two-particle correlation function is the
two-track correlated efficiency. This effect has been studied in previous work
[36] for central collisions. The effect of “splitting” is fully removed with
the help of dedicated two-track selection criteria, mentioned in Sec. 2, and
does not influence the radii. However when two particles’ trajectories are
located close to each other in the volume of the TPC detector, they may be
reconstructed as one track or not be reconstructed at all. This effect, called
“merging” in the following, results in a loss of reconstruction efficiency for
such pairs of tracks. Pairs of primary pion trajectories close in space
correspond to low relative momentum, therefore “merging” will affect the pion
correlation function exactly in the femtoscopic signal region. The two-track
efficiency was studied in Monte-Carlo simulation of the ALICE detector. For
pion pairs at low relative momentum an efficiency loss of up to 20% was
observed. A two-track selection was chosen, such that the resulting
correlation function was not affected by the inefficiency. “Merging” affects
only pairs which are spatially close in the detector. The “closeness” can be
quantified by the pseudorapidity difference $\Delta\eta$ for the pair and only
pairs with $|\Delta\eta|<0.016$ are affected. The trajectories must also be
close in the transverse plane, where they are curved by the magnetic field.
The azimuthal coordinate $\varphi^{*}$ of tracks at a radius of $1.2$ m from
the collision point (so roughly in the center of the TPC volume) is
calculated. Pairs with $\sqrt{\Delta\eta^{2}+\Delta{\varphi^{*}}^{2}}<0.045$
are affected by merging. Pairs which simultaneously satisfy this and the
previous angular criteria are removed both from the signal and the background
sample. The correlation function calculated for pairs surviving this cut is
then not affected by “merging”. As a systematic check a different procedure to
calculate $\varphi^{*}$ was used, where the value was taken not at a fixed
radius, but instead at a radius inside the TPC (i.e. between $0.5$ and $2.4$
m) where $\varphi^{*}$ was the smallest. The differences between radii for the
correlation functions calculated with the two methods is taken as systematic
uncertainty. It is from 2–13%.

A pair of same charge pions traversing a solenoidal field can have two
configurations: a “sailor” where the two trajectories bend away from one
another and never cross, or a “cowboy” where the trajectories bend toward each
other and can cross [18]. Merging affects the “cowboy” pairs, but only weakly
influences the “sailors”. The two configurations correspond to different phase
space regions in the Cartesian representation of the correlation function. We
have performed two fits to the correlations (corrected for merging),
restricting the fitting range to either the “cowboy” or the “sailor” region.
The consistency of the radii obtained in these fits was used as an estimator
of the effectiveness of the cut for removing merged tracks. A less restrictive
cut degraded agreement between the “cowboy” and “sailor” radii, while making
the cut stricter did not improve the agreement but reduced statistics in the
signal region. The comparison allowed optimization of the cut, and provided
another estimate of the systematic uncertainty on the two-track correction
procedures. The uncertainty estimated in this way is consistent with the
uncertainty determined by varying the $\varphi^{*}$ definition. This
uncertainty is largest for transverse radii, is most prominent for high
multiplicity events (central collisions), and affects a wider region in $q$
for pairs with higher $k_{\rm T}$.

The separation into the “cowboy” and “sailor” phase-space regions is not
feasible for the SH representation of the correlation function. In this case,
when the anti-merging cut is not properly applied, one observes significant
non-femtoscopic signals, especially in the $C_{2}^{2}$ component of the
correlation function and a reliable fit cannot be performed. Therefore, the
$C_{2}^{2}$ component serves as a sensitive independent check of the
effectiveness of the “anti-merging” cut. This is a good illustration on how
the two representations complement each other in the systematic studies.

The fit was performed for several values of the fitting range in $q$ (varying
with multiplicity and pair $k_{\rm T}$, following the changes in the
correlation function width). The variation of the fitted radii with the change
of the range was taken as another component of the uncertainty, which is less
than 5% for all the radii.

In addition to the uncertainties listed above, other systematic effects can
influence the extracted radii. The first is the momentum resolution, which was
studied in [36]. The correction procedure described there is used in this
work, as well. The uncertainty on the radii from this correction is 2%.
Another effect is the influence of the Bowler-Sinyukov procedure on the
extracted radii and $\lambda$ parameter (fraction of correlated pairs). The
procedure results in an uncertainty of 3% on $R_{\rm out}$, 1% on the other
radii, and lowers the $\lambda$ value by up to 5% [28].

All the systematic uncertainty components mentioned above are added in
quadrature, the range of values of the total systematic uncertainty is given
in Table 1.

The one-dimensional analysis is performed in PRF, where the total momentum of
the pair vanishes. In the transformation from LCMS to PRF $R_{\rm out}$ is
scaled by the $\gamma$ factor for the pair, depending on $k_{\mathrm{T}}$ and
as a consequence is larger than the other two components. In such case the
direction-averaged one-dimensional correlation function becomes non-Gaussian.
This produces a dependence of the fit value on the range of the fit, resulting
in a systematic uncertainty of up to 10%. Other components of the uncertainty,
such as field orientation dependence, momentum resolution and Coulomb
correction dependence are comparable to those from the three-dimensional fit.

##  4 Results

###  4.1 Three-dimensional radii

Figure 3: Femtoscopic radii as a function of pair transverse momentum
$k_{\mathrm{T}}$ for seven centrality ranges. $R_{\rm out}$ is shown in (a),
$R_{\rm side}$ in (b), $R_{\rm long}$ in (c) and $R_{\rm out}/R_{\rm side}$ in
(d). The points for centralities 5–10%, 10–20%, 30–40% and 40–50% have been
slightly shifted in the x direction for visibility. Statistical uncertainties
are shown as black lines (usually smaller than symbol size), systematic
uncertainties are shown as colored caps.

The outcome of the fitting procedure are 49 sets of femtoscopic radii, one set
for each centrality and $k_{\mathrm{T}}$ range. They are shown in panels a)–c)
of Fig. 3. The radii in all directions are in the range of 2 to 8.5 fm. The
radii universally decrease with increasing $k_{\rm T}$, in qualitative
agreement with a decreasing homogeneity length, as predicted by hydrodynamics.
Such behavior is a strong indication of a large degree of collectivity in the
created system. The radii are also universally higher for more central
collisions, which correspond to growing final-state event multiplicity. For
the lowest $k_{\rm T}$, $R_{\rm long}$ is generally the largest, whereas at
large $k_{\mathrm{T}}$ there is no universal ordering of the radii.

In the most central collisions the values of the $\lambda$ parameters are
around 0.33 for the lowest $k_{\mathrm{T}}$ range, are increasing linearly to
0.43 for $k_{\mathrm{T}}$ of $0.65$ GeV/$c$, and falling to 0.36 in the last
$k_{\mathrm{T}}$ range. For peripheral collisions, they are higher by 0.05 to
0.07. The lowering of $\lambda$ from a theoretical maximum of 1.0 can be
attributed to a number of factors. The pion sample contains daughters of long-
lived strongly decaying resonances; their fraction falls with growing
$p_{\mathrm{T}}$. As a result the source function contains non-Gaussian tails
extending to large relative separation. There may be additional factors
influencing the shape of the correlation function, coming from the source
dynamics. The exact source shape usually deviates from a Gaussian, in a way
that lowers the $\lambda$ parameter of the Gaussian fit significantly. The
detailed study of this shape requires a dedicated methodology and is beyond
the scope of this work. In addition, at the largest $k_{\mathrm{T}}$ the
electron and pion $\mathrm{d}E/\mathrm{d}x$ become comparable in the TPC, and
the pion sample is contaminated by electrons, which also lowers $\lambda$. The
approximate treatment of the Coulomb interaction in the Bowler-Sinyukov
fitting procedure lowers it by 5–10% [28]. This effects is most pronounced for
large source sizes (central collisions). Finally, possible coherent emission
of pions [51] is expected to lower $\lambda$ by a few percent. The $\lambda$
parameter values given here are for reference only and their physics
interpretation is not discussed.

In panel (d) of Fig. 3 the $R_{\rm out}/R_{\rm side}$ ratio is shown. Its
systematic uncertainty is determined independently from those of $R_{\rm out}$
and $R_{\rm side}$, to account for the fact that they may be correlated. The
ratio is consistent with unity for central collisions. Its value slowly
decreases for more peripheral collisions, and reaches 0.85 for peripheral
collisions and high $k_{\rm T}$. Based on hydrodynamic models, the $R_{\rm
out}/R_{\rm side}$ ratio has been proposed as a sensitive probe of the shape
and space-time correlation present at the freeze-out hypersurface [33, 52]. In
particular this ratio at the LHC was predicted to be lower than a value of
$1.1$ measured at top RHIC collision energies.

Figure 4: The radii plotted as a function of $\left<\mathrm{d}N_{\rm
ch}/\mathrm{d}\eta\right>^{1/3}$ for seven $k_{\mathrm{T}}$ ranges. $R_{\rm
out}$ is plotted in (a), $R_{\rm side}$ in (b), and $R_{\rm long}$ in (c). The
dashed lines represent linear fits to each set of points for a given component
and $k_{\mathrm{T}}$ range. Points for some $k_{\mathrm{T}}$ ranges have been
slightly shifted in the $x$ direction for visibility. Statistical
uncertainties are shown as black lines (usually smaller than symbol size),
systematic uncertainties are shown as colored caps.

###  4.2 Scaling of the radii

It has been argued in [20] that the femtoscopic volume scales with the final-
state event multiplicity, and that each of the three-dimensional radii
separately scales with this value taken to the power $1/3$. In Fig. 4 we
present the dependence of the radii on multiplicity for Pb–Pb collisions. The
scaling is evident for all datasets, for all three directions and all analyzed
pair momentum ranges.

Figure 5: The slope parameters of the linear fits shown in Fig. 4, as a
function of pair $m_{\mathrm{T}}$. Lines represent the power-law fits (see
text for details). Errorbars represent the uncertainty of the parameter of the
fits, in which the combined systematic and statistical uncertainties on the
radii ware taken into account.

Similarily, hydrodynamics predicts approximate scaling of the radii with pair
transverse mass $m_{\rm T}=\sqrt{k_{\rm T}^{2}+m_{\pi}^{2}}$ [35]. The slope
parameters of the lines shown in Fig. 4 are plotted in Fig. 5, as a function
of $m_{\mathrm{T}}$. They are fitted with a power law function of the form

$a(m_{\rm T})=\beta\left(\frac{m_{\rm T}}{m_{\pi}}\right)^{\alpha}$ (6)

where $\beta$ and $\alpha$ are free parameters. The slope parameters follow
the power law scaling within the current systematic uncertainties, the value
of the $\alpha$ parameter is $-0.65\pm 0.12$ for $long$, $-0.46\pm 0.13$ for
$out$, and $-0.52\pm 0.11$ for $side$ direction. The dependence of the values
of femtoscopic radii on centrality and $k_{\mathrm{T}}$ factorizes into a
linear dependence on $\left<\mathrm{d}N_{\rm ch}/\mathrm{d}\eta\right>^{1/3}$
and a power law dependence on $m_{\mathrm{T}}$.

###  4.3 One-dimensional analysis

Figure 6: One-dimensional femtoscopic radius $R_{\rm inv}$ as a function of
pair transverse momentum $k_{\mathrm{T}}$ for seven centrality ranges. Points
for 5–10%, 20–30%, and 40–50% centrality have been slightly shifted in the $x$
direction for visibility. Statistical uncertainty is shown as black lines,
systematic uncertainty is shown as colored caps. Figure 7: Comparison of
femtoscopic radii, as a function of measured charged particle multiplicity,
for a number of collision systems and collision energies [53, 18, 46]. Dashed
lines show linear fits done to heavy-ion data, excluding ALICE (dotted lines
show one sigma contour). Various experiments use differing $k_{\mathrm{T}}$
ranges, values shown on the plot are for the range for which the average
$k_{\mathrm{T}}$ is closest to the selected value of $0.4$ GeV/$c$; in case of
ALICE an average of two neighbouring ranges of $k_{\mathrm{T}}$ is shown.
Systematic uncertainties are shown where available.

The results of the one-dimensional fits with Eq. (3.2) are shown in Fig. 6.
Similarly to the three-dimensional case, the radius is increasing with event
multiplicity (decreasing centrality). Therefore, the final state shape is
reflecting the growth of the initial shape with decreasing centrality. The
$R_{\rm inv}$ is also decreasing with pair transverse momentum. This is
usually understood as a manifestation of the hydrodynamic collectivity. The
one-dimensional radius also serves as a comparison basis with the femtoscopic
analysis for heavier particles, where the one-dimensional analysis is standard
and the three-dimensional analysis is challenged by the more complicated
description of the pair interaction as well as significantly smaller
statistics [54, 55].

###  4.4 Comparison to previous measurements

In Fig. 7 the heavy-ion data from Pb–Pb collisions at the LHC reported in this
work are compared to the previous measurements, including results obtained at
lower collision energies. It has been argued [20] that three-dimensional
femtoscopic radii scale with the cube root of measured charged particle
multiplicity not only for a single energy and collision system, but
universally, across all collision energies and initial system sizes. The
dashed lines in the figure are linear fits to heavy-ion data available before
the startup of the LHC (the dotted lines show one sigma contours of these
fits). At lower energies the linear scaling was followed well in $long$ and
$side$ directions and only approximately in $out$, with some outliers such as
the most peripheral collisions reported by STAR. Our data at higher collision
energy show that the scaling in the $long$ direction is preserved. The data
for the $side$ direction fall below the scaling trend, although still within
the statistical uncertainty. A clear departure from the linear scaling is seen
in the $out$ direction; data from the LHC lie clearly below the trend from
lower energies. Such behavior was predicted by hydrodynamic calculations [33]
and is the result of the modification of the freeze-out shape. Larger initial
deposited energy produces larger temperature gradients and longer evolution
time at LHC. This results in a change from outside-in to inside-out freeze-out
and this modification of the space-time correlation drives the $R_{\rm
out}/R_{\rm side}$ ratio to values lower than at RHIC. Therefore, already for
heavy-ion data the simple universal linear scaling is broken in the transverse
direction. As already reported in [50], the femtoscopic radii for pp
collisions also exhibit linear scaling in the same variable, albeit with
significantly different parameters. In this case the scaling between different
colliding systems is broken again in the longitudinal direction.

Other scaling variables were proposed for the femtoscopic radii, based on
Monte-Carlo simulations of the initial state, such as average number of
participants $N_{\rm part}$ [46] or the characteristic initial transverse size
$\bar{R}$ [56, 57]. If data from different centralities but the same collision
energy are considered, a linear scaling is indeed observed for radii in all
directions, if they are plotted as a function of either of these variables.
However, no such scaling is observed when data from two collision energies
(e.g. top RHIC and top LHC) is compared. In that sense these variables are
less adequate than $\left<\mathrm{d}N_{\rm ch}/\mathrm{d}\eta\right>^{1/3}$,
for which the linear scaling is preserved, across many collision energies, for
at least one direction ($R_{\rm long}$). This observation is consistent with
an expectation that the final freeze-out volume, reflected in the femtoscopic
radii, should scale with the final-state observable (such as e.g.
$\left<\mathrm{d}N_{\rm ch}/\mathrm{d}\eta\right>^{1/3}$), while the simple
“geometric” initial state variables do not contain enough information. They
must be replaced with modeling of the full evolution process, such as the one
given by hydrodynamics, which depends on additional parameters apart from the
initial size, such as initial energy density.

###  4.5 Model comparisons

The hydrodynamic models predict both the centrality and pair momentum
dependence of the femtoscopic radii. Usually the parameters of the model
(initial energy density profile, the equation of state and the freeze-out
condition) are adjusted to reproduce the shape of the single particle
inclusive transverse momentum spectra as well as the elliptic flow. The
charged particle multiplicity must also be reproduced, preferably as a
function of pseudorapidity if the model employs full three-dimensional
modeling. The total particle multiplicity is usually determined on the freeze-
out hypersurface by employing statistical hadronization. After converting the
continuous medium to hadrons, final state interactions are taken into account
either in the simplified form, with propagation and decay of hadronic
resonances or with the full rescattering simulation. We compare our results to
predictions from the Therminator model coupled to (3+1)D viscous hydrodynamics
[34, 58, 35]. Similar results have been obtained in the HKM model [30].

Figure 8: Comparison of the femtoscopic radii ($R_{\rm out}$ in (a), $R_{\rm
side}$ in (b), and $R_{\rm long}$ in (c)), as a function of pair transverse
momentum, with the calculation from the Therminator and (3+1)D hydro model
[35], for four centralities (here identified by the value of the impact
parameter $b$ used in the calculation) and with the HKM model [30] for the
central data. Closed symbols are experimental data (with statistical and
systematic uncertainty), bands and dashed lines are the model calculations.
Figure 9: Comparison of the $R_{\rm out}/R_{\rm side}$ ratio, as a function of
pair transverse momentum, with the calculation from the Therminator and (3+1)D
hydro model [35], for 0–5% centrality in panel (a) and 50–60% centrality in
panel (b). The comparison to the HKM model [30] is also shown for the central
data. Closed symbols are experimental data (with statistical and systematic
uncertainty), bands and dashed lines are the model calculations.

In Fig. 8 we show the comparison of our data to the calculations from the
(3+1)D hydrodynamic model coupled to the Therminator statistical hadronization
code. The model is fully three-dimensional and it is able to reproduce values
of $R_{\rm long}$ for all centralities, with some overprediction of the
overall magnitude and the slope of the $k_{\mathrm{T}}$ dependence, especially
at low momentum. This is an indication that the longitudinal dynamics is
reasonably described in the model, both in momentum and space-time sectors.
The $R_{\rm out}$ is well described for all centralities, both in magnitude as
well in the slope of the $k_{\mathrm{T}}$ dependence. The slope of the
$k_{\mathrm{T}}$ dependence is also well described for $R_{\rm side}$, but the
magnitude is lower than in data, although within the systematic uncertainty.
The intercept of $R_{\rm side}$ at low $k_{\mathrm{T}}$ is usually associated
with the overall geometrical size of the system, while the slope of the
$k_{\mathrm{T}}$ dependence of both transverse radii depends on the amount of
flow in the system. Both are well reproduced, so the hydrodynamic approach is
in good agreement with our data.

Another model based on hydrodynamic formalism, the HKM [30] is also shown in
Fig. 8 for 0–5% most central collisions. It differs from the previous in the
implementation of the freeze-out process. It also directly treats hadron
rescattering with the UrQMD simulation. Nevertheless, the pion femtoscopy in
central Pb–Pb collisions at the LHC is reproduced in the calculation, with
some underprediction of $R_{side}$ and $R_{long}$ magnitude. Therefore, the
approximate agreement with data is a universal feature of such models, not of
a particular implementation. The particular choice of initial conditions and
the equation of state for these models was motivated by the analysis of RHIC
femtoscopic data. This choice is essential for the correct description of the
data, due to the collective flow mechanism in the hydrodynamic evolution at
the LHC energies. It also indicates that the details of the freeze-out process
have limited influence on pion femtoscopy. Some studies suggest that
femtoscopy of heavier particles might be a more sensitive probe in this case
[30].

The data to model comparison of the $R_{\rm out}/R_{\rm side}$ ratio is
plotted in Fig. 9. It shows values consistent with unity for central
collisions, both for models and data. Such low values are associated with the
change to outside-in freeze-out scenario at LHC collision energies. For most
peripheral collisions the ratio decreases with $k_{\mathrm{T}}$ even more, to
values smaller than unity. This decrease is qualitatively reproduced in the
model, although the calculations are at the upper edge of the experimental
systematic uncertainty.

##  5 Conclusions

We reported on the centrality and pair $k_{\mathrm{T}}$ dependence of the
three-dimensional and direction-averaged one-dimensional pion femtoscopic
radii in Pb–Pb collisions at $\sqrt{s_{\mathrm{NN}}}$=2.76 TeV. The behavior
of the femtoscopic radii can be factorized into a linear dependence on cube
root of charged particle density (separately for each of the three-dimensional
radii) and a power-law dependence on pair transverse momentum, with slightly
different exponents for each direction. The dependence for the longitudinal
radius is steeper than for the transverse ones. The dependence was also
compared to the one observed in heavy-ion collisions at lower energies and to
other collisions systems. The radii at the LHC follow the “universal”
$\left<\mathrm{d}N_{\rm ch}/\mathrm{d}\eta\right>^{1/3}$ scaling in the $long$
direction, but the radii in the transverse directions are below the
“universal” curve. Simple linear scaling predictions are not valid when the
collision energy is increased by an order of magnitude. The details of the
dynamic evolution of the system influence the results significantly. This is
in qualitative agreement with predictions from hydrodynamic models. In
particular, when moving from RHIC to LHC collision energies, they produce a
change in freeze-out shape, larger transverse radial flow and longer system
evolution time. Comparison of the full dataset to the calculations from the
recent hydrodynamic models, including three-dimensional evolution as well as
hadronic stage, generally show a good agreement, which is complementary to
similar agreement observed for momentum-only observables, such as momentum
spectra and elliptic flow. The existence of such agreement both in the space-
time as well as in momentum sectors, provides strong arguments for the
validity of hydrodynamic models for the description of flowing bulk matter
created in heavy-ion collisions at the LHC.

## 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: State
Committee of Science, World Federation of Scientists (WFS) and Swiss Fonds
Kidagan, Armenia, 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); National Natural Science
Foundation of China (NSFC), the Chinese Ministry of Education (CMOE) and the
Ministry of Science and Technology of China (MSTC); Ministry of Education and
Youth of the Czech Republic; Danish Natural Science Research Council, the
Carlsberg Foundation and the Danish National Research Foundation; The European
Research Council under the European Community’s Seventh Framework Programme;
Helsinki Institute of Physics and the Academy of Finland; French CNRS-IN2P3,
the ‘Region Pays de Loire’, ‘Region Alsace’, ‘Region Auvergne’ and CEA,
France; German Bundesministerium fur Bildung, Wissenschaft, Forschung und
Technologie (BMBF) and the Helmholtz Association; General Secretariat for
Research and Technology, Ministry of Development, Greece; Hungarian Orszagos
Tudomanyos Kutatasi Alappgrammok (OTKA) and National Office for Research and
Technology (NKTH); Department of Atomic Energy and Department of Science and
Technology of the Government of India; Istituto Nazionale di Fisica Nucleare
(INFN) and Centro Fermi - Museo Storico della Fisica e Centro Studi e Ricerche
”Enrico Fermi”, Italy; MEXT Grant-in-Aid for Specially Promoted Research,
Japan; Joint Institute for Nuclear Research, Dubna; National Research
Foundation of Korea (NRF); Consejo Nacional de Cienca y Tecnologia (CONACYT),
Direccion General de Asuntos del Personal Academico(DGAPA), México, :Amerique
Latine Formation academique – European Commission(ALFA-EC) and the EPLANET
Program (European Particle Physics Latin American Network) Stichting voor
Fundamenteel Onderzoek der Materie (FOM) and the Nederlandse Organisatie voor
Wetenschappelijk Onderzoek (NWO), Netherlands; Research Council of Norway
(NFR); National Science Centre, Poland; Ministry of National
Education/Institute for Atomic Physics and Consiliul Naţional al Cercetării
Ştiinţifice - Executive Agency for Higher Education Research Development and
Innovation Funding (CNCS-UEFISCDI) - Romania; Ministry of Education and
Science of Russian Federation, Russian Academy of Sciences, Russian Federal
Agency of Atomic Energy, Russian Federal Agency for Science and Innovations
and The Russian Foundation for Basic Research; Ministry of Education of
Slovakia; Department of Science and Technology, South Africa; Centro de
Investigaciones Energeticas, Medioambientales y Tecnologicas (CIEMAT),
E-Infrastructure shared between Europe and Latin America (EELA), Ministerio de
Economía y Competitividad (MINECO) of Spain, Xunta de Galicia (Consellería de
Educación), Centro de Aplicaciones Tecnológicas y Desarrollo Nuclear (CEADEN),
Cubaenergía, Cuba, and IAEA (International Atomic Energy Agency); Swedish
Research Council (VR) and Knut $\&$ Alice Wallenberg Foundation (KAW); Ukraine
Ministry of Education and Science; United Kingdom Science and Technology
Facilities Council (STFC); The United States Department of Energy, the United
States National Science Foundation, the State of Texas, and the State of Ohio;
Ministry of Science, Education and Sports of Croatia and Unity through
Knowledge Fund, Croatia. Council of Scientific and Industrial Research (CSIR),
New Delhi, India

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##  Appendix A The ALICE Collaboration

J. Adamorg40&D. Adamováorg83&M.M. Aggarwalorg87&G. Aglieri Rinellaorg36&M.
Agnelloorg111&N. Agrawalorg48&Z. Ahammedorg132&S.U. Ahnorg68&I.
Aimoorg94,org111&S. Aiolaorg137&M. Ajazorg16&A. Akindinovorg58&S.N.
Alamorg132&D. Aleksandrovorg100&B. Alessandroorg111&D. Alexandreorg102&R.
Alfaro Molinaorg64&A. Aliciorg105,org12&A. Alkinorg3&J.R.M. Almarazorg119&J.
Almeorg38&T. Altorg43&S. Altinpinarorg18&I. Altsybeevorg131&C. Alves Garcia
Pradoorg120&C. Andreiorg78&A. Andronicorg97&V. Anguelovorg93&J.
Anielskiorg54&T. Antičićorg98&F. Antinoriorg108&P. Antonioliorg105&L.
Aphecetcheorg113&H. Appelshäuserorg53&S. Arcelliorg28&N. Armestoorg17&R.
Arnaldiorg111&I.C. Arseneorg22&M. Arslandokorg53&B. Audurierorg113&A.
Augustinusorg36&R. Averbeckorg97&M.D. Azmiorg19&M. Bachorg43&A.
Badalàorg107&Y.W. Baekorg44&S. Bagnascoorg111&R. Bailhacheorg53&R.
Balaorg90&A. Baldisseriorg15&F. Baltasar Dos Santos Pedrosaorg36&R.C.
Baralorg61&A.M. Barbanoorg111&R. Barberaorg29&F. Barileorg33&G.G.
Barnaföldiorg136&L.S. Barnbyorg102&V. Barretorg70&P. Bartaliniorg7&K.
Barthorg36&J. Bartkeorg117&E. Bartschorg53&M. Basileorg28&N. Bastidorg70&S.
Basuorg132&B. Bathenorg54&G. Batigneorg113&A. Batista Camejoorg70&B.
Batyunyaorg66&P.C. Batzingorg22&I.G. Beardenorg80&H. Beckorg53&C.
Beddaorg111&N.K. Beheraorg49,org48&I. Belikovorg55&F. Belliniorg28&H. Bello
Martinezorg2&R. Bellwiedorg122&R. Belmontorg135&E. Belmont-Morenoorg64&V.
Belyaevorg76&G. Bencediorg136&S. Beoleorg27&I. Berceanuorg78&A.
Bercuciorg78&Y. Berdnikovorg85&D. Berenyiorg136&R.A. Bertensorg57&D.
Berzanoorg36,org27&L. Betevorg36&A. Bhasinorg90&I.R. Bhatorg90&A.K.
Bhatiorg87&B. Bhattacharjeeorg45&J. Bhomorg128&L. Bianchiorg122&N.
Bianchiorg72&C. Bianchinorg135,org57&J. Bielčíkorg40&J. Bielčíkováorg83&A.
Bilandzicorg80&R. Biswasorg4&S. Biswasorg79&S. Bjelogrlicorg57&J.T.
Blairorg118&F. Blancoorg10&D. Blauorg100&C. Blumeorg53&F. Bockorg93,org74&A.
Bogdanovorg76&H. Bøggildorg80&L. Boldizsárorg136&M. Bombaraorg41&J.
Bookorg53&H. Borelorg15&A. Borissovorg96&M. Borriorg82&F. Bossúorg65&E.
Bottaorg27&S. Böttgerorg52&P. Braun-Munzingerorg97&M. Bregantorg120&T.
Breitnerorg52&T.A. Brokerorg53&T.A. Browningorg95&M. Brozorg40&E.J.
Bruckenorg46&E. Brunaorg111&G.E. Brunoorg33&D. Budnikovorg99&H.
Bueschingorg53&S. Bufalinoorg27,org111&P. Buncicorg36&O. Buschorg128,org93&Z.
Butheleziorg65&J.B. Buttorg16&J.T. Buxtonorg20&D. Caffarriorg36&X. Caiorg7&H.
Cainesorg137&L. Calero Diazorg72&A. Calivaorg57&E. Calvo Villarorg103&P.
Cameriniorg26&F. Carenaorg36&W. Carenaorg36&F. Carnesecchiorg28&J. Castillo
Castellanosorg15&A.J. Castroorg125&E.A.R. Casulaorg25&C. Cavicchioliorg36&C.
Ceballos Sanchezorg9&J. Cepilaorg40&P. Cerelloorg111&J. Cerkalaorg115&B.
Changorg123&S. Chapelandorg36&M. Chartierorg124&J.L. Charvetorg15&S.
Chattopadhyayorg132&S. Chattopadhyayorg101&V. Chelnokovorg3&M. Cherneyorg86&C.
Cheshkovorg130&B. Cheynisorg130&V. Chibante Barrosoorg36&D.D.
Chinellatoorg121&P. Chochulaorg36&K. Choiorg96&M. Chojnackiorg80&S.
Choudhuryorg132&P. Christakoglouorg81&C.H. Christensenorg80&P.
Christiansenorg34&T. Chujoorg128&S.U. Chungorg96&Z. Chunhuiorg57&C.
Cicaloorg106&L. Cifarelliorg12,org28&F. Cindoloorg105&J. Cleymansorg89&F.
Colamariaorg33&D. Colellaorg36,org33,org59&A. Colluorg25&M. Colocciorg28&G.
Conesa Balbastreorg71&Z. Conesa del Valleorg51&M.E. Connorsorg137&J.G.
Contrerasorg11,org40&T.M. Cormierorg84&Y. Corrales Moralesorg27&I. Cortés
Maldonadoorg2&P. Corteseorg32&M.R. Cosentinoorg120&F. Costaorg36&P.
Crochetorg70&R. Cruz Albinoorg11&E. Cuautleorg63&L. Cunqueiroorg36&T.
Dahmsorg92,org37&A. Daineseorg108&A. Danuorg62&D. Dasorg101&I.
Dasorg51,org101&S. Dasorg4&A. Dashorg121&S. Dashorg48&S. Deorg120&A. De
Caroorg31,org12&G. de Cataldoorg104&J. de Cuvelandorg43&A. De Falcoorg25&D. De
Gruttolaorg12,org31&N. De Marcoorg111&S. De Pasqualeorg31&A.
Deistingorg97,org93&A. Delofforg77&E. Dénesorg136&G. D’Erasmoorg33&D. Di
Bariorg33&A. Di Mauroorg36&P. Di Nezzaorg72&M.A. Diaz Corcheroorg10&T.
Dietelorg89&P. Dillensegerorg53&R. Diviàorg36&Ø. Djuvslandorg18&A.
Dobrinorg57,org81&T. Dobrowolskiorg770&D. Domenicis Gimenezorg120&B.
Dönigusorg53&O. Dordicorg22&T. Drozhzhovaorg53&A.K. Dubeyorg132&A.
Dublaorg57&L. Ducrouxorg130&P. Dupieuxorg70&R.J. Ehlersorg137&D. Eliaorg104&H.
Engelorg52&B. Erazmusorg36,org113&I. Erdemirorg53&F. Erhardtorg129&D.
Eschweilerorg43&B. Espagnonorg51&M. Estienneorg113&S. Esumiorg128&J.
Eumorg96&D. Evansorg102&S. Evdokimovorg112&G. Eyyubovaorg40&L.
Fabbiettiorg37,org92&D. Fabrisorg108&J. Faivreorg71&A. Fantoniorg72&M.
Faselorg74&L. Feldkamporg54&D. Feleaorg62&A. Felicielloorg111&G.
Feofilovorg131&J. Ferenceiorg83&A. Fernández Téllezorg2&E.G. Ferreiroorg17&A.
Ferrettiorg27&A. Festantiorg30&V.J.G. Feuillardorg70,org15&J.
Figielorg117&M.A.S. Figueredoorg124,org120&S. Filchaginorg99&D.
Finogeevorg56&E.M. Fioreorg33&M.G. Fleckorg93&M. Florisorg36&S.
Foertschorg65&P. Fokaorg97&S. Fokinorg100&E. Fragiacomoorg110&A.
Francesconorg30,org36&U. Frankenfeldorg97&U. Fuchsorg36&C. Furgetorg71&A.
Fursorg56&M. Fusco Girardorg31&J.J. Gaardhøjeorg80&M. Gagliardiorg27&A.M.
Gagoorg103&M. Gallioorg27&D.R. Gangadharanorg74&P. Ganotiorg88&C. Gaoorg7&C.
Garabatosorg97&E. Garcia-Solisorg13&C. Gargiuloorg36&P. Gasikorg92,org37&M.
Germainorg113&A. Gheataorg36&M. Gheataorg62,org36&P. Ghoshorg132&S.K.
Ghoshorg4&P. Gianottiorg72&P. Giubellinoorg36&P. Giubilatoorg30&E. Gladysz-
Dziadusorg117&P. Glässelorg93&D.M. Goméz Coralorg64&A. Gomez Ramirezorg52&P.
González-Zamoraorg10&S. Gorbunovorg43&L. Görlichorg117&S. Gotovacorg116&V.
Grabskiorg64&L.K. Graczykowskiorg134&K.L. Grahamorg102&A. Grelliorg57&A.
Grigorasorg36&C. Grigorasorg36&V. Grigorievorg76&A. Grigoryanorg1&S.
Grigoryanorg66&B. Grinyovorg3&N. Grionorg110&J.F. Grosse-
Oetringhausorg36&J.-Y. Grossiordorg130&R. Grossoorg36&F. Guberorg56&R.
Guernaneorg71&B. Guerzoniorg28&K. Gulbrandsenorg80&H. Gulkanyanorg1&T.
Gunjiorg127&A. Guptaorg90&R. Guptaorg90&R. Haakeorg54&Ø. Haalandorg18&C.
Hadjidakisorg51&M. Haiducorg62&H. Hamagakiorg127&G. Hamarorg136&A.
Hansenorg80&J.W. Harrisorg137&H. Hartmannorg43&A. Hartonorg13&D.
Hatzifotiadouorg105&S. Hayashiorg127&S.T. Heckelorg53&M. Heideorg54&H.
Helstruporg38&A. Herghelegiuorg78&G. Herrera Corralorg11&B.A. Hessorg35&K.F.
Hetlandorg38&T.E. Hildenorg46&H. Hillemannsorg36&B. Hippolyteorg55&R.
Hosokawaorg128&P. Hristovorg36&M. Huangorg18&T.J. Humanicorg20&N.
Hussainorg45&T. Hussainorg19&D. Hutterorg43&D.S. Hwangorg21&R. Ilkaevorg99&I.
Ilkivorg77&M. Inabaorg128&M. Ippolitovorg76,org100&M. Irfanorg19&M.
Ivanovorg97&V. Ivanovorg85&V. Izucheevorg112&P.M. Jacobsorg74&S.
Jadlovskaorg115&C. Jahnkeorg120&H.J. Jangorg68&M.A. Janikorg134&P.H.S.Y.
Jayarathnaorg122&C. Jenaorg30&S. Jenaorg122&R.T. Jimenez Bustamanteorg97&P.G.
Jonesorg102&H. Jungorg44&A. Juskoorg102&P. Kalinakorg59&A. Kalweitorg36&J.
Kaminorg53&J.H. Kangorg138&V. Kaplinorg76&S. Karorg132&A. Karasu Uysalorg69&O.
Karavichevorg56&T. Karavichevaorg56&L. Karayanorg93,org97&E. Karpechevorg56&U.
Kebschullorg52&R. Keidelorg139&D.L.D. Keijdenerorg57&M. Keilorg36&K.H.
Khanorg16&M.M. Khanorg19&P. Khanorg101&S.A. Khanorg132&A. Khanzadeevorg85&Y.
Kharlovorg112&B. Kilengorg38&B. Kimorg138&D.W. Kimorg68,org44&D.J.
Kimorg123&H. Kimorg138&J.S. Kimorg44&M. Kimorg44&M. Kimorg138&S. Kimorg21&T.
Kimorg138&S. Kirschorg43&I. Kiselorg43&S. Kiselevorg58&A. Kisielorg134&G.
Kissorg136&J.L. Klayorg6&C. Kleinorg53&J. Kleinorg36,org93&C. Klein-
Bösingorg54&A. Klugeorg36&M.L. Knichelorg93&A.G. Knospeorg118&T.
Kobayashiorg128&C. Kobdajorg114&M. Kofaragoorg36&T. Kolleggerorg43,org97&A.
Kolojvariorg131&V. Kondratievorg131&N. Kondratyevaorg76&E. Kondratyukorg112&A.
Konevskikhorg56&M. Kopcikorg115&M. Kourorg90&C. Kouzinopoulosorg36&O.
Kovalenkoorg77&V. Kovalenkoorg131&M. Kowalskiorg117&G. Koyithatta
Meethaleveeduorg48&J. Kralorg123&I. Králikorg59&A. Kravčákováorg41&M.
Krelinaorg40&M. Kretzorg43&M. Krivdaorg102,org59&F. Krizekorg83&E.
Kryshenorg36&M. Krzewickiorg43&A.M. Kuberaorg20&V. Kučeraorg83&T.
Kugathasanorg36&C. Kuhnorg55&P.G. Kuijerorg81&I. Kulakovorg43&A. Kumarorg90&J.
Kumarorg48&L. Kumarorg79,org87&P. Kurashviliorg77&A. Kurepinorg56&A.B.
Kurepinorg56&A. Kuryakinorg99&S. Kushpilorg83&M.J. Kweonorg50&Y.
Kwonorg138&S.L. La Pointeorg111&P. La Roccaorg29&C. Lagana Fernandesorg120&I.
Lakomovorg36&R. Langoyorg42&C. Laraorg52&A. Lardeuxorg15&A. Lattucaorg27&E.
Laudiorg36&R. Leaorg26&L. Leardiniorg93&G.R. Leeorg102&S. Leeorg138&I.
Legrandorg36&F. Lehasorg81&R.C. Lemmonorg82&V. Lentiorg104&E.
Leograndeorg57&I. León Monzónorg119&M. Leoncinoorg27&P. Lévaiorg136&S.
Liorg7,org70&X. Liorg14&J. Lienorg42&R. Lietavaorg102&S. Lindalorg22&V.
Lindenstruthorg43&C. Lippmannorg97&M.A. Lisaorg20&H.M. Ljunggrenorg34&D.F.
Lodatoorg57&P.I. Loenneorg18&V. Loginovorg76&C. Loizidesorg74&X. Lopezorg70&E.
López Torresorg9&A. Loweorg136&P. Luettigorg53&M. Lunardonorg30&G.
Luparelloorg26&P.H.F.N.D. Luzorg120&A. Maevskayaorg56&M. Magerorg36&S.
Mahajanorg90&S.M. Mahmoodorg22&A. Maireorg55&R.D. Majkaorg137&M.
Malaevorg85&I. Maldonado Cervantesorg63&L. Malininaidp3821664,org66&D.
Mal’Kevichorg58&P. Malzacherorg97&A. Mamonovorg99&V. Mankoorg100&F.
Mansoorg70&V. Manzariorg36,org104&M. Marchisoneorg27&J. Marešorg60&G.V.
Margagliottiorg26&A. Margottiorg105&J. Marguttiorg57&A. Marínorg97&C.
Markertorg118&M. Marquardorg53&N.A. Martinorg97&J. Martin Blancoorg113&P.
Martinengoorg36&M.I. Martínezorg2&G. Martínez Garcíaorg113&M. Martinez
Pedreiraorg36&Y. Martynovorg3&A. Masorg120&S. Masciocchiorg97&M.
Maseraorg27&A. Masoniorg106&L. Massacrierorg113&A. Mastroserioorg33&H.
Masuiorg128&A. Matyjaorg117&C. Mayerorg117&J. Mazerorg125&M.A.
Mazzoniorg109&D. Mcdonaldorg122&F. Meddiorg24&Y. Melikyanorg76&A. Menchaca-
Rochaorg64&E. Meninnoorg31&J. Mercado Pérezorg93&M. Meresorg39&Y.
Miakeorg128&M.M. Mieskolainenorg46&K. Mikhaylovorg58,org66&L. Milanoorg36&J.
Milosevicorg22,org133&L.M. Minerviniorg104,org23&A. Mischkeorg57&A.N.
Mishraorg49&D. Miśkowiecorg97&J. Mitraorg132&C.M. Mituorg62&N.
Mohammadiorg57&B. Mohantyorg132,org79&L. Molnarorg55&L. Montaño Zetinaorg11&E.
Montesorg10&M. Morandoorg30&D.A. Moreira De Godoyorg113,org54&S.
Morettoorg30&A. Morrealeorg113&A. Morschorg36&V. Mucciforaorg72&E.
Mudnicorg116&D. Mühlheimorg54&S. Muhuriorg132&M. Mukherjeeorg132&J.D.
Mulliganorg137&M.G. Munhozorg120&S. Murrayorg65&L. Musaorg36&J.
Musinskyorg59&B.K. Nandiorg48&R. Naniaorg105&E. Nappiorg104&M.U. Naruorg16&C.
Nattrassorg125&K. Nayakorg79&T.K. Nayakorg132&S. Nazarenkoorg99&A.
Nedosekinorg58&L. Nellenorg63&F. Ngorg122&M. Nicassioorg97&M.
Niculescuorg62,org36&J. Niedzielaorg36&B.S. Nielsenorg80&S. Nikolaevorg100&S.
Nikulinorg100&V. Nikulinorg85&F. Noferiniorg105,org12&P. Nomokonovorg66&G.
Noorenorg57&J.C.C. Norisorg2&J. Normanorg124&A. Nyaninorg100&J.
Nystrandorg18&H. Oeschlerorg93&S. Ohorg137&S.K. Ohorg67&A. Ohlsonorg36&A.
Okatanorg69&T. Okuboorg47&L. Olahorg136&J. Oleniaczorg134&A.C. Oliveira Da
Silvaorg120&M.H. Oliverorg137&J. Onderwaaterorg97&C. Oppedisanoorg111&R.
Oravaorg46&A. Ortiz Velasquezorg63&A. Oskarssonorg34&J. Otwinowskiorg117&K.
Oyamaorg93&M. Ozdemirorg53&Y. Pachmayerorg93&P. Paganoorg31&G. Paićorg63&C.
Pajaresorg17&S.K. Palorg132&J. Panorg135&A.K. Pandeyorg48&D. Pantorg48&P.
Papcunorg115&V. Papikyanorg1&G.S. Pappalardoorg107&P. Pareekorg49&W.J.
Parkorg97&S. Parmarorg87&A. Passfeldorg54&V. Paticchioorg104&R.N.
Patraorg132&B. Paulorg101&T. Peitzmannorg57&H. Pereira Da Costaorg15&E.
Pereira De Oliveira Filhoorg120&D. Peresunkoorg100,org76&C.E. Pérez
Laraorg81&E. Perez Lezamaorg53&V. Peskovorg53&Y. Pestovorg5&V.
Petráčekorg40&V. Petrovorg112&M. Petroviciorg78&C. Pettaorg29&S.
Pianoorg110&M. Piknaorg39&P. Pillotorg113&O. Pinazzaorg105,org36&L.
Pinskyorg122&D.B. Piyarathnaorg122&M. Płoskońorg74&M. Planinicorg129&J.
Plutaorg134&S. Pochybovaorg136&P.L.M. Podesta-Lermaorg119&M.G.
Poghosyanorg86,org84&B. Polichtchoukorg112&N. Poljakorg129&W.
Poonsawatorg114&A. Poporg78&S. Porteboeuf-Houssaisorg70&J. Porterorg74&J.
Pospisilorg83&S.K. Prasadorg4&R. Preghenellaorg36,org105&F. Prinoorg111&C.A.
Pruneauorg135&I. Pshenichnovorg56&M. Puccioorg111&G. Pudduorg25&P.
Pujahariorg135&V. Puninorg99&J. Putschkeorg135&H. Qvigstadorg22&A.
Rachevskiorg110&S. Rahaorg4&S. Rajputorg90&J. Rakorg123&A.
Rakotozafindrabeorg15&L. Ramelloorg32&R. Raniwalaorg91&S. Raniwalaorg91&S.S.
Räsänenorg46&B.T. Rascanuorg53&D. Ratheeorg87&K.F. Readorg125&J.S.
Realorg71&K. Redlichorg77&R.J. Reedorg135&A. Rehmanorg18&P. Reicheltorg53&F.
Reidtorg93,org36&X. Renorg7&R. Renfordtorg53&A.R. Reolonorg72&A.
Reshetinorg56&F. Rettigorg43&J.-P. Revolorg12&K. Reygersorg93&V.
Riabovorg85&R.A. Ricciorg73&T. Richertorg34&M. Richterorg22&P. Riedlerorg36&W.
Rieglerorg36&F. Riggiorg29&C. Risteaorg62&A. Rivettiorg111&E. Roccoorg57&M.
Rodríguez Cahuantziorg2&A. Rodriguez Mansoorg81&K. Røedorg22&E.
Rogochayaorg66&D. Rohrorg43&D. Röhrichorg18&R. Romitaorg124&F.
Ronchettiorg72&L. Ronfletteorg113&P. Rosnetorg70&A. Rossiorg30,org36&F.
Roukoutakisorg88&A. Royorg49&C. Royorg55&P. Royorg101&A.J. Rubio
Monteroorg10&R. Ruiorg26&R. Russoorg27&E. Ryabinkinorg100&Y. Ryabovorg85&A.
Rybickiorg117&S. Sadovskyorg112&K. Šafaříkorg36&B. Sahlmullerorg53&P.
Sahooorg49&R. Sahooorg49&S. Sahooorg61&P.K. Sahuorg61&J. Sainiorg132&S.
Sakaiorg72&M.A. Salehorg135&C.A. Salgadoorg17&J. Salzwedelorg20&S.
Sambyalorg90&V. Samsonovorg85&X. Sanchez Castroorg55&L. Šándororg59&A.
Sandovalorg64&M. Sanoorg128&D. Sarkarorg132&E. Scapparoneorg105&F.
Scarlassaraorg30&R.P. Scharenbergorg95&C. Schiauaorg78&R. Schickerorg93&C.
Schmidtorg97&H.R. Schmidtorg35&S. Schuchmannorg53&J. Schukraftorg36&M.
Schulcorg40&T. Schusterorg137&Y. Schutzorg113,org36&K. Schwarzorg97&K.
Schwedaorg97&G. Scioliorg28&E. Scomparinorg111&R. Scottorg125&J.E.
Segerorg86&Y. Sekiguchiorg127&D. Sekihataorg47&I. Selyuzhenkovorg97&K.
Senosiorg65&J. Seoorg96,org67&E. Serradillaorg64,org10&A. Sevcencoorg62&A.
Shabanovorg56&A. Shabetaiorg113&O. Shaduraorg3&R. Shahoyanorg36&A.
Shangaraevorg112&A. Sharmaorg90&M. Sharmaorg90&M. Sharmaorg90&N.
Sharmaorg125,org61&K. Shigakiorg47&K. Shtejerorg9,org27&Y. Sibiriakorg100&S.
Siddhantaorg106&K.M. Sielewiczorg36&T. Siemiarczukorg77&D.
Silvermyrorg84,org34&C. Silvestreorg71&G. Simatovicorg129&G. Simonettiorg36&R.
Singarajuorg132&R. Singhorg79&S. Singhaorg132,org79&V. Singhalorg132&B.C.
Sinhaorg132&T. Sinhaorg101&B. Sitarorg39&M. Sittaorg32&T.B. Skaaliorg22&M.
Slupeckiorg123&N. Smirnovorg137&R.J.M. Snellingsorg57&T.W. Snellmanorg123&C.
Søgaardorg34&R. Soltzorg75&J. Songorg96&M. Songorg138&Z. Songorg7&F.
Soramelorg30&S. Sorensenorg125&M. Spacekorg40&E. Spiritiorg72&I.
Sputowskaorg117&M. Spyropoulou-Stassinakiorg88&B.K. Srivastavaorg95&J.
Stachelorg93&I. Stanorg62&G. Stefanekorg77&M. Steinpreisorg20&E.
Stenlundorg34&G. Steynorg65&J.H. Stillerorg93&D. Stoccoorg113&P.
Strmenorg39&A.A.P. Suaideorg120&T. Sugitateorg47&C. Suireorg51&M.
Suleymanovorg16&R. Sultanovorg58&M. Šumberaorg83&T.J.M. Symonsorg74&A.
Szaboorg39&A. Szanto de Toledoorg1200&I. Szarkaorg39&A.
Szczepankiewiczorg36&M. Szymanskiorg134&J. Takahashiorg121&G.J.
Tambaveorg18&N. Tanakaorg128&M.A. Tangaroorg33&J.D. Tapia
Takakiidp5957472,org51&A. Tarantola Peloniorg53&M. Tarhiniorg51&M.
Tariqorg19&M.G. Tarzilaorg78&A. Tauroorg36&G. Tejeda Muñozorg2&A.
Telescaorg36&K. Terasakiorg127&C. Terrevoliorg30,org25&B. Teyssierorg130&J.
Thäderorg74,org97&D. Thomasorg118&R. Tieulentorg130&A.R. Timminsorg122&A.
Toiaorg53&S. Trogoloorg111&V. Trubnikovorg3&W.H. Trzaskaorg123&T.
Tsujiorg127&A. Tumkinorg99&R. Turrisiorg108&T.S. Tveterorg22&K.
Ullalandorg18&A. Urasorg130&G.L. Usaiorg25&A. Utrobicicorg129&M.
Vajzerorg83&M. Valaorg59&L. Valencia Palomoorg70&S. Valleroorg27&J. Van Der
Maarelorg57&J.W. Van Hoorneorg36&M. van Leeuwenorg57&T. Vanatorg83&P. Vande
Vyvreorg36&D. Vargaorg136&A. Vargasorg2&M. Vargyasorg123&R. Varmaorg48&M.
Vasileiouorg88&A. Vasilievorg100&A. Vauthierorg71&V. Vecherninorg131&A.M.
Veenorg57&M. Veldhoenorg57&A. Velureorg18&M. Venaruzzoorg73&E.
Vercellinorg27&S. Vergara Limónorg2&R. Vernetorg8&M. Verweijorg135,org36&L.
Vickovicorg116&G. Viestiorg300&J. Viinikainenorg123&Z. Vilakaziorg126&O.
Villalobos Baillieorg102&A. Vinogradovorg100&L. Vinogradovorg131&Y.
Vinogradovorg990&T. Virgiliorg31&V. Vislaviciusorg34&Y.P. Viyogiorg132&A.
Vodopyanovorg66&M.A. Völklorg93&K. Voloshinorg58&S.A. Voloshinorg135&G.
Volpeorg136,org36&B. von Hallerorg36&I. Vorobyevorg37,org92&D.
Vranicorg36,org97&J. Vrlákováorg41&B. Vulpescuorg70&A. Vyushinorg99&B.
Wagnerorg18&J. Wagnerorg97&H. Wangorg57&M. Wangorg7,org113&Y. Wangorg93&D.
Watanabeorg128&Y. Watanabeorg127&M. Weberorg36&S.G. Weberorg97&J.P.
Wesselsorg54&U. Westerhofforg54&J. Wiechulaorg35&J. Wikneorg22&M.
Wildeorg54&G. Wilkorg77&J. Wilkinsonorg93&M.C.S. Williamsorg105&B.
Windelbandorg93&M. Winnorg93&C.G. Yaldoorg135&H. Yangorg57&P. Yangorg7&S.
Yanoorg47&Z. Yinorg7&H. Yokoyamaorg128&I.-K. Yooorg96&V. Yurchenkoorg3&I.
Yushmanovorg100&A. Zaborowskaorg134&V. Zaccoloorg80&A. Zamanorg16&C.
Zampolliorg105&H.J.C. Zanoliorg120&S. Zaporozhetsorg66&N. Zardoshtiorg102&A.
Zarochentsevorg131&P. Závadaorg60&N. Zaviyalovorg99&H. Zbroszczykorg134&I.S.
Zguraorg62&M. Zhalovorg85&H. Zhangorg18,org7&X. Zhangorg74&Y. Zhangorg7&C.
Zhaoorg22&N. Zhigarevaorg58&D. Zhouorg7&Y. Zhouorg80,org57&Z. Zhouorg18&H.
Zhuorg18,org7&J. Zhuorg113,org7&X. Zhuorg7&A. Zichichiorg12,org28&A.
Zimmermannorg93&M.B. Zimmermannorg54,org36&G. Zinovjevorg3&M. Zyzakorg43

## Affiliation notes

0Deceased

idp3821664Also at: M.V. Lomonosov Moscow State University, D.V. Skobeltsyn
Institute of Nuclear, Physics, Moscow, Russia

idp5957472Also at: University of Kansas, Lawrence, Kansas, United States

## 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, 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, France

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

org10Centro de Investigaciones Energéticas Medioambientales y Tecnológicas
(CIEMAT), Madrid, Spain

org11Centro de Investigación y de Estudios Avanzados (CINVESTAV), Mexico City
and Mérida, Mexico

org12Centro Fermi - Museo Storico della Fisica e Centro Studi e Ricerche
“Enrico Fermi”, Rome, Italy

org13Chicago State University, Chicago, Illinois, USA

org14China Institute of Atomic Energy, Beijing, China

org15Commissariat à l’Energie Atomique, IRFU, Saclay, France

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

org17Departamento de Física de Partículas and IGFAE, Universidad de Santiago
de Compostela, Santiago de Compostela, Spain

org18Department of Physics and Technology, University of Bergen, Bergen,
Norway

org19Department of Physics, Aligarh Muslim University, Aligarh, India

org20Department of Physics, Ohio State University, Columbus, Ohio, United
States

org21Department of Physics, Sejong University, Seoul, South Korea

org22Department of Physics, University of Oslo, Oslo, Norway

org23Dipartimento di Elettrotecnica ed Elettronica del Politecnico, Bari,
Italy

org24Dipartimento di Fisica dell’Università ’La Sapienza’ and Sezione INFN
Rome, Italy

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

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

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

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

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

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

org31Dipartimento di Fisica ‘E.R. Caianiello’ dell’Università and Gruppo
Collegato INFN, Salerno, Italy

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

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

org34Division of Experimental High Energy Physics, University of Lund, Lund,
Sweden

org35Eberhard Karls Universität Tübingen, Tübingen, Germany

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

org37Excellence Cluster Universe, Technische Universität München, Munich,
Germany

org38Faculty of Engineering, Bergen University College, Bergen, Norway

org39Faculty of Mathematics, Physics and Informatics, Comenius University,
Bratislava, Slovakia

org40Faculty of Nuclear Sciences and Physical Engineering, Czech Technical
University in Prague, Prague, Czech Republic

org41Faculty of Science, P.J. Šafárik University, Košice, Slovakia

org42Faculty of Technology, Buskerud and Vestfold University College,
Vestfold, Norway

org43Frankfurt Institute for Advanced Studies, Johann Wolfgang Goethe-
Universität Frankfurt, Frankfurt, Germany

org44Gangneung-Wonju National University, Gangneung, South Korea

org45Gauhati University, Department of Physics, Guwahati, India

org46Helsinki Institute of Physics (HIP), Helsinki, Finland

org47Hiroshima University, Hiroshima, Japan

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

org49Indian Institute of Technology Indore, Indore (IITI), India

org50Inha University, Incheon, South Korea

org51Institut de Physique Nucléaire d’Orsay (IPNO), Université Paris-Sud,
CNRS-IN2P3, Orsay, France

org52Institut für Informatik, Johann Wolfgang Goethe-Universität Frankfurt,
Frankfurt, Germany

org53Institut für Kernphysik, Johann Wolfgang Goethe-Universität Frankfurt,
Frankfurt, Germany

org54Institut für Kernphysik, Westfälische Wilhelms-Universität Münster,
Münster, Germany

org55Institut Pluridisciplinaire Hubert Curien (IPHC), Université de
Strasbourg, CNRS-IN2P3, Strasbourg, France

org56Institute for Nuclear Research, Academy of Sciences, Moscow, Russia

org57Institute for Subatomic Physics of Utrecht University, Utrecht,
Netherlands

org58Institute for Theoretical and Experimental Physics, Moscow, Russia

org59Institute of Experimental Physics, Slovak Academy of Sciences, Košice,
Slovakia

org60Institute of Physics, Academy of Sciences of the Czech Republic, Prague,
Czech Republic

org61Institute of Physics, Bhubaneswar, India

org62Institute of Space Science (ISS), Bucharest, Romania

org63Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México,
Mexico City, Mexico

org64Instituto de Física, Universidad Nacional Autónoma de México, Mexico
City, Mexico

org65iThemba LABS, National Research Foundation, Somerset West, South Africa

org66Joint Institute for Nuclear Research (JINR), Dubna, Russia

org67Konkuk University, Seoul, South Korea

org68Korea Institute of Science and Technology Information, Daejeon, South
Korea

org69KTO Karatay University, Konya, Turkey

org70Laboratoire de Physique Corpusculaire (LPC), Clermont Université,
Université Blaise Pascal, CNRS–IN2P3, Clermont-Ferrand, France

org71Laboratoire de Physique Subatomique et de Cosmologie, Université
Grenoble-Alpes, CNRS-IN2P3, Grenoble, France

org72Laboratori Nazionali di Frascati, INFN, Frascati, Italy

org73Laboratori Nazionali di Legnaro, INFN, Legnaro, Italy

org74Lawrence Berkeley National Laboratory, Berkeley, California, United
States

org75Lawrence Livermore National Laboratory, Livermore, California, United
States

org76Moscow Engineering Physics Institute, Moscow, Russia

org77National Centre for Nuclear Studies, Warsaw, Poland

org78National Institute for Physics and Nuclear Engineering, Bucharest,
Romania

org79National Institute of Science Education and Research, Bhubaneswar, India

org80Niels Bohr Institute, University of Copenhagen, Copenhagen, Denmark

org81Nikhef, Nationaal instituut voor subatomaire fysica, Amsterdam,
Netherlands

org82Nuclear Physics Group, STFC Daresbury Laboratory, Daresbury, United
Kingdom

org83Nuclear Physics Institute, Academy of Sciences of the Czech Republic, Řež
u Prahy, Czech Republic

org84Oak Ridge National Laboratory, Oak Ridge, Tennessee, United States

org85Petersburg Nuclear Physics Institute, Gatchina, Russia

org86Physics Department, Creighton University, Omaha, Nebraska, United States

org87Physics Department, Panjab University, Chandigarh, India

org88Physics Department, University of Athens, Athens, Greece

org89Physics Department, University of Cape Town, Cape Town, South Africa

org90Physics Department, University of Jammu, Jammu, India

org91Physics Department, University of Rajasthan, Jaipur, India

org92Physik Department, Technische Universität München, Munich, Germany

org93Physikalisches Institut, Ruprecht-Karls-Universität Heidelberg,
Heidelberg, Germany

org94Politecnico di Torino, Turin, Italy

org95Purdue University, West Lafayette, Indiana, United States

org96Pusan National University, Pusan, South Korea

org97Research Division and ExtreMe Matter Institute EMMI, GSI Helmholtzzentrum
für Schwerionenforschung, Darmstadt, Germany

org98Rudjer Bošković Institute, Zagreb, Croatia

org99Russian Federal Nuclear Center (VNIIEF), Sarov, Russia

org100Russian Research Centre Kurchatov Institute, Moscow, Russia

org101Saha Institute of Nuclear Physics, Kolkata, India

org102School of Physics and Astronomy, University of Birmingham, Birmingham,
United Kingdom

org103Sección Física, Departamento de Ciencias, Pontificia Universidad
Católica del Perú, Lima, Peru

org104Sezione INFN, Bari, Italy

org105Sezione INFN, Bologna, Italy

org106Sezione INFN, Cagliari, Italy

org107Sezione INFN, Catania, Italy

org108Sezione INFN, Padova, Italy

org109Sezione INFN, Rome, Italy

org110Sezione INFN, Trieste, Italy

org111Sezione INFN, Turin, Italy

org112SSC IHEP of NRC Kurchatov institute, Protvino, Russia

org113SUBATECH, Ecole des Mines de Nantes, Université de Nantes, CNRS-IN2P3,
Nantes, France

org114Suranaree University of Technology, Nakhon Ratchasima, Thailand

org115Technical University of Košice, Košice, Slovakia

org116Technical University of Split FESB, Split, Croatia

org117The Henryk Niewodniczanski Institute of Nuclear Physics, Polish Academy
of Sciences, Cracow, Poland

org118The University of Texas at Austin, Physics Department, Austin, Texas,
USA

org119Universidad Autónoma de Sinaloa, Culiacán, Mexico

org120Universidade de São Paulo (USP), São Paulo, Brazil

org121Universidade Estadual de Campinas (UNICAMP), Campinas, Brazil

org122University of Houston, Houston, Texas, United States

org123University of Jyväskylä, Jyväskylä, Finland

org124University of Liverpool, Liverpool, United Kingdom

org125University of Tennessee, Knoxville, Tennessee, United States

org126University of the Witwatersrand, Johannesburg, South Africa

org127University of Tokyo, Tokyo, Japan

org128University of Tsukuba, Tsukuba, Japan

org129University of Zagreb, Zagreb, Croatia

org130Université de Lyon, Université Lyon 1, CNRS/IN2P3, IPN-Lyon,
Villeurbanne, France

org131V. Fock Institute for Physics, St. Petersburg State University, St.
Petersburg, Russia

org132Variable Energy Cyclotron Centre, Kolkata, India

org133Vinča Institute of Nuclear Sciences, Belgrade, Serbia

org134Warsaw University of Technology, Warsaw, Poland

org135Wayne State University, Detroit, Michigan, United States

org136Wigner Research Centre for Physics, Hungarian Academy of Sciences,
Budapest, Hungary

org137Yale University, New Haven, Connecticut, United States

org138Yonsei University, Seoul, South Korea

org139Zentrum für Technologietransfer und Telekommunikation (ZTT),
Fachhochschule Worms, Worms, Germany