2019 202 18 September

3He elliptic flow in Pb–Pb collisions

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

The elliptic flow ($v_{2}$) of (anti-)3He is measured in Pb–Pb collisions at
$\sqrt{s_{\mathrm{NN}}}$ = 5.02 TeV in the transverse-momentum ($p_{\rm T}$)
range of 2–6 GeV/c for the centrality classes 0–20$\%$, 20–40$\%$, and
40–60$\%$ using the event-plane method. This measurement is compared to that
of pions, kaons, and protons at the same center-of-mass energy. A clear mass
ordering is observed at low $p_{\rm T}$, as expected from relativistic
hydrodynamics. The violation of the scaling of $v_{2}$ with the number of
constituent quarks at low $p_{\rm T}$, already observed for identified hadrons
and deuterons at LHC energies, is confirmed also for (anti-)3He. The elliptic
flow of (anti-)3He is underestimated by the Blast-Wave model and overestimated
by a simple coalescence approach based on nucleon scaling. The elliptic flow
of (anti-)3He measured in the centrality classes 0–20$\%$ and 20–40$\%$ is
well described by a more sophisticated coalescence model where the phase-space
distributions of protons and neutrons are generated using the iEBE-VISHNU
hybrid model with AMPT initial conditions.

##  1 Introduction

The primary goal of studying ultra-relativistic heavy-ion collisions is to
investigate the properties of the Quark–Gluon Plasma (QGP), a phase of matter
made of deconfined quarks and gluons, which is created under extreme
conditions of high temperature and energy density. At the Large Hadron
Collider (LHC), the QGP can be studied in a region of the phase diagram where
a cross-over transition from the deconfined phase to ordinary nuclear matter
is expected based on Quantum Chromodynamics (QCD) calculations on the lattice
[1, 2, 3].

In ultra-relativistic heavy-ion collisions, light nuclei, hypernuclei, and
their antiparticles are produced in addition to other particle species. The
production mechanism of these loosely bound composite objects in heavy-ion
collisions is not clear and is still under debate. Two phenomenological models
are typically used to describe the light (anti-)(hyper-)nuclei production: the
statistical hadronization model [4, 5, 6, 7, 8, 9] and the coalescence
approach [10, 11, 12, 13]. In the former, light nuclei are assumed to be
emitted by a source in local thermal and hadrochemical equilibrium and their
abundances are fixed at chemical freeze-out. This model reproduces the light-
flavored hadron yields measured in central nucleus–nucleus collisions,
including those of (anti-)nuclei and (anti-)hypernuclei [4]. However, the
detailed mechanism of hadron production and the explanation of the propagation
of loosely-bound states through the hadron gas phase without a significant
reduction in their yields are not addressed by this model. It has been
conjectured that such objects could be produced at the phase transition as
compact colorless quark clusters which are expected to interact little with
the surrounding matter [8]. In the coalescence approach, light nuclei are
assumed to be formed by the coalescence of protons and neutrons which are
close in phase-space at kinetic freeze-out [11]. In the simple version of this
model, nucleons are treated as point-like particles and the coalescence
process is assumed to happen if the difference between their momenta is
smaller than a given threshold, typically of the order of 100 MeV/c, which is
a free parameter of the model, while space coordinates are ignored. On the
contrary, in the state-of-the-art implementations of the coalescence approach,
the quantum-mechanical properties of nucleons and nuclei are taken into
account and the coalescence probability is calculated from the overlap between
the wave functions of protons and neutrons which are mapped onto the Wigner
density of the nucleus. The phase-space distributions of protons and neutrons
at the kinetic freeze-out are generated from particle production models, such
as A Multi-Phase Transport Model (AMPT) [14], or from hydrodynamical
simulations coupled to hadronic transport models [13]. The advanced
coalescence model qualitatively describes the deuteron-to-proton and 3He-to-
proton ratios measured in different collision systems as a function of the
charged-particle multiplicity [15], while the simple coalescence approach
provides a description of $p_{\rm T}$ spectra of light (anti-)nuclei measured
in high-energy hadronic collisions only in the low-multiplicity regime [16].

A key observable to study the production mechanism of light (anti-)nuclei is
the elliptic flow, i.e. the second harmonic ($v_{2}$) of the Fourier
decomposition of their azimuthal production distribution with respect to a
collision symmetry plane. The latter is defined by the impact parameter of the
incoming nuclei and the beam direction [17]. The elliptic flow of light nuclei
was measured by PHENIX [18] and STAR [19] at the Relativistic Heavy Ion
Collider (RHIC). The centrality dependence of $v_{2}$ for deuterons (d) and
antideuterons ($\overline{\mathrm{d}}$) was found to be qualitatively similar
to that of identified hadrons [19]. An approximate atomic mass number ($A$)
scaling was observed for the elliptic flow of light nuclei when compared to
the proton $v_{2}$ up to $p_{\mathrm{T}}/A=1.5\ \mathrm{GeV}/\textit{c}$, with
slight deviations for higher $p_{\mathrm{T}}/A$ [19]. The flow of identified
hadrons is often described using the Blast-Wave model [20, 21, 22]. This is a
model inspired by hydrodynamics, which assumes that the system produced in
heavy-ion collisions is locally thermalized and expands collectively with a
common velocity field. The system undergoes a kinetic freeze-out at the
temperature $T_{\mathrm{kin}}$ and is characterized by a common transverse
radial flow velocity ($\beta$) at the freeze-out surface. The Blast-Wave
model, however, fails in reproducing the $v_{2}$ of light nuclei measured in
Au–Au collisions at $\sqrt{s_{\mathrm{NN}}}$ = 200 GeV [19], which is instead
well described by a more sophisticated coalescence model where the phase-space
distributions of nucleons are generated using the string-melting version of
AMPT [14].

The elliptic flow of d and $\overline{\mathrm{d}}$ was measured by the ALICE
Collaboration in Pb–Pb collisions at $\sqrt{s_{\mathrm{NN}}}$ = 2.76 TeV in
the transverse-momentum range $0.8\ \leq p_{\mathrm{T}}<5\
\mathrm{GeV}/\textit{c}$ for different centrality classes [23]. The scaling of
$v_{2}$ with the number of constituent quarks ($n_{\mathrm{q}}$) is violated
for identified hadrons including deuterons, with deviations up to $20\%$ [23].
Predictions from simultaneous fits of the $p_{\rm T}$ spectra and the $v_{2}$
of charged pions, kaons, and protons using a Blast-Wave model provide a good
description of the $v_{2}$ of deuterons in the measured $p_{\rm T}$ range for
all centralities, consistent with common kinetic freeze-out conditions [23]. A
simple coalescence model, based on the $A$-scaling of $v_{2}$ [24], fails in
reproducing the data for all centralities and in the entire $p_{\rm T}$ range
[23]. The data are fairly well described by a coalescence approach which uses
as an input the phase-space distributions generated with the default AMPT
settings [13]. However, this model does not describe the coalescence parameter
$B_{2}$, defined as the ratio between the invariant yield of deuterons and the
square of the invariant yield of protons [23]. The predictions obtained using
the string-melting version of AMPT, which described RHIC data, are not
consistent with the ALICE measurement [23].

The first measurement of the (anti-)3He elliptic flow in Pb–Pb collisions at
$\sqrt{s_{\mathrm{NN}}}$ = 5.02 TeV is presented in this paper. This
measurement complements the picture obtained from that of the proton and
deuteron flow at LHC energies.

##  2 Experimental apparatus and data sample

ALICE is one of the four big experiments at the LHC dedicated to the study of
heavy-ion collisions at ultra-relativistic energies. A detailed description of
the ALICE apparatus and its performance can be found in Refs. [25] and [26].

Trajectories of charged particles are reconstructed in the ALICE central
barrel with the Inner Tracking System (ITS) [25] and the Time Projection
Chamber (TPC) [27]. These are located within a large solenoidal magnet,
providing a highly homogeneous magnetic field of 0.5 T parallel to the beam
line. The ITS consists of six cylindrical layers of silicon detectors with a
total pseudorapidity coverage $|\eta|<0.9$ with respect to the nominal
interaction region. The ITS is used in the determination of primary and
secondary vertices, and in the track reconstruction. The TPC is the largest
detector in the ALICE central barrel, with a pseudorapidity coverage
$|\eta|<0.9$. It is used for track reconstruction, charged-particle momentum
measurement and for particle identification via the measurement of the
specific energy loss of particles in the TPC gas. The transverse-momentum
resolution ranges from about 1$\%$ at 1 GeV/c to about 10$\%$ at 50 GeV/c in
Pb–Pb collisions at $\sqrt{s_{\mathrm{NN}}}$ = 2.76 TeV [26] and at
$\sqrt{s_{\mathrm{NN}}}$ = 5.02 TeV [28]. The $\textrm{d}E/\textrm{d}x$
resolution depends on centrality and is in the range 5–6.5$\%$ for minimum
ionizing particles crossing the full volume of the TPC [26]. Collision events
are triggered by two plastic scintillator arrays, V0A and V0C [29], located on
both sides of the interaction point, covering the pseudorapidity regions
$-3.7<\eta<-1.7$ and 2.8 $<\eta<$ 5.1. Each V0 array consists of four rings in
the radial direction, with each ring comprising eight cells with the same
azimuthal size. The V0 scintillators are used to determine the collision
centrality from the measured charged-particle multiplicity [30, 31], and to
measure the orientation of the symmetry plane of the collision.

The data used for this analysis were collected in 2015 during the LHC Pb–Pb
run at $\sqrt{s_{\mathrm{NN}}}$ = 5.02 TeV. A minimum bias event trigger was
used, which requires coincident signals in the V0 detectors synchronous with
the bunch crossing time defined by the LHC clock.

##  3 Data analysis

###  3.1 Event selection

In order to keep the conditions of the detectors as uniform as possible and
reject background collisions, the coordinate of the primary vertex along the
beam axis is required to be within 10 cm from the nominal interaction point.
Collisions with multiple primary vertices are tagged as pile-up events and
rejected. A centrality-dependent non-uniformity in the angular distribution of
the symmetry plane, of maximum $6\%$ is found. In order to correct for this
non-uniformity, the events are re-weighted based on the collision centrality
($C$) and the angle of the symmetry plane $\Psi_{\mathrm{2}}$. The weight for
a given two-dimensional cell ($C$,$\Psi_{\mathrm{2}}$) is defined as the ratio
between the average number of events, for all $C$ and $\Psi_{\mathrm{2}}$, and
the actual number of events in the same two-dimensional cell. The centrality
classes used for the analysis presented in this Letter are 0–20$\%$,
20–40$\%$, and 40–60$\%$. In total, approximately 20 million events are
selected in each centrality class.

###  3.2 Track selection and particle identification

(Anti-)3He candidates are selected from the charged-particle tracks
reconstructed in the ITS and TPC in the kinematic range $p_{\rm T}$ $/|z|$
$>1\ \mathrm{GeV}/\textit{c}$ and $|\eta|<0.8$, where $z$ is the particle
electric charge in units of the elementary charge. Tracks are required to have
a minimum number of clusters in the TPC, $N_{\mathrm{cls}}^{\mathrm{TPC}}$, of
at least 70 out of a maximum of 159, and in the ITS,
$N_{\mathrm{cls}}^{\mathrm{ITS}}$, of at least two with one cluster located in
any of the two innermost ITS layers. The number of TPC clusters used in the
$\textrm{d}E/\textrm{d}x$ calculation,
$N_{\mathrm{cls}}^{\mathrm{TPC}}\left(\mathrm{d}E/\mathrm{d}x\right)$ is
required to be larger than 50. Good quality of the track fit is also required,
expressed by $\chi^{2}/N_{\mathrm{cls}}^{\mathrm{TPC}}<4$ and a ratio of the
number of TPC clusters attached to the track over the number of findable TPC
clusters (accounting for track length, location, and momentum) larger than
80$\%$. The contribution from secondary tracks is reduced by requiring a
maximum Distance of Closest Approach (DCA) to the primary vertex in the
transverse plane ($\mathrm{DCA}_{\mathrm{xy}}<0.1$ cm) and in the longitudinal
direction ($\mathrm{DCA}_{\mathrm{z}}<1$ cm). These selection criteria ensure
a high track-reconstruction efficiency, which is larger than $80\%$, and a
resolution in the $\textrm{d}E/\textrm{d}x$ measured in the TPC of about $6\%$
in the centrality and $p_{\rm T}$ ranges used for this measurement.

The expected average $\textrm{d}E/\textrm{d}x$ for (anti-)3He,
$\langle\mathrm{d}E/\mathrm{d}x\rangle_{{}^{3}\mathrm{He}}$, is given by the
Bethe formula and the standard deviation of the distribution of
$\textrm{d}E/\textrm{d}x$ $-$
$\langle\mathrm{d}E/\mathrm{d}x\rangle_{{}^{3}\mathrm{He}}$, denoted
$\sigma^{{}^{3}\mathrm{He}}_{\mathrm{d}E/\mathrm{d}x}$, is the TPC
$\textrm{d}E/\textrm{d}x$ resolution measured for (anti-)3He. For the
(anti-)3He identification, the $\textrm{d}E/\textrm{d}x$ measured in the TPC
is required to be within
3$\sigma^{{}^{3}\mathrm{He}}_{\mathrm{d}E/\mathrm{d}x}$from the expected
average for 3He. The distributions of
$\left(\mathrm{d}E/\mathrm{d}x-\langle\mathrm{d}E/\mathrm{d}x\rangle_{{}^{3}\mathrm{He}}\right)/\sigma^{{}^{3}\mathrm{He}}_{\mathrm{d}E/\mathrm{d}x}$
for the transverse-momentum ranges $2\ \leq p_{\mathrm{T}}<3\
\mathrm{GeV}/\textit{c}$ and $3\ \leq p_{\mathrm{T}}<4\
\mathrm{GeV}/\textit{c}$ are shown in Fig. 1. The range used for the
(anti-)3He selection is indicated by the vertical black-dotted lines. The
contamination by (anti-)3H is estimated by fitting the measured
$\left(\mathrm{d}E/\mathrm{d}x-\langle\mathrm{d}E/\mathrm{d}x\rangle_{{}^{3}\mathrm{He}}\right)/\sigma^{{}^{3}\mathrm{He}}_{\mathrm{d}E/\mathrm{d}x}$
distribution in a given $p_{\rm T}$ range using two Gaussian functions, one
for (anti-)3H and the other for (anti-)3He. The (anti-)3H contribution is
subtracted from the distribution to extract the (anti-)3He signal in the range
within $\pm$3$\sigma^{{}^{3}\mathrm{He}}_{\mathrm{d}E/\mathrm{d}x}$. The
contamination from (anti-)3H is negligible for $p_{\mathrm{T}}>3\
\mathrm{GeV}/\textit{c}$ (see right panel of Fig. 1). The contamination from
(anti-)4He is expected to be negligible over the full $p_{\rm T}$ range
considering that its production rate measured in Pb–Pb collisions at
$\sqrt{s_{\mathrm{NN}}}$ = 2.76 TeV is suppressed compared to that of
(anti-)3He by a factor $\sim 300$ [32].

Figure 1: Distributions of
$\left(\mathrm{d}E/\mathrm{d}x-\langle\mathrm{d}E/\mathrm{d}x\rangle_{{}^{3}\mathrm{He}}\right)/\sigma^{{}^{3}\mathrm{He}}_{\mathrm{d}E/\mathrm{d}x}$
measured in the TPC for the transverse-momentum ranges $2\ \leq
p_{\mathrm{T}}<3\ \mathrm{GeV}/\textit{c}$ (left) and $3\ \leq
p_{\mathrm{T}}<4\ \mathrm{GeV}/\textit{c}$ (right). The vertical bars
represent the statistical uncertainties of the data. The blue dotted and the
red dash-dotted lines indicate the 3H and 3He contributions while the black
solid lines show the sum of both. The ranges used for the signal extraction
are indicated by the vertical black-dotted lines.

###  3.3 Secondary 3He from spallation processes

The main background for this measurement is represented by secondary 3He
produced by spallation reactions in the interactions between primary particles
and nuclei in the detector material or in the beam pipe. This background
source is relevant only for 3He, while this effect is negligible for anti-3He.
Nuclear fragments emitted in spallation processes have almost uniform angular
distributions with respect to the direction of the incoming particle, while
primary 3He tracks originate from the primary vertex. The contribution of
secondary 3He produced by spallation can be investigated from the
$\mathrm{DCA}_{\mathrm{xy}}$ distribution, which has a peak around zero for
primary 3He and is almost flat for secondary 3He. The
$\mathrm{DCA}_{\mathrm{xy}}$ distributions for 3He candidates measured in the
transverse-momentum ranges $2\ \leq p_{\mathrm{T}}<3\ \mathrm{GeV}/\textit{c}$
and $3\ \leq p_{\mathrm{T}}<4\ \mathrm{GeV}/\textit{c}$ are shown in Fig. 2.
The sign of the $\mathrm{DCA}_{\mathrm{xy}}$ is positive if the primary vertex
is inside the track curvature and negative if it lies outside. These
distributions are obtained by selecting tracks with
$|\mathrm{DCA}_{\mathrm{z}}|<$ 1 cm and applying a stricter requirement for
the selection of 3He candidates, given by $-2\leq$
$\left(\mathrm{d}E/\mathrm{d}x-\langle\mathrm{d}E/\mathrm{d}x\rangle_{{}^{3}\mathrm{He}}\right)/\sigma^{{}^{3}\mathrm{He}}_{\mathrm{d}E/\mathrm{d}x}$
$<3$. This asymmetric range is used to increase the purity of the 3He sample
by suppressing the 3H contamination. The contribution from secondary 3He
produced by spallation is found to be relevant in this analysis only in the
transverse-momentum range $2\ \leq p_{\mathrm{T}}<3\ \mathrm{GeV}/\textit{c}$.

Figure 2: $\mathrm{DCA}_{\mathrm{xy}}$ distributions of 3He candidates,
selected requiring $-2$ $<$
$\left(\mathrm{d}E/\mathrm{d}x-\langle\mathrm{d}E/\mathrm{d}x\rangle_{{}^{3}\mathrm{He}}\right)/\sigma^{{}^{3}\mathrm{He}}_{\mathrm{d}E/\mathrm{d}x}$
$<$ 3, with $|\mathrm{DCA}_{\mathrm{z}}|<1$ cm measured in the transverse-
momentum intervals $2\ \leq p_{\mathrm{T}}<3\ \mathrm{GeV}/\textit{c}$ (blue)
and $3\ \leq p_{\mathrm{T}}<4\ \mathrm{GeV}/\textit{c}$ (red).

For the measurement presented in this Letter, ${}^{3}\overline{\mathrm{He}}$
are used for $2\ \leq p_{\mathrm{T}}<3\ \mathrm{GeV}/\textit{c}$, while the
sum of 3He and ${}^{3}\overline{\mathrm{He}}$ is used for higher $p_{\rm T}$
where the contribution from secondary 3He from spallation is negligible. This
is possible because the elliptic flow of ${}^{3}\mathrm{He}$ and
${}^{3}\overline{\mathrm{He}}$ are consistent within the statistical
uncertainties in the $p_{\rm T}$ range where these two measurements can be
compared, i.e. $p_{\mathrm{T}}>3\ \mathrm{GeV}/\textit{c}$, and in all
centrality intervals. A vanishing difference between the elliptic flow of
matter and antimatter nuclei at LHC energies is already observed for
(anti-)protons [33, 34] and (anti-)deuterons [23]. This observation is
consistent with the decreasing trend of the difference between the elliptic
flow of protons and antiprotons, deuterons and antideuterons with increasing
center-of-mass energy at RHIC going from $\sqrt{s_{\mathrm{NN}}}$ = 7.7 GeV to
$\sqrt{s_{\mathrm{NN}}}$ = 200 GeV [35].

###  3.4 The event-plane method

The initial spatial anisotropy of the hot and dense matter created in non-
central nucleus–nucleus collisions results in an azimuthal anisotropy of
particle emission with respect to the symmetry plane. The azimuthal
distribution of the emitted particles can be expressed as a Fourier series
[36]

$\frac{\mathrm{d}N}{\mathrm{d}\varphi}\propto 1+2\sum_{n\geq
1}v_{n}\mathrm{cos}\big{(}n\big{(}\varphi-\Psi_{\mathrm{n}}\big{)}\big{)},$
(1)

where $\Psi_{\mathrm{n}}$ indicates the orientation of the $n$th symmetry
plane, $\varphi$ is the azimuthal angle of a particle, and the Fourier
coefficients $v_{n}$ are also referred to as the flow coefficients.

Experimentally, the true symmetry plane can only be reconstructed
approximately because of the finite detector resolution. The measured symmetry
plane is called ‘event plane’. The elliptic flow of (anti-)3He is measured
using the Event-Plane (EP) method [37]. The $v_{2}$ of (anti-)3He in each
$p_{\rm T}$ range is given by

$v_{2}\\{\mathrm{EP},|\Delta\eta|>0.9\\}\left(p_{\mathrm{T}}\right)=\frac{\pi}{4R_{\Psi_{2}}}\frac{N_{\mathrm{in\mathchar
45\relax plane}}\left(p_{\mathrm{T}}\right)-N_{\mathrm{out\mathchar 45\relax
of\mathchar 45\relax
plane}}\left(p_{\mathrm{T}}\right)}{N_{\mathrm{in\mathchar 45\relax
plane}}\left(p_{\mathrm{T}}\right)+N_{\mathrm{out\mathchar 45\relax
of\mathchar 45\relax plane}}\left(p_{\mathrm{T}}\right)},$ (2)

where the $|\Delta\eta|$ represents the minimal pseudorapidity gap between the
V0 detectors and the TPC, the $R_{\Psi_{2}}$ is the event-plane resolution for
the second harmonic, and $N_{\mathrm{in\mathchar 45\relax plane}}$ and
$N_{\mathrm{out\mathchar 45\relax of\mathchar 45\relax plane}}$ are the number
of (anti-)3He candidates in-plane and out-of-plane, respectively. Particles
are regarded as ‘in-plane’ if the azimuthal difference
$|\Delta\varphi|=|\varphi-\Psi_{2}^{\mathrm{EP}}|<45^{\circ}$ or
$|\Delta\varphi|=|\varphi-\Psi_{2}^{\mathrm{EP}}|>135^{\circ}$, and ‘out-of-
plane’ otherwise, where $\Psi_{2}^{\mathrm{EP}}$ is the orientation of the
event plane. The latter is reconstructed using the V0 detectors. The
calibrated amplitude of the signal measured in each cell of the V0 arrays is
used as a weight $w_{\mathrm{cell}}$ in the construction of the flow vector
$Q_{2}$ [37]

$Q_{2}=\sum_{j=1}^{N_{\mathrm{cell}}}w_{\mathrm{cell}}\cdot\mathrm{exp}(i2\varphi_{\mathrm{cell}})$
(3)

where $N_{\mathrm{cell}}$ is the number of cells of the V0 detectors and
$\varphi_{\mathrm{cell}}$ is the azimuthal angle of the geometric center of
each cell. In order to account for a non-uniform detector response which can
generate a bias in the $\Psi_{2}^{\mathrm{EP}}$ distribution, the components
of the $Q_{2}$-vector are adjusted using a re-centering procedure [38] . The
orientation of the event plane angle is obtained using the real and imaginary
parts of $Q_{2}$

$\Psi_{2}^{\mathrm{EP}}=\frac{1}{2}\mathrm{arctan}\left(\frac{Im(Q_{n})}{Re(Q_{n})}\right)$
(4)

The event-plane resolution $R_{\Psi_{2}}$ is calculated using the three sub-
event correlation technique with charged particles [37]

$R_{\Psi_{2}}=\sqrt{\frac{\langle\mathrm{cos}\left(2\left(\Psi_{2}^{\mathrm{A}}-\Psi^{\mathrm{B}}_{2}\right)\right)\rangle\cdot\langle\mathrm{cos}\left(2\left(\Psi_{2}^{\mathrm{A}}-\Psi^{\mathrm{C}}_{2}\right)\right)\rangle}{\langle\mathrm{cos}\left(2\left(\Psi_{2}^{\mathrm{B}}-\Psi^{\mathrm{C}}_{2}\right)\right)\rangle}},$
(5)

where A refers to the event plane measured using the V0 detectors, while B and
C refer to those obtained in the positive ($\eta>0$) and negative ($\eta<0$)
pseudorapidity regions of the TPC. For the latter two measurements, a set of
reconstructed charged tracks with $0.2\ \leq p_{\mathrm{T}}<20\
\mathrm{GeV}/\textit{c}$ and $|\eta|<0.8$ is used. Minimal quality criteria
are applied to these tracks, such as the requirement of having a number of TPC
clusters larger than 70 and a $\chi^{2}/N_{\mathrm{cls}}^{\mathrm{TPC}}<4$.
The second harmonic event-plane resolution as a function of the collision
centrality is shown in Fig. 3.

Figure 3: Event-plane resolution $R_{\Psi_{2}}$ of the second harmonic as a
function of the collision centrality.

Considering the centrality dependence of $R_{\Psi_{2}}$, the elliptic flow
measurements are performed in centrality intervals of 5$\%$ width for the
range 0–40$\%$, and of 10$\%$ width for the range 40–60$\%$. The latter two
intervals are larger due to the limited number of (anti-)3He candidates. The
resolutions for the centrality ranges 40–50$\%$ and 50–60$\%$ are given by the
weighted averages of the resolutions calculated in centrality bins of 5$\%$
width, with the number of charged tracks in the corresponding centrality
ranges as a weight. Finally, the elliptic flow measurements for the wider
centrality classes used in this analysis are obtained as weighted averages of
the measurements in the smaller centrality ranges

$v_{2}\left(p_{\mathrm{T}}\right)=\frac{\sum_{i}v_{2}^{i}\left(p_{\mathrm{T}}\right)\cdot
N^{i}_{(\mathrm{anti}\mathchar
45\relax)^{3}\mathrm{He}}\left(p_{\mathrm{T}}\right)}{\sum_{i}N^{i}_{(\mathrm{anti}\mathchar
45\relax)^{3}\mathrm{He}}\left(p_{\mathrm{T}}\right)},$ (6)

where $v_{2}^{i}\left(p_{\mathrm{T}}\right)$ is the elliptic flow measured in
a given $p_{\rm T}$ range and in the centrality interval $i$, and
$N^{i}_{(\mathrm{anti}\mathchar 45\relax)^{3}\mathrm{He}}$ is the number of
(anti-)3He candidates for the same centrality and $p_{\rm T}$ range.

##  4 Systematic uncertainties

The main sources of systematic uncertainties in this measurement are related
to the event selection criteria, track reconstruction, particle
identification, occupancy effects in the TPC, and the subtraction of the feed-
down contribution from weak decays of hypertritons. Except for the systematic
uncertainty due to the event selection, all other contributions are estimated
using Monte Carlo (MC) simulations based on the HIJING generator [39].
Simulated events are enriched by an injected sample of (anti-)(hyper-)nuclei
generated with a flat $p_{\rm T}$ distribution in the transverse-momentum
range $0<p_{\mathrm{T}}<10\ \mathrm{GeV}/\textit{c}$ and a flat rapidity
distribution in the range $-1<y<1$. The interactions of the generated
particles with the experimental apparatus are modeled by GEANT 3 [40]. The
input transverse-momentum distribution of injected (anti-)3He is corrected
using centrality and $p_{\rm T}$-dependent weights to reproduce its measured
shape, which is described by the Blast-Wave function. The parameters are taken
from the (anti-)3He measurement in Pb–Pb collisions at
$\sqrt{s_{\mathrm{NN}}}$ = 2.76 TeV [41] assuming the same spectral shape in
Pb–Pb collisions at $\sqrt{s_{\mathrm{NN}}}$ = 5.02 TeV. The systematic
uncertainties estimated using the MC simulations are found to be independent
on the input parametrization of the (anti-)3He spectrum. A good matching
between the distributions of variables used for track selection and particle
identification is found between data and MC simulations. This guarantees the
reliability of the detector response description and of the systematic
uncertainties obtained based on MC simulations.

###  4.1 Systematic uncertainties due to the event selection criteria

The effect of different event selection criteria is studied by comparing the
$v_{2}$ measurements obtained by varying the selection range of the
$z$-coordinate of the primary vertex, using different centrality estimators,
selecting events corresponding to opposite magnetic field orientations, using
different pile-up rejection criteria, and selecting events with different
interaction rates. The limited number of (anti-)3He candidates prevents the
estimation of this source of systematic uncertainties from data since the
$v_{2}$ measurements obtained using these different selection criteria are
consistent within their statistical uncertainties, i.e. the systematic
uncertainties are comparable to or smaller than the statistical ones. The
systematic uncertainty related to event selection criteria is assumed to be
identical to that of the proton $v_{2}$ measured in Pb–Pb collisions at
$\sqrt{s_{\mathrm{NN}}}$ = 5.02 TeV and it is taken from Ref. [34]. The total
systematic uncertainty due to the event selection is $2.7\%$ and is obtained
by adding all contributions in quadrature.

###  4.2 Systematic uncertainties due to tracking and particle identification

The systematic uncertainties due to track reconstruction and particle
identification are estimated using MC simulations. This is done to benefit
from the larger number of (anti-)3He in the simulation as compared to data to
reduce the interference between statistical fluctuations and systematic
uncertainties. The same azimuthal asymmetry as measured in data in each
centrality and $p_{\rm T}$ range is artificially created for the injected
(anti-)3He with respect to a randomly oriented event plane by rejecting a
fraction of the out-of-plane (anti-)3He. This is done because the injected
(anti-)3He are produced with $v_{2}=0$ by the MC generator. The $v_{2}$ of the
embedded (anti-)3He is then measured using the reconstructed tracks in the
simulation. Different track selection criteria and signal extraction ranges
are used to measure the $v_{2}$, in which the analysis parameters are selected
randomly inside a range around the default value using a uniform probability
distribution. The different selection criteria are varied simultaneously in
order to include the effects of their possible correlations. In each
centrality class and for each transverse-momentum range, the measurements
obtained using different selection criteria follow a Gaussian distribution
whose standard deviation is very similar to the statistical uncertainty,
indicating a residual correlation between systematic variations and
statistical fluctuations. Assuming that the spread of the different
measurements is only due to statistical fluctuations, the mean of the Gaussian
distribution is considered as the best estimate of the reconstructed $v_{2}$.
The difference between the injected $v_{2}$ in the simulation and the mean of
the Gaussian spread of the measurements is taken as the systematic uncertainty
due to tracking and PID. This uncertainty ranges between 1$\%$ and 4$\%$,
depending on $p_{\rm T}$ and centrality. An additional component to the
tracking uncertainty originates from the difference between the $v_{2}$
measured using the positive and negative pseudorapidity regions of the TPC.
This contribution cannot be estimated from data due to the limited number of
(anti-)3He and is assumed to be identical to that of the proton $v_{2}$
measurement, which is $2\%$ [34]. The latter is added in quadrature to the
systematic uncertainties related to tracking and particle identification.

###  4.3 Systematic uncertainty due to occupancy effects in the TPC

Different reconstruction efficiencies for in-plane and out-of-plane particles,
due to occupancy effects in the TPC, can create a bias in the $v_{2}$
measurement. This effect is studied using MC simulations by comparing the
reconstruction efficiency for different charged-particle multiplicities. The
same track selection criteria used in data are applied to the reconstructed
tracks in the simulation for the efficiency calculation. The maximum deviation
between the reconstruction efficiencies for different multiplicities is
$0.5\%$, corresponding to a ratio between in-plane and out-of-plane
efficiencies of $r=0.995\pm 0.001$. The difference between the $v_{2}$
measured assuming $r=1$ and $r=0.995$ corresponds to the maximum variation
range of $v_{2}$. The systematic uncertainty from occupancy is then given by
this maximum difference divided by $\sqrt{12}$, assuming a uniform
distribution. This uncertainty decreases with increasing $p_{\rm T}$ and
yields at maximum $2\%$ for the centrality range 0–20$\%$ and $0.5\%$ for the
centrality ranges 20–40$\%$ and 40–60$\%$.

###  4.4 Systematic uncertainty due to the feed-down subtraction

The feed-down systematic uncertainty is due to the unknown $v_{2}$ of
(anti-)3He from the weak decay of the (anti-)${}^{3}_{\Lambda}$H. The fraction
of secondary (anti-)3He from the (anti-)${}^{3}_{\Lambda}$H decays in the
reconstructed track sample is calculated using MC simulations. This fraction
is about $6\%$ for the centrality range 0–20$\%$ and $\sim 5\%$ for the
centrality ranges 20–40$\%$ and 40–60$\%$, slightly increasing with $p_{\rm
T}$. The relative abundances of (anti-)${}^{3}_{\Lambda}$H and (anti-)3He in
the simulation are adjusted to the measured values in Pb–Pb collisions at
$\sqrt{s_{\mathrm{NN}}}$ = 2.76 TeV [42], assuming that the yield ratio
between (anti-)${}^{3}_{\Lambda}$H and (anti-)3He does not differ
significantly from that in Pb–Pb collisions at $\sqrt{s_{\mathrm{NN}}}$ = 5.02
TeV, which is not published yet. The $v_{2}$ of (anti-)3He from the
(anti-)${}^{3}_{\Lambda}$H decay is assumed to be within the range of $\pm
50\%$ with respect to the $v_{2}$ of the inclusive (anti-)3He. This variation
is selected to provide a conservative estimate of the feed-down uncertainty.
For each of these extremes, the feed-down contribution is subtracted. The
systematic uncertainty due to the feed-down subtraction is given by the
difference between these two limits divided by $\sqrt{12}$. This uncertainty
is $\sim 2\%$ in all centrality ranges, almost independent of $p_{\rm T}$.

The different contributions to the systematic uncertainties of this
measurement are summarized in Table 1.

Table 1: Summary of systematic uncertainties. The ranges represent the minimum and maximum uncertainties in the case where the systematic uncertainties depend on $p_{\rm T}$ and centrality.  Source of systematic uncertainty |  |  | value ($\%$)
---|---|---|---
Primary vertex selection |  |  | 1
Centrality estimator |  |  | 1.5
Magnetic field orientation |  |  | 1
Pile-up rejection |  |  | 1
Interaction rate |  |  | 1.5
Tracking and particle identification |  |  | $2-4.5$
Occupancy in the TPC |  |  | $0.5-2$
Feed-down |  |  | $2$
Total |  |  | $4-6$

##  5 Results

###  5.1 Experimental results

The elliptic flow of (anti-)3He measured in Pb–Pb collisions at
$\sqrt{s_{\mathrm{NN}}}$ = 5.02 TeV for the centrality classes 0–20$\%$,
20–40$\%$ and 40–60$\%$ is shown in Fig. 4 as a function of $p_{\rm T}$. The
measurement in the transverse-momentum range $2<p_{\mathrm{T}}<3\
\mathrm{GeV}/\textit{c}$ is done using only ${}^{3}\overline{\mathrm{He}}$. An
increasing elliptic flow is observed going from central to semi-central
collisions, as expected. This is due to the increasing azimuthal asymmetry of
the overlap region of the colliding nuclei at the initial collision stage,
which results in a larger azimuthal asymmetry of the momenta of the final-
state particles. In each centrality class, the elliptic flow increases with
$p_{\rm T}$ in the measured $p_{\rm T}$ range.

Figure 4: Elliptic flow ($v_{2}$) of (anti-)3He measured in Pb–Pb collisions
at $\sqrt{s_{\mathrm{NN}}}$ = 5.02 TeV for the centrality classes 0–20$\%$,
20–40$\%$, and 40–60$\%$. The statistical uncertainties are shown as vertical
bars, systematic uncertainties as boxes.

The (anti-)3He elliptic flow is compared to that of pions, kaons, and protons
measured using the scalar-product method at the same center-of-mass energy
[34] in Fig. 5. Given the good event-plane resolution shown in Fig. 3 and the
large statistical uncertainties of the (anti-)3He $v_{2}$ measurements, the
difference between the scalar-product and event-plane method to calculate the
(anti-)3He elliptic flow is negligible. The $v_{2}$ of pions, kaons, and
protons is measured in smaller centrality ranges compared to those used in
this analysis. The corresponding $v_{2}$ for the centrality classes 0–20$\%$,
20–40$\%$, and 40–60$\%$ are obtained as weighted averages of the $v_{2}$
measured in smaller centrality classes using the $p_{\rm T}$ spectra taken
from [43] as weights. A clear mass ordering is observed for $p_{\mathrm{T}}<3\
\mathrm{GeV}/\textit{c}$, consistent with the expectations from relativistic
hydrodynamics [44]. The $v_{2}$ of (anti-)3He shows a slower rise with $p_{\rm
T}$ compared to that of pions, kaons, and protons due to its larger mass.

Figure 5: Comparison between the elliptic flow of (anti-)3He measured using
the event-plane method and that of pions, kaons, and protons measured using
the scalar-product method in Pb–Pb collisions at $\sqrt{s_{\mathrm{NN}}}$ =
5.02 TeV for the centrality classes 0–20$\%$ (left), 20–40$\%$ (middle) and
40–60$\%$ (right). See text for details. Vertical bars and boxes represent the
statistical and systematic uncertainties, respectively.

The comparisons between the measurements of $v_{2}/n_{\mathrm{q}}$ of
(anti-)3He, pions, kaons, and protons are shown in Fig. 6 as a function of
$p_{\mathrm{T}}/n_{\mathrm{q}}$ (upper panels), and transverse kinetic energy
per constituent quark $E^{\mathrm{kin}}_{\mathrm{T}}/n_{\mathrm{q}}$ (lower
panels). The transverse kinetic energy is defined as
$E^{\mathrm{kin}}_{\mathrm{T}}=\sqrt{m^{2}+p^{2}_{\mathrm{T}}}-m$, where $m$
is the mass of the particle. The violation of $n_{\mathrm{q}}$ scaling for the
measured range of $p_{\mathrm{T}}/n_{\mathrm{q}}\lesssim 0.7\
\mathrm{GeV}/\textit{c}$, already established for the elliptic flow
measurements of identified hadrons at the LHC [45, 34, 23], is observed also
for (anti-)3He. The $n_{\mathrm{q}}$ scaling at larger
$p_{\mathrm{T}}/n_{\mathrm{q}}$ cannot be tested with the limited data sample
used for this analysis.

Figure 6: Comparison between the elliptic flow of pions, kaons, protons, and
(anti-)3He divided by the number of constituent quarks ($n_{\mathrm{q}}$) as a
function of $p_{\mathrm{T}}/n_{\mathrm{q}}$ (upper panels) and transverse
kinetic energy per constituent quark
$E^{\mathrm{kin}}_{\mathrm{T}}/n_{\mathrm{q}}$ (lower panels) for the
centrality classes 0–20$\%$ (left), 20–40$\%$ (middle) and 40–60$\%$ (right).
See text for details. Vertical bars and boxes represent the statistical and
systematic uncertainties, respectively.

###  5.2 Model comparisons

The (anti-)3He $v_{2}$ measurements are compared with the expectations from
the Blast-Wave model and a simple coalescence approach using the same
procedure followed in [23].

The Blast-Wave predictions are obtained from a simultaneous fit of the $v_{2}$
and the $p_{\rm T}$ spectra of pions, kaons, and protons measured in Pb–Pb
collisions at $\sqrt{s_{\mathrm{NN}}}$ = 5.02 TeV [34, 43] in the transverse-
momentum ranges $0.5\leq p^{\pi}_{\mathrm{T}}<1\ \mathrm{GeV}/\textit{c}$,
$0.7\leq p^{\mathrm{K}}_{\mathrm{T}}<2\ \mathrm{GeV}/\textit{c}$, and $0.7\leq
p^{\mathrm{p}}_{\mathrm{T}}<2.5\ \mathrm{GeV}/\textit{c}$, respectively, and
in the same centrality classes. The four parameters of the Blast-Wave fits
represent the kinetic freeze-out temperature ($T_{\mathrm{kin}}$), the mean
transverse expansion rapidity ($\rho_{0}$), the amplitude of its azimuthal
variation ($\rho_{\mathrm{a}}$), and the variation in the azimuthal density of
the source ($s_{2}$), as described in [21]. The values of the Blast-Wave
parameters extracted from the fits are reported in Table 2 for each centrality
interval. The elliptic flow of (anti-)3He is calculated using the parameters
obtained from the simultaneous fit and the 3He mass, i.e., assuming the same
kinetic freeze-out conditions.

Table 2: Blast-Wave parameters extracted from the simultaneous fits of the $p_{\rm T}$ spectra and $v_{2}$ of pions, kaons, and protons. See text for details.  Fit parameters |  | Centrality classes |
---|---|---|---
| 0–20$\%$ | 20–40$\%$ | 40–60$\%$
$T_{\mathrm{kin}}$ (MeV) | $106\pm 1$ | $110\pm 1$ | $117\pm 1$
$\rho_{0}$ $\times 10^{-1}$ | $8.78\pm 0.01$ | $8.92\pm 0.02$ | $7.48\pm 0.01$
$\rho_{\mathrm{a}}$ $\times 10^{-2}$ | $1.37\pm 0.01$ | $2.98\pm 0.01$ | $3.16\pm 0.01$
$s_{2}$ $\times 10^{-2}$ | $4.06\pm 0.01$ | $9.02\pm 0.01$ | $1.29\pm 0.01$

The simple coalescence approach used in this context is based on the
assumption that the invariant yield of (anti-)3He with transverse momentum
$p_{\rm T}$ is proportional to the product of the invariant yields of its
constituent nucleons with transverse momentum $p_{\mathrm{T}}/3$ and on
isospin symmetry, for which the proton and neutron $v_{2}$ are identical.
Considering only elliptical anisotropies of the constituent nucleons, i.e.
neglecting higher order harmonics, the coalescence predictions are obtained
from the elliptic flow of protons $v_{2,\mathrm{p}}$ measured in Pb–Pb
collisions at $\sqrt{s_{\mathrm{NN}}}$ = 5.02 TeV [34] using the scaling law
[46]

$v_{2,^{3}\mathrm{He}}\left(p_{\mathrm{T}}\right)=\frac{3v_{2,\mathrm{p}}\left(p_{\mathrm{T}}/3\right)+3v^{3}_{2,\mathrm{p}}\left(p_{\mathrm{T}}/3\right)}{1+6v^{2}_{2,\mathrm{p}}\left(p_{\mathrm{T}}/3\right)}.$
(7)

Figure 7 shows the comparison of the (anti-)3He $v_{2}$ measurements with the
predictions of the Blast-Wave model and the simple coalescence approach. The
differences between the data and the model for each centrality interval are
shown in the lower panels. These are calculated using the weighted averages of
the models in the same $p_{\rm T}$ intervals of the measurement. For the
Blast-Wave model, the $p_{\rm T}$ spectrum of (anti-)3He measured in Pb–Pb
collisions at $\sqrt{s_{\mathrm{NN}}}$ = 2.76 TeV [41] is used as a weight.
This is justified considering that the (anti-)3He $p_{\rm T}$ spectrum in
Pb–Pb collisions at $\sqrt{s_{\mathrm{NN}}}$ = 5.02 TeV is expected to be
similar to that at $\sqrt{s_{\mathrm{NN}}}$ = 2.76 TeV, as observed for
lighter hadrons [43]. The proton spectrum measured in Pb–Pb collisions at
$\sqrt{s_{\mathrm{NN}}}$ = 5.02 TeV [43], with $p_{\rm T}$ scaled by $A=3$, is
used as a weight for the coalescence model. The data are located between the
two model predictions in all centrality intervals except for more peripheral
collisions, where the coalescence expectations are closer to the data.

Figure 7: Elliptic flow of (anti-)3He in comparison with the predictions from
the Blast-Wave model and a simple coalescence approach for the centrality
classes 0–20$\%$ (left), 20–40$\%$ (middle), and 40–60$\%$ (right). The lower
panels show the differences between data and models for each centrality range.
The statistical uncertainties of the data and the model are added in
quadrature. Vertical bars and boxes represent the statistical and systematic
uncertainties, respectively.

The Blast-Wave model was found to be consistent with the (anti-)deuteron
elliptic flow measured in Pb–Pb collisions at $\sqrt{s_{\mathrm{NN}}}$ = 2.76
TeV in the centrality intervals 0–10$\%$, 10–20$\%$ and 20–40$\%$, although
the (anti-)deuteron $p_{\rm T}$ distributions were slightly underestimated for
$p_{\rm T}$ $<$ 2 GeV/c in the same centrality intervals [23]. Similarly to
the results presented in this paper for (anti-)3He, the predictions from the
simple coalescence model overestimated the (anti-)deuteron $v_{2}$ in all
centrality intervals. In general, the measurements of (anti-)deuteron and
(anti-)3He elliptic flow at the LHC consistently indicate that the simple
coalescence and Blast-Wave models represent the upper and lower edges of a
region where the data are typically located. The (anti-)deuteron elliptic flow
measured in Pb–Pb collisions at $\sqrt{s_{\mathrm{NN}}}$ = 2.76 TeV is simply
closer to the lower side of this region.

The Blast-Wave model is a simplified parametrization of the system expansion
which is typically used to describe the hadron $p_{\rm T}$ spectra and $v_{2}$
with parameters tuned to data. However, this simple model cannot describe the
full collective properties and dynamics of the system. For this, an approach
based on relativistic viscous hydrodynamics coupled to an hadronic afterburner
is needed. The comparison of the measurement presented in this paper with an
actual hydrodynamical simulation is unfortunately not possible because there
are no predictions for (anti-)3He available.

The predictions from a more sophisticated coalescence model [13] are compared
to the data in the centrality ranges 0–20$\%$ and 20–40$\%$ in Fig. 8. The
lower panel shows the differences between the data and the model for these two
centrality intervals calculated taking the weighted average of the model in
each $p_{\rm T}$ range, similarly to what is done for the Blast-Wave and the
simple coalescence predictions in Fig. 7. In this model, the coalescence
probability is given by the superposition of the wave functions of the
coalescing particles, and the Wigner function of the nucleus. The coalescence
happens in a flowing medium, i.e., in the rest frame of the fluid cells. This
introduces space-momentum correlations absent in the naive coalescence
approach. The phase-space distributions of protons and neutrons are generated
from the iEBE-VISHNU hybrid model with AMPT initial conditions [13]. Although
this model underestimates the yield of (anti-)3He measured in Pb–Pb collisions
at $\sqrt{s_{\mathrm{NN}}}$ = 2.76 TeV in the transverse-momentum range of $2\
<p_{\mathrm{T}}<7\ \mathrm{GeV/\textit{c}}$ by almost a factor of two [13], it
is able to reproduce quantitatively the elliptic flow measurements in the
centrality classes 0–20$\%$ and 20–40$\%$ presented here. Moreover, this model
provides a good description of the $p_{\rm T}$ spectra and $p_{\rm
T}$-differential elliptic flow of protons and deuterons for different
centrality intervals in Au–Au collisions at $\sqrt{s_{\mathrm{NN}}}$ = 200 GeV
and in Pb–Pb collisions at $\sqrt{s_{\mathrm{NN}}}$ = 2.76 TeV [13].

Figure 8: Elliptic flow of (anti-)3He measured in the centrality classes
0–20$\%$ and 20–40$\%$ in comparison with the predictions from a coalescence
model based on phase-space distributions of protons and neutrons generated
from the iEBE-VISHNU hybrid model with AMPT initial conditions [13]. The model
predictions are shown as lines and the bands represent their statistical
uncertainties. The differences between data and model are shown in the lower
panel for both centrality classes. The statistical uncertainties of the data
and the model are added in quadrature. Vertical bars and boxes represent the
statistical and systematic uncertainties, respectively.

##  6 Summary

The first measurement of the (anti-)3He elliptic flow in Pb–Pb collisions at
$\sqrt{s_{\mathrm{NN}}}$ = 5.02 TeV is presented. An increasing trend of
$v_{2}$ with $p_{\rm T}$ and one going from central to semi-central Pb–Pb
collisions is observed. This measurement is compared to that of pions, kaons,
and protons at the same center-of-mass energy. A clear mass ordering at low
$p_{\rm T}$ is observed, as expected from relativistic hydrodynamics. The
scaling behavior of $v_{2}$ with the number of constituent quarks is violated
for the measured range of $p_{\mathrm{T}}/n_{\mathrm{q}}\lesssim 0.7\
\mathrm{GeV}/\textit{c}$ also for (anti-)3He, as observed for the $v_{2}$ of
lighter particles measured at the LHC.

The (anti-)3He elliptic flow measured in all centrality intervals lies between
the predictions from the Blast-Wave model and a simple coalescence approach.
This picture is consistent with that of the (anti-)deuteron $v_{2}$ measured
in Pb–Pb collisions at $\sqrt{s_{\mathrm{NN}}}$ = 2.76 TeV, which was also
overestimated by the simple coalescence model, although it was closer to the
Blast-Wave predictions. The results on the (anti-)deuteron and (anti-)3He
elliptic flow measured at the LHC indicate that these two simple models
represent upper and lower edges of a region where the elliptic flow of light
(anti-)nuclei are typically located.

A more sophisticated coalescence approach based on phase-space distributions
of protons and neutrons generated by the iEBE-VISHNU hybrid model with AMPT
initial conditions provides a good description of the data in the transverse-
momentum interval $2\leq p_{\mathrm{T}}<6\ \mathrm{GeV}/\textit{c}$ for the
centrality ranges 0–20$\%$ and 20–40$\%$. The same model also provides a good
description of the (anti-)deuteron $v_{2}$ measured in Pb–Pb collisions at
$\sqrt{s_{\mathrm{NN}}}$ = 2.76 TeV. This model, however, fails in the
description of the $p_{\rm T}$-dependent yield of (anti-)3He measured in Pb–Pb
collisions at $\sqrt{s_{\mathrm{NN}}}$ = 2.76 TeV.

## Acknowledgements

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

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##  Appendix A The ALICE Collaboration

S. Acharyaorg141&D. Adamováorg93&S.P. Adhyaorg141&A. Adlerorg73&J.
Adolfssonorg79&M.M. Aggarwalorg98&G. Aglieri Rinellaorg34&M. Agnelloorg31&N.
Agrawalorg10,org48,org53&Z. Ahammedorg141&S. Ahmadorg17&S.U. Ahnorg75&A.
Akindinovorg90&M. Al-Turanyorg105&S.N. Alamorg141&D.S.D. Albuquerqueorg122&D.
Aleksandrovorg86&B. Alessandroorg58&H.M. Alfandaorg6&R. Alfaro Molinaorg71&B.
Aliorg17&Y. Aliorg15&A. Aliciorg10,org27,org53&A. Alkinorg2&J. Almeorg22&T.
Altorg68&L. Altenkamperorg22&I. Altsybeevorg112&M.N. Anaamorg6&C.
Andreiorg47&D. Andreouorg34&H.A. Andrewsorg109&A. Andronicorg144&M.
Angelettiorg34&V. Anguelovorg102&C. Ansonorg16&T. Antičićorg106&F.
Antinoriorg56&P. Antonioliorg53&R. Anwarorg125&N. Apadulaorg78&L.
Aphecetcheorg114&H. Appelshäuserorg68&S. Arcelliorg27&R. Arnaldiorg58&M.
Arratiaorg78&I.C. Arseneorg21&M. Arslandokorg102&A. Augustinusorg34&R.
Averbeckorg105&S. Azizorg61&M.D. Azmiorg17&A. Badalàorg55&Y.W. Baekorg40&S.
Bagnascoorg58&X. Baiorg105&R. Bailhacheorg68&R. Balaorg99&A.
Baldisseriorg137&M. Ballorg42&S. Balouzaorg103&R.C. Baralorg84&R.
Barberaorg28&L. Barioglioorg26&G.G. Barnaföldiorg145&L.S. Barnbyorg92&V.
Barretorg134&P. Bartaliniorg6&K. Barthorg34&E. Bartschorg68&F.
Baruffaldiorg29&N. Bastidorg134&S. Basuorg143&G. Batigneorg114&B.
Batyunyaorg74&P.C. Batzingorg21&D. Bauriorg48&J.L. Bazo Albaorg110&I.G.
Beardenorg87&C. Beddaorg63&N.K. Beheraorg60&I. Belikovorg136&F.
Belliniorg34&R. Bellwiedorg125&V. Belyaevorg91&G. Bencediorg145&S.
Beoleorg26&A. Bercuciorg47&Y. Berdnikovorg96&D. Berenyiorg145&R.A.
Bertensorg130&D. Berzanoorg58&M.G. Besoiuorg67&L. Betevorg34&A.
Bhasinorg99&I.R. Bhatorg99&M.A. Bhatorg3&H. Bhattorg48&B.
Bhattacharjeeorg41&A. Bianchiorg26&L. Bianchiorg26&N. Bianchiorg51&J.
Bielčíkorg37&J. Bielčíkováorg93&A. Bilandzicorg103,org117&G. Biroorg145&R.
Biswasorg3&S. Biswasorg3&J.T. Blairorg119&D. Blauorg86&C. Blumeorg68&G.
Bocaorg139&F. Bockorg34,org94&A. Bogdanovorg91&L. Boldizsárorg145&A.
Bolozdynyaorg91&M. Bombaraorg38&G. Bonomiorg140&H. Borelorg137&A.
Borissovorg91,org144&M. Borriorg127&H. Bossiorg146&E. Bottaorg26&L.
Bratrudorg68&P. Braun-Munzingerorg105&M. Bregantorg121&T.A. Brokerorg68&M.
Brozorg37&E.J. Bruckenorg43&E. Brunaorg58&G.E. Brunoorg33,org104&M.D.
Bucklandorg127&D. Budnikovorg107&H. Bueschingorg68&S. Bufalinoorg31&O.
Bugnonorg114&P. Buhlerorg113&P. Buncicorg34&Z. Butheleziorg72&J.B.
Buttorg15&J.T. Buxtonorg95&S.A. Bysiakorg118&D. Caffarriorg88&A.
Calivaorg105&E. Calvo Villarorg110&R.S. Camachoorg44&P. Cameriniorg25&A.A.
Caponorg113&F. Carnesecchiorg10&J. Castillo Castellanosorg137&A.J.
Castroorg130&E.A.R. Casulaorg54&F. Catalanoorg31&C. Ceballos Sanchezorg52&P.
Chakrabortyorg48&S. Chandraorg141&B. Changorg126&W. Changorg6&S.
Chapelandorg34&M. Chartierorg127&S. Chattopadhyayorg141&S.
Chattopadhyayorg108&A. Chauvinorg24&C. Cheshkovorg135&B. Cheynisorg135&V.
Chibante Barrosoorg34&D.D. Chinellatoorg122&S. Choorg60&P. Chochulaorg34&T.
Chowdhuryorg134&P. Christakoglouorg88&C.H. Christensenorg87&P.
Christiansenorg79&T. Chujoorg133&C. Cicaloorg54&L. Cifarelliorg10,org27&F.
Cindoloorg53&J. Cleymansorg124&F. Colamariaorg52&D. Colellaorg52&A.
Colluorg78&M. Colocciorg27&M. Concasorg58orgI&G. Conesa Balbastreorg77&Z.
Conesa del Valleorg61&G. Continorg59,org127&J.G. Contrerasorg37&T.M.
Cormierorg94&Y. Corrales Moralesorg26,org58&P. Corteseorg32&M.R.
Cosentinoorg123&F. Costaorg34&S. Costanzaorg139&J. Crkovskáorg61&P.
Crochetorg134&E. Cuautleorg69&L. Cunqueiroorg94&D. Dabrowskiorg142&T.
Dahmsorg103,org117&A. Daineseorg56&F.P.A. Damasorg114,org137&S. Daniorg65&M.C.
Danischorg102&A. Danuorg67&D. Dasorg108&I. Dasorg108&P. Dasorg3&S. Dasorg3&A.
Dashorg84&S. Dashorg48&A. Dashiorg103&S. Deorg49,org84&A. De Caroorg30&G. de
Cataldoorg52&C. de Contiorg121&J. de Cuvelandorg39&A. De Falcoorg24&D. De
Gruttolaorg10&N. De Marcoorg58&S. De Pasqualeorg30&R.D. De Souzaorg122&S.
Deborg49&H.F. Degenhardtorg121&K.R. Dejaorg142&A. Delofforg83&S.
Delsantoorg26,org131&D. Devetakorg105&P. Dhankherorg48&D. Di Bariorg33&A. Di
Mauroorg34&R.A. Diazorg8&T. Dietelorg124&P. Dillensegerorg68&Y. Dingorg6&R.
Diviàorg34&Ø. Djuvslandorg22&U. Dmitrievaorg62&A. Dobrinorg34,org67&B.
Dönigusorg68&O. Dordicorg21&A.K. Dubeyorg141&A. Dublaorg105&S. Dudiorg98&M.
Dukhishyamorg84&P. Dupieuxorg134&R.J. Ehlersorg146&D. Eliaorg52&H.
Engelorg73&E. Eppleorg146&B. Erazmusorg114&F. Erhardtorg97&A.
Erokhinorg112&M.R. Ersdalorg22&B. Espagnonorg61&G. Eulisseorg34&J. Eumorg18&D.
Evansorg109&S. Evdokimovorg89&L. Fabbiettiorg103,org117&M. Fagginorg29&J.
Faivreorg77&A. Fantoniorg51&M. Faselorg94&P. Fecchioorg31&A.
Felicielloorg58&G. Feofilovorg112&A. Fernández Téllezorg44&A. Ferreroorg137&A.
Ferrettiorg26&A. Festantiorg34&V.J.G. Feuillardorg102&J. Figielorg118&S.
Filchaginorg107&D. Finogeevorg62&F.M. Fiondaorg22&G. Fiorenzaorg52&F.
Flororg125&S. Foertschorg72&P. Fokaorg105&S. Fokinorg86&E. Fragiacomoorg59&U.
Frankenfeldorg105&G.G. Fronzeorg26&U. Fuchsorg34&C. Furgetorg77&A.
Fursorg62&M. Fusco Girardorg30&J.J. Gaardhøjeorg87&M. Gagliardiorg26&A.M.
Gagoorg110&A. Galorg136&C.D. Galvanorg120&P. Ganotiorg82&C. Garabatosorg105&E.
Garcia-Solisorg11&K. Gargorg28&C. Gargiuloorg34&A. Garibliorg85&K.
Garnerorg144&P. Gasikorg103,org117&E.F. Gaugerorg119&M.B. Gay Ducatiorg70&M.
Germainorg114&J. Ghoshorg108&P. Ghoshorg141&S.K. Ghoshorg3&P. Gianottiorg51&P.
Giubellinoorg58,org105&P. Giubilatoorg29&P. Glässelorg102&D.M. Goméz
Coralorg71&A. Gomez Ramirezorg73&V. Gonzalezorg105&P. González-Zamoraorg44&S.
Gorbunovorg39&L. Görlichorg118&S. Gotovacorg35&V. Grabskiorg71&L.K.
Graczykowskiorg142&K.L. Grahamorg109&L. Greinerorg78&A. Grelliorg63&C.
Grigorasorg34&V. Grigorievorg91&A. Grigoryanorg1&S. Grigoryanorg74&O.S.
Groettvikorg22&J.M. Gronefeldorg105&F. Grosaorg31&J.F. Grosse-
Oetringhausorg34&R. Grossoorg105&R. Guernaneorg77&B. Guerzoniorg27&M.
Guittiereorg114&K. Gulbrandsenorg87&T. Gunjiorg132&A. Guptaorg99&R.
Guptaorg99&I.B. Guzmanorg44&R. Haakeorg146&M.K. Habiborg105&C.
Hadjidakisorg61&H. Hamagakiorg80&G. Hamarorg145&M. Hamidorg6&R.
Hanniganorg119&M.R. Haqueorg63&A. Harlenderovaorg105&J.W. Harrisorg146&A.
Hartonorg11&J.A. Hasenbichlerorg34&H. Hassanorg77&D.
Hatzifotiadouorg10,org53&P. Hauerorg42&S. Hayashiorg132&A.D.L.B.
Hechavarriaorg144&S.T. Heckelorg68&E. Hellbärorg68&H. Helstruporg36&A.
Herghelegiuorg47&E.G. Hernandezorg44&G. Herrera Corralorg9&F.
Herrmannorg144&K.F. Hetlandorg36&T.E. Hildenorg43&H. Hillemannsorg34&C.
Hillsorg127&B. Hippolyteorg136&B. Hohlwegerorg103&D. Horakorg37&S.
Hornungorg105&R. Hosokawaorg133&P. Hristovorg34&C. Huangorg61&C.
Hughesorg130&P. Huhnorg68&T.J. Humanicorg95&H. Hushnudorg108&L.A.
Husovaorg144&N. Hussainorg41&S.A. Hussainorg15&T. Hussainorg17&D.
Hutterorg39&D.S. Hwangorg19&J.P. Iddonorg34,org127&R. Ilkaevorg107&M.
Inabaorg133&M. Ippolitovorg86&M.S. Islamorg108&M. Ivanovorg105&V.
Ivanovorg96&V. Izucheevorg89&B. Jacakorg78&N. Jacazioorg27&P.M.
Jacobsorg78&M.B. Jadhavorg48&S. Jadlovskaorg116&J. Jadlovskyorg116&S.
Jaelaniorg63&C. Jahnkeorg121&M.J. Jakubowskaorg142&M.A. Janikorg142&M.
Jercicorg97&O. Jevonsorg109&R.T. Jimenez Bustamanteorg105&M. Jinorg125&F.
Jonasorg94,org144&P.G. Jonesorg109&J. Jungorg68&M. Jungorg68&A. Juskoorg109&P.
Kalinakorg64&A. Kalweitorg34&J.H. Kangorg147&V. Kaplinorg91&S. Karorg6&A.
Karasu Uysalorg76&O. Karavichevorg62&T. Karavichevaorg62&P.
Karczmarczykorg34&E. Karpechevorg62&U. Kebschullorg73&R. Keidelorg46&M.
Keilorg34&B. Ketzerorg42&Z. Khabanovaorg88&A.M. Khanorg6&S. Khanorg17&S.A.
Khanorg141&A. Khanzadeevorg96&Y. Kharlovorg89&A. Khatunorg17&A.
Khuntiaorg49,org118&B. Kilengorg36&B. Kimorg60&B. Kimorg133&D. Kimorg147&D.J.
Kimorg126&E.J. Kimorg13&H. Kimorg147&J. Kimorg147&J.S. Kimorg40&J.
Kimorg102&J. Kimorg147&J. Kimorg13&M. Kimorg102&S. Kimorg19&T. Kimorg147&T.
Kimorg147&S. Kirschorg39&I. Kiselorg39&S. Kiselevorg90&A. Kisielorg142&J.L.
Klayorg5&C. Kleinorg68&J. Kleinorg58&S. Kleinorg78&C. Klein-Bösingorg144&S.
Klewinorg102&A. Klugeorg34&M.L. Knichelorg34&A.G. Knospeorg125&C.
Kobdajorg115&M.K. Köhlerorg102&T. Kolleggerorg105&A. Kondratyevorg74&N.
Kondratyevaorg91&E. Kondratyukorg89&P.J. Konopkaorg34&L. Koskaorg116&O.
Kovalenkoorg83&V. Kovalenkoorg112&M. Kowalskiorg118&I. Králikorg64&A.
Kravčákováorg38&L. Kreisorg105&M. Krivdaorg64,org109&F. Krizekorg93&K.
Krizkova Gajdosovaorg37&M. Krügerorg68&E. Kryshenorg96&M. Krzewickiorg39&A.M.
Kuberaorg95&V. Kučeraorg60&C. Kuhnorg136&P.G. Kuijerorg88&L. Kumarorg98&S.
Kumarorg48&S. Kunduorg84&P. Kurashviliorg83&A. Kurepinorg62&A.B.
Kurepinorg62&A. Kuryakinorg107&S. Kushpilorg93&J. Kvapilorg109&M.J.
Kweonorg60&J.Y. Kwonorg60&Y. Kwonorg147&S.L. La Pointeorg39&P. La
Roccaorg28&Y.S. Laiorg78&R. Langoyorg129&K. Lapidusorg34,org146&A.
Lardeuxorg21&P. Larionovorg51&E. Laudiorg34&R. Lavickaorg37&T.
Lazarevaorg112&R. Leaorg25&L. Leardiniorg102&S. Leeorg147&F. Lehasorg88&S.
Lehnerorg113&J. Lehrbachorg39&R.C. Lemmonorg92&I. León Monzónorg120&E.D.
Lesserorg20&M. Lettrichorg34&P. Lévaiorg145&X. Liorg12&X.L. Liorg6&J.
Lienorg129&R. Lietavaorg109&B. Limorg18&S. Lindalorg21&V.
Lindenstruthorg39&S.W. Lindsayorg127&C. Lippmannorg105&M.A. Lisaorg95&V.
Litichevskyiorg43&A. Liuorg78&S. Liuorg95&W.J. Llopeorg143&I.M. Lofnesorg22&V.
Loginovorg91&C. Loizidesorg94&P. Loncarorg35&X. Lopezorg134&E. López
Torresorg8&P. Luettigorg68&J.R. Luhderorg144&M. Lunardonorg29&G.
Luparelloorg59&M. Lupiorg73&A. Maevskayaorg62&M. Magerorg34&S.M.
Mahmoodorg21&T. Mahmoudorg42&A. Maireorg136&R.D. Majkaorg146&M.
Malaevorg96&Q.W. Malikorg21&L. Malininaorg74orgII&D. Mal’Kevichorg90&P.
Malzacherorg105&A. Mamonovorg107&G. Mandaglioorg55&V. Mankoorg86&F.
Mansoorg134&V. Manzariorg52&Y. Maoorg6&M. Marchisoneorg135&J. Marešorg66&G.V.
Margagliottiorg25&A. Margottiorg53&J. Marguttiorg63&A. Marínorg105&C.
Markertorg119&M. Marquardorg68&N.A. Martinorg102&P. Martinengoorg34&J.L.
Martinezorg125&M.I. Martínezorg44&G. Martínez Garcíaorg114&M. Martinez
Pedreiraorg34&S. Masciocchiorg105&M. Maseraorg26&A. Masoniorg54&L.
Massacrierorg61&E. Massonorg114&A. Mastroserioorg138&A.M.
Mathisorg103,org117&O. Matonohaorg79&P.F.T. Matuokaorg121&A. Matyjaorg118&C.
Mayerorg118&M. Mazzilliorg33&M.A. Mazzoniorg57&A.F. Mechlerorg68&F.
Meddiorg23&Y. Melikyanorg91&A. Menchaca-Rochaorg71&E. Meninnoorg30&M.
Meresorg14&S. Mhlangaorg124&Y. Miakeorg133&L. Michelettiorg26&M.M.
Mieskolainenorg43&D.L. Mihaylovorg103&K. Mikhaylovorg74,org90&A.
Mischkeorg63org*&A.N. Mishraorg69&D. Miśkowiecorg105&C.M. Mituorg67&A.
Modakorg3&N. Mohammadiorg34&A.P. Mohantyorg63&B. Mohantyorg84&M. Mohisin
Khanorg17orgIII&M. Mondalorg141&M.M. Mondalorg65&C. Mordasiniorg103&D.A.
Moreira De Godoyorg144&L.A.P. Morenoorg44&S. Morettoorg29&A. Morrealeorg114&A.
Morschorg34&T. Mrnjavacorg34&V. Mucciforaorg51&E. Mudnicorg35&D.
Mühlheimorg144&S. Muhuriorg141&J.D. Mulliganorg78&M.G. Munhozorg121&K.
Münningorg42&R.H. Munzerorg68&H. Murakamiorg132&S. Murrayorg72&L. Musaorg34&J.
Musinskyorg64&C.J. Myersorg125&J.W. Myrchaorg142&B. Naikorg48&R.
Nairorg83&B.K. Nandiorg48&R. Naniaorg10,org53&E. Nappiorg52&M.U.
Naruorg15&A.F. Nassirpourorg79&H. Natal da Luzorg121&C. Nattrassorg130&R.
Nayakorg48&T.K. Nayakorg84,org141&S. Nazarenkoorg107&R.A. Negrao De
Oliveiraorg68&L. Nellenorg69&S.V. Nesboorg36&G. Neskovicorg39&D.
Nesterovorg112&B.S. Nielsenorg87&S. Nikolaevorg86&S. Nikulinorg86&V.
Nikulinorg96&F. Noferiniorg10,org53&P. Nomokonovorg74&G. Noorenorg63&J.
Normanorg77&N. Novitzkyorg133&P. Nowakowskiorg142&A. Nyaninorg86&J.
Nystrandorg22&M. Oginoorg80&A. Ohlsonorg102&J. Oleniaczorg142&A.C. Oliveira Da
Silvaorg121&M.H. Oliverorg146&C. Oppedisanoorg58&R. Oravaorg43&A. Ortiz
Velasquezorg69&A. Oskarssonorg79&J. Otwinowskiorg118&K. Oyamaorg80&Y.
Pachmayerorg102&V. Pacikorg87&D. Paganoorg140&G. Paićorg69&P. Palniorg6&J.
Panorg143&A.K. Pandeyorg48&S. Panebiancoorg137&V. Papikyanorg1&P.
Pareekorg49&J. Parkorg60&J.E. Parkkilaorg126&S. Parmarorg98&A.
Passfeldorg144&S.P. Pathakorg125&R.N. Patraorg141&B. Paulorg24,org58&H.
Peiorg6&T. Peitzmannorg63&X. Pengorg6&L.G. Pereiraorg70&H. Pereira Da
Costaorg137&D. Peresunkoorg86&G.M. Perezorg8&E. Perez Lezamaorg68&V.
Peskovorg68&Y. Pestovorg4&V. Petráčekorg37&M. Petroviciorg47&R.P.
Pezziorg70&S. Pianoorg59&M. Piknaorg14&P. Pillotorg114&L.O.D.L.
Pimentelorg87&O. Pinazzaorg34,org53&L. Pinskyorg125&C. Pintoorg28&S.
Pisanoorg51&D.B. Piyarathnaorg125&M. Płoskońorg78&M. Planinicorg97&F.
Pliquettorg68&J. Plutaorg142&S. Pochybovaorg145&M.G. Poghosyanorg94&B.
Polichtchoukorg89&N. Poljakorg97&W. Poonsawatorg115&A. Poporg47&H.
Poppenborgorg144&S. Porteboeuf-Houssaisorg134&V. Pozdniakovorg74&S.K.
Prasadorg3&R. Preghenellaorg53&F. Prinoorg58&C.A. Pruneauorg143&I.
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Putschkeorg143&R.E. Quishpeorg125&S. Ragoniorg109&S. Rahaorg3&S.
Rajputorg99&J. Rakorg126&A. Rakotozafindrabeorg137&L. Ramelloorg32&F.
Ramiorg136&R. Raniwalaorg100&S. Raniwalaorg100&S.S. Räsänenorg43&B.T.
Rascanuorg68&R. Rathorg49&V. Ratzaorg42&I. Ravasengaorg31&K.F.
Readorg94,org130&K. Redlichorg83orgIV&A. Rehmanorg22&P. Reicheltorg68&F.
Reidtorg34&X. Renorg6&R. Renfordtorg68&A. Reshetinorg62&J.-P. Revolorg10&K.
Reygersorg102&V. Riabovorg96&T. Richertorg79,org87&M. Richterorg21&P.
Riedlerorg34&W. Rieglerorg34&F. Riggiorg28&C. Risteaorg67&S.P. Rodeorg49&M.
Rodríguez Cahuantziorg44&K. Røedorg21&R. Rogalevorg89&E. Rogochayaorg74&D.
Rohrorg34&D. Röhrichorg22&P.S. Rokitaorg142&F. Ronchettiorg51&E.D.
Rosasorg69&K. Roslonorg142&P. Rosnetorg134&A. Rossiorg29&A. Rotondiorg139&F.
Roukoutakisorg82&A. Royorg49&P. Royorg108&O.V. Ruedaorg79&R. Ruiorg25&B.
Rumyantsevorg74&A. Rustamovorg85&E. Ryabinkinorg86&Y. Ryabovorg96&A.
Rybickiorg118&H. Rytkonenorg126&S. Sadhuorg141&S. Sadovskyorg89&K.
Šafaříkorg34,org37&S.K. Sahaorg141&B. Sahooorg48&P. Sahooorg48,org49&R.
Sahooorg49&S. Sahooorg65&P.K. Sahuorg65&J. Sainiorg141&S. Sakaiorg133&S.
Sambyalorg99&V. Samsonovorg91,org96&F.R. Sanchezorg44&A. Sandovalorg71&A.
Sarkarorg72&D. Sarkarorg143&N. Sarkarorg141&P. Sarmaorg41&V.M.
Sartiorg103&M.H.P. Sasorg63&E. Scapparoneorg53&B. Schaeferorg94&J.
Schambachorg119&H.S. Scheidorg68&C. Schiauaorg47&R. Schickerorg102&A.
Schmahorg102&C. Schmidtorg105&H.R. Schmidtorg101&M.O. Schmidtorg102&M.
Schmidtorg101&N.V. Schmidtorg68,org94&A.R. Schmierorg130&J.
Schukraftorg34,org87&Y. Schutzorg34,org136&K. Schwarzorg105&K.
Schwedaorg105&G. Scioliorg27&E. Scomparinorg58&M. Šefčíkorg38&J.E.
Segerorg16&Y. Sekiguchiorg132&D. Sekihataorg45,org132&I.
Selyuzhenkovorg91,org105&S. Senyukovorg136&D. Serebryakovorg62&E.
Serradillaorg71&P. Settorg48&A. Sevcencoorg67&A. Shabanovorg62&A.
Shabetaiorg114&R. Shahoyanorg34&W. Shaikhorg108&A. Shangaraevorg89&A.
Sharmaorg98&A. Sharmaorg99&H. Sharmaorg118&M. Sharmaorg99&N. Sharmaorg98&A.I.
Sheikhorg141&K. Shigakiorg45&M. Shimomuraorg81&S. Shirinkinorg90&Q.
Shouorg111&Y. Sibiriakorg86&S. Siddhantaorg54&T. Siemiarczukorg83&D.
Silvermyrorg79&C. Silvestreorg77&G. Simatovicorg88&G. Simonettiorg34,org103&R.
Singhorg84&R. Singhorg99&V.K. Singhorg141&V. Singhalorg141&T. Sinhaorg108&B.
Sitarorg14&M. Sittaorg32&T.B. Skaaliorg21&M. Slupeckiorg126&N.
Smirnovorg146&R.J.M. Snellingsorg63&T.W. Snellmanorg126&J. Sochanorg116&C.
Sonccoorg110&J. Songorg60,org125&A. Songmoolnakorg115&F. Soramelorg29&S.
Sorensenorg130&I. Sputowskaorg118&J. Stachelorg102&I. Stanorg67&P.
Stankusorg94&P.J. Steffanicorg130&E. Stenlundorg79&D. Stoccoorg114&M.M.
Storetvedtorg36&P. Strmenorg14&A.A.P. Suaideorg121&T. Sugitateorg45&C.
Suireorg61&M. Suleymanovorg15&M. Suljicorg34&R. Sultanovorg90&M.
Šumberaorg93&S. Sumowidagdoorg50&K. Suzukiorg113&S. Swainorg65&A.
Szaboorg14&I. Szarkaorg14&U. Tabassamorg15&G. Taillepiedorg134&J.
Takahashiorg122&G.J. Tambaveorg22&S. Tangorg6,org134&M. Tarhiniorg114&M.G.
Tarzilaorg47&A. Tauroorg34&G. Tejeda Muñozorg44&A. Telescaorg34&C.
Terrevoliorg29,org125&D. Thakurorg49&S. Thakurorg141&D. Thomasorg119&F.
Thoresenorg87&R. Tieulentorg135&A. Tikhonovorg62&A.R. Timminsorg125&A.
Toiaorg68&N. Topilskayaorg62&M. Toppiorg51&F. Torales-Acostaorg20&S.R.
Torresorg120&A. Trifiroorg55&S. Tripathyorg49&T. Tripathyorg48&S.
Trogoloorg26,org29&G. Trombettaorg33&L. Tropporg38&V. Trubnikovorg2&W.H.
Trzaskaorg126&T.P. Trzcinskiorg142&B.A. Trzeciakorg63&T. Tsujiorg132&A.
Tumkinorg107&R. Turrisiorg56&T.S. Tveterorg21&K. Ullalandorg22&E.N.
Umakaorg125&A. Urasorg135&G.L. Usaiorg24&A. Utrobicicorg97&M.
Valaorg38,org116&N. Valleorg139&S. Valleroorg58&N. van der Kolkorg63&L.V.R.
van Doremalenorg63&M. van Leeuwenorg63&P. Vande Vyvreorg34&D. Vargaorg145&Z.
Vargaorg145&M. Varga-Kofaragoorg145&A. Vargasorg44&M. Vargyasorg126&R.
Varmaorg48&M. Vasileiouorg82&A. Vasilievorg86&O. Vázquez Doceorg103,org117&V.
Vecherninorg112&A.M. Veenorg63&E. Vercellinorg26&S. Vergara Limónorg44&L.
Vermuntorg63&R. Vernetorg7&R. Vértesiorg145&M.G.D.L.C. Vicencioorg9&L.
Vickovicorg35&J. Viinikainenorg126&Z. Vilakaziorg131&O. Villalobos
Baillieorg109&A. Villatoro Telloorg44&G. Vinoorg52&A. Vinogradovorg86&T.
Virgiliorg30&V. Vislaviciusorg87&A. Vodopyanovorg74&B. Volkelorg34&M.A.
Völklorg101&K. Voloshinorg90&S.A. Voloshinorg143&G. Volpeorg33&B. von
Hallerorg34&I. Vorobyevorg103&D. Voscekorg116&J. Vrlákováorg38&B.
Wagnerorg22&M. Weberorg113&S.G. Weberorg105,org144&A. Wegrzynekorg34&D.F.
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Wiechulaorg68&J. Wikneorg21&G. Wilkorg83&J. Wilkinsonorg53&G.A.
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Wuorg128&R. Xuorg6&S. Yalcinorg76&K. Yamakawaorg45&S. Yangorg22&S.
Yanoorg137&Z. Yinorg6&H. Yokoyamaorg63,org133&I.-K. Yooorg18&J.H. Yoonorg60&S.
Yuanorg22&A. Yuncuorg102&V. Yurchenkoorg2&V. Zaccoloorg25,org58&A.
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Zhalovorg96&X. Zhangorg6&Z. Zhangorg6&C. Zhaoorg21&V. Zherebchevskiiorg112&N.
Zhigarevaorg90&D. Zhouorg6&Y. Zhouorg87&Z. Zhouorg22&J. Zhuorg6&Y. Zhuorg6&A.
Zichichiorg10,org27&M.B. Zimmermannorg34&G. Zinovjevorg2&N. Zurloorg140&

## Affiliation notes

org*Deceased

orgIDipartimento DET del Politecnico di Torino, Turin, Italy

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

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

orgIVInstitute of Theoretical Physics, University of Wroclaw, Poland

## Collaboration Institutes

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

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

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

org4Budker Institute for Nuclear Physics, Novosibirsk, Russia

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

org6Central China Normal University, Wuhan, China

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

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

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

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

org11Chicago State University, Chicago, Illinois, United States

org12China Institute of Atomic Energy, Beijing, China

org13Chonbuk National University, Jeonju, Republic of Korea

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

org15COMSATS University Islamabad, Islamabad, Pakistan

org16Creighton University, Omaha, Nebraska, United States

org17Department of Physics, Aligarh Muslim University, Aligarh, India

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

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

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

org21Department of Physics, University of Oslo, Oslo, Norway

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

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

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

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

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

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

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

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

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

org31Dipartimento DISAT del Politecnico and Sezione INFN, Turin, Italy

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

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

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

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

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

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

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

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

org40Gangneung-Wonju National University, Gangneung, Republic of Korea

org41Gauhati University, Department of Physics, Guwahati, India

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

org43Helsinki Institute of Physics (HIP), Helsinki, Finland

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

org45Hiroshima University, Hiroshima, Japan

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

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

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

org49Indian Institute of Technology Indore, Indore, India

org50Indonesian Institute of Sciences, Jakarta, Indonesia

org51INFN, Laboratori Nazionali di Frascati, Frascati, Italy

org52INFN, Sezione di Bari, Bari, Italy

org53INFN, Sezione di Bologna, Bologna, Italy

org54INFN, Sezione di Cagliari, Cagliari, Italy

org55INFN, Sezione di Catania, Catania, Italy

org56INFN, Sezione di Padova, Padova, Italy

org57INFN, Sezione di Roma, Rome, Italy

org58INFN, Sezione di Torino, Turin, Italy

org59INFN, Sezione di Trieste, Trieste, Italy

org60Inha University, Incheon, Republic of Korea

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

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

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

org64Institute of Experimental Physics, Slovak Academy of Sciences, Košice,
Slovakia

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

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

org67Institute of Space Science (ISS), Bucharest, Romania

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

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

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

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

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

org73Johann-Wolfgang-Goethe Universität Frankfurt Institut für Informatik,
Fachbereich Informatik und Mathematik, Frankfurt, Germany

org74Joint Institute for Nuclear Research (JINR), Dubna, Russia

org75Korea Institute of Science and Technology Information, Daejeon, Republic
of Korea

org76KTO Karatay University, Konya, Turkey

org77Laboratoire de Physique Subatomique et de Cosmologie, Université
Grenoble-Alpes, CNRS-IN2P3, Grenoble, France

org78Lawrence Berkeley National Laboratory, Berkeley, California, United
States

org79Lund University Department of Physics, Division of Particle Physics,
Lund, Sweden

org80Nagasaki Institute of Applied Science, Nagasaki, Japan

org81Nara Women’s University (NWU), Nara, Japan

org82National and Kapodistrian University of Athens, School of Science,
Department of Physics , Athens, Greece

org83National Centre for Nuclear Research, Warsaw, Poland

org84National Institute of Science Education and Research, Homi Bhabha
National Institute, Jatni, India

org85National Nuclear Research Center, Baku, Azerbaijan

org86National Research Centre Kurchatov Institute, Moscow, Russia

org87Niels Bohr Institute, University of Copenhagen, Copenhagen, Denmark

org88Nikhef, National institute for subatomic physics, Amsterdam, Netherlands

org89NRC Kurchatov Institute IHEP, Protvino, Russia

org90NRC «Kurchatov Institute» - ITEP, Moscow, Russia

org91NRNU Moscow Engineering Physics Institute, Moscow, Russia

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

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

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

org95Ohio State University, Columbus, Ohio, United States

org96Petersburg Nuclear Physics Institute, Gatchina, Russia

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

org98Physics Department, Panjab University, Chandigarh, India

org99Physics Department, University of Jammu, Jammu, India

org100Physics Department, University of Rajasthan, Jaipur, India

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

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

org103Physik Department, Technische Universität München, Munich, Germany

org104Politecnico di Bari, Bari, Italy

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

org106Rudjer Bošković Institute, Zagreb, Croatia

org107Russian Federal Nuclear Center (VNIIEF), Sarov, Russia

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

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

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

org111Shanghai Institute of Applied Physics, Shanghai, China

org112St. Petersburg State University, St. Petersburg, Russia

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

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

org115Suranaree University of Technology, Nakhon Ratchasima, Thailand

org116Technical University of Košice, Košice, Slovakia

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

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

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

org120Universidad Autónoma de Sinaloa, Culiacán, Mexico

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

org122Universidade Estadual de Campinas (UNICAMP), Campinas, Brazil

org123Universidade Federal do ABC, Santo Andre, Brazil

org124University of Cape Town, Cape Town, South Africa

org125University of Houston, Houston, Texas, United States

org126University of Jyväskylä, Jyväskylä, Finland

org127University of Liverpool, Liverpool, United Kingdom

org128University of Science and Technology of China, Hefei, China

org129University of South-Eastern Norway, Tonsberg, Norway

org130University of Tennessee, Knoxville, Tennessee, United States

org131University of the Witwatersrand, Johannesburg, South Africa

org132University of Tokyo, Tokyo, Japan

org133University of Tsukuba, Tsukuba, Japan

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

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

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

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

org138Università degli Studi di Foggia, Foggia, Italy

org139Università degli Studi di Pavia, Pavia, Italy

org140Università di Brescia, Brescia, Italy

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

org142Warsaw University of Technology, Warsaw, Poland

org143Wayne State University, Detroit, Michigan, United States

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

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

org146Yale University, New Haven, Connecticut, United States

org147Yonsei University, Seoul, Republic of Korea