2024 144 23 May

(Anti)nuclei production and flow in Xe–Xe collisions at
${\sqrt{\textit{s}_{\textup{NN}}}=5.44}$ TeV

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

Measurements of (anti)deuteron and (anti)3He production in the rapidity range
$|y|<$ 0.5 as a function of the transverse momentum and event multiplicity in
Xe–Xe collisions at a center-of-mass energy per nucleon–nucleon pair of
$\sqrt{s_{\mathrm{NN}}}$ = 5.44 TeV are presented. The coalescence parameters
$B_{2}$ and $B_{3}$ are measured as a function of the transverse momentum per
nucleon. The ratios between (anti)deuteron and (anti)3He yields and those of
(anti)protons and pions are reported as a function of the mean charged-
particle multiplicity density, and compared with two implementations of the
statistical hadronization model (SHM) and with coalescence predictions. The
elliptic flow of (anti)deuterons is measured for the first time in Xe–Xe
collisions and shows features similar to those already observed in Pb–Pb
collisions, i.e., the mass ordering at low transverse momentum and the
meson–baryon grouping at intermediate transverse momentum. The production of
nuclei is particularly sensitive to the chemical freeze-out temperature of the
system created in the collision, which is extracted from a grand-canonical-
ensemble-based thermal fit, performed for the first time including light
nuclei along with light-flavor hadrons in Xe–Xe collisions. The extracted
chemical freeze-out temperature $T_{\rm chem}$ = (154.2 $\pm$ 1.1) MeV in
Xe–Xe collisions is similar to that observed in Pb–Pb collisions and close to
the crossover temperature predicted by lattice QCD calculations.

##  1 Introduction

The investigation of the production mechanism of light (anti)nuclei in high-
energy hadronic collisions is one of the main topics in modern nuclear
physics. The ALICE Collaboration has significantly contributed to this field
with systematic measurements of (anti)nucleus production in different
collision systems and center-of-mass energies provided by the Large Hadron
Collider (LHC) [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18,
19]. These results extend previous experimental measurements at lower
collision energies, from the AGS [20, 21, 22, 23], SPS [24], and RHIC [25, 26,
27, 28, 29, 30], to the TeV energy scale. In addition to transverse-momentum
($p_{\rm T}$) and event-multiplicity differential measurements of
(anti)nucleus production yields, the ALICE Collaboration has also measured the
anisotropic flow of (anti)deuterons [3, 31] and (anti)3He [8], and
(anti)deuteron number fluctuations [32] in Pb–Pb collisions.

Such a large wealth of experimental data is typically described using three
categories of theoretical models: the statistical hadronization model (SHM)
[33, 34, 35, 36, 37, 38, 39], models that combine relativistic hydrodynamics
with a subsequent hadronic afterburner [40, 41], and baryon coalescence [42,
43, 44, 45, 46, 47, 48, 49]. In the former, light (anti)nuclei are assumed to
be produced by a source in local thermal and hadrochemical equilibrium at the
chemical freeze-out with a temperature of about 155 MeV [37]. Light
(anti)nuclei are bound states with binding energies of about 2.2 MeV for
deuterons, 8.48 MeV for tritons, and 7.72 MeV for 3He nuclei, orders of
magnitude smaller than the temperature of the environment created in the high-
energy nuclear collisions. In the context of the SHM, two solutions have been
proposed to explain the survival of such loosely bound states in the hot and
dense hadron gas phase produced in ultrarelativistic heavy-ion collisions. The
first assumes that light (anti)nuclei are created at the hadronization phase
boundary as compact colorless multi-quark systems with negligible interaction
cross sections with hadrons [37]. The time scale for the evolution of their
wave function is estimated to be longer than the lifetime of the hadron gas,
which is about 10 fm/$c$. The second assumes that while the abundance of
elementary hadrons, including nucleons, is determined at chemical freeze-out,
the yield of light nuclei, i.e., composite objects with a binding energy much
smaller than the temperature, continues to evolve in thermal equilibrium
between nuclei and nucleons until the kinetic freeze-out is reached [50].

Recent model developments have tackled the unresolved question of the survival
of weakly bound multi-baryon states within the hadron gas phase with intense
rescattering, combining relativistic hydrodynamics with a subsequent
afterburner of hadrons [40, 41]. Within these models, nucleons and light
nuclei are generated at the phase transition using the Cooper-Frye formula
[51], which characterizes hadron generation based on the local energy density
of the fireball. The hadron yields are set according to the values predicted
by the thermal model at the chemical freeze-out temperature. The propagation
of these particles through the hadronic medium is simulated using various
transport codes (such as UrQMD [52, 53] or SMASH [41]), considering the well-
established interaction cross sections and resonant states.

Finally, in the coalescence model, light (anti)nuclei are formed by the
coalescence of nucleons that are close in phase space and with matching spin-
isospin configurations, at kinetic freeze-out (occurring when the elastic
interactions stop and the momentum of the particles is fixed). In the state-
of-the-art implementation of the coalescence model, the formation probability
is calculated by folding the phase-space distributions of (point-like)
nucleons with the Wigner density distribution of the bound state. Significant
progress has been made over the last decade in these phenomenological
approaches driven by the growing amount of available data.

Although both SHM and coalescence models are successful in describing
different aspects of nuclear production, they are also different in some key
aspects. For instance, the coalescence model is sensitive to the size of the
nucleus and its wave function, and in particular to the relation between
nuclear size and emission source size [44, 46]. On the contrary, the SHM
predictions depend only on the mass and on the spin degeneracy factor of the
nucleus. This aspect is particularly relevant in small collision systems
(e.g., pp and p–Pb collisions), since the size of the nucleus
($r_{\rm{deuteron}}$ = 1.96 fm and $r_{\rm{{}^{3}He}}$ = 1.76 fm [54]) and
that of the baryon-emitting source ($r\sim 1$ fm in pp collisions [55] and
$r\sim 1.5$ fm in p–Pb collisions [56]) are comparable. In turn, in the SHM
the evolution of the particle yields with the event multiplicity is driven
solely by the baryon number conservation, assuming that the hadronization
temperature is constant. For this reason, an interesting observable to test
the consistency of models describing the hadron chemistry in high-energy
hadronic collisions is the ratio of the integrated yields of nuclei relative
to those of protons (and of pions, to test the SHM only). Such ratios increase
smoothly with multiplicity, and such behavior is qualitatively reproduced by
both SHM and coalescence models. In the former, the plateau of the ratios at
high multiplicity is described by the grand-canonical ensemble of the
statistical model [37, 57, 46], where all the charges are only conserved on
average, but fluctuate from one microscopic state to another. Such ensemble
holds true to describe the particle yield in the case of sufficiently large
reaction volumes, as in heavy-ion collisions. In the low-multiplicity region,
corresponding to small collision systems, the exact conservation of charges
from one microscopic state to another plays an important role in determining
the final state particle yield. Therefore, the canonical ensemble of the SHM
is used. This results in the so-called canonical suppression of the yields of
particles carrying conserved charges, relative to their grand-canonical
values. In the coalescence models, instead, the trend of the particle ratios
with multiplicity is related to the interplay of the increasing source size
and the decreasing coalescence probability with increasing multiplicity.
Finally, in the SHM nuclei are produced at the chemical freeze-out, when the
hadron species are fixed, while in the coalescence model nucleons coalesce to
form nuclei between the chemical and the kinetic freeze-out. Many efforts have
been put forward recently, in the latest developments of the SHM, to explain
the survival of nuclei in a system with $T_{\rm{chem}}\sim$ 155 MeV,
postulating the possibility of their formation at the kinetic freeze-out
(which occurs later, at $T_{\rm{kin}}\sim(100$–$120)$ MeV [58, 59]), see for
instance Refs. [60, 61, 41, 62, 63].

The current models present contrasting scenarios when describing the post-
hadronization phase of loosely bound states. Hence, it becomes important to
examine the measurements of the elliptic flow of light (anti)nuclei, namely
the second harmonic component ($v_{2}$) obtained from the Fourier
decomposition of the azimuthal distribution of their momentum with respect to
the reaction plane. These measurements offer valuable insights into the
propagation of these particles through the hadron gas phase and the dynamics
of their interactions with other particles. Specifically, according to
relativistic hydrodynamics, a clear mass ordering is expected at low $p_{\rm
T}$ (i.e., at fixed $p_{\rm T}$ lighter particles have larger $v_{2}$ compared
to heavier particles), when comparing the elliptic flow of nuclei and that of
other hadron species, as observed in Refs. [64, 31, 65]. Such mass ordering
arises from the interplay between the radial flow (quantifying the isotropic
expansion of the system of particles created in the collision) and the
anisotropic flow, and therefore provides constraints on the transport
coefficients of the medium. The mass ordering of the $v_{2}$ can also help to
shed light on the coalescence mechanism, as a scaling relation is expected to
follow from a naive quark coalescence model [66] that only allows quarks with
equal momentum to form a hadron [67].

In this article, the first measurements of (anti)deuteron and (anti)3He
production in Xe–Xe collisions at $\sqrt{s_{\mathrm{NN}}}$ = 5.44 TeV and of
the (anti)deuteron elliptic flow are presented. These results contribute to
the global picture that emerged from previous measurements, which is
characterized by a continuous evolution of the ratios of the yield of
(anti)nuclei to those of pions and protons and of the coalescence parameters
with the charged-particle multiplicity. The results presented in this paper
cover multiplicity intervals bridging between p–Pb and Pb–Pb collisions and
fill the gaps between some measurements in heavy-ion collisions. The results
are discussed in the context of the statistical hadronization and baryon
coalescence models.

##  2 Experimental apparatus

The exceptional capabilities of ALICE in tracking and particle identification
(PID), make it well-suited for the study of light nuclei and antinuclei in
various collision systems at the LHC. A detailed description of the ALICE
subdetectors and their performance can be found in Refs. [68, 69] and related
references.

The analysis described in this work employs four detectors: the Inner Tracking
System (ITS), the Time Projection Chamber (TPC), the Time-Of-Flight (TOF), and
the V0 detector [70]. These detectors (except for the V0, which is installed
in the forward region) are positioned in the central barrel inside a
solenoidal magnet generating a magnetic field with an intensity of up to B =
0.5 T.

The ITS [68, 71], which covers the entire azimuthal angle and the
pseudorapidity range $|\eta|$ < 0.9, serves primarily as a tracking detector,
allowing for the reconstruction of charged-particle tracks in the vicinity of
the collision point. This allows for the precise reconstruction of the
position of the primary and secondary vertices from weak decays, starting from
the reconstructed tracks. It comprises three subsystems of silicon detectors
arranged cylindrically around the beam axis: the two innermost layers are
Silicon Pixel Detectors (SPD), the central two layers are Silicon Drift
Detectors (SDD), and finally the two outermost layers are made of Silicon
Strip Detectors (SSD). The ITS plays a role in discriminating primary and
secondary nuclei produced in spallation processes with the detector material
and the beam vacuum tube, via the determination of the distance-of-closest
approach (DCA) of the track to the primary vertex.

The primary tracking detector, namely the TPC [72], allows for charged-
particle reconstruction with up to 159 three-dimensional space points and for
particle identification, by measuring the specific ionization energy loss
($\textrm{d}E/\textrm{d}x$) in the gas. The TPC is a cylindrical drift
chamber, coaxial with the beam vacuum tube and filled with a gas mixture
containing 90% Ne and 10% CO2 at atmospheric pressure during the Xe–Xe data
taking. With a radius ranging from 85 to 250 cm and a length of 500 cm in the
beam direction, the TPC volume covers the same pseudorapidity interval as the
ITS. The TPC provides a measurement of the specific energy loss with a
resolution ranging from about 5.2% in pp collisions to about 6.5% in central
Pb–Pb collisions [69], when traversed by minimum ionizing particles throughout
the entire detector. Charged-particle transverse momentum is measured with a
resolution ranging from about 1% at 1 $\mathrm{GeV}/\textit{c}$ to
approximately 3% at 10 $\mathrm{GeV}/\textit{c}$ using the TPC.

The TOF detector [73] covers the full azimuthal angle and the pseudorapidity
interval $|\eta|$ < 0.9. It consists of Multi-gap Resistive Plate Chambers
(MRPCs) positioned at an average distance of 3.8 m from the nominal
interaction point. The TOF time resolution is 56 ps [74], while the event time
resolution varies depending on the collision system and the track multiplicity
[75]. The start time for the time-of-flight is provided by the T0 detector
[70] and by the TOF detector itself. The TOF-based determination of the start
time is particularly useful for measurements at large multiplicities, as it is
the case of Xe–Xe collisions for which a resolution better than 20 ps is
achieved if more than 50 tracks are used for its determination. The T0
consists of two arrays of Cherenkov counters, T0A and T0C, located on opposite
sides of the interaction point, covering the pseudorapidity regions
$4.6<\eta<4.9$ and $-3.3<\eta<-3.0$. A weighted average is performed when both
T0 and TOF detectors have measured the start time [75]. For the particle
identification, the measured time-of-flight is compared with the expected time
calculated from the track momentum and length for each possible mass
hypothesis.

Finally, the V0 detector [70] is used to define the minimum-bias (MB) trigger
(requiring coincident signals in the V0 detectors to be synchronous with the
bunch crossing time defined by the LHC clock) and to select events based on
their multiplicity, which is related to the centrality of the Xe–Xe collision.
It comprises two arrays of plastic scintillators (V0A and V0C) located at
asymmetric positions, one on each side of the interaction point. They cover
the pseudorapidity regions $2.8<\eta<5.1$ and $-3.7<\eta<-1.7$, respectively.
The analysis of (anti)deuterons is conducted in several centrality classes
defined as percentiles of the measured amplitude distribution in the V0A and
V0C counters [76]: 0–10%, 10–20%, 20–40%, 40–60%, and 60–90%, where 0%
corresponds to the most central collisions and 90% to the most peripheral
ones. Instead, (anti)3He nuclei, due to their lower abundance, are analyzed in
a single wide centrality class 0–90%.

##  3 Data analysis

###  3.1 Event selection

The data used for this analysis were collected in 2017 when Xenon nuclei
(${}^{129}_{54}\text{Xe}$) collided at a center-of-mass energy per
nucleon–nucleon collision of $\sqrt{s_{\text{NN}}}$ = 5.44 TeV for the first
time at the LHC. The recorded instantaneous luminosity was $2\times
10^{-25}~{}\text{cm}^{-2}\text{s}^{-1}$, and the detected hadronic interaction
rate was around 80–150 Hz. The integrated luminosity delivered to ALICE was
fractions of 1 $\mu b^{-1}$ [77]. The solenoidal magnet of the ALICE apparatus
was operated in a low-field configuration of 0.2 T. The minimum bias event
trigger was fully efficient in the centrality interval 0–90$\%$ as
demonstrated by the flat centrality distribution [78]. The analysis is
performed in different centrality classes, selected offline, with varying
widths depending on the analysis and the nucleus species. In order to keep the
conditions of the detectors as uniform as possible and reject background
collisions, the $z$-coordinate of the primary vertex along the beam axis is
required to be within 10 cm from the nominal interaction point. Given the low
interaction rate during data taking, the pile-up of collisions in the same
bunch crossing is found to be negligible. Events with pile-up occurring during
the drift time of the TPC are rejected based on the correlation between the
total number of the space points (clusters) in the TPC and the number of SDD
and SSD clusters, as described in Ref. [79]. The residual pile-up
contribution, estimated using MC simulations anchored to the same data-taking
period, is found to be less than 1$\%$. The relative contribution of tracks
produced in out-of-bunch collisions is further reduced for (anti)deuterons
because their reconstructed tracks are required to have an associated hit in
the TOF detector, which is used for the (anti)deuteron identification. In the
case of (anti)3He, due to their low production rate, the probability for
simultaneous productions in pile-up events is less than 6$\times 10^{-9}$. Any
bias in the multiplicity of the event containing an (anti)3He does not affect
the analysis, which is performed in the full centrality interval 0–90$\%$. In
total, about 1.3 million events are selected for further analysis.

###  3.2 Track selection and identification of (anti)nuclei

(Anti)deuteron and (anti)3He candidates are selected from a sample of charged-
particle tracks reconstructed in the ITS and TPC in the pseudorapidity range
$|\eta|<0.8$. Several track quality criteria are applied, such as having a
number of TPC crossed rows larger than 70, a number of TPC clusters ($N^{\rm
TPC}_{\rm cls}$) used for the $\textrm{d}E/\textrm{d}x$ calculation larger
than 50 to ensure a good $\textrm{d}E/\textrm{d}x$ resolution, a fraction of
TPC crossed rows to findable clusters larger than 80$\%$, a minimum of two
reconstructed hits in the ITS with at least one located in any of the two
innermost layers, and a good track fit in the TPC by requiring
$\chi^{2}/N^{\rm TPC}_{\rm cls}<4$. The contribution from secondary tracks is
reduced by requiring a maximal DCA to the primary vertex in the transverse
plane ($\mathrm{DCA}_{xy}$) and in the longitudinal direction
($\mathrm{DCA}_{z}$) lower than 0.1 cm.

The (anti)3He identification is based on the energy loss per unit of track
length measured by the TPC [1, 2, 4, 7, 9, 13, 14, 16, 17]. The (anti)3He
candidates are selected by requiring that their measured
$\textrm{d}E/\textrm{d}x$ is within
3$\sigma^{\rm{}^{3}He}_{\mathrm{d}E/\mathrm{d}x}$ from the expected average
value, calculated using the Bethe–Bloch parametrization [80], where
$\sigma^{\rm{}^{3}He}_{\mathrm{d}E/\mathrm{d}x}$ is the
$\textrm{d}E/\textrm{d}x$ resolution for (anti)3He. The contamination from
other particle species is found to be negligible over the full transverse-
momentum range covered by this measurement, which is $1<p_{\rm T}<7$ GeV/$c$.
In the case of (anti)deuterons, both TPC and TOF information are used to
extract signal candidates. A sample of deuteron candidates is selected
applying a 3$\sigma$ selection on the difference between the measured
$\mathrm{d}E/\mathrm{d}x$ in the TPC and the expected average value for
deuterons. Then the (anti)deuteron signal is extracted using the TOF
information of preselected deuteron candidates [1, 3, 4, 6, 7, 10, 12, 13, 14,
16, 17, 18], from a fit to the $(\Delta t-\Delta t_{\rm exp})/\sigma_{\rm
TOF}$ distribution, where $\Delta t$ is the time-of-flight measured by the TOF
detector, $\Delta t_{\rm exp}$ is its expected value for deuterons, and
$\sigma_{\rm TOF}$ is the time-of-flight resolution of TOF. To model the
signal the fit is executed using a Gaussian function with an exponential tail,
in the range $-7<(\Delta t-\Delta t_{\rm exp})/\sigma_{\rm TOF}<$ 15\. To
model the background the fit uses an exponential, for $p_{\rm T}<4$ GeV/$c$,
or the sum of an exponential and a linear function, for $p_{\rm T}>4$ GeV/$c$.
The (anti)deuteron yield is calculated by integrating the signal counts
(counting the entries in the histogram after subtracting the background fit
function) in the range [$-3\sigma^{\rm fit}_{\mathrm{TOF}}$, $+3.5\sigma^{\rm
fit}_{\mathrm{TOF}}$], being $\sigma^{\rm fit}_{\mathrm{TOF}}$ the TOF
resolution extracted from the fit. The reason for an asymmetric interval is
the presence of an exponential tail towards higher values of $(\Delta t-\Delta
t_{\rm exp})/\sigma_{\rm TOF}$, that reflects the TOF detector time response
[81]. As an example, the signal extraction procedure, for both (anti)3He and
(anti)deuterons, is shown in Fig. 1.

Figure 1: Distribution of the
$\left(\mathrm{d}E/\mathrm{d}x-\langle\mathrm{d}E/\mathrm{d}x\rangle_{\rm{}^{3}He}\right)/\sigma^{\rm{}^{3}He}_{\mathrm{d}E/\mathrm{d}x}$
method used to extract the signal of ${}^{3}\overline{\rm{He}}$ (left), and
distribution of $(\Delta t-\Delta t_{\rm d}^{\rm exp})/\sigma_{\rm TOF}$ used
to extract the signal of $\overline{\rm{d}}$ (right). The regions highlighted
in green represent the regions of the signal integration, different for the
two signal extraction methods.

###  3.3 Corrections based on simulations

The product of the geometrical acceptance and the reconstruction and selection
efficiency (Acceptance $\times$ Efficiency) of (anti)nuclei and the
contamination from secondary nuclei from spallation are calculated using Monte
Carlo (MC) simulations. The HIJING [82] event generator is used to simulate
Xe–Xe collision events. Nuclei and antinuclei are embedded into the simulated
events with a uniform distribution in transverse momentum and rapidity, within
0 < $p_{\rm T}$ < 10 $\mathrm{GeV}/\textit{c}$ and –1 < $y$ < 1, respectively.
The interactions of (anti)nuclei with the detector materials are simulated
using GEANT4 [83] as transport code. Considering that the $p_{\rm T}$
distributions of nuclei and their relative abundances in the simulation are
different from data, centrality and $p_{\rm T}$-dependent corrections are
applied in the MC simulations using weights. These are defined as the ratio of
measured and generated $p_{\rm T}$ spectra in the simulation. A Blast-Wave
(BW) parametrization [84] is used to describe the $p_{\rm T}$ shape in real
data in the full range of transverse momentum. The parameters of the Blast-
Wave functions are obtained in the first iteration using the efficiency
calculated based on the generated $p_{\rm T}$ distributions. The obtained BW
parametrizations in different centrality intervals are then used to re-weight
the input shape in the MC and these updated efficiencies are used to correct
the raw spectra. This iterative procedure converges already after two
iterations.

The Acceptance $\times$ Efficiency is calculated, in each centrality and
$p_{\rm T}$ interval, as the ratio of reconstructed and generated primary
(anti)nuclei in the simulations. The generated (anti)nuclei are counted in
$|y|<0.5$, in order to normalize the corrected yield to one unit of rapidity.
The same track selection and particle identification criteria as in data are
applied to the reconstructed sample in the MC. Particles from pile-up events
are removed from the generated sample and kept in the reconstructed sample to
properly incorporate the pile-up correction into the efficiency. The
(anti)deuteron efficiency varies from about 20% and 30$\%$ for antimatter and
matter, respectively for $p_{\rm T}$ $<1.2$ GeV/$c$ to about 45% for
antideuterons and 50$\%$ deuterons, for $p_{\rm T}$ $>1.2$ GeV/$c$, with a
small centrality dependence, while that of (anti)3He ranges between about
60$\%$ for $p_{\rm T}$ $<2$ GeV/$c$ to about 80$\%$ at larger $p_{\rm T}$. The
${}^{3}\overline{\rm He}$ efficiency is a few percent smaller than that of 3He
because of antimatter annihilation in the detector material, but still the
difference between the 3He and ${}^{3}\overline{\rm He}$ efficiencies is
smaller compared to the statistical precision of data.

The fraction of primary deuterons is extracted in different centrality and
$p_{\rm T}$ intervals from fits to the $\mathrm{DCA}_{xy}$ distributions with
templates. Antideuterons from data are used as templates for primary
deuterons, since measured antideuterons are all primary as there are no
secondary antideuterons produced in the interactions in the material. The
$\mathrm{DCA}_{xy}$ templates for secondary deuterons from spallation are
taken from MC simulations. The $\mathrm{DCA}_{xy}$ distributions in data are
filled using a high-purity sample of deuterons selected by requiring that the
measured $\textrm{d}E/\textrm{d}x$ and time-of-flight are within 3 standard
deviations from their expected values. The fraction of primary deuterons is
calculated by integrating the primary-deuteron template from the fit in the
interval $\mathrm{DCA}_{xy}<0.1$ cm and dividing it by the number of deuterons
in the same $\mathrm{DCA}_{xy}$ range. The fractions of primary deuterons
extracted from the $\mathrm{DCA}_{xy}$ fits depend on centrality, with values
ranging from 50$\%$ in central to almost 90$\%$ in peripheral collisions at
low $p_{\rm T}$. These fractions converge to 100$\%$ for $p_{\rm T}$ $>$ 1.6
GeV/$c$. The fraction of secondary 3He from spallation could not be extracted
due to the very limited number of counts. For this reason, the 3He spectrum is
measured only for $p_{\rm T}$ $>2$ GeV/$c$ where the contribution from
spallation is negligible.

###  3.4 Elliptic-flow measurement

The azimuthal distribution of (anti)deuterons produced in the Xe–Xe collisions
with respect to the n-th order flow symmetry plane $\Psi_{n}$ [85, 86, 87, 88]
can be expressed as a Fourier series

$E\frac{\mathrm{d^{3}}N}{\mathrm{d}p^{3}}=\frac{1}{2\pi}\frac{\mathrm{d^{2}}N}{p_{\mathrm{T}}\mathrm{d}p_{\rm{T}}\mathrm{d}y}\left(1+\sum_{n=1}^{\infty}2v_{n}\cos\left(n\left(\varphi-\Psi_{n}\right)\right)\right),$
(1)

where $E$ is the energy of the particle, $p$ the momentum, $\varphi$ the
azimuthal angle, $y$ the rapidity, and

$v_{n}=\langle\cos\left(n(\varphi-\Psi_{n})\right)\rangle.$ (2)

The second coefficient of the Fourier series ($v_{2}$) is called elliptic flow
and is related to the initial geometrical spatial asymmetry of the matter
created in heavy-ion collisions. The elliptic-flow coefficients are measured
using the Scalar Product (SP) method [89, 85], as done in Refs. [3, 31]. This
is a two-particle correlation technique based on the scalar product of the
unit flow vector of the particle of interest, $k$, and the $Q$-vector. The
unit flow vector is denoted by u${}_{n,k}=\mathrm{exp}(in\varphi_{k})$, where
$\varphi_{k}$ is the azimuthal angle of the particle $k$. The $Q$-vector is
computed from the azimuthal distribution of a set of charged particles (so
called reference flow particles) as

$\textbf{{Q}}_{n}=\sum w_{i}e^{in\varphi_{i}},$ (3)

where $w_{i}$ is a weight applied to correct for non-uniform acceptance and
efficiency of the detector (as done in Refs. [64, 11, 90]), $n$ is the order
of the harmonic, and $\varphi_{i}$ is the azimuthal angle for the $i$th
reference flow particle. The $v_{n}$ flow coefficients are calculated as

$v_{n}\\{\mathrm{SP}\\}=\frac{\left\langle\langle\textbf{u}_{n,k}{\textbf{{Q}}^{*}_{n}}\rangle\right\rangle}{\sqrt{\frac{\langle\textbf{{Q}}_{n}\textbf{{Q}}^{A*}_{n}\rangle\langle\textbf{{Q}}_{n}\textbf{{Q}}^{B*}_{n}\rangle}{\langle\textbf{{Q}}^{A}_{n}\textbf{{Q}}^{B*}_{n}\rangle}}}.$
(4)

Single brackets $\langle...\rangle$ denote an average over all events, while
double brackets $\langle\langle...\rangle\rangle$ indicate an average over all
particles in all events, and ∗ denotes the complex conjugate. The denominator
is a correction factor that is introduced to take into account the resolution
of the $\textbf{{Q}}_{n}$ vector. In this analysis, the $\textbf{{Q}}_{n}$
vector is calculated from the azimuthal distribution of the energy deposition
measured in the V0A, while the $\textbf{{Q}}_{n}^{A}$ and
$\textbf{{Q}}_{n}^{B}$ vectors (used to estimate the resolution of
$\textbf{{Q}}_{n}$) are determined from the azimuthal distribution of the
energy deposited in the V0C and that of tracks reconstructed in the TPC,
respectively. Using these detectors, a pseudorapidity gap $|\Delta\eta|>2$
between the particle of interest and the reference flow particles is
introduced. Such a pseudorapidity gap reduces non-flow effects, which are
correlations not arising from the collective expansion of the system (e.g.
resonance decays and jets).

The $v_{2}$ coefficients of (anti)deuterons are calculated in three different
ranges of $\Delta M=M-M_{\rm d}$, where $M$ is the particle mass obtained from
the measured momentum and time-of-flight of each deuteron candidate track, and
$M_{\rm d}$ is the deuteron mass taken from CODATA [91]. The $v_{2}^{\rm
Tot}$($\Delta M$) contains contributions from the signal
($v_{2}^{\mathrm{sig}}$) and from the background ($v_{2}^{\mathrm{bkg}}$)

$v_{2}^{\rm Tot}(\Delta
M)=v_{2}^{\mathrm{sig}}\frac{N^{\mathrm{sig}}}{N^{\mathrm{tot}}}(\Delta
M)+v_{2}^{\mathrm{bkg}}\frac{N^{\mathrm{bkg}}}{N^{\mathrm{tot}}}(\Delta M),$
(5)

where $N^{\rm{sig}}$ is the number of deuterons, $N^{\rm{bkg}}$ the number of
background particles and $N^{\rm{tot}}$ is their sum. The $v_{2}^{\rm sig}$ is
extracted from the value of $v_{2}^{\rm Tot}$ measured in the central interval
of the $\Delta M$ distribution, in which $v_{2}^{\mathrm{bkg}}$ is evaluated
using the average between the left and right $\Delta M$ intervals and
propagating the statistical uncertainties accordingly. The $N^{\rm{sig}}$ and
$N^{\rm{bkg}}$ are obtained from the fit to the $\Delta M$ distribution using
a Gaussian with an exponential tail for the signal and an exponential for the
background. The signal extraction procedure is illustrated in Fig. 2 for
$0.8<p_{\rm T}<1.6$ GeV/$c$ in the centrality interval 0–20$\%$. To avoid
contamination from secondary deuterons produced by spallation in the detector
material, for the flow measurement only antideuterons are used for $p_{\rm
T}<1$ GeV/$c$.

Figure 2: The $\Delta M$ distribution (left) and the extracted $v_{2}$ (right)
of deuteron candidates as a function of $\Delta M$ for $0.8~{}<$ $p_{\rm T}$
$<1.6$ GeV/$c$ in the centrality interval 0–20% in Xe–Xe collisions. The
statistical uncertainties on the data points are represented by bars. The
measurement is carried out at midrapidity, i.e., $\left|y\right|<0.5$.

##  4 Systematic uncertainties

The dominant sources of systematic uncertainties on the (anti)nucleus $p_{\rm
T}$ spectra and elliptic flow are related to the event and track selections,
ITS–TPC matching, particle identification, signal extraction, absorption of
(anti)nuclei in the detector material, and material budget. These are
summarized in Table 1, reporting the uncertainties in the lowermost and
uppermost $p_{\rm T}$ intervals, as the systematic uncertainties evolve
monotonically with $p_{\rm T}$. The final systematic uncertainty assigned to
the data points is obtained by summing in quadrature all individual
contributions. The methods used to estimate the systematic uncertainties from
these sources are illustrated in the following.

Table 1: Summary of the different contributions to the systematic uncertainties on the (anti)nucleus $p_{\rm T}$-differential yields and (anti)deuteron elliptic flow, in the lowermost and uppermost $p_{\rm T}$ intervals. All values are in percentage.  | d ($\overline{\rm d}$) yield | d + $\overline{\rm d}$ elliptic flow | 3He (${}^{3}\overline{\mathrm{He}}$) yield
---|---|---|---
$p_{\rm T}$ range (GeV/$c$) | 0.8 – 1.2 | 4.0 – 5.0 | 0.8 – 1.6 | 4.0 – 5.0 | 1.0 – 2.0 | 5.0 – 7.0
Source of uncertainty |  |  |  |  |  |
Event selection | 1 (1) | 1 (1) | 1 | 1 | 1 (1) | 1 (1)
Tracking and PID | 1 (2) | 1 (2) | 2 | 2 | 1 (4) | 5 (6)
ITS–TPC matching | 2 (2) | 2 (2) | 2 | 2 | 2 (2) | 2 (2)
Signal extraction | 1 (1) | 5 (5) | 2 | 7 | – | –
Absorption | 1 (6) | 0.6 (3) | 6 | 3 | 0.3 (2) | 0.3 (1)
Material Budget | 1 (1) | 1 (1) | 1 | 1 | 1 (1) | 1 (1)

###  4.1 Event selection uncertainty

The systematic uncertainty from the event selection is estimated by varying
the event selection criteria, i.e. the requirement on the $z$-coordinate of
the primary vertex and the pile-up rejection. This contribution is found to be
about 1$\%$ for both $p_{\rm T}$ spectra and elliptic-flow analyses.

###  4.2 Track selection, PID and ITS–TPC matching efficiency uncertainty

The systematic uncertainties related to track selection and particle
identification are estimated by repeating the full analysis chain using 50
different settings with different selection criteria. These are chosen by
sampling the analysis parameters randomly from uniform probability
distributions. The standard deviation of the distribution of fully-corrected
yields is taken as systematic uncertainty in each $p_{\rm T}$ and centrality
interval. This method, based on the frequentist approach to explore the
probability density function of measurements, takes into account possible
correlations between the different analysis parameters. The contribution from
ITS–TPC matching efficiency is estimated from charged-particle tracks by
comparing the probabilities of prolonging a track from the TPC to the ITS in
data and MC [10]. This uncertainty is approximately 2$\%$ and is added in
quadrature to the previous contributions.

###  4.3 Signal extraction uncertainty

The signal extraction uncertainty is assigned only to (anti)deuteron $p_{\rm
T}$ spectra and elliptic flow, while for 3He it is found to be negligible.
Such contribution is estimated by repeating the fit to the TOF signal using
different intervals. The default fit range is $-7<(\Delta t-\Delta t_{\rm
exp})/\sigma_{\rm TOF}<15$, while for systematic uncertainties the limits are
varied with a uniform random sampling in $[-10,-7]$ for the lower limit and in
$[10,15]$ for the upper limit. The standard deviation of the extracted yields
is taken as a systematic uncertainty in each $p_{\rm T}$ and centrality
interval. Additionally, only for flow measurement, the $v_{2}^{\mathrm{bkg}}$
was evaluated by using only the left or the right $\Delta M$ interval for
$v_{2}^{\mathrm{bkg}}$ in Eq. 5.

###  4.4 Absorption and material budget uncertainties

The contribution due to the uncertainty on the measured inelastic cross
section of (anti)nuclei with the detector material is estimated using MC
productions with increased and decreased cross section according to the
measured uncertainties [92, 93, 94, 95, 96, 97], as done in Ref. [2]. The
ALICE detector material is known with a precision of 4.5$\%$ [69]. The
systematic uncertainty on the (anti)nucleus yield related to the uncertainty
in the material budget is taken from the measurement of (anti)nucleus
production in Pb–Pb collisions at $\sqrt{s_{\mathrm{NN}}}$ = 5.02 TeV [16].

##  5 Results

###  5.1 Transverse-momentum spectra

The transverse-momentum spectra of d and $\overline{\mathrm{d}}$, as well as
those of 3He and ${}^{3}\overline{\mathrm{He}}$ are found to be consistent
within the uncertainties in all centrality classes, as expected in the case of
vanishing baryochemical potential at midrapidity at LHC energies. Hence, the
average $p_{\rm T}$-differential yields of deuterons and antideuterons, and of
3He and ${}^{3}\overline{\mathrm{He}}$, are calculated, as presented in Fig.
3. The slope of the transverse-momentum distributions flattens when moving
from peripheral to central collisions, i.e., with increasing event
multiplicity, as it was already observed in p–Pb collisions at
$\sqrt{s_{\mathrm{NN}}}$ = 5.02 TeV [7] and at $\sqrt{s_{\mathrm{NN}}}$ = 8.16
TeV [17], and in Pb–Pb collisions at $\sqrt{s_{\mathrm{NN}}}$ = 2.76 TeV [2,
3] and at $\sqrt{s_{\mathrm{NN}}}$ = 5.02 TeV [16].

Figure 3: Transverse-momentum differential yields of the average of deuterons
and antideuterons in different centrality classes (left panel), and of the
average of ${}^{3}\mathrm{He}$ and ${}^{3}\overline{\mathrm{He}}$ (right
panel) in the centrality class (0–90%). Dotted lines show the Blast-Wave
individual fit to the $p_{\rm T}$ spectra. Statistical and systematic
uncertainties are shown as vertical bars and boxes, respectively.

In order to extrapolate the yields in the unmeasured $p_{\rm T}$ intervals, a
Blast-Wave function [84] is fitted to the $p_{\rm T}$ distributions of (anti)d
and (anti)3He. The resulting $p_{\rm T}$-integrated yields (d$N$/d$y$) of
(anti)deuterons and (anti)3He are calculated summing the two contributions
obtained by integrating the data points in the measured $p_{\rm T}$ region and
by integrating the fit function in the unmeasured one. The difference between
the integral of the fit function and the integral of the data points is
accounted for in the systematic uncertainty of the final yields. The resulting
d$N$/d$y$ are summarized in Table 2. The fraction of yield obtained from the
extrapolation of the fit function varies between 8% and 35% from central to
peripheral collisions for (anti)d, and $\sim 9\%$ for (anti)3He.

The systematic uncertainties on the integrated yields were obtained
extrapolating the uncertainties associated with the $p_{\rm T}$ spectra,
treating differently the $p_{\rm T}$-correlated and -uncorrelated systematic
uncertainties. The uncertainties on material budget, event selection, signal
extraction, ITS–TPC matching efficiency, and absorption are found to be highly
correlated in $p_{\rm T}$ and are considered as fully $p_{\rm T}$ correlated,
whereas the uncertainties due to track selection and PID are found to be
mostly uncorrelated with transverse momentum. For the computation of the
systematic uncertainties on the integrated yields three contributions have
been considered, as done in previous similar analyses [7, 17]: (i) the $p_{\rm
T}$-uncorrelated contribution was evaluated with the Gaussian sampling method;
(ii) the correlated part of the systematic uncertainties of the $p_{\rm T}$
spectra was used to shift accordingly the data points up and down with respect
to the mean value, allowing the refit of the $p_{\rm T}$ spectra; (iii) the
uncertainty on the extrapolation was evaluated fitting the spectra with
several alternative functions (i.e., Boltzmann [98],
$m_{\mathrm{T}}$-exponential [99], and Lévy-Tsallis [100]) and taking into
account the spread with respect to the Blast-Wave results. In case (i), the
systematic uncertainty was taken as the RMS of the distribution of the varied
integrated yield values, whereas in cases (ii) and (iii) half of the
difference between the maximum and the minimum yields was considered as
uncertainty. The final uncertainty was obtained as the sum in quadrature of
the different contributions.

Table 2: Integrated yields (d$N$/d$y$) of the average of deuterons and antideuterons and of the average of 3He and ${}^{3}\overline{\rm He}$, for each centrality class measured at midrapidity ($|y|<0.5$). The values of the average charged-particle multiplicity density ($\langle$d$N_{\rm ch}$/d$\eta$$\rangle\big{|}_{|\eta|<0.5}$) are taken from Ref. [101]. The first uncertainty on d$N$/d$y$ is statistical and the second is systematic.  Centrality class |  $\langle$d$N_{\rm ch}$/d$\eta$$\rangle\big{|}_{|\eta|<0.5}$ | d$N$/d$y$ [(d+$\overline{\mathrm{d}}$)/2] | d$N$/d$y$ [(3He+${}^{3}\overline{\mathrm{He}}$)/2]
---|---|---|---
0–10$\%$ | 1053 $\pm$ 25 | (8.72 $\pm$ 0.17 $\pm$ 0.52) $\times$ $10^{-2}$ |
10–20$\%$ | 706 $\pm$ 17 | (6.19 $\pm$ 0.12 $\pm$ 0.37) $\times$ $10^{-2}$ |
20–40$\%$ | 397 $\pm$ 9 | (3.86 $\pm$ 0.08 $\pm$ 0.23) $\times$ $10^{-2}$ |
40–60$\%$ | 158 $\pm$ 4 | (1.64 $\pm$ 0.03 $\pm$ 0.10) $\times$ $10^{-2}$ |
60–90$\%$ | 40 $\pm$ 1 | (3.25 $\pm$ 0.06 $\pm$ 0.19) $\times$ $10^{-3}$ |
0–90$\%$ | 333 $\pm$ 5 | (2.99 $\pm$ 0.06 $\pm$ 0.19) $\times$ $10^{-2}$ | (7.45 $\pm$ 0.94 $\pm$ 0.67 )$\times 10^{-5}$

###  5.2 Thermal fit

The $p_{\rm T}$-integrated yields of d and 3He for central (0–10%) Xe–Xe
collisions are shown in Fig. 4 together with those of $\pi$, K, p, and $\phi$.
At the LHC, the production of most light-flavor hadrons and light
(anti)(hyper)nuclei in nucleus–nucleus collisions can be described in the
framework of the statistical hadronization approach via thermal models based
on the grand canonical ensemble with a single chemical freeze-out temperature
($T_{\rm chem}$), and a given volume $V$ of the fireball. Thermal model fits
to the ALICE data for the yields of $\pi$, K, $\phi$, p [102], d, and 3He
measured in central (0–10%) Xe–Xe collisions at $\sqrt{s_{\rm NN}}=$ 5.44 TeV
are performed using the open source Thermal-FIST package [103]. The fit
converges at $T_{\rm chem}$ = (154.2 $\pm$ 1.1) MeV, $V=$ (3626 $\pm$ 298)
fm3, and $\chi^{2}/$NDF = 0.83. All other parameters are fixed using the
parameterizations reported in Ref. [104]. The calculations are carried out
using the energy-dependent Breit–Wigner treatment of resonance widths with
constant branching ratios [105]. Enabling the partial chemical equilibrium
[106], without baryon annihilation, does not significantly change the results
of the calculated yields of light nuclei, once the $T_{\rm chem}$ and $T_{\rm
kin}$ are fixed to 155 MeV and 100 MeV, respectively. The results for the
yields obtained from the thermal fit are shown as solid lines in Fig. 4.
Similar fits to the measured yields have been carried out using the GSI-
Heidelberg thermal model [107]. For such fit, the temperature of the system
and the baryochemical potential are fixed to the results obtained in the most
central Pb–Pb collisions at $\sqrt{s_{\mathrm{NN}}}$ = 2.76 TeV with the
S-matrix correction for the protons ($T_{\rm chem}$ = 156.6 MeV, $\mu_{B}$ =
0.7 MeV), while the volume $V$ is a free parameter [108]. The fit to the Xe–Xe
data converges at $V=$ (2996 $\pm$ 102) fm3 ($|y|<$0.5), and $\chi^{2}/$NDF =
0.55.
The main difference between the two models is in the treatment of the
interactions: while the GSI-Heidelberg approach implements the S-matrix
formalism [109, 110, 111, 112, 113] to include non-resonant pion–nucleon
interactions at LHC energies, Thermal-FIST uses the energy-dependent
Breit–Wigner resonance widths [114]. Since the pion is the most abundant
particle at freeze-out and the corresponding cross sections for hadronic
interactions are large, the handling of $\pi$N interactions is a key aspect
when analyzing observables involving nucleons in ultra-relativistic
nucleus–nucleus collisions. The different treatment of interactions is
reflected in the different results of both the volume of the system, which is
driven by the abundance of pions, and its temperature. The interplay between
these two parameters is anticorrelated. Indeed, fixing in the Thermal-FIST
model the $T_{\rm chem}$ to a higher value, e.g. the value used for the GSI-
Heidelberg fit ($T_{\rm chem}=$ 156.6 MeV), the resulting volume becomes
smaller ($V=$ (3095 $\pm$ 101) fm3), and comparable with that obtained with
the GSI-Heidelberg approach.
The resulting yields for the GSI-Heidelberg model are shown as dotted lines in
Fig. 4, being well compatible with the Thermal-FIST results. Light hadron
yields are taken from Ref. [102]. The yields of all given species are the
average of the particle and antiparticle yields. The yield of 3He in the 0–10%
centrality class is obtained using the same scaling used for alpha nuclei in
Ref. [5]. The results of the models prove that the production of light nuclei
in Xe–Xe collisions is sensitive to the temperature of the system at chemical
freeze-out. Similar fits to the most central Pb–Pb collisions at
$\sqrt{s_{\mathrm{NN}}}$ $=$ 2.76 TeV in one unit of rapidity at midrapidity,
including the S-matrix, gave as results $T_{\rm chem}$ = 156.6 MeV, $\mu_{B}$
= 0.7 MeV, and $V=$ 4175 fm3 [108]. The $T_{\rm{chem}}$ obtained from the fit
of the Thermal-FIST model to the measured light-flavor hadron yields in
central Xe–Xe collisions is similar to the $T_{\rm{chem}}$ obtained in central
Pb–Pb collisions using S-matrix based thermal model and consistent with the
pseudocritical temperature of the chiral crossover transition predicted by
lattice QCD calculations, $T=$ (156.5 $\pm$ 1.5) MeV [115].

Figure 4: Thermal fit to the measured hadron yields in Xe–Xe collisions at
$\sqrt{s_{\mathrm{NN}}}$ = 5.44 TeV, performed with two different
implementations of the statistical hadronization model, namely the Thermal-
FIST [103] and the GSI-Heidelberg model [107]. The yields shown for each given
species are the average of the particle and antiparticle yields. In the bottom
panel, the ratios of data to the model calculations are shown.

###  5.3 Ratio to proton and pion yields

The consistency of models describing the hadron chemistry in high-energy
hadronic collisions can be tested by comparing the model predictions with the
measured yields for different hadron species or, alternatively, with yield
ratios of different hadrons. The ratios of the measured yields of nuclei and
those of protons are sensitive to the production mechanism as they remove the
dependence on the volume of the system while keeping the dependence on the
freeze-out temperature. In Fig. 5 the deuteron-to-proton (top panel) and 3He-
to-proton (bottom panel) yield ratios measured in all available collision
systems at the LHC as a function of the average charged-particle
pseudorapidity density $\langle$d$N_{\mathrm{ch}}/$d$\eta\rangle$ [6, 7, 2, 4,
13, 17] are compared with the predictions from the statistical hadronization
model with canonical ensemble (CSM) and the coalescence one. The results from
all available collision systems at $\sqrt{s_{\mathrm{NN}}}$ $=$ 5.02 and 5.44
TeV are highlighted in color and show a common and smooth increasing trend
with increasing $\langle$d$N_{\mathrm{ch}}/$d$\eta\rangle$, in both d/p and
3He/p yield ratio cases. The results at $\sqrt{s_{\mathrm{NN}}}$ $=$ 5.02 and
5.44 TeV follow the same trend as the results at different collision energies
(shown in grey in Fig. 5).

Figure 5: Deuteron-to-proton (top panel) and 3He-to-proton (bottom panel)
yield ratios as a function of the average charged-particle multiplicity
density. All yields are measured at midrapidity, i.e., $\left|y\right|<$ 0.5
for pp, Xe–Xe and Pb–Pb collisions, and $-1<\left|y\right|<0$ for p–Pb
collisions. Statistical uncertainties are shown as vertical lines, whereas
systematic ones are shown as boxes. The coalescence predictions are shown as
bands, whose width represents the model uncertainty. The black and red lines
correspond to the expectations of two different hypotheses of the CSM.

For the coalescence predictions, the probability of forming an (anti)nucleus
is given by the overlap of the phase-space distributions of the constituent
nucleons in the emission source with the Wigner density of the bound state.
The latter is calculated approximating the (anti)nucleus internal wave
function with a Gaussian function [116]. From the studies shown in Ref. [49],
up to a factor 50% difference in the coalescence predictions for the momentum
distribution of deuterons can be expected using a Gaussian wave function
instead of a more realistic one, such as Argonne $v_{18}$. For 3He, the
coalescence process can happen in two ways, either as a two-step process in
which the 3He is formed by the coalescence of a deuteron and a proton (two-
body coalescence), or as a three-body coalescence process in which three
nucleons combine to form an 3He nucleus [116]. In the case of the 3He/p, the
measured ratio in Xe–Xe collisions is higher than the prediction of the
coalescence models by about $2\sigma$. Notably, the calculations with two- and
three-body coalescence yield similar results for the 3He/p ratios at the
multiplicity of Xe–Xe collisions. The difference between the two predictions
is larger at lower multiplicity, i.e., in the range covered by pp and p–Pb
collisions. In this multiplicity region, the two-body coalescence overshoots
the data by $\sim 3\sigma$, with the exception of the 20–40% centrality class
of p–Pb collisions at $\sqrt{s_{\mathrm{NN}}}$ = 5.02 TeV (corresponding to
$\langle$d$N_{\mathrm{ch}}/$d$\eta\rangle\sim$ 23), that is 5$\sigma$ away
from the model. The three-body coalescence curve is systematically
overshooting the data in the low and intermediate multiplicity region, and the
agreement with the measurements worsens up to 7$\sigma$ for the 20–40%
centrality class of p–Pb collisions at $\sqrt{s_{\mathrm{NN}}}$ = 5.02 TeV.
None of the coalescence curves predicts the decreasing trend of data at very
high multiplicity ($\langle$d$N_{\mathrm{ch}}/$d$\eta\rangle>300$), for
neither the deuteron-to-proton nor the 3He-to-proton yield ratios.

In the CSM, exact conservation of baryon number (B), electric charge (Q), and
strangeness (S) are required in a specified volume known as correlation volume
$V_{\mathrm{c}}$. Two versions of the CSM, both using $V_{\mathrm{c}}=$ 1.6
d$V$/d$y$, are shown in comparison with data: (i) the first one assumes the
system to be in full chemical equilibrium and the chemical freeze-out
temperature to be independent of multiplicity ($T_{\rm{chem}}$ = 155 MeV)
[117], (ii) the second uses the Saha equation approach [50] to compute light-
nucleus abundances in the hadronic phase, and considers the annihilation
freeze-out temperature to be dependent on
$\langle$d$N_{\mathrm{ch}}/$d$\eta\rangle$, evolving from 160 MeV for
multiplicities of about 20 to 132 MeV for multiplicity of about 2000 [106].
For these models, the extension of the correlation volume was investigated
through the event-by-event antideuteron number fluctuation measurement [32].
In such study it was found out that the correlation volume needed to describe
the net-deuteron number fluctuations in central Pb–Pb collisions is
$V_{\mathrm{c}}$ = (1.6 $\pm$ 0.3) d$V$/d$y$, well smaller than the one needed
to describe the net-proton number fluctuations in the same collision system,
$V_{\mathrm{c}}$ = (3–5) d$V$/d$y$ [118, 119, 120, 104]. In the case of the
deuteron-to-proton yield ratios, the expectations of CSM (i) show good
agreement with data in the full multiplicity range, with some tension in the
intermediate multiplicity, where the most peripheral Xe–Xe data point is lower
than the model by $\sim 3.5\sigma$. In the multiplicity region covered by
heavy-ion collisions ($\langle$d$N_{\mathrm{ch}}/$d$\eta\rangle>10^{2}$), the
predictions from CSM (i) show a plateau that matches the predictions of the
grand-canonical statistical model [37, 57, 46], while data hint towards a
decreasing trend for the highest multiplicities, as observed in the case of
the p/$\pi$ ratio [102]. Such a trend is qualitatively reproduced by CSM (ii),
which assumes that such suppression is entirely due to baryon annihilation in
the hadronic phase [106]. In summary, both the coalescence and the CSM (i)
predictions describe the absolute values of the yield ratios within $\sim
25\%$, and both reproduce the overall smoothly increasing trend of the d/p
ratio with increasing multiplicities, up to
$\langle$d$N_{\mathrm{ch}}/$d$\eta\rangle\sim$ 300\. The CSM (ii) model
reproduces the decreasing trend of data at large
$\langle$d$N_{\mathrm{ch}}/$d$\eta\rangle$ values ($>$300), but is further
from data as compared to the other two models in the remaining multiplicity
range ($\langle$d$N_{\mathrm{ch}}/$d$\eta\rangle<$300).

In the case of the 3He/p yield ratios, at high multiplicities
($10^{2}<\langle$d$N_{\mathrm{ch}}/$d$\eta\rangle<10^{3}$), the result from
Xe–Xe collisions is in agreement within 1$\sigma$ with both the CSM
predictions. In the low multiplicity range
($\langle$d$N_{\mathrm{ch}}/$d$\eta\rangle<$ 10), the CSM (i) hypothesis is in
agreement with the data within $\sim 1.5\sigma$, while in the intermediate
multiplicity range it is excluded by up to $13\sigma$. The CSM (ii) captures
the decreasing trend of the data at high multiplicity, with an agreement
within 1$\sigma$ for $\langle$d$N_{\mathrm{ch}}/$d$\eta\rangle>$ 100, although
it is further from the data as compared to CSM (i) and coalescence for
$\langle$d$N_{\mathrm{ch}}/$d$\eta\rangle<$ 100\. Overall, the coalescence
models reproduce the yield ratios within $\sim 60\%$ and the general
increasing trend of the data points, although significant discrepancies
remain.

The decreasing trend of the particle ratios, for increasing multiplicity and
$\langle$d$N_{\mathrm{ch}}/$d$\eta\rangle>$ 100, is even more pronounced when
looking at the nucleus-to-pion yield ratios, as shown in Fig. 6. Also in this
case, the colored markers show the results from all available collision
systems at $\sqrt{s_{\mathrm{NN}}}$ $=$ 5.02 and 5.44 TeV, while the results
at different energies are shown in grey. All results follow a common trend
with increasing $\langle$d$N_{\mathrm{ch}}/$d$\eta\rangle$. The data are
compared with the predictions from the CSM models (i) and (ii). For deuterons,
the measured ratios are described only qualitatively by the CSM (i) at low
multiplicities ($\langle$d$N_{\mathrm{ch}}/$d$\eta\rangle<$ 10), while the
model (i) predictions are consistent with the data at intermediate and high
multiplicities, within $\sim 1\sigma$ and 3$\sigma$, respectively, being the
most different for the most central Pb–Pb collisions at
$\sqrt{s_{\mathrm{NN}}}$ = 5.02 TeV. The predictions from CSM (ii) capture the
trend of the data at high multiplicity and agree with the Pb–Pb experimental
data within 1$\sigma$ and with the Xe–Xe results within 1.6$\sigma$, for
$\langle$d$N_{\mathrm{ch}}/$d$\eta\rangle>$ 100, while overshooting the data
points for $\langle$d$N_{\mathrm{ch}}/$d$\eta\rangle<$ 100\. For nuclei with
$A$ = 3, the ratio to pion yields shows discrepancies with CSM (i) of up to
$\sim 17\sigma$ in the intermediate multiplicity range and up to $\sim
8\sigma$ with the most central Pb–Pb data at $\sqrt{s_{\mathrm{NN}}}$ = 5.02
TeV. The CSM (ii) predictions agree within 2$\sigma$ with the data for
$\langle$d$N_{\mathrm{ch}}/$d$\eta\rangle>$ 100, but fail in reproducing the
data at $\langle$d$N_{\mathrm{ch}}/$d$\eta\rangle<$ 100.

The decrease of the yield ratio at high average charged-particle multiplicity
values is larger in Fig. 6 with respect to the corresponding ratios in Fig. 5.
This is due to the decreasing trend of both the deuteron-to-pion and proton-
to-pion yield ratios, leading to the partial cancellation of this trend in the
deuteron-to-proton yield ratio. Among all presented models only the CSM (ii)
captures the decreasing trend of the nucleus-to-proton and nucleus-to-pion
yield ratios as well as their absolute magnitude.

Figure 6: Deuteron-to-pion (top panel), and 3He-to-pion (bottom panel) yield
ratios as a function of the charged-particle multiplicity density. All yields
are measured at midrapidity, i.e., $\left|y\right|<$ 0.5 for pp, Xe–Xe and
Pb–Pb collisions, and $-1<\left|y\right|<0$ for p–Pb collisions. Lines
represent statistical uncertainties, whereas boxes show systematic ones. The
solid lines correspond to the expectations of two implementations of the CSM,
see text for details.

###  5.4 Coalescence parameters

In the coalescence models the key observable is the coalescence parameter
$B_{A}$, that quantifies the probability for $A$ nucleons to bind together
forming a nucleus of mass number $A$. This parameter can be obtained
experimentally through the ratio of the invariant yield of the nucleus with
mass number $A$ and that of protons. The former is expressed as a function of
the $p_{\rm T}$ of the nucleus, denoted as $p_{\mathrm{T}}^{A}$, while the
latter is evaluated at the transverse momentum denoted as $p_{\mathrm{T}}^{\rm
p}$, with $p_{\mathrm{T}}^{\mathrm{p}}$ = $p_{\mathrm{T}}^{A}$/$A$. The
coalescence parameter is obtained as follows

$B_{A}={\biggl{(}\dfrac{1}{2\pi
p^{A}_{\mathrm{T}}}\biggl{(}\dfrac{\rm{d}^{2}\it{N}}{\rm{d}\it{y}\rm{d}\it{p}_{\mathrm{T}}}\biggr{)}_{A}\biggr{)}}\bigg{/}{\biggl{(}\dfrac{1}{2\pi
p^{\rm
p}_{\mathrm{T}}}\biggl{(}\dfrac{\rm{d}^{2}\it{N}}{\rm{d}\it{y}\rm{d}\it{p}_{\mathrm{T}}}\biggr{)}_{\rm
p}\biggr{)}^{A}}\,,$ (6)

assuming that protons and neutrons have the same $p_{\rm T}$ distributions, as
they belong to the same isospin doublet. The coalescence parameter is related
to the production probability of the nucleus via this process and can be
theoretically evaluated from the overlap of the nucleus wave function and the
phase space distribution of the constituents via the Wigner function formalism
[46]. This formalism allows one to account for the source size and the quantum
mechanical properties of the nucleons in the calculation of $B_{A}$, using a
realistic wave function for the nucleus.

In Fig. 7 the coalescence parameters $B_{2}$ and $B_{3}$ are shown as a
function of the transverse momentum per nucleon ($p_{\rm T}$/$A$), also for
different centrality classes in the case of $B_{2}$. The transverse-momentum
spectra of protons used for the calculation of $B_{A}$ are taken from Ref.
[102]. The coalescence parameters increase with increasing $p_{\rm T}$/$A$ in
all centrality classes. This trend was already observed in previous
measurements from ALICE, in both heavy-ion and pp collisions [16, 2, 6, 7, 9,
10, 13, 14, 17]. Such behavior is not expected by simple coalescence models
that neglect the spatial extension of the baryon-emitting source. However, it
is well reproduced by state-of-the-art coalescence models that use the Wigner
function formalism and properly take into account the source size [49]. Hence,
the rising trend of the coalescence parameters with $p_{\rm T}$/$A$ reflects
the decreasing trend of the source size with $p_{\rm{T}}$ [121]: smaller
source sizes (at higher $p_{\rm T}$) correspond to larger coalescence
parameters.

Figure 7: Coalescence parameters $B_{2}$ (left panel) and $B_{3}$ (right
panel) as a function of $p_{\mathrm{T}}$/$A$, measured for deuterons and 3He,
respectively. Statistical uncertainties are represented as vertical lines
whereas boxes represent the systematic ones.

###  5.5 Elliptic flow of deuterons

The deuteron elliptic-flow coefficients measured in the centrality classes
0–20$\%$ and 20–40$\%$ are shown in Fig. 8 as a function of $p_{\rm T}$ in
comparison with the $v_{2}$ of pions, kaons, and protons taken from Ref. [65].
These are measured in narrower centrality intervals as compared to the
measurements presented in this paper. The values corresponding to the same
centrality classes are obtained as weighted averages using the $p_{\rm T}$
spectra taken from Ref. [102] as weights. A clear mass ordering is observed at
low $p_{\rm T}$, as expected from relativistic hydrodynamics [122], with a
slower rise with $p_{\rm T}$ of the (anti)deuteron $v_{2}$ as compared to that
of lighter hadrons. The mass ordering of $v_{2}$ at low $p_{\rm T}$ develops
mostly by final state rescattering in the hadronic phase [123], reflecting the
redistribution of the momentum anisotropy generated in the early QGP states
among the different hadron species, driven by the radial acceleration and
cooling of matter during the hadronic rescattering phase. Assuming that
(anti)nuclei are produced as compact multi-quark systems with negligible
final-state interactions with hadrons, their flow would be fully developed in
the partonic phase. On the other hand, if (anti)nuclei are produced by
coalescence, their flow could also have a contribution from the hadronic
rescattering phase, which is inherited from that of the coalescing nucleons.

In Fig. 8, the deuteron $v_{2}$ measurements are compared with the
expectations from the Blast-Wave and simple coalescence models using the same
procedure described in Refs. [3, 31, 8]. 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 Xe–Xe collisions at
$\sqrt{s_{\mathrm{NN}}}$ = 5.44 TeV [102, 65] in the transverse-momentum
ranges $(0.5<p^{\pi}_{\mathrm{T}}<1)\ \mathrm{GeV}/\textit{c}$,
$(0.7<p^{\mathrm{K}}_{\mathrm{T}}<2)\ \mathrm{GeV}/\textit{c}$, and
$(0.7<p^{\mathrm{p}}_{\mathrm{T}}<2.5)\ \mathrm{GeV}/\textit{c}$,
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 Ref. [124].

The values of the Blast-Wave parameters extracted from the fits are reported
in Table 3 for each centrality interval. The elliptic flow of (anti)deuterons
is calculated using the parameters obtained from the simultaneous fit and the
deuteron mass, i.e., assuming the same kinetic freeze-out conditions.

Table 3: 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 0–20$\%$ | Centrality 20–40$\%$ |
---|---|---|---
$T_{\mathrm{kin}}$ (MeV) | $112\pm 2$ | $111\pm 2$ |
$\rho_{0}$ | $1.29\pm 0.05$ | $1.31\pm 0.05$ |
$\rho_{\mathrm{a}}$ $\times 10^{-2}$ | $5.87\pm 0.02$ | $8.85\pm 0.02$ |
$s_{2}$ $\times 10^{-2}$ | $4.94\pm 0.02$ | $8.86\pm 0.02$ |
Figure 8: (Anti)deuteron $v_{2}$ measured at $|y|<0.5$ in the centrality
classes 0–20$\%$ (left) and 20–40$\%$ (right) in comparison with the Blast-
Wave predictions obtained from simultaneous fits of the $p_{\rm T}$ spectra
and $v_{2}$ of pions, kaons, and protons [65]. Statistical and systematic
uncertainties are represented by bars and boxes, respectively.

The simple coalescence model used in this context is based on the assumption
that the invariant yield of (anti)deuterons with transverse momentum $p_{\rm
T}$ is proportional to the product of the invariant yields of its constituent
nucleons with transverse momentum $p_{\mathrm{T}}/2$ and on isospin symmetry,
due to which the proton and neutron $v_{2}$ are identical. Considering only
elliptical anisotropies of the constituent nucleons, i.e., neglecting higher-
order harmonics, the (anti)deuteron $v_{2}$ from coalescence is obtained from
that of (anti)protons using the scaling law [125]

$v_{2,\mathrm{d}}(p_{\rm
T})=\frac{2v_{2,\mathrm{p}}(p_{\rm{T}}/2)}{1+2{v^{2}_{2,\rm{p}}}(p_{\mathrm{T}}/2)}.$
(7)

The comparison between the (anti)deuteron $v_{2}$ measurements and the simple
coalescence predictions is shown in Fig. 9. As observed already in elliptic-
flow measurements in Pb–Pb collisions for both (anti)deuterons and (anti)3He,
the data are closer to the Blast-Wave predictions in more central collisions
and to the coalescence model in more peripheral collisions. These two simple
models represent approximate limits for (anti)nucleus flow which describe the
measurements in complementary centrality intervals.

Figure 9: (Anti)deuteron $v_{2}$ measured in the centrality classes 0–20$\%$
(left) and 20–40$\%$ (right) in comparison with the coalescence predictions
based on the mass-number scaling. Statistical and systematic uncertainties are
shown as bars and boxes, respectively. The flow of deuterons is measured at
midrapidity, i.e., $\left|y\right|<$ 0.5.

As noted in Ref. [65], the flow coefficients at low $p_{\rm T}$ are expected
to be smaller in Pb–Pb collisions than in Xe–Xe ones, due to the larger radial
flow in the Pb–Pb case. Such an effect is expected to be larger in central
collisions and for heavier particles, such as light nuclei. The results of the
$v_{2}$ of deuteron in Xe–Xe collisions, however, seem to be above the
corresponding measurements in Pb–Pb collisions, as already observed in the
case of the flow of lighter identified particles [65]. However, the present
results have large statistical uncertainties, which do not allow for
quantitative comparisons with the Pb–Pb results. In Ref. [65], more
quantitative comparisons between the flow coefficients of light-flavor hadrons
in Pb–Pb collisions and those in Xe–Xe collisions are discussed and
interpreted as due to the interplay of the nuclear deformation of the Xe
nucleus with respect to the Pb one, and of initial-state fluctuations
proportional to the square root of the mass number of the colliding nucleus.

##  6 Summary

Measurements of (anti)deuteron and (anti)3He production and of the elliptic-
flow of (anti)deuteron in Xe–Xe collisions at $\sqrt{s_{\mathrm{NN}}}$ = 5.44
TeV are presented. These results contribute to the understanding of the light
(anti)nucleus production mechanism by complementing the existing picture,
which includes measurements in different collision systems and at different
center-of-mass energies per nucleon–nucleon pair. The hadrochemistry of light
nuclei, i.e., the relative abundance of particles, in small collision systems
(pp and p–Pb) was found to be independent of collision energies and systems
and mostly driven by $\langle$d$N_{\mathrm{ch}}/$d$\eta\rangle$. This is
further investigated for the first time in heavy-ion collisions at LHC
energies by comparing the measurements in Xe–Xe and Pb–Pb collisions, and the
measurements are found to be consistent across the two different collision
systems at similar charged particle multiplicity densities. The canonical
statistical model and the coalescence predictions are tested by comparing the
multiplicity dependence of (anti)deuteron and (anti)3He yields, relative to
proton and pion yields. The Xe–Xe results fit the behavior of the previous
ALICE measurements, which are qualitatively described by the CSM and, in the
case of the ratio of deuterons to protons, also by coalescence, across all
multiplicities. A version of the CSM with $V_{\mathrm{c}}$= 1.6 d$V$/d$y$, a
multiplicity-dependent annihilation freeze-out temperature and the Saha
equation approach [50] to compute light-nucleus abundances in the hadronic
phase, captures the decreasing trend of data at high multiplicity,
corresponding to central Pb–Pb and Xe–Xe collisions, in all reported particle
ratios. This suggests that such suppression is due to baryon annihilations in
the hadronic phase. However, the same implementation of the CSM model fails to
simultaneously reproduce the trend of the particle ratios at intermediate
multiplicities. This shows that at the moment there is no common
implementation and available parametrization of the CSM able to reproduce all
particle ratios from small collision systems to central heavy-ion collisions.
The yields of light-flavor hadrons produced in Xe–Xe collisions are described,
in the framework of the statistical hadronization model, with different
implementations of the thermal fit, namely the Thermal-FIST package [103] and
the GSI-Heidelberg model [107]. In the former case, the fit converged at
$T_{\rm chem}$ = (154.2 $\pm$ 1.1) MeV, $V=$ (3626 $\pm$ 298) fm3, while in
the latter case the temperature and baryochemical potential are fixed to
$T_{\rm chem}$= 156.6 MeV, $\mu_{B}$= 0.7 MeV and the fit converges at a
volume $V=$ (2996 $\pm$ 102) fm3. The results from the two models are
consistent with each other within 2$\sigma$, with the results obtained in
Pb–Pb collisions ($T_{\rm chem}$ = 156.6 MeV) [108], and with the pseudo-
critical temperature for the transition from QGP to hadron gas predicted by
lattice QCD calculations ($T=$ (156.5 $\pm$ 1.5) MeV) [115]. Finally, the
results of the elliptic flow of (anti)deuterons are compared to the
predictions of a simple coalescence model and to the expectations of a Blast-
Wave fit of $v_{2}$ and $p_{\rm T}$ of light-flavor hadrons measured in the
same collision system and at the same energy. Such comparison shows that the
data are closer to the Blast-Wave predictions in more central collisions and
to the coalescence model in more peripheral collisions, as already observed in
the results of (anti)deuterons and (anti)3He flow measured in Pb–Pb
collisions.

## 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; Bulgarian Ministry of Education and Science, within the National Roadmap for Research Infrastructures 2020-2027 (object CERN), Bulgaria; 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) and Institut National de Physique Nucléaire et de Physique des Particules (IN2P3) and Centre National de la Recherche Scientifique (CNRS), 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; National Research and Innovation Agency - BRIN, Indonesia; Istituto Nazionale di Fisica Nucleare (INFN), Italy; 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; Pontificia Universidad Católica del Perú, Peru; Ministry of Science and Higher Education, National Science Centre and WUT ID-UB, 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, Ministry of Research and Innovation and Institute of Atomic Physics and Universitatea Nationala de Stiinta si Tehnologie Politehnica Bucuresti, Romania; 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 (NSTDA) and National Science, Research and Innovation Fund (NSRF via PMU-B B05F650021), Thailand; Turkish Energy, Nuclear and Mineral Research Agency (TENMAK), 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. In addition, individual groups or members have received support from: Czech Science Foundation (grant no. 23-07499S), Czech Republic; European Research Council (grant no. 950692), European Union; ICSC - Centro Nazionale di Ricerca in High Performance Computing, Big Data and Quantum Computing, European Union - NextGenerationEU; Academy of Finland (Center of Excellence in Quark Matter) (grant nos. 346327, 346328), Finland.

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bibliographyempty author

##  Appendix A The ALICE Collaboration

S. Acharya 127, D. Adamová 86, A. Agarwal135, G. Aglieri Rinella 32, L.
Aglietta24, M. Agnello 29, N. Agrawal 25, Z. Ahammed 135, S. Ahmad 15, S.U.
Ahn 71, I. Ahuja 37, A. Akindinov 141, V. Akishina38, M. Al-Turany 97, D.
Aleksandrov 141, B. Alessandro 56, H.M. Alfanda 6, R. Alfaro Molina 67, B. Ali
15, A. Alici 25, N. Alizadehvandchali 116, A. Alkin 104, J. Alme 20, G. Alocco
52, T. Alt 64, A.R. Altamura 50, I. Altsybeev 95, J.R. Alvarado 44, M.N. Anaam
6, C. Andrei 45, N. Andreou 115, A. Andronic 126, E. Andronov 141, V. Anguelov
94, F. Antinori 54, P. Antonioli 51, N. Apadula 74, L. Aphecetche 103, H.
Appelshäuser 64, C. Arata 73, S. Arcelli 25, M. Aresti 22, R. Arnaldi 56,
J.G.M.C.A. Arneiro 110, I.C. Arsene 19, M. Arslandok 138, A. Augustinus 32, R.
Averbeck 97, D. Averyanov 141, M.D. Azmi 15, H. Baba124, A. Badalà 53, J. Bae
104, Y.W. Baek 40, X. Bai 120, R. Bailhache 64, Y. Bailung 48, R. Bala 91, A.
Balbino 29, A. Baldisseri 130, B. Balis 2, D. Banerjee 4, Z. Banoo 91, V.
Barbasova37, F. Barile 31, L. Barioglio 56, M. Barlou78, B. Barman41, G.G.
Barnaföldi 46, L.S. Barnby 115, E. Barreau 103, V. Barret 127, L. Barreto 110,
C. Bartels 119, K. Barth 32, E. Bartsch 64, N. Bastid 127, S. Basu 75, G.
Batigne 103, D. Battistini 95, B. Batyunya 142, D. Bauri47, J.L. Bazo Alba
101, I.G. Bearden 83, C. Beattie 138, P. Becht 97, D. Behera 48, I. Belikov
129, A.D.C. Bell Hechavarria 126, F. Bellini 25, R. Bellwied 116, S.
Belokurova 141, L.G.E. Beltran 109, Y.A.V. Beltran 44, G. Bencedi 46, A.
Bensaoula116, S. Beole 24, Y. Berdnikov 141, A. Berdnikova 94, L. Bergmann 94,
M.G. Besoiu 63, L. Betev 32, P.P. Bhaduri 135, A. Bhasin 91, B. Bhattacharjee
41, L. Bianchi 24, N. Bianchi 49, J. Bielčík 35, J. Bielčíková 86, A.P. Bigot
129, A. Bilandzic 95, G. Biro 46, S. Biswas 4, N. Bize 103, J.T. Blair 108, D.
Blau 141, M.B. Blidaru 97, N. Bluhme38, C. Blume 64, G. Boca 21,55, F. Bock
87, T. Bodova 20, J. Bok 16, L. Boldizsár 46, M. Bombara 37, P.M. Bond 32, G.
Bonomi 134,55, H. Borel 130, A. Borissov 141, A.G. Borquez Carcamo 94, H.
Bossi 138, E. Botta 24, Y.E.M. Bouziani 64, L. Bratrud 64, P. Braun-Munzinger
97, M. Bregant 110, M. Broz 35, G.E. Bruno 96,31, V.D. Buchakchiev 36, M.D.
Buckland 23, D. Budnikov 141, H. Buesching 64, S. Bufalino 29, P. Buhler 102,
N. Burmasov 141, Z. Buthelezi 68,123, A. Bylinkin 20, S.A. Bysiak107, J.C.
Cabanillas Noris 109, M.F.T. Cabrera116, M. Cai 6, H. Caines 138, A. Caliva
28, E. Calvo Villar 101, J.M.M. Camacho 109, P. Camerini 23, F.D.M. Canedo
110, S.L. Cantway 138, M. Carabas 113, A.A. Carballo 32, F. Carnesecchi 32, R.
Caron 128, L.A.D. Carvalho 110, J. Castillo Castellanos 130, M. Castoldi 32,
F. Catalano 32, S. Cattaruzzi 23, C. Ceballos Sanchez 142, R. Cerri24, I.
Chakaberia 74, P. Chakraborty 136,47, S. Chandra 135, S. Chapeland 32, M.
Chartier 119, S. Chattopadhay135, S. Chattopadhyay 135, S. Chattopadhyay 99,
M. Chen39, T. Cheng 97,6, C. Cheshkov 128, V. Chibante Barroso 32, D.D.
Chinellato 111, E.S. Chizzali II,95, J. Cho 58, S. Cho 58, P. Chochula 32,
Z.A. Chochulska136, D. Choudhury41, P. Christakoglou 84, C.H. Christensen 83,
P. Christiansen 75, T. Chujo 125, M. Ciacco 29, C. Cicalo 52, M.R. Ciupek97,
G. ClaiIII,51, F. Colamaria 50, J.S. Colburn100, D. Colella 31, M. Colocci 25,
M. Concas 32, G. Conesa Balbastre 73, Z. Conesa del Valle 131, G. Contin 23,
J.G. Contreras 35, M.L. Coquet 103,130, P. Cortese 133,56, M.R. Cosentino 112,
F. Costa 32, S. Costanza 21,55, C. Cot 131, J. Crkovská 94, P. Crochet 127, R.
Cruz-Torres 74, P. Cui 6, M.M. Czarnynoga136, A. Dainese 54, G. Dange38, M.C.
Danisch 94, A. Danu 63, P. Das 80, P. Das 4, S. Das 4, A.R. Dash 126, S. Dash
47, A. De Caro 28, G. de Cataldo 50, J. de Cuveland38, A. De Falco 22, D. De
Gruttola 28, N. De Marco 56, C. De Martin 23, S. De Pasquale 28, R. Deb 134,
R. Del Grande 95, L. Dello Stritto 32, W. Deng 6, K.C. Devereaux18, P.
Dhankher 18, D. Di Bari 31, A. Di Mauro 32, B. Diab 130, R.A. Diaz 142,7, T.
Dietel 114, Y. Ding 6, J. Ditzel 64, R. Divià 32, Ø. Djuvsland20, U. Dmitrieva
141, A. Dobrin 63, B. Dönigus 64, J.M. Dubinski 136, A. Dubla 97, P. Dupieux
127, N. Dzalaiova13, T.M. Eder 126, R.J. Ehlers 74, F. Eisenhut 64, R.
Ejima92, D. Elia 50, B. Erazmus 103, F. Ercolessi 25, B. Espagnon 131, G.
Eulisse 32, D. Evans 100, S. Evdokimov 141, L. Fabbietti 95, M. Faggin 23, J.
Faivre 73, F. Fan 6, W. Fan 74, A. Fantoni 49, M. Fasel 87, A. Feliciello 56,
G. Feofilov 141, A. Fernández Téllez 44, L. Ferrandi 110, M.B. Ferrer 32, A.
Ferrero 130, C. Ferrero IV,56, A. Ferretti 24, V.J.G. Feuillard 94, V. Filova
35, D. Finogeev 141, F.M. Fionda 52, E. Flatland32, F. Flor 138,116, A.N.
Flores 108, S. Foertsch 68, I. Fokin 94, S. Fokin 141, U. FolloIV,56, E.
Fragiacomo 57, E. Frajna 46, U. Fuchs 32, N. Funicello 28, C. Furget 73, A.
Furs 141, T. Fusayasu 98, J.J. Gaardhøje 83, M. Gagliardi 24, A.M. Gago 101,
T. Gahlaut47, C.D. Galvan 109, D.R. Gangadharan 116, P. Ganoti 78, C.
Garabatos 97, J.M. Garcia44, T. García Chávez 44, E. Garcia-Solis 9, C.
Gargiulo 32, P. Gasik 97, H.M. Gaur38, A. Gautam 118, M.B. Gay Ducati 66, M.
Germain 103, C. Ghosh135, M. Giacalone 51, G. Gioachin 29, P. Giubellino
97,56, P. Giubilato 27, A.M.C. Glaenzer 130, P. Glässel 94, E. Glimos 122,
D.J.Q. Goh76, V. Gonzalez 137, P. Gordeev 141, M. Gorgon 2, K. Goswami 48, S.
Gotovac33, V. Grabski 67, L.K. Graczykowski 136, E. Grecka 86, A. Grelli 59,
C. Grigoras 32, V. Grigoriev 141, S. Grigoryan 142,1, F. Grosa 32, J.F.
Grosse-Oetringhaus 32, R. Grosso 97, D. Grund 35, N.A. Grunwald94, G.G.
Guardiano 111, R. Guernane 73, M. Guilbaud 103, K. Gulbrandsen 83, J.J.W.K.
Gumprecht102, T. Gündem 64, T. Gunji 124, W. Guo 6, A. Gupta 91, R. Gupta 91,
R. Gupta 48, K. Gwizdziel 136, L. Gyulai 46, C. Hadjidakis 131, F.U. Haider
91, S. Haidlova 35, M. Haldar4, H. Hamagaki 76, A. Hamdi 74, Y. Han 139, B.G.
Hanley 137, R. Hannigan 108, J. Hansen 75, M.R. Haque 97, J.W. Harris 138, A.
Harton 9, M.V. Hartung 64, H. Hassan 117, D. Hatzifotiadou 51, P. Hauer 42,
L.B. Havener 138, E. Hellbär 97, H. Helstrup 34, M. Hemmer 64, T. Herman 35,
S.G. Hernandez116, G. Herrera Corral 8, S. Herrmann 128, K.F. Hetland 34, B.
Heybeck 64, H. Hillemanns 32, B. Hippolyte 129, F.W. Hoffmann 70, B. Hofman
59, G.H. Hong 139, M. Horst 95, A. Horzyk 2, Y. Hou 6, P. Hristov 32, P.
Huhn64, L.M. Huhta 117, T.J. Humanic 88, A. Hutson 116, D. Hutter 38, M.C.
Hwang 18, R. Ilkaev141, M. Inaba 125, G.M. Innocenti 32, M. Ippolitov 141, A.
Isakov 84, T. Isidori 118, M.S. Islam 99, S. Iurchenko141, M. Ivanov 97, M.
Ivanov13, V. Ivanov 141, K.E. Iversen 75, M. Jablonski 2, B. Jacak 18,74, N.
Jacazio 25, P.M. Jacobs 74, S. Jadlovska106, J. Jadlovsky106, S. Jaelani 82,
C. Jahnke 110, M.J. Jakubowska 136, M.A. Janik 136, T. Janson70, S. Ji 16, S.
Jia 10, F. Jonas 74, D.M. Jones 119, J.M. Jowett 32,97, J. Jung 64, M. Jung
64, A. Junique 32, A. Jusko 100, J. Kaewjai105, P. Kalinak 60, A. Kalweit 32,
A. Karasu Uysal V,72, D. Karatovic 89, N. Karatzenis100, O. Karavichev 141, T.
Karavicheva 141, E. Karpechev 141, M.J. Karwowska 32,136, U. Kebschull 70, R.
Keidel 140, M. Keil 32, B. Ketzer 42, S.S. Khade 48, A.M. Khan 120, S. Khan
15, A. Khanzadeev 141, Y. Kharlov 141, A. Khatun 118, A. Khuntia 35, Z.
Khuranova 64, B. Kileng 34, B. Kim 104, C. Kim 16, D.J. Kim 117, E.J. Kim 69,
J. Kim 139, J. Kim 58, J. Kim 32,69, M. Kim 18, S. Kim 17, T. Kim 139, K.
Kimura 92, A. Kirkova36, S. Kirsch 64, I. Kisel 38, S. Kiselev 141, A. Kisiel
136, J.P. Kitowski 2, J.L. Klay 5, J. Klein 32, S. Klein 74, C. Klein-Bösing
126, M. Kleiner 64, T. Klemenz 95, A. Kluge 32, C. Kobdaj 105, R. Kohara124,
T. Kollegger97, A. Kondratyev 142, N. Kondratyeva 141, J. Konig 64, S.A.
Konigstorfer 95, P.J. Konopka 32, G. Kornakov 136, M. Korwieser 95, S.D.
Koryciak 2, C. Koster84, A. Kotliarov 86, N. Kovacic89, V. Kovalenko 141, M.
Kowalski 107, V. Kozhuharov 36, I. Králik 60, A. Kravčáková 37, L. Krcal
32,38, M. Krivda 100,60, F. Krizek 86, K. Krizkova Gajdosova 32, C. Krug 66,
M. Krüger 64, D.M. Krupova 35, E. Kryshen 141, V. Kučera 58, C. Kuhn 129, P.G.
Kuijer 84, T. Kumaoka125, D. Kumar135, L. Kumar 90, N. Kumar90, S. Kumar 31,
S. Kundu 32, P. Kurashvili 79, A. Kurepin 141, A.B. Kurepin 141, A. Kuryakin
141, S. Kushpil 86, V. Kuskov 141, M. Kutyla136, A. Kuznetsov142, M.J. Kweon
58, Y. Kwon 139, S.L. La Pointe 38, P. La Rocca 26, A. Lakrathok105, M.
Lamanna 32, A.R. Landou 73, R. Langoy 121, P. Larionov 32, E. Laudi 32, L.
Lautner 32,95, R.A.N. Laveaga109, R. Lavicka 102, R. Lea 134,55, H. Lee 104,
I. Legrand 45, G. Legras 126, J. Lehrbach 38, A.M. Lejeune35, T.M. Lelek2,
R.C. Lemmon 85, I. León Monzón 109, M.M. Lesch 95, E.D. Lesser 18, P. Lévai
46, M. Li6, X. Li10, B.E. Liang-gilman 18, J. Lien 121, R. Lietava 100, I.
Likmeta 116, B. Lim 24, S.H. Lim 16, V. Lindenstruth 38, A. Lindner45, C.
Lippmann 97, D.H. Liu 6, J. Liu 119, G.S.S. Liveraro 111, I.M. Lofnes 20, C.
Loizides 87, S. Lokos 107, J. Lömker 59, X. Lopez 127, E. López Torres 7, C.
Lotteau128, P. Lu 97,120, F.V. Lugo 67, J.R. Luhder 126, M. Lunardon 27, G.
Luparello 57, Y.G. Ma 39, M. Mager 32, A. Maire 129, E.M. Majerz2, M.V.
Makariev 36, M. Malaev 141, G. Malfattore 25, N.M. Malik 91, Q.W. Malik19,
S.K. Malik 91, L. Malinina I,VIII,142, D. Mallick 131, N. Mallick 48, G.
Mandaglio 30,53, S.K. Mandal 79, A. Manea 63, V. Manko 141, F. Manso 127, V.
Manzari 50, Y. Mao 6, R.W. Marcjan 2, G.V. Margagliotti 23, A. Margotti 51, A.
Marín 97, C. Markert 108, P. Martinengo 32, M.I. Martínez 44, G. Martínez
García 103, M.P.P. Martins 110, S. Masciocchi 97, M. Masera 24, A. Masoni 52,
L. Massacrier 131, O. Massen 59, A. Mastroserio 132,50, O. Matonoha 75, S.
Mattiazzo 27, A. Matyja 107, A.L. Mazuecos 32, F. Mazzaschi 32,24, M. Mazzilli
116, J.E. Mdhluli 123, Y. Melikyan 43, A. Menchaca-Rocha 67, J.E.M. Mendez 65,
E. Meninno 102, A.S. Menon 116, M.W. Menzel32,94, M. Meres 13, Y. Miake125, L.
Micheletti 32, D.L. Mihaylov 95, K. Mikhaylov 142,141, N. Minafra 118, D.
Miśkowiec 97, A. Modak 134,4, B. Mohanty80, M. Mohisin Khan VI,15, M.A.
Molander 43, S. Monira 136, C. Mordasini 117, D.A. Moreira De Godoy 126, I.
Morozov 141, A. Morsch 32, T. Mrnjavac 32, V. Muccifora 49, S. Muhuri 135,
J.D. Mulligan 74, A. Mulliri 22, M.G. Munhoz 110, R.H. Munzer 64, H. Murakami
124, S. Murray 114, L. Musa 32, J. Musinsky 60, J.W. Myrcha 136, B. Naik 123,
A.I. Nambrath 18, B.K. Nandi 47, R. Nania 51, E. Nappi 50, A.F. Nassirpour 17,
A. Nath 94, C. Nattrass 122, M.N. Naydenov 36, A. Neagu19, A. Negru113, E.
Nekrasova141, L. Nellen 65, R. Nepeivoda 75, S. Nese 19, G. Neskovic 38, N.
Nicassio 50, B.S. Nielsen 83, E.G. Nielsen 83, S. Nikolaev 141, S. Nikulin
141, V. Nikulin 141, F. Noferini 51, S. Noh 12, P. Nomokonov 142, J. Norman
119, N. Novitzky 87, P. Nowakowski 136, A. Nyanin 141, J. Nystrand 20, S. Oh
17, A. Ohlson 75, V.A. Okorokov 141, J. Oleniacz 136, A. Onnerstad 117, C.
Oppedisano 56, A. Ortiz Velasquez 65, J. Otwinowski 107, M. Oya92, K. Oyama
76, Y. Pachmayer 94, S. Padhan 47, D. Pagano 134,55, G. Paić 65, S. Paisano-
Guzmán 44, A. Palasciano 50, S. Panebianco 130, H. Park 125, H. Park 104, J.
Park 125, J.E. Parkkila 32, Y. Patley 47, B. Paul 22, M.M.D.M. Paulino 110, H.
Pei 6, T. Peitzmann 59, X. Peng 11, M. Pennisi 24, S. Perciballi 24, D.
Peresunko 141, G.M. Perez 7, Y. Pestov141, M.T. Petersen83, V. Petrov 141, M.
Petrovici 45, S. Piano 57, M. Pikna 13, P. Pillot 103, O. Pinazza 51,32, L.
Pinsky116, C. Pinto 95, S. Pisano 49, M. Płoskoń 74, M. Planinic89, F.
Pliquett64, D.K. Plociennik2, M.G. Poghosyan 87, B. Polichtchouk 141, S.
Politano 29, N. Poljak 89, A. Pop 45, S. Porteboeuf-Houssais 127, V.
Pozdniakov I,142, I.Y. Pozos 44, K.K. Pradhan 48, S.K. Prasad 4, S. Prasad 48,
R. Preghenella 51, F. Prino 56, C.A. Pruneau 137, I. Pshenichnov 141, M.
Puccio 32, S. Pucillo 24, S. Qiu 84, L. Quaglia 24, S. Ragoni 14, A. Rai 138,
A. Rakotozafindrabe 130, L. Ramello 133,56, F. Rami 129, M. Rasa 26, S.S.
Räsänen 43, R. Rath 51, M.P. Rauch 20, I. Ravasenga 32, K.F. Read 87,122, C.
Reckziegel 112, A.R. Redelbach 38, K. Redlich VII,79, C.A. Reetz 97, H.D.
Regules-Medel44, A. Rehman20, F. Reidt 32, H.A. Reme-Ness 34, Z. Rescakova37,
K. Reygers 94, A. Riabov 141, V. Riabov 141, R. Ricci 28, M. Richter 20, A.A.
Riedel 95, W. Riegler 32, A.G. Riffero 24, C. Ripoli28, C. Ristea 63, M.V.
Rodriguez 32, M. Rodríguez Cahuantzi 44, S.A. Rodríguez Ramírez 44, K. Røed
19, R. Rogalev 141, E. Rogochaya 142, T.S. Rogoschinski 64, D. Rohr 32, D.
Röhrich 20, S. Rojas Torres 35, P.S. Rokita 136, G. Romanenko 25, F. Ronchetti
49, E.D. Rosas65, K. Roslon 136, A. Rossi 54, A. Roy 48, S. Roy 47, N. Rubini
25, J.A. Rudolph84, D. Ruggiano 136, R. Rui 23, P.G. Russek 2, R. Russo 84, A.
Rustamov 81, E. Ryabinkin 141, Y. Ryabov 141, A. Rybicki 107, J. Ryu 16, W.
Rzesa 136, S. Sadhu 31, S. Sadovsky 141, J. Saetre 20, K. Šafařík 35, S.K.
Saha 4, S. Saha 80, B. Sahoo 48, R. Sahoo 48, S. Sahoo61, D. Sahu 48, P.K.
Sahu 61, J. Saini 135, K. Sajdakova37, S. Sakai 125, M.P. Salvan 97, S.
Sambyal 91, D. Samitz 102, I. Sanna 32,95, T.B. Saramela110, D. Sarkar 83, P.
Sarma 41, V. Sarritzu 22, V.M. Sarti 95, M.H.P. Sas 32, S. Sawan 80, E.
Scapparone 51, J. Schambach 87, H.S. Scheid 64, C. Schiaua 45, R. Schicker 94,
F. Schlepper 94, A. Schmah97, C. Schmidt 97, H.R. Schmidt93, M.O. Schmidt 32,
M. Schmidt93, N.V. Schmidt 87, A.R. Schmier 122, R. Schotter 129, A. Schröter
38, J. Schukraft 32, K. Schweda 97, G. Scioli 25, E. Scomparin 56, J.E. Seger
14, Y. Sekiguchi124, D. Sekihata 124, M. Selina 84, I. Selyuzhenkov 97, S.
Senyukov 129, J.J. Seo 94, D. Serebryakov 141, L. Serkin 65, L. Šerkšnytė 95,
A. Sevcenco 63, T.J. Shaba 68, A. Shabetai 103, R. Shahoyan32, A. Shangaraev
141, B. Sharma 91, D. Sharma 47, H. Sharma 54, M. Sharma 91, S. Sharma 76, S.
Sharma 91, U. Sharma 91, A. Shatat 131, O. Sheibani116, K. Shigaki 92, M.
Shimomura77, J. Shin12, S. Shirinkin 141, Q. Shou 39, Y. Sibiriak 141, S.
Siddhanta 52, T. Siemiarczuk 79, T.F. Silva 110, D. Silvermyr 75, T.
Simantathammakul105, R. Simeonov 36, B. Singh91, B. Singh 95, K. Singh 48, R.
Singh 80, R. Singh 91, R. Singh 97, S. Singh 15, V.K. Singh 135, V. Singhal
135, T. Sinha 99, B. Sitar 13, M. Sitta 133,56, T.B. Skaali19, G. Skorodumovs
94, N. Smirnov 138, R.J.M. Snellings 59, E.H. Solheim 19, J. Song 16, C.
Sonnabend 32,97, J.M. Sonneveld 84, F. Soramel 27, A.B. Soto-hernandez 88, R.
Spijkers 84, I. Sputowska 107, J. Staa 75, J. Stachel 94, I. Stan 63, P.J.
Steffanic 122, S.F. Stiefelmaier 94, D. Stocco 103, I. Storehaug 19, N.J.
Strangmann 64, P. Stratmann 126, S. Strazzi 25, A. Sturniolo 30,53, C.P.
Stylianidis84, A.A.P. Suaide 110, C. Suire 131, M. Sukhanov 141, M. Suljic 32,
R. Sultanov 141, V. Sumberia 91, S. Sumowidagdo 82, I. Szarka 13, M.
Szymkowski 136, S.F. Taghavi 95, G. Taillepied 97, J. Takahashi 111, G.J.
Tambave 80, S. Tang 6, Z. Tang 120, J.D. Tapia Takaki 118, N. Tapus113, L.A.
Tarasovicova 126, M.G. Tarzila 45, G.F. Tassielli 31, A. Tauro 32, A. Tavira
García 131, G. Tejeda Muñoz 44, A. Telesca 32, L. Terlizzi 24, C. Terrevoli
50, S. Thakur 4, D. Thomas 108, A. Tikhonov 141, N. Tiltmann 32,126, A.R.
Timmins 116, M. Tkacik106, T. Tkacik 106, A. Toia 64, R. Tokumoto92, S.
Tomassini25, K. Tomohiro92, N. Topilskaya 141, M. Toppi 49, V.V. Torres 103,
A.G. Torres Ramos 31, A. Trifiró 30,53, T. Triloki96, A.S. Triolo 32,30,53, S.
Tripathy 32, T. Tripathy 47, V. Trubnikov 3, W.H. Trzaska 117, T.P. Trzcinski
136, C. Tsolanta19, R. Tu39, A. Tumkin 141, R. Turrisi 54, T.S. Tveter 19, K.
Ullaland 20, B. Ulukutlu 95, A. Uras 128, M. Urioni 134, G.L. Usai 22, M.
Vala37, N. Valle 55, L.V.R. van Doremalen59, M. van Leeuwen 84, C.A. van Veen
94, R.J.G. van Weelden 84, P. Vande Vyvre 32, D. Varga 46, Z. Varga 46, P.
Vargas Torres65, M. Vasileiou 78, A. Vasiliev 141, O. Vázquez Doce 49, O.
Vazquez Rueda 116, V. Vechernin 141, E. Vercellin 24, S. Vergara Limón44, R.
Verma47, L. Vermunt 97, R. Vértesi 46, M. Verweij 59, L. Vickovic33, Z.
Vilakazi123, O. Villalobos Baillie 100, A. Villani 23, A. Vinogradov 141, T.
Virgili 28, M.M.O. Virta 117, A. Vodopyanov 142, B. Volkel 32, M.A. Völkl 94,
S.A. Voloshin 137, G. Volpe 31, B. von Haller 32, I. Vorobyev 32, N. Vozniuk
141, J. Vrláková 37, J. Wan39, C. Wang 39, D. Wang39, Y. Wang 39, Y. Wang 6,
A. Wegrzynek 32, F.T. Weiglhofer38, S.C. Wenzel 32, J.P. Wessels 126, J.
Wiechula 64, J. Wikne 19, G. Wilk 79, J. Wilkinson 97, G.A. Willems 126, B.
Windelband 94, M. Winn 130, J.R. Wright 108, W. Wu39, Y. Wu 120, Z. Xiong120,
R. Xu 6, A. Yadav 42, A.K. Yadav 135, Y. Yamaguchi 92, S. Yang20, S. Yano 92,
E.R. Yeats18, Z. Yin 6, I.-K. Yoo 16, J.H. Yoon 58, H. Yu12, S. Yuan20, A.
Yuncu 94, V. Zaccolo 23, C. Zampolli 32, M. Zang6, F. Zanone 94, N. Zardoshti
32, A. Zarochentsev 141, P. Závada 62, N. Zaviyalov141, M. Zhalov 141, B.
Zhang 6, C. Zhang 130, L. Zhang 39, M. Zhang127,6, S. Zhang 39, X. Zhang 6, Y.
Zhang120, Z. Zhang 6, M. Zhao 10, V. Zherebchevskii 141, Y. Zhi10, D. Zhou 6,
Y. Zhou 83, J. Zhu 54,6, S. Zhu120, Y. Zhu6, S.C. Zugravel 56, N. Zurlo 134,55

## Affiliation Notes

I Deceased
II Also at: Max-Planck-Institut fur Physik, Munich, Germany
III Also at: Italian National Agency for New Technologies, Energy and
Sustainable Economic Development (ENEA), Bologna, Italy
IV Also at: Dipartimento DET del Politecnico di Torino, Turin, Italy
V Also at: Yildiz Technical University, Istanbul, Türkiye
VI Also at: Department of Applied Physics, Aligarh Muslim University, Aligarh,
India
VII Also at: Institute of Theoretical Physics, University of Wroclaw, Poland
VIII Also at: An institution covered by a cooperation agreement with CERN

## Collaboration Institutes

1 A.I. Alikhanyan National Science Laboratory (Yerevan Physics Institute)
Foundation, Yerevan, Armenia
2 AGH University of Krakow, Cracow, Poland
3 Bogolyubov Institute for Theoretical Physics, National Academy of Sciences
of Ukraine, Kiev, Ukraine
4 Bose Institute, Department of Physics and Centre for Astroparticle Physics
and Space Science (CAPSS), Kolkata, India
5 California Polytechnic State University, San Luis Obispo, California, United
States
6 Central China Normal University, Wuhan, China
7 Centro de Aplicaciones Tecnológicas y Desarrollo Nuclear (CEADEN), Havana,
Cuba
8 Centro de Investigación y de Estudios Avanzados (CINVESTAV), Mexico City and
Mérida, Mexico
9 Chicago State University, Chicago, Illinois, United States
10 China Institute of Atomic Energy, Beijing, China
11 China University of Geosciences, Wuhan, China
12 Chungbuk National University, Cheongju, Republic of Korea
13 Comenius University Bratislava, Faculty of Mathematics, Physics and
Informatics, Bratislava, Slovak Republic
14 Creighton University, Omaha, Nebraska, United States
15 Department of Physics, Aligarh Muslim University, Aligarh, India
16 Department of Physics, Pusan National University, Pusan, Republic of Korea
17 Department of Physics, Sejong University, Seoul, Republic of Korea
18 Department of Physics, University of California, Berkeley, California,
United States
19 Department of Physics, University of Oslo, Oslo, Norway
20 Department of Physics and Technology, University of Bergen, Bergen, Norway
21 Dipartimento di Fisica, Università di Pavia, Pavia, Italy
22 Dipartimento di Fisica dell’Università and Sezione INFN, Cagliari, Italy
23 Dipartimento di Fisica dell’Università and Sezione INFN, Trieste, Italy
24 Dipartimento di Fisica dell’Università and Sezione INFN, Turin, Italy
25 Dipartimento di Fisica e Astronomia dell’Università and Sezione INFN,
Bologna, Italy
26 Dipartimento di Fisica e Astronomia dell’Università and Sezione INFN,
Catania, Italy
27 Dipartimento di Fisica e Astronomia dell’Università and Sezione INFN,
Padova, Italy
28 Dipartimento di Fisica ‘E.R. Caianiello’ dell’Università and Gruppo
Collegato INFN, Salerno, Italy
29 Dipartimento DISAT del Politecnico and Sezione INFN, Turin, Italy
30 Dipartimento di Scienze MIFT, Università di Messina, Messina, Italy
31 Dipartimento Interateneo di Fisica ‘M. Merlin’ and Sezione INFN, Bari,
Italy
32 European Organization for Nuclear Research (CERN), Geneva, Switzerland
33 Faculty of Electrical Engineering, Mechanical Engineering and Naval
Architecture, University of Split, Split, Croatia
34 Faculty of Engineering and Science, Western Norway University of Applied
Sciences, Bergen, Norway
35 Faculty of Nuclear Sciences and Physical Engineering, Czech Technical
University in Prague, Prague, Czech Republic
36 Faculty of Physics, Sofia University, Sofia, Bulgaria
37 Faculty of Science, P.J. Šafárik University, Košice, Slovak Republic
38 Frankfurt Institute for Advanced Studies, Johann Wolfgang Goethe-
Universität Frankfurt, Frankfurt, Germany
39 Fudan University, Shanghai, China
40 Gangneung-Wonju National University, Gangneung, Republic of Korea
41 Gauhati University, Department of Physics, Guwahati, India
42 Helmholtz-Institut für Strahlen- und Kernphysik, Rheinische Friedrich-
Wilhelms-Universität Bonn, Bonn, Germany
43 Helsinki Institute of Physics (HIP), Helsinki, Finland
44 High Energy Physics Group, Universidad Autónoma de Puebla, Puebla, Mexico
45 Horia Hulubei National Institute of Physics and Nuclear Engineering,
Bucharest, Romania
46 HUN-REN Wigner Research Centre for Physics, Budapest, Hungary
47 Indian Institute of Technology Bombay (IIT), Mumbai, India
48 Indian Institute of Technology Indore, Indore, India
49 INFN, Laboratori Nazionali di Frascati, Frascati, Italy
50 INFN, Sezione di Bari, Bari, Italy
51 INFN, Sezione di Bologna, Bologna, Italy
52 INFN, Sezione di Cagliari, Cagliari, Italy
53 INFN, Sezione di Catania, Catania, Italy
54 INFN, Sezione di Padova, Padova, Italy
55 INFN, Sezione di Pavia, Pavia, Italy
56 INFN, Sezione di Torino, Turin, Italy
57 INFN, Sezione di Trieste, Trieste, Italy
58 Inha University, Incheon, Republic of Korea
59 Institute for Gravitational and Subatomic Physics (GRASP), Utrecht
University/Nikhef, Utrecht, Netherlands
60 Institute of Experimental Physics, Slovak Academy of Sciences, Košice,
Slovak Republic
61 Institute of Physics, Homi Bhabha National Institute, Bhubaneswar, India
62 Institute of Physics of the Czech Academy of Sciences, Prague, Czech
Republic
63 Institute of Space Science (ISS), Bucharest, Romania
64 Institut für Kernphysik, Johann Wolfgang Goethe-Universität Frankfurt,
Frankfurt, Germany
65 Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México,
Mexico City, Mexico
66 Instituto de Física, Universidade Federal do Rio Grande do Sul (UFRGS),
Porto Alegre, Brazil
67 Instituto de Física, Universidad Nacional Autónoma de México, Mexico City,
Mexico
68 iThemba LABS, National Research Foundation, Somerset West, South Africa
69 Jeonbuk National University, Jeonju, Republic of Korea
70 Johann-Wolfgang-Goethe Universität Frankfurt Institut für Informatik,
Fachbereich Informatik und Mathematik, Frankfurt, Germany
71 Korea Institute of Science and Technology Information, Daejeon, Republic of
Korea
72 KTO Karatay University, Konya, Turkey
73 Laboratoire de Physique Subatomique et de Cosmologie, Université Grenoble-
Alpes, CNRS-IN2P3, Grenoble, France
74 Lawrence Berkeley National Laboratory, Berkeley, California, United States
75 Lund University Department of Physics, Division of Particle Physics, Lund,
Sweden
76 Nagasaki Institute of Applied Science, Nagasaki, Japan
77 Nara Women’s University (NWU), Nara, Japan
78 National and Kapodistrian University of Athens, School of Science,
Department of Physics , Athens, Greece
79 National Centre for Nuclear Research, Warsaw, Poland
80 National Institute of Science Education and Research, Homi Bhabha National
Institute, Jatni, India
81 National Nuclear Research Center, Baku, Azerbaijan
82 National Research and Innovation Agency - BRIN, Jakarta, Indonesia
83 Niels Bohr Institute, University of Copenhagen, Copenhagen, Denmark
84 Nikhef, National institute for subatomic physics, Amsterdam, Netherlands
85 Nuclear Physics Group, STFC Daresbury Laboratory, Daresbury, United Kingdom
86 Nuclear Physics Institute of the Czech Academy of Sciences, Husinec-Řež,
Czech Republic
87 Oak Ridge National Laboratory, Oak Ridge, Tennessee, United States
88 Ohio State University, Columbus, Ohio, United States
89 Physics department, Faculty of science, University of Zagreb, Zagreb,
Croatia
90 Physics Department, Panjab University, Chandigarh, India
91 Physics Department, University of Jammu, Jammu, India
92 Physics Program and International Institute for Sustainability with Knotted
Chiral Meta Matter (SKCM2), Hiroshima University, Hiroshima, Japan
93 Physikalisches Institut, Eberhard-Karls-Universität Tübingen, Tübingen,
Germany
94 Physikalisches Institut, Ruprecht-Karls-Universität Heidelberg, Heidelberg,
Germany
95 Physik Department, Technische Universität München, Munich, Germany
96 Politecnico di Bari and Sezione INFN, Bari, Italy
97 Research Division and ExtreMe Matter Institute EMMI, GSI Helmholtzzentrum
für Schwerionenforschung GmbH, Darmstadt, Germany
98 Saga University, Saga, Japan
99 Saha Institute of Nuclear Physics, Homi Bhabha National Institute, Kolkata,
India
100 School of Physics and Astronomy, University of Birmingham, Birmingham,
United Kingdom
101 Sección Física, Departamento de Ciencias, Pontificia Universidad Católica
del Perú, Lima, Peru
102 Stefan Meyer Institut für Subatomare Physik (SMI), Vienna, Austria
103 SUBATECH, IMT Atlantique, Nantes Université, CNRS-IN2P3, Nantes, France
104 Sungkyunkwan University, Suwon City, Republic of Korea
105 Suranaree University of Technology, Nakhon Ratchasima, Thailand
106 Technical University of Košice, Košice, Slovak Republic
107 The Henryk Niewodniczanski Institute of Nuclear Physics, Polish Academy of
Sciences, Cracow, Poland
108 The University of Texas at Austin, Austin, Texas, United States
109 Universidad Autónoma de Sinaloa, Culiacán, Mexico
110 Universidade de São Paulo (USP), São Paulo, Brazil
111 Universidade Estadual de Campinas (UNICAMP), Campinas, Brazil
112 Universidade Federal do ABC, Santo Andre, Brazil
113 Universitatea Nationala de Stiinta si Tehnologie Politehnica Bucuresti,
Bucharest, Romania
114 University of Cape Town, Cape Town, South Africa
115 University of Derby, Derby, United Kingdom
116 University of Houston, Houston, Texas, United States
117 University of Jyväskylä, Jyväskylä, Finland
118 University of Kansas, Lawrence, Kansas, United States
119 University of Liverpool, Liverpool, United Kingdom
120 University of Science and Technology of China, Hefei, China
121 University of South-Eastern Norway, Kongsberg, Norway
122 University of Tennessee, Knoxville, Tennessee, United States
123 University of the Witwatersrand, Johannesburg, South Africa
124 University of Tokyo, Tokyo, Japan
125 University of Tsukuba, Tsukuba, Japan
126 Universität Münster, Institut für Kernphysik, Münster, Germany
127 Université Clermont Auvergne, CNRS/IN2P3, LPC, Clermont-Ferrand, France
128 Université de Lyon, CNRS/IN2P3, Institut de Physique des 2 Infinis de
Lyon, Lyon, France
129 Université de Strasbourg, CNRS, IPHC UMR 7178, F-67000 Strasbourg, France,
Strasbourg, France
130 Université Paris-Saclay, Centre d’Etudes de Saclay (CEA), IRFU, Départment
de Physique Nucléaire (DPhN), Saclay, France
131 Université Paris-Saclay, CNRS/IN2P3, IJCLab, Orsay, France
132 Università degli Studi di Foggia, Foggia, Italy
133 Università del Piemonte Orientale, Vercelli, Italy
134 Università di Brescia, Brescia, Italy
135 Variable Energy Cyclotron Centre, Homi Bhabha National Institute, Kolkata,
India
136 Warsaw University of Technology, Warsaw, Poland
137 Wayne State University, Detroit, Michigan, United States
138 Yale University, New Haven, Connecticut, United States
139 Yonsei University, Seoul, Republic of Korea
140 Zentrum für Technologie und Transfer (ZTT), Worms, Germany
141 Affiliated with an institute covered by a cooperation agreement with CERN
142 Affiliated with an international laboratory covered by a cooperation
agreement with CERN.