2019 173 8 August

Global polarization of hyperons in Pb–Pb collisions at the LHC

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

The global polarization of the $\Lambda$ and $\overline{\Lambda}$ hyperons is
measured for Pb–Pb collisions at $\sqrt{s_{\rm NN}}=2.76$ and 5.02 TeV
recorded with the ALICE at the LHC. The results are reported differentially as
a function of collision centrality and hyperon’s transverse momentum ($p_{\rm
T}$) for the range of centrality 5–50%, $0.5<p_{\rm T}<5$ GeV/$c$, and
rapidity $|y|<0.5$. The hyperon global polarization averaged for Pb–Pb
collisions at $\sqrt{s_{\rm NN}}=2.76$ and 5.02 TeV is found to be consistent
with zero, $\langle P_{\rm H}\rangle(\%)\approx 0.01\pm
0.06~{}\mbox{(stat.)}\pm 0.03~{}\mbox{(syst.)}$ in the collision centrality
range 15–50%, where the largest signal is expected. The results are compatible
with expectations based on an extrapolation from measurements at lower
collision energies at RHIC, hydrodynamical model calculations, and empirical
estimates based on collision energy dependence of directed flow, all of which
predict the global polarization values at LHC energies of the order of
$0.01\%$.

##  1 Introduction

The system created in a non-central nucleus–nucleus collision might retain a
significant fraction of the large orbital angular momentum of the colliding
nuclei. Due to the spin-orbit coupling, particles produced in such a collision
can become globally polarized [1, 2, 3, 4]. The global polarization is a
phenomena when spins of all emitted final state particles in a non-central
nucleus–nucleus collision are aligned along one preferential direction defined
by the initial angular orbital momentum. Its measurement provides important
information about the initial conditions and dynamics of the quark-gluon
plasma (QGP), as well as the hadronization process [5, 6, 7]. The global
polarization for a specific particle and corresponding anti-particle is
expected to be very similar, or even identical, in a system with small or zero
baryon chemical potential.

High-energy heavy-ion collisions are also characterized by ultra-strong
magnetic fields [8, 9], which on average are aligned with the direction of the
angular momentum. While the peak values of the magnetic fields, which reach up
to $\rm 10^{18}$ Gauss, can be estimated rather accurately [8, 9], the time
evolution, which depends on the QGP electric conductivity, is practically
unknown. These fields can also contribute to the global polarization, but
their action on particles and anti-particles is expected to be in an opposite
direction. Thus the measurement of the splitting between particle and anti-
particle global polarizations provides very valuable information about the QGP
properties.

The measurements of the global polarization $P_{\rm H}$ for spin one half
$\Lambda$ ($\overline{\Lambda}$) strange hyperons are experimentally
favourable because their spin direction can be reconstructed via their weak
decay topology into proton (anti-proton) and charged pion. Recently, the STAR
Collaboration observed non-zero global polarization of $\Lambda$ and
$\overline{\Lambda}$ hyperons in Au–Au collisions, first for the RHIC beam
energy scan (BES) energies of $\sqrt{s_{\rm NN}}=7-39$ GeV and, later, with
more data, at $\sqrt{s_{\rm NN}}=200$ GeV [10, 11]. The magnitude of the
observed polarization varies from a few to a fraction of a percent. While the
$P_{\rm H}$ values for $\Lambda$ and $\overline{\Lambda}$ agree within the
experimental uncertainties, they are systematically higher for
$\overline{\Lambda}$ than for $\Lambda$. Assuming that this difference
originates due to the magnetic fields one estimates the field strength in
units of elementary charge $e$ to be $eB\sim 0.01m_{\pi}^{2}$ [12].

The exact nature of the spin-orbit interaction leading to the global
polarization is not known. It is unclear at what stage of the system evolution
(the QGP, hadronization, or the hadronic rescattering) the polarization is
acquired, neither the corresponding relaxation times are known. Most of the
recent calculations of the global polarization assume complete thermal
equilibrium and validity of the hydrodynamical description of the system [13,
12, 14, 6, 15]. They relate the particle polarization to the system’s thermal
vorticity at the hadronization time. In a non-relativistic limit, assuming
complete thermal equilibrium, the polarization of the particles can be
evaluated as $\bm{\zeta}=\langle{\bf s}\rangle/s=(s+1)\bm{\omega}/(3T)$, where
$s$ is the particle’s spin, $T$ is the system temperature,
${\bm{\omega}}=(1/2)({\bf\nabla}\times{\bf v})$ is a nonrelativistic
vorticity, and ${\bf v}$ is the local fluid velocity [12].

The global polarization is determined by the average vorticity component
perpendicular to the collision reaction plane, which is spanned by the beam
direction and the impact parameter vector. The global polarization
measurements with the produced particle provide important information on both
the nature of the spin-orbit interaction and the profile of velocity fields of
the expanding system. Both, the magnitude and the direction of the vorticity,
can strongly vary within the system [16]. In particular, a significant
component along the beam direction can be acquired due to the transverse
anisotropic flow [16, 17].

The vorticity of the system, especially its component along the system’s
orbital momentum, is directly related to the asymmetries in the initial
velocity fields. This links the vorticity with the directed flow $v_{1}$, that
is also strongly dependent on those asymmetries. The $v_{1}$ is defined by the
first Fourier moment $v_{1}=\langle\cos(\varphi-\Psi_{\rm RP})\rangle$ of the
produced particle’s azimuthal asymmetry relative to the collision reaction
plane angle $\Psi_{\rm RP}$. Hydrodynamic simulations show that the orbital
angular momentum stored in the system and the directed flow of charged
particles are almost directly proportional to each other [5]. This allows for
an empirical estimate of the collision energy dependence of the global
polarization [16]. The STAR results for the directed flow [18, 19] and the
hyperon global polarization [10, 11] from the BES program show that the slopes
of $v_{1}$ at midrapidity (${\rm d}v_{1}/{\rm d}\eta$) for charged hadrons
(pions) and the hyperon polarization are indeed strongly correlated. The
charged-particle directed flow in Pb–Pb collisions at $\sqrt{s_{\rm NN}}=2.76$
TeV is about three times smaller [20] than at the top RHIC energy of 200 GeV.
This suggest that the global polarization at the LHC energies should be also
about three times smaller than at RHIC (around $\sim 0.08$%) and decreasing
from $\sqrt{s_{\rm NN}}=2.76$ TeV to 5.02 TeV by about $\sim$30% [21]. Even
smaller polarization values at the LHC are expected when the directed flow is
seen as a combination of the two effects – the tilt of the source in the
longitudinal direction and the dipole flow originating from the asymmetry in
the initial energy density distributions [22]. Taking into account that only
the contribution to the directed flow from the tilted source is related to the
vorticity and that its contribution relative to the dipole flow decreases with
the collision energy [22], one arrives to an estimate for the global
polarization at the LHC energies of the order of $\sim 0.04$%.

In this paper, the measurements of the global polarization of the $\Lambda$
and $\overline{\Lambda}$ hyperons in Pb–Pb collisions at $\sqrt{s_{\rm
NN}}=2.76$ and 5.02 TeV recorded with ALICE at the LHC are reported. The paper
is organized as follows. In Sec. 2 the analysis details are presented, and the
global polarization observable is introduced, as well as the measurement
technique. The various sources of systematic uncertainties are discussed in
Sec. 3. The results for the $\Lambda$ and $\overline{\Lambda}$ global
polarization at two collision energies as a function of the hyperon transverse
momentum and collision centrality are presented in Sec. 4.

##  2 Data analysis

###  2.1 The observable

In this measurement, $\Lambda$ and $\overline{\Lambda}$ hyperons are
reconstructed through their weak decay topologies $\Lambda\rightarrow{\rm
p}+\pi^{-}$ and $\overline{\Lambda}\rightarrow\bar{\rm p}+\pi^{+}$ (64%
branching ratio). The global polarization of the hyperons is determined from
the angular distributions of their decay (anti-)protons. In the hyperon rest
frame, the (anti-)proton angular probability distribution, ${\rm d}w/{\rm
d}\bm{n}^{*}_{\mathrm{p}}$, is given by

$\frac{{\rm d}w}{{\rm d}\bm{n}^{*}_{\mathrm{p}}}=1+\alpha_{\rm
H}\,\bm{\zeta}_{\rm H}\cdot\bm{n}^{*}_{\mathrm{p}},$ (1)

where $\bm{n}^{*}_{\mathrm{p}}$ is the unit vector of the (anti-)proton
direction. The same absolute value from [23] for the hyperon decay parameter
$\alpha_{\mathrm{H}}=0.642\pm 0.013$, positive for $\Lambda$ and negative for
$\overline{\Lambda}$, is used. Recent measurement by the BESIII Collaboration
[24] extracted a new values for $\alpha_{\Lambda}=0.750\pm 0.010$ and
$\alpha_{\bar{\Lambda}}=-0.758\pm 0.012$, which are about 17% larger than in
[23]. Given the statistical and systematical uncertainties of the results
reported below for the hyperon global polarization the new values for
$\alpha_{\mathrm{H}}$ will not change the conclusions of this paper but they
should be considered for future hight precision measurements. The polarization
vector $\bm{\zeta}_{\mathrm{H}}$ in Eq. (1), which is satisfying condition
$|\bm{\zeta}_{\mathrm{H}}|\leq 1$, can be measured experimentally as [25]

$\bm{\zeta}_{\rm H}=\frac{3}{\alpha_{\rm H}}\left<\bm{n}^{*}_{\rm p}\right>,$
(2)

where the brackets $\left<\dots\right>$ denote an event-by-event averaging
over all hyperon decays.

The polarization vector $\bm{\zeta}_{\rm H}$ generally depends on the hyperon
kinematics, namely the transverse momentum $p_{\rm T}$, rapidity $y$, and its
azimuthal angle with respect to the reaction plane, $\varphi-\Psi_{\rm RP}$,
as well as the collision centrality. The global polarization reported in this
paper is determined by the component of the polarization vector perpendicular
to the reaction plane. The magnitude $P_{\rm H}$ of the global polarization
can be measured by averaging a corresponding projection of the
$\bm{n}^{*}_{\rm p}$ vector, which in the laboratory coordinate system is
given by $n^{*}_{{\rm p}\perp\rm RP}=\,\sin\theta^{*}_{\rm
p}\,\sin\left(\varphi^{*}_{\rm p}-\Psi_{\rm RP}\right)$. Here $\theta^{*}_{\rm
p}$ ($\varphi^{*}_{\rm p}$) is the polar angle with respect to the collision
axis (azimuthal angle) of the (anti-)proton direction in the hyperon rest
frame. Substituting $n^{*}_{p\perp\rm RP}$ into Eq. (2) and assuming an ideal
detector acceptance, an average over the $\theta^{*}_{\rm p}$ yields

$P_{\rm H}=\frac{8}{\pi\alpha_{\rm H}}\left<\sin(\varphi^{*}_{\rm p}-\Psi_{\rm
RP})\right>.$ (3)

Here the brackets $\left<\dots\right>$ imply averaging over individual
hyperons in all events. The polarization is defined to be positive if the
hyperon spin has a positive component along the system’s angular momentum –
the same convention as employed in [10]. The detector acceptance effects are
treated in this work as systematic uncertainty and discussed in Sec. 3.

A significant fraction of $\Lambda$ and $\overline{\Lambda}$ hyperons
originates from decay of heavier particles. Existing estimates [13, 6, 12] of
the feed-down effect on the hyperon global polarization measurements, based on
the assumption of thermal equilibrium and the particle yields from the
statistical model [26], suggest that the primary $\Lambda$ and
$\overline{\Lambda}$ polarization should be by about 15–20% larger than what
is measured at RHIC. Taking into account that feed-down effects are expected
to be small compared to other uncertainties in the current analysis, no
correction to the data have been applied.

###  2.2 Measurement technique

The main components of the ALICE detector system [27, 28] used for this
measurement are the Time Projection Chamber (TPC) [29], the silicon detectors
of the Inner Tracking System (ITS) [30] and the two neutron Zero-Degree
Calorimeters (ZDC) [31]. The analyzed data samples were recorded by ALICE in
2010 and 2011 for Pb–Pb collisions at $\sqrt{s_{\rm NN}}=2.76$ TeV, and in
2015 for collisions at $\sqrt{s_{\rm NN}}=5.02$ TeV.

During the data taking, the trigger required a hit in a pair of V0 detectors
[32]. In 2010 and 2011, events with only one V0 hit and at least two hits in
the outer layer of the Silicon Pixel Detector (SPD) were accepted as well.
Contamination from beam-induced background was removed offline, as discussed
in [33, 34]. The events with poor correlation between multiplicities in V0,
ITS and TPC detectors were rejected. The analysis was restricted to the events
with the primary vertex along the beam direction, $V_{z}$, within $\pm 10$ cm
from the nominal center of the TPC. This yielded for all collision
centralities approximately 49 (75) million of Pb–Pb collisions at
$\sqrt{s_{\rm NN}}=2.76$ (5.02) TeV. The collision centrality was determined
using the energy deposition in the V0 detectors [35].

The reaction plane angle $\Psi_{\rm RP}$ was estimated using the spectator
plane angle $\Psi_{\rm SP}$, characterizing the deflection direction of the
spectator neutrons. The spectator deflections at positive and negative
rapidity were reconstructed with a pair of neutron ZDC detectors located 114 m
away from the interaction point. The $\Psi_{\rm SP}$ angle was evaluated
separately for the two detectors using the transverse profile of the spectator
energy distribution provided by the $2\times 2$ segmentation of the ZDCs. For
this, a pair of two-dimensional vectors ${\rm\bf Q}^{\rm t,p}$ were
constructed for two ZDCs following the procedure described in [20]:

${\rm\bf Q}^{\rm t,p}\equiv\left(Q_{\rm x}^{\rm t,p},Q_{\rm y}^{\rm
t,p}\right)=\left.\sum\limits_{i=1}^{4}{\bf n}_{i}E_{i}^{\rm
t,p}\right/{\sum\limits_{i=1}^{4}}E_{i}^{\rm t,p},$ (4)

where indices ${\rm p}$ and ${\rm t}$ denote the ZDC on the projectile
($\eta>0$) and target ($\eta<0$) side of the interaction point, respectively;
$E_{i}$ is the measured signal and ${\bf n}_{i}=\left(x_{i},y_{i}\right)$ are
the coordinates of the $i$-th ZDC segment. The event averaged $\left<{\rm\bf
Q}^{\rm t,p}\right>$ revealed a strong dependence on the collision centrality
as well as on the three collision vertex coordinates, which is imposed by the
offset of the LHC beam transverse spot positions relative to the nominal
center of the ZDCs. Moreover, the $\left<{\rm\bf Q}^{\rm t,p}\right>$
demonstrated a strong time dependence in some of the 2015 runs. To compensate
for these variations an event-by-event re-centering correction [36] was
applied as a function of collision centrality, three components of the
collision vertex position, and beam time variation

${\rm\bf Q}^{\prime}={\rm\bf Q}-\langle{\rm\bf Q}\rangle.$ (5)

Additionally to the procedure described in [20], the width of the ${\rm\bf
Q}^{\prime}$ distributions was equalized as a function of centrality, which
together with Eq. (5) resulted in an overall ${\rm\bf Q}$-vector correction

$Q_{\rm x}^{\prime\prime}=\frac{Q_{\rm x}^{\prime}-\left<Q_{\rm
x}\right>}{\left<Q_{\rm x}^{\prime 2}\right>},\quad Q_{\rm
y}^{\prime\prime}=\frac{Q_{\rm y}^{\prime}-\left<Q_{\rm
y}\right>}{\left<Q_{\rm y}^{\prime 2}\right>}.$ (6)

The width equalization, up to 20%, turned out to be particularly useful for
the 2015 data sample, where one of the two neutron ZDC detectors lost signal
from one of its four channels.

The $\Psi_{\rm SP}$ angle estimated from each ZDC is then given by the
direction of the corrected ${\rm\bf Q}^{\prime\prime}$ vector

${\rm\bf Q}^{\prime\prime}=|{\rm\bf Q}^{\prime\prime}|\exp\left\\{i\Psi_{\rm
SP}\right\\}.$ (7)

To account for a finite resolution of the spectator plane angle $\Psi_{\rm
SP}$, a correction $R_{\rm SP}^{(1)}$ is introduce in the Eq. (3) following
the method described in [25]

$P_{\rm H}=\frac{8}{\pi\alpha_{\rm H}}\frac{\left<\sin(\varphi^{*}_{\rm
p}-\Psi_{\rm SP})\right>}{R_{\rm SP}^{(1)}}.$ (8)

The polarization values obtained with Eq. (8) for each of the two ZDC
detectors were found to be similar within the statistical uncertainties and
were combined.

The correction $R_{\rm SP}^{(1)}$ was extracted from correlations between
${\rm\bf Q}$-vector angles from different ALICE detectors following the
technique described in [37]. Figure 1 presents the $R_{\rm SP}^{(1)}$ as a
function of collision centrality for different data sets.

Figure 1:  (color online) The correction $R_{\rm SP}^{(1)}$ for finite
resolution of the spectator plane angle $\Psi_{\rm SP}$ as a function of
collision centrality for three data sets used in the analysis. Only
statistical uncertainties, which are smaller than a symbol size, are shown.

The most central (0–5%) collisions are excluded from the analysis, because the
small number of spectators does not allow for reliable estimation of the
spectator deflection with the ZDCs. During the Pb–Pb data taking in 2011
($\sqrt{s_{\rm NN}}=2.76$ TeV) and 2015 ($\sqrt{s_{\rm NN}}=5.02$ TeV), the
beams were collided at a non-zero vertical crossing angle [28]. This resulted
in a partial screening of the spectator neutrons by the LHC tertiary
collimators [38] and in a degradation of the spectator plane resolution. The
V0s, TPC, and two forward multiplicity detectors (FMD) [39] were used to
estimate a possible uncertainties in $R_{\rm SP}^{(1)}$ extraction for the two
ZDC detectors. In all data samples, these uncertainties turned out to be at a
level of several percent.

The $\Lambda$ and $\overline{\Lambda}$ hyperons were reconstructed via their
weak decay topology following the method and selection criteria described in
[28, 40]. Charged daughter tracks from hyperon decay were required to have the
pseudo-rapidity $|\eta|<0.9$ and at least 70 space points in the TPC. The pion
and (anti-)proton particle type assignments were based on the track charge and
specific energy loss (${\rm d}E/{\rm d}x$) measured in the TPC. The daughter
tracks were paired to form $\Lambda$ and $\overline{\Lambda}$ candidates. The
candidates were required to have transverse momentum $p_{\rm T}>0.5$ GeV/$c$,
rapidity $|y|<0.5$, and the momentum vector pointing back to the primary
collision vertex within a cone of opening angle less than 0.1 (0.08) radians
for Pb–Pb collisions at $\sqrt{s_{\rm NN}}=2.76$ (5.02) TeV.

The hyperon global polarization $P_{\rm H}$ was extracted with the fit to the
measured correlation $\left<\sin(\varphi^{*}_{\rm p}-\Psi_{\rm SP})\right>$ as
a function of the $\Lambda$ or $\overline{\Lambda}$ candidate invariant mass,
$\mathrm{M}_{\mathrm{inv}}$:

$\left<\sin(\varphi^{*}_{\rm p}-\Psi_{\rm
SP})\right>(\mathrm{M}_{\mathrm{inv}})=[1-f_{\mathrm{BG}}(\mathrm{M}_{\mathrm{inv}})]\times
S_{\mathrm{H}}+f_{\mathrm{BG}}(\mathrm{M}_{\mathrm{inv}})\times
L_{\mathrm{BG}}(\mathrm{M}_{\mathrm{inv}}).$ (9)

Here the constant $S_{\mathrm{H}}$ gives the numerator of Eq. (8) and
$L(\mathrm{M}_{\mathrm{inv}})$ is a linear parameterization of the background
correlation as a function of $\mathrm{M}_{\mathrm{inv}}$. The background
fraction $f_{\mathrm{BG}}(\mathrm{M}_{\mathrm{inv}})$ was evaluated as

$f_{\mathrm{BG}}(\mathrm{M}_{\mathrm{inv}})=\frac{N_{\rm
BG}(\mathrm{M}_{\mathrm{inv}})}{N_{\rm tot}(\mathrm{M}_{\mathrm{inv}})}.$ (10)

Here $N_{\rm tot}(\mathrm{M}_{\mathrm{inv}})$ is the total measured yield of
the $\Lambda$ or $\overline{\Lambda}$ candidates. The $N_{\rm
BG}(\mathrm{M}_{\mathrm{inv}})$ is given by the 4-th order polynomial fit to
the $N_{\rm tot}(\mathrm{M}_{\mathrm{inv}})$ outside of the $\Lambda$ and
$\overline{\Lambda}$ invariant mass peak range,
$\mathrm{M}_{\mathrm{inv}}<1.107$ GeV/$c^{2}$ and
$\mathrm{M}_{\mathrm{inv}}>1.125$ GeV/$c^{2}$.

The fitting procedure is illustrated in Fig. 2 for 20–30% centrality range in
Pb–Pb collisions at $\sqrt{s_{\rm NN}}=2.76$ TeV using data collected during
the LHC operation in 2011.

Figure 2:  (color online) (Upper panels) invariant mass distributions of
$\Lambda$ (left) and $\overline{\Lambda}$ (right) candidates for 20–30%
centrality range in Pb–Pb collisions at $\sqrt{s_{\rm NN}}=2.76$ TeV using
data collected during the LHC operation in 2011. Dashed lines show the result
of the fit for $N_{\rm BG}(\mathrm{M}_{\mathrm{inv}})$ in Eq. (10). (Bottom
panels) Global polarization extraction via fit to $\left<\sin(\varphi^{*}_{\rm
p}-\Psi_{\rm SP})\right>$ as a function of the invariant mass, with $\Psi_{\rm
SP}$ reconstructed with the ZDC on the target ($\eta<0$) side. Dashed and
solid lines show $L_{\mathrm{BG}}(\mathrm{M}_{\mathrm{inv}})$ and the combined
fit with Eq. (9). See text for more details.

##  3 Systematic uncertainties

The considered sources of systematic uncertainties are summarized in Table 1.
The significance of a given systematical variation is determined following the
procedure presented in [41].

Table 1: Systematic uncertainties in global polarization measurements for different data sets. Values reported as a fraction of the corresponding statistical uncertainty. Data sample | centrality |  $\Lambda$/$\overline{\Lambda}$ candidate selection |  Fitting procedure | Acceptance | $R_{\rm SP}^{(1)}$
---|---|---|---|---|---
2010 |  5–15% 15–50% | 20% |  30% 5% | 10% | $<2\%$
2011 |  5–15% 15–50% | 30% |  20% 12% | 10% |  $<2$%
2015 | 5–50% | 30% |  20% | 10% |  $<4$%

The selection on the primary vertex position $V_{z}$ was varied to $\pm 7$ cm
and $\pm 8$ cm instead of the default $\pm 10$ cm. The analysis was repeated
with the collision centrality estimated with either ITS or TPC detectors
(instead of default V0 detector). Variations of the results when changing the
event selection criteria described above and centrality estimators are found
to be negligible and were not included into the total systematic uncertainty.

The following $\Lambda$ and $\overline{\Lambda}$ candidate selection criteria
were varied: the distance of closest approach to the primary vertex, decay
daughter track selection via specific energy loss in the TPC, the distance of
closest approach between the pair of the daughter tracks, and the criteria on
the hyperon candidates momentum pointing angle to the primary vertex. The
corresponding contribution from these variations to the total systematic
uncertainty is about 20–30% of the statistical uncertainty. The main
contribution to the systematic uncertainty from the fitting procedure in Eq.
(9) comes from a variation of the fit region.

In Eq. (8) a perfect acceptance of the hyperons and their decay daughters is
assumed. In the case of an imperfect detector, there is a overall scale
correction of the measured polarization as well as a possible admixture of
higher-order harmonics in a Fourier decomposition of the
$\mathrm{d}N_{\Lambda/\overline{\Lambda}}/\mathrm{d}(\varphi^{*}_{\rm
p}-\Psi_{\rm RP})$ distribution. Using the method described in [42, 25] the
corresponding relative uncertainty was estimated to be about 10% independent
of centrality. This uncertainty comes primarily from the admixture of the
higher-order harmonics when hyperon $p_{\rm T}\lesssim 2$ GeV/$c$.

A detailed study was performed for the evaluation of the systematic
uncertainties of $R_{\rm SP}^{(1)}$ as well as for the evaluation of the
difference between the two neutron ZDC detectors. The correlations between the
flow vectors from different detectors, including TPC and pairs of ZDC, V0, FMD
detectors were studied. The contribution the total systematic uncertainties
due to the $R_{\rm SP}^{(1)}$ extraction were found to be at a level of a few
percent.

##  4 Results

Figures 3 and 4 show the measured hyperon global polarization $P_{\rm H}$ as a
function of centrality and hyperon transverse momentum, $p_{\rm T}$, in Pb–Pb
collisions for two collision energies. The results from 2010 and 2011 data
samples were combined accounting for the corresponding statistical and
systematic uncertainty.

Figure 3:  (color online) The global hyperon polarization as function of
centrality for Pb–Pb collisions at $\sqrt{s_{\rm NN}}=2.76$ TeV (left) and
$5.02$ TeV (right). The systematic uncertainties are shown as shaded boxes.
Points are slightly shifted along the horizontal axis for better visibility.
Figure 4:  (color online) The global hyperon polarization as function of
transverse momentum $p_{\rm T}$ for Pb–Pb collisions at $\sqrt{s_{\rm
NN}}=2.76$ TeV (upper) and $5.02$ TeV (lower) in 5–15% (left) and 15–50%
(right) centrality classes. The systematic uncertainties are shown as shaded
boxes. Points are slightly shifted along the horizontal axis for better
visibility.

At RHIC energies, the global polarization exhibited a clear centrality
dependence with three times large magnitude in peripheral collisions compared
to that in central, while no significant $p_{\rm T}$ dependence within the
accessible $p_{\rm T}$ range was observed [11]. The $P_{\rm H}$ at the LHC is
found to be consistent with zero within the experimental uncertainties for all
studied centrality classes (Fig. 3) and $p_{\rm T}$ ranges (Fig. 4). By
repeating a similar analysis, no signal signal was observed as a function of
rapidity either.

The average global polarization for two centrality ranges, 5–15% and 15–50%,
are presented in Fig. 5, while numerical values are reported in Tab. 2.

Figure 5:  (color online) The global hyperon polarization as a function of
collision energy. Results are compared with the STAR data at lower energies
[10, 11]. The insert shows zoomed-in comparison with the data at the top RHIC
energy. The systematic uncertainties are shown as shaded boxes. Points are
slightly shifted along the horizontal axis for better visibility.

Figure 5 also presents the comparison with the STAR data [10, 11] for lower
collision energies. Despite large uncertainties, the ALICE measurements
confirm the trend of the global polarization decreasing with increasing
collision energy.

Assuming the same values of the global polarization for $\Lambda$ and
$\overline{\Lambda}$ and neglecting the possible difference of about 30%
(according to the empirical estimates discussed above) between the two LHC
energies, one can average all four ALICE data points for 15–50% centrality,
where the largest signal is expected. This yields a value $\langle P_{\rm
H}\rangle(\%)\approx 0.01\pm 0.06~{}\mbox{(stat.)}\pm 0.03~{}\mbox{(syst.)}$
for 15–50% centrality, which is consistent with the empirical estimates of
$P_{\rm H}(\%)\approx 0.04-0.08$ based on directed flow measurements.

Table 2: The global polarization of $\Lambda$ and $\overline{\Lambda}$ hyperons in Pb–Pb collisions at $\sqrt{s_{\rm NN}}=2.76$ TeV and $5.02$ TeV for centrality ranges 5–15% and 15–50%. $\sqrt{s_{\rm NN}}$ | centrality | $P_{\Lambda}\,(\%)$ | $P_{\overline{\Lambda}}\,(\%)$
---|---|---|---
2.76 TeV | 5–15% |  $0.01\pm 0.13~{}\mbox{(stat.)}\pm 0.04~{}\mbox{(syst.)}$ |  $0.09\pm 0.13~{}\mbox{(stat.)}\pm 0.08~{}\mbox{(syst.)}$
15–50% |  $0.08\pm 0.10~{}\mbox{(stat.)}\pm 0.04~{}\mbox{(syst.)}$ | $-0.05\pm 0.10~{}\mbox{(stat.)}\pm 0.03~{}\mbox{(syst.)}$
5.02 TeV | 5–15% |  $0.08\pm 0.18~{}\mbox{(stat.)}\pm 0.08~{}\mbox{(syst.)}$ | $-0.07\pm 0.18~{}\mbox{(stat.)}\pm 0.03~{}\mbox{(syst.)}$
15–50% | $-0.13\pm 0.11~{}\mbox{(stat.)}\pm 0.04~{}\mbox{(syst.)}$ |  $0.14\pm 0.12~{}\mbox{(stat.)}\pm 0.03~{}\mbox{(syst.)}$
average | 15–50% | $\langle P_{\rm H}\rangle(\%)\approx 0.01\pm 0.06~{}\mbox{(stat.)}\pm 0.03~{}\mbox{(syst.)}$

##  5 Summary

The first measurements of $\Lambda$ and $\overline{\Lambda}$ hyperons global
polarization are reported for Pb–Pb collisions at $\sqrt{s_{\rm NN}}=2.76$ and
5.02 TeV recorded with ALICE at the LHC. The hyperon global polarization has
been measured differentially as a function of centrality and transverse
momentum ($p_{\rm T}$) for the range of collision centrality 5–50%,
$0.5<p_{\rm T}<5$ GeV/$c$, and rapidity $|y|<0.5$. No significant dependences
neither splitting between the global polarization values for $\Lambda$ and
$\overline{\Lambda}$ has been observed. The average $\Lambda$ and
$\overline{\Lambda}$ polarization for 15–50% centrality range at two collision
energies is found to be consistent with zero, $\langle P_{\rm
H}\rangle(\%)\approx 0.01\pm 0.06~{}\mbox{(stat.)}\pm 0.03~{}\mbox{(syst.)}$.
This confirms the observed earlier trend of the global polarization decrease
with increasing collision energy. The results are compatible with the
extrapolation of the RHIC results and empirical estimates of $P_{\rm
H}(\%)\approx 0.04-0.08$ based on the similarity of collision energy
dependence of the global polarization and the slope of the directed flow in
the midrapidity region. The high luminosity LHC run after the 2019-2021 long
shutdown with the upgraded ALICE detector will bring more than 100 times more
data, which should allow tests of the previously mentioned prediction with
much better accuracy.

## Acknowledgements

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

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##  Appendix A The ALICE Collaboration

S. Acharyaorg141&D. Adamováorg93&S.P. Adhyaorg141&A. Adlerorg73&J.
Adolfssonorg79&M.M. Aggarwalorg98&G. Aglieri Rinellaorg34&M. Agnelloorg31&N.
Agrawalorg10,org48,org53&Z. Ahammedorg141&S. Ahmadorg17&S.U. Ahnorg75&A.
Akindinovorg90&M. Al-Turanyorg105&S.N. Alamorg141&D.S.D. Albuquerqueorg122&D.
Aleksandrovorg86&B. Alessandroorg58&H.M. Alfandaorg6&R. Alfaro Molinaorg71&B.
Aliorg17&Y. Aliorg15&A. Aliciorg10,org27,org53&A. Alkinorg2&J. Almeorg22&T.
Altorg68&L. Altenkamperorg22&I. Altsybeevorg112&M.N. Anaamorg6&C.
Andreiorg47&D. Andreouorg34&H.A. Andrewsorg109&A. Andronicorg144&M.
Angelettiorg34&V. Anguelovorg102&C. Ansonorg16&T. Antičićorg106&F.
Antinoriorg56&P. Antonioliorg53&R. Anwarorg125&N. Apadulaorg78&L.
Aphecetcheorg114&H. Appelshäuserorg68&S. Arcelliorg27&R. Arnaldiorg58&M.
Arratiaorg78&I.C. Arseneorg21&M. Arslandokorg102&A. Augustinusorg34&R.
Averbeckorg105&S. Azizorg61&M.D. Azmiorg17&A. Badalàorg55&Y.W. Baekorg40&S.
Bagnascoorg58&X. Baiorg105&R. Bailhacheorg68&R. Balaorg99&A.
Baldisseriorg137&M. Ballorg42&S. Balouzaorg103&R.C. Baralorg84&R.
Barberaorg28&L. Barioglioorg26&G.G. Barnaföldiorg145&L.S. Barnbyorg92&V.
Barretorg134&P. Bartaliniorg6&K. Barthorg34&E. Bartschorg68&F.
Baruffaldiorg29&N. Bastidorg134&S. Basuorg143&G. Batigneorg114&B.
Batyunyaorg74&P.C. Batzingorg21&D. Bauriorg48&J.L. Bazo Albaorg110&I.G.
Beardenorg87&C. Beddaorg63&N.K. Beheraorg60&I. Belikovorg136&F.
Belliniorg34&R. Bellwiedorg125&V. Belyaevorg91&G. Bencediorg145&S.
Beoleorg26&A. Bercuciorg47&Y. Berdnikovorg96&D. Berenyiorg145&R.A.
Bertensorg130&D. Berzanoorg58&M.G. Besoiuorg67&L. Betevorg34&A.
Bhasinorg99&I.R. Bhatorg99&M.A. Bhatorg3&H. Bhattorg48&B.
Bhattacharjeeorg41&A. Bianchiorg26&L. Bianchiorg26&N. Bianchiorg51&J.
Bielčíkorg37&J. Bielčíkováorg93&A. Bilandzicorg103,org117&G. Biroorg145&R.
Biswasorg3&S. Biswasorg3&J.T. Blairorg119&D. Blauorg86&C. Blumeorg68&G.
Bocaorg139&F. Bockorg34,org94&A. Bogdanovorg91&L. Boldizsárorg145&A.
Bolozdynyaorg91&M. Bombaraorg38&G. Bonomiorg140&H. Borelorg137&A.
Borissovorg91,org144&M. Borriorg127&H. Bossiorg146&E. Bottaorg26&L.
Bratrudorg68&P. Braun-Munzingerorg105&M. Bregantorg121&T.A. Brokerorg68&M.
Brozorg37&E.J. Bruckenorg43&E. Brunaorg58&G.E. Brunoorg33,org104&M.D.
Bucklandorg127&D. Budnikovorg107&H. Bueschingorg68&S. Bufalinoorg31&O.
Bugnonorg114&P. Buhlerorg113&P. Buncicorg34&Z. Butheleziorg72&J.B.
Buttorg15&J.T. Buxtonorg95&S.A. Bysiakorg118&D. Caffarriorg88&A.
Calivaorg105&E. Calvo Villarorg110&R.S. Camachoorg44&P. Cameriniorg25&A.A.
Caponorg113&F. Carnesecchiorg10,org27&J. Castillo Castellanosorg137&A.J.
Castroorg130&E.A.R. Casulaorg54&F. Catalanoorg31&C. Ceballos Sanchezorg52&P.
Chakrabortyorg48&S. Chandraorg141&B. Changorg126&W. Changorg6&S.
Chapelandorg34&M. Chartierorg127&S. Chattopadhyayorg141&S.
Chattopadhyayorg108&A. Chauvinorg24&C. Cheshkovorg135&B. Cheynisorg135&V.
Chibante Barrosoorg34&D.D. Chinellatoorg122&S. Choorg60&P. Chochulaorg34&T.
Chowdhuryorg134&P. Christakoglouorg88&C.H. Christensenorg87&P.
Christiansenorg79&T. Chujoorg133&C. Cicaloorg54&L. Cifarelliorg10,org27&F.
Cindoloorg53&J. Cleymansorg124&F. Colamariaorg52&D. Colellaorg52&A.
Colluorg78&M. Colocciorg27&M. Concasorg58orgI&G. Conesa Balbastreorg77&Z.
Conesa del Valleorg61&G. Continorg59,org127&J.G. Contrerasorg37&T.M.
Cormierorg94&Y. Corrales Moralesorg26,org58&P. Corteseorg32&M.R.
Cosentinoorg123&F. Costaorg34&S. Costanzaorg139&P. Crochetorg134&E.
Cuautleorg69&P. Cuiorg6&L. Cunqueiroorg94&D. Dabrowskiorg142&T.
Dahmsorg103,org117&A. Daineseorg56&F.P.A. Damasorg114,org137&S. Daniorg65&M.C.
Danischorg102&A. Danuorg67&D. Dasorg108&I. Dasorg108&P. Dasorg3&S. Dasorg3&A.
Dashorg84&S. Dashorg48&A. Dashiorg103&S. Deorg49,org84&A. De Caroorg30&G. de
Cataldoorg52&C. de Contiorg121&J. de Cuvelandorg39&A. De Falcoorg24&D. De
Gruttolaorg10&N. De Marcoorg58&S. De Pasqualeorg30&R.D. De Souzaorg122&S.
Deborg49&H.F. Degenhardtorg121&K.R. Dejaorg142&A. Delofforg83&S.
Delsantoorg26,org131&D. Devetakorg105&P. Dhankherorg48&D. Di Bariorg33&A. Di
Mauroorg34&R.A. Diazorg8&T. Dietelorg124&P. Dillensegerorg68&Y. Dingorg6&R.
Diviàorg34&Ø. Djuvslandorg22&U. Dmitrievaorg62&A. Dobrinorg34,org67&B.
Dönigusorg68&O. Dordicorg21&A.K. Dubeyorg141&A. Dublaorg105&S. Dudiorg98&M.
Dukhishyamorg84&P. Dupieuxorg134&R.J. Ehlersorg146&D. Eliaorg52&H.
Engelorg73&E. Eppleorg146&B. Erazmusorg114&F. Erhardtorg97&A.
Erokhinorg112&M.R. Ersdalorg22&B. Espagnonorg61&G. Eulisseorg34&J. Eumorg18&D.
Evansorg109&S. Evdokimovorg89&L. Fabbiettiorg103,org117&M. Fagginorg29&J.
Faivreorg77&F. Fanorg6&A. Fantoniorg51&M. Faselorg94&P. Fecchioorg31&A.
Felicielloorg58&G. Feofilovorg112&A. Fernández Téllezorg44&A. Ferreroorg137&A.
Ferrettiorg26&A. Festantiorg34&V.J.G. Feuillardorg102&J. Figielorg118&S.
Filchaginorg107&D. Finogeevorg62&F.M. Fiondaorg22&G. Fiorenzaorg52&F.
Flororg125&S. Foertschorg72&P. Fokaorg105&S. Fokinorg86&E. Fragiacomoorg59&U.
Frankenfeldorg105&G.G. Fronzeorg26&U. Fuchsorg34&C. Furgetorg77&A.
Fursorg62&M. Fusco Girardorg30&J.J. Gaardhøjeorg87&M. Gagliardiorg26&A.M.
Gagoorg110&A. Galorg136&C.D. Galvanorg120&P. Ganotiorg82&C. Garabatosorg105&E.
Garcia-Solisorg11&K. Gargorg28&C. Gargiuloorg34&A. Garibliorg85&K.
Garnerorg144&P. Gasikorg103,org117&E.F. Gaugerorg119&M.B. Gay Ducatiorg70&M.
Germainorg114&J. Ghoshorg108&P. Ghoshorg141&S.K. Ghoshorg3&P. Gianottiorg51&P.
Giubellinoorg58,org105&P. Giubilatoorg29&P. Glässelorg102&D.M. Goméz
Coralorg71&A. Gomez Ramirezorg73&V. Gonzalezorg105&P. González-Zamoraorg44&S.
Gorbunovorg39&L. Görlichorg118&S. Gotovacorg35&V. Grabskiorg71&L.K.
Graczykowskiorg142&K.L. Grahamorg109&L. Greinerorg78&A. Grelliorg63&C.
Grigorasorg34&V. Grigorievorg91&A. Grigoryanorg1&S. Grigoryanorg74&O.S.
Groettvikorg22&F. Grosaorg31&J.F. Grosse-Oetringhausorg34&R. Grossoorg105&R.
Guernaneorg77&B. Guerzoniorg27&M. Guittiereorg114&K. Gulbrandsenorg87&T.
Gunjiorg132&A. Guptaorg99&R. Guptaorg99&I.B. Guzmanorg44&R. Haakeorg146&M.K.
Habiborg105&C. Hadjidakisorg61&H. Hamagakiorg80&G. Hamarorg145&M. Hamidorg6&R.
Hanniganorg119&M.R. Haqueorg63&A. Harlenderovaorg105&J.W. Harrisorg146&A.
Hartonorg11&J.A. Hasenbichlerorg34&H. Hassanorg77&D.
Hatzifotiadouorg10,org53&P. Hauerorg42&S. Hayashiorg132&A.D.L.B.
Hechavarriaorg144&S.T. Heckelorg68&E. Hellbärorg68&H. Helstruporg36&A.
Herghelegiuorg47&E.G. Hernandezorg44&G. Herrera Corralorg9&F.
Herrmannorg144&K.F. Hetlandorg36&T.E. Hildenorg43&H. Hillemannsorg34&C.
Hillsorg127&B. Hippolyteorg136&B. Hohlwegerorg103&D. Horakorg37&S.
Hornungorg105&R. Hosokawaorg16,org133&P. Hristovorg34&C. Huangorg61&C.
Hughesorg130&P. Huhnorg68&T.J. Humanicorg95&H. Hushnudorg108&L.A.
Husovaorg144&N. Hussainorg41&S.A. Hussainorg15&D. Hutterorg39&D.S.
Hwangorg19&J.P. Iddonorg34,org127&R. Ilkaevorg107&M. Inabaorg133&M.
Ippolitovorg86&M.S. Islamorg108&M. Ivanovorg105&V. Ivanovorg96&V.
Izucheevorg89&B. Jacakorg78&N. Jacazioorg27,org53&P.M. Jacobsorg78&M.B.
Jadhavorg48&S. Jadlovskaorg116&J. Jadlovskyorg116&S. Jaelaniorg63&C.
Jahnkeorg121&M.J. Jakubowskaorg142&M.A. Janikorg142&M. Jercicorg97&O.
Jevonsorg109&R.T. Jimenez Bustamanteorg105&M. Jinorg125&F.
Jonasorg94,org144&P.G. Jonesorg109&A. Juskoorg109&P. Kalinakorg64&A.
Kalweitorg34&J.H. Kangorg147&V. Kaplinorg91&S. Karorg6&A. Karasu Uysalorg76&O.
Karavichevorg62&T. Karavichevaorg62&P. Karczmarczykorg34&E. Karpechevorg62&U.
Kebschullorg73&R. Keidelorg46&M. Keilorg34&B. Ketzerorg42&Z.
Khabanovaorg88&A.M. Khanorg6&S. Khanorg17&S.A. Khanorg141&A.
Khanzadeevorg96&Y. Kharlovorg89&A. Khatunorg17&A. Khuntiaorg49,org118&B.
Kilengorg36&B. Kimorg60&B. Kimorg133&D. Kimorg147&D.J. Kimorg126&E.J.
Kimorg13&H. Kimorg147&J. Kimorg147&J.S. Kimorg40&J. Kimorg102&J. Kimorg147&J.
Kimorg13&M. Kimorg102&S. Kimorg19&T. Kimorg147&T. Kimorg147&S. Kirschorg39&I.
Kiselorg39&S. Kiselevorg90&A. Kisielorg142&J.L. Klayorg5&C. Kleinorg68&J.
Kleinorg58&S. Kleinorg78&C. Klein-Bösingorg144&S. Klewinorg102&A.
Klugeorg34&M.L. Knichelorg34&A.G. Knospeorg125&C. Kobdajorg115&M.K.
Köhlerorg102&T. Kolleggerorg105&A. Kondratyevorg74&N. Kondratyevaorg91&E.
Kondratyukorg89&P.J. Konopkaorg34&M. Konyushikhinorg143&L. Koskaorg116&O.
Kovalenkoorg83&V. Kovalenkoorg112&M. Kowalskiorg118&I. Králikorg64&A.
Kravčákováorg38&L. Kreisorg105&M. Krivdaorg64,org109&F. Krizekorg93&K.
Krizkova Gajdosovaorg37&M. Krügerorg68&E. Kryshenorg96&M. Krzewickiorg39&A.M.
Kuberaorg95&V. Kučeraorg60&C. Kuhnorg136&P.G. Kuijerorg88&L. Kumarorg98&S.
Kumarorg48&S. Kunduorg84&P. Kurashviliorg83&A. Kurepinorg62&A.B.
Kurepinorg62&A. Kuryakinorg107&S. Kushpilorg93&J. Kvapilorg109&M.J.
Kweonorg60&J.Y. Kwonorg60&Y. Kwonorg147&S.L. La Pointeorg39&P. La
Roccaorg28&Y.S. Laiorg78&R. Langoyorg129&K. Lapidusorg34,org146&A.
Lardeuxorg21&P. Larionovorg51&E. Laudiorg34&R. Lavickaorg37&T.
Lazarevaorg112&R. Leaorg25&L. Leardiniorg102&S. Leeorg147&F. Lehasorg88&S.
Lehnerorg113&J. Lehrbachorg39&R.C. Lemmonorg92&I. León Monzónorg120&E.D.
Lesserorg20&M. Lettrichorg34&P. Lévaiorg145&X. Liorg12&X.L. Liorg6&J.
Lienorg129&R. Lietavaorg109&B. Limorg18&S. Lindalorg21&V.
Lindenstruthorg39&S.W. Lindsayorg127&C. Lippmannorg105&M.A. Lisaorg95&V.
Litichevskyiorg43&A. Liuorg78&S. Liuorg95&W.J. Llopeorg143&I.M. Lofnesorg22&V.
Loginovorg91&C. Loizidesorg94&P. Loncarorg35&X. Lopezorg134&E. López
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Mahmoudorg42&A. Maireorg136&R.D. Majkaorg146&M. Malaevorg96&Q.W. Malikorg21&L.
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Mankoorg86&F. Mansoorg134&V. Manzariorg52&Y. Maoorg6&M. Marchisoneorg135&J.
Marešorg66&G.V. Margagliottiorg25&A. Margottiorg53&J. Marguttiorg63&A.
Marínorg105&C. Markertorg119&M. Marquardorg68&N.A. Martinorg102&P.
Martinengoorg34&J.L. Martinezorg125&M.I. Martínezorg44&G. Martínez
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Masoniorg54&L. Massacrierorg61&E. Massonorg114&A. Mastroserioorg52,org138&A.M.
Mathisorg103,org117&O. Matonohaorg79&P.F.T. Matuokaorg121&A. Matyjaorg118&C.
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Morettoorg29&A. Morrealeorg114&A. Morschorg34&T. Mrnjavacorg34&V.
Mucciforaorg51&E. Mudnicorg35&D. Mühlheimorg144&S. Muhuriorg141&J.D.
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Nazarenkoorg107&A. Neaguorg21&R.A. Negrao De Oliveiraorg68&L. Nellenorg69&S.V.
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Nikolaevorg86&S. Nikulinorg86&V. Nikulinorg96&F. Noferiniorg10,org53&P.
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Ohlsonorg102&J. Oleniaczorg142&A.C. Oliveira Da Silvaorg121&M.H.
Oliverorg146&C. Oppedisanoorg58&R. Oravaorg43&A. Ortiz Velasquezorg69&A.
Oskarssonorg79&J. Otwinowskiorg118&K. Oyamaorg80&Y. Pachmayerorg102&V.
Pacikorg87&D. Paganoorg140&G. Paićorg69&P. Palniorg6&J. Panorg143&A.K.
Pandeyorg48&S. Panebiancoorg137&P. Pareekorg49&J. Parkorg60&J.E.
Parkkilaorg126&S. Parmarorg98&S.P. Pathakorg125&R.N. Patraorg141&B.
Paulorg24,org58&H. Peiorg6&T. Peitzmannorg63&X. Pengorg6&L.G. Pereiraorg70&H.
Pereira Da Costaorg137&D. Peresunkoorg86&G.M. Perezorg8&E. Perez
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Petroviciorg47&R.P. Pezziorg70&S. Pianoorg59&M. Piknaorg14&P.
Pillotorg114&L.O.D.L. Pimentelorg87&O. Pinazzaorg34,org53&L. Pinskyorg125&C.
Pintoorg28&S. Pisanoorg51&D. Pistoneorg55&D.B. Piyarathnaorg125&M.
Płoskońorg78&M. Planinicorg97&F. Pliquettorg68&J. Plutaorg142&S.
Pochybovaorg145&M.G. Poghosyanorg94&B. Polichtchoukorg89&N. Poljakorg97&A.
Poporg47&H. Poppenborgorg144&S. Porteboeuf-Houssaisorg134&V.
Pozdniakovorg74&S.K. Prasadorg3&R. Preghenellaorg53&F. Prinoorg58&C.A.
Pruneauorg143&I. Pshenichnovorg62&M. Puccioorg26,org34&V. Puninorg107&K.
Puranapandaorg141&J. Putschkeorg143&R.E. Quishpeorg125&S. Ragoniorg109&S.
Rahaorg3&S. Rajputorg99&J. Rakorg126&A. Rakotozafindrabeorg137&L.
Ramelloorg32&F. Ramiorg136&R. Raniwalaorg100&S. Raniwalaorg100&S.S.
Räsänenorg43&B.T. Rascanuorg68&R. Rathorg49&V. Ratzaorg42&I.
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Revolorg10&K. Reygersorg102&V. Riabovorg96&T. Richertorg79,org87&M.
Richterorg21&P. Riedlerorg34&W. Rieglerorg34&F. Riggiorg28&C. Risteaorg67&S.P.
Rodeorg49&M. Rodríguez Cahuantziorg44&K. Røedorg21&R. Rogalevorg89&E.
Rogochayaorg74&D. Rohrorg34&D. Röhrichorg22&P.S. Rokitaorg142&F.
Ronchettiorg51&E.D. Rosasorg69&K. Roslonorg142&P. Rosnetorg134&A.
Rossiorg29,org56&A. Rotondiorg139&F. Roukoutakisorg82&A. Royorg49&P.
Royorg108&O.V. Ruedaorg79&R. Ruiorg25&B. Rumyantsevorg74&A. Rustamovorg85&E.
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Schmidtorg101&M.O. Schmidtorg102&M. Schmidtorg101&N.V. Schmidtorg68,org94&A.R.
Schmierorg130&J. Schukraftorg34,org87&Y. Schutzorg34,org136&K.
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Šefčíkorg38&J.E. Segerorg16&Y. Sekiguchiorg132&D. Sekihataorg45,org132&I.
Selyuzhenkovorg91,org105&S. Senyukovorg136&D. Serebryakovorg62&E.
Serradillaorg71&P. Settorg48&A. Sevcencoorg67&A. Shabanovorg62&A.
Shabetaiorg114&R. Shahoyanorg34&W. Shaikhorg108&A. Shangaraevorg89&A.
Sharmaorg98&A. Sharmaorg99&H. Sharmaorg118&M. Sharmaorg99&N. Sharmaorg98&A.I.
Sheikhorg141&K. Shigakiorg45&M. Shimomuraorg81&S. Shirinkinorg90&Q.
Shouorg111&Y. Sibiriakorg86&S. Siddhantaorg54&T. Siemiarczukorg83&D.
Silvermyrorg79&C. Silvestreorg77&G. Simatovicorg88&G. Simonettiorg34,org103&R.
Singhorg84&R. Singhorg99&V.K. Singhorg141&V. Singhalorg141&T. Sinhaorg108&B.
Sitarorg14&M. Sittaorg32&T.B. Skaaliorg21&M. Slupeckiorg126&N.
Smirnovorg146&R.J.M. Snellingsorg63&T.W. Snellmanorg43,org126&J.
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Soramelorg29&S. Sorensenorg130&I. Sputowskaorg118&J. Stachelorg102&I.
Stanorg67&P. Stankusorg94&P.J. Steffanicorg130&E. Stenlundorg79&D.
Stoccoorg114&M.M. Storetvedtorg36&P. Strmenorg14&A.A.P. Suaideorg121&T.
Sugitateorg45&C. Suireorg61&M. Suleymanovorg15&M. Suljicorg34&R.
Sultanovorg90&M. Šumberaorg93&S. Sumowidagdoorg50&K. Suzukiorg113&S.
Swainorg65&A. Szaboorg14&I. Szarkaorg14&U. Tabassamorg15&G.
Taillepiedorg134&J. Takahashiorg122&G.J. Tambaveorg22&S. Tangorg6,org134&M.
Tarhiniorg114&M.G. Tarzilaorg47&A. Tauroorg34&G. Tejeda Muñozorg44&A.
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Timminsorg125&A. Toiaorg68&N. Topilskayaorg62&M. Toppiorg51&F. Torales-
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Vergara Limónorg44&L. Vermuntorg63&R. Vernetorg7&R. Vértesiorg145&M.G.D.L.C.
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Zbroszczykorg142&M. Zhalovorg96&X. Zhangorg6&Z. Zhangorg6&C. Zhaoorg21&V.
Zherebchevskiiorg112&N. Zhigarevaorg90&D. Zhouorg6&Y. Zhouorg87&Z.
Zhouorg22&J. Zhuorg6&Y. Zhuorg6&A. Zichichiorg10,org27&M.B. Zimmermannorg34&G.
Zinovjevorg2&N. Zurloorg140&

## Affiliation notes

org*Deceased

orgIDipartimento DET del Politecnico di Torino, Turin, Italy

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

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

orgIVInstitute of Theoretical Physics, University of Wroclaw, Poland

## Collaboration Institutes

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

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

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

org4Budker Institute for Nuclear Physics, Novosibirsk, Russia

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

org6Central China Normal University, Wuhan, China

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

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

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

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

org11Chicago State University, Chicago, Illinois, United States

org12China Institute of Atomic Energy, Beijing, China

org13Chonbuk National University, Jeonju, Republic of Korea

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

org15COMSATS University Islamabad, Islamabad, Pakistan

org16Creighton University, Omaha, Nebraska, United States

org17Department of Physics, Aligarh Muslim University, Aligarh, India

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

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

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

org21Department of Physics, University of Oslo, Oslo, Norway

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

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

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

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

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

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

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

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

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

org31Dipartimento DISAT del Politecnico and Sezione INFN, Turin, Italy

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

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

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

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

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

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

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

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

org40Gangneung-Wonju National University, Gangneung, Republic of Korea

org41Gauhati University, Department of Physics, Guwahati, India

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

org43Helsinki Institute of Physics (HIP), Helsinki, Finland

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

org45Hiroshima University, Hiroshima, Japan

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

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

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

org49Indian Institute of Technology Indore, Indore, India

org50Indonesian Institute of Sciences, Jakarta, Indonesia

org51INFN, Laboratori Nazionali di Frascati, Frascati, Italy

org52INFN, Sezione di Bari, Bari, Italy

org53INFN, Sezione di Bologna, Bologna, Italy

org54INFN, Sezione di Cagliari, Cagliari, Italy

org55INFN, Sezione di Catania, Catania, Italy

org56INFN, Sezione di Padova, Padova, Italy

org57INFN, Sezione di Roma, Rome, Italy

org58INFN, Sezione di Torino, Turin, Italy

org59INFN, Sezione di Trieste, Trieste, Italy

org60Inha University, Incheon, Republic of Korea

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

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

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

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

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

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

org67Institute of Space Science (ISS), Bucharest, Romania

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

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

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

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

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

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

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

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

org76KTO Karatay University, Konya, Turkey

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

org78Lawrence Berkeley National Laboratory, Berkeley, California, United
States

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

org80Nagasaki Institute of Applied Science, Nagasaki, Japan

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

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

org83National Centre for Nuclear Research, Warsaw, Poland

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

org85National Nuclear Research Center, Baku, Azerbaijan

org86National Research Centre Kurchatov Institute, Moscow, Russia

org87Niels Bohr Institute, University of Copenhagen, Copenhagen, Denmark

org88Nikhef, National institute for subatomic physics, Amsterdam, Netherlands

org89NRC Kurchatov Institute IHEP, Protvino, Russia

org90NRC «Kurchatov» Institute - ITEP, Moscow, Russia

org91NRNU Moscow Engineering Physics Institute, Moscow, Russia

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

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

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

org95Ohio State University, Columbus, Ohio, United States

org96Petersburg Nuclear Physics Institute, Gatchina, Russia

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

org98Physics Department, Panjab University, Chandigarh, India

org99Physics Department, University of Jammu, Jammu, India

org100Physics Department, University of Rajasthan, Jaipur, India

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

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

org103Physik Department, Technische Universität München, Munich, Germany

org104Politecnico di Bari, Bari, Italy

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

org106Rudjer Bošković Institute, Zagreb, Croatia

org107Russian Federal Nuclear Center (VNIIEF), Sarov, Russia

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

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

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

org111Shanghai Institute of Applied Physics, Shanghai, China

org112St. Petersburg State University, St. Petersburg, Russia

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

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

org115Suranaree University of Technology, Nakhon Ratchasima, Thailand

org116Technical University of Košice, Košice, Slovakia

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

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

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

org120Universidad Autónoma de Sinaloa, Culiacán, Mexico

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

org122Universidade Estadual de Campinas (UNICAMP), Campinas, Brazil

org123Universidade Federal do ABC, Santo Andre, Brazil

org124University of Cape Town, Cape Town, South Africa

org125University of Houston, Houston, Texas, United States

org126University of Jyväskylä, Jyväskylä, Finland

org127University of Liverpool, Liverpool, United Kingdom

org128University of Science and Techonology of China, Hefei, China

org129University of South-Eastern Norway, Tonsberg, Norway

org130University of Tennessee, Knoxville, Tennessee, United States

org131University of the Witwatersrand, Johannesburg, South Africa

org132University of Tokyo, Tokyo, Japan

org133University of Tsukuba, Tsukuba, Japan

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

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

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

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

org138Università degli Studi di Foggia, Foggia, Italy

org139Università degli Studi di Pavia, Pavia, Italy

org140Università di Brescia, Brescia, Italy

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

org142Warsaw University of Technology, Warsaw, Poland

org143Wayne State University, Detroit, Michigan, United States

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

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

org146Yale University, New Haven, Connecticut, United States

org147Yonsei University, Seoul, Republic of Korea