2020 92 19 May

Quarkonium polarization in nuclear collisions at the LHC

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

The polarization of inclusive J/$\psi$ and $\Upsilon(1{\rm S})$ produced in
Pb–Pb collisions at $\sqrt{s_{\rm{NN}}}=5.02$ TeV at the LHC is measured with
the ALICE detector. The study is carried out by reconstructing the quarkonium
through its decay to muon pairs in the rapidity region $2.5<y<4$ and measuring
the polar and azimuthal angular distributions of the muons. The polarization
parameters $\lambda_{\theta}$, $\lambda_{\phi}$ and $\lambda_{\theta\phi}$ are
measured in the helicity and Collins-Soper reference frames, in the transverse
momentum interval $2<p_{\rm T}<10$ GeV/$c$ and $p_{\rm T}<15$ GeV/$c$ for the
J/$\psi$ and $\Upsilon(1{\rm S})$, respectively. The polarization parameters
for the J/$\psi$ are found to be compatible with zero, within a maximum of
about two standard deviations at low $p_{\rm T}$, for both reference frames
and over the whole $p_{\rm T}$ range. The values are compared with the
corresponding results obtained for pp collisions at $\sqrt{s}=7$ and 8 TeV in
a similar kinematic region by the ALICE and LHCb experiments. Although with
much larger uncertainties, the polarization parameters for $\Upsilon(1{\rm
S})$ production in Pb–Pb collisions are also consistent with zero.

##  1 Introduction

Quarkonia, bound states of charm (c) and anticharm ($\overline{\rm c}$) or
bottom (b) and antibottom ($\overline{\rm b}$) quarks, represent an important
tool to test our understanding of quantum chromodynamics (QCD), since their
production process involves both perturbative and non-perturbative aspects. At
high energy, the creation of the heavy quark-antiquark pair is a process that
can be described using a perturbative QCD approach, due to the large value of
the charm and bottom quark masses ($m_{\rm c}\sim 1.3$ GeV/$c^{2}$, $m_{\rm
b}\sim 4.2$ GeV/$c^{2}$ [1]). However, the subsequent formation of the bound
state is a non-perturbative process that can be described only by empirical
models or effective field theory approaches. Among those, models based on Non-
Relativistic QCD (NRQCD) [2] give the most successful description of the
production cross section, as measured at high-energy hadron colliders
(Tevatron, RHIC, LHC) [3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14]. In the NRQCD
approach, the non-perturbative aspects are parameterized via long-distance
matrix elements (LDME), corresponding to the possible intermediate color, spin
and angular momentum states of the evolving quark-antiquark pair. The values
of LDMEs need to be fitted on a subset of the available measurements and can
be then considered as universal quantities, in the sense that they can be used
in the calculation of production cross sections and other observables
corresponding, for example, to different collision systems and energies. Other
theory approaches, as the Color Singlet Model [15], the Color Evaporation
Model [16] and the $k_{\rm T}$-factorization [17] are also used to describe
the quarkonium production process.

Among the various charmonium states, the J/$\psi$ meson, with quantum numbers
$J^{\rm{PC}}=1^{--}$, was the first to be discovered. It is surely the most
studied, also due to the sizeable decay branching ratio to dilepton pairs
(($5.961\pm 0.033$)% for the $\mu^{+}\mu^{-}$ channel [1]) that represents an
excellent experimental signature. While the J/$\psi$ production cross sections
are well reproduced by NRQCD-based models, it was soon realized that
describing the measured polarization of this state represents a much more
difficult problem [18]. The polarization, corresponding to the orientation of
the particle spin with respect to a chosen axis, can be accessed via a study
of the polar ($\theta)$ and azimuthal ($\phi$) production angles, relative to
that axis, of the two-body decay products in the quarkonium rest frame. Their
angular distribution $W(\theta,\phi)$ is parameterized as

$\displaystyle W(\theta,\phi)$ $\displaystyle\propto$
$\displaystyle\frac{1}{3+\lambda_{\theta}}\left(1+\lambda_{\theta}\cos^{2}{\theta}+\lambda_{\phi}\sin^{2}{\theta}\cos{2\phi}+\lambda_{\theta\phi}\sin{2\theta}\cos{\phi}\right),$
(1)

with the polarization parameters $\lambda_{\theta}$, $\lambda_{\phi}$ and
$\lambda_{\theta\phi}$ corresponding to various combinations of the elements
of the spin density matrix of J/$\psi$ production [19]. In particular, the two
cases ($\lambda_{\theta}=1$, $\lambda_{\phi}=0$, $\lambda_{\theta\phi}=0$) and
($\lambda_{\theta}=-1$, $\lambda_{\phi}=0$, $\lambda_{\theta\phi}=0$)
correspond to the so-called transverse and longitudinal polarizations,
respectively. At leading order, the high-$p_{\rm T}$ production is dominated
by gluon fragmentation and therefore the J/$\psi$ would be expected to be
transversely polarized [18]. However, the results from the CDF experiment at
Tevatron showed that the J/$\psi$ exhibits a very small polarization [20, 21],
an observation which was impossible to reconcile with the NRQCD prediction. As
of today, on the experimental side, accurate results on inclusive and prompt
(i.e., removing contributions from b-quark decays) J/$\psi$ polarization have
become available at LHC energies [22, 23, 24, 25]. They confirm that this
state shows little or no polarization in a wide rapidity (up to $y=4.5$) and
transverse momentum region (from 2 to 70 GeV/$c$), with the exception of the
LHCb measurements at $\sqrt{s}=7$ TeV [24], where the value
$\lambda_{\theta}=-0.145\pm 0.027$, corresponding to a weak longitudinal
polarization, was obtained in the interval $2<p_{\rm T}<15$ GeV/$c$ and
$2<y<4.5$, in the helicity frame (its definition will be given later in Sec.
3). On the theory side, a huge effort was pursued in order to move to a
complete next-to-leading order (NLO) description of the J/$\psi$ production
process [26, 27], and to the calculation of the polarization variables [28,
29]. Further important progress includes a quantitative evaluation of the
contribution of feed-down processes (J/$\psi$ coming from the decay of
$\chi_{\rm c}$ and $\psi(2{\rm S})$ states) on the polarization observables
[30]. It was shown that at NLO there are rather large cancellations between
contributions corresponding to the different possible combinations of the spin
and angular momentum of the intermediate ${\rm c}{\rm\overline{c}}$ states,
reaching a more satisfactory description of the absence of polarization
observed in the data [31]. However, those descriptions usually require the
inclusion of both cross section and polarization results in the fit of the
LDME, leading to a more limited predictive power on the polarization
observables and to large variations in the values of the extracted LDME
values, depending on the set of data used for their determination. Finally,
the description of the J/$\psi$ production in the NRQCD framework was recently
extended to the low-$p_{\rm T}$ region, and the polarization parameters were
studied in a color glass condensate (CGC) + NRQCD formalism, obtaining a fair
agreement with LHC data at forward rapidity [32]. Measurements of the
polarization parameters are also available for several bottomonium states, and
in particular for the $\Upsilon(1{\rm S})$, $\Upsilon(2{\rm S})$ and
$\Upsilon(3{\rm S})$ resonances, which were shown to exhibit little or no
polarization at LHC energies [33, 34, 35]. Approaches similar to that adopted
for charmonium, which also need to take into account the rather complex feed-
down decay structure for these states, lead to a fair agreement with the
experimental results [36].

In this Letter, we move a step forward by presenting the first measurement of
J/$\psi$ and $\Upsilon(1{\rm S})$ polarization in ultrarelativistic heavy-ion
interactions performed by the ALICE Collaboration by studying Pb–Pb collisions
at $\sqrt{s_{\rm NN}}=5.02$ TeV. Such collisions represent an important source
of information for the investigation of the phase diagram of QCD [37], and in
particular for the study of the properties of the quark–gluon plasma (QGP), a
state of matter where quarks and gluons are not confined inside hadrons [38].
Among the experimental observables studied in heavy-ion collisions the
suppression of heavy quarkonium production is a fundamental signal, since QGP
formation prevents the binding of the heavy-quark pair due to the screening of
the color charge [39] and, more generally, has strong effects on the spectral
functions [40]. At LHC energies, another mechanism, corresponding to the
(re)generation of charmonium states in the QGP and/or when the system
hadronizes, becomes relevant [41, 42], in particular at low $p_{\rm T}$, due
to the large charm-quark multiplicity ($>100$ pairs in a central Pb–Pb
collision). The presence of a deconfined system may in principle affect also
the polarization of quarkonium states. In Ref. [43] the observation of a
partial transverse polarization for the J/$\psi$ was predicted in case of QGP
formation, due to a modification of the non-perturbative effects in the high
energy-density phase. More generally, the observed prompt J/$\psi$ are known
to be a mixture of direct production and decay products from higher-mass
charmonium states ($\psi(2{\rm S})$, $\chi_{\rm c}$). In nuclear collisions,
since suppression effects are expected to affect more strongly the less bound
states, the relative contribution of direct and feed-down production would
change with respect to that in pp collisions, and the overall measured
polarization may be different according to the potentially different
polarization of the various states [44, 45]. On the other hand, the
contribution of the regeneration mechanism in the J/$\psi$ formation process
by recombination of uncorrelated ${\rm c}{\rm\overline{c}}$ pairs is likely to
give rise to unpolarized production at low $p_{\rm T}$. Finally, the possible
presence of polarization is known to strongly affect the acceptance for
J/$\psi$ detection in the dilepton decay (up to 20–30% in ALICE [22]), and its
measurement is an important requisite for an unbiased evaluation of the
absolute yields in nuclear collisions. A first measurement of $\Upsilon(1{\rm
S})$ polarization in Pb–Pb collisions is also presented in this Letter, even
if the corresponding candidate sample is smaller by a factor $\sim$30, leading
to larger uncertainties. For such a state, considerations similar to those
discussed for the J/$\psi$ should hold, except that the contribution of the
regeneration mechanism should be negligible due to the much lower multiplicity
of bottom quarks with respect to charm.

The next sections of the Letter are organized as follows. Section 2 contains a
short description of the experimental apparatus and some details on the data
sample used in this analysis. The analysis procedure and the evaluation of
systematic uncertainties are presented in Sec. 3, while the results on the
J/$\psi$ and $\Upsilon(1{\rm S})$ polarization parameters $\lambda_{\theta}$,
$\lambda_{\phi}$ and $\lambda_{\theta\phi}$ are shown in Sec. 4. The
conclusions are presented in Sec. 5.

##  2 Experimental setup and data sample

The measurement described in this Letter is performed with the ALICE detector
[46, 47], whose main components are a central barrel and a forward muon
spectrometer. The latter covers the pseudorapidity region $-4<\eta<-2.5$ and
is used to detect muon pairs from quarkonium decays [48]. The muon
spectrometer includes a hadron absorber made of concrete, carbon and steel
with a thickness of 10 interaction lengths, followed by five tracking stations
(cathode-pad chambers), with the central one embedded inside a dipole magnet
with a 3 T$\cdot$m field integral. Downstream of the tracking system, an iron
wall filters out the remaining hadrons as well as low-momentum muons
originating from pion and kaon decays, and is followed by two trigger stations
(resistive plate chambers). Another forward detector, the V0 [49], composed of
two scintillator arrays located at opposite sides of the interaction point
(IP) and covering the pseudorapidity intervals $-3.7<\eta<-1.7$ and
$2.8<\eta<5.1$, provides the minimum bias (MB) trigger which is given by a
coincidence of signals from the two sides. Among the central barrel detectors,
the two layers of the Silicon Pixel Detector (SPD), with $|\eta|<2$ and
$|\eta|<1.4$ coverage, and corresponding to the inner part of the ALICE Inner
Tracking System (ITS) [50], are used to determine the position of the
interaction vertex. Finally, the Zero Degree Calorimeters (ZDC) [51], located
on either side of the IP at $\pm$ 112.5 m along the beam axis, detect
spectator nucleons emitted at zero degrees with respect to the LHC beam axis
and are used to reject electromagnetic Pb–Pb interactions.

The analysis is based on events where, in addition to the MB condition, two
opposite-sign tracks are detected in the triggering system of the muon
spectrometer (dimuon trigger). The dimuon trigger selects tracks each having a
transverse momentum above a threshold nominally set at $p_{\rm T}^{\mu}=1$
GeV/$c$, corresponding to the value for which the single-muon trigger
efficiency reaches 50% [52]. The single-muon trigger efficiency reaches a
plateau value of 98% at $\sim 2.5$ GeV/$c$.

The events are further characterized according to their centrality, i.e., the
degree of geometric overlap of the colliding nuclei. It is estimated by means
of a Glauber model fit to the V0 signal amplitude distribution [53, 54], with
more central events leading to a larger signal in the V0. In this analysis,
events corresponding to the most central 90% of the inelastic Pb–Pb cross
section are selected, as for these events the MB trigger is fully efficient
and the residual contamination from electromagnetic processes is negligible.

The results of the analysis are obtained using the $\sqrt{s_{\mathrm{NN}}}$ =
5.02 TeV Pb–Pb data samples collected by the ALICE experiment during the years
2015 and 2018, corresponding to an integrated luminosity
$L_{\mathrm{int}}\sim$ 750 $\mu{\rm b}^{-1}$.

##  3 Data analysis

The J/$\psi$ and $\Upsilon(1{\rm S})$ candidates are formed by combining
opposite-sign muons reconstructed using the tracking algorithm described in
Ref. [48]. In order to reject tracks at the edge of the spectrometer
acceptance, the condition $-4<\eta_{\mu}<-2.5$ is required. In addition,
tracks must have a radial transverse position at the end of the absorber in
the range $17.6<R_{\mathrm{abs}}<88.9$ cm. This selection is applied to remove
tracks passing through the inner and denser part of the absorber, which are
strongly affected by multiple scattering. For each muon candidate, a match
between tracks reconstructed in the tracking system and track segments in the
muon trigger system is required.

The J/$\psi$ polarization parameters $\lambda_{\theta}$, $\lambda_{\phi}$ and
$\lambda_{\theta\phi}$ are studied as a function of transverse momentum in the
intervals $2<p_{\rm T}<4$, $4<p_{\rm T}<6$ and $6<p_{\rm T}<10$ GeV/$c$. For
each $p_{\rm T}$ interval, a two–dimensional (2D) grid of dimuon invariant-
mass spectra is created, corresponding to intervals in $\cos\theta$ and
$\phi$, where $\theta$ and $\phi$ are the polar and azimuthal emission angles,
respectively, of the decay products in the J/$\psi$ rest frame, with respect
to the reference axis. More in detail, the 2D grid covers the fiducial region
$-0.8<\cos\theta<0.8$ (17 intervals), $0.5<\phi<\pi-0.5$ rad (8 intervals,
assuming a symmetric distribution around $\phi=\pi$), with the choice of the
boundaries as well as the width of the intervals dictated by acceptance
considerations.

The analysis is performed choosing two different reference systems for the
determination of the angular variables. In the Collins-Soper (CS) frame the
$z$-axis is defined as the bisector of the angle between the direction of one
beam and the opposite of the direction of the other one in the rest frame of
the decaying particle, allowing therefore an evaluation of the polarization
parameters with respect to the direction of motion of the colliding hadrons.
In the helicity (HE) reference frame the $z$-axis is given by the direction of
the decaying particle in the center-of-mass frame of the collision, and
therefore the polarization can be evaluated with respect to the momentum
direction of the J/$\psi$ itself. The $\phi=0$ plane is the one containing the
two beams in the J/$\psi$ rest frame.

For each dimuon invariant-mass spectrum, the J/$\psi$ raw yield is obtained by
means of a binned maximum likelihood fit in the interval $2.1<m_{\mu\mu}<4.9$
GeV/$c^{2}$. The background continuum is parameterized with a Gaussian
distribution whose width varies linearly with the mass or, alternatively, with
a fourth degree polynomial function times an exponential. The J/$\psi$ signal
is modeled with a pseudo-Gaussian function or with a Crystal Ball function
with asymmetric tails on both sides of the peak [55].

The J/$\psi$ mass is kept free in the fits, while for each interval ($i$,$j$)
in ($\cos\theta$,$\phi$) the width is fixed to $\sigma_{{\rm
J}/\psi}^{i,j}=\sigma_{{\rm J}/\psi}^{i,j,{\rm MC}}\cdot(\sigma_{{\rm
J}/\psi}/\sigma_{{\rm J}/\psi}^{\mathrm{MC}})$, i.e., scaling the resonance
width extracted from Monte Carlo (MC) simulations ($\sigma_{{\rm
J}/\psi}^{i,j,\rm{MC}}$) by the ratio between the width obtained by fitting
the angle-integrated spectrum in data ($\sigma_{{\rm J}/\psi}$) and MC
($\sigma_{{\rm J}/\psi}^{\mathrm{MC}}$) for the $p_{\rm T}$ interval under
consideration. The parameters of the non-Gaussian tails of the resonance are
kept fixed to the MC values. The $\psi(2\mathrm{S})$ contribution, although
comparatively negligible, is also taken into account in the fits, with its
width and mass fixed in each fit to those of the J/$\psi$ according to the
relations $\sigma_{\psi(2\mathrm{S})}=\sigma_{{\rm
J}/\psi}\cdot\sigma_{\psi(2\mathrm{S})}^{\mathrm{MC}}/\sigma_{{\rm
J}/\psi}^{\mathrm{MC}}$ and $m_{\psi(2\mathrm{S})}=m_{{\rm
J}/\psi}+m_{\psi(2\mathrm{S})}^{\mathrm{PDG}}-m_{{\rm
J}/\psi}^{\mathrm{PDG}}$, with the Particle Data Group (PDG) masses taken from
Ref. [1]. In Fig. 1 (left) an example of a fit to the invariant-mass spectrum
in the J/$\psi$ mass region is shown. Due to the stability of the extracted
J/$\psi$ parameters (mass, width), the fits were carried out directly on the
sum of the 2015 and 2018 invariant mass spectra.

Figure 1: Examples of fits to the invariant-mass distributions in the helicity
reference frame. The left plot corresponds to the J/$\psi$ mass region, while
on the right a fit to the $\Upsilon(1S)$ mass region is shown. The fits are
performed using an extended Crystal Ball function for the resonance signals,
while the background is parameterized with a variable width Gaussian.

The J/$\psi$ raw yields as a function of the angular variables are then
corrected by the product of the acceptance and detector efficiency
($A\times\varepsilon$), which is evaluated as a function of $\cos\theta$ and
$\phi$ on a 2D grid via MC simulations. The J/$\psi$ are generated according
to $p_{\rm T}$ and $y$ distributions directly tuned on data [56] via an
iterative procedure [57], and their decay muons are propagated inside a
realistic description of the ALICE setup, based on GEANT 3.21 [58]. The
misalignment of the detection elements and the time-dependent status of each
electronic channel during the data taking period are taken into account as
well. In the J/$\psi$ generation an isotropic distribution of decay products,
corresponding to the assumption of no polarization, is adopted. Due to the
choice of relatively small ($\cos\theta$, $\phi$) intervals, the
$A\times\varepsilon$ values for each interval are quite insensitive to the
specific angular distribution assumed in the generation.

The three polarization parameters $\lambda_{\theta}$, $\lambda_{\phi}$ and
$\lambda_{\theta\phi}$ are obtained through $\chi^{2}$-minimization fits of
the 2D J/$\psi$ distributions, corrected for acceptance and efficiency,
according to Eq. 1. For each combination of signal and background shape used
in the fit to the dimuon invariant-mass spectra, a separate evaluation of the
polarization parameters is carried out and their average is taken as the best
estimate. The statistical uncertainty is given by the average of the
statistical uncertainties of the 2D fits, while the root mean square of the
results provides the systematic uncertainty on the signal extraction, with the
absolute values ranging between 0.002 and 0.039. The overall procedure
described above was checked beforehand with a MC closure test. The 2D fits on
the ($\cos\theta$, $\phi$) distributions only allow a determination of the
absolute value of $\lambda_{\theta\phi}$, due to the presence of $\sin
2\theta$ in the corresponding term that induces an ambiguity in its sign. It
is checked that the values of $\lambda_{\theta}$ and $\lambda_{\phi}$ are
stable against the choice of the sign of the $\lambda_{\theta\phi}$ term. In
the following the $\lambda_{\theta\phi}$ values corresponding to the choice of
a positive sign are quoted. Figure 2 illustrates an example of the fit to the
angular distributions. For better visibility, both the distribution and the
fitted function are projected along one dimension.

Figure 2:  Fit to the J/$\psi$ 2D angular distributions in the helicity
reference frame projected along $\cos\theta$ (left) and $\phi$ (right) for
$2.5<y<4$ and $4<\mbox{$p_{\rm T}$}<6$ GeV/$c$. The displayed uncertainties
are statistical.

In addition to the systematic uncertainty related to the choice of the mass
shapes for signal and background, several other sources are taken into
account. First, an alternative procedure for extracting the J/$\psi$ signal is
carried out, by keeping its width as a free parameter in the invariant-mass
fits. The corresponding results for the polarization parameters are then
obtained and the averages of the values corresponding to fixing the width or
not are taken as the central values for $\lambda_{\theta}$, $\lambda_{\phi}$
and $\lambda_{\theta\phi}$. Half the difference between the results obtained
with free or MC-anchored widths is then considered as a further systematic
uncertainty related to the signal extraction. This uncertainty is found to be
the leading contribution to the total absolute systematic uncertainty on the
polarization parameters, and ranges between 0.001 and 0.063, the latter value
corresponding to the uncertainty on $\lambda_{\theta}^{\rm HE}$ for $2<p_{\rm
T}<4$ GeV/$c$.

Another source of systematic uncertainty is related to the evaluation of the
trigger efficiency. The muon trigger response function as a function of the
single muon transverse momentum $p_{\rm T}^{\mu}$ can be obtained via MC or
with a procedure based on data [59]. Small deviations are found for
$p_{\mathrm{\textsc{t}}}^{\mu}<2$ GeV/$c$ which induce an effect on
$A\times\varepsilon$ for the J/$\psi$. Therefore, the polarization parameters
are re-calculated with $A\times\varepsilon$ values weighted in such a way to
account for the deviations. The variation of the polarization parameters
between the different trigger efficiency estimates is taken as the related
systematic uncertainty, with values ranging from 0.001 to 0.043, the highest
values being found for $\lambda_{\theta}^{\rm HE}$ in $2<p_{\rm T}<4$ GeV/$c$.
The systematic uncertainty related to the evaluation of the muon tracking
efficiency is found to be negligible for this analysis, allowing a significant
reduction of the total systematic uncertainty with respect to previous pp
analyses [23]. Indeed, although the difference between efficiencies calculated
via MC or from data [59] is of the order of 2%, a detailed investigation has
shown no dependence on the angular variables and therefore no effect on the
polarization parameters.

Finally, the systematic uncertainty induced by the choice of the $p_{\rm T}$
and $y$ distributions used as an input for the calculation of
$A\times\varepsilon$ is evaluated testing alternative $p_{\rm T}$ and $y$
parameterizations, which are obtained by varying within their uncertainties
the default distributions directly tuned on Pb–Pb data. The polarization
parameters extracted with the modified values of $A\times\varepsilon$ are
compared with those obtained with the default input shapes and the
corresponding systematic uncertainty extracted in this way is found to range
between 0.001 and 0.030, with the largest value assigned to
$\lambda_{\theta}^{\rm HE}$ for $2<p_{\rm T}<4$ GeV/$c$. The influence of the
choice of the angular distributions of the J/$\psi$ decay products for the
$A\times\varepsilon$ calculation is also investigated by means of an iterative
procedure on these input distributions. The effect is found to be negligible,
also due to the fact that the 2D correction procedure on the angular variables
is by definition relatively insensitive to the specific choice of the
corresponding distributions. A summary of the values of all the absolute
systematic uncertainties, which are considered as uncorrelated as a function
of $p_{\rm T}$, is reported in Table 1. The total systematic uncertainties are
obtained, for each parameter and $p_{\rm T}$ interval, as the quadratic sum of
the values.

Table 1: Summary of the absolute systematic uncertainties on the evaluation of the J/$\psi$ polarization parameters. All the uncertainties are considered as uncorrelated as a function of $p_{\rm T}$. |  | Helicity | Collins-Soper
---|---|---|---
|  | Signal | J/$\psi$ | Trigger | Input | Signal | J/$\psi$ | Trigger | Input
|  $p_{\rm T}$ (GeV/c) | extr. | width | eff. | MC | extr. | width | eff. | MC
$\lambda_{\theta}$ | 2$<$$p_{\rm T}$ $<$4 | 0.030 | 0.063 | 0.043 | 0.030 | 0.026 | 0.049 | 0.015 | 0.009
4$<$$p_{\rm T}$ $<$6 | 0.017 | 0.046 | 0.040 | 0.024 | 0.002 | 0.052 | 0.018 | 0.007
6$<$$p_{\rm T}$ $<$10 | 0.039 | 0.005 | 0.018 | 0.017 | 0.022 | 0.001 | 0.011 | 0.006
$\lambda_{\phi}$ | 2$<$$p_{\rm T}$ $<$4 | 0.007 | 0.030 | 0.004 | 0.002 | 0.024 | 0.010 | 0.020 | 0.003
4$<$$p_{\rm T}$ $<$6 | 0.003 | 0.035 | 0.003 | 0.003 | 0.002 | 0.010 | 0.020 | 0.003
6$<$$p_{\rm T}$ $<$10 | 0.002 | 0.009 | 0.001 | 0.002 | 0.005 | 0.013 | 0.011 | 0.002
$\lambda_{\theta\phi}$ | 2$<$$p_{\rm T}$ $<$4 | 0.021 | 0.029 | 0.024 | 0.001 | 0.013 | 0.010 | 0.017 | 0.015
4$<$$p_{\rm T}$ $<$6 | 0.007 | 0.011 | 0.017 | 0.006 | 0.002 | 0.042 | 0.010 | 0.015
6$<$$p_{\rm T}$ $<$10 | 0.020 | 0.019 | 0.007 | 0.008 | 0.007 | 0.042 | 0.003 | 0.013

A similar procedure is followed for the extraction of the $\Upsilon(1{\rm S})$
polarization parameters. Due to the smaller candidate sample, integrated
values over the kinematic interval $2.5<y<4$, $p_{\rm T}<15$ GeV/$c$ are
obtained. The main difference with respect to the 2D approach followed for the
J/$\psi$ is the use of a simultaneous fit to the 1D angular distributions
[23], after integration over the other variables. The requirement $p_{\rm
T}^{\mu}>2$ GeV/$c$, which helps reducing the combinatorial background, is
included [60]. The $\Upsilon(1{\rm S})$ signal extraction in the various
$\cos\theta$ and $\phi$ intervals is performed by means of invariant-mass fits
(see the right panel of Fig. 1 for an example). The functions chosen for the
resonances are the same as in the J/$\psi$ analysis (pseudo-Gaussian or
Crystal Ball), the mass value is fixed to that obtained from a fit to the
integrated invariant-mass distribution, while the width for each angular
interval is fixed to the MC value scaled by the ratio of the widths between
data and MC for the angle-integrated distributions. The tail parameters are
fixed to MC values. The small contribution from $\Upsilon(2{\rm S})$ is also
included in the fits [60]. The background continuum is parameterized with a
Gaussian distribution whose width varies linearly with the mass or,
alternatively, with a second degree polynomial function times an exponential.
The systematic uncertainty on the signal extraction is calculated with the
same procedure adopted for the J/$\psi$. An uncertainty related to the choice
of the signal width has also been considered, taken as the half-difference
between the results obtained with the prescription described above and using
as an alternative prescription the pure MC values. The uncertainty on the
trigger efficiency is negligible, due to the additional requirement on the
single-muon transverse momentum which selects a $p_{\rm T}$-region where the
trigger efficiency is very high and its evaluation via data and MC is
consistent. Finally, the procedure for the determination of the uncertainty
related to the $\Upsilon(1{\rm S})$ kinematic distributions used in the MC is
the same as for the J/$\psi$. The total systematic uncertainties for the
$\Upsilon(1{\rm S})$ analysis are reported in Table 3, together with the
results.

##  4 Results

The polarization parameters for J/$\psi$ inclusive production in Pb–Pb
collisions at $\sqrt{s_{{}_{\mathrm{NN}}}}=$ 5.02 TeV in the helicity and
Collins-Soper reference frames are shown in Fig. 3 and the corresponding
numerical values are reported in Table 2. In Fig. 3, $\lambda_{\theta}$,
$\lambda_{\phi}$ and $\lambda_{\theta\phi}$ are also compared with the LHCb
[24] and ALICE [23] measurements in pp collisions at $\sqrt{s}=$ 7 and 8 TeV,
respectively.

Table 2: J/$\psi$ polarization parameters, measured for Pb–Pb collisions at $\sqrt{s_{\rm NN}}=5.02$ TeV, in the helicity and Collins-Soper reference frames in the rapidity interval $2.5<y<4$. The first uncertainty is statistical and the second systematic. |  $p_{\rm T}$ (GeV/c) | Helicity | Collins-Soper
---|---|---|---
$\lambda_{\theta}$ | 2$<$$p_{\rm T}$ $<$4 | $0.218\pm 0.060\pm 0.087$ | $-0.157\pm 0.049\pm 0.058$
4$<$$p_{\rm T}$ $<$6 | $0.151\pm 0.071\pm 0.068$ | $-0.057\pm 0.059\pm 0.055$
6$<$$p_{\rm T}$ $<$10 | $-0.070\pm 0.068\pm 0.047$ | $-0.008\pm 0.063\pm 0.026$
$\lambda_{\phi}$ | 2$<$$p_{\rm T}$ $<$4 | $-0.029\pm 0.017\pm 0.031$ | $0.061\pm 0.015\pm 0.033$
4$<$$p_{\rm T}$ $<$6 | $-0.013\pm 0.019\pm 0.036$ | $0.047\pm 0.024\pm 0.023$
6$<$$p_{\rm T}$ $<$10 | $0.047\pm 0.021\pm 0.010$ | $0.024\pm 0.032\pm 0.018$
$\lambda_{\theta\phi}$ | 2$<$$p_{\rm T}$ $<$4 | $-0.124\pm 0.028\pm 0.043$ | $-0.090\pm 0.027\pm 0.029$
4$<$$p_{\rm T}$ $<$6 | $-0.059\pm 0.030\pm 0.021$ | $-0.040\pm 0.034\pm 0.046$
6$<$$p_{\rm T}$ $<$10 | $-0.025\pm 0.031\pm 0.030$ | $0.018\pm 0.035\pm 0.044$
Figure 3: Inclusive J/$\psi$ polarization parameters as a function of
transverse momentum for Pb–Pb collisions at $\sqrt{s_{{}_{\mathrm{NN}}}}=$
5.02 TeV, compared with results obtained in pp collisions by ALICE at
$\sqrt{s}=$ 8 TeV [23] and by LHCb for prompt J/$\psi$ at $\sqrt{s}=$ 7 TeV
[24] (the LHCb markers were shifted horizontally by +0.3 GeV/c for better
visibility) in the rapidity interval $3<y<3.5$. The error bars represent the
total uncertainties for the pp results, while for Pb–Pb statistical and
systematic uncertainties are plotted separately as a vertical bar and a shaded
box, respectively. In the left part of the plot the polarization parameters in
the helicity reference frame are reported, in the right those for the Collins-
Soper frame.

For all the $p_{\rm T}$ intervals and in both reference frames the values of
the polarization parameters exhibit at most slight deviations from zero. In
particular, $\lambda_{\theta}^{\rm HE}$ indicates a slight transverse
polarization at low $p_{\rm T}$ ($\sim 2.1\sigma$ effect, calculated using the
Gaussian approximation), while $\lambda_{\theta}^{\rm CS}$ shows a weak
longitudinal polarization ($\sim 2.1\sigma$). When increasing $p_{\rm T}$, the
central values of $\lambda_{\theta}$ become close to zero. All values of
$\lambda_{\phi}$ and $\lambda_{\theta\phi}$ are, in absolute value, smaller
than 0.1, except for $\lambda_{\theta\phi}^{\rm HE}$, which is $-0.124$ at low
$p_{\rm T}$ and deviates from zero by $\sim 2.4\sigma$.

When comparing with the pp results, no significant difference is found with
respect to ALICE results at $\sqrt{s}=8$ TeV, which are compatible with zero.
A significant difference is found with respect to the higher-precision LHCb
results at $\sqrt{s}=7$ TeV, reaching 3.3$\sigma$ in the interval $2<p_{\rm
T}<4$ GeV/$c$ in the helicity reference frame, where pp data [24] indicate a
small but significant degree of longitudinal polarization, while the Pb–Pb
results favor a slightly transverse polarization. In Pb–Pb collisions at LHC
energies, a significant fraction of the detected J/$\psi$ originates from the
recombination of ${\rm c}{\rm\overline{c}}$ pairs in the QGP phase or when the
system hadronizes. Moreover, the contribution from higher-mass charmonium
states decaying to J/$\psi$ could vary between pp and Pb-Pb due to different
suppression effects for each state in nuclear collisions. Therefore, the
observed hint for a different polarization in pp and Pb–Pb might be a
reflection of the different production and suppression mechanisms in the two
systems, but more precise data, along with quantitative theory estimates, are
needed for a definite conclusion. It should also be noted that the ALICE
results refer to inclusive production, while LHCb has measured prompt
J/$\psi$. However, as discussed in Ref. [22], the size of the non-prompt
component is small in the covered $p_{\rm T}$ region (of the order of 15% at
high $p_{\rm T}$) and its polarization was also measured to be small by CDF
($\lambda_{\theta}^{\rm{HE}}\sim-0.1$ [21]), implying that the net effect of
this source on inclusive J/$\psi$ polarization should be negligible.

In Table 3 the values of the $\Upsilon(1{\rm S})$ polarization parameters are
shown. The $\lambda_{\theta}$ values are consistent with zero, with large
uncertainties that prevent a firm conclusion on the absence of polarization in
nuclear collisions. The $\lambda_{\phi}$ and $\lambda_{\theta\phi}$ values are
also consistent with zero. The relatively smaller uncertainties for these
parameters are related to a more uniform acceptance distribution as a function
of the azimuthal angular variable.

Table 3: $\Upsilon(1{\rm S})$ polarization parameters in the helicity and Collins-Soper reference frames measured in Pb–Pb collisions at $\sqrt{s_{\rm NN}}=5.02$ TeV in the rapidity interval $2.5<y<4$ and for transverse momentum $p_{\rm T}<15$ GeV/$c$. The first uncertainty is statistical and the second systematic. | Helicity | Collins-Soper
---|---|---
$\lambda_{\theta}$ | $-0.090\pm 0.395\pm 0.101$ | $0.418\pm 0.526\pm 0.178$
$\lambda_{\phi}$ | $-0.094\pm 0.072\pm 0.020$ | $-0.141\pm 0.087\pm 0.033$
$\lambda_{\theta\phi}$ | $-0.074\pm 0.099\pm 0.020$ | $0.017\pm 0.113\pm 0.024$

##  5 Conclusions

The first measurement of the polarization parameters for J/$\psi$ production
in nuclear collisions at LHC energies was carried out by the ALICE
Collaboration in Pb–Pb interactions at $\sqrt{s_{\rm NN}}=5.02$ TeV. The
$\lambda_{\theta}$, $\lambda_{\phi}$ and $\lambda_{\theta\phi}$ parameters
were evaluated in the helicity and Collins-Soper reference frames in the
rapidity interval $2.5<y<4$ and in the transverse momentum interval $2<p_{\rm
T}<10$ GeV/$c$. All the parameter values are close to zero, with a $\sim
2.1\sigma$ indication for a small transverse polarization in the helicity
frame at low $p_{\rm T}$, and a corresponding indication for a small
longitudinal polarization in the Collins-Soper frame ($\sim 2.1\sigma$
effect). When comparing these results with pp data taken at higher energy at
the LHC, an interesting feature is a significant difference in
$\lambda_{\theta}^{\rm HE}$ with respect to the LHCb results which showed
instead a small longitudinal polarization in a similar kinematic domain. This
first result obtained for J/$\psi$ in nuclear collisions and described in this
Letter represents therefore a starting point for future studies connecting
such features with the known differences in the production mechanisms between
pp and nucleus–nucleus collisions. Results were also obtained for the first
time for the $\Upsilon(1{\rm S})$ polarization, integrated over $p_{\rm T}$
and $y$, showing, within the large uncertainties of the measurement, values
compatible with the absence of polarization.

## 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) 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; 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, 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 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. Adamováorg95&A. Adlerorg74&J. Adolfssonorg81&M.M.
Aggarwalorg100&G. Aglieri Rinellaorg34&M. Agnelloorg30&N.
Agrawalorg10,org54&Z. Ahammedorg141&S. Ahmadorg16&S.U. Ahnorg76&Z.
Akbarorg51&A. Akindinovorg92&M. Al-Turanyorg107&S.N. Alamorg40,org141&D.S.D.
Albuquerqueorg122&D. Aleksandrovorg88&B. Alessandroorg59&H.M. Alfandaorg6&R.
Alfaro Molinaorg71&B. Aliorg16&Y. Aliorg14&A. Aliciorg10,org26,org54&N.
Alizadehvandchaliorg125&A. Alkinorg2,org34&J. Almeorg21&T. Altorg68&L.
Altenkamperorg21&I. Altsybeevorg113&M.N. Anaamorg6&C. Andreiorg48&D.
Andreouorg34&A. Andronicorg144&M. Angelettiorg34&V. Anguelovorg104&C.
Ansonorg15&T. Antičićorg108&F. Antinoriorg57&P. Antonioliorg54&N.
Apadulaorg80&L. Aphecetcheorg115&H. Appelshäuserorg68&S. Arcelliorg26&R.
Arnaldiorg59&M. Arratiaorg80&I.C. Arseneorg20&M. Arslandokorg104&A.
Augustinusorg34&R. Averbeckorg107&S. Azizorg78&M.D. Azmiorg16&A.
Badalàorg56&Y.W. Baekorg41&S. Bagnascoorg59&X. Baiorg107&R. Bailhacheorg68&R.
Balaorg101&A. Balbinoorg30&A. Baldisseriorg137&M. Ballorg43&S.
Balouzaorg105&D. Banerjeeorg3&R. Barberaorg27&L. Barioglioorg25&G.G.
Barnaföldiorg145&L.S. Barnbyorg94&V. Barretorg134&P. Bartaliniorg6&C.
Bartelsorg127&K. Barthorg34&E. Bartschorg68&F. Baruffaldiorg28&N.
Bastidorg134&S. Basuorg143&G. Batigneorg115&B. Batyunyaorg75&D.
Bauriorg49&J.L. Bazo Albaorg112&I.G. Beardenorg89&C. Beattieorg146&C.
Beddaorg63&N.K. Beheraorg61&I. Belikovorg136&A.D.C. Bell Hechavarriaorg144&F.
Belliniorg34&R. Bellwiedorg125&V. Belyaevorg93&G. Bencediorg145&S.
Beoleorg25&A. Bercuciorg48&Y. Berdnikovorg98&D. Berenyiorg145&R.A.
Bertensorg130&D. Berzanoorg59&M.G. Besoiuorg67&L. Betevorg34&A.
Bhasinorg101&I.R. Bhatorg101&M.A. Bhatorg3&H. Bhattorg49&B.
Bhattacharjeeorg42&A. Bianchiorg25&L. Bianchiorg25&N. Bianchiorg52&J.
Bielčíkorg37&J. Bielčíkováorg95&A. Bilandzicorg105&G. Biroorg145&R.
Biswasorg3&S. Biswasorg3&J.T. Blairorg119&D. Blauorg88&C. Blumeorg68&G.
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Zamanorg14&C. Zampolliorg34&H.J.C. Zanoliorg63&N. Zardoshtiorg34&A.
Zarochentsevorg113&P. Závadaorg66&N. Zaviyalovorg109&H. Zbroszczykorg142&M.
Zhalovorg98&S. Zhangorg40&X. Zhangorg6&Z. Zhangorg6&V. Zherebchevskiiorg113&Y.
Zhiorg12&D. Zhouorg6&Y. Zhouorg89&Z. Zhouorg21&J. Zhuorg6,org107&Y. Zhuorg6&A.
Zichichiorg10,org26&G. Zinovjevorg2&N. Zurloorg140&

## Affiliation notes

org*Deceased

orgIItalian National Agency for New Technologies, Energy and Sustainable
Economic Development (ENEA), Bologna, Italy

orgIIDipartimento DET del Politecnico di Torino, Turin, Italy

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

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

orgVInstitute 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

org13Comenius University Bratislava, Faculty of Mathematics, Physics and
Informatics, Bratislava, Slovakia

org14COMSATS University Islamabad, Islamabad, Pakistan

org15Creighton University, Omaha, Nebraska, United States

org16Department of Physics, Aligarh Muslim University, Aligarh, India

org17Department of Physics, Pusan National University, Pusan, Republic of
Korea

org18Department of Physics, Sejong University, Seoul, Republic of Korea

org19Department of Physics, University of California, Berkeley, California,
United States

org20Department of Physics, University of Oslo, Oslo, Norway

org21Department of Physics and Technology, University of Bergen, Bergen,
Norway

org22Dipartimento di Fisica dell’Università ’La Sapienza’ and Sezione INFN,
Rome, Italy

org23Dipartimento di Fisica dell’Università and Sezione INFN, Cagliari, Italy

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

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

org26Dipartimento di Fisica e Astronomia dell’Università and Sezione INFN,
Bologna, Italy

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

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

org29Dipartimento di Fisica ‘E.R. Caianiello’ dell’Università and Gruppo
Collegato INFN, Salerno, Italy

org30Dipartimento DISAT del Politecnico and Sezione INFN, Turin, Italy

org31Dipartimento di Scienze e Innovazione Tecnologica dell’Università del
Piemonte Orientale and INFN Sezione di Torino, Alessandria, Italy

org32Dipartimento di Scienze MIFT, Università di Messina, Messina, 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

org40Fudan University, Shanghai, China

org41Gangneung-Wonju National University, Gangneung, Republic of Korea

org42Gauhati University, Department of Physics, Guwahati, India

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

org44Helsinki Institute of Physics (HIP), Helsinki, Finland

org45High Energy Physics Group, Universidad Autónoma de Puebla, Puebla, Mexico

org46Hiroshima University, Hiroshima, Japan

org47Hochschule Worms, Zentrum für Technologietransfer und Telekommunikation
(ZTT), Worms, Germany

org48Horia Hulubei National Institute of Physics and Nuclear Engineering,
Bucharest, Romania

org49Indian Institute of Technology Bombay (IIT), Mumbai, India

org50Indian Institute of Technology Indore, Indore, India

org51Indonesian Institute of Sciences, Jakarta, Indonesia

org52INFN, Laboratori Nazionali di Frascati, Frascati, Italy

org53INFN, Sezione di Bari, Bari, Italy

org54INFN, Sezione di Bologna, Bologna, Italy

org55INFN, Sezione di Cagliari, Cagliari, Italy

org56INFN, Sezione di Catania, Catania, Italy

org57INFN, Sezione di Padova, Padova, Italy

org58INFN, Sezione di Roma, Rome, Italy

org59INFN, Sezione di Torino, Turin, Italy

org60INFN, Sezione di Trieste, Trieste, Italy

org61Inha University, Incheon, Republic of Korea

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

org73Jeonbuk National University, Jeonju, Republic of Korea

org74Johann-Wolfgang-Goethe Universität Frankfurt Institut für Informatik,
Fachbereich Informatik und Mathematik, Frankfurt, Germany

org75Joint Institute for Nuclear Research (JINR), Dubna, Russia

org76Korea Institute of Science and Technology Information, Daejeon, Republic
of Korea

org77KTO Karatay University, Konya, Turkey

org78Laboratoire de Physique des 2 Infinis, Irène Joliot-Curie, Orsay, France

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

org80Lawrence Berkeley National Laboratory, Berkeley, California, United
States

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

org82Nagasaki Institute of Applied Science, Nagasaki, Japan

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

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

org85National Centre for Nuclear Research, Warsaw, Poland

org86National Institute of Science Education and Research, Homi Bhabha
National Institute, Jatni, India

org87National Nuclear Research Center, Baku, Azerbaijan

org88National Research Centre Kurchatov Institute, Moscow, Russia

org89Niels Bohr Institute, University of Copenhagen, Copenhagen, Denmark

org90Nikhef, National institute for subatomic physics, Amsterdam, Netherlands

org91NRC Kurchatov Institute IHEP, Protvino, Russia

org92NRC «Kurchatov» Institute - ITEP, Moscow, Russia

org93NRNU Moscow Engineering Physics Institute, Moscow, Russia

org94Nuclear Physics Group, STFC Daresbury Laboratory, Daresbury, United
Kingdom

org95Nuclear Physics Institute of the Czech Academy of Sciences, Řež u Prahy,
Czech Republic

org96Oak Ridge National Laboratory, Oak Ridge, Tennessee, United States

org97Ohio State University, Columbus, Ohio, United States

org98Petersburg Nuclear Physics Institute, Gatchina, Russia

org99Physics department, Faculty of science, University of Zagreb, Zagreb,
Croatia

org100Physics Department, Panjab University, Chandigarh, India

org101Physics Department, University of Jammu, Jammu, India

org102Physics Department, University of Rajasthan, Jaipur, India

org103Physikalisches Institut, Eberhard-Karls-Universität Tübingen, Tübingen,
Germany

org104Physikalisches Institut, Ruprecht-Karls-Universität Heidelberg,
Heidelberg, Germany

org105Physik Department, Technische Universität München, Munich, Germany

org106Politecnico di Bari, Bari, Italy

org107Research Division and ExtreMe Matter Institute EMMI, GSI
Helmholtzzentrum für Schwerionenforschung GmbH, Darmstadt, Germany

org108Rudjer Bošković Institute, Zagreb, Croatia

org109Russian Federal Nuclear Center (VNIIEF), Sarov, Russia

org110Saha Institute of Nuclear Physics, Homi Bhabha National Institute,
Kolkata, India

org111School of Physics and Astronomy, University of Birmingham, Birmingham,
United Kingdom

org112Sección Física, Departamento de Ciencias, Pontificia Universidad
Católica del Perú, Lima, Peru

org113St. Petersburg State University, St. Petersburg, Russia

org114Stefan Meyer Institut für Subatomare Physik (SMI), Vienna, Austria

org115SUBATECH, IMT Atlantique, Université de Nantes, CNRS-IN2P3, Nantes,
France

org116Suranaree University of Technology, Nakhon Ratchasima, Thailand

org117Technical University of Košice, Košice, Slovakia

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

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

org120Universidad Autónoma de Sinaloa, Culiacán, Mexico

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

org122Universidade Estadual de Campinas (UNICAMP), Campinas, Brazil

org123Universidade Federal do ABC, Santo Andre, Brazil

org124University of Cape Town, Cape Town, South Africa

org125University of Houston, Houston, Texas, United States

org126University of Jyväskylä, Jyväskylä, Finland

org127University of Liverpool, Liverpool, United Kingdom

org128University of Science and Technology of China, Hefei, China

org129University of South-Eastern Norway, Tonsberg, Norway

org130University of Tennessee, Knoxville, Tennessee, United States

org131University of the Witwatersrand, Johannesburg, South Africa

org132University of Tokyo, Tokyo, Japan

org133University of Tsukuba, Tsukuba, Japan

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

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

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

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

org138Università degli Studi di Foggia, Foggia, Italy

org139Università degli Studi di Pavia, Pavia, Italy

org140Università di Brescia, Brescia, Italy

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

org142Warsaw University of Technology, Warsaw, Poland

org143Wayne State University, Detroit, Michigan, United States

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

org145Wigner Research Centre for Physics, Budapest, Hungary

org146Yale University, New Haven, Connecticut, United States

org147Yonsei University, Seoul, Republic of Korea