2018 098 8 May

Forward J/$\psi$ polarization in pp at $\sqrt{s}=8$ TeV

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

We report on the measurement of the inclusive J/$\psi$ polarization parameters
in pp collisions at a center of mass energy $\sqrt{s}=8$ TeV with the ALICE
detector at the LHC. The analysis is based on a data sample corresponding to
an integrated luminosity of 1.23 pb-1. J/$\psi$ resonances are reconstructed
in their di-muon decay channel in the rapidity interval $2.5<y<4.0$ and over
the transverse-momentum interval $2<p_{\rm T}<15$
$\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc$. The three polarization
parameters ($\lambda_{\theta}$, $\lambda_{\varphi}$,
$\lambda_{\theta\varphi}$) are measured as a function of $p_{\rm T}$ both in
the helicity and Collins-Soper reference frames. The measured J/$\psi$
polarization parameters are found to be compatible with zero within
uncertainties, contrary to expectations from all available predictions. The
results are compared with the measurement in pp collisions at $\sqrt{s}=7$
TeV.

##  1 Introduction

More than 40 years after the J/$\psi$ discovery, its production mechanism in
hadronic collisions remains an open issue [1]. Quarkonia states constitute an
important test bench for the study of Quantum ChromoDynamics (QCD) both in the
vacuum and in high-energy density environments, as those produced in heavy-ion
collisions, where the creation of the Quark–Gluon Plasma (QGP) is observed
[2]. Consequently, the understanding of the J/$\psi$ production mechanism is
an important scientific question in the sense that it addresses basic concepts
of QCD, the theory of the strong interaction, and its application to heavy-ion
collisions allows the characterisation of the QGP properties created in the
laboratory.

Different theoretical models have been developed in an attempt to describe the
whole production mechanism from partonic interaction to heavy-quark pair
(Q$\overline{\rm Q}$) hadronisation in quarkonia. All approaches are based on
the factorisation hypothesis between hard and soft scales. First
phenomenological attempts (e.g. the Color Evaporation Model [3]) have been
replaced by a rigorous effective field theory, the Non-Relativistic QCD
(NRQCD) [4]. In this framework, two models can be derived according to the
sub-processes taken into account: the Color-Singlet Model (CSM) [5, 6] and the
Color-Octet Mechanism (COM) [4]. The CSM assumes no evolution of the quantum
color-singlet state between the Q$\overline{\rm Q}$ production and the
quarkonium formation, with a wave function computed at zero Q$\overline{\rm
Q}$ separation, i.e. without any free parameter. The COM introduces Long-
Distance Matrix Elements (LDMEs) for the hadronisation probability in a
quarkonium state. The LDMEs are free parameters of the theory which must be
fixed from experimental data.

Recent measurements at the LHC confirm that color-octet terms are crucial for
a good description of the J/$\psi$ and $\psi$(2S) differential production
cross sections [7]. However, the failure in predicting the $\eta_{\rm c}$
production cross section [8, 9] poses serious challenges to the NRQCD
approach.

In this context, alternative measurements at different energies and in
different rapidity regions can help to disentangle tensions between quarkonium
measurements and the theoretical predictions. One of the most relevant
observables apart from the production cross section is the polarization of
quarkonia. The polarization of $\rm J^{\rm PC}=1^{--}$ states like the
J/$\psi$ is specified by three polarization parameters ($\lambda_{\theta}$,
$\lambda_{\varphi}$, $\lambda_{\theta\varphi}$), which are a function of the
three decay amplitudes with respect to the three angular momentum states. The
two cases ($\lambda_{\theta}=1$, $\lambda_{\varphi}=0$,
$\lambda_{\theta\varphi}=0$) and ($\lambda_{\theta}=-1$,
$\lambda_{\varphi}=0$, $\lambda_{\theta\varphi}=0$) correspond to the so-
called transverse and longitudinal polarizations, respectively. Theoretical
models at Next-to-Leading Order (NLO) predict strongly transverse-momentum
dependent polarization states with a partial longitudinal polarization in the
CSM and a partial transverse polarization when color-octet contributions are
included in the NRQCD calculation [10].

Experimentally, the polarization parameters can be determined in the
quarkonium dilepton decay channel by studying the angular distribution ($W$)
of the leptons in the quarkonium rest-frame [11]:

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

where $\theta$ and $\varphi$ are the polar and the azimuthal angles,
respectively, defining the orientation of one lepton (for instance the
negative one) in the quarkonium rest-frame with respect to a reference axis.
In the analysis presented here, the selected reference axes are: (i) the
helicity axis corresponding to the quarkonium flight direction in the center-
of-mass of the colliding beams, and (ii) the Collins-Soper axis defined by the
direction of the relative velocity of the colliding beams in the quarkonium
rest-frame. In the following, the J/$\psi$ rest-frame associated to the
helicity axis will be referred to as helicity (HX) frame and the one defined
from the Collins-Soper axis will be called Collins-Soper (CS) frame.

Since the beginning of the LHC operations, the study of the J/$\psi$
polarization in pp collisions has been carried out at $\sqrt{s}=7$ TeV both at
midrapidity by the CMS [12] experiment, and at forward rapidity by the ALICE
[13] and LHCb [14] experiments. The midrapidity and forward rapidity results
are complementary in terms of the explored transverse-momentum ($p_{\rm T}$)
interval, which is $14<p_{\rm T}<70$
$\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc$ for CMS, $2<p_{\rm T}<15$
$\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc$ for LHCb and $2<p_{\rm T}<8$
$\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc$ for ALICE.

In this paper we present the polarization measurement of inclusively-produced
J/$\psi$ mesons in pp collisions at $\sqrt{s}=8$ TeV in the transverse-
momentum interval $2<p_{\rm T}<15$
$\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc$. This is the first measurement
of the J/$\psi$ polarization at this energy, and extends the $p_{\rm T}$ reach
of the previous ALICE measurement at $\sqrt{s}=7$ TeV [13]. The paper starts
with a brief description of the experimental apparatus and the used data
sample in Section 2, followed by a description of the analysis in Section 3,
including a discussion of the systematic uncertainties. The results are
presented in Section 4 and compared with those obtained from $\sqrt{s}=7$ TeV
and with model calculations. Conclusions are finally drawn in Section 5.

##  2 Experimental apparatus and data sample

The ALICE apparatus and its performance are described in detail in [15] and
[16], respectively. In this paper we focus on the two sub-detectors relevant
for the analysis: the forward muon spectrometer [17] and the first two layers
of the Inner Tracking System (ITS) [18].

The muon spectrometer detects muons in the pseudorapidity range111Although the
muon spectrometer covers negative pseudorapidities ($\eta$) in the ALICE
reference frame, we use positive rapidity values when referring to the
rapidity ($y$) of quarkonia states reconstructed via their di-muon decay
channel. $-4.0<\eta<-2.5$. It consists of five tracking stations with two
detection planes of multi-wire proportional chambers with cathode pad readout
and two trigger stations, each comprising of two detection planes of resistive
plate chambers. A set of absorbers completes the system, to decrease the
hadronic background: the front-absorber (before the first tracking station)
reduces the contamination of light hadron decays, a shield surrounding the
beam pipe decreases the background from particles produced in the interaction
at large pseudorapidity, and an iron wall shields the trigger stations from
residual punch through. The momenta of charged tracks are measured with the
help of a 3 T$\cdot$m dipole magnet surrounding the third tracking station.

The ITS consists of six layers of silicon detectors with cylindrical geometry
surrounding the beam pipe, with radii ranging from 3.9 to 43 cm from the beam
axis. This analysis makes use of the two innermost layers that are equipped
with Silicon Pixel Detectors (SPD) and cover the pseudorapidity ranges
$|\eta|<2$ and $|\eta|<1.4$ for the first and the second layer, respectively.
The SPD is used to reconstruct the position of the primary vertex of the
collision.

The data used for this analysis were collected in 2012. The online event
selection is based on the opposite-sign di-muon trigger, with a $p_{\rm T}$
threshold of about 1 $\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc$ applied on
each muon candidate. This di-muon trigger runs in coincidence with the
crossing of two beam bunches at the interaction point. The data sample
recorded with this trigger configuration is the same as in [19] and
corresponds to an integrated luminosity of about 1.23 pb-1.

##  3 Analysis

### Track selection.

The opposite-sign di-muon pair candidates are reconstructed with the following
track selection criteria (see [19] for details):

  * •

the track pseudorapidity must be in the range corresponding to the muon
spectrometer acceptance $-4<\eta<-2.5$,

  * •

the polar angle $\theta_{\rm abs}$ measured at the rear-end plane of the front
absorber must be in the interval
$170<\theta_{\rm abs}<178$ degrees,

  * •

the maximum allowed value for the $p$DCA variable, defined as the product of
the total momentum $p$ of the track and its distance of closest approach DCA
to the primary vertex in the transverse plane, must be less than
$6\times\sigma_{p{\rm DCA}}$, where the resolution $\sigma_{p{\rm DCA}}$ is 54
cm$\cdot$$\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc$ for $170<\theta_{\rm
abs}<177$ degrees and 80
cm$\cdot$$\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc$ for
$177\leq\theta_{\rm abs}<178$ degrees,

  * •

each track reconstructed in the muon tracking system must match a track in the
trigger system and in addition must pass the low-$p_{\rm T}$ trigger threshold
of $\sim 1$ $\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc$.

Finally, each unlike-sign di-muon pair is required to be in the rapidity
interval $2.5<y<4.0$.

### J/$\psi$ polarization formalism.

A polarization analysis performed by fitting for each $p_{\rm T}$ interval the
two-dimensional angular distribution of Eq. (1) requires a large reconstructed
J/$\psi$ sample. In the present analysis, given the limited statistics, the
two-dimensional angular distribution is integrated over one angle at a time,
to obtain the three following normalised one-dimensional distributions:

$W_{1}(\cos\theta)=\frac{3N}{2(3+\lambda_{\theta})}\left[1+\lambda_{\theta}\cos^{2}\theta\right]$
(2)
$W_{2}(\varphi)=\frac{N}{2\pi}\left[1+\frac{2\lambda_{\varphi}}{3+\lambda_{\theta}}\cos(2\varphi)\right]$
(3)
$W_{3}(\widetilde{\varphi})=\frac{N}{2\pi}\left[1+\frac{\sqrt{2}\lambda_{\theta\varphi}}{3+\lambda_{\theta}}\cos\widetilde{\varphi}\right]$
(4)

with $\widetilde{\varphi}=\varphi-\frac{3}{4}\pi$ for $\cos\theta<0$ and
$\widetilde{\varphi}=\varphi-\frac{1}{4}\pi$ for $\cos\theta>0$, while $N$
corresponds to the normalisation factor common to the three distributions.

### Analysis strategy.

In order to extract the polarization parameters as a function of $p_{\rm T}$,
the three angular distributions $W_{1}(\cos\theta)$, $W_{2}(\varphi)$ and
$W_{3}(\widetilde{\varphi})$ are built by classifying the di-muon candidates
in $\cos\theta$, $\varphi$ and $\widetilde{\varphi}$ intervals, respectively,
for each $p_{\rm T}$ interval. The raw number of J/$\psi$ mesons is extracted
in each interval of $p_{\rm T}$ and angle via a fit of the corresponding
invariant mass distribution. The fit is performed in the invariant mass range
$2<M_{\mu^{+}\mu^{-}}<5$ $\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc^{2}$
using a variable-width Gaussian function to describe the background shape and
two extended Crystal Ball functions [20] to describe the J/$\psi$ and
$\psi$(2S) resonances. The total number of J/$\psi$ in the analyzed data
sample is about $50\,000$ in the transverse momentum range $2<p_{\rm T}<15$
$\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc$. The extracted raw yields are
then corrected for the acceptance and efficiency of the detector
($A$$\times$$\epsilon$).

### Acceptance and efficiency evaluation.

This is estimated with Monte Carlo (MC) simulations of unpolarized J/$\psi$
mesons with $p_{\rm T}$ and rapidity input distributions parameterized from
the measured ones at the same energy [19]. Next, the J/$\psi$ mesons are
forced to decay into $\mu^{+}\mu^{-}$ pairs [21], including a fraction (5.4%)
of radiative decays $\mu^{+}\mu^{-}\gamma$ [22] in agreement with the
prediction from [23]. In the simulation, the particles are propagated through
the ALICE apparatus using GEANT 3.21 [24] with a realistic description of the
detector response. The ($A$$\times$$\epsilon$) factor is calculated in each
interval of $p_{\rm T}$ and angle as the ratio of reconstructed J/$\psi$
satisfying the selection criteria to the number of generated J/$\psi$ in the
rapidity range $2.5<y<4.0$. As an example, Fig. 1 (left) shows the
($A$$\times$$\epsilon$) map in the plane ($\cos\theta$, $p_{\rm T}$) for the
CS frame. A similar map is obtained in the HX frame, but with a vanishing
($A$$\times$$\epsilon$) in the interval $0.9<|\cos\theta|<1$ for $2<p_{\rm
T}<15$ $\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc$. The maps as a function
of $\varphi$ and $\tilde{\varphi}$ in both frames do not exhibit any hole in
the ($A$$\times$$\epsilon$), as illustrated in Fig. 1 (right) in the plane
($\varphi$, $p_{\rm T}$) for the CS frame. Due to the natural symmetry of the
angular distributions the analysis is performed in the intervals
$0\leq\cos\theta\leq 1$, $0\leq\varphi\leq\frac{\pi}{2}$ and
$0\leq\widetilde{\varphi}\leq\pi$. The $p_{\rm T}$ interval explored in this
analysis is constrained by a vanishing ($A$$\times$$\epsilon$) at low $p_{\rm
T}$ and high $|\cos\theta|$, and by the limited statistics at high $p_{\rm
T}$. The angular distribution intervals for the analysis are defined in order
to have a significance222The significance is defined as ${\cal
S}=S/\sqrt{S+B}$ with $S$ the number of signal events and $B$ the number of
background events in the mass range of $\pm 3\sigma$ around the J/$\psi$ mass
peak, $\sigma$ being the J/$\psi$ mass resolution. larger than five. The grid
in Fig. 1 shows the defined $p_{\rm T}$ ranges as well as the $\cos\theta$
(left plot) and $\varphi$ (right plot) intervals in the CS frame.

Figure 1: ($A$$\times$$\epsilon$) 2-D maps in the planes ($\cos\theta$,
$p_{\rm T}$) (left) and ($\varphi$, $p_{\rm T}$) (right) in the Collins-Soper
frame. The plots illustrate the symmetry with respect to $\cos\theta=0$ (left)
and with respect to $\varphi=\pi$ and $\pi/2$ (right), while the grid shows
the binning used to build the $W_{1}(\cos\theta)$ and $W_{2}(\varphi)$
distributions in each $p_{\rm T}$ range.

### Extraction of the polarization parameters.

After acceptance and efficiency correction of the number of reconstructed
J/$\psi$ candidates, a simultaneous fit of the three angular distributions is
performed by minimizing the following $\chi^{2}$-function for each $p_{\rm T}$
interval

$\displaystyle\chi^{2}$ $\displaystyle=$
$\displaystyle\sum_{i=1}^{n_{\cos\theta}}\left(\frac{N_{i}^{\rm
J/\psi}-W_{1}(\cos\theta\,;\,N,\lambda_{\theta})}{\sigma_{i}}\right)^{2}$ (5)
$\displaystyle+\sum_{j=1}^{n_{\varphi}}\left(\frac{N_{j}^{\rm
J/\psi}-W_{2}(\varphi\,;\,N,\lambda_{\theta},\lambda_{\varphi})}{\sigma_{j}}\right)^{2}$
$\displaystyle+\sum_{k=1}^{n_{\widetilde{\varphi}}}\left(\frac{N_{k}^{\rm
J/\psi}-W_{3}(\widetilde{\varphi}\,;\,N,\lambda_{\theta},\lambda_{\theta\varphi})}{\sigma_{k}}\right)^{2}$

with four free parameters: the normalization factor $N$ common to the three
distributions and the three polarization parameters ($\lambda_{\theta}$,
$\lambda_{\varphi}$, $\lambda_{\theta\varphi}$). In this expression,
$N_{i,j,k}^{\rm J/\psi}$ and $\sigma_{i,j,k}$ are the corrected numbers of
J/$\psi$ and their associated statistical uncertainties in the $i^{\rm th}$,
$j^{\rm th}$ and $k^{\rm th}$ bins of the angular distributions
$W_{1}(\cos\theta)$, $W_{2}(\varphi)$ and $W_{3}(\widetilde{\varphi})$, with a
total number of bins $n_{\cos\theta}$, $n_{\varphi}$ and
$n_{\widetilde{\varphi}}$, respectively. Figure 2 illustrates the fit results
of the angular distributions in the HX frame for the transverse-momentum range
$4<p_{\rm T}<5$ $\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc$ (similar fits
are obtained in all $p_{\rm T}$ intervals and in both frames).

Figure 2: Acceptance corrected angular distributions of J/$\psi$ reconstructed
in the di-muon decay channel $W_{1}(\cos\theta)$, $W_{2}(\varphi)$ and
$W_{3}(\widetilde{\varphi})$ in the helicity frame for the transverse momentum
interval $4<p_{\rm T}<5$ $\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc$,
together with the results of the simultaneous fit (see text for details).
Vertical bars correspond to statistical uncertainties.

### Systematic uncertainty evaluation.

The J/$\psi$ signal is extracted using five different fitting approaches. The
initial approach of the invariant mass fit presented above is varied in the
following way. The range of the fit is increased to $1.5<M_{\mu^{+}\mu^{-}}<6$
$\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc^{2}$ or decreased to
$2.2<M_{\mu^{+}\mu^{-}}<4.5$
$\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc^{2}$. The product of a Gaussian
and an exponential is used as an alternative background shape, and finally the
two Crystal Ball functions are replaced by the function used by the NA60
Collaboration [20]. For each approach the analysis is repeated and the
polarization parameters are determined. The final values of the polarization
parameters $\lambda_{\alpha}$ (with $\alpha=\theta$ or $\varphi$ or
$\theta\varphi$) correspond to the mean values $\overline{\lambda}_{\alpha}$
of the five sets of results, and the associated statistical uncertainties are
the mean values of the statistical uncertainties returned by each fit. The
systematic uncertainties on the $\lambda_{\alpha}$ parameters due to the
signal extraction are the sum of the quadratic difference of each
configuration result with respect to the mean values. The uncertainties range
from 0.012 to 0.108 (see Table 1) with the biggest effect observed on
$\lambda_{\varphi}$ in the HX frame.

An exhaustive investigation of potential biases in the ($A$$\times$$\epsilon$)
map is carried out. Firstly, the input distributions of the J/$\psi$ in the MC
simulation are modified by: (i) varying the $p_{\rm T}$ and (ii) the $y$
shapes of the J/$\psi$ parameterization within the uncertainties of the
measured cross sections [19], (iii) removing the radiative decay part, (iv)
varying the $\lambda_{\theta}$ parameter in the range
$-0.2<\lambda_{\theta}<0.2$, corresponding to 1-sigma deviation of the
measured value of $\lambda_{\theta}$ in the HX frame on average over the whole
$p_{\rm T}$ interval. The four corresponding uncertainties on the
$\lambda_{\alpha}$ are summed quadratically to get the total simulation input
uncertainties ranging from 0.004 to 0.175. This is the main systematic
uncertainty for the $\lambda_{\theta}$ parameter, dominated by the variation
of its input value in simulation, especially at low $p_{\rm T}$. Secondly, any
uncertainty in the simulation of the trigger threshold of $\sim 1$
$\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc$ could bias the
($A$$\times$$\epsilon$) estimation. To evaluate this effect, the full
simulation of the trigger response function is replaced with a
parameterization of the trigger response function as a function of transverse
momenta. The parameterization is obtained both in MC and in data by using
minimum bias events recorded in parallel with the triggered data sample. The
analysis is then repeated using either of the two parameterizations, and the
resulting difference is taken as the systematic uncertainty. The effect is
small ($<0.022$) for $p_{\rm T}>4$
$\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc$, and a maximum uncertainty of
0.070 is estimated for $\lambda_{\varphi}$ in the first $p_{\rm T}$ interval
of the CS frame. Thirdly, the uncertainty on the detector efficiency includes
the uncertainty on the tracking efficiency, the trigger chamber efficiency and
the matching between tracks reconstructed in the tracker and in the trigger
system. The resulting uncertainty on the J/$\psi$ yields is evaluated with the
same procedure as the one described in [25] and is propagated to the corrected
yields of the angular distributions by adding it in quadrature with the
statistical ones. Finally, the fits are redone and the associated uncertainty
on $\lambda_{\alpha}$ parameters is estimated as the square root of the
quadratic difference between the new uncertainty returned by the fit and the
statistical one. Its value ranges from 0.046 to 0.133. This is the main
uncertainty for the $\lambda_{\theta\varphi}$ parameter.

The different sources of systematic uncertainties are summarized in Tab. 1.
The four sources of systematics are independent and can be summed in
quadrature to obtain the total systematic uncertainty on each
$\lambda_{\alpha}$ parameter. Systematic uncertainties are considered
uncorrelated among the three polarization parameters and among the $p_{\rm T}$
intervals.

Source | $\lambda_{\theta}^{\rm HX}$ | $\lambda_{\varphi}^{\rm HX}$ | $\lambda_{\theta\varphi}^{\rm HX}$ | $\lambda_{\theta}^{\rm CS}$ | $\lambda_{\varphi}^{\rm CS}$ | $\lambda_{\theta\varphi}^{\rm CS}$
---|---|---|---|---|---|---
Signal | 0.035–0.087 | 0.021–0.108 | 0.014–0.032 | 0.022–0.074 | 0.022–0.052 | 0.012–0.063
Inputs | 0.076–0.155 | 0.007–0.024 | 0.006–0.033 | 0.013–0.175 | 0.006–0.040 | 0.004–0.018
Trigger | 0.001–0.064 | 0.001–0.060 | 0.005–0.020 | 0.006–0.036 | 0.007–0.070 | 0.006–0.017
Efficiency | 0.076–0.133 | 0.046–0.069 | 0.064–0.076 | 0.081–0.121 | 0.058–0.072 | 0.073–0.081
Table 1: Absolute systematic uncertainties on J/$\psi$ polarization parameters
in the HX and CS frames. The four different uncertainty sources are the signal
extraction (signal), the input distributions of the J/$\psi$ in the MC
simulations (inputs), the low-$p_{\rm T}$ trigger response (trigger) and the
detector efficiency (efficiency). The last three sources enter in the
computation of the acceptance and efficiency factor ($A$$\times$$\epsilon$).

##  4 Results

The inclusive J/$\psi$ polarization parameters in the interval $2.5<y<4.0$ and
$2<p_{\rm T}<15$ $\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc$ measured in pp
collisions at $\sqrt{s}=8$ TeV are shown in Fig. 3 for the HX (right) and the
CS (left) frames and summarized in Tab. 2 and 3, respectively. In the figure,
the error bars represent the total uncertainties computed by adding in
quadrature the statistical and systematic uncertainties. This is the first
measurement of the J/$\psi$ polarization parameters at this energy and extends
the $p_{\rm T}$ reach of the previous ALICE measurement at $\sqrt{s}=7$ TeV
from 8 to 15 $\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc$. The results show
that the polarization of inclusive J/$\psi$ mesons is compatible with zero
within uncertainties, with a maximum deviation of 1.8 standard deviations away
from zero for the highest $p_{\rm T}$ interval for the $\lambda_{\theta}$ and
$\lambda_{\theta\varphi}$ parameters in the HX frame.

$p_{\rm T}$ ($\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc$) | $\lambda_{\theta}^{\rm HX}$ | $\lambda_{\varphi}^{\rm HX}$ | $\lambda_{\theta\varphi}^{\rm HX}$
---|---|---|---
$2-3$ | $0.035\pm 0.048\pm 0.215$ | $-0.037\pm 0.025\pm 0.093$ | $-0.024\pm 0.032\pm 0.082$
$3-4$ | $-0.085\pm 0.053\pm 0.189$ | $-0.065\pm 0.026\pm 0.134$ | $-0.080\pm 0.035\pm 0.077$
$4-5$ | $0.083\pm 0.066\pm 0.188$ | $-0.003\pm 0.033\pm 0.096$ | $-0.024\pm 0.043\pm 0.080$
$5-7$ | $-0.036\pm 0.058\pm 0.154$ | $0.055\pm 0.029\pm 0.069$ | $-0.001\pm 0.039\pm 0.078$
$7-10$ | $-0.092\pm 0.078\pm 0.168$ | $0.090\pm 0.039\pm 0.056$ | $0.089\pm 0.055\pm 0.082$
$10-15$ | $-0.329\pm 0.121\pm 0.130$ | $-0.003\pm 0.070\pm 0.052$ | $0.222\pm 0.099\pm 0.079$
Table 2: Inclusive J/$\psi$ polarization parameters in the HX frame in the rapidity interval $2.5<y<4.0$. The first uncertainty is statistical and the second systematic. $p_{\rm T}$ ($\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc$) | $\lambda_{\theta}^{\rm CS}$ | $\lambda_{\varphi}^{\rm CS}$ | $\lambda_{\theta\varphi}^{\rm CS}$
---|---|---|---
$2-3$ | $0.002\pm 0.046\pm 0.228$ | $-0.030\pm 0.024\pm 0.095$ | $0.041\pm 0.032\pm 0.076$
$3-4$ | $-0.011\pm 0.052\pm 0.185$ | $-0.065\pm 0.026\pm 0.098$ | $-0.075\pm 0.035\pm 0.084$
$4-5$ | $0.001\pm 0.056\pm 0.124$ | $-0.019\pm 0.030\pm 0.086$ | $0.006\pm 0.041\pm 0.080$
$5-7$ | $0.063\pm 0.048\pm 0.088$ | $-0.020\pm 0.031\pm 0.087$ | $-0.042\pm 0.041\pm 0.082$
$7-10$ | $0.175\pm 0.070\pm 0.096$ | $0.001\pm 0.045\pm 0.082$ | $-0.009\pm 0.060\pm 0.096$
$10-15$ | $-0.021\pm 0.110\pm 0.106$ | $-0.052\pm 0.084\pm 0.077$ | $-0.065\pm 0.110\pm 0.098$
Table 3: Inclusive J/$\psi$ polarization parameters in the CS frame in the
rapidity interval $2.5<y<4.0$. The first uncertainty is statistical and the
second systematic.

As the differences between the J/$\psi$ polarization in pp collisions at
$\sqrt{s}=7$ TeV and 8 TeV are expected to be negligible (see Kniehl et al.
predictions in Ref. [14] and in this paper), the measurements at the two
energies can be directly compared. This comparison is shown in Fig. 3 with the
published results by ALICE [13] (inclusive J/$\psi$) and LHCb [14] (prompt
J/$\psi$, i.e. without the contribution from b-hadron decays) in the same
rapidity interval for pp collisions at $\sqrt{s}=7$ TeV. The two ALICE
measurements agree within one standard deviation. Concerning the comparison
between ALICE and LHCb results, a rather good agreement is observed for all
polarization parameters over the full $p_{\rm T}$ interval. The observed
agreement between the ALICE and LHCb results seems to indicate that J/$\psi$
from b-hadron decays do not introduce any observable difference in the
polarization parameters.

Figure 3: (color online) ALICE inclusive J/$\psi$ polarization parameters in
pp collisions at $\sqrt{s}=8$ TeV (black points) compared with ALICE [13]
inclusive J/$\psi$ (orange squares, shifted horizontally by $-0.3$
$\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc$) and LHCb [14] prompt J/$\psi$
(blue open diamonds, shifted horizontally by $+0.3$
$\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc$) measurements at $\sqrt{s}=7$
TeV in the rapidity interval $2.5<y<4.0$. The error bars represent the total
uncertainties. Left and right plots show results in the Collins-Soper and
helicity frames, respectively, for $\lambda_{\theta}$ (top plots),
$\lambda_{\varphi}$ (middle plots) and $\lambda_{\theta\varphi}$ (bottom
plots).

Figure 4 shows the comparison of all the measured polarization parameters with
the NLO CSM (blue filled band) and NRQCD (red shaded band) predictions from
[10] and with another NRQCD (light blue hatched band) prediction from [26] for
$\lambda_{\theta}$ in the helicity frame (labeled as NLO NRQCD2 in Fig. 4).
The shown error bands of the models are evaluated by adding in quadrature the
uncertainties due to the different scale variations (renormalization,
factorization and NRQCD scales) in the calculation and LDME variations. The
difference between the two NRQCD calculations originates from the data used to
compute the LDMEs. Moreover, in [10] only direct J/$\psi$ (i.e. without feed-
down from excited states) are considered, while in [26] feed-down from excited
states is included in the J/$\psi$ prediction.

The CSM and NRQCD calculations from [10] predict an opposite $p_{\rm T}$ trend
for all polarization parameters in the two frames. The $p_{\rm T}$ dependence
is relatively small over the considered $p_{\rm T}$ interval, except for the
$\lambda_{\theta}$ parameter in the HX frame. The NRQCD calculation including
both color-singlet and color-octet contributions provides a qualitatively
better description of the J/$\psi$ polarization measurement, except for
$\lambda_{\theta}$ in the HX frame where the large transverse J/$\psi$
polarization predicted by the NRQCD [10] is in contradiction with the
experimental observations. The NRQCD prediction from [26] favours either zero
or small longitudinal polarization, with large theoretical uncertainties, and
shows a good agreement with the measurements in the intermediate $p_{\rm T}$
interval ($5<p_{\rm T}<15$ $\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc$),
but gives no prediction for $p_{\rm T}<5$
$\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc$. This agreement is not
surprising because this model includes the measurements of the J/$\psi$
polarization performed at Tevatron [27, 28] to determine the LDMEs. As this
model gives no prediction for the other polarization parameters in the HX
frame, as well as for the whole set of polarization parameters in the CS
frame, it is difficult to draw a clear conclusion about its ability to
describe the measurements.

Figure 4: (color online) Inclusive J/$\psi$ polarization parameters in pp
collisions at $\sqrt{s}=8$ TeV (black points, error bars represent the total
uncertainties) compared with model predictions: NLO CSM [10] (blue filled
bands), NRQCD [10] (red shaded bands) and NRQCD2 [26] (light blue hatched
band). Left and right plots show the results in the Collins-Soper and helicity
frames, respectively, for $\lambda_{\theta}$ (top plots), $\lambda_{\varphi}$
(middle plots) and $\lambda_{\theta\varphi}$ (bottom plots).

As shown by Faccioli et al. [11], frame-invariant observables do exist and the
most commonly considered one is

$\widetilde{\lambda}=\frac{\lambda_{\theta}+3\lambda_{\varphi}}{1-\lambda_{\varphi}}.$
(6)

Figure 5 shows the $p_{\rm T}$ dependence of this invariant quantity for both
frames in comparison with the NLO CSM and NRQCD predictions from [10]. To
propagate the uncertainties on $\lambda_{\theta}$ and $\lambda_{\varphi}$ to
the frame-invariant quantity $\widetilde{\lambda}$, the correlation
coefficient $\rho_{\lambda_{\theta},\lambda_{\varphi}}$ returned by the
simultaneous fit of the angular distributions are taken into account to
compute the statistical uncertainties, while the systematic uncertainties are
assumed to be uncorrelated. For the model predictions, the quoted error bands
are computed by adding the uncertainties due to the different scales and LDME
variations in quadrature, after propagation of the correlated effects between
$\lambda_{\theta}$ and $\lambda_{\varphi}$. The comparison of the frame-
invariant quantity $\widetilde{\lambda}$ shows that the ALICE measurements in
both frames are in good agreement within uncertainties, confirming the
consistency of the results. Both the CSM and the NRQCD model respect the frame
invariance for $\widetilde{\lambda}$, but clearly none of them is able to
describe the measured $p_{\rm T}$ dependence, even if the NRQCD prediction
shows a better agreement with data ($\chi^{2}_{\rm/NDF}=1.7$ compared to
$\chi^{2}_{\rm/NDF}=2.0$ by CSM), although with large uncertainties especially
for $p_{\rm T}<6$ $\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc$.

Figure 5: (color online) Inclusive J/$\psi$ frame-invariant quantity
$\widetilde{\lambda}$ in pp collisions at $\sqrt{s}=8$ TeV in the Collins-
Soper (red points, shifted horizontally by $-0.1$
$\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc$) and helicity (green squares,
shifted horizontally by $+0.1$ $\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc$)
frames compared with the NLO CSM (blue full band) and NRQCD (red shaded band)
model predictions from [10].

Using the ALICE inclusive J/$\psi$ cross section measurement at $\sqrt{s}=8$
TeV [19], an average value for the polarization parameters over $p_{\rm T}$
can be computed in the following way

$\langle\lambda_{\alpha}\rangle=\frac{1}{\sigma_{\rm
tot}}\sum_{j=1}^{6}\sigma_{j}\lambda_{\alpha}^{j},$ (7)

with

$\sigma_{\rm tot}=\sum_{j=1}^{6}\sigma_{j}.$ (8)

In these equations, $j$ is running over the six $p_{\rm T}$ bins of this
analysis, $\sigma_{j}$ is the integrated inclusive J/$\psi$ cross section in
the $p_{\rm T}$ bin $j$ and $\lambda_{\alpha}^{j}$ is the measured
polarization parameter in the corresponding bin. The resulting average values
of the polarization parameters over $2<p_{\rm T}<15$
$\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc$ are summarized in Tab. 4. The
uncertainties are computed by propagating the total uncertainty on the
polarization parameters and the uncorrelated uncertainty on the cross section
measurements from [19]. All averaged values of the polarization parameters are
consistent with zero within uncertainties.

Figure 6: (color online) Average $p_{\rm T}$-integrated (in rapidity range
$2.5<y<4.0$) inclusive J/$\psi$ polarization parameters
$\langle\lambda_{\theta}\rangle$, $\langle\lambda_{\varphi}\rangle$ and
$\langle\lambda_{\theta\varphi}\rangle$ in allowed 2-D regions (white areas)
for $3<p_{\rm T}<15$ $\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc$. Full
(dashed) ellipses show 1-$\sigma$ (2-$\sigma$) contours in Collins-Sopper (CS,
red) and helicity (HX, green) frames. Model predictions [10] are represented
by filled contours, full filled for the CSM and shaded filled for the NRQCD
model, in green for the HX frame and in red for the CS frame.

The $p_{\rm T}$-integrated values can be used to check the consistency of the
measured polarization parameters with respect to the theoretically allowed
parameter space in 2-D plots, as shown in Fig. 6 for $3<p_{\rm T}<15$
$\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc$. This figure takes into account
the correlation coefficients $\rho_{\lambda_{\theta},\lambda_{\varphi}}$,
$\rho_{\lambda_{\theta},\lambda_{\theta\varphi}}$ and
$\rho_{\lambda_{\varphi},\lambda_{\theta\varphi}}$ between the polarization
parameters returned by the simultaneous fit of the angular distributions.
Their values are averaged over $p_{\rm T}$ as for the $\lambda_{\alpha}$. The
average coefficient correlations, in both HX and CS frames, are in the range
$[-0.05\,;\,0.05]$ for $\rho_{\lambda_{\theta},\lambda_{\theta\varphi}}$ and
$\rho_{\lambda_{\varphi},\lambda_{\theta\varphi}}$, while
$\rho_{\lambda_{\theta},\lambda_{\varphi}}$ is about 0.2. Contour ellipses
show that the $p_{\rm T}$-integrated polarization parameters are well within
the allowed theoretical parameter-space and highlight the observed absence of
polarization of inclusive J/$\psi$ at forward rapidity in pp collisions at
$\sqrt{s}=8$ TeV. The comparison with the $p_{\rm T}$-integrated NLO CSM and
NRQCD predictions is shown in Fig. 6 (right). These 2-D plots confirm the
difficulty of the models to reproduce the ALICE measurements and show also
that the discrepancy from data is larger for the CSM than for the NRQCD
calculation, especially in the plane $(\lambda_{\theta},\lambda_{\varphi})$ in
the CS frame.

Parameter | HX frame | CS frame
---|---|---
$\langle\lambda_{\theta}\rangle$ | $-0.006\pm 0.115$ | $0.012\pm 0.116$
$\langle\lambda_{\varphi}\rangle$ | $-0.024\pm 0.058$ | $-0.036\pm 0.053$
$\langle\lambda_{\theta\varphi}\rangle$ | $-0.029\pm 0.047$ | $-0.006\pm 0.047$
Table 4: Average $p_{\rm T}$-integrated (over $2<p_{\rm T}<15$
$\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc$ in the rapidity range
$2.5<y<4.0$) inclusive J/$\psi$ polarization parameters
$\langle\lambda_{\theta}\rangle$, $\langle\lambda_{\varphi}\rangle$ and
$\langle\lambda_{\theta\varphi}\rangle$ in the HX and CS frames.

##  5 Conclusion

The polarization parameters of inclusive J/$\psi$ mesons are measured with the
ALICE detector at forward rapidity ($2.5<y<4.0$) in pp collisions at
$\sqrt{s}=8$ TeV. Detailed investigations of their transverse momentum
dependence in the interval $2<p_{\rm T}<15$
$\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc$ show that no polarization is
observed for the measured J/$\psi$ mesons. This result is further highlighted
by the $p_{\rm T}$-integrated polarization parameters. The comparisons with
the theoretical predictions from the Color-Singlet Model and the Non-
Relativistic QCD model show that none of the two approaches is able to
describe all polarization parameters over the studied $p_{\rm T}$ interval. It
follows that a full understanding of the production mechanism of J/$\psi$ in
hadronic collisions remains an open question.

## 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 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), Universidade Federal do
Rio Grande do Sul (UFRGS), Financiadora de Estudos e Projetos (Finep) and
Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP), Brazil;
Ministry of Science & Technology of China (MSTC), National Natural Science
Foundation of China (NSFC) and Ministry of Education of China (MOEC) , China;
Ministry of Science and Education, Croatia; Ministry of Education, Youth and
Sports of the Czech Republic, Czech Republic; The Danish Council for
Independent Research — Natural Sciences, the Carlsberg Foundation 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, Wissenschaft, Forschung und Technologie (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), Japan Society
for the Promotion of Science (JSPS) KAKENHI and Japanese Ministry of
Education, Culture, Sports, Science and Technology (MEXT), 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 Romanian National Agency
for Science, Technology and Innovation, Romania; Joint Institute for Nuclear
Research (JINR), Ministry of Education and Science of the Russian Federation
and National Research Centre Kurchatov Institute, Russia; Ministry of
Education, Science, Research and Sport of the Slovak Republic, Slovakia;
National Research Foundation of South Africa, South Africa; Centro de
Aplicaciones Tecnológicas y Desarrollo Nuclear (CEADEN), Cubaenergía, Cuba and
Centro de Investigaciones Energéticas, Medioambientales y Tecnológicas
(CIEMAT), Spain; Swedish Research Council (VR) and Knut & Alice Wallenberg
Foundation (KAW), Sweden; European Organization for Nuclear Research,
Switzerland; National Science and Technology Development Agency (NSDTA),
Suranaree University of Technology (SUT) 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. Acharyaorg138&F.T.-. Acostaorg22&D. Adamováorg94&J. Adolfssonorg81&M.M.
Aggarwalorg98&G. Aglieri Rinellaorg36&M. Agnelloorg33&N. Agrawalorg49&Z.
Ahammedorg138&S.U. Ahnorg77&S. Aiolaorg143&A. Akindinovorg65&M. Al-
Turanyorg104&S.N. Alamorg138&D.S.D. Albuquerqueorg120&D. Aleksandrovorg88&B.
Alessandroorg59&R. Alfaro Molinaorg73&Y. Aliorg16&A. Aliciorg11,org54,org29&A.
Alkinorg3&J. Almeorg24&T. Altorg70&L. Altenkamperorg24&I. Altsybeevorg137&C.
Andreiorg48&D. Andreouorg36&H.A. Andrewsorg108&A. Andronicorg141,org104&M.
Angelettiorg36&V. Anguelovorg102&C. Ansonorg17&T. Antičićorg105&F.
Antinoriorg57&P. Antonioliorg54&R. Anwarorg124&N. Apadulaorg80&L.
Aphecetcheorg112&H. Appelshäuserorg70&S. Arcelliorg29&R. Arnaldiorg59&O.W.
Arnoldorg103,org115&I.C. Arseneorg23&M. Arslandokorg102&B. Audurierorg112&A.
Augustinusorg36&R. Averbeckorg104&M.D. Azmiorg18&A. Badalàorg56&Y.W.
Baekorg61,org42&S. Bagnascoorg59&R. Bailhacheorg70&R. Balaorg99&A.
Baldisseriorg134&M. Ballorg44&R.C. Baralorg86&A.M. Barbanoorg28&R.
Barberaorg30&F. Barileorg53&L. Barioglioorg28&G.G. Barnaföldiorg142&L.S.
Barnbyorg93&V. Barretorg131&P. Bartaliniorg7&K. Barthorg36&E. Bartschorg70&N.
Bastidorg131&S. Basuorg140&G. Batigneorg112&A. Batista Camejoorg131&B.
Batyunyaorg76&P.C. Batzingorg23&J.L. Bazo Albaorg109&I.G. Beardenorg89&H.
Beckorg102&C. Beddaorg64&N.K. Beheraorg61&I. Belikovorg133&F. Belliniorg36&H.
Bello Martinezorg2&R. Bellwiedorg124&L.G.E. Beltranorg118&V. Belyaevorg92&G.
Bencediorg142&S. Beoleorg28&A. Bercuciorg48&Y. Berdnikovorg96&D.
Berenyiorg142&R.A. Bertensorg127&D. Berzanoorg36,org59&L. Betevorg36&P.P.
Bhaduriorg138&A. Bhasinorg99&I.R. Bhatorg99&H. Bhattorg49&B.
Bhattacharjeeorg43&J. Bhomorg116&A. Bianchiorg28&L. Bianchiorg124&N.
Bianchiorg52&J. Bielčíkorg39&J. Bielčíkováorg94&A. Bilandzicorg115,org103&G.
Biroorg142&R. Biswasorg4&S. Biswasorg4&J.T. Blairorg117&D. Blauorg88&C.
Blumeorg70&G. Bocaorg135&F. Bockorg36&A. Bogdanovorg92&L. Boldizsárorg142&M.
Bombaraorg40&G. Bonomiorg136&M. Bonoraorg36&H. Borelorg134&A.
Borissovorg20,org141&M. Borriorg126&E. Bottaorg28&C. Bourjauorg89&L.
Bratrudorg70&P. Braun-Munzingerorg104&M. Bregantorg119&T.A. Brokerorg70&M.
Brozorg39&E.J. Bruckenorg45&E. Brunaorg59&G.E. Brunoorg36,org35&D.
Budnikovorg106&H. Bueschingorg70&S. Bufalinoorg33&P. Buhlerorg111&P.
Buncicorg36&O. Buschorg130org*&Z. Butheleziorg74&J.B. Buttorg16&J.T.
Buxtonorg19&J. Cabalaorg114&D. Caffarriorg90&H. Cainesorg143&A.
Calivaorg104&E. Calvo Villarorg109&R.S. Camachoorg2&P. Cameriniorg27&A.A.
Caponorg111&F. Carenaorg36&W. Carenaorg36&F. Carnesecchiorg29,org11&J.
Castillo Castellanosorg134&A.J. Castroorg127&E.A.R. Casulaorg55&C. Ceballos
Sanchezorg9&S. Chandraorg138&B. Changorg125&W. Changorg7&S. Chapelandorg36&M.
Chartierorg126&S. Chattopadhyayorg138&S. Chattopadhyayorg107&A.
Chauvinorg103,org115&C. Cheshkovorg132&B. Cheynisorg132&V. Chibante
Barrosoorg36&D.D. Chinellatoorg120&S. Choorg61&P. Chochulaorg36&T.
Chowdhuryorg131&P. Christakoglouorg90&C.H. Christensenorg89&P.
Christiansenorg81&T. Chujoorg130&S.U. Chungorg20&C. Cicaloorg55&L.
Cifarelliorg11,org29&F. Cindoloorg54&J. Cleymansorg123&F. Colamariaorg53&D.
Colellaorg66,org36,org53&A. Colluorg80&M. Colocciorg29&M. Concasorg59orgI&G.
Conesa Balbastreorg79&Z. Conesa del Valleorg62&J.G. Contrerasorg39&T.M.
Cormierorg95&Y. Corrales Moralesorg59&P. Corteseorg34&M.R. Cosentinoorg121&F.
Costaorg36&S. Costanzaorg135&J. Crkovskáorg62&P. Crochetorg131&E.
Cuautleorg71&L. Cunqueiroorg141,org95&T. Dahmsorg103,org115&A. Daineseorg57&S.
Daniorg67&M.C. Danischorg102&A. Danuorg69&D. Dasorg107&I. Dasorg107&S.
Dasorg4&A. Dashorg86&S. Dashorg49&S. Deorg50&A. De Caroorg32&G. de
Cataldoorg53&C. de Contiorg119&J. de Cuvelandorg41&A. De Falcoorg26&D. De
Gruttolaorg11,org32&N. De Marcoorg59&S. De Pasqualeorg32&R.D. De
Souzaorg120&H.F. Degenhardtorg119&A. Deistingorg104,org102&A. Delofforg85&S.
Delsantoorg28&C. Deplanoorg90&P. Dhankherorg49&D. Di Bariorg35&A. Di
Mauroorg36&B. Di Ruzzaorg57&R.A. Diazorg9&T. Dietelorg123&P.
Dillensegerorg70&Y. Dingorg7&R. Diviàorg36&Ø. Djuvslandorg24&A. Dobrinorg36&D.
Domenicis Gimenezorg119&B. Dönigusorg70&O. Dordicorg23&L.V.R.
Doremalenorg64&A.K. Dubeyorg138&A. Dublaorg104&L. Ducrouxorg132&S.
Dudiorg98&A.K. Duggalorg98&M. Dukhishyamorg86&P. Dupieuxorg131&R.J.
Ehlersorg143&D. Eliaorg53&E. Endressorg109&H. Engelorg75&E. Eppleorg143&B.
Erazmusorg112&F. Erhardtorg97&M.R. Ersdalorg24&B. Espagnonorg62&G.
Eulisseorg36&J. Eumorg20&D. Evansorg108&S. Evdokimovorg91&L.
Fabbiettiorg103,org115&M. Fagginorg31&J. Faivreorg79&A. Fantoniorg52&M.
Faselorg95&L. Feldkamporg141&A. Felicielloorg59&G. Feofilovorg137&A. Fernández
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Figielorg116&M.A.S. Figueredoorg119&S. Filchaginorg106&D. Finogeevorg63&F.M.
Fiondaorg24&G. Fiorenzaorg53&F. Flororg124&M. Florisorg36&S. Foertschorg74&P.
Fokaorg104&S. Fokinorg88&E. Fragiacomoorg60&A. Francesconorg36&A.
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Furgetorg79&A. Fursorg63&M. Fusco Girardorg32&J.J. Gaardhøjeorg89&M.
Gagliardiorg28&A.M. Gagoorg109&K. Gajdosovaorg89&M. Gallioorg28&C.D.
Galvanorg118&P. Ganotiorg84&C. Garabatosorg104&E. Garcia-Solisorg12&K.
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Grabskiorg73&L.K. Graczykowskiorg139&K.L. Grahamorg108&L. Greinerorg80&A.
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Grigoryanorg76&J.M. Gronefeldorg104&F. Grosaorg33&J.F. Grosse-
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## 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

org2Benemérita Universidad Autónoma de Puebla, Puebla, Mexico

org3Bogolyubov Institute for Theoretical Physics, National Academy of Sciences
of Ukraine, Kiev, Ukraine

org4Bose Institute, Department of Physics and Centre for Astroparticle Physics
and Space Science (CAPSS), Kolkata, India

org5Budker Institute for Nuclear Physics, Novosibirsk, Russia

org6California Polytechnic State University, San Luis Obispo, California,
United States

org7Central China Normal University, Wuhan, China

org8Centre de Calcul de l’IN2P3, Villeurbanne, Lyon, France

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

org10Centro de Investigación y de Estudios Avanzados (CINVESTAV), Mexico City
and Mérida, Mexico

org11Centro Fermi - Museo Storico della Fisica e Centro Studi e Ricerche
“Enrico Fermi’, Rome, Italy

org12Chicago State University, Chicago, Illinois, United States

org13China Institute of Atomic Energy, Beijing, China

org14Chonbuk National University, Jeonju, Republic of Korea

org15Comenius University Bratislava, Faculty of Mathematics, Physics and
Informatics, Bratislava, Slovakia

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

org17Creighton University, Omaha, Nebraska, United States

org18Department of Physics, Aligarh Muslim University, Aligarh, India

org19Department of Physics, Ohio State University, Columbus, Ohio, United
States

org20Department of Physics, Pusan National University, Pusan, Republic of
Korea

org21Department of Physics, Sejong University, Seoul, Republic of Korea

org22Department of Physics, University of California, Berkeley, California,
United States

org23Department of Physics, University of Oslo, Oslo, Norway

org24Department of Physics and Technology, University of Bergen, Bergen,
Norway

org25Dipartimento di Fisica dell’Università ’La Sapienza’ and Sezione INFN,
Rome, Italy

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

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

org28Dipartimento di Fisica dell’Università and Sezione INFN, Turin, Italy

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

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

org31Dipartimento di Fisica e Astronomia dell’Università and Sezione INFN,
Padova, Italy

org32Dipartimento di Fisica ‘E.R. Caianiello’ dell’Università and Gruppo
Collegato INFN, Salerno, Italy

org33Dipartimento DISAT del Politecnico and Sezione INFN, Turin, Italy

org34Dipartimento di Scienze e Innovazione Tecnologica dell’Università del
Piemonte Orientale and INFN Sezione di Torino, Alessandria, Italy

org35Dipartimento Interateneo di Fisica ‘M. Merlin’ and Sezione INFN, Bari,
Italy

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

org37Faculty of Electrical Engineering, Mechanical Engineering and Naval
Architecture, University of Split, Split, Croatia

org38Faculty of Engineering and Science, Western Norway University of Applied
Sciences, Bergen, Norway

org39Faculty of Nuclear Sciences and Physical Engineering, Czech Technical
University in Prague, Prague, Czech Republic

org40Faculty of Science, P.J. Šafárik University, Košice, Slovakia

org41Frankfurt Institute for Advanced Studies, Johann Wolfgang Goethe-
Universität Frankfurt, Frankfurt, Germany

org42Gangneung-Wonju National University, Gangneung, Republic of Korea

org43Gauhati University, Department of Physics, Guwahati, India

org44Helmholtz-Institut für Strahlen- und Kernphysik, Rheinische Friedrich-
Wilhelms-Universität Bonn, Bonn, Germany

org45Helsinki Institute of Physics (HIP), Helsinki, Finland

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

org62Institut 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

org63Institute for Nuclear Research, Academy of Sciences, Moscow, Russia

org64Institute for Subatomic Physics, Utrecht University/Nikhef, Utrecht,
Netherlands

org65Institute for Theoretical and Experimental Physics, Moscow, Russia

org66Institute of Experimental Physics, Slovak Academy of Sciences, Košice,
Slovakia

org67Institute of Physics, Bhubaneswar, India

org68Institute of Physics of the Czech Academy of Sciences, Prague, Czech
Republic

org69Institute of Space Science (ISS), Bucharest, Romania

org70Institut für Kernphysik, Johann Wolfgang Goethe-Universität Frankfurt,
Frankfurt, Germany

org71Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México,
Mexico City, Mexico

org72Instituto de Física, Universidade Federal do Rio Grande do Sul (UFRGS),
Porto Alegre, Brazil

org73Instituto de Física, Universidad Nacional Autónoma de México, Mexico
City, Mexico

org74iThemba LABS, National Research Foundation, Somerset West, South Africa

org75Johann-Wolfgang-Goethe Universität Frankfurt Institut für Informatik,
Fachbereich Informatik und Mathematik, Frankfurt, Germany

org76Joint Institute for Nuclear Research (JINR), Dubna, Russia

org77Korea Institute of Science and Technology Information, Daejeon, Republic
of Korea

org78KTO Karatay University, Konya, Turkey

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, HBNI, 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

org92NRNU Moscow Engineering Physics Institute, Moscow, Russia

org93Nuclear Physics Group, STFC Daresbury Laboratory, Daresbury, United
Kingdom

org94Nuclear Physics Institute of the Czech Academy of Sciences, Řež u Prahy,
Czech Republic

org95Oak Ridge National Laboratory, Oak Ridge, Tennessee, 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

org104Research Division and ExtreMe Matter Institute EMMI, GSI
Helmholtzzentrum für Schwerionenforschung GmbH, Darmstadt, Germany

org105Rudjer Bošković Institute, Zagreb, Croatia

org106Russian Federal Nuclear Center (VNIIEF), Sarov, Russia

org107Saha Institute of Nuclear Physics, Kolkata, India

org108School of Physics and Astronomy, University of Birmingham, Birmingham,
United Kingdom

org109Sección Física, Departamento de Ciencias, Pontificia Universidad
Católica del Perú, Lima, Peru

org110Shanghai Institute of Applied Physics, Shanghai, China

org111Stefan Meyer Institut für Subatomare Physik (SMI), Vienna, Austria

org112SUBATECH, IMT Atlantique, Université de Nantes, CNRS-IN2P3, Nantes,
France

org113Suranaree University of Technology, Nakhon Ratchasima, Thailand

org114Technical University of Košice, Košice, Slovakia

org115Technische Universität München, Excellence Cluster ’Universe’, Munich,
Germany

org116The Henryk Niewodniczanski Institute of Nuclear Physics, Polish Academy
of Sciences, Cracow, Poland

org117The University of Texas at Austin, Austin, Texas, United States

org118Universidad Autónoma de Sinaloa, Culiacán, Mexico

org119Universidade de São Paulo (USP), São Paulo, Brazil

org120Universidade Estadual de Campinas (UNICAMP), Campinas, Brazil

org121Universidade Federal do ABC, Santo Andre, Brazil

org122University College of Southeast Norway, Tonsberg, Norway

org123University of Cape Town, Cape Town, South Africa

org124University of Houston, Houston, Texas, United States

org125University of Jyväskylä, Jyväskylä, Finland

org126University of Liverpool, Department of Physics Oliver Lodge Laboratory ,
Liverpool, United Kingdom

org127University of Tennessee, Knoxville, Tennessee, United States

org128University of the Witwatersrand, Johannesburg, South Africa

org129University of Tokyo, Tokyo, Japan

org130University of Tsukuba, Tsukuba, Japan

org131Université Clermont Auvergne, CNRS/IN2P3, LPC, Clermont-Ferrand, France

org132Université de Lyon, Université Lyon 1, CNRS/IN2P3, IPN-Lyon,
Villeurbanne, Lyon, France

org133Université de Strasbourg, CNRS, IPHC UMR 7178, F-67000 Strasbourg,
France, Strasbourg, France

org134 Université Paris-Saclay Centre d¿Études de Saclay (CEA), IRFU,
Department de Physique Nucléaire (DPhN), Saclay, France

org135Università degli Studi di Pavia, Pavia, Italy

org136Università di Brescia, Brescia, Italy

org137V. Fock Institute for Physics, St. Petersburg State University, St.
Petersburg, Russia

org138Variable Energy Cyclotron Centre, Kolkata, India

org139Warsaw University of Technology, Warsaw, Poland

org140Wayne State University, Detroit, Michigan, United States

org141Westfälische Wilhelms-Universität Münster, Institut für Kernphysik,
Münster, Germany

org142Wigner Research Centre for Physics, Hungarian Academy of Sciences,
Budapest, Hungary

org143Yale University, New Haven, Connecticut, United States

org144Yonsei University, Seoul, Republic of Korea