2019 014 12 May

Inclusive $\text{J}/\psi$ production in ${\rm pp}$ collisions at
$\sqrt{s}=5.02$ TeV

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

Inclusive $\text{J}/\psi$ production is studied in minimum-bias proton-proton
collisions at a centre-of-mass energy of $\sqrt{s}=5.02$ TeV by ALICE at the
CERN LHC. The measurement is performed at mid-rapidity ($|y|<0.9$) in the
dielectron decay channel down to zero transverse momentum $p_{\text{T}}$,
using a data sample corresponding to an integrated luminosity of $L_{\rm
int}=19.4\pm 0.4$ nb-1. The measured $p_{\text{T}}$-integrated inclusive
$\text{J}/\psi$ production cross section is ${\rm d}\sigma/{\rm d}y=5.64\pm
0.22\text{(stat.)}\pm 0.33\text{(syst.)}\pm 0.12\text{(lumi.)}$ $\mu$b. The
$p_{\text{T}}$-differential cross section ${\rm d}^{2}\sigma/{\rm
d}p_{\text{T}}{\rm d}y$ is measured in the $p_{\text{T}}$ range $0-10~{}{\rm
GeV}/c$ and compared with state-of-the-art QCD calculations. The
$\text{J}/\psi$ $\langle p_{\text{T}}\rangle$ and $\langle
p_{\text{T}}^{2}\rangle$ are extracted and compared with results obtained at
other collision energies.

##  1 Introduction

At LHC energies, charmonium is mainly produced from gluon–gluon scatterings
producing $\text{c}\overline{\text{c}}$ pairs [1] which form a bound state.
While the hard gluon–gluon scattering can be described within perturbative
Quantum Chromodynamics (QCD), the hadronisation of the
$\text{c}\overline{\text{c}}$ pair into charmonium is essentially non-
perturbative and cannot be yet calculated from the QCD Lagrangian. There are
several phenomenological approaches for the description of charmonium
production: the Colour Evaporation Model (CEM) [2, 3], the Colour Singlet
Model (CSM) [4] and the Non-Relativistic QCD model (NRQCD) [5] which differ
mainly in the way the charmonium states are formed in the hadronisation
process. In the CEM model, the production rate of a given charmonium state is
proportional to the production cross section of $\text{c}\overline{\text{c}}$
pairs integrated between $m_{\text{c}\overline{\text{c}}}$ and twice the mass
of the lightest D-meson, where $m_{\text{c}\overline{\text{c}}}$ is twice the
mass of the charm quark, or, according to a recent conjecture [6, 7], the mass
of the bound state itself. In the CSM model, the pre-resonant
$\text{c}\overline{\text{c}}$ state is assumed to be directly produced
colourless and with the same quantum numbers as the final-state charmonium.
The NRQCD model includes all possible colour and quantum number states for the
pre-resonant $\text{c}\overline{\text{c}}$ pair, with each configuration
having a probability to transform into a given bound state, described by a set
of universal long-distance matrix elements determined from global fits to
experimental data. Detailed reviews of the state-of-the-art calculations for
charmonium production can be found in Refs. [8, 9, 10].

$\text{J}/\psi$ production is a probe of the hot and dense medium created in
ultrarelativistic heavy-ion collisions [11, 12]. Moreover, it is also
sensitive to nuclear effects not related to the creation of deconfined matter,
called cold-nuclear-matter effects, such as modification of the parton
distribution functions [13, 14]. In order to gauge both the hot and cold
medium effects, precise knowledge of the $\text{J}/\psi$ production rates in
the absence of a nucleus in the initial state is of paramount importance. The
$\text{J}/\psi$ measurement in ${\rm pp}$ collisions constitutes a baseline
for the quantification of nuclear effects in both nucleus–nucleus and
proton–nucleus collisions.

In this paper, results for the transverse momentum ($p_{\text{T}}$) dependence
of the inclusive $\text{J}/\psi$ production cross section at mid-rapidity
($|y|<0.9$) in ${\rm pp}$ collisions at the centre-of-mass energy
$\sqrt{s}~{}=5.02$ TeV are presented. The inclusive cross section contains a
prompt contribution, which includes directly produced $\text{J}/\psi$ as well
as the feed-down from the prompt decay of heavier charmonium states (mainly
$\psi(2S)$ and $\chi_{c}$), and a non-prompt contribution from the weak decay
of beauty hadrons.

The $\text{J}/\psi$ production is measured in the dielectron decay channel
using the ALICE central barrel detectors. The $p_{\text{T}}$-differential
cross section is measured for $p_{\text{T}}<10~{}{\rm GeV}/c$ supplementing
the existing mid-rapidity measurements at high $p_{\text{T}}$ by ATLAS [15]
and CMS [16] down to zero $p_{\text{T}}$. Thus, ALICE can measure the
$p_{\text{T}}$-integrated inclusive $\text{J}/\psi$ production cross section,
the mean transverse momentum $\langle p_{\text{T}}\rangle$ and the second
moment of the transverse momentum $\langle p_{\text{T}}^{2}\rangle$. Similar
measurements in ${\rm pp}$ collisions were performed by ALICE at
$\sqrt{s}=2.76$ TeV [17] and at $\sqrt{s}=7$ TeV [18] at mid- and forward
rapidity ($2.5<y<4.0$), and at $\sqrt{s}=5.02$, $8$ and $13$ TeV at forward-
rapidity [19, 20, 21]. Prompt $\text{J}/\psi$ production cross sections were
measured at $\sqrt{s}=7$ TeV by ALICE [22] and LHCb [23] and at $\sqrt{s}=8$
and $13$ TeV by LHCb [24, 25].

The paper is organised as follows: the ALICE apparatus and the data sample are
described in Section 2, the data analysis is detailed in Section 3 and the
results are discussed in Section 4 in comparison with other measurements and
theoretical calculations. Conclusions are given in Section 5.

##  2 Apparatus and data sample

The central barrel of the ALICE detector [26, 27] allows the reconstruction of
$\text{J}/\psi$ in the ${\rm e}^{+}{\rm e}^{-}$ decay channel at mid-rapidity.
The entire setup is placed in a solenoidal magnetic field of $B=0.5$ T
oriented along the beam direction.

In this analysis, the Inner Tracking System (ITS) [28] and the Time Projection
Chamber (TPC) [29] are used for tracking whereas the TPC provides the electron
identification. The ITS is subdivided into six cylindrically-shaped layers of
silicon detectors around the beam pipe with radii from $3.9$ to $43.0$ cm. The
two innermost layers form the high granularity Silicon Pixel Detector (SPD),
the two intermediate layers the Silicon Drift Detector (SDD), and the
outermost layers the Silicon Strip Detector (SSD). The ITS provides precise
tracking close to the interaction point and collision vertex position
determination. The TPC is a large drift detector with a cylindrical geometry
which extends radially between $85<r<250$ cm and longitudinally between
$-250<z<250$ cm, where $z=0$ and $r=0$ correspond to the nominal interaction
point. It is the main tracking device, with a full azimuthal acceptance for
tracks in the pseudorapidity range $|\eta|<0.9$. Additionally, the TPC can be
used for the particle identification of charged particles via the measurement
of the specific ionisation energy loss $\text{d}E/\text{d}x$ in the TPC gas.

The minimum bias (MB) trigger is provided by the V0 detector which consists of
two forward scintillator arrays [30] placed on both sides of the nominal
interaction point at $z=-90$ and $+340$ cm covering the $\eta$ range
$-3.7<\eta<-1.7$ and $2.8<\eta<5.1$. The trigger signal consists of a
coincident signal on both sides and is fully efficient in inelastic collisions
containing a $\text{J}/\psi$.

For this analysis, the data recorded by ALICE in the 2017 LHC pp run at a
centre-of-mass collision energy of $\sqrt{s}=5.02$ TeV are used. A total of
987 million MB events are used in this analysis corresponding to an integrated
luminosity of $L_{\rm int}=19.4\pm 0.4$ nb-1. The integrated luminosity is
obtained following a procedure [31] which employs the Van der Meer technique
[32].

##  3 Analysis, corrections, and systematic uncertainties

###  3.1 Event and track selection

The $\text{J}/\psi$ candidates are searched in the dielectron decay channel,
with the electron tracks being reconstructed in the ITS and the TPC. The
events fulfill the MB trigger condition and have the collision vertex within
the longitudinal interval $|z_{\rm vtx}|<10$ cm to ensure uniform detector
acceptance. Beam-gas events are rejected using offline timing cuts with the V0
detector. The probability for collision pile-up was $\leq$1% during the entire
data taking period and these events are rejected using a vertex finding
algorithm based on SPD tracklets [27].

Electron candidates are required to have a minimum transverse momentum of
$1~{}{\rm GeV}/c$ and a pseudorapidity in the range of $|\eta|<0.9$. Due to
the short decay time of the $\text{J}/\psi$ and its decay mothers, if any, the
daughter electrons are reconstructed as primary particles [33]. The candidate
daughter tracks are required to have a maximum distance-of-closest-approach to
the reconstructed collision vertex of $0.2$ cm in the radial direction and
$0.4$ cm along the beam-axis direction. Monte Carlo (MC) simulations are used
to verify that this requirement does not reject electrons from the decays of
non-prompt $\text{J}/\psi$. Tracks which originate from long-lived weak decays
of charged particles (e.g. $\pi^{\pm}\rightarrow\mu^{\pm}\nu$ or
$K^{\pm}\rightarrow\mu^{\pm}\nu$) are rejected from the analysis. A hit in at
least one of the two SPD layers is required for both electron candidates to
improve the tracking resolution and reduce the number of electrons from photon
conversions. Electron candidates are required to have at least $70$ out of a
maximum of $159$ attached clusters and the track fit
$\chi^{2}/N_{\mathrm{dof}}<2$ in the TPC.

Electron candidates are selected such that their specific ionisation energy
loss $\text{d}E/\text{d}x$ in the TPC lies within the interval
$[-2,+3]~{}\sigma_{\rm e}$ relative to the expectation for electrons with same
momentum as the candidate, where $\sigma_{\rm e}$ is the specific energy-loss
resolution for electrons in the TPC. Similarly, to further reject
contamination, particles compatible within $3\sigma$ with being a proton or a
pion, according to the measured $\text{d}E/\text{d}x$, are rejected.

The dominant source of background electrons is photon conversions. Electrons
from conversions in the material at large radii (typically beyond the SPD
layers) are removed using the requirement on the SPD hits described above.
Electrons from conversions occuring in the beam pipe or in the SPD material
can pass the primary track selection criteria. Therefore, further rejection of
this background is done by employing a method which relies on a second set of
electrons selected with looser criteria. Electrons from the first (primary)
set are paired with those of the second set. For pairs with an invariant mass
below the threshold of $50~{}{\rm MeV}/c^{2}$, the corresponding electron from
the primary set is excluded from further analysis. The looser selection
criteria of the second set are optimized in a data driven way such that the
signal to background ratio is improved, but the loss of signal with respect to
not applying this procedure remains negligible.

###  3.2 Signal extraction

Figure 1: (Colour online) Same-event opposite-sign dielectron invariant mass
distributions for several $p_{\text{T}}$-intervals with signal (blue),
correlated background (green), and combinatorial background (red) components.

The $\text{J}/\psi$ signal is extracted from the invariant mass distribution
of all opposite-sign pairs obtained by making all possible combinations with
the electrons and positrons selected with the criteria described above.
Examples of invariant mass distributions of opposite-sign (OS) electron pairs
are shown in Fig. 1 for the $p_{\text{T}}$-integrated case and for a few
selected $p_{\text{T}}$ intervals. These distributions contain contributions
from the $\text{J}/\psi$ signal and the combinatorial and correlated
backgrounds. For the combinatorial background, kinematic correlations do not
play a significant role and this component can be modelled using a mixed event
technique, while the correlated background in the $\text{J}/\psi$ mass region
originates mainly from semi-leptonic decays of correlated open heavy-flavour
hadrons [34]. The signal component corresponds to the electron pairs from
$\text{J}/\psi$ decays and has an asymmetric shape due to the radiative
component and to the energy lost by the electrons in the detector material via
brehmsstrahlung.

In order to obtain the raw number of $\text{J}/\psi$ counts, a two-step
procedure is employed. First, the combinatorial background is obtained using a
mixed event (ME) technique and scaled such that the invariant mass
distribution of like-sign (LS) pairs from ME matches the same-event LS
distribution in the invariant mass range $1.2<m_{\rm ee}<5.0$ ${\rm
GeV}/c^{2}$. Second, the combinatorial background is subtracted and the
remaining distribution is fit with a two-component function, an exponential
(or a second order polynomial) for the correlated background and the MC
template of the $\text{J}/\psi$ signal shape. This strategy provides a good
fit quality for all the $p_{\text{T}}$ intervals, as indicated by the
$\chi^{2}/N_{\mathrm{dof}}$ values shown in the panels of Fig. 1. The number
of $\text{J}/\psi$ candidates is obtained by counting the bin entries in the
mass interval $2.92<m_{\rm ee}<3.16~{}{\rm GeV}/c^{2}$ after subtracting all
background components. The background-subtracted signal distribution is also
fit with a Crystal Ball function [35] and the $p_{\text{T}}$-integrated
dielectron mass resolution at the $\text{J}/\psi$ peak region obtained from
the Gaussian core of the function is found to be $23$ ${\rm MeV}/c^{2}$.

Alternative fit strategies for the same event OS invariant mass distribution
are considered. A first strategy is to make a template fit to the total OS
invariant mass distribution, where the mixed event LS background is used as
the template for the combinatorial background with the normalisation used as a
free parameter, while the correlated background and signal components are
defined similarly as for the standard method. A second alternative is to fit
the OS mass distribution with the MC template for the signal component, while
for the sum of the combinatorial and correlated background an ad-hoc function
is used (ratio of small order polynomials). These alternative methods produce
compatible results.

###  3.3 Corrections

In order to correct the observed $\text{J}/\psi$ signal for detector effects
and the selection procedure, MC events are generated by adding a single
$\text{J}/\psi$ meson to a simulated MB pp collision. PYTHIA 6.4 [36] is used
to simulate the MB events and the non-prompt $\text{J}/\psi$ component, while
the prompt component is produced uniformly distributed in rapidity with a
$p_{\text{T}}$ spectrum based on a phenomenological interpolation of
measurements at RHIC, CDF, and the LHC [37]. The $\text{J}/\psi$ decays,
including the radiative component, are handled by PHOTOS [38]. The transport
through the ALICE detector material is handled by GEANT3 [39] with tracks
being reconstructed from the simulated hits using the same algorithm as for
the real data. The $p_{\text{T}}$-integrated acceptance times efficiency
$\langle A\times\epsilon\rangle$ is $9.9$%, varying between $8.1$% and $13$%
as a function of $p_{\text{T}}$, and is the product of the acceptance factor,
the reconstruction efficiency including the track quality cuts, the electron
identification cuts and the fraction of the signal within the mass counting
interval of $2.92<m_{\rm ee}<3.16~{}{\rm GeV}/c^{2}$. Due to the variation of
$\langle A\times\epsilon\rangle$ with the $\text{J}/\psi$ transverse momentum
in the considered $p_{\text{T}}$ intervals, the calculated correction factors
have a mild dependence on the shape of the $p_{\text{T}}$ distribution and the
fraction of non-prompt $\text{J}/\psi$, $f_{\mathrm{B}}$, used in the
simulation. In order to correct for this effect, the corrected $\text{J}/\psi$
cross-section, obtained initially using efficiencies weighted with the
$\text{J}/\psi$ spectrum from simulations, is used to reweight the acceptance
times efficiency factor and obtain an updated cross-section. This procedure
can be iteratively employed until the variation of the $\text{J}/\psi$ cross
section between two iterations is smaller than a desired precision. Already
after the first iteration, the inclusive $\text{J}/\psi$
$p_{\text{T}}$-integrated cross section varied by less than $1$%, while for
the $p_{\text{T}}$-differential cross section the changes were even smaller,
so the procedure is stopped after one iteration. Due to the fact that in our
analysis there is a $1$–$2$% difference in acceptance times efficiency between
prompt and non-prompt $\text{J}/\psi$ and that the $f_{\mathrm{B}}$ value in
simulation is larger with respect to existing measurements at Tevatron [40]
and LHC [41, 22, 42] energies, the acceptance times efficiency factors are
reweighted to account for these differences. The largest impact from this
correction is observed at high $p_{\text{T}}$, where the difference between
simulation and existing $f_{\mathrm{B}}$ measurements is largest, and shifts
the cross section upwards by $0.3$%.

The differential cross section in a rapidity interval $\Delta y$ and
transverse momentum interval $\Delta p_{\text{T}}$ is calculated as

$\frac{{\rm d}^{2}\sigma_{\text{J}/\psi}}{{\rm d}y{\rm
d}p_{\text{T}}}=\frac{N_{\text{J}/\psi}(\Delta y,\Delta
p_{\text{T}})}{\text{BR}(\text{J}/\psi\to\text{e}^{+}\text{e}^{-})\cdot\langle
A\times\epsilon\rangle(\Delta y,\Delta p_{\text{T}})\cdot\Delta y\cdot\Delta
p_{\text{T}}\cdot L_{\rm int}},$ (1)

where $N_{\text{J}/\psi}$ is the number of reconstructed $\text{J}/\psi$
candidates, $\text{BR}(\text{J}/\psi\to\text{e}^{+}\text{e}^{-})$ is the
branching ratio of the $\text{J}/\psi$ mesons decaying into dielectrons [43],
and $L_{\rm int}$ is the integrated luminosity of the data sample.

###  3.4 Systematic uncertainties

The sources of systematic uncertainties are related to the ITS-TPC tracking,
electron identification, signal extraction procedure, the $\text{J}/\psi$
input kinematic distributions used in the MC production, the integrated
luminosity determination, and the branching ratio of the dielectron decay
channel. A summary of all the systematic uncertainties is provided in Table 1.

Table 1: Summary of the contributions to the systematic uncertainty (in percentage) for the inclusive $p_{\text{T}}$-integrated cross section ${\rm d}\sigma/{\rm d}y$ and in the different $p_{\text{T}}$ intervals. All sources of systematic uncertainty are considered to be highly correlated over $p_{\text{T}}$, except for the background fit which is considered fully uncorrelated. Source |  $p_{\text{T}}$ (${\rm GeV}/c$)
---|---
| $p_{\text{T}}>0$ | 0$-$1 | 1$-$2 | 2$-$3 | 3$-$4 | 4$-$5 | 5$-$7 | 7$-$10
Tracking | 5.3 | 4.8 | 5.1 | 5.4 | 5.5 | 5.2 | 5.6 | 5.7
PID | 0.43 | 0.21 | 0.42 | 0.17 | 0.04 | 0.40 | 1.1 | 2.5
Signal shape | 1.9 | 1.8 | 1.8 | 1.8 | 1.8 | 1.8 | 2.9 | 2.9
Background fit | 0.21 | 1.0 | 0.30 | 0.36 | 0.18 | 0.27 | 0.21 | 0.21
MC input | 1.4 | 0.24 | 0.35 | 0.10 | 0.15 | 0.11 | 0.15 | 0.69
Luminosity | 2.1
Branching ratio | 0.53
Total uncorrelated syst. | 0.21 | 1.0 | 0.30 | 0.36 | 0.18 | 0.27 | 0.21 | 0.21
Total correlated syst. | 5.8 | 5.1 | 5.5 | 5.7 | 5.8 | 5.6 | 6.4 | 6.9
Global syst. | 2.2
Total | 6.2 | 5.6 | 5.9 | 6.1 | 6.2 | 6.1 | 6.8 | 7.3

The dominant source of systematic uncertainty is related to the ITS-TPC
tracking and has two components, one related to the ITS-TPC matching
efficiency and the other to the track quality requirements. The component due
to the ITS-TPC matching efficiency is the largest and is determined by
comparing the probability to match the TPC tracks to hits in the ITS in both
data and simulation [44].

After propagation to the $\text{J}/\psi$ candidate pairs, this uncertainty is
found to vary between $4.3$% at low $p_{\text{T}}$ up to $5.4$% at high
$p_{\text{T}}$. The uncertainty due to the track quality requirements amounts
to approximately $2$% in all $p_{\text{T}}$ intervals and was obtained by
varying the selection criteria and computing the RMS of the cross-section
distribution obtained after these variations. This tracking uncertainty is
considered to be correlated over $p_{\text{T}}$.

The systematic uncertainty due to the electron identification is estimated by
comparing the response of the TPC electron identification of a clean sample of
electrons from tagged photon conversions in data to true electrons from the MC
simulation. Half the difference between the selection efficiency in data and
simulation is taken as the systematic uncertainty on the single electron PID
efficiency and propagated to that on the $\text{J}/\psi$ selection using a toy
MC simulating $\text{J}/\psi$ decays in the dielectron channel.

The uncertainty due to the TPC PID ranges between $0.1$% at intermediate and
$2.5$% at high $p_{\text{T}}$ and is considered to be correlated over
$p_{\text{T}}$.

The uncertainty on the signal extraction procedure has contributions from the
choice of the $\text{J}/\psi$ invariant mass shape and from the fit procedure
used to describe the correlated background. It is estimated by varying the
mass interval used for the signal counting and the mass range used for the
fitting. The value of the uncertainty is determined as the RMS of the
distribution of cross sections obtained from the cases which give
statistically significant variations, similar to the procedure described by
Barlow [45]. The uncertainty on the $\text{J}/\psi$ signal shape ranges
between $1.8$% in the low- and $2.9$% in the high-$p_{\text{T}}$ intervals and
is treated to be correlated over $p_{\text{T}}$. The uncertainty due to the
background fitting is $1$% in the lowest $p_{\text{T}}$-interval and less than
$0.5$% otherwise. It is considered as uncorrelated.

The uncertainty from the $\text{J}/\psi$ $p_{\text{T}}$-distribution which is
used to compute the corrections is related to the precision of the fit to the
measured $\text{J}/\psi$ spectrum which is used in the iterative procedure
described in Section 3.3. The fit parameters are varied randomly within their
allowed fit uncertainty taking into account their correlation matrix. The
resulting uncertainty amounts to $1.4$% for the $p_{\text{T}}$-integrated
cross section and less than $1$% in each of the considered
$p_{\text{T}}$-intervals.

The systematic uncertainty on the integrated beam luminosity is described in
detail in Ref. [31] and amounts to $2.1$%. This uncertainty is taken as a
global uncertainty for the $p_{\text{T}}$-integrated and the
$p_{\text{T}}$-differential cross sections.

The uncertainty on the branching ratio
$\text{BR}(\text{J}/\psi\to\text{e}^{+}\text{e}^{-})=(5.97\pm 0.03)$% [43] is
treated as fully correlated between all bins.

##  4 Results

The inclusive $\text{J}/\psi$ cross section in ${\rm pp}$ collisions at
$\sqrt{s}=5.02$ TeV measured at mid-rapidity in the interval $|y|<0.9$ is

${\rm d}\sigma_{\text{J}/\psi}/{\rm d}y=5.64\pm 0.22\text{(stat.)}\pm
0.33\text{(syst.)}\pm 0.12\text{(lumi.)}~{}\mu{\rm b}.$

The systematic uncertainty contains all the sources described in Section 3
added in quadrature, assuming that the $\text{J}/\psi$ is produced
unpolarised. Although the existing measurements in ${\rm pp}$ collisions at
LHC energies indicate a null or only a small polarisation [46, 47, 48], there
are no polarisation measurements for $\text{J}/\psi$ at low $p_{\text{T}}$ and
mid-rapidity at LHC energies. In order to estimate the impact on the measured
inclusive $\text{J}/\psi$ cross section, the acceptance and efficiency factors
are reweighted to take into account various polarisation scenarios. In the
extreme cases of a fully transverse ($\lambda=+1$) or a fully longitudinal
($\lambda=-1$) polarisation in the helicity frame, the
$p_{\text{T}}$-integrated cross section would increase by $15$% or decrease by
$24$%, respectively.

Figure 2: Left: Inclusive $\text{J}/\psi$ cross section as a function of
rapidity compared to the ALICE results at forward rapidity [21] and to
calculations from [49] to which a non-prompt component is added as computed in
[50]. Right: Inclusive $\text{J}/\psi$ cross section at mid-rapidity [51, 52,
40, 17, 18] as a function of collision energy compared to the calculations
from [49]. The data points from PHENIX and STAR, both at $\sqrt{s}=0.2$ TeV,
are slightly shifted for improved visibility.

In the left panel of Fig. 2, the inclusive $p_{\text{T}}$-integrated cross
section ${\rm d}\sigma/{\rm d}y$ is compared with the ALICE measurements at
forward rapidity in the dimuon channel [21]. The systematic uncertainties are
represented as boxes and the statistical uncertainties are shown by vertical
error bars. The reported $\text{J}/\psi$ cross sections are inclusive and
contain both the prompt and non-prompt components. The rapidity-dependent
cross section is compared with results for prompt $\text{J}/\psi$ from Leading
Order (LO) NRQCD calculations coupled to a Colour Glass Condensate (CGC)
description of the gluon distributions in the proton from Ma and Venugopalan
[49]. This model includes a soft-gluon resummation which allows the
calculation of the $\text{J}/\psi$ cross section down to zero $p_{\text{T}}$.
The Long Distance Matrix Elements (LDME) used are obtained by fitting the
prompt component of high-$p_{\text{T}}$ $\text{J}/\psi$ at Tevatron [53].
Feed-down from higher mass charmonia, $\psi$(2S) and $\chi_{c}$, are
considered. The non-prompt component is calculated with Fixed-Order Next-to-
Leading Logarithm (FONLL) [50] from beauty quarks with a $\text{J}/\psi$ in
the final state. The prompt component from Ref. [49] and the non-prompt
component from Ref. [50] are then added together in order to generate the
inclusive $\text{J}/\psi$ cross section shown in the left panel of Fig. 2. The
uncertainties of the prompt and non-prompt component are assumed to be
uncorrelated when calculating the error band of the sum. The non-prompt
contribution to the inclusive cross section is of the order of $10$–$20$% in
the considered low-$p_{\text{T}}$ regime. The relatively large uncertainty
band of the model is mainly due to variations of the charm-quark mass, and the
renormalisation and factorisation scales. Assuming that the rapidity
dependence in the calculation is not affected by the change of these scales,
the rapidity dependence of the $\text{J}/\psi$ cross section is well
reproduced in the model. The overall normalisation of the calculation has very
large uncertainties and these data represent a strong constrain to the model
assumptions.

The energy dependence of the $\text{J}/\psi$ cross section in ${\rm pp}$
collisions at mid-rapidity is shown in the right panel of Fig. 2. The results
are compared with the PHENIX [51] and STAR [52] measurements at $\sqrt{s}=0.2$
TeV, the CDF measurement at $\sqrt{s}=1.96$ TeV [40], and previous ALICE
measurements at $\sqrt{s}=2.76$ [17] and $7$ TeV [18], where statistical and
systematic uncertainties are added in quadrature. A steady increase,
approximately logarithmic in $\sqrt{s}$, of ${\rm d}\sigma/{\rm d}y$ at mid-
rapidity is observed. The data are compared with the calculated prompt
$\text{J}/\psi$ cross section from Ref. [49]. Since the non-prompt component
is known to be of the order of $10$% of the inclusive cross section, the
qualitative comparison to the data is not affected. As in the case of the
rapidity dependence discussed above, the calculations are compatible with the
logarithmic trend seen in the data, while the absolute normalisation has large
uncertainties.

Figure 3: $p_{\text{T}}$-differential inclusive $\text{J}/\psi$ cross section
compared with prompt $\text{J}/\psi$ calculations from NLO NRQCD [54, 55] and
LO NRQCD+CGC [49] and non-prompt $\text{J}/\psi$ calculations from FONLL [50].
The calculations for the prompt and non-prompt components are shown separately
in the left panel while in the right panel the FONLL calculation is added to
the prompt $\text{J}/\psi$ calculations.

In the left panel of Fig. 3, the $p_{\text{T}}$-differential cross section
${\rm d}^{2}\sigma/{\rm d}p_{\text{T}}{\rm d}y$ is compared to three
calculations of the prompt $\text{J}/\psi$ cross section: two NLO NRQCD
calculations from Ma et al. [54] and Butenschoen et al. [55], and the above-
mentioned calculations usind leading order NRQCD and CGC [49]. The non-prompt
component obtained using FONLL [50] is shown separately. In the right panel of
Fig. 3, the non-prompt FONLL calculation is added to each of the three prompt
calculations and compared with results of the present analysis. Within the
model uncertainties, the NRQCD+CGC model provides a good description of the
trend over the covered $p_{\text{T}}$ interval, with the lower part of the
band being favoured by the data. Although employing a very similar approach
for the small distance coefficients, the two NLO NRQCD calculations use quite
different LDME values, extracted by fitting charmonium cross-sections measured
at Tevatron and HERA with different low $p_{\text{T}}$ cut-offs. This limits
the range of validity to $p_{\text{T}}>3$ and $p_{\text{T}}>5$ ${\rm GeV}/c$
for the cross sections obtained in Ref. [55] and Ref. [54], respectively. In
addition, the calculations from Ref. [55] predict a strong transversal
$\text{J}/\psi$ polarization, which is in contradiction to the recent ALICE
measurement at forward-rapidity in pp collisions at $\sqrt{s}=8$ TeV [47]
which favours zero or a small amount of polarisation. The cross sections from
Ref. [55] do not include feed-down contributions from higher mass charmonia.
Both predictions are in agreement to the data considering the uncertainties,
however, the above mentioned differences in model assumptions together with
the large scale uncertainties prevent drawing firm conclusions. There are
recent alternative works, not at the presented energy, using an improved CEM
model [6, 7] or NRQCD in the $k_{\text{T}}$ factorisation approach [56, 57,
58] that could further help interpret our data.

In Fig. 4, the $p_{\text{T}}$-differential cross section ${\rm
d}^{2}\sigma/{\rm d}p_{\text{T}}{\rm d}y$ is compared with the
high-$p_{\text{T}}$ measurements from ATLAS [15] and CMS [16] at mid-rapidity
and same collision energy. It should be noted that the ATLAS and CMS
measurements extend to higher $p_{\text{T}}$ but are truncated to a region
which is relevant for the comparison to ALICE. The ATLAS and CMS measurements
of the prompt and non-prompt contributions were summed in order to obtain the
inclusive cross section needed to compare with our measurement. Good agreement
is observed between the results in the overlapping $p_{\text{T}}$ region.

Figure 4: $p_{\text{T}}$-differential inclusive $\text{J}/\psi$ cross section
compared with ATLAS [15] and CMS [16] results at mid-rapidity. Luminosity
uncertainties are indicated in the legend, except in the case of ATLAS for
which these are included in the boxes.

The energy dependence of the $p_{\text{T}}$-differential $\text{J}/\psi$ cross
section can be studied by using its moments, the average transverse momentum
$\langle p_{\text{T}}\rangle$ and the squared average transverse momentum
$\langle p_{\text{T}}^{2}\rangle$. In this analysis, the inclusive
$\text{J}/\psi$ $\langle p_{\text{T}}\rangle$ and $\langle
p_{\text{T}}^{2}\rangle$ are obtained by fitting the measured spectrum with a
power law function of the form

$f(p_{\text{T}})=C\times\frac{p_{\text{T}}}{\left\\{1+\left(p_{\text{T}}/p_{0}\right)^{2}\right\\}^{n}},$
(2)

where $C$, $p_{0}$, and $n$ are free fit parameters. In the interval
$p_{\text{T}}<10~{}{\rm GeV}/c$, the first two moments of the fitted function
are

$\displaystyle\langle p_{\text{T}}\rangle$ $\displaystyle=$ $\displaystyle
2.66\pm 0.06\text{(stat.)}\pm 0.01\text{(syst.)}~{}{\rm GeV}/c,$
$\displaystyle\langle p_{\text{T}}^{2}\rangle$ $\displaystyle=$ $\displaystyle
10.2\pm 0.5\text{(stat.)}\pm 0.1\text{(syst.)}~{}{\rm GeV}^{2}/c^{2}.$

The systematic uncertainty is obtained by fitting the measured $\text{J}/\psi$
spectrum only with the systematic uncertainty of the
$p_{\text{T}}$-differential cross section. The statistical uncertainty on the
$\langle p_{\text{T}}\rangle$ and $\langle p_{\text{T}}^{2}\rangle$ takes into
account the correlation matrix of the parameters from the fit procedure. A
cross check of these results is performed considering a fit to the dielectron
$\langle p_{\text{T}}\rangle$ and $\langle p_{\text{T}}^{2}\rangle$
distribution as a function of the invariant mass. A polynomial fit function is
used to parameterise the background $\langle p_{\text{T}}\rangle$ and $\langle
p_{\text{T}}^{2}\rangle$ as a function of invariant mass, and the signal-over-
background ratio obtained from the signal extraction procedure as discussed in
Section 3.2. The values obtained with this cross check are found to be
compatible with the ones obtained from the spectrum fit.

Figure 5: The $\langle p_{\text{T}}\rangle$ (lower panel) and $\langle
p_{\text{T}}^{2}\rangle$ (upper panel) of inclusive $\text{J}/\psi$ at mid-
rapidity as a function of the collision energy. These results are compared to
previous results from ALICE at LHC [18, 22], Tevatron [40], RHIC [51, 52] and
SPS [59].

The energy dependences of the $\langle p_{\text{T}}\rangle$ and $\langle
p_{\text{T}}^{2}\rangle$ moments are shown in Fig. 5. A steady increase with
energy is observed for both $\langle p_{\text{T}}\rangle$ and $\langle
p_{\text{T}}^{2}\rangle$ over a wide collision energy range which includes
results from SPS [59], RHIC [51, 52], Tevatron [40], and LHC [18, 22].
Statistical and systematic uncertainties are added in quadrature. This
behaviour is a consequence of the opening of the phase space with increasing
collision energy, i.e. for a fixed Bjorken-$x$ the momentum-exchange $Q^{2}$
grows with increasing collision energy leading to a hardening of the
$\text{J}/\psi$ $p_{\text{T}}$ spectrum. Also, the faster increase with energy
of the $\text{b}\overline{\text{b}}$ cross section compared to the
$\text{c}\overline{\text{c}}$ cross section leads to a growth of the non-
prompt $\text{J}/\psi$ fraction, which further hardens the $\text{J}/\psi$
$p_{\text{T}}$ spectrum. In order to quantify the energy dependence of the
$\text{J}/\psi$ $\langle p_{\text{T}}\rangle$ and $\langle
p_{\text{T}}^{2}\rangle$, we performed similar fits to those used in Ref. [51,
60], where linear or quadratic functions of the logarithm of the centre-of-
mass collision energy were used. These simple parametrisations describe the
existing measurements over nearly three orders of magnitude in collision
energy, with values of the $\chi^{2}/{N_{\rm dof}}$ of 1.7 and 0.98 for the
$\text{J}/\psi$ $\langle p_{\text{T}}\rangle$ and $\langle
p_{\text{T}}^{2}\rangle$, respectively.

##  5 Conclusions

The inclusive $\text{J}/\psi$ production cross section in proton–proton
collisions at $\sqrt{s}=5.02$ TeV in the rapidity range $|y|<0.9$ is measured
down to zero $p_{\text{T}}$ using the dielectron decay channel. The
measurement is performed using a minimum-bias data sample corresponding to an
integrated luminosity of $L_{\rm int}=19.4\pm 0.4$ nb-1 and yields a
$p_{\text{T}}$-integrated cross section of ${\rm d}\sigma/{\rm d}y=5.64\pm
0.22\text{(stat.)}\pm 0.33\text{(syst.)}\pm 0.12\text{(lumi.)}$ $\mu$b.

Comparisons of the inclusive $p_{\text{T}}$-integrated and
$p_{\text{T}}$-differential cross section of three NRQCD calculations for
prompt $\text{J}/\psi$ summed with a non-prompt $\text{J}/\psi$ component
calculated with FONLL are compatible with the data if the large scale
uncertainties are considered as uncorrelated over rapidity, collision energy
or $p_{\text{T}}$. A more refined approach, which would consider correlations
between model parameters will allow to differentiate between the different
theoretical approaches.

A good agreement to the complementary ATLAS and CMS measurements at the same
collision energy is observed in the overlapping $p_{\text{T}}$ interval. The
energy dependence of the $\langle p_{\text{T}}\rangle$ and $\langle
p_{\text{T}}^{2}\rangle$ indicate a hardening of the
$p_{\text{T}}$-differential cross section with increasing collision energy.
This is well described by a linear and squared logarithmic increase of
$\langle p_{\text{T}}\rangle$ and $\langle p_{\text{T}}^{2}\rangle$ with
$\sqrt{s}$, respectively.

## 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), 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; Croatian Science Foundation and Ministry
of Science and Education, 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 Carlsberg Foundation and Danish
National Research Foundation (DNRF), Denmark; Helsinki Institute of Physics
(HIP), Finland; Commissariat à l’Energie Atomique (CEA), Institut National de
Physique Nucléaire et de Physique des Particules (IN2P3) and Centre National
de la Recherche Scientifique (CNRS) and Région des Pays de la Loire, France;
Bundesministerium für Bildung und Forschung (BMBF) and GSI Helmholtzzentrum
für Schwerionenforschung GmbH, Germany; General Secretariat for Research and
Technology, Ministry of Education, Research and Religions, Greece; National
Research, Development and Innovation Office, Hungary; Department of Atomic
Energy Government of India (DAE), Department of Science and Technology,
Government of India (DST), University Grants Commission, Government of India
(UGC) and Council of Scientific and Industrial Research (CSIR), India;
Indonesian Institute of Science, Indonesia; Centro Fermi - Museo Storico della
Fisica e Centro Studi e Ricerche Enrico Fermi and Istituto Nazionale di Fisica
Nucleare (INFN), Italy; Institute for Innovative Science and Technology ,
Nagasaki Institute of Applied Science (IIST), 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 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; 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. Acharyaorg141&D. Adamováorg93&S.P. Adhyaorg141&A. Adlerorg74&J.
Adolfssonorg80&M.M. Aggarwalorg98&G. Aglieri Rinellaorg34&M. Agnelloorg31&N.
Agrawalorg48,org10&Z. Ahammedorg141&S. Ahmadorg17&S.U. Ahnorg76&A.
Akindinovorg64&M. Al-Turanyorg105&S.N. Alamorg141&D.S.D. Albuquerqueorg122&D.
Aleksandrovorg87&B. Alessandroorg58&H.M. Alfandaorg6&R. Alfaro Molinaorg72&B.
Aliorg17&Y. Aliorg15&A. Aliciorg10,org53,org27&A. Alkinorg2&J. Almeorg22&T.
Altorg69&L. Altenkamperorg22&I. Altsybeevorg112&M.N. Anaamorg6&C.
Andreiorg47&D. Andreouorg34&H.A. Andrewsorg109&A. Andronicorg144&M.
Angelettiorg34&V. Anguelovorg102&C. Ansonorg16&T. Antičićorg106&F.
Antinoriorg56&P. Antonioliorg53&R. Anwarorg126&N. Apadulaorg79&L.
Aphecetcheorg114&H. Appelshäuserorg69&S. Arcelliorg27&R. Arnaldiorg58&M.
Arratiaorg79&I.C. Arseneorg21&M. Arslandokorg102&A. Augustinusorg34&R.
Averbeckorg105&S. Azizorg61&M.D. Azmiorg17&A. Badalàorg55&Y.W. Baekorg40&S.
Bagnascoorg58&X. Baiorg105&R. Bailhacheorg69&R. Balaorg99&A.
Baldisseriorg137&M. Ballorg42&S. Balouzaorg103&R.C. Baralorg85&R.
Barberaorg28&L. Barioglioorg26&G.G. Barnaföldiorg145&L.S. Barnbyorg92&V.
Barretorg134&P. Bartaliniorg6&K. Barthorg34&E. Bartschorg69&F.
Baruffaldiorg29&N. Bastidorg134&S. Basuorg143&G. Batigneorg114&B.
Batyunyaorg75&P.C. Batzingorg21&D. Bauriorg48&J.L. Bazo Albaorg110&I.G.
Beardenorg88&C. Beddaorg63&N.K. Beheraorg60&I. Belikovorg136&F.
Belliniorg34&R. Bellwiedorg126&V. Belyaevorg91&G. Bencediorg145&S.
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Wagnerorg22&Y. Watanabeorg133&M. Weberorg113&S.G. Weberorg144,org105&A.
Wegrzynekorg34&D.F. Weiserorg102&S.C. Wenzelorg34&J.P. Wesselsorg144&E.
Widmannorg113&J. Wiechulaorg69&J. Wikneorg21&G. Wilkorg84&J.
Wilkinsonorg53&G.A. Willemsorg34&E. Willsherorg109&B. Windelbandorg102&W.E.
Wittorg130&Y. Wuorg129&R. Xuorg6&S. Yalcinorg77&K. Yamakawaorg45&S.
Yangorg22&S. Yanoorg137&Z. Yinorg6&H. Yokoyamaorg63&I.-K. Yooorg18&J.H.
Yoonorg60&S. Yuanorg22&A. Yuncuorg102&V. Yurchenkoorg2&V.
Zaccoloorg58,org25&A. Zamanorg15&C. Zampolliorg34&H.J.C. Zanoliorg121&N.
Zardoshtiorg34&A. Zarochentsevorg112&P. Závadaorg67&N. Zaviyalovorg107&H.
Zbroszczykorg142&M. Zhalovorg96&X. Zhangorg6&Z. Zhangorg6,org134&C.
Zhaoorg21&V. Zherebchevskiiorg112&N. Zhigarevaorg64&D. Zhouorg6&Y.
Zhouorg88&Z. Zhouorg22&J. Zhuorg6&Y. Zhuorg6&A. Zichichiorg27,org10&M.B.
Zimmermannorg34&G. Zinovjevorg2&N. Zurloorg140&

## Affiliation notes

org*Deceased

orgIDipartimento DET del Politecnico di Torino, Turin, Italy

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

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

orgIVInstitute of Theoretical Physics, University of Wroclaw, Poland

## Collaboration Institutes

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

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

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

org4Budker Institute for Nuclear Physics, Novosibirsk, Russia

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

org6Central China Normal University, Wuhan, China

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

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

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

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

org11Chicago State University, Chicago, Illinois, United States

org12China Institute of Atomic Energy, Beijing, China

org13Chonbuk National University, Jeonju, Republic of Korea

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

org15COMSATS University Islamabad, Islamabad, Pakistan

org16Creighton University, Omaha, Nebraska, United States

org17Department of Physics, Aligarh Muslim University, Aligarh, India

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

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

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

org21Department of Physics, University of Oslo, Oslo, Norway

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

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

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

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

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

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

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

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

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

org31Dipartimento DISAT del Politecnico and Sezione INFN, Turin, Italy

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

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

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

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

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

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

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

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

org40Gangneung-Wonju National University, Gangneung, Republic of Korea

org41Gauhati University, Department of Physics, Guwahati, India

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

org43Helsinki Institute of Physics (HIP), Helsinki, Finland

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

org45Hiroshima University, Hiroshima, Japan

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

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

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

org49Indian Institute of Technology Indore, Indore, India

org50Indonesian Institute of Sciences, Jakarta, Indonesia

org51INFN, Laboratori Nazionali di Frascati, Frascati, Italy

org52INFN, Sezione di Bari, Bari, Italy

org53INFN, Sezione di Bologna, Bologna, Italy

org54INFN, Sezione di Cagliari, Cagliari, Italy

org55INFN, Sezione di Catania, Catania, Italy

org56INFN, Sezione di Padova, Padova, Italy

org57INFN, Sezione di Roma, Rome, Italy

org58INFN, Sezione di Torino, Turin, Italy

org59INFN, Sezione di Trieste, Trieste, Italy

org60Inha University, Incheon, Republic of Korea

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

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

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

org64Institute for Theoretical and Experimental Physics, Moscow, Russia

org65Institute of Experimental Physics, Slovak Academy of Sciences, Košice,
Slovakia

org66Institute of Physics, Homi Bhabha National Institute, Bhubaneswar, India

org67Institute of Physics of the Czech Academy of Sciences, Prague, Czech
Republic

org68Institute of Space Science (ISS), Bucharest, Romania

org69Institut für Kernphysik, Johann Wolfgang Goethe-Universität Frankfurt,
Frankfurt, Germany

org70Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México,
Mexico City, Mexico

org71Instituto de Física, Universidade Federal do Rio Grande do Sul (UFRGS),
Porto Alegre, Brazil

org72Instituto de Física, Universidad Nacional Autónoma de México, Mexico
City, Mexico

org73iThemba LABS, National Research Foundation, Somerset West, South Africa

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

org79Lawrence Berkeley National Laboratory, Berkeley, California, United
States

org80Lund University Department of Physics, Division of Particle Physics,
Lund, Sweden

org81Nagasaki Institute of Applied Science, Nagasaki, Japan

org82Nara Women’s University (NWU), Nara, Japan

org83National and Kapodistrian University of Athens, School of Science,
Department of Physics , Athens, Greece

org84National Centre for Nuclear Research, Warsaw, Poland

org85National Institute of Science Education and Research, Homi Bhabha
National Institute, Jatni, India

org86National Nuclear Research Center, Baku, Azerbaijan

org87National Research Centre Kurchatov Institute, Moscow, Russia

org88Niels Bohr Institute, University of Copenhagen, Copenhagen, Denmark

org89Nikhef, National institute for subatomic physics, Amsterdam, Netherlands

org90NRC Kurchatov Institute IHEP, Protvino, Russia

org91NRNU Moscow Engineering Physics Institute, Moscow, Russia

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

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

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

org95Ohio State University, Columbus, Ohio, United States

org96Petersburg Nuclear Physics Institute, Gatchina, Russia

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

org98Physics Department, Panjab University, Chandigarh, India

org99Physics Department, University of Jammu, Jammu, India

org100Physics Department, University of Rajasthan, Jaipur, India

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

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

org103Physik Department, Technische Universität München, Munich, Germany

org104Politecnico di Bari, Bari, Italy

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

org106Rudjer Bošković Institute, Zagreb, Croatia

org107Russian Federal Nuclear Center (VNIIEF), Sarov, Russia

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

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

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

org111Shanghai Institute of Applied Physics, Shanghai, China

org112St. Petersburg State University, St. Petersburg, Russia

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

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

org115Suranaree University of Technology, Nakhon Ratchasima, Thailand

org116Technical University of Košice, Košice, Slovakia

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

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

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

org120Universidad Autónoma de Sinaloa, Culiacán, Mexico

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

org122Universidade Estadual de Campinas (UNICAMP), Campinas, Brazil

org123Universidade Federal do ABC, Santo Andre, Brazil

org124University College of Southeast Norway, Tonsberg, Norway

org125University of Cape Town, Cape Town, South Africa

org126University of Houston, Houston, Texas, United States

org127University of Jyväskylä, Jyväskylä, Finland

org128University of Liverpool, Liverpool, United Kingdom

org129University of Science and Techonology of China, Hefei, China

org130University of Tennessee, Knoxville, Tennessee, United States

org131University of the Witwatersrand, Johannesburg, South Africa

org132University of Tokyo, Tokyo, Japan

org133University of Tsukuba, Tsukuba, Japan

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

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

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

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

org138Università degli Studi di Foggia, Foggia, Italy

org139Università degli Studi di Pavia, Pavia, Italy

org140Università di Brescia, Brescia, Italy

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

org142Warsaw University of Technology, Warsaw, Poland

org143Wayne State University, Detroit, Michigan, United States

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

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

org146Yale University, New Haven, Connecticut, United States

org147Yonsei University, Seoul, Republic of Korea