2021 057 12 April

Energy dependence of $\phi$ meson production in pp collisions at the LHC

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

The production of $\phi$ mesons has been studied in pp collisions at LHC
energies with the ALICE detector via the dimuon decay channel in the rapidity
region $2.5<y<4$. Measurements of the differential cross section ${\rm
d}^{2}\sigma/{\rm d}y{\rm d}p_{\mathrm{T}}$ are presented as a function of the
transverse momentum ($p_{\mathrm{T}}$) at the center-of-mass energies
$\sqrt{s}=5.02$, 8 and 13 TeV and compared with the ALICE results at
midrapidity. The differential cross sections at $\sqrt{s}=5.02$ and 13 TeV are
also studied in several rapidity intervals as a function of $p_{\mathrm{T}}$,
and as a function of rapidity in three $p_{\mathrm{T}}$ intervals. A hardening
of the $p_{\mathrm{T}}$-differential cross section with the collision energy
is observed, while, for a given energy, $p_{\mathrm{T}}$ spectra soften with
increasing rapidity and, conversely, rapidity distributions get slightly
narrower at increasing $p_{\mathrm{T}}$. The new results, complementing the
published measurements at $\sqrt{s}=2.76$ and 7 TeV, allow one to establish
the energy dependence of $\phi$ meson production and to compare the measured
cross sections with phenomenological models. None of the considered models
manages to describe the evolution of the cross section with $p_{\mathrm{T}}$
and rapidity at all the energies.

##  1 Introduction

Measurements of production cross sections and kinematic distributions of
strange hadrons represent an effective tool to investigate strangeness
production in high energy hadronic collisions, testing predictions from
phenomenological models inspired by quantum chromodynamics (QCD). In this
context, the hardness of the specific partonic processes roughly separates two
different regimes. At low transverse momentum ($p_{\mathrm{T}}\lesssim 2$
GeV/$c$), non-perturbative processes dominate, described by phenomenological
models where different approaches may be considered, such as the rope
hadronization and color reconnection mechanisms implemented in PYTHIA 8 [1].
In this regime, strangeness production in hadronic collisions with no strange
valence quark component in the initial state, such as proton–proton (pp),
proton–nucleus and nucleus–nucleus collisions, depends on the s-quark content
of the sea-parton wave function in nucleons. At high $p_{\mathrm{T}}$
($p_{\mathrm{T}}\gtrsim 5$ GeV/$c$), strangeness production can typically be
described in terms of hard partonic scattering processes via flavor creation
and excitation, and gluon splitting, for which predictions can be obtained
from perturbative calculations [2]. The intermediate $p_{\mathrm{T}}$ region
($2<p_{\mathrm{T}}<5$ GeV/$c$) is characterized by a smooth transition between
the production mechanisms dominating at low and high $p_{\mathrm{T}}$, whose
implementation in theoretical models is, however, not well defined and
therefore data in this $p_{\mathrm{T}}$ range are of particular importance.

In addition, strangeness production is also addressed within the
phenomenological statistical model approach [3]. In small hadronic systems, in
particular, the effect of canonical suppression can play a significant role in
determining the relative abundances of strange and lighter flavor hadrons,
with the $\phi$ meson playing a special role due to its hidden strangeness
composition [4, 5]. A precise theoretical characterization of this mechanism
in pp collisions, however, has yet to be established for the $\phi$ meson, and
predictions are currently not available.

Measurements of $\phi$ meson production in small hadronic systems like pp
collisions also provide the mandatory reference for the measurements in
nucleus–nucleus collisions, where a precise pp baseline is needed to single
out and characterize hot medium effects affecting particle production.

In this paper, results on the transverse momentum, rapidity and energy
dependence of the $\phi$ meson production cross section at forward rapidity in
pp collisions at the LHC energies are presented. Results are based on the data
samples collected by ALICE (A Large Ion Collider Experiment) at various
energies during the LHC Run 1 and Run 2 and are compared with the predictions
from the QCD-inspired models PYTHIA 8 [1], PHOJET [6, 7], and EPOS [8, 9, 10].

The production of $\phi$ meson is studied by reconstructing the 2-body decay
$\phi\to\mu^{+}\mu^{-}$ with the ALICE muon spectrometer. Results are reported
in the forward rapidity ($y$) interval $2.5<y<4$ and for $p_{\mathrm{T}}$
values ranging from 0.75 to 10 GeV/$c$, probing both soft and hard regimes of
$\phi$ meson production.

##  2 Experimental apparatus

A full description of the ALICE detector can be found in [11, 12]. The results
presented in this paper have been obtained using muon pairs detected with the
forward muon spectrometer, which covers the pseudorapidity region
$-4<\eta<-2.5$. Throughout this paper, the sign of $\eta$ is determined by the
choice of the ALICE reference system, while the kinematics of the
reconstructed $\phi$ meson is referring to the positive rapidity hemisphere.
The other detectors relevant for the current analysis are the Silicon Pixel
Detector (SPD) of the Inner Tracking System (ITS), the V0 detector and the T0
detector.

The muon spectrometer is composed of a hadron absorber, followed by a set of
tracking stations, a dipole magnet, an iron wall acting as muon filter, and a
set of trigger stations. The hadron absorber, made of carbon, concrete and
steel, is placed 0.9 m away from the interaction point. Its total material
budget corresponds to 10 hadronic interaction lengths. The dipole magnet
provides an integrated magnetic field of 3 $\mathrm{T}\,\mathrm{m}$ in the
horizontal direction, perpendicular to the beam axis. The muon tracking is
provided by five tracking stations, each one composed of two cathode pad
chambers. The first two stations are located upstream of the dipole magnet,
the third one in the middle of its gap and the last two downstream of it. A
1.2 m thick iron wall, corresponding to 7.2 hadronic interaction lengths, is
placed between the tracking and trigger detectors and absorbs the residual
secondary hadrons emerging from the hadron absorber. The combined material
budget of the hadron absorber and the iron wall stops muons with total
momentum lower than $\sim 4$ GeV/$c$. The muon trigger system consists of two
stations, each one composed of two planes of resistive plate chambers (RPC),
installed downstream of the muon filter.

The SPD consists of two silicon pixel layers, covering the pseudorapidity
regions $|\eta|<2.0$ and $|\eta|<1.4$ for the inner and outer layer,
respectively. It is used for the determination of the primary interaction
vertex position. The V0 detector is composed of two scintillator hodoscopes
covering the pseudorapidity regions $-3.7<\eta<-1.7$ and $2.8<\eta<5.1$. The
T0 detector is composed of two arrays of quartz Cherenkov counters, covering
the pseudorapidity ranges $-3.3<\eta<-3$ and $4.6<\eta<4.9$. The coincidence
of a signal in both sides of either the T0 (8 TeV) or the V0 detectors (5.02
and 13 TeV) is used to define the minimum bias (MB) trigger and serves as
input for the luminosity determination. It also allows for the offline
rejection of beam–halo and beam–gas interactions.

##  3 Data analysis

The analysis presented in this paper is based on the data samples collected by
ALICE at $\sqrt{s}=5.02,~{}8$ and 13 TeV. They complement the results already
published at $\sqrt{s}=2.76$ [13] and 7 TeV [14].

### Signal Extraction

The data considered for the signal extraction were collected with a dimuon
trigger, defined as the coincidence of a MB trigger and at least one pair of
track segments reconstructed in the muon trigger system. The muon trigger
system is configured to select muon tracks with a transverse momentum above a
low-$p_{\mathrm{T}}^{\mu}$ threshold, resulting in the conditions
$p_{\mathrm{T}}^{\mu}\gtrsim 1$ GeV/$c$ for the data sample at $\sqrt{s}=8$
TeV, and $p_{\mathrm{T}}^{\mu}\gtrsim 0.5$ GeV/$c$ for the data samples at
$\sqrt{s}=5.02$ and 13 TeV111 Because of the design of the muon trigger
system, the selection on the muon transverse momentum does not correspond to a
sharp value. The reported values are the ones for which the trigger efficiency
is $\sim 50$ % [15]. The different trigger thresholds are due to the fact that
the data taking at $\sqrt{s}=8$ TeV was optimized for high invariant mass
studies. The higher $p_{\mathrm{T}}$ threshold was chosen to reduce the
bandwidth in the data acquisition.. The number of dimuon trigger events thus
selected are $\sim 2\times 10^{7}$ at $\sqrt{s}=5.02$ TeV, $\sim 8.4\times
10^{5}$ at $\sqrt{s}=8$ TeV and $\sim 2.8\times 10^{8}$ at $\sqrt{s}=13$ TeV.

Track reconstruction in the muon spectrometer is based on a Kalman filter
algorithm [16, 17]. Tracks reconstructed in the tracking chambers are
requested to match a track segment reconstructed in the trigger chambers. In
order to remove the tracks close to the acceptance borders, the muon
pseudorapidity is required to be within the interval $-4<\eta_{\mu}<-2.5$.
Dimuons are formed by combining a pair of selected muon tracks, and their
rapidity is explicitly imposed to be within the range $2.5<y<4$.

The opposite-sign dimuon invariant mass spectrum contains a contribution of
both uncorrelated and correlated pairs. The former mainly comes from decays of
pions and kaons, which constitute the combinatorial background. This
background is evaluated with an event mixing technique, in which a muon coming
from an event is paired with a muon from a different event, so that the
resulting muon pairs are uncorrelated by construction. This technique is
described in detail in [14].

The processes contributing to the correlated dimuon mass spectrum in the low
mass region, after combinatorial background subtraction, are the 2-body and
Dalitz decays of the light resonances ($\eta$, $\rho$, $\omega$,
$\eta^{\prime}$, and $\phi$), usually referred to as the hadronic cocktail,
superimposed onto a continuum mainly originating from semi-muonic decays of
charm and beauty hadrons. In extracting the $\phi\to\mu\mu$ signal, however,
no attempt is made to describe the underlying correlated continuum in terms of
open charm and open beauty processes [18]. Instead, a fit is applied to the
mass spectrum after subtraction of the hadronic cocktail with an empirical
function chosen among three options, all providing data description of similar
quality: a polynomial of an appropriate degree, a single or double
exponential222 The double exponential function has the form
$f(m)=(m-2m_{\mu})(A_{1}e^{-m/m_{1}}+A_{2}e^{-m/m_{2}})$, where $A_{1}$,
$A_{2}$, $m_{1}$, $m_{2}$ are the free parameters of the fit. and a Gaussian
function whose width varies as a function of the mass as
$\sigma(m)=\sigma_{0}(1-e^{-\alpha m})$ and which will be referred to as
“variable-width Gaussian” in the following. The degree of the polynomial is
chosen to be the lowest one that satisfactorily fits the data, according to a
statistical criterion based on the F-test, which can be briefly described as
follows. The correlated continuum is first fitted with two polynomials of
degree $n$ and $n+1$ respectively. The null hypothesis is that the continuum
is equivalently described by the lower and the higher degree functions. This
hypothesis is tested by applying the F-test to the results of the fit. If the
resulting $p$-value is larger than 5%, the lowest degree polynomial is used,
otherwise the null hypothesis is rejected and the higher degree polynomial is
chosen. The procedure starts from $n=3$ and is iterated until the F-test
fails. The degree of the polynomial determined by means of the F-test is
typically $n=4$. The F-test criterion is also applied, properly adapted, to
choose among the single or double exponential options.

The reconstructed opposite-sign dimuon mass spectrum is then fitted with a
superposition of the hadronic cocktail and the regularized continuum discussed
above: the procedure is applied independently for each of the three options
considered for the empirical function describing the continuum. The free
parameters of the fit are the normalization of the continuum and the
$\eta\rightarrow\mu\mu\gamma$, $\omega\rightarrow\mu\mu$, and
$\phi\rightarrow\mu\mu$ contributions, while the other processes are fixed
according to the relative branching ratios or cross sections known from
existing measurements [14, 19, 20, 21]. The mass shapes of the processes
included in the hadronic cocktail are extracted through full Monte Carlo (MC)
simulations that include the resolution effects induced by the apparatus. The
raw number of $\phi$ for each $(\Delta p_{\mathrm{T}},\Delta y)$ interval is
then calculated as the mean of the results from the fits with the three
different descriptions of the continuum. The typical reduced $\chi^{2}$ of
these fits is around unity. In Fig. 1 the raw dimuon invariant mass spectrum
after combinatorial background subtraction is shown for $\sqrt{s}=5.02$, 8 and
13 TeV, in their respective $p_{\mathrm{T}}$ ranges. The components of the fit
are also shown. Additional details on the signal extraction procedure are
reported in Ref. [18].

The differential cross section for the $\phi$ meson is calculated as

$\frac{\mathrm{d}^{2}\sigma_{\phi}}{\mathrm{d}y\mathrm{d}p_{\mathrm{T}}}=\frac{1}{\Delta
y\Delta p_{\mathrm{T}}}\times\frac{N^{\mathrm{raw}}_{\phi\to\mu\mu}(\Delta
p_{\mathrm{T}},\Delta y)}{[A\times\varepsilon](\Delta p_{\mathrm{T}},\Delta
y)\times BR_{\phi\to\mu\mu}\times L_{\mathrm{int}}}~{},$

where $N^{\mathrm{raw}}_{\phi\to\mu\mu}(\Delta p_{\mathrm{T}},\Delta y)$ is
the raw number of dimuons in the $\phi\to\mu\mu$ decay channel in a given
$\Delta p_{\mathrm{T}},\Delta y$ interval as obtained from the fit procedure
described above, $[A\times\varepsilon](\Delta p_{\mathrm{T}},\Delta y)$ is the
corresponding product of the geometrical acceptance and the reconstruction
efficiency, $BR_{\phi\to\mu\mu}$ is the branching ratio for the
$\phi\to\mu\mu$ decay, and $L_{\mathrm{int}}$ is the integrated luminosity of
the analyzed data sample. The $[A\times\varepsilon](\Delta
p_{\mathrm{T}},\Delta y)$ factor is evaluated by means of MC simulations,
where the generation of the $\phi\to\mu\mu$ process is based on a parametric
generator that takes as input $p_{\mathrm{T}}$ and $y$ distributions
iteratively tuned to the results of the present analyses. In detail, a first
set of $p_{\mathrm{T}}$ and $y$ distributions, corresponding to the results of
the measurements at $\sqrt{s}=7$ TeV, is taken as an input to the calculation.
The resulting $[A\times\varepsilon](\Delta p_{\mathrm{T}},\Delta y)$ values
are then used to correct the raw distributions obtained from the fits of the
invariant mass spectra at the different energies. The corrected distributions
are then used as input for another $[A\times\varepsilon](\Delta
p_{\mathrm{T}},\Delta y)$ calculation, until convergence is reached. For the
branching ratio of the $\phi\to\mu\mu$ decay, the value measured for the
dielectron channel $BR_{\phi\rightarrow ee}=(2.954\pm 0.030)\times 10^{-4}$
[22] is used instead of the one of the dimuon channel, assuming lepton
universality (i.e. electroweak interaction coupling to all leptons with the
same strength), because the latter is affected by a larger uncertainty. The
integrated luminosity is evaluated for each data set as
$L_{\mathrm{int}}=N_{\mu\mu}\times F_{\mathrm{norm}}/\sigma_{\mathrm{MB}}$,
where $N_{\mu\mu}$ is the number of analyzed opposite-sign dimuon triggered
events, $F_{\mathrm{norm}}$ is the inverse probability to obtain an opposite-
sign dimuon trigger in a MB-triggered event, and $\sigma_{\mathrm{MB}}$ is the
MB cross section measured using the van der Meer scan method [23]. The
resulting values are $L_{\mathrm{int}}(5.02~{}\mathrm{TeV})=1.19\pm 0.03$ pb-1
[24], $L_{\mathrm{int}}(8~{}\mathrm{TeV})=2.32\pm 0.06$ pb-1 [25], and
$L_{\mathrm{int}}(13~{}\mathrm{TeV})=7.35\pm 0.40$ pb-1 [26], where the quoted
uncertainties are the systematic ones, as the statistical uncertainties are
negligible.

Figure 1: Examples of fits to the invariant mass spectra with the hadronic
cocktail in pp collisions at $\sqrt{s}=5.02$, 8 and 13 TeV, for muon pairs in
$2.5<y<4$. The red histograms represent the sum of all simulated
contributions. The correlated continuum has been fitted with a variable-width
Gaussian function.

### Systematic Uncertainties

The systematic uncertainties on the measurement of the $\phi$ meson cross
section include the following contributions: signal extraction,
$A\times\varepsilon$ factor, branching ratio and integrated luminosity.

Three sources of systematic uncertainty have been considered for the
evaluation of $N^{\mathrm{raw}}_{\phi\to\mu\mu}$: the choice of the function
used to describe the correlated continuum, the choice of the fit range, and
the uncertainty on the relative branching ratios or cross sections used to
adjust some of the processes contributing to the hadronic cocktail.

For the description of the correlated continuum, the three empirical functions
described above were considered, providing descriptions of the data of
equivalent quality.

The stability of the results under the choice of the fit range was studied by
modifying the default range $2m_{\mu}<M_{\mu\mu}<2$ GeV/$c^{2}$. Two
alternative upper limits were considered: $2m_{\mu}<M_{\mu\mu}<1.8$
GeV/$c^{2}$ and $2m_{\mu}<M_{\mu\mu}<2.2$ GeV/$c^{2}$.

The third contribution to the systematic uncertainty on the signal extraction
was determined by varying the normalization of the $\rho\to\mu\mu$,
$\eta^{\prime}\to\mu\mu\gamma$, $\eta\to\mu\mu$ and $\omega\to\mu\mu\pi^{0}$
processes relative to the main contributions to the hadronic cocktail
($\eta\to\mu\mu\gamma$, $\omega\to\mu\mu$ and $\phi\to\mu\mu$), by modifying
the relative branching ratios or cross sections. To test the sensitivity of
the fit results on the normalization of the first two processes, the
$\sigma_{\rho}/\sigma_{\omega}$ ratio was varied by 10 % [21], while the
$\sigma_{\eta^{\prime}}/\sigma_{\eta}$ ratio was varied by 50 %, according to
the differences between $\sigma_{\eta^{\prime}}/\sigma_{\phi}$ obtained with
calculations performed with PHOJET and with the PYTHIA 6 tunes D6T [27],
ATLAS-CSC [28], Perugia 0 and Perugia 11 [29]. To account for the variation of
the other two processes, the relative branching ratios of the 2-body and
Dalitz decay channels of $\eta$ and $\omega$ mesons were varied by one
standard deviation, taking into account the values and the uncertainties
reported in Ref. [22].

Table 1: Sources of systematic uncertainties in the measurement of the $\phi$ yield at various energies for rapidity-integrated ($y$-int.) and double-differential (2-diff.) analysis. $\sqrt{s}$ | 5 TeV | 8 TeV | 13 TeV
---|---|---|---
|  |  $y$-int. | 2-diff. |  $y$-int. |  $y$-int. | 2-diff.
$p_{\mathrm{T}},y$ dependent, bin-to-bin uncorr. | Extraction (%) | 3.7 | 3.1-4.2 | 2.1 | 3 - 12 | 2.6 - 20
$p_{\mathrm{T}},y$ dependent, bin-to-bin corr. | Tracking (%) | 2 | 2 | 7 | 4 | 4
Trigger (%) | 2.4-10.5 | 2.4-10.5 | 3.9-8.5 | 2.4 - 13 | 1 - 17
Matching (%) | 1 | 1 | 1 | 1 | 1
$A\times\varepsilon$ (%) |  $<$1 |  $<$1 | 3 |  $<$1 |  $<$1
Global | Branching Ratio (%) | 1 | 1 | 1 | 1 | 1
Luminosity (%) | 2.3 | 2.3 | 2.6 | 5.1 | 5.1

The total systematic uncertainty on $N^{\mathrm{raw}}_{\phi\to\mu\mu}$ is
evaluated as the RMS of the values resulting from the above tests. At
$\sqrt{s}=5.02$ and 8 TeV the variations of this contribution as a function of
$p_{\mathrm{T}}$ are found to be small, so their mean value is assumed as
final systematic uncertainty for the signal extraction. At $\sqrt{s}=13$ TeV,
the systematic uncertainty takes larger values in the lowest region of the
measured $p_{\mathrm{T}}$ range, mainly due to a progressive worsening in the
description of the correlated continuum above the $\phi$ meson mass.

A potential source of systematic uncertainty on the correction for geometrical
acceptance and reconstruction efficiency is associated to the choice of the
input kinematic distributions used to generate the $\phi$ meson in the MC
simulations. However, at $\sqrt{s}=5.02$ and $13$ TeV these distributions are
tuned to the measured data and the corrections are performed in sufficiently
small $p_{\mathrm{T}}$ and rapidity intervals. The resulting uncertainty,
evaluated by varying the parameters of the $\phi$ meson kinematic
distributions, is found to be negligible. At $\sqrt{s}=8$ TeV only the
$p_{\mathrm{T}}$ distribution was tuned to the data. To evaluate the
uncertainty due to the input rapidity distribution, alternative MC simulations
at $\sqrt{s}=8$ TeV were performed using as input the rapidity distributions
measured at $\sqrt{s}=5.02$ and $13$ TeV, and the corresponding
$A\times\varepsilon$ factors were calculated. The half-difference between the
two results is taken as the uncertainty due to the input rapidity distribution
at $\sqrt{s}=8$ TeV and amounts to 3%.

In addition to that, three specific sources of systematic uncertainty were
considered for the reconstruction efficiency: tracking efficiency, trigger
efficiency and matching efficiency. The tracking efficiency was evaluated both
from data and MC simulations. To this purpose, the MC was tuned to the
detector condition during data taking, in order to reproduce the uncertainties
arising from correlated and anticorrelated dead areas in the muon tracker. As
the same tracking algorithm is applied on MC and data, the difference observed
between the two estimates is assumed as the systematic uncertainty on the
tracking efficiency. The uncertainty on the trigger efficiency is mainly
related to the imperfections in the description of two effects in the MC
simulations: the interaction of the muons with the hadron absorber and the
muon filter, and the occupancy of the trigger chambers. The uncertainty
corresponding to the first effect was estimated as the difference between
$A\times\varepsilon$ obtained from simulations implementing GEANT3 or GEANT4
as alternative transport codes. The uncertainty on the occupancy of the
trigger chambers was evaluated comparing $A\times\varepsilon$ resulting from
simulations where the MC signal was simulated either as generated or by
embedding it in the environment of a real event. The uncertainty on the
matching efficiency is related to the choice of the $\chi^{2}$ cut used to
define the matching between the tracks reconstructed in the tracking system
and the track segments reconstructed in the trigger chambers, and amounts to 1
% for all data samples.

The remaining contributions to the systematic uncertainty are the ones due to
the branching ratio of the $\phi\to ee$ decay channel ($\sim$1 %) [22] and to
the integrated luminosity (2.1 %, 2.4 % and 5.0 % at $\sqrt{s}=5.02,~{}8$ and
13 TeV respectively). Two terms contribute to the uncertainty on the
luminosity: the uncertainty on the visible cross section evaluated with the
van der Meer scan technique and the difference between the luminosity measured
with the T0 and the V0 detectors [24, 25, 26], while the uncertainty on the
normalization factor $F_{\mathrm{norm}}$, evaluated by calculating it with two
different methods, amounts to 1% for all data samples.

The systematic uncertainties listed above depend on both transverse momentum
and rapidity, with the exception of the ones on the branching ratio and
integrated luminosity. The sources of systematic uncertainty characterized by
a dependence on transverse momentum and rapidity are classified into bin-to-
bin uncorrelated (signal extraction) and bin-to-bin correlated (tracking and
trigger efficiency, $A\times\varepsilon$ estimation, matching efficiency).

The contributions from the different sources of systematic uncertainties are
reported in Table 1, for both the rapidity-integrated and the double-
differential analyses.

##  4 Results

Figure 2: Differential $\phi$ meson production cross section
$\mathrm{d}^{2}\sigma/(\mathrm{d}y\mathrm{d}p_{\mathrm{T}})$ as a function of
$p_{\mathrm{T}}$ at $\sqrt{s}=5.02$ TeV, $\sqrt{s}=8$ TeV and $\sqrt{s}=13$
TeV, measured in the $\mu^{+}\mu^{-}$ decay channel in the rapidity interval
$2.5<y<4$ (full symbols) and in the K+K- channel at midrapidity (open
symbols). The boxes represent the systematic uncertainties, the error bars the
statistical uncertainties. The data points are fitted with a Levy-Tsallis
function. The ratio between the fit function at forward rapidity and the data
at midrapidity is plotted in the bottom panels. Figure 3: Top: differential
$\phi$ meson production cross section
$\mathrm{d}^{2}\sigma/(\mathrm{d}y\mathrm{d}p_{\mathrm{T}}$) as a function of
$p_{\mathrm{T}}$ at $\sqrt{s}=$2.76, 5.02, 7, 8 and 13 TeV. The boxes
represent the systematic uncertainties, the error bars the statistical
uncertainties. Bottom: ratio between the cross sections measured at several
energies to the one obtained at $\sqrt{s}=13$ TeV.

The differential $\phi$ meson production cross section at $\sqrt{s}=5.02$, 8
and 13 TeV, measured in the rapidity range $2.5<y<4$, is shown in Fig. 2 as a
function of the transverse momentum. The cross sections are fitted with a
Levy-Tsallis function [30, 31]:

$f(p_{\mathrm{T}})=N_{0}\frac{(n-1)(n-2)}{nT[nT+m(n-2)]}p_{\mathrm{T}}\left[1+\frac{m_{\mathrm{T}}-m}{nT}\right]^{-n},$

where $m_{\mathrm{T}}=\sqrt{p_{\mathrm{T}}^{2}+m_{\phi}^{2}}$ is the
transverse mass and $N_{0}$, $n$ and $T$ are the free parameters of the fit.
While the total systematic uncertainty is shown in the spectra of Fig. 2, only
the contribution coming from the signal extraction (added in quadrature to the
statistical uncertainty) is considered when performing the fit, since the
signal extraction is the only source of systematic uncertainty resulting in
fully bin-to-bin uncorrelated fluctuations of the measured points.

Table 2: Parameters of the Levy-Tsallis fits to the differential cross sections. The average $p_{\mathrm{T}}$, calculated using the fit functions, is also reported. Rapidity interval |  ${\mathchoice{\raisebox{0.0pt}{$\displaystyle\chi$}}{\raisebox{0.0pt}{$\textstyle\chi$}}{\raisebox{0.0pt}{$\scriptstyle\chi$}}{\raisebox{0.0pt}{$\scriptscriptstyle\chi$}}}^{2}$/NdF |  $T$ (GeV) | $n$ |  $\langle p_{\mathrm{T}}\rangle$ (GeV/$c$)
---|---|---|---|---
$\sqrt{s}=5.02$ TeV |
$2.5<y<4$ | 1.41 | $0.273\pm 0.011$ | $7.86\pm 0.38$ | $1.031\pm 0.016$
$2.5<y<3$ | 1.57 | 0.273 (fixed) | $7.49\pm 0.21$ | $1.045\pm 0.009$
$3<y<3.25$ | 0.95 | 0.273 (fixed) | $7.41\pm 0.21$ | $1.050\pm 0.010$
$3.25<y<3.5$ | 0.72 | 0.273 (fixed) | $7.85\pm 0.22$ | $1.029\pm 0.009$
$3.5<y<4$ | 1.91 | 0.273 (fixed) | $8.74\pm 0.32$ | $0.999\pm 0.009$
$\sqrt{s}=8$ TeV |
$2.5<y<4$ | 0.52 | $0.310\pm 0.045$ | $7.92\pm 1.00$ | $1.132\pm 0.049$
$\sqrt{s}=13$ TeV |
$2.5<y<4$ | 1.13 | $0.341\pm 0.005$ | $8.24\pm 0.14$ | $1.206\pm 0.006$
$2.5<y<2.75$ | 2.03 | 0.341 (fixed) | $7.71\pm 0.09$ | $1.231\pm 0.005$
$2.75<y<3$ | 1.90 | 0.341 (fixed) | $8.45\pm 0.09$ | $1.196\pm 0.004$
$3<y<3.25$ | 0.92 | 0.341 (fixed) | $8.26\pm 0.09$ | $1.204\pm 0.004$
$3.25<y<3.5$ | 0.61 | 0.341 (fixed) | $8.54\pm 0.11$ | $1.192\pm 0.004$
$3.5<y<4$ | 0.75 | 0.341 (fixed) | $8.69\pm 0.12$ | $1.186\pm 0.005$

The results of the fits are summarized in Table 2. The average
$p_{\mathrm{T}}$, calculated using the fit functions, increases by about 20 %
when increasing the center-of-mass energy from 5.02 to 13 TeV.

In the same figure, the spectra at midrapidity measured by ALICE [32, 33, 34],
normalized using the inelastic cross sections measured in [35], are also
reported for comparison. In the bottom panels, the ratio between the fits with
the Levy-Tsallis functions at forward rapidity and the data at midrapidity is
shown. The cross section in the rapidity range covered by this analysis is
approximately one half of the one measured at midrapidity. The
$p_{\mathrm{T}}$ spectra are harder at midrapidity. The difference between the
slopes at forward and midrapidity is more evident at $\sqrt{s}=5.02$ TeV, the
lowest energy considered.

Figure 4: Top: differential $\phi$ meson production cross section
$\mathrm{d}^{2}\sigma/\mathrm{d}y\mathrm{d}p_{\mathrm{T}}$ as a function of
$p_{\mathrm{T}}$ at $\sqrt{s}=5.02$ TeV (left), $\sqrt{s}=8$ TeV (center) and
$\sqrt{s}=13$ TeV (right) in the rapidity interval $2.5<y<4$, compared with
EPOS 3 [8, 9, 10], PHOJET [6, 7] and the Monash 2013 tune of PYTHIA 8.1 [1].
The boxes represent the systematic uncertainties, the error bars the
statistical uncertainties. Bottom: ratio between the measured cross section
and the calculations.

Figure 5: Differential $\phi$ meson production cross section
$\mathrm{d}^{2}\sigma/\mathrm{d}y\mathrm{d}p_{\mathrm{T}}$ as a function of
$p_{\mathrm{T}}$ at $\sqrt{s}=5.02$ TeV (left) and $\sqrt{s}=13$ TeV (right)
in several rapidity intervals. The boxes represent the systematic
uncertainties, the error bars the statistical uncertainties. Data are fitted
with a Levy-Tsallis function.

In Fig. 3, the differential cross sections are compared with the previously
published results at $\sqrt{s}=2.76$ TeV [13] and $\sqrt{s}=7$ TeV [14]. The
ratio to the measurement at $\sqrt{s}=13$ TeV is also reported in the bottom
panel for a direct comparison. A hardening of the $p_{\mathrm{T}}$ spectra is
observed when increasing the center-of-mass energy. The values of the ratio at
$p_{\mathrm{T}}\sim 5$ GeV/$c$ change from $\sim 0.2$ for $\sqrt{s}=2.76$ TeV
to $\sim 0.65$ for $\sqrt{s}=8$ TeV.

In Fig. 4 data are compared with the calculations performed with the models
EPOS 3 [8, 9, 10], PHOJET [6, 7] and the Monash 2013 tune of PYTHIA 8.1 [1].
At all collision energies, EPOS 3 underestimates the cross section at low
$p_{\mathrm{T}}$, while it describes the data for $p_{\mathrm{T}}>4$ GeV/$c$.
Vice versa, PHOJET reproduces the low-$p_{\mathrm{T}}$ region up to
$p_{\mathrm{T}}\sim 2$ GeV/$c$, but does not describe the shape of the
spectra, which is predicted to be harder by the model. PYTHIA 8.1 with the
Monash 2013 tune better reproduces the shape of the differential cross section
at all energies. However, it still underestimates the measurement at
$\sqrt{s}=5.02$ and 8 TeV, and reproduces the results at $\sqrt{s}=13$ TeV at
high $p_{\mathrm{T}}$ only, while it underestimates the data by about 20% at
low $p_{\mathrm{T}}$.

Figure 6: Differential $\phi$ meson production cross section
$\mathrm{d}^{2}\sigma/\mathrm{d}y\mathrm{d}p_{\mathrm{T}}$ as a function of
rapidity at $\sqrt{s}=5.02$ TeV (left) and $\sqrt{s}=13$ TeV (right) in
several $p_{\mathrm{T}}$ intervals, compared with EPOS 3 [8, 9, 10], PHOJET
[6, 7] and the Monash 2013 tune of PYTHIA 8.1 [1]. The ratio of the data to
the lowest $p_{\mathrm{T}}$ interval is shown in the bottom panel. The boxes
represent the systematic uncertainties, the error bars the statistical
uncertainties.

At $\sqrt{s}=5.02$ and 13 TeV, the $p_{\mathrm{T}}$ dependence of the
differential cross section was also measured in several rapidity intervals.
Results are shown in Fig. 5. The $p_{\mathrm{T}}$ coverage depends on the
rapidity interval: in fact, at low $p_{\mathrm{T}}$, $A\times\varepsilon$
significantly increases with rapidity; on the other side, at high
$p_{\mathrm{T}}$, high rapidity dimuons are more affected by statistical
limitations than low rapidity ones. A significant dependence on
$p_{\mathrm{T}}$ and rapidity is also observed for the systematic uncertainty,
namely for the contributions coming from the signal extraction and the trigger
efficiency. Since this effect is related to the S/B and the data taking
conditions, the impact on the results depends on the considered data sample:
this explains the slight difference in the $p_{\mathrm{T}}$ and rapidity
coverage of the measurements at $\sqrt{s}=5$ and 13 TeV. The
$p_{\mathrm{T}}-$differential cross sections are fitted with a Levy-Tsallis
function, fixing the $T$ parameter to the value obtained from the fit in the
full range $2.5<y<4$. Fit results are reported in Tab. 2, together with the
average $p_{\mathrm{T}}$ calculated using the fit functions. For both
energies, $\sqrt{s}=5.02$ and 13 TeV, a moderate decrease of $\langle
p_{\mathrm{T}}\rangle$ as a function of rapidity is observed. However, the
relatively large uncertainties do not allow to draw any firm conclusion on
this trend.

To cross check the consistency between the results shown in Fig. 2 and 5, the
latter were integrated over the rapidity range $2.5<y<4$. The differences
between the two methods in the common $p_{\mathrm{T}}$ region amounts to about
$5\,\%$. As a comparison, the systematic uncertainty on the cross section due
to signal extraction is about $4\,\%$.

The differential cross sections measured at $\sqrt{s}=5.02$ and 13 TeV are
shown in Fig. 6 as a function of rapidity for several $p_{\mathrm{T}}$
intervals, together with the corresponding values at midrapidity [32, 33, 34].
The calculations performed with EPOS 3, PHOJET and PYTHIA 8.1 are also
plotted. None of the considered models manages to reproduce the measured
rapidity spectra in all the $p_{\mathrm{T}}$ ranges, neither at 5 TeV nor at
13 TeV.

In the bottom panel of Fig. 6, the ratio of the rapidity distributions in a
given $p_{\mathrm{T}}$ interval to the lowest is shown, scaled such that the
ratio at midrapidity is set to unity. A moderate narrowing of the rapidity
distribution is observed when increasing the transverse momentum. This effect
depends on the collision energy, being stronger for the lowest $\sqrt{s}$.

Figure 7: $\phi$ meson production cross section as a function of $\sqrt{s}$
for $1.5<p_{\mathrm{T}}<5$ GeV/$c$ and $2.5<y<4$, compared with EPOS 3 [8, 9,
10], PHOJET [6, 7] and the Monash 2013 tune of PYTHIA 8.1 [1]. The boxes
represent the systematic uncertainties, the error bars the statistical
uncertainties.

The $\phi$ meson production cross section integrated in the $p_{\mathrm{T}}$
range $1.5<p_{\mathrm{T}}<5$ GeV/$c$, common to the five energies, is plotted
as a function of $\sqrt{s}$ in Fig. 7. Results are compared with EPOS 3,
PHOJET and PYTHIA 8.1 with the Monash 2013 tune. In the $p_{\mathrm{T}}$
interval considered for this study, the evolution of the cross section with
the collision energy is well described by PHOJET. Both EPOS 3 and PYTHIA
8.1/Monash 2013 underestimate the absolute values by a factor ranging from
about 1.2 to 1.7, while reproducing the trend as a function of the center-of-
mass energy. The differences between the measurement and the calculations are
mainly due to the overestimation of the cross section at the lowest
$p_{\mathrm{T}}$ accessible to the measurement.

##  5 Conclusions

The $\phi$ meson production cross section was measured in pp collisions at the
center-of-mass energies $\sqrt{s}=5.02,~{}8,~{}13$ TeV in the forward rapidity
region $2.5<y<4$, complementing the previously published results at
$\sqrt{s}=2.76$ and 7 TeV. The $p_{\mathrm{T}}$ spectra are well described by
a Levy-Tsallis function. A hardening of the $p_{\mathrm{T}}$-differential
cross section with the collision energy is observed, as is evinced from the
comparison between the average values of the transverse momentum or from the
ratios between the differential cross sections as a function of
$p_{\mathrm{T}}$. At each energy, the $p_{\mathrm{T}}$ spectra at midrapidity
are harder than the corresponding ones at forward rapidity. Results were
compared with the predictions from PYTHIA 8.1-Monash 2013, EPOS 3 and PHOJET.
PHOJET reproduces the cross section at low $p_{\mathrm{T}}$, while EPOS 3
better approaches the data for $p_{\mathrm{T}}>4$ GeV/$c$. PYTHIA 8.1 with the
Monash 2013 tune fairly describes the shape of the
$p_{\mathrm{T}}$-differential cross section at all energies and reproduces the
results at $\sqrt{s}=13$ TeV, but underestimates the measurement at lower
energies.

At $\sqrt{s}=5.02$ and 13 TeV, a double differential study of the $\phi$ meson
production cross section was performed as a function of $p_{\mathrm{T}}$ and
rapidity. None of the calculations manages to reproduce the rapidity spectra
both at low and high $p_{\mathrm{T}}$. A small decrease of the $\langle
p_{\mathrm{T}}\rangle$ value was observed with increasing rapidity, although
with relatively large uncertainties. Analogously, the dependence of the cross
section on rapidity appears to be slightly narrower when going towards higher
$p_{\mathrm{T}}$ values, thus showing that the correlation between
$p_{\mathrm{T}}$ and rapidity cannot be neglected in this rapidity range.

## Acknowledgements

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

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##  Appendix A The ALICE Collaboration

S. Acharya142, D. Adamová97, A. Adler75, J. Adolfsson82, G. Aglieri Rinella35,
M. Agnello31, N. Agrawal55, Z. Ahammed142, S. Ahmad16, S.U. Ahn77, I. Ahuja39,
Z. Akbar52, A. Akindinov94, M. Al-Turany109, D. Aleksandrov90, B.
Alessandro60, H.M. Alfanda7, R. Alfaro Molina72, B. Ali16, Y. Ali14, A.
Alici26, N. Alizadehvandchali126, A. Alkin35, J. Alme21, T. Alt69, L.
Altenkamper21, I. Altsybeev114, M.N. Anaam7, C. Andrei49, D. Andreou92, A.
Andronic145, M. Angeletti35, V. Anguelov106, F. Antinori58, P. Antonioli55, C.
Anuj16, N. Apadula81, L. Aphecetche116, H. Appelshäuser69, S. Arcelli26, R.
Arnaldi60, I.C. Arsene20, M. Arslandok147,106, A. Augustinus35, R.
Averbeck109, S. Aziz79, M.D. Azmi16, A. Badalà57, Y.W. Baek42, X. Bai109, R.
Bailhache69, Y. Bailung51, R. Bala103, A. Balbino31, A. Baldisseri139, M.
Ball44, D. Banerjee4, R. Barbera27, L. Barioglio107,25, M. Barlou86, G.G.
Barnaföldi146, L.S. Barnby96, V. Barret136, C. Bartels129, K. Barth35, E.
Bartsch69, F. Baruffaldi28, N. Bastid136, S. Basu82,144, G. Batigne116, B.
Batyunya76, D. Bauri50, J.L. Bazo Alba113, I.G. Bearden91, C. Beattie147, I.
Belikov138, A.D.C. Bell Hechavarria145, F. Bellini26,35, R. Bellwied126, S.
Belokurova114, V. Belyaev95, G. Bencedi70, S. Beole25, A. Bercuci49, Y.
Berdnikov100, A. Berdnikova106, D. Berenyi146, L. Bergmann106, M.G. Besoiu68,
L. Betev35, P.P. Bhaduri142, A. Bhasin103, I.R. Bhat103, M.A. Bhat4, B.
Bhattacharjee43, P. Bhattacharya23, L. Bianchi25, N. Bianchi53, J. Bielčík38,
J. Bielčíková97, J. Biernat119, A. Bilandzic107, G. Biro146, S. Biswas4, J.T.
Blair120, D. Blau90, M.B. Blidaru109, C. Blume69, G. Boca29, F. Bock98, A.
Bogdanov95, S. Boi23, J. Bok62, L. Boldizsár146, A. Bolozdynya95, M.
Bombara39, P.M. Bond35, G. Bonomi141, H. Borel139, A. Borissov83, H. Bossi147,
E. Botta25, L. Bratrud69, P. Braun-Munzinger109, M. Bregant122, M. Broz38,
G.E. Bruno108,34, M.D. Buckland129, D. Budnikov110, H. Buesching69, S.
Bufalino31, O. Bugnon116, P. Buhler115, Z. Buthelezi73,133, J.B. Butt14, S.A.
Bysiak119, D. Caffarri92, M. Cai28,7, H. Caines147, A. Caliva109, E. Calvo
Villar113, J.M.M. Camacho121, R.S. Camacho46, P. Camerini24, F.D.M. Canedo122,
A.A. Capon115, F. Carnesecchi35,26, R. Caron139, J. Castillo Castellanos139,
E.A.R. Casula23, F. Catalano31, C. Ceballos Sanchez76, P. Chakraborty50, S.
Chandra142, S. Chapeland35, M. Chartier129, S. Chattopadhyay142, S.
Chattopadhyay111, A. Chauvin23, T.G. Chavez46, C. Cheshkov137, B. Cheynis137,
V. Chibante Barroso35, D.D. Chinellato123, S. Cho62, P. Chochula35, P.
Christakoglou92, C.H. Christensen91, P. Christiansen82, T. Chujo135, C.
Cicalo56, L. Cifarelli26, F. Cindolo55, M.R. Ciupek109, G. ClaiII,55, J.
CleymansI,125, F. Colamaria54, J.S. Colburn112, D. Colella108,54,34,146, A.
Collu81, M. Colocci35,26, M. ConcasIII,60, G. Conesa Balbastre80, Z. Conesa
del Valle79, G. Contin24, J.G. Contreras38, T.M. Cormier98, P. Cortese32, M.R.
Cosentino124, F. Costa35, S. Costanza29, P. Crochet136, E. Cuautle70, P. Cui7,
L. Cunqueiro98, A. Dainese58, F.P.A. Damas116,139, M.C. Danisch106, A. Danu68,
I. Das111, P. Das88, P. Das4, S. Das4, S. Dash50, S. De88, A. De Caro30, G. de
Cataldo54, L. De Cilladi25, J. de Cuveland40, A. De Falco23, D. De Gruttola30,
N. De Marco60, C. De Martin24, S. De Pasquale30, S. Deb51, H.F. Degenhardt122,
K.R. Deja143, L. Dello Stritto30, S. Delsanto25, W. Deng7, P. Dhankher19, D.
Di Bari34, A. Di Mauro35, R.A. Diaz8, T. Dietel125, Y. Ding137,7, R. Divià35,
D.U. Dixit19, Ø. Djuvsland21, U. Dmitrieva64, J. Do62, A. Dobrin68, B.
Dönigus69, O. Dordic20, A.K. Dubey142, A. Dubla109,92, S. Dudi102, M.
Dukhishyam88, P. Dupieux136, T.M. Eder145, R.J. Ehlers98, V.N. Eikeland21, D.
Elia54, B. Erazmus116, F. Ercolessi26, F. Erhardt101, A. Erokhin114, M.R.
Ersdal21, B. Espagnon79, G. Eulisse35, D. Evans112, S. Evdokimov93, L.
Fabbietti107, M. Faggin28, J. Faivre80, F. Fan7, A. Fantoni53, M. Fasel98, P.
Fecchio31, A. Feliciello60, G. Feofilov114, A. Fernández Téllez46, A.
Ferrero139, A. Ferretti25, V.J.G. Feuillard106, J. Figiel119, S. Filchagin110,
D. Finogeev64, F.M. Fionda56,21, G. Fiorenza35,108, F. Flor126, A.N.
Flores120, S. Foertsch73, P. Foka109, S. Fokin90, E. Fragiacomo61, E.
Frajna146, U. Fuchs35, N. Funicello30, C. Furget80, A. Furs64, J.J.
Gaardhøje91, M. Gagliardi25, A.M. Gago113, A. Gal138, C.D. Galvan121, P.
Ganoti86, C. Garabatos109, J.R.A. Garcia46, E. Garcia-Solis10, K. Garg116, C.
Gargiulo35, A. Garibli89, K. Garner145, P. Gasik109, E.F. Gauger120, A.
Gautam128, M.B. Gay Ducati71, M. Germain116, J. Ghosh111, P. Ghosh142, S.K.
Ghosh4, M. Giacalone26, P. Gianotti53, P. Giubellino109,60, P. Giubilato28,
A.M.C. Glaenzer139, P. Glässel106, V. Gonzalez144, L.H. González-Trueba72, S.
Gorbunov40, L. Görlich119, S. Gotovac36, V. Grabski72, L.K. Graczykowski143,
L. Greiner81, A. Grelli63, C. Grigoras35, V. Grigoriev95, A. GrigoryanI,1, S.
Grigoryan76,1, O.S. Groettvik21, F. Grosa35,60, J.F. Grosse-Oetringhaus35, R.
Grosso109, G.G. Guardiano123, R. Guernane80, M. Guilbaud116, M. Guittiere116,
K. Gulbrandsen91, T. Gunji134, A. Gupta103, R. Gupta103, I.B. Guzman46, S.P.
Guzman46, L. Gyulai146, M.K. Habib109, C. Hadjidakis79, H. Hamagaki84, G.
Hamar146, M. Hamid7, R. Hannigan120, M.R. Haque143,88, A. Harlenderova109,
J.W. Harris147, A. Harton10, J.A. Hasenbichler35, H. Hassan98, D.
Hatzifotiadou55, P. Hauer44, L.B. Havener147, S. Hayashi134, S.T. Heckel107,
E. Hellbär69, H. Helstrup37, T. Herman38, E.G. Hernandez46, G. Herrera
Corral9, F. Herrmann145, K.F. Hetland37, H. Hillemanns35, C. Hills129, B.
Hippolyte138, B. Hohlweger92,107, J. Honermann145, G.H. Hong148, D. Horak38,
S. Hornung109, R. Hosokawa15, P. Hristov35, C. Huang79, C. Hughes132, P.
Huhn69, T.J. Humanic99, H. Hushnud111, L.A. Husova145, N. Hussain43, D.
Hutter40, J.P. Iddon35,129, R. Ilkaev110, H. Ilyas14, M. Inaba135, G.M.
Innocenti35, M. Ippolitov90, A. Isakov38,97, M.S. Islam111, M. Ivanov109, V.
Ivanov100, V. Izucheev93, B. Jacak81, N. Jacazio35, P.M. Jacobs81, S.
Jadlovska118, J. Jadlovsky118, S. Jaelani63, C. Jahnke123,122, M.J.
Jakubowska143, M.A. Janik143, T. Janson75, M. Jercic101, O. Jevons112, F.
Jonas98,145, P.G. Jones112, J.M. Jowett 35,109, J. Jung69, M. Jung69, A.
Junique35, A. Jusko112, J. Kaewjai117, P. Kalinak65, A. Kalweit35, V.
Kaplin95, S. Kar7, A. Karasu Uysal78, D. Karatovic101, O. Karavichev64, T.
Karavicheva64, P. Karczmarczyk143, E. Karpechev64, A. Kazantsev90, U.
Kebschull75, R. Keidel48, D.L.D. Keijdener63, M. Keil35, B. Ketzer44, Z.
Khabanova92, A.M. Khan7, S. Khan16, A. Khanzadeev100, Y. Kharlov93, A.
Khatun16, A. Khuntia119, B. Kileng37, B. Kim17,62, D. Kim148, D.J. Kim127,
E.J. Kim74, J. Kim148, J.S. Kim42, J. Kim106, J. Kim148, J. Kim74, M. Kim106,
S. Kim18, T. Kim148, S. Kirsch69, I. Kisel40, S. Kiselev94, A. Kisiel143, J.L.
Klay6, J. Klein35, S. Klein81, C. Klein-Bösing145, M. Kleiner69, T.
Klemenz107, A. Kluge35, A.G. Knospe126, C. Kobdaj117, M.K. Köhler106, T.
Kollegger109, A. Kondratyev76, N. Kondratyeva95, E. Kondratyuk93, J. Konig69,
S.A. Konigstorfer107, P.J. Konopka35,2, G. Kornakov143, S.D. Koryciak2, L.
Koska118, A. Kotliarov97, O. Kovalenko87, V. Kovalenko114, M. Kowalski119, I.
Králik65, A. Kravčáková39, L. Kreis109, M. Krivda112,65, F. Krizek97, K.
Krizkova Gajdosova38, M. Kroesen106, M. Krüger69, E. Kryshen100, M.
Krzewicki40, V. Kučera35, C. Kuhn138, P.G. Kuijer92, T. Kumaoka135, D.
Kumar142, L. Kumar102, N. Kumar102, S. Kundu35,88, P. Kurashvili87, A.
Kurepin64, A.B. Kurepin64, A. Kuryakin110, S. Kushpil97, J. Kvapil112, M.J.
Kweon62, J.Y. Kwon62, Y. Kwon148, S.L. La Pointe40, P. La Rocca27, Y.S. Lai81,
A. Lakrathok117, M. Lamanna35, R. Langoy131, K. Lapidus35, P. Larionov53, E.
Laudi35, L. Lautner35,107, R. Lavicka38, T. Lazareva114, R. Lea141,24, J.
Lee135, J. Lehrbach40, R.C. Lemmon96, I. León Monzón121, E.D. Lesser19, M.
Lettrich35,107, P. Lévai146, X. Li11, X.L. Li7, J. Lien131, R. Lietava112, B.
Lim17, S.H. Lim17, V. Lindenstruth40, A. Lindner49, C. Lippmann109, A. Liu19,
J. Liu129, I.M. Lofnes21, V. Loginov95, C. Loizides98, P. Loncar36, J.A.
Lopez106, X. Lopez136, E. López Torres8, J.R. Luhder145, M. Lunardon28, G.
Luparello61, Y.G. Ma41, A. Maevskaya64, M. Mager35, T. Mahmoud44, A. Maire138,
M. Malaev100, Q.W. Malik20, L. MalininaIV,76, D. Mal’Kevich94, N. Mallick51,
P. Malzacher109, G. Mandaglio33,57, V. Manko90, F. Manso136, V. Manzari54, Y.
Mao7, J. Mareš67, G.V. Margagliotti24, A. Margotti55, A. Marín109, C.
Markert120, M. Marquard69, N.A. Martin106, P. Martinengo35, J.L. Martinez126,
M.I. Martínez46, G. Martínez García116, S. Masciocchi109, M. Masera25, A.
Masoni56, L. Massacrier79, A. Mastroserio140,54, A.M. Mathis107, O.
Matonoha82, P.F.T. Matuoka122, A. Matyja119, C. Mayer119, A.L. Mazuecos35, F.
Mazzaschi25, M. Mazzilli35,54, M.A. Mazzoni59, J.E. Mdhluli133, A.F.
Mechler69, F. Meddi22, Y. Melikyan64, A. Menchaca-Rocha72, E. Meninno115,30,
A.S. Menon126, M. Meres13, S. Mhlanga125,73, Y. Miake135, L. Micheletti60,25,
L.C. Migliorin137, D.L. Mihaylov107, K. Mikhaylov76,94, A.N. Mishra146, D.
Miśkowiec109, A. Modak4, A.P. Mohanty63, B. Mohanty88, M. Mohisin Khan16, Z.
Moravcova91, C. Mordasini107, D.A. Moreira De Godoy145, L.A.P. Moreno46, I.
Morozov64, A. Morsch35, T. Mrnjavac35, V. Muccifora53, E. Mudnic36, D.
Mühlheim145, S. Muhuri142, J.D. Mulligan81, A. Mulliri23, M.G. Munhoz122, R.H.
Munzer69, H. Murakami134, S. Murray125, L. Musa35, J. Musinsky65, C.J.
Myers126, J.W. Myrcha143, B. Naik50, R. Nair87, B.K. Nandi50, R. Nania55, E.
Nappi54, M.U. Naru14, A.F. Nassirpour82, A. Nath106, C. Nattrass132, A.
Neagu20, L. Nellen70, S.V. Nesbo37, G. Neskovic40, D. Nesterov114, B.S.
Nielsen91, S. Nikolaev90, S. Nikulin90, V. Nikulin100, F. Noferini55, S.
Noh12, P. Nomokonov76, J. Norman129, N. Novitzky135, P. Nowakowski143, A.
Nyanin90, J. Nystrand21, M. Ogino84, A. Ohlson82, V.A. Okorokov95, J.
Oleniacz143, A.C. Oliveira Da Silva132, M.H. Oliver147, A. Onnerstad127, C.
Oppedisano60, A. Ortiz Velasquez70, T. Osako47, A. Oskarsson82, J.
Otwinowski119, K. Oyama84, Y. Pachmayer106, S. Padhan50, D. Pagano141, G.
Paić70, A. Palasciano54, J. Pan144, S. Panebianco139, V. Papikyan1, P.
Pareek142, J. Park62, J.E. Parkkila127, S.P. Pathak126, R.N. Patra103, B.
Paul23, J. Pazzini141, H. Pei7, T. Peitzmann63, X. Peng7, L.G. Pereira71, H.
Pereira Da Costa139, D. Peresunko90, G.M. Perez8, S. Perrin139, Y. Pestov5, V.
Petráček38, M. Petrovici49, R.P. Pezzi71, S. Piano61, M. Pikna13, P.
Pillot116, O. Pinazza55,35, L. Pinsky126, C. Pinto27, S. Pisano53, M.
Płoskoń81, M. Planinic101, F. Pliquett69, M.G. Poghosyan98, B. Polichtchouk93,
S. Politano31, N. Poljak101, A. Pop49, S. Porteboeuf-Houssais136, J. Porter81,
V. Pozdniakov76, S.K. Prasad4, R. Preghenella55, F. Prino60, C.A. Pruneau144,
I. Pshenichnov64, M. Puccio35, S. Qiu92, L. Quaglia25, R.E. Quishpe126, S.
Ragoni112, A. Rakotozafindrabe139, L. Ramello32, F. Rami138, S.A.R. Ramirez46,
A.G.T. Ramos34, R. Raniwala104, S. Raniwala104, S.S. Räsänen45, R. Rath51, I.
Ravasenga92, K.F. Read98,132, A.R. Redelbach40, K. RedlichV,87, A. Rehman21,
P. Reichelt69, F. Reidt35, H.A. Reme-ness37, R. Renfordt69, Z. Rescakova39, K.
Reygers106, A. Riabov100, V. Riabov100, T. Richert82,91, M. Richter20, W.
Riegler35, F. Riggi27, C. Ristea68, S.P. Rode51, M. Rodríguez Cahuantzi46, K.
Røed20, R. Rogalev93, E. Rogochaya76, T.S. Rogoschinski69, D. Rohr35, D.
Röhrich21, P.F. Rojas46, P.S. Rokita143, F. Ronchetti53, A. Rosano33,57, E.D.
Rosas70, A. Rossi58, A. Rotondi29, A. Roy51, P. Roy111, S. Roy50, N. Rubini26,
O.V. Rueda82, R. Rui24, B. Rumyantsev76, A. Rustamov89, E. Ryabinkin90, Y.
Ryabov100, A. Rybicki119, H. Rytkonen127, W. Rzesa143, O.A.M. Saarimaki45, R.
Sadek116, S. Sadovsky93, J. Saetre21, K. Šafařík38, S.K. Saha142, S. Saha88,
B. Sahoo50, P. Sahoo50, R. Sahoo51, S. Sahoo66, D. Sahu51, P.K. Sahu66, J.
Saini142, S. Sakai135, S. Sambyal103, V. SamsonovI,100,95, D. Sarkar144, N.
Sarkar142, P. Sarma43, V.M. Sarti107, M.H.P. Sas147, J. Schambach98,120, H.S.
Scheid69, C. Schiaua49, R. Schicker106, A. Schmah106, C. Schmidt109, H.R.
Schmidt105, M.O. Schmidt106, M. Schmidt105, N.V. Schmidt98,69, A.R.
Schmier132, R. Schotter138, J. Schukraft35, Y. Schutz138, K. Schwarz109, K.
Schweda109, G. Scioli26, E. Scomparin60, J.E. Seger15, Y. Sekiguchi134, D.
Sekihata134, I. Selyuzhenkov109,95, S. Senyukov138, J.J. Seo62, D.
Serebryakov64, L. Šerkšnytė107, A. Sevcenco68, T.J. Shaba73, A. Shabanov64, A.
Shabetai116, R. Shahoyan35, W. Shaikh111, A. Shangaraev93, A. Sharma102, H.
Sharma119, M. Sharma103, N. Sharma102, S. Sharma103, O. Sheibani126, K.
Shigaki47, M. Shimomura85, S. Shirinkin94, Q. Shou41, Y. Sibiriak90, S.
Siddhanta56, T. Siemiarczuk87, T.F. Silva122, D. Silvermyr82, G. Simonetti35,
B. Singh107, R. Singh88, R. Singh103, R. Singh51, V.K. Singh142, V.
Singhal142, T. Sinha111, B. Sitar13, M. Sitta32, T.B. Skaali20, G.
Skorodumovs106, M. Slupecki45, N. Smirnov147, R.J.M. Snellings63, C.
Soncco113, J. Song126, A. Songmoolnak117, F. Soramel28, S. Sorensen132, I.
Sputowska119, J. Stachel106, I. Stan68, P.J. Steffanic132, S.F.
Stiefelmaier106, D. Stocco116, M.M. Storetvedt37, C.P. Stylianidis92, A.A.P.
Suaide122, T. Sugitate47, C. Suire79, M. Suljic35, R. Sultanov94, M.
Šumbera97, V. Sumberia103, S. Sumowidagdo52, S. Swain66, A. Szabo13, I.
Szarka13, U. Tabassam14, S.F. Taghavi107, G. Taillepied136, J. Takahashi123,
G.J. Tambave21, S. Tang136,7, Z. Tang130, M. Tarhini116, M.G. Tarzila49, A.
Tauro35, G. Tejeda Muñoz46, A. Telesca35, L. Terlizzi25, C. Terrevoli126, G.
Tersimonov3, S. Thakur142, D. Thomas120, R. Tieulent137, A. Tikhonov64, A.R.
Timmins126, M. Tkacik118, A. Toia69, N. Topilskaya64, M. Toppi53, F. Torales-
Acosta19, S.R. Torres38, A. Trifiró33,57, S. Tripathy55,70, T. Tripathy50, S.
Trogolo35,28, G. Trombetta34, V. Trubnikov3, W.H. Trzaska127, T.P.
Trzcinski143, B.A. Trzeciak38, A. Tumkin110, R. Turrisi58, T.S. Tveter20, K.
Ullaland21, A. Uras137, M. Urioni141, G.L. Usai23, M. Vala39, N. Valle29, S.
Vallero60, N. van der Kolk63, L.V.R. van Doremalen63, M. van Leeuwen92, P.
Vande Vyvre35, D. Varga146, Z. Varga146, M. Varga-Kofarago146, A. Vargas46, M.
Vasileiou86, A. Vasiliev90, O. Vázquez Doce107, V. Vechernin114, E.
Vercellin25, S. Vergara Limón46, L. Vermunt63, R. Vértesi146, M. Verweij63, L.
Vickovic36, Z. Vilakazi133, O. Villalobos Baillie112, G. Vino54, A.
Vinogradov90, T. Virgili30, V. Vislavicius91, A. Vodopyanov76, B. Volkel35,
M.A. Völkl106, K. Voloshin94, S.A. Voloshin144, G. Volpe34, B. von Haller35,
I. Vorobyev107, D. Voscek118, J. Vrláková39, B. Wagner21, C. Wang41, D.
Wang41, M. Weber115, A. Wegrzynek35, S.C. Wenzel35, J.P. Wessels145, J.
Wiechula69, J. Wikne20, G. Wilk87, J. Wilkinson109, G.A. Willems145, E.
Willsher112, B. Windelband106, M. Winn139, W.E. Witt132, J.R. Wright120, W.
Wu41, Y. Wu130, R. Xu7, S. Yalcin78, Y. Yamaguchi47, K. Yamakawa47, S. Yang21,
S. Yano47,139, Z. Yin7, H. Yokoyama63, I.-K. Yoo17, J.H. Yoon62, S. Yuan21, A.
Yuncu106, V. Zaccolo24, A. Zaman14, C. Zampolli35, H.J.C. Zanoli63, N.
Zardoshti35, A. Zarochentsev114, P. Závada67, N. Zaviyalov110, H.
Zbroszczyk143, M. Zhalov100, S. Zhang41, X. Zhang7, Y. Zhang130, V.
Zherebchevskii114, Y. Zhi11, D. Zhou7, Y. Zhou91, J. Zhu7,109, A. Zichichi26,
G. Zinovjev3, N. Zurlo141

## Affiliation notes

I Deceased
II Also at: Italian National Agency for New Technologies, Energy and
Sustainable Economic Development (ENEA), Bologna, Italy
III Also at: Dipartimento DET del Politecnico di Torino, Turin, Italy
IV Also at: M.V. Lomonosov Moscow State University, D.V. Skobeltsyn Institute
of Nuclear, Physics, Moscow, Russia
V Also at: Institute of Theoretical Physics, University of Wroclaw, Poland

## Collaboration Institutes

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