EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH (CERN)

 CERN-EP-2021-108 LHCb-PAPER-2021-013 7th July 2021

Study of coherent ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ production

in lead-lead collisions

at $\sqrt{s_{\scriptscriptstyle\rm NN}}=5\mathrm{\,Te\kern-2.07413ptV}$

LHCb collaboration†††Authors are listed at the end of this paper.

Coherent production of ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ mesons
is studied in ultraperipheral lead-lead collisions at a nucleon-nucleon
centre-of-mass energy of $5\mathrm{\,Te\kern-1.00006ptV}$, using a data sample
collected by the LHCb experiment corresponding to an integrated luminosity of
about $10{\mathrm{\,\upmu b}^{-1}}$. The
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ mesons are reconstructed in the
dimuon final state and are required to have transverse momentum below
$1\mathrm{\,Ge\kern-1.00006ptV}$. The cross-section within the rapidity range
of $2.0<y<4.5$ is measured to be
$4.45\pm{0.24}\pm{0.18}\pm{0.58}{\color[rgb]{1,0,0}}\mathrm{\,mb}$, where the
first uncertainty is statistical, the second systematic and the third
originates from the luminosity determination. The cross-section is also
measured in ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ rapidity intervals.
The results are compared to predictions from phenomenological models.

Submitted to JHEP

© 2024 CERN for the benefit of the LHCb collaboration. CC BY 4.0 licence.

##  1 Introduction

In ultra-relativistic collisions of heavy-nuclei at the LHC, vector mesons can
be produced through two-photon and photonuclear interactions in
ultraperipheral collisions (UPCs), where the impact parameter of the two
nuclei collision is larger than the sum of their radii. The cross-sections for
photon-induced reactions are large because the intensity of the photon flux is
enhanced by the strong electromagnetic field of the nucleus, which increases
with the square of the atomic number. The interactions are either coherent,
where the photon couples to all nucleons, or incoherent, where the photon
couples to a single nucleon. In the incoherent case the nucleus is likely to
break up, leading to a higher transverse momentum, $p_{\mathrm{T}}$, of the
meson.

Coherent ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$-meson production in
UPCs can be described by the interaction of photons with gluons, identified as
a single object with vacuum quantum numbers, which in the Regge theory is
referred to as pomeron (IP) [1, 2, 3, 4, 5]. An illustration of this process
is given in Fig. 1. This interaction probes the gluon distribution at a hard
momentum transfer $Q^{2}$ of about $m_{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}^{2}/4$, where $m_{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}$ is
the ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ mass [6, 7].111In this
paper natural units where $c$ = 1 are used.

Figure 1: Illustration of the (left) coherent scatter with the lead nucleus
and (right) incoherent interaction with a single nucleon leading to exclusive
production of ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ mesons in
ultraperipheral heavy-ion collisions. The symbol Pb’ represents any final
state for the nucleus inelastic scattering in the incoherent process.

In this paper, a measurement of coherent
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ production is reported in lead-
lead collisions at a nucleon-nucleon centre-of-mass energy of
$\sqrt{s_{\scriptscriptstyle\rm NN}}=5\mathrm{\,Te\kern-1.00006ptV}$ collected
with the LHCb detector in 2015, corresponding to an integrated luminosity of
about $10{\mathrm{\,\upmu b}^{-1}}$. Results of UPC studies have also been
reported by RHIC and LHC experiments [8, 9, 10, 11, 12, 13, 14, 15]. The
forward rapidity range $2.0<{y}<4.5$ covered by the present measurement
corresponds to values of the Bjorken variable
$x\approx(m_{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}/\sqrt{s_{\scriptscriptstyle\rm NN}})e^{\pm{y}}$ down to $10^{-5}$. At
these $x$ values, current uncertainties on the gluon distributions inside the
nucleon are sizeable [16, 17], thus new measurements should reduce the
uncertainties [18, 19, 20].

The paper is organised as follows. The LHCb detector and the event selection
are described in Sec. 2. The analysis strategy and the systematic
uncertainties are discussed in Secs. 3 and 4, respectively. The differential
cross-section results for ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$
production in UPCs are detailed in Sec. 5. Conclusions are given in Sec. 6.

##  2 Detector description and candidate selection

The LHCb detector [21, 22] is a single-arm forward spectrometer covering the
pseudorapidity range $2<\eta<5$, designed for the study of particles
containing $b$ or $c$ quarks. The detector includes a high-precision tracking
system consisting of a silicon-strip vertex detector (VELO) surrounding the
interaction region, a silicon-strip detector located upstream of a dipole
magnet with a bending power of about $4{\mathrm{\,Tm}}$, and three stations of
silicon-strip detectors and straw drift tubes placed downstream of the magnet.
The tracking system provides a measurement of momentum, $p$, of charged
particles with a relative uncertainty that varies from 0.5% at low momentum to
1.0% at 200$\mathrm{\,Ge\kern-1.00006ptV}$. The VELO has a material budget of
one fifth of a radiation length that allows reconstruction and rejection of
events with additional low-momentum tracks [23]. Different types of charged
hadrons are distinguished using information from two ring-imaging Cherenkov
detectors. Photons, electrons and hadrons are identified by a calorimeter
system consisting of scintillating-pad (SPD) and preshower (PRS) detectors, an
electromagnetic calorimeter and a hadronic calorimeter. Muons are identified
by a system composed of alternating layers of iron and multiwire proportional
chambers. The pseudorapidity coverage is extended by forward shower counters
(HeRSCheL) consisting of five planes of scintillators with three planes at
$114$, $19.7$ and $7.5\mathrm{\,m}$ upstream of the interaction point, and two
downstream at $20$ and $114\mathrm{\,m}$. The HeRSCheL detector significantly
extends the acceptance in which hadron showers can be detected to classify
central exclusive production and UPC events by covering a pseudorapidity
region of approximately $-10<\eta<-5$ and $5<\eta<10$ [24]. The real-time
event selection is performed by a trigger, which consists of a hardware stage,
based on information from the calorimeter and muon systems, followed by a
software stage, which applies a full event reconstruction.

In this analysis, ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ candidates
are selected through their decay into two oppositely charged muons. The events
are selected by the trigger system, requiring information from the muon system
to be compatible with at least one muon with $p_{\mathrm{T}}$ larger than
$900\mathrm{\,Me\kern-1.00006ptV}$ at the hardware level, and the invariant
mass of the two muons, $m_{\mu^{+}\mu^{-}}$, exceeding
$2.7\mathrm{\,Ge\kern-1.00006ptV}$ at the software level. In the offline
selection, candidates are identified by requiring both muons to have
$p_{\mathrm{T}}>800\mathrm{\,Me\kern-1.00006ptV}$ within the pseudorapidity
region $2.0<\eta<4.5$, and $m_{\mu^{+}\mu^{-}}$ to be within
$65\mathrm{\,Me\kern-1.00006ptV}$ of the known
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ mass [25]. Only
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ candidates with reconstructed
$p_{\mathrm{T}}<1\mathrm{\,Ge\kern-1.00006ptV}$ and an azimuthal opening angle
between the muons larger than $0.9\pi$ are retained.

In order to suppress background from more central lead-lead collisions, events
with more than 20 deposits in the SPD are vetoed. In addition, events with an
extra VELO track in the spatial vicinity of the reconstructed
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ candidate are rejected.
Finally, a requirement on the activity in the HeRSCheL detector, based upon a
figure-of-merit that combines detector signals of all stations [24], is used
to discard events with significant activity in the HeRSCheL acceptance region.

##  3 Cross-section measurement

The differential cross-section for coherent
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ production is evaluated as

$\displaystyle\frac{d\sigma}{dy}$
$\displaystyle=\frac{n_{\text{coh}}}{\varepsilon_{y}\,\Delta
y\,\mathcal{L}\,{\mathcal{B}}}\,,$ (1)

where $n_{\text{coh}}$ is the signal yield, $\varepsilon_{y}$ is the total
efficiency in each rapidity interval, $\Delta y$ is the rapidity interval
width, $\mathcal{L}$ is the integrated luminosity, and
${\mathcal{B}}=(5.961\pm 0.033)\%$ is the
${{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}\\!\rightarrow{\mu^{+}\mu^{-}}$
branching fraction [25].

The luminosity is determined with the same method as for proton-proton
collisions [26, 27]. The leading source of systematic uncertainty is the
unexplained dependence of the luminosity ratio on the value of the actual
observable. The integrated luminosity of the data sample is determined to be
$10.1\pm 1.3$${\mathrm{\,\upmu b}^{-1}}$, where the absolute calibration is
performed with Van der Meer scans [27].

###  3.1 Signal yield determination

The signal yield is determined in two steps. First, a fit to the dimuon
invariant mass spectrum is performed to obtain the
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ yield, which includes the
contribution of coherent and incoherent ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}$ mesons, and feed-down from ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}$ mesons originating from $\psi{(2S)}$ decays. Second, a fit to the
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ transverse momentum is used to
isolate the coherent ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ yield.

The yield of ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ mesons is
estimated by fitting the dimuon invariant mass distribution to signal and
background components. The ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ and
$\psi{(2S)}$ mass shapes are modelled by double-sided Crystal Ball functions
[28], and the nonresonant background by an exponential function multiplied by
a first-order polynomial function. The $\psi{(2S)}$ parameters, aside from the
mean, are constrained to be the same as for the
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ meson. The fit is performed in
the range $2.7<m_{\mu^{+}\mu^{-}}<4\mathrm{\,Ge\kern-1.00006ptV}$. The dimuon
mass distribution along with the fit projection is shown in Fig. 2.

For the determination of the coherent yield two resonant background sources
are considered: incoherent ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$
photoproduction and ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ meson feed-
down from photoproduced $\psi{(2S)}$ decays. In order to determine the signal
yield in the presence of these backgrounds, an unbinned maximum-likelihood fit
to the natural logarithm of the transverse momentum squared,
$\log(p_{\mathrm{T}}^{2})$, of ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$
candidates inside the chosen mass window is performed. The signal and
background probability density functions are estimated using the STARlight
generator[2] and the LHCb detector simulation. The amount of nonresonant
background is constrained by the dimuon invariant mass fit. The feed-down
background is assumed to have the same $\log(p_{\mathrm{T}}^{2})$ distribution
as simulated ${\psi{(2S)}}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{\pi}^{+}}{{\pi}^{-}}$ decays, where the
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ is reconstructed and both pions
escape the rejection requirements on additional tracks. Figure 3 shows the
$\log(p_{\mathrm{T}}^{2})$ data distribution along with the fit projection in
the rapidity interval $2.5<y<3$. All ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}$ yields are reported in Table 3.1.

Figure 2:  The dimuon invariant mass spectrum in the range between $2.7$ and
$4.0\mathrm{\,Ge\kern-1.00006ptV}$. The contribution of
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ (solid purple line) and
$\psi{(2S)}$ (solid dark green line) mesons, and non-resonant background
(dashed black line) are shown individually along with the sum of all
contributions (solid orange line).  Table 1: Total and coherent
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ yields after the invariant mass
and the transverse momentum fits, in ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}$ rapidity intervals.

Rapidity $y$ | Total ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ yield | Coherent ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ yield
---|---|---
$2.0-2.5$ | $\phantom{0}69\pm\phantom{0}9$ | $\phantom{0}53\pm\phantom{0}8$
$2.5-3.0$ | $208\pm 15$ | $153\pm 14$
$3.0-3.5$ | $233\pm 16$ | $176\pm 15$
$3.5-4.0$ | $131\pm 12$ | $\phantom{0}95\pm 11$
$4.0-4.5$ | $\phantom{0}32\pm\phantom{0}6$ | $\phantom{0}12\pm\phantom{0}5$
Figure 3:  The $\log(p_{\mathrm{T}}^{2})$ distribution of dimuon candidates in
the interval $2.5<y<3.0$, with $p_{\mathrm{T}}$ given in GeV, after all
requirements have been applied. The solid orange line represents the combined
fit to data; the solid blue line shows the coherent contribution; the
incoherent component is displayed by the dashed red line; and the dashed green
(black) line shows the feed-down (nonresonant) components.

###  3.2 Efficiency determination

For any given ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ rapidity
interval, the total efficiency is evaluated as the product of the acceptance
and the reconstruction and selection efficiencies. The acceptance includes the
requirements on the kinematic properties of the
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ decay products, and is
evaluated using a sample of coherently photoproduced
${{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}\rightarrow{\mu^{+}\mu^{-}}$
events produced with the STARlight event generator. The reconstruction
efficiency includes track reconstruction and muon identification. The
selection efficiency includes requirements on the SPD deposits, VELO track
multiplicities, and dimuon invariant mass. The hardware trigger efficiency is
determined using simulated events, calibrated with data. The software trigger
efficiency is measured using ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$
candidates in events selected with a minimum bias trigger requiring at least
one VELO track. Partially reconstructed inclusive
${{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}\\!\rightarrow{\mu^{+}\mu^{-}}$
candidates from proton-proton collision data at a centre-of-mass energy
$\sqrt{s}$=13$\mathrm{\,Te\kern-1.00006ptV}$ are used to evaluate the tracking
efficiency [29]. The muon identification efficiency has been determined from
simulated events generated with the STARlight generator in lead-lead
collisions and validated with lead-lead data.

The dimuon invariant mass requirement efficiency is determined using the
integral of the double-sided Crystal Ball function. A similar method is used
to determine the efficiencies of the multiplicity requirements on the VELO
tracks and SPD deposits. The veto efficiency of the HeRSCheL detector activity
is evaluated with a sample of nonresonant dimuon events from lead-lead data
using a fit obtained from STARlight simulated
$\gamma\gamma\rightarrow{\mu^{+}\mu^{-}}$ events, and comparing the number of
events satisfying and failing the requirement. The total efficiency for this
selection is about 90%.

##  4 Systematic uncertainties

Systematic uncertainties on the measured cross-section are considered from the
integrated luminosity calculation, the determination of the muon
reconstruction and selection efficiencies, the trigger efficiency, the mass
fit signal model, the modelling of the feed-down background, and the knowledge
of the ${{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}\rightarrow\mu^{+}\mu^{-}$ branching fraction. They are described below
and summarised in Table 2. The largest uncertainty originates from the
integrated luminosity determination and is estimated to be 13%.

The uncertainties related to the ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}$ reconstruction efficiency include effects on the track reconstruction
and muon identification, and they are dominated by the limited size of the
control sample. Several contributions to the selection efficiency are
considered. The impact of the requirement on the SPD multiplicity is estimated
from a data control sample. Effects related to the dimuon invariant mass
efficiency are taken from the uncertainty of the integral of the double-sided
Crystal Ball function. The inefficiency of the VELO track multiplicity
requirement is found to be negligible and no uncertainty is assigned. The
uncertainty due to the HeRSCheL selection is estimated by comparing the
efficiency evaluated in different samples, selected by applying requirements
that do not affect the signal.

The efficiency of the hardware trigger is determined from simulated events. It
is compared to the efficiency obtained on a smaller data sample selected by
independent triggers, and the difference is taken as systematic uncertainty.
The software-stage trigger efficiency evaluation is cross-checked with an
independent estimation based on data, where events are selected with a
different trigger requirement. The efficiencies are consistent within
statistical uncertainties, which are used to assign a systematic uncertainty.

Possible cross-section variations associated to the signal model in the fit to
the dimuon invariant mass spectrum is assessed using an alternative model. A
Bukin function [30] is used for the signal and the difference in the signal
yields with respect to the default fit is assigned as uncertainty.

In order to estimate the systematic uncertainty due to the feed-down
component, the ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ candidate
selection is modified to select a mixture of coherently and incoherently
produced ${\psi{(2S)}}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{\pi}^{+}}{{\pi}^{-}}$ events. After requiring the reconstructed mass
of the $\psi{(2S)}$ candidates to be within $65\mathrm{\,Me\kern-1.00006ptV}$
of the known $\psi{(2S)}$ mass [25], 22 candidates are obtained. In the
simulation, ${\psi{(2S)}}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{\pi}^{+}}{{\pi}^{-}}$ events are used as a proxy for all
${\psi{(2S)}}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}X$
feed-down. The ratio between
${\psi{(2S)}}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{\pi}^{+}}{{\pi}^{-}}$ candidates, where the pions left no VELO track,
and fully reconstructed candidates is determined and scaled assuming that
${\psi{(2S)}}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{\pi}^{+}}{{\pi}^{-}}$ events are representative for all
${\psi{(2S)}}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}X$
events. From this ratio and the ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$
yield, the number of ${{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}\\!\rightarrow{\mu^{+}}{\mu^{-}}$ candidates originating from
$\psi{(2S)}$ decays in the signal sample is determined to be $42.5\pm 9.1$.
This yield is assigned to the different intervals in meson rapidity using a
template from simulated coherent
${\psi{(2S)}}\\!\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{\pi}^{+}}{{\pi}^{-}}$ events. The uncertainty is dominated by the
limited size of the data sample.

Table 2: Systematic uncertainties considered for the differential cross-section measurement of coherent ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ production, relative to the central value. Uncertainty ranges correspond to variation over the rapidity intervals. The dominant uncertainty arises from the luminosity determination and is correlated over all intervals.  Source | Relative uncertainty (%)
---|---
Luminosity | $13.0$
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ reconstruction efficiency |  $1.7$–$4.8$
Selection efficiency | $1.7$
HeRSCheL requirement efficiency | $1.0$
Hardware trigger efficiency | $1.0$
Software trigger efficiency | $1.0$
Mass fit model | $1.0-1.6$
Feed-down background | $0.4-1.0$
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ branching fraction | $0.6$

##  5 Results and discussion

Using Eq. (1), the cross-section for coherent
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ production within the fiducial
region is determined to be
σ=$4.45\pm{0.24}\pm{0.18}\pm{0.58}{\color[rgb]{1,0,0}}$$\mathrm{\,mb}$, where
the first uncertainty is statistical, the second is systematic and the third
is due to the luminosity determination. The
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ candidates are reconstructed
from dimuon final states, where the muons are detected within the
pseudorapidity region $2.0<\eta<4.5$ and the
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ meson is required to have
$p_{\mathrm{T}}<1\mathrm{\,Ge\kern-1.00006ptV}$ and $2.0<{y}<4.5$. The
coherent differential ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$
production cross-section, measured in ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}$ rapidity intervals, is given in Table 3. A comparison with theoretical
predictions discussed below is shown in Fig. 4.

In the model of Gonçalves et al. [4, 31], the cross-section is calculated
within the framework of the Colour-Dipole model. Three different
parametrisations of the dipole-proton cross-section (IIM, IP-SAT, bCGC),
including saturation effects at low Bjorken-x, are combined with two different
models of vector-meson wave functions, namely boosted Gaussian (BG) and Gauss-
LC (GLC). All the parameters are tuned using HERA data[32, 33, 34]. The solid
(dashed) curves in Fig. 4 correspond to the IP-SAT+GLC (IIM+BG) model. The
combination of IIM [35] with the boosted Gaussian wave function is disfavoured
by the data.

The model from Cepila et al. [36] is a variation of the Colour-Dipole model.
The main differences with respect to Gonçalves et al. come from the
parametrisation of the dipole-proton cross-section and the prescription used
to propagate it to the dipole-nucleus scattering amplitudes. In this model,
the Glauber-Gribov methodology (GG) or a geometric scaling between the nuclear
saturation scale and the saturation scale in the proton (GS) are used. Both
prescriptions are able to describe the data.

In the model proposed by Mäntysaari et al. [37], the cross-section is also
calculated using the Colour-Dipole model including subnucleon scale
fluctuations. Predictions with and without subnucleonic fluctuations using the
IP-SAT parametrisation for the dipole-proton cross-section and the GLC for the
vector-meson wave function are compared to this measurement. Both
prescriptions are able to describe the data.

The model provided by Guzey et al. [1] is based on a perturbative QCD
calculation. The coherent ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$
production cross-section on a proton target is calculated at leading order
within the leading-log approximation. Different models for the nuclear
structure are used: weaker (LTA_W) and stronger (LTA_S) nuclear shadowing
scenarios with a leading twist nuclear shadowing model [38] as well as EPS09
[16] nuclear parton distribution functions. The measurement can be described
by these models.

Table 3:  Measured cross-section $\sigma$ with breakdown of statistical, systematic and luminosity uncertainties measured as a function of the ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ rapidity. Note that the cross-sections are not normalised by the $y$ interval width.  $y$ interval | $\sigma\ [\mathrm{\,mb}]$ | Stat. $[\mathrm{\,mb}]$ | Syst. $[\mathrm{\,mb}]$ | Lumi. $[\mathrm{\,mb}]$
---|---|---|---|---
$2.0-4.5$ | 4.45 | 0.24 | 0.18 | 0.58
$2.0-2.5$ | 1.35 | 0.19 | 0.06 | 0.17
$2.5-3.0$ | 1.09 | 0.09 | $0.05$ | 0.14
$3.0-3.5$ | 0.89 | 0.07 | 0.04 | 0.12
$3.5-4.0$ | 0.65 | 0.06 | $0.03$ | 0.08
$4.0-4.5$ | 0.48 | 0.09 | 0.02 | 0.06
Figure 4:  Differential cross-section as a function of rapidity for coherent
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ production compared to
different phenomenological predictions [1, 4, 31, 36, 37]. The measurements
are shown as points, where inner and outer error bars represent the
statistical and the total uncertainties, respectively.

##  6 Conclusions

The coherent ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ production cross-
section in lead-lead collisions at $\sqrt{s_{\scriptscriptstyle\rm
NN}}=5\mathrm{\,Te\kern-1.00006ptV}$, using a data sample collected by the
LHCb experiment and corresponding to an integrated luminosity of about
$10{\mathrm{\,\upmu b}^{-1}}$, is measured to be
$4.45\pm{0.24}\pm{0.18}\pm{0.58}{\color[rgb]{1,0,0}}\mathrm{\,mb}$, where the
first uncertainty is statistical, the second is systematic and the third is
due to the luminosity determination. The measurement uses
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ mesons reconstructed in the
dimuon final state with $p_{\mathrm{T}}<1\mathrm{\,Ge\kern-1.00006ptV}$ and
$2.0<{y}<4.5$, where muons are detected within the pseudorapidity region
$2.0<\eta<4.5$. The cross-section is also measured in five
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ rapidity intervals and the
results are compared to predictions from different phenomenological models.
Future measurements with different mesons and larger data samples will further
constrain these models.

## Acknowledgements

We express our gratitude to our colleagues in the CERN accelerator departments
for the excellent performance of the LHC. We thank the technical and
administrative staff at the LHCb institutes. We acknowledge support from CERN
and from the national agencies: CAPES, CNPq, FAPERJ and FINEP (Brazil); MOST
and NSFC (China); CNRS/IN2P3 (France); BMBF, DFG and MPG (Germany); INFN
(Italy); NWO (Netherlands); MNiSW and NCN (Poland); MEN/IFA (Romania); MSHE
(Russia); MICINN (Spain); SNSF and SER (Switzerland); NASU (Ukraine); STFC
(United Kingdom); DOE NP and NSF (USA). We acknowledge the computing resources
that are provided by CERN, IN2P3 (France), KIT and DESY (Germany), INFN
(Italy), SURF (Netherlands), PIC (Spain), GridPP (United Kingdom), RRCKI and
Yandex LLC (Russia), CSCS (Switzerland), IFIN-HH (Romania), CBPF (Brazil), PL-
GRID (Poland) and NERSC (USA). We are indebted to the communities behind the
multiple open-source software packages on which we depend. Individual groups
or members have received support from ARC and ARDC (Australia); AvH Foundation
(Germany); EPLANET, Marie Skłodowska-Curie Actions and ERC (European Union);
A*MIDEX, ANR, Labex P2IO and OCEVU, and Région Auvergne-Rhône-Alpes (France);
Key Research Program of Frontier Sciences of CAS, CAS PIFI, CAS CCEPP,
Fundamental Research Funds for the Central Universities, and Sci. & Tech.
Program of Guangzhou (China); RFBR, RSF and Yandex LLC (Russia); GVA, XuntaGal
and GENCAT (Spain); the Leverhulme Trust, the Royal Society and UKRI (United
Kingdom).

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LHCb collaboration

R. Aaij32, C. Abellán Beteta50, T. Ackernley60, B. Adeva46, M. Adinolfi54, H.
Afsharnia9, C.A. Aidala86, S. Aiola25, Z. Ajaltouni9, S. Akar65, J.
Albrecht15, F. Alessio48, M. Alexander59, A. Alfonso Albero45, Z. Aliouche62,
G. Alkhazov38, P. Alvarez Cartelle55, S. Amato2, Y. Amhis11, L. An48, L.
Anderlini22, A. Andreianov38, M. Andreotti21, F. Archilli17, A. Artamonov44,
M. Artuso68, K. Arzymatov42, E. Aslanides10, M. Atzeni50, B. Audurier12, S.
Bachmann17, M. Bachmayer49, J.J. Back56, P. Baladron Rodriguez46, V.
Balagura12, W. Baldini21, J. Baptista Leite1, R.J. Barlow62, S. Barsuk11, W.
Barter61, M. Bartolini24, F. Baryshnikov83, J.M. Basels14, G. Bassi29, B.
Batsukh68, A. Battig15, A. Bay49, M. Becker15, F. Bedeschi29, I. Bediaga1, A.
Beiter68, V. Belavin42, S. Belin27, V. Bellee49, K. Belous44, I. Belov40, I.
Belyaev41, G. Bencivenni23, E. Ben-Haim13, A. Berezhnoy40, R. Bernet50, D.
Berninghoff17, H.C. Bernstein68, C. Bertella48, A. Bertolin28, C.
Betancourt50, F. Betti48, Ia. Bezshyiko50, S. Bhasin54, J. Bhom35, L. Bian73,
M.S. Bieker15, S. Bifani53, P. Billoir13, M. Birch61, F.C.R. Bishop55, A.
Bitadze62, A. Bizzeti22,k, M. Bjørn63, M.P. Blago48, T. Blake56, F. Blanc49,
S. Blusk68, D. Bobulska59, J.A. Boelhauve15, O. Boente Garcia46, T.
Boettcher65, A. Boldyrev82, A. Bondar43, N. Bondar38,48, S. Borghi62, M.
Borisyak42, M. Borsato17, J.T. Borsuk35, S.A. Bouchiba49, T.J.V. Bowcock60, A.
Boyer48, C. Bozzi21, M.J. Bradley61, S. Braun66, A. Brea Rodriguez46, M.
Brodski48, J. Brodzicka35, A. Brossa Gonzalo56, D. Brundu27, A. Buonaura50, C.
Burr48, A. Bursche72, A. Butkevich39, J.S. Butter32, J. Buytaert48, W.
Byczynski48, S. Cadeddu27, H. Cai73, R. Calabrese21,f, L. Calefice15,13, L.
Calero Diaz23, S. Cali23, R. Calladine53, M. Calvi26,j, M. Calvo Gomez85, P.
Camargo Magalhaes54, A. Camboni45,85, P. Campana23, A.F. Campoverde Quezada6,
S. Capelli26,j, L. Capriotti20,d, A. Carbone20,d, G. Carboni31, R.
Cardinale24, A. Cardini27, I. Carli4, P. Carniti26,j, L. Carus14, K. Carvalho
Akiba32, A. Casais Vidal46, G. Casse60, M. Cattaneo48, G. Cavallero48, S.
Celani49, J. Cerasoli10, A.J. Chadwick60, M.G. Chapman54, M. Charles13, Ph.
Charpentier48, G. Chatzikonstantinidis53, C.A. Chavez Barajas60, M.
Chefdeville8, C. Chen3, S. Chen4, A. Chernov35, V. Chobanova46, S. Cholak49,
M. Chrzaszcz35, A. Chubykin38, V. Chulikov38, P. Ciambrone23, M.F. Cicala56,
X. Cid Vidal46, G. Ciezarek48, P.E.L. Clarke58, M. Clemencic48, H.V. Cliff55,
J. Closier48, J.L. Cobbledick62, V. Coco48, J.A.B. Coelho11, J. Cogan10, E.
Cogneras9, L. Cojocariu37, P. Collins48, T. Colombo48, L. Congedo19,c, A.
Contu27, N. Cooke53, G. Coombs59, G. Corti48, C.M. Costa Sobral56, B.
Couturier48, D.C. Craik64, J. Crkovská67, M. Cruz Torres1, R. Currie58, C.L.
Da Silva67, E. Dall’Occo15, J. Dalseno46, C. D’Ambrosio48, A. Danilina41, P.
d’Argent48, A. Davis62, O. De Aguiar Francisco62, K. De Bruyn79, S. De
Capua62, M. De Cian49, J.M. De Miranda1, L. De Paula2, M. De Serio19,c, D. De
Simone50, P. De Simone23, J.A. de Vries80, C.T. Dean67, D. Decamp8, L. Del
Buono13, B. Delaney55, H.-P. Dembinski15, A. Dendek34, V. Denysenko50, D.
Derkach82, O. Deschamps9, F. Desse11, F. Dettori27,e, B. Dey77, P. Di Nezza23,
S. Didenko83, L. Dieste Maronas46, H. Dijkstra48, V. Dobishuk52, A.M.
Donohoe18, F. Dordei27, A.C. dos Reis1, L. Douglas59, A. Dovbnya51, A.G.
Downes8, K. Dreimanis60, M.W. Dudek35, L. Dufour48, V. Duk78, P. Durante48,
J.M. Durham67, D. Dutta62, A. Dziurda35, A. Dzyuba38, S. Easo57, U. Egede69,
V. Egorychev41, S. Eidelman43,v, S. Eisenhardt58, S. Ek-In49, L. Eklund59,w,
S. Ely68, A. Ene37, E. Epple67, S. Escher14, J. Eschle50, S. Esen13, T.
Evans48, A. Falabella20, J. Fan3, Y. Fan6, B. Fang73, S. Farry60, D.
Fazzini26,j, M. Féo48, A. Fernandez Prieto46, J.M. Fernandez-tenllado
Arribas45, A.D. Fernez66, F. Ferrari20,d, L. Ferreira Lopes49, F. Ferreira
Rodrigues2, S. Ferreres Sole32, M. Ferrillo50, M. Ferro-Luzzi48, S.
Filippov39, R.A. Fini19, M. Fiorini21,f, M. Firlej34, K.M. Fischer63, D.S.
Fitzgerald86, C. Fitzpatrick62, T. Fiutowski34, F. Fleuret12, M. Fontana13, F.
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E. Franzoso21, G. Frau17, C. Frei48, D.A. Friday59, J. Fu25, Q. Fuehring15, W.
Funk48, E. Gabriel32, T. Gaintseva42, A. Gallas Torreira46, D. Galli20,d, S.
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Garcia Martin56, P. Garcia Moreno45, J. García Pardiñas26,j, B. Garcia
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Prasanth35, L. Promberger48, C. Prouve46, V. Pugatch52, H. Pullen63, G.
Punzi29,n, W. Qian6, J. Qin6, R. Quagliani13, B. Quintana8, N.V. Raab18, R.I.
Rabadan Trejo10, B. Rachwal34, J.H. Rademacker54, M. Rama29, M. Ramos
Pernas56, M.S. Rangel2, F. Ratnikov42,82, G. Raven33, M. Reboud8, F. Redi49,
F. Reiss62, C. Remon Alepuz47, Z. Ren3, V. Renaudin63, R. Ribatti29, S.
Ricciardi57, K. Rinnert60, P. Robbe11, G. Robertson58, A.B. Rodrigues49, E.
Rodrigues60, J.A. Rodriguez Lopez74, A. Rollings63, P. Roloff48, V.
Romanovskiy44, M. Romero Lamas46, A. Romero Vidal46, J.D. Roth86, M.
Rotondo23, M.S. Rudolph68, T. Ruf48, J. Ruiz Vidal47, A. Ryzhikov82, J.
Ryzka34, J.J. Saborido Silva46, N. Sagidova38, N. Sahoo56, B. Saitta27,e, M.
Salomoni48, D. Sanchez Gonzalo45, C. Sanchez Gras32, R. Santacesaria30, C.
Santamarina Rios46, M. Santimaria23, E. Santovetti31,p, D. Saranin83, G.
Sarpis62, M. Sarpis75, A. Sarti30, C. Satriano30,o, A. Satta31, M. Saur15, D.
Savrina41,40, H. Sazak9, L.G. Scantlebury Smead63, S. Schael14, M.
Schellenberg15, M. Schiller59, H. Schindler48, M. Schmelling16, B. Schmidt48,
O. Schneider49, A. Schopper48, M. Schubiger32, S. Schulte49, M.H. Schune11, R.
Schwemmer48, B. Sciascia23, S. Sellam46, A. Semennikov41, M. Senghi Soares33,
A. Sergi24, N. Serra50, L. Sestini28, A. Seuthe15, P. Seyfert48, Y. Shang5,
D.M. Shangase86, M. Shapkin44, I. Shchemerov83, L. Shchutska49, T. Shears60,
L. Shekhtman43,v, Z. Shen5, V. Shevchenko81, E.B. Shields26,j, E. Shmanin83,
J.D. Shupperd68, B.G. Siddi21, R. Silva Coutinho50, G. Simi28, S. Simone19,c,
N. Skidmore62, T. Skwarnicki68, M.W. Slater53, I. Slazyk21,f, J.C.
Smallwood63, J.G. Smeaton55, A. Smetkina41, E. Smith50, M. Smith61, A.
Snoch32, M. Soares20, L. Soares Lavra9, M.D. Sokoloff65, F.J.P. Soler59, A.
Solovev38, I. Solovyev38, F.L. Souza De Almeida2, B. Souza De Paula2, B.
Spaan15, E. Spadaro Norella25,i, P. Spradlin59, F. Stagni48, M. Stahl65, S.
Stahl48, P. Stefko49, O. Steinkamp50,83, O. Stenyakin44, H. Stevens15, S.
Stone68, M.E. Stramaglia49, M. Straticiuc37, D. Strekalina83, F. Suljik63, J.
Sun27, L. Sun73, Y. Sun66, P. Svihra62, P.N. Swallow53, K. Swientek34, A.
Szabelski36, T. Szumlak34, M. Szymanski48, S. Taneja62, F. Teubert48, E.
Thomas48, K.A. Thomson60, V. Tisserand9, S. T’Jampens8, M. Tobin4, L.
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C. Trippl49, G. Tuci29,n, A. Tully49, N. Tuning32,48, A. Ukleja36, D.J.
Unverzagt17, E. Ursov83, A. Usachov32, A. Ustyuzhanin42,82, U. Uwer17, A.
Vagner84, V. Vagnoni20, A. Valassi48, G. Valenti20, N. Valls Canudas85, M. van
Beuzekom32, M. Van Dijk49, E. van Herwijnen83, C.B. Van Hulse18, M. van
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Cardona85, E. Vilella Figueras60, P. Vincent13, D. Vom Bruch10, A. Vorobyev38,
V. Vorobyev43,v, N. Voropaev38, R. Waldi17, J. Walsh29, C. Wang17, J. Wang5,
J. Wang4, J. Wang3, J. Wang73, M. Wang3, R. Wang54, Y. Wang7, Z. Wang50, Z.
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2Universidade Federal do Rio de Janeiro (UFRJ), Rio de Janeiro, Brazil 3Center
for High Energy Physics, Tsinghua University, Beijing, China 4Institute Of
High Energy Physics (IHEP), Beijing, China 5School of Physics State Key
Laboratory of Nuclear Physics and Technology, Peking University, Beijing,
China 6University of Chinese Academy of Sciences, Beijing, China 7Institute of
Particle Physics, Central China Normal University, Wuhan, Hubei, China 8Univ.
Savoie Mont Blanc, CNRS, IN2P3-LAPP, Annecy, France 9Université Clermont
Auvergne, CNRS/IN2P3, LPC, Clermont-Ferrand, France 10Aix Marseille Univ,
CNRS/IN2P3, CPPM, Marseille, France 11Université Paris-Saclay, CNRS/IN2P3,
IJCLab, Orsay, France 12Laboratoire Leprince-Ringuet, CNRS/IN2P3, Ecole
Polytechnique, Institut Polytechnique de Paris, Palaiseau, France 13LPNHE,
Sorbonne Université, Paris Diderot Sorbonne Paris Cité, CNRS/IN2P3, Paris,
France 14I. Physikalisches Institut, RWTH Aachen University, Aachen, Germany
15Fakultät Physik, Technische Universität Dortmund, Dortmund, Germany 16Max-
Planck-Institut für Kernphysik (MPIK), Heidelberg, Germany 17Physikalisches
Institut, Ruprecht-Karls-Universität Heidelberg, Heidelberg, Germany 18School
of Physics, University College Dublin, Dublin, Ireland 19INFN Sezione di Bari,
Bari, Italy 20INFN Sezione di Bologna, Bologna, Italy 21INFN Sezione di
Ferrara, Ferrara, Italy 22INFN Sezione di Firenze, Firenze, Italy 23INFN
Laboratori Nazionali di Frascati, Frascati, Italy 24INFN Sezione di Genova,
Genova, Italy 25INFN Sezione di Milano, Milano, Italy 26INFN Sezione di
Milano-Bicocca, Milano, Italy 27INFN Sezione di Cagliari, Monserrato, Italy
28Universita degli Studi di Padova, Universita e INFN, Padova, Padova, Italy
29INFN Sezione di Pisa, Pisa, Italy 30INFN Sezione di Roma La Sapienza, Roma,
Italy 31INFN Sezione di Roma Tor Vergata, Roma, Italy 32Nikhef National
Institute for Subatomic Physics, Amsterdam, Netherlands 33Nikhef National
Institute for Subatomic Physics and VU University Amsterdam, Amsterdam,
Netherlands 34AGH - University of Science and Technology, Faculty of Physics
and Applied Computer Science, Kraków, Poland 35Henryk Niewodniczanski
Institute of Nuclear Physics Polish Academy of Sciences, Kraków, Poland
36National Center for Nuclear Research (NCBJ), Warsaw, Poland 37Horia Hulubei
National Institute of Physics and Nuclear Engineering, Bucharest-Magurele,
Romania 38Petersburg Nuclear Physics Institute NRC Kurchatov Institute (PNPI
NRC KI), Gatchina, Russia 39Institute for Nuclear Research of the Russian
Academy of Sciences (INR RAS), Moscow, Russia 40Institute of Nuclear Physics,
Moscow State University (SINP MSU), Moscow, Russia 41Institute of Theoretical
and Experimental Physics NRC Kurchatov Institute (ITEP NRC KI), Moscow, Russia
42Yandex School of Data Analysis, Moscow, Russia 43Budker Institute of Nuclear
Physics (SB RAS), Novosibirsk, Russia 44Institute for High Energy Physics NRC
Kurchatov Institute (IHEP NRC KI), Protvino, Russia, Protvino, Russia 45ICCUB,
Universitat de Barcelona, Barcelona, Spain 46Instituto Galego de Física de
Altas Enerxías (IGFAE), Universidade de Santiago de Compostela, Santiago de
Compostela, Spain 47Instituto de Fisica Corpuscular, Centro Mixto Universidad
de Valencia - CSIC, Valencia, Spain 48European Organization for Nuclear
Research (CERN), Geneva, Switzerland 49Institute of Physics, Ecole
Polytechnique Fédérale de Lausanne (EPFL), Lausanne, Switzerland 50Physik-
Institut, Universität Zürich, Zürich, Switzerland 51NSC Kharkiv Institute of
Physics and Technology (NSC KIPT), Kharkiv, Ukraine 52Institute for Nuclear
Research of the National Academy of Sciences (KINR), Kyiv, Ukraine
53University of Birmingham, Birmingham, United Kingdom 54H.H. Wills Physics
Laboratory, University of Bristol, Bristol, United Kingdom 55Cavendish
Laboratory, University of Cambridge, Cambridge, United Kingdom 56Department of
Physics, University of Warwick, Coventry, United Kingdom 57STFC Rutherford
Appleton Laboratory, Didcot, United Kingdom 58School of Physics and Astronomy,
University of Edinburgh, Edinburgh, United Kingdom 59School of Physics and
Astronomy, University of Glasgow, Glasgow, United Kingdom 60Oliver Lodge
Laboratory, University of Liverpool, Liverpool, United Kingdom 61Imperial
College London, London, United Kingdom 62Department of Physics and Astronomy,
University of Manchester, Manchester, United Kingdom 63Department of Physics,
University of Oxford, Oxford, United Kingdom 64Massachusetts Institute of
Technology, Cambridge, MA, United States 65University of Cincinnati,
Cincinnati, OH, United States 66University of Maryland, College Park, MD,
United States 67Los Alamos National Laboratory (LANL), Los Alamos, United
States 68Syracuse University, Syracuse, NY, United States 69School of Physics
and Astronomy, Monash University, Melbourne, Australia, associated to 56
70Pontifícia Universidade Católica do Rio de Janeiro (PUC-Rio), Rio de
Janeiro, Brazil, associated to 2 71Physics and Micro Electronic College, Hunan
University, Changsha City, China, associated to 7 72Guangdong Provincial Key
Laboratory of Nuclear Science, Guangdong-Hong Kong Joint Laboratory of Quantum
Matter, Institute of Quantum Matter, South China Normal University, Guangzhou,
China, associated to 3 73School of Physics and Technology, Wuhan University,
Wuhan, China, associated to 3 74Departamento de Fisica , Universidad Nacional
de Colombia, Bogota, Colombia, associated to 13 75Universität Bonn -
Helmholtz-Institut für Strahlen und Kernphysik, Bonn, Germany, associated to
17 76Institut für Physik, Universität Rostock, Rostock, Germany, associated to
17 77Eotvos Lorand University, Budapest, Hungary, associated to 48 78INFN
Sezione di Perugia, Perugia, Italy, associated to 21 79Van Swinderen
Institute, University of Groningen, Groningen, Netherlands, associated to 32
80Universiteit Maastricht, Maastricht, Netherlands, associated to 32
81National Research Centre Kurchatov Institute, Moscow, Russia, associated to
41 82National Research University Higher School of Economics, Moscow, Russia,
associated to 42 83National University of Science and Technology “MISIS”,
Moscow, Russia, associated to 41 84National Research Tomsk Polytechnic
University, Tomsk, Russia, associated to 41 85DS4DS, La Salle, Universitat
Ramon Llull, Barcelona, Spain, associated to 45 86University of Michigan, Ann
Arbor, United States, associated to 68

aUniversidade Federal do Triângulo Mineiro (UFTM), Uberaba-MG, Brazil
bHangzhou Institute for Advanced Study, UCAS, Hangzhou, China cUniversità di
Bari, Bari, Italy dUniversità di Bologna, Bologna, Italy eUniversità di
Cagliari, Cagliari, Italy fUniversità di Ferrara, Ferrara, Italy gUniversità
di Firenze, Firenze, Italy hUniversità di Genova, Genova, Italy iUniversità
degli Studi di Milano, Milano, Italy jUniversità di Milano Bicocca, Milano,
Italy kUniversità di Modena e Reggio Emilia, Modena, Italy lUniversità di
Padova, Padova, Italy mScuola Normale Superiore, Pisa, Italy nUniversità di
Pisa, Pisa, Italy oUniversità della Basilicata, Potenza, Italy pUniversità di
Roma Tor Vergata, Roma, Italy qUniversità di Siena, Siena, Italy rUniversità
di Urbino, Urbino, Italy sMSU - Iligan Institute of Technology (MSU-IIT),
Iligan, Philippines tAGH - University of Science and Technology, Faculty of
Computer Science, Electronics and Telecommunications, Kraków, Poland uP.N.
Lebedev Physical Institute, Russian Academy of Science (LPI RAS), Moscow,
Russia vNovosibirsk State University, Novosibirsk, Russia wDepartment of
Physics and Astronomy, Uppsala University, Uppsala, Sweden xHanoi University
of Science, Hanoi, Vietnam