2019 205 26 September

Measurement of electrons from semileptonic heavy-flavour hadron decays ALICE
Collaboration††thanks: See Appendix A for the list of collaboration members
ALICE Collaboration

The differential invariant yield as a function of transverse momentum
($p_{\mathrm{T}}$) of electrons from semileptonic heavy-flavour hadron decays
was measured at midrapidity in central (0–10%), semi-central (30–50%) and
peripheral (60–80%) lead–lead (Pb–Pb) collisions at
$\sqrt{s_{\mathrm{NN}}}=5.02\text{ TeV}$ in the $p_{\mathrm{T}}$ intervals
0.5–26 GeV/$c$ (0–10% and 30–50%) and 0.5–10 GeV/$c$ (60–80%). The production
cross section in proton–proton (pp) collisions at $\sqrt{s}=5.02$ TeV was
measured as well in $0.5<p_{\mathrm{T}}<10$ GeV/$c$ and it lies close to the
upper band of perturbative QCD calculation uncertainties up to
$p_{\mathrm{T}}=5$ GeV/$c$ and close to the mean value for larger
$p_{\mathrm{T}}$. The modification of the electron yield with respect to what
is expected for an incoherent superposition of nucleon–nucleon collisions is
evaluated by measuring the nuclear modification factor $R_{\mathrm{AA}}$. The
measurement of the $R_{\mathrm{AA}}$ in different centrality classes allows
in-medium energy loss of charm and beauty quarks to be investigated. The
$R_{\mathrm{AA}}$ shows a suppression with respect to unity at intermediate
$p_{\mathrm{T}}$, which increases while moving towards more central
collisions. Moreover, the measured $R_{\mathrm{AA}}$ is sensitive to the
modification of the parton distribution functions (PDF) in nuclei, like
nuclear shadowing, which causes a suppression of the heavy-quark production at
low $p_{\mathrm{T}}$ in heavy-ion collisions at LHC.

##  1 Introduction

The main goal of ALICE is the study of the Quark-Gluon Plasma (QGP), a state
of matter which is expected to be created in ultra-relativistic heavy-ion
collisions where high temperatures and high energy densities are reached at
the LHC [1]. Due to their large masses ($m_{\text{c}}\approx 1.5\mbox{
GeV/}c^{2}$, $m_{\text{b}}\approx 4.8\mbox{ GeV/}c^{2}$), charm and beauty
quarks (heavy-flavour) are mostly produced via partonic scattering processes
with high momentum transfer, which have typical time scales smaller than the
QGP thermalisation time (1 fm/$c$ [2]). Furthermore, additional thermal
production, as well as annihilation rates, of charm and beauty quarks in the
strongly-interacting matter are expected to be small in Pb–Pb collisions even
at LHC energies [3, 4]. Consequently, charm and beauty quarks experience the
full evolution of the hot and dense medium produced in high-energy heavy-ion
collisions, therefore they are ideal probes to investigate the properties of
the QGP.

Quarks and gluons interact strongly with the medium and they are expected to
lose energy through elastic collisions [5, 6] and radiative processes [7, 8].
Quarks have a smaller colour coupling factor with respect to gluons, hence the
energy loss for quarks is expected to be smaller than that for gluons. In
addition, the dead-cone effect is expected to reduce small-angle gluon
radiation for heavy quarks with moderate energy to mass ratio [9], thus
further attenuating the effect of the medium. The combination of all these
effects results in the observed hierarchical mass dependent energy loss [8,
10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22].

In order to quantify medium effects on heavy-flavour observables measured in
heavy-ion collisions, they are compared with measurements in proton–proton
(pp) collisions, where these effects are expected to be absent.

In pp collisions, heavy-quark production can be described by perturbative
Quantum Chromodynamics (pQCD) calculations for all transverse momenta, whereas
pQCD is not applicable for the calculation of light quark and gluon production
at low transverse momenta [3]. Moreover, measurements of heavy-flavour
production cross sections in pp collisions provide the necessary experimental
reference for heavy-ion collisions.

The medium effects on heavy quarks are quantified through the measurement of
the nuclear modification factor, defined as the ratio between the yield of
particles produced in ion–ion collisions
($\mathrm{d}^{2}N_{\mathrm{AA}}/\mathrm{d}p_{\mathrm{T}}\mathrm{d}y$) and the
cross section measured in proton-proton collisions at the same energy
($\mathrm{d}^{2}\sigma_{\mathrm{pp}}/\mathrm{d}p_{\mathrm{T}}\mathrm{d}y$),
normalised by the average nuclear overlap function $\langle
T_{\mathrm{AA}}\rangle$:

$R_{\mathrm{AA}}(p_{\mathrm{T}},y)=\frac{1}{\langle
T_{\mathrm{AA}}\rangle}\cdot\frac{\mathrm{d}^{2}N_{\mathrm{AA}}/\mathrm{d}p_{\mathrm{T}}\mathrm{d}y}{\mathrm{d}^{2}\sigma_{\mathrm{pp}}/\mathrm{d}p_{\mathrm{T}}\mathrm{d}y}\hskip
2.84526pt.$ (1)

The $\langle T_{\text{AA}}\rangle$ is defined as the average number of
nucleon–nucleon collisions $\langle N_{\textrm{coll}}\rangle$, which can be
estimated via Glauber model calculations [23, 24], divided by the inelastic
nucleon-nucleon cross section. In-medium energy loss shifts the transverse
momenta towards lower values, therefore at intermediate and high
$p_{\mathrm{T}}$ ($p_{\mathrm{T}}\apprge 2\text{ GeV/}c$) a suppression of the
production is expected ($R_{\mathrm{AA}}<1$). Assuming the total cross section
evaluated using $\langle N_{\textrm{coll}}\rangle$ scaling is not modified,
the nuclear modification factor is expected to increase towards lower
$p_{\mathrm{T}}$, compensating the depletion at higher momenta. Such a rise
was measured by the PHENIX and STAR experiments at RHIC in Au–Au and Cu–Cu
collisions at $\sqrt{s_{\mathrm{NN}}}=200\text{ GeV}$ for electrons from
heavy-flavour hadron decays [25, 26, 27]. The nuclear modification factor for
electrons from semileptonic heavy-flavour hadron decays was also measured by
the ALICE collaboration in Pb–Pb collisions at
$\sqrt{s_{\mathrm{NN}}}=2.76\text{ TeV}$ [28, 29], where the mentioned trend
of $R_{\mathrm{AA}}$ was also observed. At low $p_{\mathrm{T}}$, the nuclear
modification factor reaches a maximum around $1\text{ GeV/}c$ and tends to
decrease at lower $p_{\mathrm{T}}$. This trend can be explained by initial and
final state effects, like the collective expansion of the hot and dense system
[30, 31, 32], the interplay between hadronisation via fragmentation and
coalescence [33, 34, 22] and the modification of the parton distribution
functions (PDF) inside bound nucleons [35].

Initial-state effects at the LHC are explored with proton–nucleus collisions,
where an extended QGP phase is not expected to be formed. The nuclear
modification factor of electrons from charm and beauty hadron decays [14, 36]
and of D mesons [37] in p–Pb collisions at $\sqrt{s_{\mathrm{NN}}}=5.02\text{
TeV}$ was found to be consistent with unity within uncertainties. From this,
one can conclude that the strong suppression observed in Pb–Pb collisions is
due to substantial final-state interactions of heavy quarks with the QGP
formed in these collisions. However, it is important to note that recently the
measurement of the elliptic flow of electrons from semileptonic heavy-flavour
hadron decays [38] and of D mesons [39] have been published, showing
intriguing and not yet fully understood collective effects in high-
multiplicity p–Pb collisions in the heavy-flavour sector.

This paper reports the measurement of the production cross section in pp
collisions, the invariant yields and the nuclear modification factor,
$R_{\mathrm{AA}}$, in Pb–Pb collisions as a function of $p_{\mathrm{T}}$ of
electrons from semileptonic heavy-flavour hadron decays at mid-rapidity at the
centre-of-mass energy per nucleon pair $\sqrt{s_{\mathrm{NN}}}=5.02\text{
TeV}$. In order to study how the yield and $R_{\mathrm{AA}}$ change with
centrality in Pb–Pb collisions, the measurement was done in three
representative classes: the 0-10% class for central Pb–Pb collisions, the
30-50% for semi-central Pb–Pb collisions and 60-80% for peripheral Pb–Pb
collisions.

##  2 Experimental apparatus and data sample

The ALICE detector is described in detail in Refs. [1, 40]. The experiment
mainly consists of a central barrel at midrapidity ($|\eta|<0.9$), embedded in
a cylindrical solenoid which provides a magnetic field of 0.5 T parallel to
the beam direction, and a muon spectrometer at forward rapidity
($-4<\eta<-2.5$).

Charged particles produced in the collisions and originating from particle
decays are tracked by the Inner Tracking System (ITS) [41] and the Time
Projection Chamber (TPC) [42]. The ITS detector, composed of the Silicon Pixel
Detector (SPD), Silicon Drift Detector (SDD), and Silicon Strip Detector
(SSD), consists of six cylindrical silicon layers surrounding the beam vacuum
pipe. These provide measurements of particle momenta and energy loss
(d$E$/d$x$) used for charged-particle identification (PID), together with the
TPC. The particle identification is complemented by a Time-Of-Flight (TOF)
[43] detector, which measures the time-of-flight of charged particles. The TOF
detector distinguishes electrons from kaons, protons, and pions up to
$p_{\mathrm{T}}\simeq 2.5$ GeV/$c$, $p_{\mathrm{T}}\simeq 4$ GeV/$c$ and
$p_{\mathrm{T}}\simeq 1$ GeV/$c$, respectively. The ElectroMagnetic
Calorimeter (EMCal) [44] covers a pseudorapidity region of $|\eta|<0.7$ and it
is used to measure electrons, photons, and jets in an azimuthal region of
$\sim 107^{\text{o}}$. The electron identification in the EMCal is based on
the measurement of the $E/p$ ratio, where $E$ is the energy of the EMCal
cluster matched to the prolongation of the track with momentum $p$
reconstructed with the TPC and ITS detectors. The V0 detectors [45] consist of
two arrays of 32 scintillator tiles covering the pseudorapidity ranges
$2.8<\eta<5.1$ (V0A) and $-3.7<\eta<-1.7$ (V0C), respectively, and are used
for event characterisation.

The results presented in this paper are based on data samples of Pb–Pb
collisions recorded in 2015 and of pp collisions at the same energy recorded
in 2017. The analysed events were collected with a minimum bias (MB) trigger
of a logic AND between the V0A and V0C detectors. Pb–Pb collisions were also
recorded using the EMCal trigger, which requires an EMCal cluster energy
summed over a group of 4$\times$4 calorimeter cells larger than an energy
threshold of 10 GeV. The EMCAL triggered events were used for electron
measurements for $p_{\mathrm{T}}>12$ GeV/$c$. The centrality classes were
defined in terms of percentiles of the hadronic Pb–Pb cross section, defined
by selections on the sum of the V0 signal amplitudes [46].

For both collision systems, only events with at least two tracks and a
reconstructed primary vertex located between $\pm$ 10 cm with respect to the
nominal interaction point along the $z$-axis are considered. Events affected
by pile-up from different bunch crossings, which constitute less than 1% of
the recorded sample, were rejected [28]. The number of events analysed in the
two collision systems with the different trigger configurations is summarised
in Table 1, together with the average nuclear overlap function $\langle
T_{\mathrm{AA}}\rangle$ [46, 47].

Table 1:  Number of events and $\langle T_{\mathrm{AA}}\rangle$ [46, 47] used in the analysis, split by collisions system, trigger configuration, and centrality class.  | centrality | MB | EMCal trigger |  $\langle T_{\mathrm{AA}}\rangle$ (mb-1)
---|---|---|---|---
pp | – | 881$\times 10^{6}$ | – | –
Pb–Pb | 0–10% | 6 $\times 10^{6}$ | 1.2 $\times 10^{6}$ | $23.26\pm 0.17$
30–50% | 12 $\times 10^{6}$ | 0.3 $\times 10^{6}$ | $3.917\pm 0.065$
60–80% | 12 $\times 10^{6}$ | – | $0.4188\pm 0.0106$

##  3 Data analysis

The $p_{\rm T}$-differential yield of electrons from semileptonic heavy-
flavour hadron decays is computed by measuring the inclusive electron yield
and subtracting the contribution of electrons that do not originate from
semileptonic heavy-flavour hadron decays. In the following, the inclusive
electron identification strategy and the subtraction of electrons originating
from background sources are described.

###  3.1 Track selection and electron identification

The selection criteria are similar to the ones described in Refs. [28, 29].
They are summarised together with the kinematic cuts applied in the analyses
in Table 2.

It is important to note that only tracks that have hits on both SPD layers are
accepted so that electrons from late photon conversions in the detector
material are significantly reduced. In the Pb–Pb analysis for $p_{\mathrm{T}}$
$>$3 GeV/$c$, also tracks with a single hit in the SPD are considered, since
the amount of photonic background starts to become negligible. In the analysis
in which the EMCal detector is used, specific track-cluster matching criteria
are adopted.

Table 2: Track selection criteria used in the analyses.“DCA” is an abbreviation for “distance of closest approach” of a track to the primary vertex.  Parameter | pp | Pb–Pb | Pb–Pb
---|---|---|---
|  | ($p_{\mathrm{T}}$ $<$ 3 GeV/$c$) | ($p_{\mathrm{T}}$ $>$ 3 GeV/$c$)
$|y|$ |  $<$ 0.8 |  $<$ 0.8 |  $<$ 0.6
Number of clusters in TPC | $\geq 100$ | $\geq 120$ | $\geq 80$
TPC clusters in d$E$/d$x$ calculation | $\geq 80$ | $\geq 80$ | –
Number of clusters in ITS | $\geq 3$ | $\geq 4$ | $\geq 3$
Minimum number of clusters in SPD | 2 | 2 | 1
$|$DCA${}_{\text{xy}}|$ |  $<1$ cm |  $<1$ cm |  $<2.4$ cm
$|$DCA${}_{\text{z}}|$ |  $<2$ cm |  $<2$ cm |  $<3.2$ cm
Found / findable clusters in TPC | $>0.6$ | $>0.6$ | $>0.6$
$\chi^{2}$/clusters in TPC |  $<$ 4 |  $<$ 4 |  $<$ 4
track-cluster matching in EMCal | – | – | $\sqrt{\Delta\varphi^{2}+\Delta\eta^{2}}<0.02$

As in the procedure followed in Refs. [28, 29], electron candidates are
identified according to the criteria listed in Table 3. These requirements
depend on the data sample and on the transverse momentum interval in which the
analyses are performed.

The electron identification in pp collisions is performed by evaluating the
signal from the TPC and TOF detectors. The discriminant variable in the former
detector is the deviation of d$E$/d$x$ from the parameterised electron Bethe-
Bloch [48] expectation value, expressed in units of the d$E$/d$x$ resolution,
$n_{\sigma\textrm{,e}}^{\rm TPC}$, while in the latter one the analogous
variable $n_{\sigma\textrm{,e}}^{\rm TOF}$, referring to the particle time-of-
flight, is considered. The criterion
$|n_{\sigma\textrm{,e}}^{\textrm{TOF}}|<3$, used for electron identification
up to $p_{\mathrm{T}}=3$ GeV/$c$, is required to reduce background from kaons
and protons. A momentum dependent criterion on
$n_{\sigma\textrm{,e}}^{\textrm{TPC}}$ is adopted to guarantee a constant
electron identification efficiency of 70% for $p_{\mathrm{T}}<3$ GeV/$c$ and
of 50% for higher transverse momenta by reducing the selection window in
$n_{\sigma\textrm{,e}}^{\textrm{TPC}}$, in order to keep the hadron
contamination sufficiently low. In the Pb–Pb analysis for $p_{\mathrm{T}}<3$
GeV/$c$, the electron identification is performed by applying the same
requirement on TOF and due to the large densities of tracks, a selection
between $-4<n_{\sigma\textrm{,e}}^{\rm ITS}<2$ on the energy deposited in the
SDD and SSD detectors is applied in all centrality classes. Finally, the
selection on $n_{\sigma\textrm{,e}}^{\textrm{TPC}}$ ensures a constant
electron identification efficiency of 50% for all centrality classes. The
hadron contamination fraction after the PID is estimated by fitting the
$n_{\sigma\textrm{,e}}^{\text{TPC}}$ distribution for each particle species
with an analytic function in different momentum intervals [28, 29]. The
inclusive electron sample is then selected by applying a further criterion on
$n_{\sigma\textrm{,e}}^{\text{TPC}}$, which is chosen in order to have a
constant efficiency as a function of the momentum, as well as to have the
hadron contamination under control. This criterion is loosened for
$p_{\mathrm{T}}>3$ GeV/$c$, due to the lower amount of selected hadrons when
the EMCal detector is employed.

In the Pb–Pb analysis for $p_{\mathrm{T}}>3$ GeV/$c$, the electron candidates
are first selected by the measurement of the TPC d$E$/d$x$ with the criterion
$-1<n_{\sigma\textrm{,e}}^{\textrm{TPC}}<$3\. Then, the selection
$0.8<E/p<1.3$ on the energy over momentum ratio is applied. Unlike for
hadrons, the ratio $E/p$ is close to 1 for electrons because they deposit most
of their energy in the EMCal. Furthermore, the electromagnetic showers of
electrons are more circular than the ones produced by hadrons. Generally, the
shower shape produced in the calorimeter has an elliptical shape which can be
characterised by its two axes: $\sigma_{l}^{2}$ for the long, and
$\sigma_{s}^{2}$ for the short axis. A rather lose selection of
$0.01<\sigma_{s}^{2}<0.35$ is chosen, since it reduces the hadron
contamination while at the same time it does not affect significantly the
electron signal [29]. The residual hadron background in the electron sample is
evaluated using the $E/p$ distribution for hadron-dominated tracks selected
with $n_{\sigma\textrm{,e}}^{\text{TPC}}<-3.5$. The $E/p$ distribution of the
hadrons is then normalised to match the distribution of the electron
candidates in $0.4<E/p<0.7$ (away from the true electron peak), so that the
fraction of contaminating hadrons under the electron peak can be estimated.

Table 3: Electron identification criteria. The following momentum-dependent function is used for the electron identification in pp collisions, based on the TPC d$E$/d$x$: $f(p)=\textrm{Min}(0.12,0.02+0.07p)$. For the electron selection based on clusters in the EMCAL, a criterion on the “$\sigma_{s}^{2}$" parameter [29], corresponding to the shorter-axis of the shower shape, is used. For brevity, the “low $p_{\mathrm{T}}$" label is used in place of “$p_{\mathrm{T}}<3$ GeV/$c$", as well as “high $p_{\mathrm{T}}$" in place of “$p_{\mathrm{T}}>3$ GeV/$c$".  | centrality | n${}_{\sigma\textrm{,e}}^{\text{TPC}}$ | n${}_{\sigma\textrm{,e}}^{\text{TOF}}$ | n${}_{\sigma\textrm{,e}}^{\text{ITS}}$ | $E/p$ | shower shape
---|---|---|---|---|---|---
pp (low $p_{\mathrm{T}}$) | – |  $[-0.5+f(p),$ $3]$ | $[-3,3]$ | – | – | –
pp (high $p_{\mathrm{T}}$) | – |  $[0.12,$ $3]$ | – | – | – | –
Pb–Pb (low $p_{\mathrm{T}}$) | 0–10% | $[-0.16,3]$ |  |  |  |
30–50% | $[0,3]$ | $[-3,3]$ | $[-4,2]$ | – | –
60–80% | $[0.2,3]$ |  |  |  |
Pb–Pb (high $p_{\mathrm{T}}$) | 0–10% |  |  |  |  |
30–50% | $[-1,3]$ | – | – | [0.8, 1.3] | $0.01<\text{$\sigma_{s}^{2}$}<0.35$
60–80% |  |  |  |  |

In pp events, the hadron contamination is below $1\%$ at low $p_{\mathrm{T}}$,
while it reaches about $40\%$ at $p_{\mathrm{T}}=10$ GeV/$c$. In Pb–Pb, the
largest hadron contamination is measured in the most central collisions, where
a contamination of about $7\%$ and $10\%$ mainly due to kaon and proton
crossing the electron band at $p_{\mathrm{T}}=0.5$ GeV/$c$ and
$p_{\mathrm{T}}=1$ GeV/$c$ respectively is present. The total hadron
contamination contribution amounts to $5\%$ at $p_{\mathrm{T}}=3$ GeV/$c$ in
central events and tends to decrease towards more peripheral collisions. In
the EMCal analysis a maximum residual contamination of about $10\%$ is
subtracted at the highest transverse momenta in the 0–10% centrality class. In
both collision systems, the hadron contamination is subtracted statistically
from the inclusive electron candidate yield.

In Pb–Pb collisions, the rapidity ranges used in the ITS-TPC-TOF
($p_{\mathrm{T}}$ $<$ 3 GeV/$c$) and TPC-EMCal ($p_{\mathrm{T}}$ $>$ 3
GeV/$c$) analyses are restricted to $|y|$ $<$ 0.8 and $|y|$ $<$ 0.6,
respectively, to avoid the edges of the detectors, where the systematic
uncertainties related to particle identification increase.

###  3.2 Subtraction of electrons from non heavy-flavour sources

The selected inclusive electron sample does not only contain electrons from
open heavy-flavour hadron decays, but also different sources of background:

  1. 1.

electrons from Dalitz decays of light neutral mesons, mainly $\pi^{0}$ and
$\eta$, and from photon conversions in the detector material as well as from
thermal and hard scattering processes, called photonic in the following ;

  2. 2.

electrons from weak decays of kaons: ${\rm K^{0/\pm}}\rightarrow{\rm
e}^{\pm}\pi^{\mp/0}\,\overset{\scriptscriptstyle(-)}{\nu_{e}}$ (${\rm K}_{{\rm
e}3}$) ;

  3. 3.

di-electron decays of quarkonia: J$/\psi$, $\Upsilon\to$ e+e- ;

  4. 4.

di-electron decays of light vector mesons: $\omega,\phi,\rho_{0}\to$ e+e- ;

  5. 5.

electrons from $\mathrm{W}$ and $\mathrm{Z}/\gamma^{*}$ .

The photonic tagging method [28, 29, 36, 49, 21] is the technique adopted in
the present analyses to estimate the contribution from photonic electrons.
With a contribution of 80% to the inclusive electron sample, photonic
electrons constitute the main background at $p_{\mathrm{T}}=0.5$ GeV/$c$ [28].
Their contribution decreases with $p_{\mathrm{T}}$ reaching 25% at about $3$
GeV/$c$. The contribution from di-electron decays of light vector mesons
($\rho$, $\omega$ and $\phi$) is negligible compared to the contributions from
the photonic sources [50].

Photonic electrons are reconstructed statistically by pairing electron
(positron) tracks with opposite charge tracks identified as positrons
(electrons), called associated electrons in the following, forming the so-
called unlike-sign pairs. The combinatorial background is subtracted using the
like-sign invariant mass distribution in the same interval. Associated
electrons are selected with the criteria listed in Table 4, which are
intentionally looser than the ones applied for the inclusive electron
selection, shown in Table 2, in order to maximise the probability to find the
photonic partners.

Table 4: Selection criteria for tagging photonic electrons. Associated electron | pp | Pb–Pb | Pb–Pb
---|---|---|---
|  | ($p_{\mathrm{T}}$ $<$ 3 GeV/$c$) | ($p_{\mathrm{T}}$ $>$ 3 GeV/$c$)
$p_{\mathrm{T}}^{\text{min}}$ (GeV/$c$) | 0.1 | 0.1 | 0.2
$|y|$ |  $<$ 0.8 |  $<$ 0.8 |  $<$ 0.9
Number of clusters in TPC | $\geq 60$ | $\geq 60$ | $\geq 70$
TPC clusters in d$E$/d$x$ calculation | $\geq 60$ | $\geq 60$ | –
Number of clusters in ITS | $\geq 2$ | $\geq 2$ | $\geq 2$
$|$DCA${}_{\text{xy}}|$ |  $<1$ cm |  $<1$ cm |  $<2.4$ cm
$|$DCA${}_{\text{z}}|$ |  $<2$ cm |  $<2$ cm |  $<3.2$ cm
Found / findable clusters in TPC | $>0.6$ | $>0.6$ | –
$\chi^{2}$/d.o.f TPC |  $<$ 4 |  $<$ 4 |  $<$ 4
$n_{\sigma\textrm{,e}}^{\text{TPC}}$ | $[-3,3]$ | $[-3,3]$ | $[-3,3]$
$m_{\text{e}^{+}\text{e}^{-}}$ (MeV/$c^{2}$) | $<140$ | $<140$ | $<100$

Due to the limited acceptance of the detector and the rejection of some
associated electrons by applying the mentioned criteria, a certain fraction of
photonic pairs is not reconstructed. Therefore, the raw yield of tagged
photonic electrons is corrected for efficiency to find the associated electron
(positron), the so called tagging efficiency ($\varepsilon_{\text{tag}}$).
This is evaluated using Monte Carlo (MC) simulations; pp and Pb–Pb collisions
are simulated by the PYTHIA 6 [51] and HIJING [52] event generators,
respectively. Primary particle generation is followed by particle transport
with GEANT3 [53] and a detailed detector response simulation and
reconstruction. The tagging efficiency is defined as the ratio of the number
of true reconstructed unlike-sign pair electrons and the number of those
generated in the simulations. The simulated $p_{\mathrm{T}}$ distributions of
$\pi^{0}$ or $\eta$ mesons are weighted in MC to match the measured spectra.
In both pp and Pb–Pb collisions, the weighting factor for $\pi^{0}$ is
provided by using the measured distributions of charged pions [54]. The
weighting factor for $\eta$ mesons is computed using an $m_{\text{T}}$–scaling
approach [55, 56]. The total tagging efficiency has a monotonic trend. In pp
collisions, it starts at $0.4$ for $p_{\mathrm{T}}=0.5$ GeV/$c$ and rises
until $p_{\mathrm{T}}=3$ GeV/$c$, where it flattens at $0.7$. In Pb–Pb
collisions, it follows the same trend, increasing from $0.3$ to $0.7$ in the
same $p_{\mathrm{T}}$ range.

It was observed in the previous analysis [28] that the contribution from
J/$\psi$ decays reaches a maximum of around 5% in the region
$2<p_{\mathrm{T}}<3$ GeV/$c$ in central Pb–Pb collisions, decreasing to a few
percent in more peripheral events. At lower and higher momenta, this
contribution quickly decreases and becomes negligible, hence it is not
subtracted in the present analyses. The associated systematic uncertainty is
taken from similar works [28, 29]. Due to the requirement of hits in both
pixel layers, it was also observed from similar studies in previous
measurements [28] that the relative contribution from $K_{e{3}}$ decays to the
electron background is negligible, hence this contribution is not subtracted
in the present analyses. Additional sources of background, such as electrons
from $W$ and $Z/\gamma^{*}$ decays, are subtracted from the fully corrected
and normalised electron yield in Pb–Pb collisions at high $p_{\mathrm{T}}$.
These contributions are obtained from calculations using the POWHEG event
generator [57] for pp collisions and scaling it by $\langle
N_{\text{coll}}\rangle$, assuming $R_{\mathrm{AA}}=1$. The contribution from
$W$ decays increases from 1% at $p_{\mathrm{T}}=10$ GeV/$c$ to about 20% at
$p_{\mathrm{T}}=25$ GeV/$c$ in the 0–10% centrality class, while the $Z$
contribution reaches about $10\%$ at the same transverse momentum.

###  3.3 Efficiency correction and normalisation

After the statistical subtraction of the hadron contamination and the
background from photonic electrons, the raw yield of electrons and positrons
in bins of $p_{\mathrm{T}}$ is divided by the number of analysed events
($N_{\text{ev}}^{\text{MB}}$), by the transverse momentum value at the bin
centre $p_{\mathrm{T}}^{\text{centre}}$ and the bin width $\Delta
p_{\mathrm{T}}$, by the width $\Delta y$ of the covered rapidity interval, by
the geometrical acceptance ($\varepsilon^{\text{geo}}$) times the
reconstruction ($\varepsilon^{\text{reco}}$) and PID efficiencies
($\varepsilon^{\text{eID}}$), and by a factor of two to obtain the charge
averaged invariant differential yield, since in the analyses the distinction
between positive and negative charges is not done:

$\frac{1}{2\pi
p_{\mathrm{T}}}\frac{\text{d}^{2}N^{e^{\pm}}}{\text{d}p_{\mathrm{T}}\text{d}y}=\frac{1}{2}\frac{1}{2\pi
p_{\mathrm{T}}^{\text{centre}}}\frac{1}{N_{\text{ev}}^{\text{MB}}}\frac{1}{\Delta
y\Delta
p_{\mathrm{T}}}\frac{N^{e^{\pm}}_{\text{raw}}(p_{\mathrm{T}})}{(\varepsilon^{\text{geo}}\times\varepsilon^{\text{reco}}\times\varepsilon^{\text{eID}})}\hskip
2.84544pt.$ (2)

The production cross section in pp collisions is calculated by multiplying the
invariant yield of Eq. 2 by the minimum bias trigger cross section at
$\sqrt{s}=5.02$ TeV, that is 50.9 $\pm$ 0.9 mb [58]. The per-event yield of
electrons from the EMCal triggered sample was scaled to the minimum bias yield
by normalisation factors determined with a data-driven method based on the
ratio of the energy distributions of EMCal clusters for the two triggers, as
described in Ref. [29]. The normalisation is 64.5 $\pm$ 0.5 in 0–10% and 246
$\pm$ 2.6 in 30–50% centrality intervals, respectively.

The efficiencies are determined using specific MC simulations, where every
collision event is produced with at least either a $c\overline{c}$ or
$b\overline{b}$ pair and heavy-flavour hadrons are forced to decay
semileptonically to electrons [28, 29]. The underlying Pb–Pb events were
simulated using the HIJING generator [52] and heavy-flavour signals were added
using the PYTHIA 6 generator [51]. The efficiency of reconstructing electrons
from semileptonic heavy-flavour hadron decays is about $20\%$ at
$p_{\mathrm{T}}=0.5$ GeV/$c$, then it increases with $p_{\mathrm{T}}$ up to
$58\%$ in pp collisions. In Pb–Pb collisions, it follows the same trend,
increasing from $5\%$ to $10\%$ in the same $p_{\mathrm{T}}$ range.

###  3.4 Systematic uncertainties

The overall systematic uncertainties on the $p_{\mathrm{T}}$ spectra are
calculated summing in quadrature the different contributions, which are
assumed to be uncorrelated. They are summarised in Table 5 and discussed in
the following.

The systematic uncertainties on the total reconstruction efficiency arising
from the comparison between MC and data are estimated by varying the track
selection and PID requirements around the default values chosen in the
analyses. The analysis is repeated with tighter and looser conditions with
respect to the default selection criteria and the systematic uncertainty is
calculated as the root mean square (RMS) of the distribution of the resulting
corrected yields (or cross sections in pp) in each centrality and
$p_{\mathrm{T}}$ interval. The systematic uncertainty estimated in pp
collisions is less than 2%, while in Pb–Pb collisions it reaches a maximum
value of 4% in 0–10% centrality class for $p_{\mathrm{T}}<0.9$ GeV/$c$.

Similarly, the systematic uncertainty arising from the photonic-electron
subtraction technique is estimated as the RMS of the distribution of yields
obtained by varying the selection criteria listed in Table 4. In pp collisions
this contribution has a maximum of 4% for $0.5<p_{\mathrm{T}}<0.7$ GeV/$c$ and
then it gradually decreases with increasing $p_{\mathrm{T}}$, while in the
0–10% Pb–Pb centrality class it is the dominant source of systematic
uncertainty, being 13% in the first $p_{\mathrm{T}}$ interval. This systematic
uncertainty mainly arises when the invariant mass criterion on the photonic
pairs is varied and it reflects the large contribution of photonic electrons
in the low-$p_{\mathrm{T}}$ region.

In order to further test the robustness of the photonic electron tagging, the
requirement on the number of clusters for electron candidates in the SPD is
relaxed in order to increase the fraction of electrons coming from photon
conversions in the detector material. A variation of 3% is observed for the
measured pp cross section in the full $p_{\mathrm{T}}$ range, while in central
Pb–Pb collisions the observed deviation amounts to 10% for
$0.5<p_{\mathrm{T}}<0.7$ GeV/$c$, decreasing with increasing $p_{\mathrm{T}}$.
This systematic uncertainty is less relevant in semi-central collisions, and
it is compatible with the variation determined in pp measurements for
$1.5<p_{\mathrm{T}}<3$ GeV/$c$.

In addition, the systematic uncertainty related to the subtraction of the
background electrons from W and $Z/\gamma^{*}$ is estimated by propagating 15%
of uncertainty, which covers the possible difference between the measurements
and the theoretical calculations [59, 60, 61]. The uncertainty from the
subtraction on the final result, which is relevant only at high
$p_{\mathrm{T}}$, is less than 4% for electrons from semileptonic heavy-
flavour hadron decays in central (0–10%) Pb–Pb collisions for
24$<p_{\textrm{T}}<$ 26 GeV/$c$, and less than 1% in other centrality classes
for the same $p_{\mathrm{T}}$ interval. In the pp analysis, a 5% systematic
uncertainty is found while varying the selection criterion in the TPC for
$p_{\mathrm{T}}>8$ GeV/$c$ due to the increasing relative amount of hadrons.
An additional systematic uncertainty of 5%, related to the precision of the
estimated hadron contamination, is assigned for $p_{\mathrm{T}}>8$ GeV/$c$. In
Pb–Pb collisions, a 10% systematic uncertainty is assigned for
$p_{\mathrm{T}}>12$ GeV/$c$ due to the variation of electron identification in
the TPC, while this contribution is within 5% at lower $p_{\mathrm{T}}$.
Moreover, a 6% uncertainty is assigned due to the $E/p$ selection criterion.
Finally, for $p_{\mathrm{T}}<3$ GeV/$c$, different functional forms are used
for the parametrisation of the pion contribution in the fitting procedure
adopted to evaluate the hadron contamination. A systematic uncertainty of
about 6% is assigned for $p_{\mathrm{T}}<3$ GeV/$c$ in the 0–10% centrality
class, while this contribution decreases for more peripheral collisions.

In the pp (Pb–Pb) analysis, a systematic uncertainty of about 2% (3%) is
assigned due to the incomplete knowledge of the efficiency in matching tracks
reconstructed in the ITS and TPC and another 2% (5%) for the track matching
between TPC and TOF.

The effects due to the presence of non-uniformity in the correction for the
space-charge distortion in the TPC drift volume or irregularities in the
detector coverage are then evaluated by repeating the analysis in different
geometrical regions. In pp collisions, a maximum systematic uncertainty of 5%
is estimated from varying the pseudorapidity range used for the cross section
measurement. The same value is assigned in the 30–50% and 60–80% Pb–Pb
centrality intervals, while a 10% systematic uncertainty is assigned for
$0.5<p_{\mathrm{T}}<0.7$ GeV/$c$ in the 0–10% centrality interval, due to the
larger sensitivity to the electrons from photon conversions. An additional
uncertainty of 10% for $p_{\mathrm{T}}<1$ GeV/$c$ and of 5% up to
$p_{\mathrm{T}}=3$ GeV/$c$ is estimated from varying the azimuthal region in
central Pb–Pb collisions. Furthermore, the analysis of Pb–Pb collisions is
repeated using different interaction rate regimes. A 5% deviation is observed
at low $p_{\mathrm{T}}$ in central Pb–Pb collisions when selecting only high
($>$ 5 kHz) or low ($<$ 5 kHz) interaction rate events.

The uncertainty from the EMCal trigger normalisation in Pb–Pb collisions at
$p_{\mathrm{T}}>12$ GeV/$c$ is estimated as the RMS of the rejection factor
values computed at different transverse momenta [29]. The RMS is 4% and
assigned as the systematic uncertainty.

The uncertainties on the $R_{\mathrm{AA}}$ normalisation are the quadratic sum
of the uncertainties on the average nuclear overlap functions in Table 1, the
normalisation uncertainty due to the luminosity and the uncertainty related to
the determination of the centrality intervals, which reflects the uncertainty
on the fraction of the hadronic cross section used in the Glauber fit to
determine the centrality [16, 62].

Table 5:  Contributions to the systematic uncertainties on the cross section (yield) of electrons from heavy-flavour hadron decays in pp (Pb–Pb) collisions, quoted for the transverse momentum intervals $0.5<p_{\mathrm{T}}<0.7$ GeV/$c$ and $8<p_{\mathrm{T}}<10$ GeV/$c$. These $p_{\mathrm{T}}$ intervals are listed because the detectors used for particle identification in the two cases are different. In addition, they also represent the first and the last $p_{\mathrm{T}}$ intervals in common for the centrality classes in Pb–Pb collisions, as well as for the pp cross section. At higher $p_{\mathrm{T}}$ the uncertainties are generally lower, apart from the one related to the electroweak background, which stays below 4%. The uncertainties quoted with * are not summed in quadrature together with the others, because they are the $R_{\mathrm{AA}}$ normalization uncertainties.  | pp | Pb–Pb (0–10%) | Pb–Pb (30–50%) | Pb–Pb (60–80%)
---|---|---|---|---
$\boldsymbol{p_{\mathrm{T}}}$ (GeV/$c$) | 0.5–0.7 | 8–10 | 0.5–0.7 | 8–10 | 0.5–0.7 | 8–10 | 0.5–0.7 | 8–10
Track selections | 1% | 1% | 4% | 2% | 1% | 2% | 2% | 2%
Photonic tagging | 4% | – | 13% | 4% | 7% | 4% | 7% | 4%
SPD hit requirement | 3% | 3% | 10% | – | – | – | – | –
J/$\psi$$\rightarrow$e | – | – | 2% | – | 2% | – | 2% | –
W$\rightarrow$e | – | – | – |  $<$4% | – |  $<$1% | – |  $<$1%
Z/$\gamma\rightarrow$e | – | – | – |  $<$1% | – |  $<$1% | – |  $<$1%
$n_{\sigma\textrm{,e}}^{\textrm{TPC}}$ selection | – | 5% | – | 5% | – | 5% | – | 2%
$E/p$ selection | – | – | – | 6% | – | 6% | – | 6%
Hadron contamination | – | 5% | 6% | – | 2% | – | – | –
ITS–TPC matching | 2% | 2% | 2% | 2% | 2% | 2% | 2% | 2%
TPC–TOF matching | 2% | – | 3% | – | – | – | – | –
$\eta$ | 5% | 4% | 10% | – | 5% | – | 5% | –
$\varphi$ | – | – | 10% | – | – | – | – | –
Interaction rate | – | – | 5% | – | – | – | – | –
Centrality limit* | – |  $<1$% |  $2$% |  $3$%
Luminosity* | 2.1% | – | – | –
Total uncertainty | 9% | 9% | 24% | 9% | 9% | 9% | 9% | 8%

##  4 Results

###  4.1 $p_{\mathrm{T}}$-differential cross section in pp collisions and
invariant yield in Pb–Pb collisions

The $p_{\mathrm{T}}$-differential production cross section of electrons from
semileptonic heavy-flavour hadron decays in pp collisions at $\sqrt{s}=5.02$
TeV is shown in Fig. 1. The data in the region $0.5<p_{\mathrm{T}}<10$ GeV/$c$
is compared with the Fixed-Order-Next-to-Leading-Log (FONLL) [63] pQCD
calculation. The uncertainties of the FONLL calculations (dashed area) reflect
different choices for the charm and beauty quark masses, the factorisation and
renormalisation scales as well as the uncertainty on the set of parton
distribution functions (PDF) used in the pQCD calculation (CTEQ6.6 [64]). The
measured cross section is close to the upper edge of the theoretical
prediction up to $p_{\mathrm{T}}\simeq 5$ GeV/$c$, as observed in pp
collisions at $\sqrt{s}=2.76$ and 7 TeV [28, 49, 50], while at higher
$p_{\textrm{T}}$, where electrons from semileptonic beauty hadron decays are
expected to dominate, the measurement is close to the mean value of the FONLL
prediction.

The $p_{\mathrm{T}}$-differential invariant yield of electrons from
semileptonic heavy-flavour hadron decays measured in central (0–10%), semi-
central (30–50%), and peripheral (60–80%) Pb–Pb collisions at
$\sqrt{s_{\mathrm{NN}}}=5.02$ TeV is shown in Fig. 2. The measurements are
performed in the $p_{\mathrm{T}}$ interval 0.5–26 GeV/$c$ in the 0–10% and in
the 30–50% centrality intervals, and only up to $p_{\mathrm{T}}$ = 10 GeV/$c$
in the 60–80% centrality class due to limited statistics in Pb-Pb data
recorded in 2015.

Figure 1: $p_{\mathrm{T}}$-differential invariant production cross section of
electrons from semileptonic heavy-flavour hadron decays in pp collisions at
$\sqrt{s}=5.02$ TeV. The measurement is compared with the FONLL calculation
[63]. In the bottom panel, the ratios with respect to the central values of
the FONLL calculation are shown. An additional 2.1% normalisation uncertainty,
due to the measurement of the minimum bias triggered cross section [46], is
not shown in the results. Figure 2: $p_{\mathrm{T}}$-differential invariant
yield in central (0–10%), semi-central (30–50%), and peripheral (60–80%) Pb–Pb
collisions at $\sqrt{s_{\mathrm{NN}}}=5.02$ TeV.

###  4.2 Nuclear modification factor

The nuclear modification factor of electrons from semileptonic heavy-flavour
hadron decays measured in central (0–10%), semi-central (30–50%), and
peripheral (60–80%) Pb–Pb collisions at $\sqrt{s_{\mathrm{NN}}}=5.02$ TeV is
shown in Fig. 3. The measured cross section in pp collisions at
$\sqrt{s}=5.02$ TeV (Fig. 1) is used as a reference up to $p_{\mathrm{T}}=10$
GeV/$c$. For $p_{\textrm{T}}>10$ GeV/$c$, the reference is obtained by a
$p_{\mathrm{T}}$-dependent scaling of the measurement at $\sqrt{s}=7$ TeV by
the ATLAS collaboration [65] with the ratio of the cross section at the two
collision energies computed with the FONLL calculation [66]. This ratio is
performed by considering the different rapidity coverage of the ATLAS
measurement ($|y|<2$ excluding $1.37<|y|<1.52$). The systematic uncertainties
of the cross section at $\sqrt{s}=5.02$ TeV range from 13% to 18% depending on
the $p_{\mathrm{T}}$ interval, and they are computed as the propagation of the
uncertainties associated with FONLL calculations at $\sqrt{s}=5.02$ TeV and
$\sqrt{s}=7$ TeV and the systematic uncertainties of the ATLAS measurement.
The statistical uncertainties are from the ATLAS measurement.

Statistical and systematic uncertainties of the $p_{\mathrm{T}}$-differential
yields and cross sections in Pb–Pb and pp collisions, respectively, are
propagated as uncorrelated uncertainties. The uncertainties on the
$R_{\mathrm{AA}}$ normalisation are reported in Fig. 3 as boxes at unity. The
measured $R_{\mathrm{AA}}$ shows a clear dependence on the collision
centrality, since in most central events it reaches a minimum of about $0.3$
around $p_{\mathrm{T}}=7$ GeV/$c$, while moving to more peripheral Pb–Pb
collisions the $R_{\mathrm{AA}}$ gets closer to unity at $p_{\mathrm{T}}>3$
GeV/$c$. Such a suppression is not observed in proton-lead collisions at the
same energy where the QGP is not expected to be formed and the nuclear
modification factor is consistent with unity [14, 36, 37]. Thus the
suppression of electron production is due to final-state effects, such as
partonic energy loss in the medium. Since electrons from semileptonic beauty
decays are expected to dominate the spectrum at high $p_{\textrm{T}}$ while
charm production dominates at low $p_{\textrm{T}}$ [14], the measurements show
that charm and beauty quarks lose energy in the medium. The centrality
dependence of the $R_{\textrm{AA}}$ is compatible with the hypothesis of a
partonic energy loss dependence on medium density, being larger in a hotter
and denser QGP, like the one created in the most central collisions. In
addition, it reflects a path-length dependence of energy loss. Moreover, it
has been shown in Refs. [67, 68] that a centrality selection bias is present
in peripheral Pb–Pb collisions which reduces the $R_{\mathrm{AA}}$ below unity
even in the absence of any nuclear modification effects. This effect may be
responsible for a significant part of the apparent suppression seen in the
$R_{\mathrm{AA}}$ of electrons from semileptonic heavy-flavour hadron decays
in the 60-80% centrality class.

For $p_{\mathrm{T}}<7$ GeV/$c$, the $R_{\mathrm{AA}}$ of electrons from
semileptonic heavy-flavour hadron decays increases with decreasing
$p_{\mathrm{T}}$ as a consequence of the scaling of the total heavy-flavour
yield with the number of binary collisions among nucleons in Pb–Pb collisions.
On the other hand, the nuclear modification factor at low $p_{\mathrm{T}}$
does not rise above unity. This kinematic region is sensitive to the effects
of nuclear shadowing: the depletion of parton densities in nuclei at low
Bjorken $x$ values can reduce the heavy-quark production cross section per
binary collision in Pb–Pb with respect to the pp case [28]. This initial-state
effect is studied in p–Pb collisions, however, the present uncertainties on
the $R_{\mathrm{pPb}}$ measurement do not allow quantitative conclusions on
the modification of the PDF in nuclei in the low $p_{\mathrm{T}}$ region to be
made [36]. Furthermore, the amount of electrons from semileptonic heavy-
flavour hadron decays is reduced due to the presence of hadrochemistry
effects. For example, $\Lambda_{\rm c}^{+}$ baryons decay into electrons with
a branching ratio of $5\%$, while for the D mesons the branching ratio is less
than $10\%$. Since in Pb–Pb collisions more charm quarks might hadronize into
baryons [69], this effect reduces the total amount of electrons from
semileptonic heavy-flavour hadron decays. Additional effects, such as
collective motion induced by the medium, also have an influence on the
measured $R_{\mathrm{AA}}$. Also, it has been observed that the radial flow
can provoke an additional yield enhancement at intermediate
$p_{\mathrm{T}}$[70, 71, 72, 73]. In this case, the radial flow pushes up slow
particles to higher momenta, causing a small increase in the nuclear
modification factor around $p_{\mathrm{T}}=1$ GeV/$c$.

Figure 3: Nuclear modification factor of electrons from semileptonic heavy-
flavour hadron decays measured in the three centrality intervals in Pb–Pb
collisions at $\sqrt{s_{\mathrm{NN}}}=5.02$ TeV.

It should be noted that the $R_{\mathrm{AA}}$ measurements in the most central
collisions at $\sqrt{s_{\mathrm{NN}}}$ = 2.76 TeV [28] and 5.02 TeV are
compatible within uncertainties, as shown in Fig. 3. This effect was predicted
by the Djordjevic model [74], and it results from the combination of a higher
medium temperature at 5.02 TeV, which would decrease the $R_{\mathrm{AA}}$ by
about 10%, with a harder $p_{\mathrm{T}}$ distribution of heavy quarks at 5.02
TeV, which would increase the $R_{\mathrm{AA}}$ by about 5% if the medium
temperature were the same as at 2.76 TeV. An analogous behaviour between the
measured $R_{\mathrm{AA}}$ at the two energies is also observed for the D
mesons [16].

###  4.3 Comparison with model predictions

In Fig. 4 the measured $R_{\mathrm{AA}}$ in the 0–10% (left panel) and 30–50%
(right panel) centrality intervals are compared with model calculations [75,
76, 77, 74, 78, 79, 80, 81]. The model calculations take into account
different hypotheses about mass dependence of energy loss processes, transport
dynamics, charm and beauty quark interactions with the QGP constituents,
hadronisation mechanisms of heavy quarks in the plasma, and heavy-quark
production cross section in nucleus–nucleus collisions.

Most of the models provide a fair description of the data in the region
$p_{\mathrm{T}}$ $<$ 5 GeV/$c$ in both centrality classes, except for BAMPS
[76]. The predictions from the MC@sHQ+EPOS2 [81], PHSD [77], TAMU [78], and
POWLANG [80] models also include nuclear modification of the parton
distribution functions, which is necessary to predict the observed suppression
of the $R_{\mathrm{AA}}$ at low $p_{\mathrm{T}}$. The following observations
about the comparison with model calculations are fully in agreement with what
is observed in the $R_{\mathrm{AA}}$ measurements of D mesons [16].

The nuclear modification factor for central Pb–Pb collisions is well described
by the TAMU [78] prediction at $p_{\mathrm{T}}<3$ GeV/$c$ within the
uncertainties related to the shadowing effect on charm quarks. However, this
model tends to overestimate the $R_{\mathrm{AA}}$ for $p_{\mathrm{T}}>3$
GeV/$c$, probably due to the missing implementation of the radiative energy
loss in the model, which may become the dominant energy loss mechanism at high
$p_{\mathrm{T}}$.

The agreement with TAMU [78] at low $p_{\mathrm{T}}$, on the other hand,
confirms the dominance of elastic collisions at low momenta, together with the
importance of the inclusion of shadowing effects in the model calculations
[35], which reduce the total heavy-flavour production in Pb–Pb collisions with
respect to an expectation from the binary scaling.

In semi-central Pb–Pb collisions the TAMU [78] and POWLANG [80] predictions
are close to the lower edge of the uncertainties of the measured
$R_{\mathrm{AA}}$ for $p_{\mathrm{T}}<3$ GeV/$c$. The latter calculation
describes the data better up to $p_{\mathrm{T}}\simeq 8$ GeV/$c$, while the
former provides a good description even at higher transverse momenta. The
CUJET3.0 [75] and Djordjevic [74, 79] models provide a good description of the
$R_{\mathrm{AA}}$ within the uncertainties in both centrality intervals for
$p_{\mathrm{T}}$ $>$ 5 GeV/$c$, suggesting that the dependence of radiative
energy loss on the path length in the hot and dense medium is well understood.

(a)  (b)

Figure 4: Nuclear modification factor of electrons semileptonic from heavy-
flavour hadron decays measured in 0–10% and 30–50% centrality in Pb–Pb
collisions at $\sqrt{s_{\mathrm{NN}}}=5.02$ TeV compared with model
predictions [75, 76, 77, 74, 78, 79, 80, 81].

##  5 Conclusions

The invariant yield of electrons from semileptonic heavy-flavour hadron decays
was measured in central (0–10%), semi-central (30–50%), and peripheral
(60–80%) Pb–Pb collisions at $\sqrt{s_{\mathrm{NN}}}=5.02$ TeV. The
measurement of the nuclear modification factor in all the centrality classes
for $p_{\mathrm{T}}<10$ GeV/$c$ is provided using as reference the cross
section measured in pp collisions at the same centre-of-mass energy. The
systematic uncertainties of this measurement are reduced by a factor of about
2 compared to the published reference in pp collisions at $\sqrt{s}=2.76$ TeV
[28] and the measured cross section is close to the upper edge of the FONLL
uncertainty band. At higher $p_{\mathrm{T}}$ the reference is obtained by a
$p_{\mathrm{T}}$-dependent scaling of the measurement at $\sqrt{s}=7$ TeV by
the ATLAS collaboration [65] with the ratio of the cross section at the two
collision energies computed with the FONLL calculation [66]. As in the Pb–Pb
analysis at $\sqrt{s_{\mathrm{NN}}}=2.76$ TeV [28, 29], the main source of
background electrons, constituted by photonic electrons, is removed via the
photonic tagging method. In addition, compared with the measurements performed
in pp and Pb–Pb collisions at $2.76$ TeV, the $p_{\mathrm{T}}$ range is
extended, and an additional centrality class is added.

The measured $R_{\mathrm{AA}}$ confirms the evidence of a strong suppression
with respect to what is expected from a simple binary scaling for large
$p_{\mathrm{T}}$. This is a clear signature of the medium induced energy loss
on heavy quarks traversing the QGP produced in heavy-ion collisions.

The measurement of electrons from semileptonic heavy-flavour hadron decays in
different centrality classes exhibits the dependence of energy loss on the
path length and energy density in the hot and dense medium. The
$R_{\mathrm{AA}}$ at high $p_{\mathrm{T}}$ (above 5 GeV/$c$) is fairly
described in the 0–10% and 30–50% centrality intervals by model calculations
that include both radiative and collisional energy loss. This indicates that
the centrality dependence of radiative energy loss is theoretically
understood. Further investigations and measurement of electrons from
semileptonic decays of beauty hadrons will give more information about the
mass dependence of the energy loss in the heavy-flavour sector.

With the good precision of the results presented here, the Pb–Pb data exhibit
their sensitivity to the modification of the PDF in nuclei, like nuclear
shadowing, which causes a suppression of the heavy-quark productionin heavy-
ion collisions. The implementation of the nuclear modification of the PDF in
theoretical calculations is a necessary ingredient in order for the model
predictions to correctly describe the measured $R_{\mathrm{AA}}$ [28].

## 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), Institut National de Physique Nucléaire et de Physique des Particules (IN2P3) and Centre National de la Recherche Scientifique (CNRS) and Région des Pays de la Loire, France; Bundesministerium für Bildung und Forschung (BMBF) and GSI Helmholtzzentrum für Schwerionenforschung GmbH, Germany; General Secretariat for Research and Technology, Ministry of Education, Research and Religions, Greece; National Research, Development and Innovation Office, Hungary; Department of Atomic Energy Government of India (DAE), Department of Science and Technology, Government of India (DST), University Grants Commission, Government of India (UGC) and Council of Scientific and Industrial Research (CSIR), India; Indonesian Institute of Science, Indonesia; Centro Fermi - Museo Storico della Fisica e Centro Studi e Ricerche Enrico Fermi and Istituto Nazionale di Fisica Nucleare (INFN), Italy; Institute for Innovative Science and Technology , Nagasaki Institute of Applied Science (IIST), Japanese Ministry of Education, Culture, Sports, Science and Technology (MEXT) and Japan Society for the Promotion of Science (JSPS) KAKENHI, Japan; Consejo Nacional de Ciencia (CONACYT) y Tecnología, through Fondo de Cooperación Internacional en Ciencia y Tecnología (FONCICYT) and Dirección General de Asuntos del Personal Academico (DGAPA), Mexico; Nederlandse Organisatie voor Wetenschappelijk Onderzoek (NWO), Netherlands; The Research Council of Norway, Norway; Commission on Science and Technology for Sustainable Development in the South (COMSATS), Pakistan; Pontificia Universidad Católica del Perú, Peru; Ministry of Science and Higher Education and National Science Centre, Poland; Korea Institute of Science and Technology Information and National Research Foundation of Korea (NRF), Republic of Korea; Ministry of Education and Scientific Research, Institute of Atomic Physics and Ministry of Research and Innovation and Institute of Atomic Physics, Romania; Joint Institute for Nuclear Research (JINR), Ministry of Education and Science of the Russian Federation, National Research Centre Kurchatov Institute, Russian Science Foundation and Russian Foundation for Basic Research, Russia; Ministry of Education, Science, Research and Sport of the Slovak Republic, Slovakia; National Research Foundation of South Africa, South Africa; Swedish Research Council (VR) and Knut & Alice Wallenberg Foundation (KAW), Sweden; European Organization for Nuclear Research, Switzerland; Suranaree University of Technology (SUT), National Science and Technology Development Agency (NSDTA) and Office of the Higher Education Commission under NRU project of Thailand, Thailand; Turkish Atomic Energy Agency (TAEK), Turkey; National Academy of Sciences of Ukraine, Ukraine; Science and Technology Facilities Council (STFC), United Kingdom; National Science Foundation of the United States of America (NSF) and United States Department of Energy, Office of Nuclear Physics (DOE NP), United States of America.

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##  Appendix A The ALICE Collaboration

S. Acharyaorg141&D. Adamováorg93&S.P. Adhyaorg141&A. Adlerorg73&J.
Adolfssonorg79&M.M. Aggarwalorg98&G. Aglieri Rinellaorg34&M. Agnelloorg31&N.
Agrawalorg10,org48,org53&Z. Ahammedorg141&S. Ahmadorg17&S.U. Ahnorg75&A.
Akindinovorg90&M. Al-Turanyorg105&S.N. Alamorg141&D.S.D. Albuquerqueorg122&D.
Aleksandrovorg86&B. Alessandroorg58&H.M. Alfandaorg6&R. Alfaro Molinaorg71&B.
Aliorg17&Y. Aliorg15&A. Aliciorg10,org27,org53&A. Alkinorg2&J. Almeorg22&T.
Altorg68&L. Altenkamperorg22&I. Altsybeevorg112&M.N. Anaamorg6&C.
Andreiorg47&D. Andreouorg34&H.A. Andrewsorg109&A. Andronicorg144&M.
Angelettiorg34&V. Anguelovorg102&C. Ansonorg16&T. Antičićorg106&F.
Antinoriorg56&P. Antonioliorg53&R. Anwarorg125&N. Apadulaorg78&L.
Aphecetcheorg114&H. Appelshäuserorg68&S. Arcelliorg27&R. Arnaldiorg58&M.
Arratiaorg78&I.C. Arseneorg21&M. Arslandokorg102&A. Augustinusorg34&R.
Averbeckorg105&S. Azizorg61&M.D. Azmiorg17&A. Badalàorg55&Y.W. Baekorg40&S.
Bagnascoorg58&X. Baiorg105&R. Bailhacheorg68&R. Balaorg99&A.
Baldisseriorg137&M. Ballorg42&S. Balouzaorg103&R.C. Baralorg84&R.
Barberaorg28&L. Barioglioorg26&G.G. Barnaföldiorg145&L.S. Barnbyorg92&V.
Barretorg134&P. Bartaliniorg6&K. Barthorg34&E. Bartschorg68&F.
Baruffaldiorg29&N. Bastidorg134&S. Basuorg143&G. Batigneorg114&B.
Batyunyaorg74&P.C. Batzingorg21&D. Bauriorg48&J.L. Bazo Albaorg110&I.G.
Beardenorg87&C. Beddaorg63&N.K. Beheraorg60&I. Belikovorg136&F.
Belliniorg34&R. Bellwiedorg125&V. Belyaevorg91&G. Bencediorg145&S.
Beoleorg26&A. Bercuciorg47&Y. Berdnikovorg96&D. Berenyiorg145&R.A.
Bertensorg130&D. Berzanoorg58&M.G. Besoiuorg67&L. Betevorg34&A.
Bhasinorg99&I.R. Bhatorg99&M.A. Bhatorg3&H. Bhattorg48&B.
Bhattacharjeeorg41&A. Bianchiorg26&L. Bianchiorg26,org125&N. Bianchiorg51&J.
Bielčíkorg37&J. Bielčíkováorg93&A. Bilandzicorg103,org117&G. Biroorg145&R.
Biswasorg3&S. Biswasorg3&J.T. Blairorg119&D. Blauorg86&C. Blumeorg68&G.
Bocaorg139&F. Bockorg34,org94&A. Bogdanovorg91&L. Boldizsárorg145&A.
Bolozdynyaorg91&M. Bombaraorg38&G. Bonomiorg140&H. Borelorg137&A.
Borissovorg91,org144&M. Borriorg127&H. Bossiorg146&E. Bottaorg26&L.
Bratrudorg68&P. Braun-Munzingerorg105&M. Bregantorg121&T.A. Brokerorg68&M.
Brozorg37&E.J. Bruckenorg43&E. Brunaorg58&G.E. Brunoorg33,org104&M.D.
Bucklandorg127&D. Budnikovorg107&H. Bueschingorg68&S. Bufalinoorg31&O.
Bugnonorg114&P. Buhlerorg113&P. Buncicorg34&Z. Butheleziorg72&J.B.
Buttorg15&J.T. Buxtonorg95&S.A. Bysiakorg118&D. Caffarriorg88&A.
Calivaorg105&E. Calvo Villarorg110&R.S. Camachoorg44&P. Cameriniorg25&A.A.
Caponorg113&F. Carnesecchiorg10&J. Castillo Castellanosorg137&A.J.
Castroorg130&E.A.R. Casulaorg54&F. Catalanoorg31&C. Ceballos Sanchezorg52&P.
Chakrabortyorg48&S. Chandraorg141&B. Changorg126&W. Changorg6&S.
Chapelandorg34&M. Chartierorg127&S. Chattopadhyayorg141&S.
Chattopadhyayorg108&A. Chauvinorg24&C. Cheshkovorg135&B. Cheynisorg135&V.
Chibante Barrosoorg34&D.D. Chinellatoorg122&S. Choorg60&P. Chochulaorg34&T.
Chowdhuryorg134&P. Christakoglouorg88&C.H. Christensenorg87&P.
Christiansenorg79&T. Chujoorg133&C. Cicaloorg54&L. Cifarelliorg10,org27&F.
Cindoloorg53&M.R. Ciupekorg105&J. Cleymansorg124&F. Colamariaorg52&D.
Colellaorg52&A. Colluorg78&M. Colocciorg27&M. Concasorg58orgI&G. Conesa
Balbastreorg77&Z. Conesa del Valleorg61&G. Continorg59,org127&J.G.
Contrerasorg37&T.M. Cormierorg94&Y. Corrales Moralesorg26,org58&P.
Corteseorg32&M.R. Cosentinoorg123&F. Costaorg34&S. Costanzaorg139&J.
Crkovskáorg61&P. Crochetorg134&E. Cuautleorg69&L. Cunqueiroorg94&D.
Dabrowskiorg142&T. Dahmsorg103,org117&A. Daineseorg56&F.P.A.
Damasorg114,org137&S. Daniorg65&M.C. Danischorg102&A. Danuorg67&D.
Dasorg108&I. Dasorg108&P. Dasorg3&S. Dasorg3&A. Dashorg84&S. Dashorg48&A.
Dashiorg103&S. Deorg49,org84&A. De Caroorg30&G. de Cataldoorg52&C. de
Contiorg121&J. de Cuvelandorg39&A. De Falcoorg24&D. De Gruttolaorg10&N. De
Marcoorg58&S. De Pasqualeorg30&R.D. De Souzaorg122&S. Deborg49&H.F.
Degenhardtorg121&K.R. Dejaorg142&A. Delofforg83&S. Delsantoorg26,org131&P.
Dhankherorg48&D. Di Bariorg33&A. Di Mauroorg34&R.A. Diazorg8&T.
Dietelorg124&P. Dillensegerorg68&Y. Dingorg6&R. Diviàorg34&Ø.
Djuvslandorg22&U. Dmitrievaorg62&A. Dobrinorg34,org67&B. Dönigusorg68&O.
Dordicorg21&A.K. Dubeyorg141&A. Dublaorg105&S. Dudiorg98&M. Dukhishyamorg84&P.
Dupieuxorg134&R.J. Ehlersorg146&D. Eliaorg52&H. Engelorg73&E. Eppleorg146&B.
Erazmusorg114&F. Erhardtorg97&A. Erokhinorg112&M.R. Ersdalorg22&B.
Espagnonorg61&G. Eulisseorg34&J. Eumorg18&D. Evansorg109&S. Evdokimovorg89&L.
Fabbiettiorg103,org117&M. Fagginorg29&J. Faivreorg77&A. Fantoniorg51&M.
Faselorg94&P. Fecchioorg31&A. Felicielloorg58&G. Feofilovorg112&A. Fernández
Téllezorg44&A. Ferreroorg137&A. Ferrettiorg26&A. Festantiorg34&V.J.G.
Feuillardorg102&J. Figielorg118&S. Filchaginorg107&D. Finogeevorg62&F.M.
Fiondaorg22&G. Fiorenzaorg52&F. Flororg125&S. Foertschorg72&P. Fokaorg105&S.
Fokinorg86&E. Fragiacomoorg59&U. Frankenfeldorg105&G.G. Fronzeorg26&U.
Fuchsorg34&C. Furgetorg77&A. Fursorg62&M. Fusco Girardorg30&J.J.
Gaardhøjeorg87&M. Gagliardiorg26&A.M. Gagoorg110&A. Galorg136&C.D.
Galvanorg120&P. Ganotiorg82&C. Garabatosorg105&E. Garcia-Solisorg11&K.
Gargorg28&C. Gargiuloorg34&A. Garibliorg85&K. Garnerorg144&P.
Gasikorg103,org117&E.F. Gaugerorg119&M.B. Gay Ducatiorg70&M. Germainorg114&J.
Ghoshorg108&P. Ghoshorg141&S.K. Ghoshorg3&P. Gianottiorg51&P.
Giubellinoorg58,org105&P. Giubilatoorg29&P. Glässelorg102&D.M. Goméz
Coralorg71&A. Gomez Ramirezorg73&V. Gonzalezorg105&P. González-Zamoraorg44&S.
Gorbunovorg39&L. Görlichorg118&S. Gotovacorg35&V. Grabskiorg71&L.K.
Graczykowskiorg142&K.L. Grahamorg109&L. Greinerorg78&A. Grelliorg63&C.
Grigorasorg34&V. Grigorievorg91&A. Grigoryanorg1&S. Grigoryanorg74&O.S.
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Herrmannorg144&K.F. Hetlandorg36&T.E. Hildenorg43&H. Hillemannsorg34&C.
Hillsorg127&B. Hippolyteorg136&B. Hohlwegerorg103&D. Horakorg37&S.
Hornungorg105&R. Hosokawaorg133&P. Hristovorg34&C. Huangorg61&C.
Hughesorg130&P. Huhnorg68&T.J. Humanicorg95&H. Hushnudorg108&L.A.
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Ivanovorg96&V. Izucheevorg89&B. Jacakorg78&N. Jacazioorg27&P.M.
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Jaelaniorg63&C. Jahnkeorg121&M.J. Jakubowskaorg142&M.A. Janikorg142&M.
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Karasu Uysalorg76&O. Karavichevorg62&T. Karavichevaorg62&P.
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Keilorg34&B. Ketzerorg42&Z. Khabanovaorg88&A.M. Khanorg6&S. Khanorg17&S.A.
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Khuntiaorg49,org118&B. Kilengorg36&B. Kimorg60&B. Kimorg133&D. Kimorg147&D.J.
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Piknaorg14&P. Pillotorg114&L.O.D.L. Pimentelorg87&O. Pinazzaorg34,org53&L.
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Pochybovaorg145&M.G. Poghosyanorg94&B. Polichtchoukorg89&N. Poljakorg97&W.
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Puninorg107&K. Puranapandaorg141&J. Putschkeorg143&R.E. Quishpeorg125&S.
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Zinovjevorg2&N. Zurloorg140&

## Affiliation notes

org*Deceased

orgIDipartimento DET del Politecnico di Torino, Turin, Italy

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

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

orgIVInstitute of Theoretical Physics, University of Wroclaw, Poland

## Collaboration Institutes

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

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

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

org4Budker Institute for Nuclear Physics, Novosibirsk, Russia

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

org6Central China Normal University, Wuhan, China

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

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

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

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

org11Chicago State University, Chicago, Illinois, United States

org12China Institute of Atomic Energy, Beijing, China

org13Chonbuk National University, Jeonju, Republic of Korea

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

org15COMSATS University Islamabad, Islamabad, Pakistan

org16Creighton University, Omaha, Nebraska, United States

org17Department of Physics, Aligarh Muslim University, Aligarh, India

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

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

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

org21Department of Physics, University of Oslo, Oslo, Norway

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

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

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

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

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

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

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

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

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

org31Dipartimento DISAT del Politecnico and Sezione INFN, Turin, Italy

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

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

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

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

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

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

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

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

org40Gangneung-Wonju National University, Gangneung, Republic of Korea

org41Gauhati University, Department of Physics, Guwahati, India

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

org43Helsinki Institute of Physics (HIP), Helsinki, Finland

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

org45Hiroshima University, Hiroshima, Japan

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

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

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

org49Indian Institute of Technology Indore, Indore, India

org50Indonesian Institute of Sciences, Jakarta, Indonesia

org51INFN, Laboratori Nazionali di Frascati, Frascati, Italy

org52INFN, Sezione di Bari, Bari, Italy

org53INFN, Sezione di Bologna, Bologna, Italy

org54INFN, Sezione di Cagliari, Cagliari, Italy

org55INFN, Sezione di Catania, Catania, Italy

org56INFN, Sezione di Padova, Padova, Italy

org57INFN, Sezione di Roma, Rome, Italy

org58INFN, Sezione di Torino, Turin, Italy

org59INFN, Sezione di Trieste, Trieste, Italy

org60Inha University, Incheon, Republic of Korea

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

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

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

org64Institute of Experimental Physics, Slovak Academy of Sciences, Košice,
Slovakia

org65Institute of Physics, Homi Bhabha National Institute, Bhubaneswar, India

org66Institute of Physics of the Czech Academy of Sciences, Prague, Czech
Republic

org67Institute of Space Science (ISS), Bucharest, Romania

org68Institut für Kernphysik, Johann Wolfgang Goethe-Universität Frankfurt,
Frankfurt, Germany

org69Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México,
Mexico City, Mexico

org70Instituto de Física, Universidade Federal do Rio Grande do Sul (UFRGS),
Porto Alegre, Brazil

org71Instituto de Física, Universidad Nacional Autónoma de México, Mexico
City, Mexico

org72iThemba LABS, National Research Foundation, Somerset West, South Africa

org73Johann-Wolfgang-Goethe Universität Frankfurt Institut für Informatik,
Fachbereich Informatik und Mathematik, Frankfurt, Germany

org74Joint Institute for Nuclear Research (JINR), Dubna, Russia

org75Korea Institute of Science and Technology Information, Daejeon, Republic
of Korea

org76KTO Karatay University, Konya, Turkey

org77Laboratoire de Physique Subatomique et de Cosmologie, Université
Grenoble-Alpes, CNRS-IN2P3, Grenoble, France

org78Lawrence Berkeley National Laboratory, Berkeley, California, United
States

org79Lund University Department of Physics, Division of Particle Physics,
Lund, Sweden

org80Nagasaki Institute of Applied Science, Nagasaki, Japan

org81Nara Women’s University (NWU), Nara, Japan

org82National and Kapodistrian University of Athens, School of Science,
Department of Physics , Athens, Greece

org83National Centre for Nuclear Research, Warsaw, Poland

org84National Institute of Science Education and Research, Homi Bhabha
National Institute, Jatni, India

org85National Nuclear Research Center, Baku, Azerbaijan

org86National Research Centre Kurchatov Institute, Moscow, Russia

org87Niels Bohr Institute, University of Copenhagen, Copenhagen, Denmark

org88Nikhef, National institute for subatomic physics, Amsterdam, Netherlands

org89NRC Kurchatov Institute IHEP, Protvino, Russia

org90NRC « Kurchatov Institute » - ITEP, Moscow, Russia

org91NRNU Moscow Engineering Physics Institute, Moscow, Russia

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

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

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

org95Ohio State University, Columbus, Ohio, United States

org96Petersburg Nuclear Physics Institute, Gatchina, Russia

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

org98Physics Department, Panjab University, Chandigarh, India

org99Physics Department, University of Jammu, Jammu, India

org100Physics Department, University of Rajasthan, Jaipur, India

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

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

org103Physik Department, Technische Universität München, Munich, Germany

org104Politecnico di Bari, Bari, Italy

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

org106Rudjer Bošković Institute, Zagreb, Croatia

org107Russian Federal Nuclear Center (VNIIEF), Sarov, Russia

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

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

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

org111Shanghai Institute of Applied Physics, Shanghai, China

org112St. Petersburg State University, St. Petersburg, Russia

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

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

org115Suranaree University of Technology, Nakhon Ratchasima, Thailand

org116Technical University of Košice, Košice, Slovakia

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

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

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

org120Universidad Autónoma de Sinaloa, Culiacán, Mexico

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

org122Universidade Estadual de Campinas (UNICAMP), Campinas, Brazil

org123Universidade Federal do ABC, Santo Andre, Brazil

org124University of Cape Town, Cape Town, South Africa

org125University of Houston, Houston, Texas, United States

org126University of Jyväskylä, Jyväskylä, Finland

org127University of Liverpool, Liverpool, United Kingdom

org128University of Science and Technology of China, Hefei, China

org129University of South-Eastern Norway, Tonsberg, Norway

org130University of Tennessee, Knoxville, Tennessee, United States

org131University of the Witwatersrand, Johannesburg, South Africa

org132University of Tokyo, Tokyo, Japan

org133University of Tsukuba, Tsukuba, Japan

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

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

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

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

org138Università degli Studi di Foggia, Foggia, Italy

org139Università degli Studi di Pavia, Pavia, Italy

org140Università di Brescia, Brescia, Italy

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

org142Warsaw University of Technology, Warsaw, Poland

org143Wayne State University, Detroit, Michigan, United States

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

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

org146Yale University, New Haven, Connecticut, United States

org147Yonsei University, Seoul, Republic of Korea