2023 194 30 August

Dielectron production in central Pb–Pb collisions at
$\sqrt{s_{\mathrm{NN}}}=5.02$ TeV

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

The first measurement of the ${\rm e}^{+}{\rm e}^{-}$ pair production at
midrapidity and low invariant mass in central Pb–Pb collisions at
$\sqrt{s_{\mathrm{NN}}}=5.02$ TeV at the LHC is presented. The yield of ${\rm
e}^{+}{\rm e}^{-}$ pairs is compared with a cocktail of expected hadronic
decay contributions in the invariant mass ($m_{\rm ee}$) and pair transverse
momentum ($p_{\rm T,ee}$) ranges $m_{\rm ee}<3.5$ GeV$/c^{2}$ and $p_{\rm
T,ee}<8$ GeV$/c$. For $0.18<m_{\rm ee}<0.5$ GeV$/c^{2}$ the ratio of data to
the cocktail of hadronic contributions without $\rho$ mesons amounts to
$1.42\pm 0.12\ ({\rm stat.})\pm 0.17\ ({\rm syst.})\pm 0.12\ ({\rm cocktail})$
and $1.44\pm 0.12\ ({\rm stat.})\pm 0.17\ ({\rm syst.})^{+0.17}_{-0.21}\ ({\rm
cocktail})$, including or not including medium effects in the estimation of
the heavy-flavor background, respectively. It is consistent with predictions
from two different models for an additional contribution of thermal ${\rm
e}^{+}{\rm e}^{-}$ pairs from the hadronic and partonic phases. In the
intermediate-mass range ($1.2<m_{\rm ee}<2.6$ GeV$/c^{2}$), the pair
transverse impact parameter of the ${\rm e}^{+}{\rm e}^{-}$ pairs (DCAee) is
used for the first time in Pb–Pb collisions to separate displaced dielectrons
from heavy-flavor hadron decays from a possible (thermal) contribution
produced at the interaction point. The data are consistent with a suppression
of ${\rm e}^{+}{\rm e}^{-}$ pairs from ${\rm c\overline{c}}$ and an additional
prompt component. Finally, the first direct-photon measurement in the 10% most
central Pb–Pb collisions at $\sqrt{s_{\mathrm{NN}}}=5.02$ TeV is reported via
the study of virtual direct photons in the transverse momentum range $1<p_{\rm
T}<5$ GeV$/c$. A model including prompt photons, as well as photons from the
pre-equilibrium and fluid-dynamic phases, can reproduce the result, while
being at the upper edge of the data uncertainties.

##  1 Introduction

Ultra-relativistic heavy-ion collisions at the Large Hadron Collider (LHC)
allow the study of strongly interacting matter at high temperature and small
net-baryon density [1]. Under these conditions, the theory of the strong
interaction, quantum chromodynamics (QCD), predicts a transition from ordinary
matter made of hadrons to a quark–gluon plasma (QGP) in which quarks and
gluons are deconfined [2, 3, 4, 5]. In this QGP phase, chiral symmetry is also
expected to be restored [6, 7]. Photons and dileptons, i.e. lepton–antilepton
pairs originating from the internal conversion of virtual photons, are
produced at all stages of the heavy-ion collision with negligible final-state
interactions, unlike hadrons. Therefore, they carry undistorted information
about the whole space–time evolution of the medium created in such collisions.

Direct photons are photons not originating from hadronic decays. They are
emitted by various sources as discussed in Ref. [8]. Prompt direct photons are
produced in the initial hard parton–parton scatterings. Additional photons,
still generated before the system reaches sufficient equilibrium to be
described by relativistic viscous hydrodynamics, are called pre-equilibrium
photons. Thermal photons are emitted from the deconfined QGP and hot hadronic
matter and are characterized by the thermal distributions of partons and
hadrons, respectively. Other direct photon production mechanisms are not
excluded, like the interaction of hard-scattered partons from jets with the
plasma [9, 10]. Each source of direct photons populates different transverse
momentum ($p_{\rm T}$) regions. Prompt direct photons follow a power-law
spectrum and dominate at high $p_{\rm T}$ ($p_{\rm T}\gtrsim 5$ GeV$/c$). At
lower $p_{\rm T}$ ($p_{\rm T}\lesssim 2$ GeV$/c$), thermal photons are
expected to contribute significantly with an approximately exponential $p_{\rm
T}$ spectrum containing information on the initial temperature and space–time
evolution of the medium [11, 12]. Pre-equilibrium photons may play a role in
the intermediate $p_{\rm T}$ range [13].

The first measurement of a direct photon signal in relativistic heavy-ion
collisions was reported by the WA98 collaboration [14] in central Pb–Pb
collisions at the center-of-mass energy per nucleon pair
$\sqrt{s_{\mathrm{NN}}}=17.3$ GeV. The spectrum is consistent with
calculations for thermal photon radiation from a quark–gluon plasma and a hot
hadronic phase, as well as with predictions including multiple soft
scatterings of the incoming partons without the formation of a QGP [12]. At
the Relativistic Heavy Ion Collider (RHIC), the first $p_{\rm T}$-differential
yield of direct photons was measured by the PHENIX collaboration in Au–Au
collisions at $\sqrt{s_{\mathrm{NN}}}=0.2$ TeV [15], followed by subsequent
results at the same center-of-mass energy per nucleon pair [16, 17, 18, 19,
20] as well as at lower energies [21, 22]. On the one hand, the measured
direct-photon yields are well described by the expected yields of prompt
direct photons at high $p_{\rm T}$ ($p_{\rm T}\gtrsim 5$ GeV$/c$), showing
that the high-$p_{\rm T}$ direct photons are predominantly from initial hard-
scattering processes. The prompt component is estimated either from
measurements in pp and d–Au collisions at the same collision energy [23, 24,
25] or perturbative QCD calculations [26], both scaled with the number of
binary nucleon–nucleon collisions ($N_{\rm coll}$). On the other hand, a large
excess of direct photons is observed at low $p_{\rm T}$ ($p_{\rm T}<2$
GeV$/c$) with respect to the expected prompt direct photon yields. The STAR
collaboration also reported an enhancement of direct photons at low $p_{\rm
T}$ in Au–Au collisions at $\sqrt{s_{\mathrm{NN}}}=0.2$ TeV [27], which
appears to be about a factor three smaller than the one measured by PHENIX.
The large yield of direct photons is accompanied by a large azimuthal
anisotropy (elliptic flow) with respect to the reaction plane [17, 20],
similar in magnitude to the one of charged hadrons, suggesting a large
contribution from the late stages of the collision. A simultaneous description
of the $p_{\rm T}$-differential yields and elliptic flow results remains
challenging for models [28, 13, 29, 30, 31]. At the LHC, direct photon yield
[32] and elliptic flow [33] measurements in Pb–Pb collisions at
$\sqrt{s_{\mathrm{NN}}}=2.76$ TeV by the ALICE collaboration show similar
trends as those from PHENIX within the experimental uncertainties. Recent
results by the PHENIX collaboration, obtained with a factor ten larger dataset
of Au–Au collisions at $\sqrt{s_{\mathrm{NN}}}=0.2$ TeV, reduce the tension
between the measured direct-photon yield in central Au–Au collisions [19] and
the predictions from a state-of-the-art model [13] including prompt, pre-
equilibrium, and thermal photons. The observed direct-photon yields in more
peripheral Au–Au collisions remain nevertheless a factor two to three larger
than the calculations. Effective temperatures ($T_{\rm eff}$) were extracted
from the measured $p_{\rm T}$ spectra at low $p_{\rm T}$ in Au–Au collisions
at $\sqrt{s_{\mathrm{NN}}}=0.2$ TeV [19] and in Pb–Pb collisions at
$\sqrt{s_{\mathrm{NN}}}=2.76$ TeV [32] by the PHENIX and ALICE collaborations,
respectively. The measured $T_{\rm eff}$ values are significantly larger than
the critical temperature for chiral symmetry restoration and color
deconfinement. This does not prove that the radiation is emitted from a QGP,
since radiation from the late stages of the collision with strong radial flow
could lead to a significant blue shift. Detailed studies of the direct-photon
yield as a function of the collision system size by PHENIX show a power-law
dependence on the charged-particle multiplicity at midrapidity ($\frac{{\rm
d}N_{\rm ch}}{{\rm d}\eta}|_{\rm\eta=0}$) at low $p_{\rm T}$. The measured
power $\alpha$ seems to have a weak dependence on centrality or collision
energy [21, 22] and no apparent dependence on $p_{\rm T}$, in particular in
Au–Au collisions at $\sqrt{s_{\mathrm{NN}}}=0.2$ TeV [19]. However, model
calculations predict different $\alpha$ for radiation from different phases
[34].

In contrast to real photons, virtual photons, i.e. dileptons, carry a mass,
the invariant mass of the lepton and antilepton pair ($m_{\rm l^{+}l^{-}}$).
This provides an additional means to disentangle the different sources of
electromagnetic radiation. For $m_{\rm l^{+}l^{-}}>1.2$ GeV$/c^{2}$, virtual
direct photons are foreseen to originate from the partonic phase of the heavy-
ion collision [35]. In the mass region $1.2<m_{\rm l^{+}l^{-}}<2.6$
GeV$/c^{2}$ thermal radiation from the QGP is expected to contribute
significantly to the virtual direct-photon yield [36]. The slope of their
$m_{\rm l^{+}l^{-}}$ distribution is predicted to carry information about the
early temperature in the medium without distortion due to blueshift effect
[35]. Nevertheless, correlated background from semileptonic decays of open
heavy-flavor hadrons has to be subtracted or rejected first. Moreover, initial
hard parton–parton scatterings generate also direct dileptons via the Drell-
Yan process. While this process contributes significantly to the measured
dilepton spectra down to small invariant masses ($m_{\rm l^{+}l^{-}}\approx
1.5$ GeV$/c^{2}$) at SPS energies, it is estimated to be negligible for masses
up to about $3$ GeV$/c^{2}$ at the LHC. On the other hand, recent theoretical
calculations for Pb–Pb collisions at $\sqrt{s_{\mathrm{NN}}}=5.02$ TeV show
that additional ${\rm l^{+}l^{-}}$ pairs, still produced before the system
reaches local thermal equilibrium, may play a role for $m_{\rm
l^{+}l^{-}}>1.5$ GeV$/c^{2}$ [37, 38]. At lower $m_{\rm l^{+}l^{-}}$ ($m_{\rm
l^{+}l^{-}}<1.2$ GeV$/c^{2}$), the dilepton invariant mass can be used to
study the decay of massive particles, such as the in-medium modified spectral
shape of vector mesons. Dileptons produced in the medium in the vicinity of
the transition temperatures are sensitive to effects related to chiral
symmetry restoration [39, 40]. Due to its strong coupling to the
$\pi^{+}\pi^{-}$ channel and its life time of only 1.3 fm$/c$, much smaller
than that of the fireball at the LHC ($\approx 10$ fm$/c$), the $\rho$ meson
is expected to be the most sensitive to such medium effects. Finally, in the
zero mass limit, the fraction of virtual direct photons over inclusive virtual
photons is expected to be identical to that of real photons [41]. Therefore
the measured dilepton yield in the quasi-real virtual-photon region, where the
pair transverse momenta $p_{\rm T,ll}$ is much larger than $m_{\rm
l^{+}l^{-}}$, can be used to measure the $p_{\rm T}$-differential yield of
direct photons.

Precision measurements of virtual photons were performed at the CERN SPS by
the CERES [42, 43, 44] and NA60 [45, 46, 47, 48] collaborations in the
dielectron and dimuon channels, respectively. An average temperature of about
200 MeV, significantly above the transition temperatures, was extracted from
the mass spectrum in $1.2<m_{\rm l^{+}l^{-}}<2$ GeV$/c^{2}$ in 158A GeV In–In
collisions by the NA60 collaboration [48]. The capability of the NA60
experiment to disentangle prompt muons, originating from the primary vertex,
and non-prompt muons from displaced open-charm hadron decays, allowed them to
explicitly attribute the observed dimuon signal in this mass range to a prompt
source. Together with studies of the effective temperature $T_{\rm eff}$ from
the dimuon $p_{\rm T}$ spectrum as a function of mass [47], this temperature
value suggested that dilepton radiation in the intermediate-mass region
originates from the partonic phase [49, 50]. For increasing
$\sqrt{s_{\mathrm{NN}}}$, the correlated background from heavy-flavor hadron
decays becomes very large with respect to the QGP radiation, preventing the
PHENIX [51], STAR [52], and ALICE [53] collaborations at RHIC and the LHC from
extracting an unambiguous dilepton signal in the intermediate-mass range
without the use of high-precision vertex detectors. At lower mass, the $\rho$
properties in the hot medium created in heavy-ion collisions were measured by
the CERES and NA60 collaboration at SPS energies. The dilepton excess,
obtained after subtraction of the expected contribution of other light-flavor
meson decays happening at a later stage in the collision, was found to be well
described by the calculations of a microscopic many-body model [54, 55]. This
model predicted a very strong broadening of the $\rho$ spectral function with
essentially no mass shift, consistent with chiral symmetry restoration [40].
At the top RHIC energy, an enhancement of dileptons in the low-mass region was
reported by both the STAR [52] and the PHENIX [51] collaborations in central
Au–Au collisions at $\sqrt{s_{\mathrm{NN}}}=0.2$ TeV. Models reproducing the
SPS data and involving the broadening of the $\rho$ meson [56, 57] were shown
to describe the RHIC data as well. The first low-mass dilepton results at the
LHC, published by the ALICE collaboration in central Pb–Pb collisions at
$\sqrt{s_{\mathrm{NN}}}=2.76$ TeV [53], are in line with the expectations from
these models, although no significant excess was observed within the limited
precision of the data.

Measurements of direct photons and dileptons at LHC energies could shed light
on the remaining discrepancy between those results and theory predictions.
Heavy-ion collisions at the LHC provide nowadays the highest-temperature and
longest-lived experimentally accessible QGP. Therefore, the thermal radiation
yield is expected to be the largest with respect to measurements at other
accelerator facilities. Moreover, the in-medium modifications of vector mesons
can be probed under conditions that are most closely related to the regime
accessible by lattice QCD (vanishing net-baryon density). However, the large
combinatorial and heavy-flavor backgrounds pose a serious challenge.

In this article, the first dielectron and resulting direct-photon measurements
in the 10% most central Pb–Pb collisions at $\sqrt{s_{\mathrm{NN}}}=5.02$ TeV
are presented and compared to measurements at lower energies (RHIC and LHC)
and with model predictions. The uncertainties could be reduced compared to the
previous publication in central Pb–Pb collisions at lower energy [53] due to
the three times larger data sample. While direct photons have already been
measured in central collisions at $\sqrt{s_{\rm NN}}=2.76$ TeV as part of a
real-photon analysis [32, 33], a direct-photon measurement is now available
for the first time at the highest collision energy. Finally, the larger data
sample allows for the first studies in Pb–Pb collisions of a topological
separation of prompt dielectrons and dielectrons originating from displaced
correlated heavy-flavor hadron decays. The article is organized as follows.
Section 2 contains a brief description of the ALICE apparatus and the used
data sample. Section 3 illustrates the data analysis techniques. Section 4
explains how the expected dielectron yields from known hadronic sources are
calculated. The results are presented and discussed in Sec. 5 for the
inclusive dielectron production, Sec. 6 for the topological separation of
${\rm e}^{+}{\rm e}^{-}$ sources, and Sec. 7 for the direct-photon
measurement. Finally, they are summarized in Sec. 8.

##  2 Detector and data sample

A detailed description of the ALICE apparatus and its performance can be found
in Refs. [58, 59]. The main detectors used for the track reconstruction and
electron identification at midrapidity ($|\eta|<0.9$) are the Inner Tracking
System (ITS) [60], the Time Projection Chamber (TPC) [61], and the Time-Of-
Flight (TOF) detector [62]. They are located inside a large solenoidal magnet,
providing a uniform magnetic field of 0.5 T parallel to the LHC beam
direction. Charged-particle trajectories are reconstructed from their signals
in the ITS and the TPC. The ITS consists of a six-layer silicon detector with
the innermost layer installed at a radius of 3.9 cm from the beam axis. It is
used for tracking, for the reconstruction of the main vertex of the collision,
and for the measurement of the distance-of-closest-approach (DCA) of the track
to this primary vertex. Moreover, the four outer layers, made of silicon drift
detectors and silicon strip detectors, provide charged-particle identification
(PID) via the measurement of their specific energy loss (${\rm d}E/{\rm d}x$)
in the detector material. The TPC, a $500$ cm long gas filled cylinder
providing up to $159$ three-dimensional space points per track, is the main
tracking detector. The measured ${\rm d}E/{\rm d}x$ of the charged particles
in the gas allows electron identification over a large momentum range (up to a
momentum of 10 GeV$/c$). The TOF detector extends at intermediate momenta
($0.4<p<1.3$ GeV$/c$) the PID capabilities of the TPC and ITS via the
measurement of the time-of-flight of charged particles from the interaction
point to the detector.

The data used in this article were collected by ALICE in 2018 during Pb–Pb
runs at $\sqrt{s_{\mathrm{NN}}}=5.02$ TeV. A minimum bias interaction trigger
was provided by the V0 detector [63]. Simultaneous signals in the two
scintillator arrays covering the pseudorapidity intervals $-3.7<\eta<-1.7$
(V0C) and $2.8<\eta<5.1$ (V0A) were required. In addition, events were
selected online based on the signal amplitude in these detectors in order to
enrich the sample of central Pb–Pb collisions. Further selection criteria were
applied later offline. Events due to the interaction of the beams with
residual gas in the beam pipe were rejected using the V0 and the Zero Degree
Calorimeter (ZDC) [64] timing information. Pileup collisions occurring during
the TPC readout time were removed using the correlation between the number of
tracks reconstructed in the TPC and in the ITS, which grants a faster readout.
Only events with a primary vertex reconstructed within $\pm 10$ cm from the
center of the detector along the beam axis were considered. Finally, the 10%
most central Pb–Pb collisions were defined in terms of percentiles of the
hadronic Pb–Pb cross section using the sum of the V0 signal amplitudes as
described in detail in Ref. [65]. The corresponding average value of the
nuclear overlap function, $\langle T_{\rm AA}\rangle$, is $(23.26\pm
0.17)~{}{\rm mb^{-1}}$ [65]. The total number of selected events ($N_{\rm
events}$) is about $65\times 10^{6}$ corresponding to an integrated luminosity
of ${\rm 85~{}\mu b^{-1}}$ [66].

##  3 Data analysis

###  3.1 Dielectron raw yields

Electron candidates are selected in the transverse momentum range $0.2<p_{\rm
T,e}<10$ GeV$/c$ and at midrapidity ($|\eta_{\rm e}|<0.8$). For the analysis
using the DCA information to separate dielectrons from different sources, the
tracks must have a $p_{\rm T}>0.4$ GeV$/c$ to assure a sufficient separation
between prompt ${\rm e}^{+}{\rm e}^{-}$ pairs originating from the primary
vertex and non-prompt ones arising from displaced open heavy-flavor hadron
decays. The DCA resolution worsens at low $p_{\rm T}$. For tracks
reconstructed in the ITS and TPC with a transverse momentum smaller than
$0.35$ GeV$/c$ the DCA resolution in the plane perpendicular to the beam axis
is larger than $150$ $\mu$m [67] and thus comparable to the decay length of
the D0 and D${}^{\pm}_{\rm s}$ mesons. The same tracking selection criteria as
those described in Ref. [68] are applied. In particular, a hit in the first
ITS layer is required to be attached to the reconstructed track and a maximum
of one ITS cluster, not placed in the first ITS layer, may be shared with any
other track candidate. These requirements reduce the amount of electron tracks
originating from photon conversion in the detector material by $98.8$%,
keeping $93.7$% of the signal electrons.

The electron identification is based on the complementary information provided
by the ITS, TPC, and TOF. The detector PID signals, $n(\sigma_{i}^{\rm DET})$,
are expressed in terms of the deviation between the measured and expected
value of the specific ionization energy loss in the ITS (TPC) or time-of-
flight in the TOF for a given particle hypothesis $i$ and momentum, normalized
to the respective detector resolution. Electrons are identified in a similar
way as described in Ref. [68]. To increase the electron purity, an asymmetric
electron selection criterium is applied in the TPC, i.e. $-2<n(\sigma_{\rm
e}^{\rm TPC})<3$. Kaons, protons and pions are rejected with the requirements
$|n(\sigma_{\rm K}^{\rm TPC})|>3$, $|n(\sigma_{\rm p}^{\rm TPC})|>3$ and
$n(\sigma_{\rm\pi}^{\rm TPC})>3.5$, respectively. To increase the PID
efficiency ($\epsilon_{\rm PID}$) and avoid a strong momentum dependence of
$\epsilon_{\rm PID}$, the ITS and TOF are used to recover electrons with an
energy loss in the TPC in the range where the charged kaon and proton bands
cross the one of electrons. It exploits the fact that kaons (protons) and
electrons are still separated in the energy loss measurements in the ITS or
the measured time-of-flight in the TOF, at momenta where they have a very
similar energy loss in the TPC. Tracks which fulfill only the TPC electron
selection and pion rejection but have an associated TOF signal with
$-3<n(\sigma_{\rm e}^{\rm TOF})<3$ or an associated ITS signal with
$n(\sigma_{\rm e}^{\rm ITS})<2$ not consistent with the kaon ($|n(\sigma_{\rm
K}^{\rm ITS})|<2$) or proton ($|n(\sigma_{\rm p}^{\rm ITS})|<2$) hypothesis
are accepted. The final hadron contamination in the single-electron candidate
sample is estimated to be less than $3.3$% integrated over $p_{\rm T}$.

A statistical approach is applied to extract the yield of correlated signal
pairs ($S$). To this end, all electron and positron candidates from the same
event are combined into opposite-sign pairs ($N^{\rm same}_{\rm+-}$),
characterised by their invariant mass $m_{\rm ee}$, pair transverse momentum
$p_{\rm T,ee}$ and pair DCAee, similarly to the approach followed by the NA60
collaboration [69]. The latter is calculated from the single-electron DCAs as

${\rm DCA_{ee}}=\sqrt{\frac{({\rm DCA}_{xy,1}/\sigma_{xy,1})^{2}+({\rm
DCA}_{xy,2}/\sigma_{xy,2})^{2}}{2}},$ (1)

where DCAxy,i is the DCA of the electron $i$ in the transverse plane and
$\sigma_{xy,i}$ is its resolution estimated from the covariance matrix of the
track reconstruction parameters obtained with the Kalman filter technique,
similarly as in Ref. [70]. The combinatorial background ($B$) is estimated via
the geometric mean of same-sign pairs from the same event $\sqrt{N^{\rm
same}_{\rm++}N^{\rm same}_{\rm--}}$, corrected for the different acceptance
for opposite-sign and same-sign pairs [70, 53]. The correction factor $R$ is
calculated using uncorrelated opposite- ($N^{\rm mix}_{\rm+-}$) and same-sign
($N^{\rm mix}_{\rm++}$ and $N^{\rm mix}_{\rm--}$) pairs from mixed events with
similar global properties as $R=N^{\rm mix}_{\rm+-}/(2\sqrt{N^{\rm
mix}_{\rm++}N^{\rm mix}_{\rm--}})$ and is found to deviate significantly from
unity only at low $m_{\rm ee}$ ($m_{\rm ee}<0.2$ GeV$/c^{2}$). The raw
dielectron yield is then obtained as $S=N^{\rm same}_{\rm+-}-2R\sqrt{N^{\rm
same}_{\rm++}N^{\rm same}_{\rm--}}$. Additional photon conversion rejection is
achieved at low $m_{\rm ee}$ ($m_{\rm ee}<0.1$ GeV$/c^{2}$) by removing pairs
based on their characteristic orientation relative to the magnetic field
quantified by the so-called $\varphi_{\rm V}$ angle defined in Ref. [53]. The
remaining contribution of dielectrons from photon conversions is found to be
negligible, below 1%. The opposite-sign pair spectrum, the combinatorial
background and the extracted raw dielectron yield are shown on the left panel
of Fig. 1 as a function of $m_{\rm ee}$ in the 10% most central Pb–Pb
collisions, together with the $S/B$ ratio on the right panel.

Figure 1: Raw yield ($S$) overlaid with the opposite-sign pair distribution
and the combinatorial background (left panel), as well as signal-over-
background ratio (right panel), in the 10% most central Pb–Pb collisions at
$\sqrt{s_{\mathrm{NN}}}=5.02$ TeV.

###  3.2 Yield corrections

The corrected yield of ${\rm e}^{+}{\rm e}^{-}$ pairs in the ALICE acceptance
($0.2$ or $0.4<p_{\rm T,e}<10$ GeV$/c$ and $|\eta_{\rm e}|<0.8$) before
integration over one or the other variables is expressed as

$\frac{{\rm d^{3}}N_{\rm{\rm e}^{+}{\rm e}^{-}}}{{\rm d}m_{\rm ee}{\rm
d}p_{\rm T,ee}{\rm dDCA_{\rm ee}}}=\frac{1}{\Delta p_{\rm
T,ee}}\frac{1}{\Delta m_{\rm ee}}\frac{1}{\Delta{\rm DCA_{ee}}}\frac{S(m_{\rm
ee},p_{\rm T,ee},{\rm DCA_{\rm ee}})}{\epsilon^{\rm ee}_{\rm rec}(m_{\rm
ee},p_{\rm T,ee})\times N_{\rm events}},$ (2)

where $\Delta p_{\rm T,ee}$, $\Delta m_{\rm ee}$ and $\Delta\rm DCA_{ee}$ are
the width of the $p_{\rm T,ee}$, $m_{\rm ee}$ and DCAee intervals,
respectively. The pair efficiency $\epsilon^{\rm ee}_{\rm rec}(m_{\rm
ee},p_{\rm T,ee})$, including all tracking and PID selection criteria, is
calculated using detailed MC simulations. A realistic detector response is
modelled using GEANT 3 [71] with the same detector configurations as in data
and the DCA detector resolution is corrected a posteriori to reproduce the one
measured in the data. To estimate $\epsilon^{\rm ee}_{\rm rec}(m_{\rm
ee},p_{\rm T,ee})$ with a high statistical precision, samples of dielectron
sources are embedded into hadronic collisions simulated with the HIJING event
generator [72]. Light-flavor hadrons
($\pi^{0}$,$\eta$,$\eta^{\prime}$,$\rho$,$\omega$, and $\phi$) and $J/\psi$
mesons, forced to decay into dielectrons with a phenomenological generator
[70] and PHOTOS [73], respectively, are used together with an enriched sample
of heavy-flavor hadron sources with enforced semileptonic decay channels
generated with the Perugia 2011 tune [74] of PYTHIA 6.4 [75]. The pair
efficiency is computed as explained in Ref. [68]. Since the reconstruction
efficiency for single electron tracks does not show any significant dependence
on the electron DCA, for which loose selection criteria are applied,
$\epsilon^{\rm ee}_{\rm rec}(m_{\rm ee},p_{\rm T,ee})$ is applied to the data
as a function of $m_{\rm ee}$ and $p_{\rm T,ee}$. The average reconstruction
efficiency of a signal ${\rm e}^{+}{\rm e}^{-}$ pair ranges from 15% to 25%.

###  3.3 Systematic uncertainties of measured dielectron spectra

The systematic uncertainties on the measured $p_{\rm T,ee}$\- and $m_{\rm
ee}$-differential yields originate from tracking, electron identification and
purity, and background subtraction. They are evaluated by simultaneous
variations of the tracking and PID selection criteria, as described in Ref.
[70], implying relative changes of the pair efficiencies and $S/B$ ratio by up
to 30% and 40%, respectively. In particular, modifying the requirements on the
ITS, TPC and TOF PID signals allows for probing possible biases due to
differences in the detector responses in data and MC and remaining hadron
contamination in the electron sample. The systematic uncertainty is calculated
as the root mean square of the variation of the data points. It is found to be
larger at low $p_{\rm T,ee}$, up to about 10% for $p_{\rm T,ee}<2$ GeV$/c$
where the $S/B$ is smaller. Similar to Ref. [68], additional uncertainties
related to the conversion rejection criterion ($\varphi_{\rm V}$), the
criteria on the number of shared ITS clusters, and the requirement of a hit in
the first ITS layer, as well as to the TPC–ITS and TPC–TOF matching
efficiencies, are added in quadrature. The first two sources of systematic
uncertainties are estimated by varying the selection criteria, whereas the
others are determined for single electrons and propagated to the ${\rm
e}^{+}{\rm e}^{-}$ pairs using a MC method. The resulting systematic
uncertainties are listed in Table 1.

An additional source of systematic uncertainty is considered for the DCAee-
differential analysis. To take into account possible systematic effects
related to the correlation between $p_{\rm T,ee}$ and DCAee, the latter is
studied in each mass region under interest. The difference of the pair
efficiency at the maximum and minimum mean $p_{\rm T,ee}$, seen as a function
of DCAee, in a given mass region is used to assign a systematic uncertainty
[70]. It is found to be of the order of 3%. The total systematic uncertainty
is given in Table 1 for the $p_{\rm T,ee}$ and $m_{\rm ee}$ analysis, as well
as the DCAee analysis.

Table 1: Summary of the total systematic uncertainties of the measured dielectron yields in the 10% most central Pb–Pb collisions at $\sqrt{s_{\mathrm{NN}}}=5.02$ TeV. The values presented as a range correspond to the smallest and largest observed systematic uncertainties. Analysis | ($m_{\rm ee}$,$p_{\rm T,ee}$) | DCAee
---|---|---
/sources |  |
Tracking and PID selection | 5–11% | 4–11%
Conversion rejection | 2–4% | N/A
Number of shared ITS clusters | 4–12% | 4–12%
Hit in the first ITS layer | 3% | 3%
TPC–ITS matching | 8–12% | 8–12%
TPC–TOF matching | 0–3% | 0–3%
DCAee–$p_{\rm T,ee}$ correlation | N/A | 3%
Total | 12–20% | 15–21%

##  4 Estimation of hadronic sources

The dielectron measurement is compared with the sum of expected contributions
from light- and heavy-flavor hadron decays within the kinematic range under
study, i.e. the hadronic cocktail. They are estimated with simulations
including the angular, momentum and DCA resolution of the detector for the
given data-taking period, as well as bremsstrahlung effects, which are not
corrected for in the data analysis [76, 70].

###  4.1 Dielectron yield from hadronic decays as a function of $m_{\rm ee}$
and $p_{\rm T,ee}$

####  4.1.1 Decays of light-flavor hadrons and $J/\psi$ mesons

The expected dielectron yield from the decays of known light-flavor
($\pi^{0}$, $\eta$, $\eta^{\prime}$, $\omega$, $\rho$, $\phi$) and $J/\psi$
hadrons is calculated as described in Ref. [68]. Parameterizations of the
$p_{\rm T}$-differential yields of the different hadrons are taken as input to
a fast Monte Carlo simulation, that performs the decays and allows retrieving
the corresponding expected dielectron yields [70]. Since the $\pi^{\pm}$
measurement extends down to $p_{\rm T}=0.1$ GeV$/c$ and exhibits small
uncertainties [77], charged pions are used to approximate neutral pions. An
additional 10% systematic uncertainty is considered to take into account
differences due to isospin-violating decays as described in Refs. [78, 68].
The $p_{\rm T}$ spectrum of $\eta$ is computed using the same approach as in
Ref. [79]. First, the $\eta/\pi^{0}$ ratios measured as a function of $p_{\rm
T}$ in hadronic collisions by ALICE [80, 81, 82, 83] and CERES/TAPS [84] at
different energies are parameterized to obtain a pp reference. Second, radial
flow effects in Pb–Pb collisions are evaluated with the double ratio of the
${\rm K^{\pm}/\pi^{\pm}}$ $p_{\rm T}$ spectra measured at midrapidity
($|y|<0.5$) in the 10% most central Pb–Pb collisions and in pp collisions
[77]. Due to their similar masses, ${\rm K^{\pm}}$ and $\eta$ are expected to
be affected by radial flow in a similar way. The corresponding $\eta/\pi^{0}$
ratio in central Pb–Pb collisions is computed as

$\left(\frac{\eta}{\pi^{0}}\right)_{\rm\scriptsize
PbPb}=\left(\frac{\eta}{\pi^{0}}\right)_{\rm pp}\times R_{\rm
flow}=\left(\frac{\eta}{\pi^{0}}\right)_{\rm pp}\times\frac{\left(\frac{{\rm
K^{\pm}}}{\pi^{\pm}}\right)_{\rm\scriptsize PbPb}^{*}}{\left(\frac{{\rm
K^{\pm}}}{\pi^{\pm}}\right)_{\rm pp}^{*}},$ (3)

where ∗ means that the value is not taken at $p_{\rm T}$ but $m_{\eta}/m_{\rm
K^{\pm}}\times p_{\rm T}$ to take into account the small difference in mass
between $\eta$ and $\rm K^{\pm}$ of about 10%. In the left panel of Fig. 2,
the correction factor $R_{\rm flow}$ is presented for the 0–5% and 5–10%
centrality intervals based on the $\rm K^{\pm}$ and $\pi^{\pm}$ measurements
[77], considering the systematic uncertainties of the published ${\rm
K^{\pm}/\pi^{\pm}}$ ratios as uncorrelated between the Pb–Pb and pp colliding
systems. For $p_{\rm T}<9$ GeV$/c$ $R_{\rm flow}$ is consistent with unity and
an universal constant behavior in hadronic and heavy-ion collisions is
assumed. The resulting $\eta/\pi^{0}$ ratio in central Pb–Pb collisions is
parameterized as a function of $p_{\rm T}$ for the two centrality classes
separately, as shown in the right panel of Fig. 2 together with the measured
$\eta/\pi^{0}$ ratios in hadronic collisions [84, 80, 81, 82, 83]. A similar
trend is observed in central Pb–Pb collisions at $\sqrt{s_{\mathrm{NN}}}=2.76$
TeV, where the $\eta/\pi^{0}$ ratio was measured by the ALICE collaboration
[85] at midrapidity. The corresponding calculated dielectron yields in both
centrality classes are combined together to obtain the expected ${\rm
e}^{+}{\rm e}^{-}$ yield in the 10% most central Pb–Pb collisions assuming
fully correlated systematic uncertainties of the $\eta/\pi^{0}$ ratios. The
$\eta^{\prime}$, $\omega$, and $\rho$ $p_{\rm T}$ distributions are generated
assuming $m_{\rm T}$-scaling, implying that the spectra of all light mesons as
a function of $m_{\rm T}=\sqrt{m^{\rm 2}+p_{\rm T}^{\rm 2}}$ follow a
universal form and differ only by a normalization factor. Finally, the
measured $\phi$ [86] and $J/\psi$ [87] $p_{\rm T}$-differential yields in
central Pb–Pb collisions are fitted and in case of the $\phi$ extrapolated
down to low $p_{\rm T}$ ($p_{\rm T}<0.4$ GeV$/c$) using $m_{\rm T}$-scaling.

Figure 2: Left panel: double ratio of the measured ${\rm K^{\pm}/\pi^{\pm}}$
$p_{\rm T}$ spectra in central Pb–Pb collisions and in pp collisions at
$\sqrt{s_{\mathrm{NN}}}=5.02$ TeV [77] dilated as a function of $p_{\rm T}$ by
the ratio of the $\eta$ and $\rm K^{\pm}$ meson mass (see text). Right panel:
measured [84, 80, 81, 82, 83] and parameterized $\frac{\eta}{\pi^{0}}$ ratios
in hadronic collisions and central Pb–Pb collisions, respectively.

####  4.1.2 Open-charm and open-beauty hadron decays

Figure 3: Left panel: measured nuclear modification factor of single electrons
from heavy-flavor hadron decays [88], as well as its parameterization and the
estimated nuclear modification factor caused by pure cold-nuclear matter
effects with EPS09 nPDFs [89], in the 10% most central Pb–Pb collisions at
$\sqrt{s_{\mathrm{NN}}}=5.02$ TeV. Right panel: resulting nuclear modification
factor of ${\rm e}^{+}{\rm e}^{-}$ pairs from correlated open heavy-flavor
hadron decays computed with a toy MC (see text) for two different $p_{\rm
T,ee}$.

Two different calculations for the contributions of correlated semileptonic
heavy-flavor hadron decays are considered. One is based on the dielectron
measurements in pp collisions at the same center-of-mass energy per nucleon
pair [90] scaled with the average number of binary nucleon–nucleon collisions
$\langle N_{\rm coll}\rangle$. The resulting cocktail is called in the
following $N_{\rm coll}$-scaled HF cocktail. For this purpose, the expected
${\rm e}^{+}{\rm e}^{-}$ yields of correlated semileptonic heavy-flavor hadron
decays, estimated with the POWHEG event generator [91, 92, 93, 94] using
PYTHIA 6 [75] as parton shower, are first fitted to the measured ${\rm
e}^{+}{\rm e}^{-}$ spectra in pp collisions to extract ${\rm
d\sigma_{c\overline{c}}}/{\rm d}y|_{{y=0}}$ and ${\rm
d\sigma_{b\overline{b}}}/{\rm d}y|_{{y=0}}$, as explained in Ref. [90]. The
calculations are then scaled with the average nuclear overlap function in the
0–10% centrality interval. The uncertainties originating from the branching
ratio of the semileptonic decays of the open heavy-flavor hadrons and the
fragmentation functions of charm and beauty quarks are omitted assuming that
these do not change from pp to central Pb–Pb collisions. This approach ignores
shadowing and suppression effects due to the interactions of charm and beauty
quarks with other partons in the medium, as well as any modification of the
hadronization processes. Measurements of the nuclear modification factor
$R^{{\rm c,b\to e^{\pm}}}_{\rm AA}$ of single electrons from charm and beauty
hadron decays, however, do show significant modifications of the $p_{\rm T}$
spectra in Pb–Pb collisions compared to pp collisions [88]. These
modifications are due to initial cold nuclear matter (CNM) effects as well as
final hot nuclear matter (HNM) effects like partonic energy loss and
collective flow. Both affect differently the ${\rm e}^{+}{\rm e}^{-}$ pairs.
Whereas the former alters the initial production of heavy-quark pairs and per
consequence of dielectrons, the latter acts on the ${\rm e^{+}}$ and ${\rm
e^{-}}$ mostly independently with the exception of flow.

In a second approach, a simple model is considered to include the single
heavy-flavor decay electron measurements in the cocktail inputs. First, CNM
and HNM effects are disentangled assuming

$R^{{\rm c,b\to e^{\pm}}}_{\rm AA}=R^{{\rm c,b\to e^{\pm}}}_{\rm AA,CNM}\times
R^{{\rm c,b\to e^{\pm}}}_{\rm AA,HNM},$ (4)

where $R^{{\rm c,b\to e^{\pm}}}_{\rm AA}$ is the parameterized single-electron
measurement and $R^{{\rm c,b\to e^{\pm}}}_{\rm AA,CNM}$ is computed using the
EPS09 nuclear parton distribution function (nPDF) [89]. Both are shown as a
function of $p_{\rm T}$ on the left panel of Fig. 3, together with the
measured nuclear modification factor of heavy-flavor decay electrons in the
10% most central Pb–Pb collisions at $\sqrt{s_{\mathrm{NN}}}=5.02$ TeV. The
modifications are then propagated to ${\rm e}^{+}{\rm e}^{-}$ pairs using
Monte Carlo simulations and a weighting procedure. The HNM effects are assumed
to fully factorize between the ${\rm e^{+}}$ and ${\rm e^{-}}$:

$R_{\rm AA,HNM}^{\rm c,b\to e^{+}e^{-}}=R^{{\rm c,b\to e^{\pm}}}_{\rm
AA,HNM}(p_{\rm T,e^{+}})\times R^{{\rm c,b\to e^{\pm}}}_{\rm AA,HNM}(p_{\rm
T,e^{-}}),$ (5)

where $R_{\rm AA,HNM}^{\rm c,b\to e^{+}e^{-}}$ is the dielectron nuclear
modification factor due to HNM effects. Similarly, the CNM effects are
estimated on the ${\rm e}^{+}{\rm e}^{-}$ pair with the dielectron nuclear
modification factor due to CNM effects ($R_{\rm AA,CNM}^{\rm c,b\to
e^{+}e^{-}}$) by taking the mean of the single electron $R^{{\rm c,b\to
e^{\pm}}}_{\rm AA,CNM}$

$R_{\rm AA,CNM}^{\rm c,b\to e^{+}e^{-}}=\frac{R^{{\rm c,b\to e^{\pm}}}_{\rm
AA,CNM}(p_{\rm T,e^{+}})+R^{{\rm c,b\to e^{\pm}}}_{\rm AA,CNM}(p_{\rm
T,e^{-}})}{2}.$ (6)

The resulting dielectron nuclear modification factor ($R_{\rm AA}^{\rm c,b\to
e^{+}e^{-}}$),

$R^{{\rm c,b\to e^{+}e^{-}}}_{\rm AA}=R^{{\rm c,b\to e^{+}e^{-}}}_{\rm
AA,CNM}\times R^{{\rm c,b\to e^{+}e^{-}}}_{\rm AA,HNM},$ (7)

is reported on the right panel of Fig. 3 for two different $p_{\rm T,ee}$
values as a function of $m_{\rm ee}$. Dielectrons with a large $m_{\rm ee}$
and/or $p_{\rm T,ee}$ originate on average from heavy-flavor hadrons with
higher $p_{\rm T}$ than ${\rm e}^{+}{\rm e}^{-}$ pairs at smaller $m_{\rm ee}$
or $p_{\rm T,ee}$ and are therefore more affected by HNM effects. In this
approach, CNM and HNM effects seem to cancel out within large uncertainties at
low $m_{\rm ee}$ and $p_{\rm T,ee}$ ($R^{{\rm c,b\to e^{+}e^{-}}}_{\rm
AA,CNM}\times R^{{\rm c,b\to e^{+}e^{-}}}_{\rm AA,HNM}\approx 1$). The
dielectron $R_{\rm AA}^{\rm c,b\to e^{+}e^{-}}$ is then applied to the
contributions of correlated semileptonic open-charm and open-beauty hadron
decays estimated from pp collisions at the same $\sqrt{s_{\mathrm{NN}}}$, as
explained above. The resulting cocktail is called $R^{{\rm c,b\to
e^{\pm}}}_{\rm AA}$-modified HF cocktail.

####  4.1.3 Systematic uncertainties

The systematic uncertainties of the hadronic cocktail originate from the
following sources: the $\pi^{\pm}$, $\phi$, and $J/\psi$ parameterizations as
a function of $p_{\rm T}$, the $\eta$/$\pi^{\rm 0}$ ratio, the $m_{\rm
T}$-scaling parameters used for $\rho$, $\omega$, $\eta^{\prime}$ and $\phi$,
the branching ratios of the different light-flavor hadron decay channels, and
the heavy-flavor cross sections in pp collisions. In case of the $N_{\rm
coll}$-scaled HF cocktail, the nuclear overlap function is also considered as
a source of uncertainty, whereas for the $R^{{\rm c,b\to e^{\pm}}}_{\rm
AA}$-modified HF cocktail the uncertainties of the measured $R^{{\rm c,b\to
e^{\pm}}}_{\rm AA}$ and the EPS09 nPDF are propagated to the final expected
dielectron yield resulting in two uncorrelated uncertainties of similar
magnitude depending on $m_{\rm ee}$ and $p_{\rm T,ee}$. The different
contributions added in quadrature amount to a total systematic uncertainty
between 10% and 20% depending on $m_{\rm ee}$ and $p_{\rm T,ee}$ for the
$N_{\rm coll}$-scaled HF cocktail. The $R^{{\rm c,b\to e^{\pm}}}_{\rm
AA}$-modified HF cocktail has significantly larger uncertainties, where the
heavy-flavor contributions are dominant, i.e. up to about 40% in the
intermediate-mass range ($1.2<m_{\rm ee}<2.6$ GeV$/c^{2}$).

###  4.2 DCAee template distributions

The DCAee distributions of the different dielectron sources are determined by
the convolution of the DCA detector resolution, the decay length of the mother
particles, and the decay kinematics. Dielectrons produced at the primary
vertex are expected to have smaller DCAee than ${\rm e}^{+}{\rm e}^{-}$ pairs
originating from the decays of correlated open-charm and open-beauty hadrons
with finite decay lengths ($c\tau_{\rm D}\approx 150$ $\mu{\rm m}$ and
$c\tau_{\rm B}\approx 470$ $\mu{\rm m}$). A full GEANT 3 [71] simulation of
the ALICE central barrel, tuned to describe the performance of each detector
subsystem, in particular the ITS, is utilized. The same analysis selection
criteria as in data are applied to extract the DCAee spectra of ${\rm
e}^{+}{\rm e}^{-}$ pairs originating from the decays of prompt and non-prompt
$J/\psi$ mesons, as well as open-beauty and open-charm hadrons. Contrary to
open-beauty hadrons, the various open-charm hadrons have significantly
different decay lengths (e.g. $59.9$ $\mu$m for $\Lambda^{\pm}_{\rm c}$ and
$311.8$ $\mu$m for ${\rm D^{\pm}}$ mesons [95]). Therefore their relative
yields are particularly relevant. The measured production ratios of prompt
open-charm hadrons in pp [96, 97] and Pb–Pb collisions [98], together with
their semileptonic decay branching ratios [95], are used to obtain the ${\rm
c\overline{c}}$ DCAee distribution calculated as the combination of semi-
leptonic decays of the different open-charm hadrons. The ${\rm D^{\pm}/D^{0}}$
ratio is found to be similar in pp and Pb–Pb collisions, whereas possible
enhancements of the $\rm D^{\pm}_{s}/D^{0}$ and $\Lambda_{\rm c}/{\rm D^{0}}$
ratios in Pb–Pb compared to pp collisions are taken into account. Finally, the
fraction of non-prompt $J/\psi$, $f_{\rm B}$, as a function of $p_{\rm T}$
measured by ALICE [87] in central Pb–Pb collisions is taken as input to build
the inclusive DCAee template of the $J/\psi$. Each contribution is normalized
to its expected yield from the hadronic cocktail in the same $m_{\rm ee}$ and
$p_{\rm T,ee}$ range after the same fiducial selection criteria ($|\eta_{\rm
e}|<0.8$ and $p_{\rm T,e}>0.4$ GeV$/c$).

Three sources of systematic uncertainties additional to those mentioned in
Section 4.1.3, depending on DCAee, are considered and added in quadrature.
First, the DCA single-track resolution is not perfectly reproduced in the
simulation. The DCA templates obtained with MC simulations using a post-
correction of the DCA resolution in order to reproduce the one in data are
compared to those estimated without. As a conservative estimate, half of the
difference between the two spectra is attributed to the systematic
uncertainty. This leads to a systematic uncertainty between 10 and 25% varying
with the DCAee value for prompt ${\rm e}^{+}{\rm e}^{-}$ pairs, while for non-
prompt dielectrons (${\rm c\overline{c}}$ and $\rm b\overline{b}$) a maximum
of 10% systematic uncertainty is observed at small DCAee, i.e. for DCAee
values smaller than one. Second, the uncertainties of the charm and beauty-
hadron production ratios, of their semileptonic decay branching ratios, and of
$f_{\rm B}$ are propagated to the corresponding DCAee distributions and amount
to about 10%. Third, the uncertainty related to the $p_{\rm T}$ spectra of the
open-charm and open-beauty mother hadrons is found to be of the order of 5% at
large DCAee.

##  5 Inclusive dielectron production

###  5.1 Dielectron invariant-mass spectra

The yield of ${\rm e}^{+}{\rm e}^{-}$ pairs in the ALICE acceptance
($|\eta_{\rm e}|<0.8$ and $0.2<p_{\rm T,e}<10$ GeV$/c$) is shown as a function
of $m_{\rm ee}$ in the 10% most central Pb–Pb collisions at
$\sqrt{s_{\mathrm{NN}}}=5.02$ TeV in Fig. 4. In the left panel, the data are
compared with the expected contributions from known hadronic sources, i.e. the
$R^{{\rm c,b\to e^{\pm}}}_{\rm AA}$-modified HF cocktail shown with dashed
lines and the $N_{\rm coll}$-scaled HF cocktail displayed as full lines, both
explained in Section 4.1.2. In the $\pi^{0}$ ($m_{\rm ee}<0.135$ GeV$/c^{2}$)
and $J/\psi$ ($2.7<m_{\rm ee}<3.3$ GeV$/c^{2}$) mass regions, where
dielectrons from $\pi^{0}$-Dalitz and $J/\psi$ decays are expected to dominate
the yield of ${\rm e}^{+}{\rm e}^{-}$ pairs, respectively, the data are well
reproduced by the hadronic cocktails.

Figure 4: Upper panels: dielectron $m_{\rm ee}$-differential yields in the 10%
most central Pb–Pb collisions at $\sqrt{s_{\mathrm{NN}}}=5.02$ TeV, compared
with the expected e+e- contributions from known hadronic decays, including two
different estimations for dielectrons from correlated heavy-flavor hadron
decays (left panel), and two predictions for thermal radiation from the medium
[36, 99] (right panel). Bottom panels: ratios data to cocktails, together with
the expected ratios from the models. The error bars and boxes represent the
statistical and systematic uncertainties of the data, respectively, whereas
the bands show the uncertainties of the hadronic cocktails.

In the bottom and middle left panels of Fig. 4, the ratio of the data and the
different hadronic cocktails are presented. At low $m_{\rm ee}$ ($0.18<m_{\rm
ee}<0.5$ GeV$/c^{2}$), the ratios are systematically above one, although
consistent with unity within $1.7\sigma$ ($1.5\sigma$) for the $N_{\rm
coll}$-scaled ($R^{{\rm c,b\to e^{\pm}}}_{\rm AA}$-modified) HF cocktail. The
hint for an excess does not depend significantly on the method used to
estimate the heavy-flavor contribution. In both cocktails, the contribution
from $\rho$ mesons is estimated neglecting any medium effect and amounts to
about 18% of the total yield of known hadronic sources at $m_{\rm\rho}$.
However, a significant contribution of ${\rm e}^{+}{\rm e}^{-}$ pairs
originating from $\rho$ mesons produced thermally in the medium is expected at
low $m_{\rm ee}$. Due to its short lifetime compared to the one of the hot
fireball and its strong coupling to the $\pi^{+}\pi^{-}$ channel, the $\rho$
meson is likely to be regenerated in the hot hadronic phase with a medium-
modified spectral function broader than in vacuum. In the intermediate-mass
range (IMR), i.e. $1.2<m_{\rm ee}<2.6$ GeV$/c^{2}$, the heavy-flavor modified
cocktail can better describe the data, systematically below the expectations
from the $N_{\rm coll}$-scaled HF cocktail. Nevertheless, the former cocktail
suffers from large uncertainties.

In the right panel of Fig. 4, the data are compared with the $R^{{\rm c,b\to
e^{\pm}}}_{\rm AA}$-modified and the $N_{\rm coll}$-scaled HF cocktails
excluding the contribution from the $\rho$ meson. In addition, expectations
from two theoretical models for thermal dielectrons from the partonic and
hadronic phase, referred to as QGP and in-medium $\rho$, are shown. As for the
hadronic cocktail, detector resolution effects were applied to the predictions
[76, 68]. In both calculations, $\rho$ mesons produced in the hot hadronic
phase are a relevant source of thermal radiation for $m_{\rm ee}<0.8$
GeV$/c^{2}$. The model from R. Rapp [36] is an expanding fireball model, where
the thermal emission rate of dielectrons from the hadronic phase is calculated
based on a hadronic many-body theory with in-medium modified $\rho$, whereas a
lattice-QCD inspired approach is used for the equation of state in the QGP.
The Parton-Hadron-String Dynamics (PHSD) model is a transport model [99] with
in-medium modified electromagnetic spectral functions of low-mass vector
mesons. The predictions were added to the hadronic cocktails to obtain the
total expected yield of dielectrons. In the bottom and middle right panels of
Fig. 4, the ratio between the data and the different hadronic cocktails
excluding the $\rho$ meson contribution are shown together with the ratio of
the total expected dielectron yield to the hadronic cocktails. The data-to-
cocktail ratio integrated in the $m_{\rm ee}$ range $0.18<m_{\rm ee}<0.5$
GeV$/c^{2}$ is found to be $R=1.42\pm 0.12\ {\rm(stat.)}\pm 0.17\
{\rm(syst.)}\pm 0.12\ {\rm(cocktail)}$ for the $N_{\rm coll}$-scaled HF
cocktail and $R=1.44\pm 0.12\ {\rm(stat.)}\pm 0.17\
{\rm(syst.)}^{+0.17}_{-0.21}\ {\rm(cocktail)}$ for the $R^{{\rm c,b\to
e^{\pm}}}_{\rm AA}$-modified HF cocktail, where the systematic uncertainty
related to the cocktail is reported separately to those originating from the
data. Both are consistent with the predicted ratios using the model
calculations for thermal contributions and the hadronic cocktails. Both models
can reproduce the data for $0<m_{\rm ee}<0.5$ GeV$/c^{2}$, but tend to
overestimate them for $0.5<m_{\rm ee}<0.7$ GeV$/c^{2}$. In the IMR, the QGP is
the main source of predicted thermal radiation. The expected thermal
contribution to the total dielectron yield is small, i.e. around 15%
integrated over this mass range, which is below the sensitivity of the data
and much smaller than the uncertainties of the heavy-flavor modified cocktail.

To better investigate the hint for an excess of ${\rm e}^{+}{\rm e}^{-}$ pairs
at low $m_{\rm ee}$, the expected dielectron yield from known hadronic sources
is subtracted from the data to obtain a so-called excess spectrum. The excess
spectra computed with the two different cocktails ($R^{{\rm c,b\to
e^{\pm}}}_{\rm AA}$-modified and $N_{\rm coll}$-scaled HF cocktails) are shown
in Fig. 5 for $0.14<m_{\rm ee}<1.1$ GeV$/c^{2}$. Upper limits at 90% C.L.
using the Feldman and Cousins method [100] are reported for the values which
are found to be statistically consistent with zero within one standard
deviation. In the $m_{\rm ee}$ range $0.18<m_{\rm ee}<0.5$ GeV$/c^{2}$, where
the significance of the excess reaches $1.53\sigma$ and $1.79\sigma$ using the
$R^{{\rm c,b\to e^{\pm}}}_{\rm AA}$-modified and $N_{\rm coll}$-scaled HF
cocktails, respectively, the result is not very sensitive to the different
implementations of the heavy-flavor background. The excess spectra are
compared with the same models [36, 99] as above. The computed contributions
from $\rho$ mesons produced thermally in the hot hadronic matter and thermal
radiation from the QGP are shown separately. In the case of the PHSD model
(right panel of Fig. 5), the dielectron production in the QGP is calculated by
implementing the off-shell cross sections of ${\rm q\overline{q}}\to{\rm
e^{+}e^{-}}$, ${\rm q\overline{q}}\to{\rm e^{+}e^{-}g}$ and ${\rm qg}\to{\rm
qe^{+}e^{-}}$ (${\rm\overline{q}g}\to{\rm\overline{q}e^{+}e^{-}}$) reactions
from the dynamical quasiparticle model [101] into the PHSD transport approach.
The yield of thermal radiation from the hadronic phase (in-medium $\rho$)
predicted by PHSD is smaller than the one estimated by the model of R. Rapp
(right panel of Fig. 5) [36]. Both calculations are nevertheless compatible
with the data within their statistical and systematic uncertainties.

Figure 5: Excess yield of dielectrons in the 10% most central Pb–Pb collisions
at $\sqrt{s_{\mathrm{NN}}}=5.02$ TeV with respect to the expected ${\rm
e}^{+}{\rm e}^{-}$ contributions from known hadronic sources, including or not
including medium effects for the heavy-flavor contributions, and compared with
predictions from the model of R. Rapp [36] (left) and from the PHSD transport
approach [99] (right).

###  5.2 Dielectron $p_{\rm T,ee}$ spectra

The yield of ${\rm e}^{+}{\rm e}^{-}$ pairs in the $m_{\rm ee}$ range where a
hint for an excess is observed and the heavy-flavor contribution is expected
to be still relatively small ($0.18<m_{\rm ee}<0.34$ GeV$/c^{2}$) is shown as
a function of $p_{\rm T,ee}$ in the left panel of Fig. 6. The data are
compared with the two different cocktails discussed in Sec. 4. In this $m_{\rm
ee}$ range, $\eta$ Dalitz decays ($\eta\to{\rm\gamma e^{+}e^{-}}$) are
expected to contribute significantly at low $p_{\rm T,ee}$, whereas correlated
open-beauty hadron decays play a role at high $p_{\rm T,ee}$. The data-to-
cocktail ratios, shown on the bottom and middle left panels of Fig. 6, are
consistent with unity, while being systematically above but still within
$1.53\sigma$ ($1.45\sigma$) in the $p_{\rm T,ee}$ range $0.9<p_{\rm T,ee}<2$
GeV$/c$ for the $N_{\rm coll}$\- ($R^{{\rm c,b\to e^{\pm}}}_{\rm
AA}$)-modified HF cocktail. The ratios are compared with the expected
inclusive dielectron yield-to-cocktail ratio estimated with the two different
calculations for thermal radiation from the partonic and hadronic phase [36,
99] presented in Sec. 5.1. Both models predict thermal contributions relevant
only at low $p_{\rm T,ee}$ ($p_{\rm T,ee}<4$ GeV$/c$) and are compatible with
the data within uncertainties.

Figure 6: Upper panels: dielectron $p_{\rm T,ee}$-differential yields in two
different $m_{\rm ee}$ ranges, $0.18<m_{\rm ee}<0.34$ GeV$/c^{2}$ (left) and
$1.2<m_{\rm ee}<2.6$ GeV$/c^{2}$ (right), in the 10% most central Pb–Pb
collisions at $\sqrt{s_{\mathrm{NN}}}=5.02$ TeV, compared with the expected
e+e- contributions from known hadronic decays, including two different
estimations for dielectrons from correlated heavy-flavor hadron decays (see
text). Bottom panels: ratios data to cocktails, excluding the contribution
from vacuum $\rho$, together with two predictions for thermal radiation from
the medium [36, 99]. The error bars and boxes represent the statistical and
systematic uncertainties of the data, respectively, whereas the bands show the
uncertainties of the hadronic cocktails.

The IMR is dominated by correlated ${\rm e}^{+}{\rm e}^{-}$ pairs from
semileptonic decays of charm and beauty hadrons. The $p_{\rm
T,ee}$-differential yield of ${\rm e}^{+}{\rm e}^{-}$ pairs measured in this
$m_{\rm ee}$ region is shown in comparison with the two different hadronic
cocktails, as well as predictions for thermal radiation [36, 99] in the data-
to-cocktail ratios, in the right panel of Fig. 6. The contribution of ${\rm
e}^{+}{\rm e}^{-}$ pairs from ${\rm c\overline{c}}$ is expected to be the
dominant dielectron source for $p_{\rm T,ee}<2$ GeV$/c$, whereas most of the
${\rm e}^{+}{\rm e}^{-}$ pairs originate from ${\rm b\overline{b}}$ for
$p_{\rm T,ee}>4$ GeV$/c$. The data are systematically below the $N_{\rm
coll}$-scaled HF cocktail, particularly at high $p_{\rm T,ee}$ where the
difference reaches $2\sigma$ in the last $p_{\rm T,ee}$ interval ($6<p_{\rm
T,ee}<8$ GeV$/c$). This is in agreement with a heavy-flavor suppression,
increasing with $p_{\rm T,ee}$, with respect to pp collisions at the same
center-of-mass energy per nucleon pair. The trend is reproduced by the
$R^{{\rm c,b\to e^{\pm}}}_{\rm AA}$-modified HF cocktail based on the measured
single heavy-flavor decay electron $R_{\rm AA}$ [88], although this cocktail
has large uncertainties. The contribution of thermal radiation from the QGP is
predicted to be at most 15% of the inclusive dielectrons for $p_{\rm T,ee}<2$
GeV/c, as can be seen on the bottom and middle right panels of Fig. 6. It is
much smaller than the uncertainties of the heavy-flavor modified cocktail.
Therefore a different approach is mandatory to address the production of ${\rm
e}^{+}{\rm e}^{-}$ pairs in the partonic phase.

##  6 Topological separation of ${\rm e}^{+}{\rm e}^{-}$ sources

Dielectron measurements in the IMR provide a handle to disentangle the
contributions of hadronic and QGP thermal radiation. However, dielectrons from
correlated heavy-flavor hadron decays dominate the ${\rm e}^{+}{\rm e}^{-}$
pair production in this phase space and make the extraction of the thermal QGP
signal very challenging. The pair ${\rm{DCA_{ee}}}$ variable offers
experimental means to disentangle displaced dielectrons produced in the decays
of heavy-flavor hadrons from a prompt thermal contribution.

###  6.1 $J/\psi$ invariant-mass region

The contributions from prompt and non-prompt $J/\psi$ are well constrained by
independent ALICE measurements which combine the inclusive yield with the
fraction of $J/\psi$ originating from beauty hadron decays [87]. These
components are dominant for $2.6<m_{\rm ee}<3.1$ GeV$/c^{2}$, making this mass
range well suited to test the understanding of the detector DCAee resolution.
The measured DCAee-differential yield in this mass range is compared with the
different expected hadronic components, i.e. dielectrons from prompt and non-
prompt $J/\psi$ decays, as well as from open heavy-flavor hadron decays in
Fig. 7. The $R^{{\rm c,b\to e^{\pm}}}_{\rm AA}$-modified heavy-flavor
calculations are used to estimate the heavy-flavor yields, which are found to
be a subleading contribution at all DCAee. The data are described by the sum
of the DCAee templates, validating the description of the DCAee resolution in
the simulations.

Figure 7: Upper panel: inclusive ${\rm e}^{+}{\rm e}^{-}$ yield in the 10%
most central Pb–Pb collisions at $\sqrt{s_{\mathrm{NN}}}=5.02$ TeV as a
function of DCAee in the mass range $2.6<m_{\rm ee}<3.1$ GeV$/c^{2}$, compared
with a cocktail of expected sources, including medium effects for the heavy-
flavor contributions. Bottom panel: corresponding data to cocktail ratio.
Statistical and systematic uncertainties on the data are shown as vertical
bars and boxes, respectively. The total uncertainty of the cocktail is
represented as a grey band.

###  6.2 Intermediate-mass range and QGP thermal radiation

The DCAee-differential yield measured in the mass range $1.2<m_{\rm ee}<2.6$
GeV$/c^{2}$ is shown in Fig. 8 together with the expected contributions of
known hadronic decays, including or not including medium effects for
dielectrons from heavy-flavor hadron decays ($N_{\rm coll}$-scaled and
$R^{{\rm c,b\to e^{\pm}}}_{\rm AA}$-modified HF cocktails, respectively). The
$J/\psi$ contribution in this mass range originates principally from electrons
affected by bremsstrahlung in the detector material and reconstructed with a
smaller $p_{\rm T}$ compared to their true one, shifting the measured
dielectron invariant mass towards smaller values. The upper boundary of the
$m_{\rm ee}$ range (2.6 GeV$/c^{2}$) was chosen such that the $J/\psi$
contribution is one order of magnitude smaller than the measured dielectron
yield. On the contrary, the ${\rm b\overline{b}}\to{\rm ee}$ contribution,
with the large decay length of open-beauty hadrons ($c\tau_{\rm B}\approx$ 470
$\mu{\rm m}$), dominates the spectrum at high DCAee, while the ${\rm
c\overline{c}}\to{\rm ee}$ component defines the spectrum at low DCAee values
($c\tau_{\rm D}\approx$ 150 $\mu{\rm m}$). Overall, the data are below the
$N_{\rm coll}$-scaled HF cocktail, indicating a heavy-flavor suppression in
Pb–Pb collisions compared to pp collisions. A better agreement is observed
with the $R^{{\rm c,b\to e^{\pm}}}_{\rm AA}$-modified HF cocktail. The data-
to-cocktail ratios are compared with the ratio of the total expected
dielectron yield and the hadronic cocktail, using predictions for thermal
radiation from the two different models [36, 99] discussed in Sec. 5.1. For
this purpose, the DCAee template for prompt ${\rm e}^{+}{\rm e}^{-}$ pairs is
normalized to the expected thermal radiation yield from the models. The
contribution of thermal radiation is expected to be between 10 and 40% around
DCAee values of 1.5$\sigma$ according to these calculations and the DCAee
detector resolution. It is consistent with the data using the $R^{{\rm c,b\to
e^{\pm}}}_{\rm AA}$-modified HF cocktail to describe the heavy-flavor
background.

Figure 8: Upper panel: inclusive ${\rm e}^{+}{\rm e}^{-}$ yield in the 10%
most central Pb–Pb collisions at $\sqrt{s_{\mathrm{NN}}}=5.02$ TeV as a
function of DCAee in the mass range $1.2<m_{\rm ee}<2.6$ GeV$/c^{2}$, compared
with the expected e+e- contributions from known hadronic decays, including two
different estimations for dielectrons from correlated heavy-flavor hadron
decays (see text). Bottom panels: ratios data to cocktail, together with two
predictions for thermal radiation from the medium [36, 99]. Statistical and
systematic uncertainties on the data are shown as vertical bars and boxes,
respectively. The total uncertainty of the cocktails are represented as band.

The description of the data can be improved by fitting the DCAee templates of
the different expected contributions to the data as shown in Fig. 9 (left) and
explained below. The $J/\psi$ DCAee template $\left(f^{\rm fixed}_{\rm
DCA}(J/\psi\rm\to e^{+}e^{-})\right)$ is given by the cocktail. The beauty
contribution $\left(f^{\rm fixed}_{\rm DCA}(\rm b\overline{b}\to
e^{+}e^{-})\right)$ is fixed to reproduce the data at high $p_{\rm T,ee}$
($p_{\rm T,ee}>3$ GeV$/c$). In this $p_{\rm T,ee}$ region, the beauty
contribution dominates the spectra, while other components (charm, $J/\psi$,
and thermal) are expected to contribute less than 26% to the dielectron yield.
This approach leads to a suppression by a factor $0.74\pm 0.24\
{\rm(stat.)}\pm 0.12\ {\rm(syst.)}$ for beauty compared to $N_{\rm
coll}$-scaling. Finally, the data points are fitted with a four-component
function

$f_{\rm DCA}=a\times f_{\rm DCA}({\rm prompt})+b\times f_{\rm DCA}({\rm
c\overline{c}\to e^{+}e^{-}})+f^{\rm fixed}_{{\rm DCA}}({\rm b\overline{b}\to
e^{+}e^{-}})+f^{{\rm fixed}}_{{\rm DCA}}({\rm J/\psi\to e^{+}e^{-}}),$ (8)

where $a$ and $b$ are the two fit parameters, whereas $f_{\rm DCA}(\rm
prompt)$ and $f_{\rm DCA}(\rm c\overline{c}\to e^{+}e^{-})$ are the thermal
and open charm contributions, whose yields are given by the model of R. Rapp
[36] and the $N_{\rm coll}$-scaled HF cocktail, respectively. The data are
found to be consistent with a charm suppression by a factor $0.43\pm 0.4\
{\rm(stat.)}\pm 0.22\ {\rm(syst.)}$ with respect to $N_{\rm coll}$-scaling and
an additional prompt component that is a factor $3.17\pm 3.81\ {\rm(stat.)}\pm
0.35\ {\rm(syst.)}$ larger than the predictions from R. Rapp [36] and $1.15\pm
1.38\ {\rm(stat.)}\pm 0.13\ {\rm(syst.)}$ times the expected yield from the
PHSD model [99]. The $\chi^{2}$ of the DCAee fit is reported as a function of
the ratio of the yield of ${\rm e}^{+}{\rm e}^{-}$ pairs originating from a
prompt source and from correlated open-charm hadron decays to the total
measured dielectron yield on the right-hand panel of Fig. 9. The full line
shows the systematic uncertainties originating from those of the data,
determined by moving the data points coherently upward and downward by their
systematic uncertainties. The smallest source of uncertainty is related to the
systematic uncertainties of the DCAee templates, represented as a dashed line.
The fit procedure is repeated after changing the DCAee resolution in the
simulations used to build the templates, as well as after varying the
semileptonic decay branching ratios and fragmentation functions of the charm
hadrons according to their uncertainties. The former source of systematic
uncertainty dominates the latter one. Finally, the statistical uncertainties
of the fit, directly related to those of the data, are displayed by an
ellipse. They are by far the biggest uncertainty and limit the interpretation
of the results, since the data are consistent with no as well as a 65% prompt
contribution in the measured dielectron yield. The larger expected data sample
of Pb–Pb collisions during the LHC Run 3 and 4 periods, up to a factor 100,
will allow a significant reduction of the statistical uncertainties [102, 103,
104, 105, 106]. At the same time, the better single-track DCA resolution of
the detector, by a factor 3 and 6 in the transverse plane and in the direction
of the beam axis, respectively, for Run 3 [107] and even more for Run 4 [108],
will further improve the separation of prompt and non-prompt dielectron
sources [109]. According to the present pioneer analysis of DCAee, a
significant extraction of QGP radiation in the IMR should be then possible in
Run 3 and 4 [110].

Figure 9: Left panel: fit of the inclusive ${\rm e}^{+}{\rm e}^{-}$ yield in
the 10% most central Pb–Pb collisions at $\sqrt{s_{\mathrm{NN}}}=5.02$ TeV as
a function of DCAee in the mass range $1.2<m_{\rm ee}<2.6$ GeV$/c^{2}$. Right
panel: corresponding $\chi^{2}$ as a function of the two fit parameters, i.e.
the ratio of the yield of ${\rm e}^{+}{\rm e}^{-}$ pairs originating from a
prompt source or from open-charm hadron decays to the measured ${\rm
e}^{+}{\rm e}^{-}$ yield. See text for more details.

##  7 Direct-photon production

###  7.1 Inclusive to decay photon ratio

In the quasi-real virtual-photon region where the $p_{\rm T,ee}$ of the
dilepton pair is much larger than its mass ($p^{2}_{\rm T,ee}\gg m^{2}_{\rm
ee}$), the fraction of virtual direct photons over inclusive photons can be
extracted from the measured dielectron yield. To this end, the $m_{\rm ee}$
spectra in different $p_{\rm T,ee}$ intervals are fitted in the range
$0.12<m_{\rm ee}<0.34$ GeV$/c^{2}$ with a three-component function

$f{\rm(}m_{\rm ee}{\rm)}=rf_{\rm dir}{\rm(}m_{\rm
ee}{\rm)}+{\rm(1-}r{\rm)}f_{\rm LF}{\rm(}m_{\rm ee}{\rm)}+f_{\rm
HF}{\rm(}m_{\rm ee}{\rm)}.$ (9)

In the above equation, $f_{\rm dir}{\rm(}m_{\rm ee}{\rm)}$ is the expected
invariant-mass distribution of virtual direct photons, described by the
Kroll–Wada equation [111], and $f_{\rm LF}{\rm(}m_{\rm ee}{\rm)}$ and $f_{\rm
HF}{\rm(}m_{\rm ee}{\rm)}$ are the mass distributions of the light-flavor
contributions without $\rho$ and the heavy-flavor components of the hadronic
cocktail, respectively. The $R^{{\rm c,b\to e^{\pm}}}_{\rm AA}$-modified HF
cocktail is used for this purpose. Both $f_{\rm LF}{\rm(}m_{\rm ee}{\rm)}$ and
$f_{\rm dir}{\rm(}m_{\rm ee}{\rm)}$ are independently normalized to the data
in the mass range $0<m_{\rm ee}<0.03$ GeV$/c^{2}$, whereas $f_{\rm
HF}{\rm(}m_{\rm ee}{\rm)}$ is normalized accordingly to the hadronic cocktail.
The only fit parameter $r$ represents the fraction of virtual direct photons
at vanishing mass, directly related to the one of real direct photons:

$r=\left(\frac{\gamma^{*}_{\rm dir}}{\gamma^{*}_{\rm
inclusive}}\right)_{m_{\rm ee}\to 0}=\left(\frac{\gamma_{\rm dir}}{\gamma_{\rm
inclusive}}\right).$ (10)

This approach has the advantage that the background of photons originating
from hadronic decays, dominated by $\pi^{0}$ decays, can be suppressed by
selecting ${\rm e}^{+}{\rm e}^{-}$ pairs with sufficiently large $m_{\rm ee}$
($m_{\rm ee}>m_{\rm\pi^{0}}$). However, the internal conversion probability is
small ($\approx 10^{-2}$) and the dielectron yield decreases rapidly as a
function of $m_{\rm ee}$ ($\propto 1/m_{\rm ee}$). The fit of the measured
$m_{\rm ee}$-differential dielectron yield in the $p_{\rm T,ee}$ range
$1<p_{\rm T,ee}<2$ GeV$/c$ is shown in the left panel of Fig. 10, together
with its individual contributions.

Figure 10: Left panel: fit of the dielectron yield with the three-component
function defined by Eq. 10 in the 10% most central Pb–Pb collisions at
$\sqrt{s_{\mathrm{NN}}}=5.02$ TeV as a function of $m_{\rm ee}$ in the $p_{\rm
T,ee}$ range $1<p_{\rm T,ee}<2$ GeV$/c$. Right panel: ratio of direct to
inclusive photon yields extracted from the dielectron spectra as a function of
$p_{\rm T}$ in central Pb–Pb collisions at $\sqrt{s_{\mathrm{NN}}}=5.02$ TeV.
Statistical and systematic uncertainties on the data are shown separately as
vertical bars and boxes, respectively.

Systematic uncertainties arise from the data, the hadronic cocktail components
and the choice of the normalization and fit ranges. They are estimated in a
similar way as in Refs. [70, 112, 53]. On the one hand, the uncertainties from
the data are evaluated by shifting all data points coherently to their upper
and lower systematic uncertainties and by repeating the fit procedure. On the
other hand, the different contributions of the cocktail are shifted separately
according to their respective uncertainties. The limited knowledge of the
$\eta/\pi^{0}$ ratio dominates the systematic uncertainties for the first
$p_{\rm T,ee}$ interval, whereas the choice of the fit range becomes relevant
with increasing $p_{\rm T,ee}$. The latter is estimated by varying the lower
bound of the fit, keeping the upper one fixed to assure the $p^{2}_{\rm
T,ee}\gg m^{2}_{\rm ee}$ condition and avoid a significant contribution from
$\rho$ hadron decays. The total systematic uncertainties on $r$ are obtained
by summing in quadrature all individual contributions and are ranging from 77%
to 60% from low to high $p_{\rm T}$.

The ratio of direct to inclusive photons ($r$) measured in the 10% most
central Pb–Pb collisions is shown as a function of $p_{\rm T}$ ($=p_{\rm
T,ee}$) in the right panel of Fig. 10. The data differ from zero suggesting a
source of photons that is not originating from hadronic decays. The
significance of a direct photon signal is ranging from $1.07$ to $1.2\sigma$
from the low to high $p_{\rm T}$ interval for virtual photons.

###  7.2 Direct-photon $p_{\rm T}$ spectrum

Figure 11: Direct-photon invariant yield in the 10% most central Pb–Pb
collisions at $\sqrt{s_{\mathrm{NN}}}=5.02$ TeV, compared with the predictions
from a state-of-the-art model [13]. The error bars and boxes represent the
statistical and systematic uncertainties of the data, respectively.

The $p_{\rm T}$-differential invariant yield of direct photons can be obtained
from $r$ and the inclusive photon yield ($\frac{{\rm d}N_{\rm\gamma}^{\rm
incl}}{{\rm d}p_{\rm T}}$). The latter is determined for each $p_{\rm T}$
interval from the yield of low mass ${\rm e}^{+}{\rm e}^{-}$ pairs in the
range $m_{\rm ee}<30$ MeV/$c^{\rm 2}$ ($\frac{{\rm d}N_{\rm ee}^{\rm
data}}{{\rm d}p_{\rm T}}$) following the approach used by the PHENIX
collaboration [41]. The relation between real photon production and the
associated ${\rm e}^{+}{\rm e}^{-}$ production becomes process independent for
very low $m_{\rm ee}$ (within a few percent for $m_{\rm ee}<30$ MeV/$c^{\rm
2}$). The ratio of the expected yield of real photons from known hadronic
decays ($\frac{{\rm d}N_{\rm\gamma}^{\rm cocktail}}{{\rm d}p_{\rm T}}$) to the
one of dielectrons from the same hadronic sources for $m_{\rm ee}<30$
MeV/$c^{\rm 2}$ ($\frac{{\rm d}N_{\rm ee}^{\rm cocktail}}{{\rm d}p_{\rm T}}$)
can be then used to estimate the inclusive real photon yield from the
dielectron yield at low $m_{\rm ee}$, i.e.

$\frac{{\rm d}N_{\rm\gamma}^{\rm incl}}{{\rm d}p_{\rm T}}=\frac{{\rm d}N_{\rm
ee}^{\rm data}}{{\rm d}p_{\rm T}}\times\left(\frac{{\rm d}N_{\rm\gamma}^{\rm
cocktail}}{{\rm d}p_{\rm T}}\middle/\frac{{\rm d}N_{\rm ee}^{\rm
cocktail}}{{\rm d}p_{\rm T}}\right).$ (11)

Most of the uncertainties related to the parameterized $p_{\rm T}$ spectra
used as input for the cocktail calculations cancel in the cocktail ratio. The
resulting direct-photon $p_{\rm T}$-differential spectrum in the 10% most
central Pb–Pb collisions at $\sqrt{s_{\mathrm{NN}}}=5.02$ TeV is shown in Fig.
11. Within each $p_{\rm T}$ bin, the mean $p_{\rm T}$ is calculated with an
iterative procedure using an exponential function to interpolate the $p_{\rm
T}$ spectrum [113]. The data are compared to a hybrid model that describes all
stages of the heavy-ion collisions [13]. The calculations include the
contribution from prompt photons computed with next-to-leading-order
perturbative QCD using INCNLO [114], nCTEQ15 parton distribution functions
corrected for nuclear matter effects [115], and BFG-II fragmentation functions
[116]. The measured direct-photon invariant yield is consistent with the
prompt photon contribution alone, but the central values of the data points
are systematically higher. The model predicts additional contributions from
the pre-equilibrium, as well as fluid-dynamical, phases. The very early
nuclear medium is described using the IP-Glasma model [117, 118] with a time-
evolution determined by Yang–Mills equations. It is followed by an out-of-
equilibrium phase where the energy-momentum tensor is evolved with non-
equilibrium linear response functions [119, 120]. This pre-hydrodynamical
K$\varnothing$MP$\varnothing$ST [120] phase feeds into a fluid-dynamical
evolution, modelled with MUSIC [121]. The contribution of thermal photons is
obtained by integrating photon emission rates over the entire space-time
volume occupied by the fluid-dynamical phase. Thermal photons are the largest
source of direct photons at $p_{\rm T}<3$ GeV$/c$, whereas the pre-equilibrium
contribution never dominates, but exceeds the thermal contribution for $p_{\rm
T}>3.5$ GeV$/c$. The predicted invariant yield of all direct-photon
contributions together can describe the measurement, although it tends to
overestimate the data by about $1\sigma$.

###  7.3 Charged-particle multiplicity dependence of direct-photon production

Figure 12: Integrated direct-photon yield in the $p_{\rm T}$ range $1<p_{\rm
T}<5$ GeV$/c$ (or $1<p_{\rm T}<3$ GeV$/c$) in Pb–Pb collisions at
$\sqrt{s_{\mathrm{NN}}}=5.02$ TeV and $\sqrt{s_{\mathrm{NN}}}=2.76$ TeV [32],
in Au–Au collisions at $\sqrt{s_{\mathrm{NN}}}=0.2$ TeV as measured by the
PHENIX [19] and STAR [27] collaborations, and in pp collisions at
$\sqrt{s}=0.2$ TeV [18]. The data are compared to predictions from a state-of-
the-art model [13]. The error bars and boxes represent the statistical and
systematic uncertainties of the data along the y-axis, respectively. The
horizontal width of the boxes shows the total uncertainty of the measured
$\frac{{\rm d}N_{\rm ch}}{{\rm d}\eta}|_{\eta=0}$ [122].

The $p_{\rm T}$-integrated direct-photon yields are shown in Fig. 12 as a
function of the measured charged-particle multiplicity at midrapidity [122]
for Pb–Pb collisions at $\sqrt{s_{\mathrm{NN}}}=5.02$ (this analysis) and
$2.76$ TeV [32], for Au–Au collisions at $\sqrt{s_{\mathrm{NN}}}=0.2$ TeV [19,
27], as well as for pp collisions at $\sqrt{s}=0.2$ TeV [18]. The yields are
integrated over the $p_{\rm T}$ range $1<p_{\rm T}<5$ GeV$/c$, except for the
STAR data where the range is $1<p_{\rm T}<3$ GeV$/c$. The systematic
uncertainties are assumed fully correlated as a function of $p_{\rm T}$ for
the results at $\sqrt{s_{\mathrm{NN}}}=5.02$ TeV. The magenta band gives the
integrated direct-photon yield in pp collisions at $\sqrt{s}=0.2$ TeV, scaled
by the number of binary nucleon–nucleon collisions to the corresponding
$\frac{{\rm d}N_{\rm ch}}{{\rm d}\eta}|_{\eta=0}$ for Au–Au collisions at
$\sqrt{s_{\mathrm{NN}}}=0.2$ TeV. The data are compared with predictions from
the same model as the one used for the $p_{\rm T}$-differential invariant
yield discussed above [13]. The calculations can reproduce the measured
direct-photon yields at the LHC and in central Au–Au collisions at RHIC,
although they tend to slightly overestimate the observed yield at the highest
charged-particle multiplicity reported here. At lower $\frac{{\rm d}N_{\rm
ch}}{{\rm d}\eta}|_{\eta=0}$ ($\frac{{\rm d}N_{\rm ch}}{{\rm
d}\eta}|_{\eta=0}<300$), the predicted direct-photon yields are smaller than
the measured values by the PHENIX collaboration, with a difference increasing
when moving to lower multiplicity. However, the comparison between the
calculations and the data reported by the STAR collaboration for the same
colliding system shows a better agreement. The discrepancy between the PHENIX
and STAR results remains unresolved to this day.

The PHENIX collaboration reported an approximate power-law dependence on
$\frac{{\rm d}N_{\rm ch}}{{\rm d}\eta}|_{\eta=0}$ of the direct-photon yields
at low $p_{\rm T}$, with a power $\alpha$ independent of centrality or
collision energy and similar to what would correspond to a scaling with the
number of binary nucleon–nucleon collisions ($\alpha=1.25\pm 0.02$) shown with
the magenta band in Fig. 12. However, the extracted value of $\alpha$ from the
latest PHENIX Au–Au data presented here is smaller than 1.25, i.e.
$\alpha=1.11\pm 0.02\ (\rm stat.)^{+0.09}_{-0.08}\ (\rm syst.)$ [19]. For
comparison, the calculations predict $\alpha$ values of $1.25$, $1.32$ and
$1.34$ for Au–Au collisions at $\sqrt{s_{\mathrm{NN}}}=0.2$ TeV and for Pb–Pb
collisions at $\sqrt{s_{\mathrm{NN}}}=2.76$ and $5.02$ TeV, respectively. The
results at LHC energies are not yet sensitive to the difference between the
different predicted or measured $\alpha$ values.

##  8 Summary and outlook

The first measurement at the LHC of low-mass dielectrons ($0<m_{\rm ee}<3.5$
GeV$/c^{2}$) in the 10% most central Pb–Pb collisions at
$\sqrt{s_{\mathrm{NN}}}=5.02$ TeV is presented. The ${\rm e}^{+}{\rm e}^{-}$
pair production is measured with the ALICE detector at midrapidity
($|\eta_{\rm e}|<0.8$) and compared with a cocktail of expected contributions
from decays of known hadrons, excluding the $\rho$ meson. The data to cocktail
ratio for $0.18<m_{\rm ee}<0.5$ GeV$/c^{2}$ amounts to $1.42\pm 0.12\ (\rm
stat.)\pm 0.17\ (\rm syst.)\pm 0.12\ (\rm cocktail)$ for a cocktail where the
background from open heavy-flavor hadron decays is taken from dielectron
measurements in pp collisions at the same center-of-mass energy per nucleon
pair [90] and scaled with $N_{\rm coll}$, and $1.44\pm 0.12\ (\rm stat.)\pm
0.17\ (\rm syst.)^{+0.17}_{-0.21}\ (\rm cocktail)$ for a cocktail including a
modification of the heavy-flavor background based on the measured single
electrons from heavy-flavor hadron decays [88] and the EPS09 nPDF [89]. The
latter approach suffers from large uncertainties. The excess spectra, obtained
after subtracting the hadronic cocktails, are consistent with predictions from
two models that include thermal radiation from the partonic and hadronic
phases [36, 99], the latter being dominant in the $m_{\rm ee}$ range
considered ($0.2<m_{\rm ee}<0.7$ GeV$/c^{2}$). The uncertainties of the data
do not allow the extraction of a significant thermal signal. A different
method, based on the pair transverse impact parameter of the ${\rm e}^{+}{\rm
e}^{-}$ pairs, is used for the first time in Pb–Pb collisions to disentangle
displaced dielectrons from heavy-flavor hadron decays from a prompt thermal
contribution. The data are found to be consistent with a large suppression of
${\rm e}^{+}{\rm e}^{-}$ pairs from ${\rm c\overline{c}}$, larger than for
${\rm e}^{+}{\rm e}^{-}$ pairs from ${\rm b\overline{b}}$, and an additional
prompt component in the intermediate-mass range ($1.2<m_{\rm ee}<2.6$
GeV$/c^{2}$), where thermal radiation from the QGP is predicted [36, 99]. The
small systematic uncertainties of the results, limited by the statistical
precision of the data, show the potential of such an approach for future ALICE
dielectron studies with the upgraded LHC and ALICE detector, for which a
significant increase of the pointing detector resolution, as well as of the
size of the data sample, are expected [110]. In the quasi-real virtual-photon
region ($m_{\rm ee}<0.34$ GeV$/c^{2}$ and $1<p_{\rm T,ee}<5$ GeV$/c$), the
fraction of direct photons over inclusive photons is obtained from a fit of
the $m_{\rm ee}$ spectra above the $\pi^{0}$ mass. Combined with the inclusive
real-photon yield estimated from the inclusive dielectron yield at very low
$m_{\rm ee}$, the first direct-photon measurement in the 10% most central
Pb–Pb collisions at $\sqrt{s_{\mathrm{NN}}}=5.02$ TeV is reported. A model
[13] including prompt photons, as well as photons from the pre-equilibrium and
fluid-dynamical (thermal photons) phases can reproduce the results, while
being at the upper edge of the data uncertainties.

## 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; Bulgarian Ministry of Education and Science, within the National Roadmap for Research Infrastructures 2020-2027 (object CERN), Bulgaria; Ministry of Education of China (MOEC) , Ministry of Science & Technology of China (MSTC) and National Natural Science Foundation of China (NSFC), China; Ministry of Science and Education and Croatian Science Foundation, Croatia; Centro de Aplicaciones Tecnológicas y Desarrollo Nuclear (CEADEN), Cubaenergía, Cuba; Ministry of Education, Youth and Sports of the Czech Republic, Czech Republic; The Danish Council for Independent Research | Natural Sciences, the VILLUM FONDEN and Danish National Research Foundation (DNRF), Denmark; Helsinki Institute of Physics (HIP), Finland; Commissariat à l’Energie Atomique (CEA) and Institut National de Physique Nucléaire et de Physique des Particules (IN2P3) and Centre National de la Recherche Scientifique (CNRS), France; Bundesministerium für Bildung und Forschung (BMBF) and GSI Helmholtzzentrum für Schwerionenforschung GmbH, Germany; General Secretariat for Research and Technology, Ministry of Education, Research and Religions, Greece; National Research, Development and Innovation Office, Hungary; Department of Atomic Energy Government of India (DAE), Department of Science and Technology, Government of India (DST), University Grants Commission, Government of India (UGC) and Council of Scientific and Industrial Research (CSIR), India; National Research and Innovation Agency - BRIN, Indonesia; Istituto Nazionale di Fisica Nucleare (INFN), Italy; Japanese Ministry of Education, Culture, Sports, Science and Technology (MEXT) and Japan Society for the Promotion of Science (JSPS) KAKENHI, Japan; Consejo Nacional de Ciencia (CONACYT) y Tecnología, through Fondo de Cooperación Internacional en Ciencia y Tecnología (FONCICYT) and Dirección General de Asuntos del Personal Academico (DGAPA), Mexico; Nederlandse Organisatie voor Wetenschappelijk Onderzoek (NWO), Netherlands; The Research Council of Norway, Norway; Commission on Science and Technology for Sustainable Development in the South (COMSATS), Pakistan; Pontificia Universidad Católica del Perú, Peru; Ministry of Education and Science, National Science Centre and WUT ID-UB, Poland; Korea Institute of Science and Technology Information and National Research Foundation of Korea (NRF), Republic of Korea; Ministry of Education and Scientific Research, Institute of Atomic Physics, Ministry of Research and Innovation and Institute of Atomic Physics and University Politehnica of Bucharest, Romania; 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 (NSTDA) and National Science, Research and Innovation Fund (NSRF via PMU-B B05F650021), Thailand; Turkish Energy, Nuclear and Mineral Research Agency (TENMAK), Turkey; National Academy of Sciences of Ukraine, Ukraine; Science and Technology Facilities Council (STFC), United Kingdom; National Science Foundation of the United States of America (NSF) and United States Department of Energy, Office of Nuclear Physics (DOE NP), United States of America. In addition, individual groups or members have received support from: European Research Council, Strong 2020 - Horizon 2020 (grant nos. 950692, 824093), European Union; Academy of Finland (Center of Excellence in Quark Matter) (grant nos. 346327, 346328), Finland.

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##  Appendix A The ALICE Collaboration

S. Acharya 126, D. Adamová 86, G. Aglieri Rinella 33, M. Agnello 30, N.
Agrawal 51, Z. Ahammed 134, S. Ahmad16, S.U. Ahn 71, I. Ahuja 38, A. Akindinov
142, M. Al-Turany 97, D. Aleksandrov 142, B. Alessandro 56, H.M. Alfanda 6, R.
Alfaro Molina 67, B. Ali 16, A. Alici 26, N. Alizadehvandchali 115, A. Alkin
33, J. Alme 21, G. Alocco 52, T. Alt 64, A.R. Altamura 50, I. Altsybeev 95,
M.N. Anaam 6, C. Andrei 46, N. Andreou 114, A. Andronic 137, V. Anguelov 94,
F. Antinori 54, P. Antonioli 51, N. Apadula 74, L. Aphecetche 103, H.
Appelshäuser 64, C. Arata 73, S. Arcelli 26, M. Aresti 23, R. Arnaldi 56,
J.G.M.C.A. Arneiro 110, I.C. Arsene 20, M. Arslandok 139, A. Augustinus 33, R.
Averbeck 97, M.D. Azmi16, H. Baba123, A. Badalà 53, J. Bae 104, Y.W. Baek 41,
X. Bai 119, R. Bailhache 64, Y. Bailung 48, A. Balbino 30, A. Baldisseri 129,
B. Balis 2, D. Banerjee 4, Z. Banoo 91, R. Barbera 27, F. Barile 32, L.
Barioglio 95, M. Barlou78, B. Barman42, G.G. Barnaföldi 138, L.S. Barnby 85,
V. Barret 126, L. Barreto 110, C. Bartels 118, K. Barth 33, E. Bartsch 64, N.
Bastid 126, S. Basu 75, G. Batigne 103, D. Battistini 95, B. Batyunya 143, D.
Bauri47, J.L. Bazo Alba 101, I.G. Bearden 83, C. Beattie 139, P. Becht 97, D.
Behera 48, I. Belikov 128, A.D.C. Bell Hechavarria 137, F. Bellini 26, R.
Bellwied 115, S. Belokurova 142, Y.A.V. Beltran 45, G. Bencedi 138, S. Beole
25, Y. Berdnikov 142, A. Berdnikova 94, L. Bergmann 94, M.G. Besoiu 63, L.
Betev 33, P.P. Bhaduri 134, A. Bhasin 91, M.A. Bhat 4, B. Bhattacharjee 42, L.
Bianchi 25, N. Bianchi 49, J. Bielčík 36, J. Bielčíková 86, J. Biernat 107,
A.P. Bigot 128, A. Bilandzic 95, G. Biro 138, S. Biswas 4, N. Bize 103, J.T.
Blair 108, D. Blau 142, M.B. Blidaru 97, N. Bluhme39, C. Blume 64, G. Boca
22,55, F. Bock 87, T. Bodova 21, A. Bogdanov142, S. Boi 23, J. Bok 58, L.
Boldizsár 138, M. Bombara 38, P.M. Bond 33, G. Bonomi 133,55, H. Borel 129, A.
Borissov 142, A.G. Borquez Carcamo 94, H. Bossi 139, E. Botta 25, Y.E.M.
Bouziani 64, L. Bratrud 64, P. Braun-Munzinger 97, M. Bregant 110, M. Broz 36,
G.E. Bruno 96,32, M.D. Buckland 24, D. Budnikov 142, H. Buesching 64, S.
Bufalino 30, P. Buhler 102, N. Burmasov 142, Z. Buthelezi 68,122, A. Bylinkin
21, S.A. Bysiak107, M. Cai 6, H. Caines 139, A. Caliva 29, E. Calvo Villar
101, J.M.M. Camacho 109, P. Camerini 24, F.D.M. Canedo 110, M. Carabas 125,
A.A. Carballo 33, F. Carnesecchi 33, R. Caron 127, L.A.D. Carvalho 110, J.
Castillo Castellanos 129, F. Catalano 33,25, C. Ceballos Sanchez 143, I.
Chakaberia 74, P. Chakraborty 47, S. Chandra 134, S. Chapeland 33, M. Chartier
118, S. Chattopadhyay 134, S. Chattopadhyay 99, T.G. Chavez 45, T. Cheng 97,6,
C. Cheshkov 127, B. Cheynis 127, V. Chibante Barroso 33, D.D. Chinellato 111,
E.S. Chizzali I,95, J. Cho 58, S. Cho 58, P. Chochula 33, D. Choudhury42, P.
Christakoglou 84, C.H. Christensen 83, P. Christiansen 75, T. Chujo 124, M.
Ciacco 30, C. Cicalo 52, F. Cindolo 51, M.R. Ciupek97, G. ClaiII,51, F.
Colamaria 50, J.S. Colburn100, D. Colella 96,32, M. Colocci 26, M. Concas
III,33, G. Conesa Balbastre 73, Z. Conesa del Valle 130, G. Contin 24, J.G.
Contreras 36, M.L. Coquet 129, P. Cortese 132,56, M.R. Cosentino 112, F. Costa
33, S. Costanza 22,55, C. Cot 130, J. Crkovská 94, P. Crochet 126, R. Cruz-
Torres 74, P. Cui 6, A. Dainese 54, M.C. Danisch 94, A. Danu 63, P. Das 80, P.
Das 4, S. Das 4, A.R. Dash 137, S. Dash 47, R.M.H. David45, A. De Caro 29, G.
de Cataldo 50, J. de Cuveland39, A. De Falco 23, D. De Gruttola 29, N. De
Marco 56, C. De Martin 24, S. De Pasquale 29, R. Deb 133, R. Del Grande 95, L.
Dello Stritto 29, W. Deng 6, P. Dhankher 19, D. Di Bari 32, A. Di Mauro 33, B.
Diab 129, R.A. Diaz 143,7, T. Dietel 113, Y. Ding 6, J. Ditzel 64, R. Divià
33, D.U. Dixit 19, Ø. Djuvsland21, U. Dmitrieva 142, A. Dobrin 63, B. Dönigus
64, J.M. Dubinski 135, A. Dubla 97, S. Dudi 90, P. Dupieux 126, M. Durkac106,
N. Dzalaiova13, T.M. Eder 137, R.J. Ehlers 74, F. Eisenhut 64, R. Ejima92, D.
Elia 50, B. Erazmus 103, F. Ercolessi 26, B. Espagnon 130, G. Eulisse 33, D.
Evans 100, S. Evdokimov 142, L. Fabbietti 95, M. Faggin 28, J. Faivre 73, F.
Fan 6, W. Fan 74, A. Fantoni 49, M. Fasel 87, A. Feliciello 56, G. Feofilov
142, A. Fernández Téllez 45, L. Ferrandi 110, M.B. Ferrer 33, A. Ferrero 129,
C. Ferrero 56, A. Ferretti 25, V.J.G. Feuillard 94, V. Filova 36, D. Finogeev
142, F.M. Fionda 52, E. Flatland33, F. Flor 115, A.N. Flores 108, S. Foertsch
68, I. Fokin 94, S. Fokin 142, E. Fragiacomo 57, E. Frajna 138, U. Fuchs 33,
N. Funicello 29, C. Furget 73, A. Furs 142, T. Fusayasu 98, J.J. Gaardhøje 83,
M. Gagliardi 25, A.M. Gago 101, T. Gahlaut47, C.D. Galvan 109, D.R.
Gangadharan 115, P. Ganoti 78, C. Garabatos 97, A.T. Garcia 130, J.R.A. Garcia
45, E. Garcia-Solis 9, C. Gargiulo 33, P. Gasik 97, A. Gautam 117, M.B. Gay
Ducati 66, M. Germain 103, A. Ghimouz124, C. Ghosh134, M. Giacalone 51, G.
Gioachin 30, P. Giubellino 97,56, P. Giubilato 28, A.M.C. Glaenzer 129, P.
Glässel 94, E. Glimos 121, D.J.Q. Goh76, V. Gonzalez 136, P. Gordeev142, M.
Gorgon 2, K. Goswami 48, S. Gotovac34, V. Grabski 67, L.K. Graczykowski 135,
E. Grecka 86, A. Grelli 59, C. Grigoras 33, V. Grigoriev 142, S. Grigoryan
143,1, F. Grosa 33, J.F. Grosse-Oetringhaus 33, R. Grosso 97, D. Grund 36,
N.A. Grunwald94, G.G. Guardiano 111, R. Guernane 73, M. Guilbaud 103, K.
Gulbrandsen 83, T. Gündem 64, T. Gunji 123, W. Guo 6, A. Gupta 91, R. Gupta
91, R. Gupta 48, S.P. Guzman 45, K. Gwizdziel 135, L. Gyulai 138, C.
Hadjidakis 130, F.U. Haider 91, S. Haidlova 36, H. Hamagaki 76, A. Hamdi 74,
Y. Han 140, B.G. Hanley 136, R. Hannigan 108, J. Hansen 75, M.R. Haque 135,
J.W. Harris 139, A. Harton 9, H. Hassan 116, D. Hatzifotiadou 51, P. Hauer 43,
L.B. Havener 139, S.T. Heckel 95, E. Hellbär 97, H. Helstrup 35, M. Hemmer 64,
T. Herman 36, G. Herrera Corral 8, F. Herrmann137, S. Herrmann 127, K.F.
Hetland 35, B. Heybeck 64, H. Hillemanns 33, B. Hippolyte 128, F.W. Hoffmann
70, B. Hofman 59, G.H. Hong 140, M. Horst 95, A. Horzyk2, Y. Hou 6, P. Hristov
33, C. Hughes 121, P. Huhn64, L.M. Huhta 116, T.J. Humanic 88, A. Hutson 115,
D. Hutter 39, R. Ilkaev142, H. Ilyas 14, M. Inaba 124, G.M. Innocenti 33, M.
Ippolitov 142, A. Isakov 84,86, T. Isidori 117, M.S. Islam 99, M. Ivanov 97,
M. Ivanov13, V. Ivanov 142, K.E. Iversen 75, M. Jablonski 2, B. Jacak 74, N.
Jacazio 26, P.M. Jacobs 74, S. Jadlovska106, J. Jadlovsky106, S. Jaelani 82,
C. Jahnke 110, M.J. Jakubowska 135, M.A. Janik 135, T. Janson70, S. Ji 17, S.
Jia 10, A.A.P. Jimenez 65, F. Jonas 87, D.M. Jones 118, J.M. Jowett 33,97, J.
Jung 64, M. Jung 64, A. Junique 33, A. Jusko 100, M.J. Kabus 33,135, J.
Kaewjai105, P. Kalinak 60, A.S. Kalteyer 97, A. Kalweit 33, V. Kaplin 142, A.
Karasu Uysal 72, D. Karatovic 89, O. Karavichev 142, T. Karavicheva 142, P.
Karczmarczyk 135, E. Karpechev 142, U. Kebschull 70, R. Keidel 141, D.L.D.
Keijdener59, M. Keil 33, B. Ketzer 43, S.S. Khade 48, A.M. Khan 119, S. Khan
16, A. Khanzadeev 142, Y. Kharlov 142, A. Khatun 117, A. Khuntia 36, B. Kileng
35, B. Kim 104, C. Kim 17, D.J. Kim 116, E.J. Kim 69, J. Kim 140, J.S. Kim 41,
J. Kim 58, J. Kim 69, M. Kim 19, S. Kim 18, T. Kim 140, K. Kimura 92, S.
Kirsch 64, I. Kisel 39, S. Kiselev 142, A. Kisiel 135, J.P. Kitowski 2, J.L.
Klay 5, J. Klein 33, S. Klein 74, C. Klein-Bösing 137, M. Kleiner 64, T.
Klemenz 95, A. Kluge 33, A.G. Knospe 115, C. Kobdaj 105, T. Kollegger97, A.
Kondratyev 143, N. Kondratyeva 142, E. Kondratyuk 142, J. Konig 64, S.A.
Konigstorfer 95, P.J. Konopka 33, G. Kornakov 135, M. Korwieser 95, S.D.
Koryciak 2, A. Kotliarov 86, V. Kovalenko 142, M. Kowalski 107, V. Kozhuharov
37, I. Králik 60, A. Kravčáková 38, L. Krcal 33,39, M. Krivda 100,60, F.
Krizek 86, K. Krizkova Gajdosova 33, M. Kroesen 94, M. Krüger 64, D.M. Krupova
36, E. Kryshen 142, V. Kučera 58, C. Kuhn 128, P.G. Kuijer 84, T. Kumaoka124,
D. Kumar134, L. Kumar 90, N. Kumar90, S. Kumar 32, S. Kundu 33, P. Kurashvili
79, A. Kurepin 142, A.B. Kurepin 142, A. Kuryakin 142, S. Kushpil 86, V.
Kuskov142, M.J. Kweon 58, Y. Kwon 140, S.L. La Pointe 39, P. La Rocca 27, A.
Lakrathok105, M. Lamanna 33, R. Langoy 120, P. Larionov 33, E. Laudi 33, L.
Lautner 33,95, R. Lavicka 102, R. Lea 133,55, H. Lee 104, I. Legrand 46, G.
Legras 137, J. Lehrbach 39, T.M. Lelek2, R.C. Lemmon 85, I. León Monzón 109,
M.M. Lesch 95, E.D. Lesser 19, P. Lévai 138, X. Li10, J. Lien 120, R. Lietava
100, I. Likmeta 115, B. Lim 25, S.H. Lim 17, V. Lindenstruth 39, A. Lindner46,
C. Lippmann 97, D.H. Liu 6, J. Liu 118, G.S.S. Liveraro 111, I.M. Lofnes 21,
C. Loizides 87, S. Lokos 107, J. Lomker 59, P. Loncar 34, X. Lopez 126, E.
López Torres 7, P. Lu 97,119, F.V. Lugo 67, J.R. Luhder 137, M. Lunardon 28,
G. Luparello 57, Y.G. Ma 40, M. Mager 33, A. Maire 128, M.V. Makariev 37, M.
Malaev 142, G. Malfattore 26, N.M. Malik 91, Q.W. Malik20, S.K. Malik 91, L.
Malinina VI,143, D. Mallick 130,80, N. Mallick 48, G. Mandaglio 31,53, S.K.
Mandal 79, V. Manko 142, F. Manso 126, V. Manzari 50, Y. Mao 6, R.W. Marcjan
2, G.V. Margagliotti 24, A. Margotti 51, A. Marín 97, C. Markert 108, P.
Martinengo 33, M.I. Martínez 45, G. Martínez García 103, M.P.P. Martins 110,
S. Masciocchi 97, M. Masera 25, A. Masoni 52, L. Massacrier 130, O. Massen 59,
A. Mastroserio 131,50, O. Matonoha 75, S. Mattiazzo 28, A. Matyja 107, C.
Mayer 107, A.L. Mazuecos 33, F. Mazzaschi 25, M. Mazzilli 33, J.E. Mdhluli
122, Y. Melikyan 44, A. Menchaca-Rocha 67, J.E.M. Mendez 65, E. Meninno
102,29, A.S. Menon 115, M. Meres 13, S. Mhlanga113,68, Y. Miake124, L.
Micheletti 33, D.L. Mihaylov 95, K. Mikhaylov 143,142, A.N. Mishra 138, D.
Miśkowiec 97, A. Modak 4, B. Mohanty80, M. Mohisin KhanIV,16, M.A. Molander
44, S. Monira 135, C. Mordasini 116, D.A. Moreira De Godoy 137, I. Morozov
142, A. Morsch 33, T. Mrnjavac 33, V. Muccifora 49, S. Muhuri 134, J.D.
Mulligan 74, A. Mulliri23, M.G. Munhoz 110, R.H. Munzer 64, H. Murakami 123,
S. Murray 113, L. Musa 33, J. Musinsky 60, J.W. Myrcha 135, B. Naik 122, A.I.
Nambrath 19, B.K. Nandi 47, R. Nania 51, E. Nappi 50, A.F. Nassirpour 18, A.
Nath 94, C. Nattrass 121, M.N. Naydenov 37, A. Neagu20, A. Negru125, E.
Nekrasova142, L. Nellen 65, R. Nepeivoda 75, S. Nese 20, G. Neskovic 39, N.
Nicassio 50, B.S. Nielsen 83, E.G. Nielsen 83, S. Nikolaev 142, S. Nikulin
142, V. Nikulin 142, F. Noferini 51, S. Noh 12, P. Nomokonov 143, J. Norman
118, N. Novitzky 87, P. Nowakowski 135, A. Nyanin 142, J. Nystrand 21, M.
Ogino 76, S. Oh 18, A. Ohlson 75, V.A. Okorokov 142, J. Oleniacz 135, A.C.
Oliveira Da Silva 121, A. Onnerstad 116, C. Oppedisano 56, A. Ortiz Velasquez
65, J. Otwinowski 107, M. Oya92, K. Oyama 76, Y. Pachmayer 94, S. Padhan 47,
D. Pagano 133,55, G. Paić 65, A. Palasciano 50, S. Panebianco 129, H. Park
124, H. Park 104, J. Park 58, J.E. Parkkila 33, Y. Patley 47, R.N. Patra91, B.
Paul 23, H. Pei 6, T. Peitzmann 59, X. Peng 11, M. Pennisi 25, S. Perciballi
25, D. Peresunko 142, G.M. Perez 7, Y. Pestov142, V. Petrov 142, M. Petrovici
46, R.P. Pezzi 103,66, S. Piano 57, M. Pikna 13, P. Pillot 103, O. Pinazza
51,33, L. Pinsky115, C. Pinto 95, S. Pisano 49, M. Płoskoń 74, M. Planinic89,
F. Pliquett64, M.G. Poghosyan 87, B. Polichtchouk 142, S. Politano 30, N.
Poljak 89, A. Pop 46, S. Porteboeuf-Houssais 126, V. Pozdniakov 143, I.Y.
Pozos 45, K.K. Pradhan 48, S.K. Prasad 4, S. Prasad 48, R. Preghenella 51, F.
Prino 56, C.A. Pruneau 136, I. Pshenichnov 142, M. Puccio 33, S. Pucillo 25,
Z. Pugelova106, S. Qiu 84, L. Quaglia 25, S. Ragoni 15, A. Rai 139, A.
Rakotozafindrabe 129, L. Ramello 132,56, F. Rami 128, S.A.R. Ramirez 45, T.A.
Rancien73, M. Rasa 27, S.S. Räsänen 44, R. Rath 51, M.P. Rauch 21, I.
Ravasenga 84, K.F. Read 87,121, C. Reckziegel 112, A.R. Redelbach 39, K.
Redlich V,79, C.A. Reetz 97, A. Rehman21, F. Reidt 33, H.A. Reme-Ness 35, Z.
Rescakova38, K. Reygers 94, A. Riabov 142, V. Riabov 142, R. Ricci 29, M.
Richter 20, A.A. Riedel 95, W. Riegler 33, A.G. Riffero 25, C. Ristea 63, M.V.
Rodriguez 33, M. Rodríguez Cahuantzi 45, K. Røed 20, R. Rogalev 142, E.
Rogochaya 143, T.S. Rogoschinski 64, D. Rohr 33, D. Röhrich 21, P.F. Rojas45,
S. Rojas Torres 36, P.S. Rokita 135, G. Romanenko 26, F. Ronchetti 49, A.
Rosano 31,53, E.D. Rosas65, K. Roslon 135, A. Rossi 54, A. Roy 48, S. Roy 47,
N. Rubini 26, D. Ruggiano 135, R. Rui 24, P.G. Russek 2, R. Russo 84, A.
Rustamov 81, E. Ryabinkin 142, Y. Ryabov 142, A. Rybicki 107, H. Rytkonen 116,
J. Ryu 17, W. Rzesa 135, O.A.M. Saarimaki 44, S. Sadhu 32, S. Sadovsky 142, J.
Saetre 21, K. Šafařík 36, P. Saha42, S.K. Saha 4, S. Saha 80, B. Sahoo 47, B.
Sahoo 48, R. Sahoo 48, S. Sahoo61, D. Sahu 48, P.K. Sahu 61, J. Saini 134, K.
Sajdakova38, S. Sakai 124, M.P. Salvan 97, S. Sambyal 91, D. Samitz 102, I.
Sanna 33,95, T.B. Saramela110, P. Sarma 42, V. Sarritzu 23, V.M. Sarti 95,
M.H.P. Sas 33, S. Sawan80, J. Schambach 87, H.S. Scheid 64, C. Schiaua 46, R.
Schicker 94, F. Schlepper 94, A. Schmah97, C. Schmidt 97, H.R. Schmidt93, M.O.
Schmidt 33, M. Schmidt93, N.V. Schmidt 87, A.R. Schmier 121, R. Schotter 128,
A. Schröter 39, J. Schukraft 33, K. Schweda 97, G. Scioli 26, E. Scomparin 56,
J.E. Seger 15, Y. Sekiguchi123, D. Sekihata 123, M. Selina 84, I. Selyuzhenkov
97, S. Senyukov 128, J.J. Seo 94,58, D. Serebryakov 142, L. Šerkšnytė 95, A.
Sevcenco 63, T.J. Shaba 68, A. Shabetai 103, R. Shahoyan33, A. Shangaraev 142,
A. Sharma90, B. Sharma 91, D. Sharma 47, H. Sharma 54, M. Sharma 91, S. Sharma
76, S. Sharma 91, U. Sharma 91, A. Shatat 130, O. Sheibani115, K. Shigaki 92,
M. Shimomura77, J. Shin12, S. Shirinkin 142, Q. Shou 40, Y. Sibiriak 142, S.
Siddhanta 52, T. Siemiarczuk 79, T.F. Silva 110, D. Silvermyr 75, T.
Simantathammakul105, R. Simeonov 37, B. Singh91, B. Singh 95, K. Singh 48, R.
Singh 80, R. Singh 91, R. Singh 48, S. Singh 16, V.K. Singh 134, V. Singhal
134, T. Sinha 99, B. Sitar 13, M. Sitta 132,56, T.B. Skaali20, G. Skorodumovs
94, M. Slupecki 44, N. Smirnov 139, R.J.M. Snellings 59, E.H. Solheim 20, J.
Song 17, C. Sonnabend 33,97, F. Soramel 28, A.B. Soto-hernandez 88, R.
Spijkers 84, I. Sputowska 107, J. Staa 75, J. Stachel 94, I. Stan 63, P.J.
Steffanic 121, S.F. Stiefelmaier 94, D. Stocco 103, I. Storehaug 20, P.
Stratmann 137, S. Strazzi 26, A. Sturniolo 31,53, C.P. Stylianidis84, A.A.P.
Suaide 110, C. Suire 130, M. Sukhanov 142, M. Suljic 33, R. Sultanov 142, V.
Sumberia 91, S. Sumowidagdo 82, S. Swain61, I. Szarka 13, M. Szymkowski 135,
S.F. Taghavi 95, G. Taillepied 97, J. Takahashi 111, G.J. Tambave 80, S. Tang
6, Z. Tang 119, J.D. Tapia Takaki 117, N. Tapus125, L.A. Tarasovicova 137,
M.G. Tarzila 46, G.F. Tassielli 32, A. Tauro 33, G. Tejeda Muñoz 45, A.
Telesca 33, L. Terlizzi 25, C. Terrevoli 115, S. Thakur 4, D. Thomas 108, A.
Tikhonov 142, N. Tiltmann 33,137, A.R. Timmins 115, M. Tkacik106, T. Tkacik
106, A. Toia 64, R. Tokumoto92, K. Tomohiro92, N. Topilskaya 142, M. Toppi 49,
T. Tork 130, P.V. Torres65, V.V. Torres 103, A.G. Torres Ramos 32, A. Trifiró
31,53, A.S. Triolo 33,31,53, S. Tripathy 51, T. Tripathy 47, S. Trogolo 33, V.
Trubnikov 3, W.H. Trzaska 116, T.P. Trzcinski 135, A. Tumkin 142, R. Turrisi
54, T.S. Tveter 20, K. Ullaland 21, B. Ulukutlu 95, A. Uras 127, G.L. Usai 23,
M. Vala38, N. Valle 22, L.V.R. van Doremalen59, M. van Leeuwen 84, C.A. van
Veen 94, R.J.G. van Weelden 84, P. Vande Vyvre 33, D. Varga 138, Z. Varga 138,
M. Vasileiou 78, A. Vasiliev 142, O. Vázquez Doce 49, O. Vazquez Rueda 115, V.
Vechernin 142, E. Vercellin 25, S. Vergara Limón45, R. Verma47, L. Vermunt 97,
R. Vértesi 138, M. Verweij 59, L. Vickovic34, Z. Vilakazi122, O. Villalobos
Baillie 100, A. Villani 24, A. Vinogradov 142, T. Virgili 29, M.M.O. Virta
116, V. Vislavicius75, A. Vodopyanov 143, B. Volkel 33, M.A. Völkl 94, K.
Voloshin142, S.A. Voloshin 136, G. Volpe 32, B. von Haller 33, I. Vorobyev 95,
N. Vozniuk 142, J. Vrláková 38, J. Wan40, C. Wang 40, D. Wang40, Y. Wang 40,
Y. Wang 6, A. Wegrzynek 33, F.T. Weiglhofer39, S.C. Wenzel 33, J.P. Wessels
137, S.L. Weyhmiller 139, J. Wiechula 64, J. Wikne 20, G. Wilk 79, J.
Wilkinson 97, G.A. Willems 137, B. Windelband 94, M. Winn 129, J.R. Wright
108, W. Wu40, Y. Wu 119, R. Xu 6, A. Yadav 43, A.K. Yadav 134, S. Yalcin 72,
Y. Yamaguchi 92, S. Yang21, S. Yano 92, Z. Yin 6, I.-K. Yoo 17, J.H. Yoon 58,
H. Yu12, S. Yuan21, A. Yuncu 94, V. Zaccolo 24, C. Zampolli 33, F. Zanone 94,
N. Zardoshti 33, A. Zarochentsev 142, P. Závada 62, N. Zaviyalov142, M. Zhalov
142, B. Zhang 6, C. Zhang 129, L. Zhang 40, S. Zhang 40, X. Zhang 6, Y.
Zhang119, Z. Zhang 6, M. Zhao 10, V. Zherebchevskii 142, Y. Zhi10, D. Zhou 6,
Y. Zhou 83, J. Zhu 97,6, Y. Zhu6, S.C. Zugravel 56, N. Zurlo 133,55

## Affiliation Notes

I Also at: Max-Planck-Institut für Physik, Munich, Germany
II Also at: Italian National Agency for New Technologies, Energy and
Sustainable Economic Development (ENEA), Bologna, Italy
III Also at: Dipartimento DET del Politecnico di Torino, Turin, Italy
IV Also at: Department of Applied Physics, Aligarh Muslim University, Aligarh,
India
V Also at: Institute of Theoretical Physics, University of Wroclaw, Poland
VI Also at: An institution covered by a cooperation agreement with CERN

## Collaboration Institutes

1 A.I. Alikhanyan National Science Laboratory (Yerevan Physics Institute)
Foundation, Yerevan, Armenia
2 AGH University of Krakow, Cracow, Poland
3 Bogolyubov Institute for Theoretical Physics, National Academy of Sciences
of Ukraine, Kiev, Ukraine
4 Bose Institute, Department of Physics and Centre for Astroparticle Physics
and Space Science (CAPSS), Kolkata, India
5 California Polytechnic State University, San Luis Obispo, California, United
States
6 Central China Normal University, Wuhan, China
7 Centro de Aplicaciones Tecnológicas y Desarrollo Nuclear (CEADEN), Havana,
Cuba
8 Centro de Investigación y de Estudios Avanzados (CINVESTAV), Mexico City and
Mérida, Mexico
9 Chicago State University, Chicago, Illinois, United States
10 China Institute of Atomic Energy, Beijing, China
11 China University of Geosciences, Wuhan, China
12 Chungbuk National University, Cheongju, Republic of Korea
13 Comenius University Bratislava, Faculty of Mathematics, Physics and
Informatics, Bratislava, Slovak Republic
14 COMSATS University Islamabad, Islamabad, Pakistan
15 Creighton University, Omaha, Nebraska, United States
16 Department of Physics, Aligarh Muslim University, Aligarh, India
17 Department of Physics, Pusan National University, Pusan, Republic of Korea
18 Department of Physics, Sejong University, Seoul, Republic of Korea
19 Department of Physics, University of California, Berkeley, California,
United States
20 Department of Physics, University of Oslo, Oslo, Norway
21 Department of Physics and Technology, University of Bergen, Bergen, Norway
22 Dipartimento di Fisica, Università di Pavia, Pavia, Italy