2018 117 9 May Direct photon elliptic flow in Pb–Pb ALICE
Collaboration††thanks: See Appendix A for the list of collaboration members
ALICE Collaboration

The elliptic flow of inclusive and direct photons was measured at mid-rapidity
in two centrality classes 0–20% and 20–40% in Pb–Pb collisions at
$\sqrt{s_{{}_{\mathrm{NN}}}}=2.76$ TeV by ALICE. Photons were detected with
the highly segmented electromagnetic calorimeter PHOS and via conversions in
the detector material with the $e^{+}e^{-}$ pairs reconstructed in the central
tracking system. The results of the two methods were combined and the direct-
photon elliptic flow was extracted in the transverse momentum range
$0.9<p_{\mathrm{T}}<6.2~{}\mathrm{GeV}/c$. A comparison to RHIC data shows a
similar magnitude of the measured direct-photon elliptic flow. Hydrodynamic
and transport model calculations are systematically lower than the data, but
are found to be compatible.

##  1 Introduction

The theory of the strong interaction, Quantum ChromoDynamics (QCD), predicts a
transition from ordinary hadronic matter to a new state where quarks and
gluons are no longer confined to hadrons [1, 2]. Lattice calculations predict
a chiral and deconfinement crossover transitions over the temperature range
145–163 MeV [1, 2], which is accessible in collisions of ultrarelativistic
heavy ions. The creation and study of the properties of this hot strongly
interacting matter – Quark-Gluon Plasma (QGP) – are the main objectives of the
ALICE experiment.

The hot strongly interacting matter, created in nucleus–nucleus collisions,
expands, cools and finally transforms to ordinary hadronic matter. To
experimentally study the quark matter properties, several observables were
proposed. Here, we concentrate on studying the development of collective flow
using direct photons. Direct photons are the photons not originating from
hadronic decays but produced in electromagnetic interactions. Unlike hadrons,
direct photons are produced at all stages of the collision. Incoming nuclei
passing through each other produce direct photons in scatterings of their
partonic constituents. In addition, (thermal) photons are emitted in the
deconfined quark-gluon plasma and hadronic matter, characterized by the
thermal distributions of partons and hadrons, respectively. Since the mean
free path of a photon in hot matter is much larger than the typical sizes of
the created fireball [3], direct photons escape the collision zone unaffected,
delivering direct information on the conditions at the production time and on
the development of collective flow.

The observations of a strong azimuthal asymmetry of particle production over a
wide rapidity range in nucleus-nucleus collisions was one of the key results
obtained at RHIC [4, 5, 6, 7] and LHC [8, 9, 10, 11, 12] energies. It was
interpreted as a consequence of collective expansion – collective flow – of
the matter having an initial spatial asymmetry, which is more prominent in
collisions with non-zero impact parameter. To quantify the collective flow,
the azimuthal distributions of final state particles are expanded in the
series $1+2\sum v_{n}\cos[n(\varphi-\Psi_{RP})]$ [13], depending on the
difference between the particle azimuthal angle $\varphi$ and the reaction
plane orientation $\Psi_{RP}$, defined by the impact parameter and beam axis.
At mid-rapidity the second harmonic $v_{2}$ (elliptic flow) reflects the
expansion of the almond-like shape of the hot matter created by the mutual
penetration of the colliding nuclei. Higher harmonics $v_{3}$, $v_{4}$, etc.
are sensitive to fluctuations of the initial shape of the created hot matter
and are typically much smaller than $v_{2}$, except for central collisions,
where $v_{2}$ decreases due to a more symmetric geometry. Collective flow is
sensitive to the equation of state of hot matter and the amount of shear
viscosity. The initial spatial asymmetry of the expanding fireball diminishes
with time, for any equation of state. For strongly interacting matter this
asymmetry translates into an azimuthal anisotropy in momentum space, while for
free streaming weakly interacting matter there is no final particle azimuthal
anisotropy.

Hadrons provide the possibility to test with high precision the flow pattern
of the latest stage of the collision, when the hot matter decouples into final
particles. Complementary to them, direct photons provide the possibility to
investigate the development of flow during the evolution of hot matter. First
calculations predicted that the photon emission rate from the hot quark-gluon
or hadron matter increases with temperature as $\propto
T^{2}\,\exp(-E_{\gamma}/T)$ [14], where $E_{\gamma}$ is the photon energy and
$T$ is the temperature of the matter. Then, the low transverse momentum
($p_{\mathrm{T}}\lesssim 4$ GeV$/c$) part is controlled by the cooler latest
stage, and the high $p_{\mathrm{T}}$ part ($p_{\mathrm{T}}\gtrsim 5$ GeV$/c$)
of the spectrum by the hot initial state. However, detailed calculations which
include the full hydrodynamic evolution (see e.g. [15]) show that
contributions of all stages are comparable for all $p_{\mathrm{T}}$ regions as
a higher temperature of the initial stage is compensated by a larger space-
time volume and stronger radial flow of the later stages. Since the observed
direct-photon flow is the convolution of all stages of the collision,
including the contribution from the initial stage when the flow pattern has
not yet developed, the calculations predict much smaller azimuthal anisotropy
for thermal photons than for hadrons [16, 17].

The first measurement of a direct-photon spectrum in relativistic nucleus-
nucleus collisions was presented by the WA98 collaboration [18], and later
also by the PHENIX Collaboration [19, 20, 21, 22], and by the ALICE
Collaboration [23]. The first measurement of elliptic flow of direct photons
in Au–Au collisions at $\sqrt{s_{{}_{\mathrm{NN}}}}=200$ GeV was performed by
the PHENIX Collaboration [24]. Surprisingly, it was found to be close to the
flow of hadrons [25]. Recent PHENIX results, presenting more precise
measurements of elliptic and triangular flow extended to lower
$p_{\mathrm{T}}$ [26], confirmed this early result. The discrepancy between
experimental results and theory predictions triggered a set of theoretical
studies, which can be split into two classes. The main idea in the first class
of models [27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43,
44] is to increase the emission of direct photons from the later stages of the
collision and/or suppress emission of the initial stage. In the second class
of models [45, 46, 47], a new azimuthally asymmetric source of direct photons
is considered like jet-matter interactions or synchrotron radiation in the
field of colliding nuclei. These theoretical efforts considerably reduce the
discrepancy, but consistent reproduction of both the direct-photon spectra and
flow is still missing. The measurement of direct-photon flow at higher
collision energy is important as an independent confirmation of the results at
lower energy, and could also allow to disentangle between different
contributions.

In this paper, we present the first measurement of the direct-photon flow in
Pb–Pb collisions at the LHC and compare our findings to RHIC results and to
predictions of hydrodynamic as well as transport models.

##  2 Detector setup

The direct photon flow is based on the measurement of the elliptic flow of
inclusive photons and the estimation of the contribution of decay photons
using the available hadron flow results. Photons are reconstructed via two
independent methods: the Photon Conversion Method (PCM) and with the
electromagnetic calorimeter PHOS.

In the conversion method, the electron and positron tracks from photon
conversions are measured with the Inner Tracking System (ITS) and/or the Time
Projection Chamber (TPC). The ITS [48] consists of two layers of Silicon Pixel
Detectors (SPD) positioned at radial distances of 3.9 cm and 7.6 cm, two
layers of Silicon Drift Detectors (SDD) at 15.0 cm and 23.9 cm, and two layers
of Silicon Strip Detectors (SSD) at 38.0 cm and 43.0 cm. The two innermost
layers cover a pseudorapidity range of $|\eta|<2$ and $|\eta|<1.4$,
respectively. The TPC [49] is a large (85 m3) cylindrical drift detector
filled with a Ne-CO2-N2 (85.7/9.5/4.8%) gas mixture. It covers the
pseudorapidity range $|\eta|<0.9$ over the full azimuthal angle with a maximum
track length of 159 reconstructed space points. With the solenoidal magnetic
field of $B=0.5~{}\mathrm{T}$, electron and positron tracks can be
reconstructed down to $p_{\mathrm{T}}\approx 50~{}\mathrm{MeV}/c$. The TPC
provides particle identification via the measurement of the specific energy
loss (d$E$/d$x$) with a resolution of 5.2% in pp collisions and 6.5% in
central Pb-Pb collisions [50]. The ITS and the TPC were aligned with respect
to each other to the level of less than $100~{}\mathrm{\mathit{\mu}m}$ using
cosmic-ray and pp collision data [51]. Particle identification is also
provided by the Time-of-Flight (TOF) detector [52] located at a radial
distance of $370<r<399~{}\mathrm{cm}$. This detector consists of Multigap
Resistive Plate Chambers (MRPC) and provides timing information with an
intrinsic resolution of 50 ps.

PHOS [53] is an electromagnetic calorimeter which consists of three modules
installed at a radial distance of 4.6 m from the interaction point. It
subtends $260^{\circ}<\varphi<320^{\circ}$ in azimuth and $|\eta|<0.12$ in
pseudorapidity. Each module consists of 3584 detector cells arranged in a
matrix of $64\times 56$ lead tungstate crystals each of size $2.2\times
2.2\times 18$ cm3. The signal from each cell is measured by an avalanche
photodiode (APD) associated with a low-noise charge-sensitive preamplifier. To
increase the light yield, reduce electronic noise, and improve energy
resolution, the APDs and preamplifiers are cooled to a temperature of
$-25~{}^{\circ}$C. The resulting energy resolution is
$\sigma_{E}/E=(1.8\%/E)\oplus(3.3\%/\sqrt{E})\oplus 1.1$%, where $E$ is in
units of GeV. The energy deposition in each PHOS cell is calibrated in pp
collisions by aligning the $\pi^{0}$ peak position in the two-photon invariant
mass distribution.

For the minimum bias trigger in the Pb–Pb run and event plane orientation
calculation, two scintillator array detectors (V0–A and V0–C) [54] are used,
which subtend $2.8<\eta<5.1$ and $-3.7<\eta<-1.7$, respectively. Each of the
V0 arrays consists of 32 channels and is segmented in four rings in the radial
direction, and each ring is divided into eight sectors in the azimuthal
direction. The sum of the signal amplitudes of the V0–A and V0–C detectors
serves as a measure of centrality in the Pb–Pb collisions.

##  3 Data analysis

This analysis is based on data recorded by the ALICE experiment in the first
LHC heavy-ion run in the fall of 2010. The detector readout was triggered by
the minimum bias interaction trigger based on signals from the V0–A, V0–C, and
SPD detectors. The efficiency for triggering on a Pb–Pb hadronic interaction
ranged between 98.4% and 99.7%. The events are divided into the central and
semi-central centrality classes 0–20% and 20–40%, respectively, according to
the V0–A and V0–C summed amplitudes [55]. To ensure a uniform track acceptance
in pseudorapidity $\eta$, only events with a primary vertex within $\pm
10~{}\mathrm{cm}$ from the nominal interaction point along the beam line
($z$-direction) are used. After offline event selection, $13.6\times 10^{6}$
events are available for the PCM analysis and $18.8\times 10^{6}$ events for
the PHOS analysis.

The direct-photon elliptic flow is extracted on a statistical basis by
subtracting the elliptic flow of photons from hadron decays from the inclusive
photon elliptic flow. We assume that in each bin of the photon transverse
momentum the measured inclusive photon flow can be decomposed as

$v_{2}^{{\rm\gamma,inc}}=\frac{N_{{\rm\gamma,dir}}}{N_{{\rm\gamma,inc}}}v_{2}^{{\rm\gamma,dir}}+\frac{N_{{\rm\gamma,dec}}}{N_{{\rm\gamma,inc}}}v_{2}^{{\rm\gamma,dec}},$
(1)

where $N_{{\rm\gamma,inc}}=N_{{\rm\gamma,dir}}+N_{{\rm\gamma,dec}}$ is the
inclusive photon yield which can be decomposed into the contributions of
direct ($N_{{\rm\gamma,dir}}$) and decay ($N_{{\rm\gamma,dec}}$) photons. The
$v_{2}^{{\rm\gamma,inc}}$, $v_{2}^{{\rm\gamma,dir}}$ and
$v_{2}^{{\rm\gamma,dec}}$ are the corresponding photon flows. It is convenient
to express direct-photon flow in terms of the ratio
$R_{\rm\gamma}=N_{{\rm\gamma,inc}}/N_{{\rm\gamma,dec}}$, the inclusive photon
flow $v_{2}^{{\rm\gamma,inc}}$, and the decay photon flow
$v_{2}^{{\rm\gamma,dec}}$:

$v_{2}^{{\rm\gamma,dir}}=\frac{v_{2}^{{\rm\gamma,inc}}R_{\rm\gamma}-v_{2}^{{\rm\gamma,dec}}}{R_{\rm\gamma}-1}.$
(2)

The ratio $R_{\rm\gamma}$ was measured in the same dataset in [23], whereas
$v_{2}^{{\rm\gamma,dec}}$ is calculated with a simulation of photons from
decays which is also known as cocktail simulation. The PCM and PHOS
measurements of inclusive photon flow are performed independently. They are
then combined and used with the combined ratio $R_{\rm\gamma}$ as well as the
calculated decay photon flow.

The photon elliptic flow $v_{2}$ is calculated with the Scalar Product (SP)
method, which is a two-particle correlation method [56], using a
pseudorapidity gap of $|\Delta\eta|>0.9$ between the photon and the reference
flow particles. The applied gap reduces correlations not related to the event
plane $\Psi_{n}$, such as the ones due to resonance decays and jets, known as
non–flow effects. The SP method uses the $Q$-vector, computed from a set of
reference flow particles (RFP) defined as:

$\vec{Q}_{n}=\sum_{i\in\mathrm{RFP}}w_{i}e^{in\varphi_{i}},$ (3)

where $\varphi_{i}$ is the azimuthal angle of the $i$-th RFP, $n$ is the order
of the harmonic and $w_{i}$ is a weight applied for every RFP. The RFPs are
taken from the V0–A and V0–C detectors. Since these detectors do not provide
tracking information, we sum over the V0–A/V0–C cells, while the amplitudes of
the signal from each cell, which are proportional to the number of particles
that cause a hit, are used as a weight $w_{i}$. The non-uniformity of the
detector azimuthal efficiency is taken into account by applying the inverse of
the event-averaged signal as a weight for each of the V0 segments, together
with a recentering procedure [50, 57]. More specifically, the elliptic flow
$v_{2}$ is calculated using the unit flow vector
$\vec{\mathrm{u}}_{2}=e^{i2\varphi}$ built from reconstructed photons

$v_{2}=\sqrt{\frac{\big{\langle}\big{\langle}\vec{\mathrm{u}}_{2}\cdot\frac{\vec{Q}_{2}^{\mathrm{A*}}}{M_{\mathrm{A}}}\big{\rangle}\big{\rangle}\big{\langle}\big{\langle}\vec{\mathrm{u}}_{2}\cdot\frac{\vec{Q}_{2}^{\mathrm{C*}}}{M_{\mathrm{C}}}\big{\rangle}\big{\rangle}}{\big{\langle}\frac{\vec{Q}_{2}^{\mathrm{A}}}{M_{\mathrm{A}}}\cdot\frac{\vec{Q}_{2}^{\mathrm{C*}}}{M_{\mathrm{C}}}\big{\rangle}}},$
(4)

where the two pairs of brackets in the numerator indicate an average over all
photons and over all events; $M_{\mathrm{A}}$ and $M_{\mathrm{C}}$ are the
estimates of multiplicity from the V0–A and V0–C detectors, respectively; and
$\vec{Q}_{2}^{\mathrm{A*}}$, $\vec{Q}_{2}^{\mathrm{C*}}$ are the complex
conjugates of the flow vector calculated in sub-event A and C, respectively.

In the PCM analysis, photons converting into e+e- pairs are reconstructed with
an algorithm which searches for displaced vertices with two oppositely charged
daughter tracks. Only good quality TPC tracks with a transverse momentum above
50 MeV/$c$ and a pseudorapidity of $|\eta|<0.9$ are considered. The vertex
finding algorithm uses the Kalman filter technique for the decay/conversion
point and four-momentum determination of the neutral parent particle ($V^{0}$)
[58]. Further selection is performed on the level of the reconstructed
$V^{0}$. Only $V^{0}$s with a conversion points at radii between
$5<R<180~{}\mathrm{cm}$ are accepted such that the $\pi^{0}$ and $\eta$-meson
Dalitz decays are rejected and to ensure a good coverage by the tracking
detectors of the conversion daughters. To identify an e+e- pair, the specific
energy loss (d$E$/d$x$) in the TPC [50] of both daughters is used. The
transverse momentum component $q_{T}$ of the electron momentum, $p_{e}$, with
respect to the $V^{0}$ momentum-vector is restricted to be
$q_{T}<0.05\sqrt{1-\left(\alpha/0.95\right)^{2}}$ GeV/$c$, where $\alpha$ is
the energy asymmetry of the conversion daughters. Random associations of
electrons and positrons are further reduced by selecting $V^{0}$s with
$\mathrm{cos}(\theta)>0.85$, where $\theta$ is the pointing angle, which is
the angle between the momentum-vector of the $e^{+}e^{-}$ pair and the vector
that connects the primary vertex and the conversion point. Based on the
invariant mass of the $e^{+}e^{-}$ pair and the pointing angle of the $V^{0}$
to the primary vertex, the vertex finder calculates a $\chi^{2}$ value which
reflects the level of consistency with the hypothesis that the $V^{0}$ comes
from a photon originating from the primary vertex. A selection based on this
$\chi^{2}$ value is used to further reduce contamination in the photon sample.
The main sources of background that remain after these selection criteria are
V0s reconstructed from $\pi^{\pm}\mathrm{e}^{\mp}$, $\pi^{\pm}\pi^{\mp}$,
$\pi^{\pm}K^{\mp}$ and e${}^{\pm}K^{\mp}$ pairs, which is important to take
into account as shown in [59]. The elliptic flow of this background is
subtracted using a side-band method approach. In this method, the d$E$/d$x$
information of both conversion daughters is combined into a 1-dimensional
quantity. The signal is a peaked distribution and the side-bands are dominated
by background sources. The $v_{2}$ of the side-bands is measured and
subtracted from the main signal region using the purity of the photon sample,
which is obtained by fitting Monte Carlo templates to the data. The correction
to the measured inclusive photon flow is of the order of 5% for central and
2.5% for semi-central collisions, respectively.

The systematic uncertainties of the inclusive photon flow measured with PCM
are summarized in Tab. 1. The uncertainties related to the photon selection
($|\eta|$, $R$, min $p_{\mathrm{T}}$, $q_{\mathrm{T}}$,
$\chi^{2}/\mathrm{ndf}$ and $\cos(\theta)$) are obtained by varying the
selection criteria, and the systematic uncertainties related to the
contamination of the photon sample are quantified by the uncertainty on the
background flow subtraction. The energy resolution uncertainties, which are
due to detector resolution effects and bremsstrahlung of electrons, are
estimated by comparing $v_{2}^{{\rm\gamma,inc}}$ distributions as a function
of the reconstructed and true $p_{\mathrm{T}}$ using MC simulations. The
uncertainties related to the variation of reconstruction efficiency in- and
out-of-plane are calculated from studying the photon reconstruction efficiency
as a function of the track multiplicity. For most of these sources only a
small dependence on $p_{\mathrm{T}}$ and collision centrality is observed.

Centrality | 0–20% | 20–40%
---|---|---
$p_{\mathrm{T}}$ (GeV/$c$) | 2.0 | 5.0 | 2.0 | 5.0
PCM |  |  |  |
Photon selection | 2.4 | 4.2 | 2.1 | 4.0
Energy resolution | 1.0 | 1.0 | 1.0 | 1.0
Efficiency | 3 | 3 | 1.9 | 1.9
Total | 4.0 | 5.3 | 3.0 | 4.5
PHOS |  |  |  |
Efficiency & contamination | 3.0 | 3.0 | 0.7 | 0.7
Event plane flatness | 2.0 | 2.0 | 1.4 | 1.4
Total | 3.5 | 3.5 | 1.6 | 1.6
Decay photon calculation |  |  |  |
Parameterization of $v_{2}^{\pi}$ | 1.3 | 3.6 | 0.8 | 2.2
$\eta/\pi^{0}$ normalization | 1.7 | 3.2 | 1.7 | 2.4
Total | 2.2 | 4.8 | 1.9 | 3.3
Table 1:  Summary of the relative systematic uncertainties (in %) of the
inclusive photon elliptic flow in the PCM and PHOS analysis, and of the decay
photon simulation. All contributions are expected to be correlated in
$p_{\mathrm{T}}$ with the magnitude of the relative uncertainty varying point-
by-point.

In the PHOS analysis, the same photon selection criteria are applied as in the
direct-photon spectra analysis [23]. Cells with a common edge with another
cell that are both above the energy threshold of 25 MeV are combined into
clusters which are used as photon candidates. To estimate the photon energy,
the energies of all cells or only those with centers within a radius $R_{\rm
core}=3.5~{}\mathrm{cm}$ from the cluster center of gravity are summed.
Compared to the full cluster energy, the core energy is less sensitive to
overlaps with low-energy clusters in a high multiplicity environment, and is
well reproduced by GEANT3 Monte Carlo simulations [23].The full energy is used
for the systematic uncertainty estimate. The contribution of hadronic clusters
is reduced by requiring $E_{\rm cluster}>0.3~{}\mathrm{GeV}$,
$N_{\mathrm{cells}}>2$ and by accepting only clusters above a minimum lateral
cluster dispersion [60]. The latter selection rejects rare events when hadrons
punch through the crystal and hadronically interact with APD, producing a
large signal in one cell of a cluster, not proportional to the energy
deposition. In addition to these cuts, we also apply a
$p_{\mathrm{T}}$-dependent dispersion cut and perform a charged particle veto
(CPV). The CPV removes clusters based on the minimal distance between the PHOS
cluster position and the position of extrapolated charged tracks on the PHOS
surface, and is used to suppress hadron contribution [60]. Both dispersion and
CPV cuts are tuned using pp collision data to provide the photon
reconstruction and identification efficiency at the level of 96–99%.
Measurements with different combinations of dispersion and CPV cuts are used
for the estimate of systematic uncertainties. Possible pileup contribution
from other bunch crossings is removed by a loose cut on the cluster arrival
time $|t|<150~{}\mathrm{ns}$, which is small compared to a minimum time
between bunch crossings of 525 ns.

To estimate the reconstruction and identification efficiencies and correction
for energy smearing with their possible dependence on the angle with respect
to the event plane, we embedded simulated photon clusters into real data
events and applied the standard reconstruction procedure. PHOS properties
(energy and position resolutions, residual de-calibration, absolute
calibration, non-linear energy response) are tuned in the simulation to
reproduce the $p_{\mathrm{T}}$-dependence of the $\pi^{0}$ peak position and
width [60]. The correction for the event plane dependence of the
reconstruction and identification efficiencies, which comes as additive to the
observed photon flow, is less than $10^{-3}$ both in central and mid-central
collisions and is comparable to the statistical uncertainties of the embedding
procedure. The correction due to the energy smearing, is estimated to be 4%
and 1% for central and semi-central collisions, respectively. The
contamination of the photon sample measured with PHOS originates mainly from
$\pi^{\pm}$ and $\bar{p}$, $\bar{n}$ annihilation, with other contributions
being much smaller. The application of the dispersion and CPV cuts reduces the
overall contamination at $p_{\mathrm{T}}\approx 1.5$ GeV/$c$ from about 15% to
2–3% and down to 1–2% at $p_{\mathrm{T}}\sim 3$–$4~{}\mathrm{GeV}/c$. To
estimate and subtract the hadron contribution, the PHOS response matrices are
constructed for $\pi^{\pm}$, K, p and $\bar{p}$ using real data or Monte Carlo
simulations and convoluted with the measured spectra, flow and relative yields
of hadrons.

Systematic uncertainties of the inclusive photon flow measured with PHOS are
summarized in Tab. 1. They can be split into two groups: contributions related
to the contamination and dependence of reconstruction, identification and
smearing efficiency on the angle with respect to the event plane, and
uncertainties related to the flatness of the event plane calculation, the
event plane resolution and the contribution of non-flow effects. Uncertainties
of the first group are estimated by comparing the fully corrected photon flow
measured with different sets of identification criteria and with full and core
energy. Uncertainties of the second group are estimated by comparing inclusive
photon flows measured separately with the V0–A and V0–C detectors. Note that
because of the limited azimuthal acceptance, PHOS is much more sensitive to
the non-flatness of the event plane distribution compared to PCM.

In the combination of the inclusive photon $v_{2}$ results from PCM and PHOS,
both measurements are treated as independent. Possible correlations due to the
use of the same V0A and V0C event plane vectors are found to be negligible. To
take into account correlations of the individual measurements in bins of
transverse momentum, we describe the measured inclusive photon flows as
vectors $\vec{v}_{2}^{\gamma,\mathrm{inc,PCM}}$,
$\vec{v}_{2}^{\gamma,\mathrm{inc,PHOS}}$, where the vector components
correspond to the measured $p_{\mathrm{T}}$ bins, and the correlations of the
total uncertainties are described by covariance matrices
$V_{v_{2},\mathrm{PCM}}$ and $V_{v_{2},\mathrm{PHOS}}$, respectively. The
elements of the covariance matrix are calculated assuming uncorrelated
statistical uncertainties and fully correlated $(\rho=1)$ systematic
uncertainties; $V_{ij}=V_{\mathrm{stat},ij}+V_{\mathrm{syst},ij}$, where
$V_{\mathrm{syst},ij}=\rho\sigma_{\mathrm{syst},i}\sigma_{\mathrm{syst},j}$,
for $p_{\mathrm{T}}$ bin $i$ and $j$. Then, the combined inclusive photon flow
is the vector

$\vec{v}_{2}^{\gamma,\mathrm{inc}}=(V_{v_{2},\mathrm{PCM}}^{-1}+V_{v_{2},\mathrm{PHOS}}^{-1})^{-1}(V_{v_{2},\mathrm{PCM}}^{-1}\vec{v}_{2}^{\gamma,\mathrm{inc,PCM}}+V_{v_{2},\mathrm{PHOS}}^{-1}\vec{v}_{2}^{\gamma,\mathrm{inc,PHOS}}).$
(5)

The inclusive photon $v_{2}$ measured with PCM and PHOS are compared in Fig.
1, which shows the ratio of the individual values to the combined flow. The
PCM and PHOS measurements are found to be consistent with each other with
$p$-values of 0.93 and 0.43 for the centrality classes 0–20% and 20–40%,
respectively.

Figure 1:  (Color online) Comparison of the measured inclusive photon flow
$(v_{2}^{{\rm\gamma,inc}})$ to the individual PCM and PHOS measurements
$(v_{2}^{\rm\gamma,ind})$ in the 0–20% (left) and 20–40% (right) centrality
classes. The individual results are divided by the combined
$v_{2}^{{\rm\gamma,inc}}$. The vertical bars on each data point indicate the
statistical uncertainties and the boxes indicate the systematic uncertainties.

Figure 2:  (Color online) Elliptic flow of decay photons from $\pi^{0}$,
$\eta$, $\omega$, and the total cocktail simulation as a function of
transverse momentum in the 0–20% (left) and 20–40% (right) centrality classes.
The band represents the total uncertainty of the total cocktail simulation.

The decay photon flow is estimated using a cocktail simulation. Decays that
contribute more than 1% of the total decay photon yield are taken into
account: $\pi^{0}\to 2\gamma$, $\eta\to 2\gamma$, $\omega\to\gamma\pi^{0}$,
$K_{s}^{0}\to 2\pi^{0}\to 4\gamma$. Other contributions are negligible
compared to the systematic uncertainties of the cocktail. In decays of $\eta$
and $\omega$ mesons only photons produced directly in decays are accounted,
while those coming from daughter $\pi^{0}$ decays are already accounted in
$\pi^{0}$ contribution. The $K_{s}^{0}$ decay does not contribute
significantly to the photon sample measured with the PCM approach. Therefore,
we correct the PHOS measurement for this contribution before combining the
PHOS and PCM measurements. Here we use the same approach as in the direct-
photon spectrum analysis [23], but this time the simulation of the elliptic
flow is added. To estimate the elliptic flow of neutral pions, a
parametrization has been made of the charged pion flow measured under the same
conditions, i.e., charged pions measured in the TPC and reference particles in
the V0–A and V0–C detectors [61, 62] are used. To estimate the contribution of
$\eta$ and $\omega$ mesons, the measured elliptic flow of charged and neutral
kaons [61] is scaled, assuming scaling with the transverse kinetic energy
$KE_{\mathrm{T}}=m_{\mathrm{T}}-m$. The comparison of different contributions
and overall decay photon flow is shown in Fig. 2. The $v_{2}$ contributions
were added with weights, proportional to the relative decay photon yield of a
meson in total decay yield [23]. The width of the colored band represents the
systematic uncertainties of the decay photon elliptic flow
$v_{2}^{{\rm\gamma,dec}}$. The decay photon flow is mainly determined by the
$\pi^{0}$ flow, while other contributions make relatively small corrections:
the $\eta$ and $\omega$ contributions slightly reduce the decay photon
elliptic flow at $p_{\mathrm{T}}<2$ GeV/$c$ and increase it compared to the
$\pi^{0}$ contribution at higher $p_{\mathrm{T}}$. The systematic
uncertainties of the decay photon flow are summarized in Tab. 1. The largest
uncertainties come from the parametrization of the charged pion elliptic flow
and from the relative yield $\eta/\pi^{0}$.

##  4 Results

The $v_{2}^{{\rm\gamma,inc}}$ measured in two centrality classes are shown in
Fig. 3. The elliptic flow coefficients of inclusive photons and decay photons
are very similar over the full range $0.9<p_{\mathrm{T}}<6.2$ GeV/$c$. As the
fraction of direct photon over the inclusive photon yield is relatively small,
$\sim 10$% in our $p_{\mathrm{T}}$ range [23], the collective flow of
inclusive photons is dominated by the decay photon flow. In models based on
relativistic hydrodynamics the medium is assumed to be in or close to local
thermal equilibrium. An equation of state is used to relate thermodynamic
quantities like temperature, energy density, and pressure. Photon production
is modeled by folding the space-time evolution of a collision with
temperature-dependent photon production rates in the QGP and the hadron gas.
Another approach is taken, e.g., in the PHSD transport model in which the QGP
degrees of freedom are modeled as massive strongly-interacting quasi-particles
[63]. For both classes of models the development of a strong early elliptic
flow, necessary to reproduce the observed direct-photon flow, gives rise to a
large pion elliptic flow at freeze-out and therefore to a large inclusive
photon elliptic flow. It is therefore an important test to check whether a
model can describe both the inclusive and the direct-photon elliptic flow. The
prediction of the hydrodynamic model described in [64] for the inclusive
photon $v_{2}$ in the range $1<p_{\mathrm{T}}<3$ GeV/$c$ is about 40% above
the data, though the magnitude of the elliptic flow of unidentified hadrons is
reproduced within 10–20% accuracy in this $p_{\mathrm{T}}$ range [65]. The
PHSD model [63] also predicts an $\sim$ 40% higher inclusive photon flow, even
though it reproduces the unidentified hadron flow well.

Figure 3: (Color online) Elliptic flow of inclusive photons and decay photons,
compared to hydrodynamic [31] and transport PHSD [30] model predictions in the
0–20% (left) and 20–40% (right) centrality classes. The vertical bars on each
data point indicate the statistical uncertainties and the boxes indicate the
sizes of the total uncertainties.

The direct-photon $v_{2}$ is calculated from the combined PCM and PHOS photon
excess $R_{\rm\gamma}$ [23], the combined inclusive $v_{2}$, and the
calculated decay photon $v_{2}$. In the propagation of uncertainties, the
relatively small significance of the photon excess of about 1–3 standard
deviations (depending on the centrality class and $p_{\mathrm{T}}$ interval)
requires special attention. This is illustrated for a selected
$p_{\mathrm{T}}$ interval in the left panel of Fig. 4 which shows the obtained
$v_{2}^{{\rm\gamma,dir}}$ and its uncertainty as a function of the photon
excess $R_{\rm\gamma}$. The Gaussian function in this panel represents the
measured value of $R_{\rm\gamma}$ in this $p_{\mathrm{T}}$ interval (dashed
line) and its $1\sigma$ total uncertainty (dark blue shaded area). For
$R_{\rm\gamma}\lesssim 1.05$ one loses the sensitivity to
$v_{2}^{{\rm\gamma,dir}}$ as the uncertainties, indicated by the red shaded
band, increase drastically. With the current uncertainties on $R_{\rm\gamma}$
we cannot rule out completely that $R_{\rm\gamma}\lesssim 1.05$.

Figure 4:  (Color online) Left: Central value (solid red line) and uncertainty
of the direct-photon $v_{2}$ for a selected $p_{\mathrm{T}}$ interval. The
upper and lower edges of the red shaded area correspond to the total
uncertainty of $v_{2}^{{\rm\gamma,dir}}$ as obtained from linear Gaussian
propagation of the uncertainties $\sigma(v_{2}^{{\rm\gamma,inc}})$ and
$\sigma(v_{2}^{{\rm\gamma,dec}})$. The Gaussian (with arbitrary normalization)
reflects the measured value of $R_{\rm\gamma}$ in this $p_{\mathrm{T}}$
interval (blue dashed line) and its $\pm 1\sigma$ uncertainty (dark-blue
shaded interval). Right: Posterior distribution of the true value of
$v_{2}^{{\rm\gamma,dir}}$ for the same interval in the Bayesian approach. Note
that the distribution has a non-Gaussian shape, implying that the
$\pm$2$\sigma$ interval typically corresponds to a probability of less than
95.45% as would be the case for a Gaussian.

We address the limited significance of the direct-photon excess by employing a
Bayesian approach. The parameters $R_{\mathrm{\gamma,t}}$,
$v_{2}^{\mathrm{\gamma,inc,t}}$, $v_{2}^{\mathrm{\gamma,dec,t}}$ denoting the
true values carry the index “t” and the measured quantities
$R_{\mathrm{\gamma,m}}$, $v_{2}^{\mathrm{\gamma,dec,m}}$,
$v_{2}^{\mathrm{\gamma,dec,m}}$ the index “m”. Note that
$R_{\mathrm{\gamma,t}}$ is restricted to its physically allowed range
($R_{\mathrm{\gamma,t}}\geq 1$), while the measured value
$R_{\mathrm{\gamma,m}}$ can fluctuate below unity. The posterior distribution
of the true parameters can be written as

$P(\vec{\vartheta}|\vec{m})\propto
P(\vec{m}|\vec{\vartheta})\pi(\vec{\vartheta}),\quad\pi(\vec{\vartheta})\equiv\pi(\vec{R}_{\mathrm{\gamma,t}})=\Theta(R_{\mathrm{\gamma,t},1}-1,...,R_{\mathrm{\gamma,t},n}-1),$
(6)

where in
$\vec{m}=(\vec{R}_{\mathrm{\gamma,m}},\vec{v}_{2}^{\mathrm{\gamma,inc,m}},\vec{v}_{2}^{\mathrm{\gamma,dec,m}})$,
$\vec{\vartheta}=(\vec{R}_{\mathrm{\gamma,t}},\vec{v}_{2}^{\mathrm{\gamma,inc,t}},\vec{v}_{2}^{\mathrm{\gamma,dec,t}})$.
Here we use the notation introduced in Eq. (5): vectors represent sets of
measurements in different $p_{\mathrm{T}}$ bins and $n$ is the number of these
bins. The function $\pi(\vec{R}_{\mathrm{\gamma,t}})$ encodes the prior
knowledge about $R_{\gamma}$. The multivariate Heaviside $\Theta$ function
corresponds to a constant (improper) prior for $R_{\mathrm{\gamma,t}}\geq 1$.
The probability to observe a certain set of measured values given the true
values is modeled with multivariate Gaussians $G(\vec{x};\,\vec{\mu},V)$
(where $\vec{\mu}$ is the vector of mean values and $V$ is the covariance
matrix):

$P(\vec{m}|\vec{\vartheta})=\prod_{x=R_{\gamma},\,v_{2}^{\mathrm{\gamma,inc}},\,v_{2}^{\mathrm{\gamma,dec}}}G(\vec{x}_{\mathrm{m}};\,\vec{x}_{\mathrm{t}},V_{x}).$
(7)

By sampling the posterior distribution $P(\vec{\vartheta}|\vec{m})$, we obtain
triplets $(R_{\rm\gamma},v_{2}^{{\rm\gamma,inc}},v_{2}^{{\rm\gamma,dec}})$ for
each $p_{\mathrm{T}}$ bin from which we calculate $v_{2}^{{\rm\gamma,dir}}$
according to Eq. 2. An example of the resulting distribution for
$v_{2}^{{\rm\gamma,dir}}$ is shown in Fig. 4 (right panel). The medians of the
$v_{2}^{{\rm\gamma,dir}}$ distributions are taken as central values. The lower
and upper edges of the error bars correspond to values of
$v_{2}^{\mathrm{dir}}$ at which the integral of the $v_{2}$ distribution is
15.87% and 84.13% of the total integral. In case of a Gaussian distribution
this corresponds to $1\sigma$ uncertainties.

The results for the direct-photon elliptic flow for the two centrality
classes, 0–20% and 20–40%, are shown in Fig. 5. The total uncertainties,
reflecting the Bayesian posterior distributions, are shown as boxes, and the
error bars represent statistical uncertainties. The correlation of
$v_{\mathrm{2,dir}}$ points for different $p_{\mathrm{T}}$ bins as quantified
by the correlation matrix is strong at low $p_{\mathrm{T}}\lesssim
2~{}\mathrm{GeV}/c$ (correlation coefficients typically in the range 0.6–0.75)
whereas the uncertainties at high $p_{\mathrm{T}}$ are dominated by
statistical uncertainties. We compare our results to measurements made at RHIC
energies by the PHENIX collaboration [26]. The inclusive photon $v_{2}$ was
measured by PHENIX through the reconstruction of $e^{+}e^{-}$ pairs from
photon conversions and with an electromagnetic calorimeter. The direct-photon
elliptic flow in Au–Au collisions at RHIC and in Pb–Pb collisions at the LHC
are found to be compatible within uncertainties. A simple explanation of the
large and similar direct-photon elliptic flow for $p_{\mathrm{T}}\lesssim
2~{}\mathrm{GeV}/c$ at RHIC and the LHC is that the bulk of the thermal direct
photons is produced late at temperatures close to the transition temperature
$T_{\mathrm{c}}$. This is interesting as naïvely one would expect the $T^{2}$
temperature dependence of the photon emission rate to make the early hot QGP
phase after thermalization also the brightest phase.

Figure 5: (Color online) Elliptic flow of direct photons compared with PHENIX
results [26] for the 0–20% (left) and 20–40% (right) centrality classes. The
vertical bars on each data point indicate the statistical uncertainties and
the boxes the total uncertainty.

Figure 6: (Color online) Elliptic flow of direct photons compared to model
calculations in the 0–20% (left) and 20–40% (right) centrality classes. The
vertical bars on each data point indicate the statistical uncertainties and
the boxes the total uncertainty.

Figure 6 compares the measured direct-photon elliptic flow
$v_{2}^{{\rm\gamma,dir}}$ to the estimated decay photon elliptic flow
$v_{2}^{{\rm\gamma,dec}}$, marked as cocktail, and to the predictions of
several theoretical models. Similarly to measurements at RHIC energies [24],
we find that the direct and decay photon elliptic flow are similar. We compare
our measurements to state-of-the-art hydrodynamic model calculations [31, 66]
and the PHSD transport model [63]. The measured direct-photon elliptic flow is
systematically higher than theoretical predictions, but is still compatible.

In order to quantify the deviation of the direct-photon $v_{2}$ measurement
from a certain hypothesis with a frequentist $p$-value or, equivalently, the
corresponding number of standard deviations, we use a Bayesian-inspired method
[67]. In this approach, the likelihood
$L(\vec{v}_{2}^{\mathrm{\gamma,inc,m}}|\vec{v}_{2}^{\mathrm{\gamma,dir,t}})$
serves as a test statistic and is obtained by integrating over the nuisance
parameters $\vec{v}_{2}^{\mathrm{\gamma,dec,t}}$ and $\vec{R}_{\gamma,t}$
using their Bayesian posterior distributions as weights. We focus on the
interval $0.9<p_{\mathrm{T}}<2.1~{}\mathrm{GeV}/c$ in which the contribution
of thermal photons is expected to be important. The significance of the
deviation from the hypothesis $v_{2}^{\mathrm{\gamma,dir,t}}=0$ for individual
$p_{\mathrm{T}}$ bins is in the range 1.8–2.1$\sigma$ for the 0–20% class and
0.9–1.5$\sigma$ for the 20–40% class. We also go a step further and estimate
the combined significance of the deviation from the hypothesis
$v_{2}^{{\rm\gamma,dir}}\equiv 0$ for this $p_{\mathrm{T}}$ interval. This
tests in addition how well the shape of $v_{2}^{\mathrm{\gamma,inc,m}}$ as a
function of $p_{\mathrm{T}}$ agrees with
$v_{2}^{\mathrm{\gamma,dec,m}}/R_{\gamma}$, i.e., with the expectation for
$v_{2}^{{\rm\gamma,dir}}\equiv 0$. We estimate the covariance matrix
describing the correlation by characterizing the different sources of
systematic uncertainties of $R_{\gamma}$, the inclusive, and the decay photon
flow as either fully uncorrelated or fully correlated in $p_{\mathrm{T}}$.
Varying the assumptions about the correlation of the data points we obtain
significances of typically less than $1\sigma$ for both centrality classes.
While the applied method is essential for a meaningful comparison of the
$v_{2}^{\mathrm{\gamma,dir}}$ data with different model predictions, the
methods to estimate the covariance matrix can be improved in future analyses.

##  5 Conclusions

In summary, we report the first measurement of elliptic flow of inclusive and
direct photons as a function of transverse momentum in the range
$0.9<p_{\mathrm{T}}<6.2$ GeV/$c$ for central and semi-central Pb–Pb collisions
at $\sqrt{s_{{}_{\mathrm{NN}}}}=2.76$ TeV. The elliptic flow of inclusive
photons was measured with the scalar product method, independently in the
electromagnetic calorimeter PHOS and with the photon conversion method where
the reference particles in both cases were measured by the V0–A and V0–C
detectors. The combined inclusive photon $v_{2}^{{\rm\gamma,inc}}$, together
with the calculated decay photon $v_{2}^{{\rm\gamma,dec}}$ and the previously
measured $R_{\rm\gamma}$ are used to calculate the elliptic flow of direct
photons. The measured direct-photon flow $v_{2}^{{\rm\gamma,dir}}$ appears to
be close to the decay photon flow for both centrality classes, similar to
observations at lower collision energies. Moreover, the measured
$v_{2}^{{\rm\gamma,dir}}$ is similar to the measurements by the PHENIX
collaboration at RHIC. The considered hydrodynamic and transport models
predict a larger inclusive photon elliptic flow (by approximately $40$%) and a
smaller direct-photon elliptic flow than observed. With current uncertainties,
however, these models are consistent with the presented direct-photon elliptic
flow data. Future measurements using a larger statistics dataset will greatly
increase the precision of this measurement and allow us to extend the
measurement to higher $p_{\mathrm{T}}$, since the statistical uncertainty is
dominating the total uncertainty for $p_{\mathrm{T}}>2.0$ GeV/$c$ and
$p_{\mathrm{T}}>3.0$ GeV/$c$ for the PHOS and PCM inclusive photon flow
measurement, respectively. In addition, a larger statistics dataset will also
help to constrain the systematic uncertainties on the inclusive and decay
photon flow, as well as the measurement of $R_{\rm\gamma}$ over the whole
$p_{\mathrm{T}}$ range. A further reduction of the systematic uncertainties is
expected from improved detector knowledge. For instance, in case of PCM the
largest systematic uncertainty in the measurement of $R_{\rm\gamma}$ is
related to modeling the material in which the photons convert. Calibrating
regions of the detector with less well known material budget based on regions
with very well known material might significantly reduce the overall material
budget uncertainty. The $R_{\rm\gamma}$ measurement can be improved further by
measuring neutral pion and eta meson spectra in a combined PCM-calorimeter
approach in which one decay photon is measured through conversion and the
other with a calorimeter.

## Acknowledgements

We would like to thank Elena Bratkovskaya and Jean-François Paquet for
providing calculations shown in this paper and for useful discussions.

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 and Nationalstiftung für Forschung,
Technologie und Entwicklung, Austria; Ministry of Communications and High
Technologies, National Nuclear Research Center, Azerbaijan; Conselho Nacional
de Desenvolvimento Científico e Tecnológico (CNPq), Universidade Federal do
Rio Grande do Sul (UFRGS), Financiadora de Estudos e Projetos (Finep) and
Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP), Brazil;
Ministry of Science & Technology of China (MSTC), National Natural Science
Foundation of China (NSFC) and Ministry of Education of China (MOEC) , China;
Ministry of Science and Education, Croatia; Ministry of Education, Youth and
Sports of the Czech Republic, Czech Republic; The Danish Council for
Independent Research — Natural Sciences, the Carlsberg Foundation and Danish
National Research Foundation (DNRF), Denmark; Helsinki Institute of Physics
(HIP), Finland; Commissariat à l’Energie Atomique (CEA) and Institut National
de Physique Nucléaire et de Physique des Particules (IN2P3) and Centre
National de la Recherche Scientifique (CNRS), France; Bundesministerium für
Bildung, Wissenschaft, Forschung und Technologie (BMBF) and GSI
Helmholtzzentrum für Schwerionenforschung GmbH, Germany; General Secretariat
for Research and Technology, Ministry of Education, Research and Religions,
Greece; National Research, Development and Innovation Office, Hungary;
Department of Atomic Energy Government of India (DAE), Department of Science
and Technology, Government of India (DST), University Grants Commission,
Government of India (UGC) and Council of Scientific and Industrial Research
(CSIR), India; Indonesian Institute of Science, Indonesia; Centro Fermi -
Museo Storico della Fisica e Centro Studi e Ricerche Enrico Fermi and Istituto
Nazionale di Fisica Nucleare (INFN), Italy; Institute for Innovative Science
and Technology , Nagasaki Institute of Applied Science (IIST), Japan Society
for the Promotion of Science (JSPS) KAKENHI and Japanese Ministry of
Education, Culture, Sports, Science and Technology (MEXT), Japan; Consejo
Nacional de Ciencia (CONACYT) y Tecnología, through Fondo de Cooperación
Internacional en Ciencia y Tecnología (FONCICYT) and Dirección General de
Asuntos del Personal Academico (DGAPA), Mexico; Nederlandse Organisatie voor
Wetenschappelijk Onderzoek (NWO), Netherlands; The Research Council of Norway,
Norway; Commission on Science and Technology for Sustainable Development in
the South (COMSATS), Pakistan; Pontificia Universidad Católica del Perú, Peru;
Ministry of Science and Higher Education and National Science Centre, Poland;
Korea Institute of Science and Technology Information and National Research
Foundation of Korea (NRF), Republic of Korea; Ministry of Education and
Scientific Research, Institute of Atomic Physics and Romanian National Agency
for Science, Technology and Innovation, Romania; Joint Institute for Nuclear
Research (JINR), Ministry of Education and Science of the Russian Federation
and National Research Centre Kurchatov Institute, Russia; Ministry of
Education, Science, Research and Sport of the Slovak Republic, Slovakia;
National Research Foundation of South Africa, South Africa; Centro de
Aplicaciones Tecnológicas y Desarrollo Nuclear (CEADEN), Cubaenergía, Cuba and
Centro de Investigaciones Energéticas, Medioambientales y Tecnológicas
(CIEMAT), Spain; Swedish Research Council (VR) and Knut & Alice Wallenberg
Foundation (KAW), Sweden; European Organization for Nuclear Research,
Switzerland; National Science and Technology Development Agency (NSDTA),
Suranaree University of Technology (SUT) and Office of the Higher Education
Commission under NRU project of Thailand, Thailand; Turkish Atomic Energy
Agency (TAEK), Turkey; National Academy of Sciences of Ukraine, Ukraine;
Science and Technology Facilities Council (STFC), United Kingdom; National
Science Foundation of the United States of America (NSF) and United States
Department of Energy, Office of Nuclear Physics (DOE NP), United States of
America.

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##  Appendix A The ALICE Collaboration

S. Acharyaorg139&F.T.-. Acostaorg21&D. Adamováorg94&J. Adolfssonorg81&M.M.
Aggarwalorg98&G. Aglieri Rinellaorg35&M. Agnelloorg32&N. Agrawalorg49&Z.
Ahammedorg139&S.U. Ahnorg77&S. Aiolaorg144&A. Akindinovorg65&M. Al-
Turanyorg104&S.N. Alamorg139&D.S.D. Albuquerqueorg121&D. Aleksandrovorg88&B.
Alessandroorg59&R. Alfaro Molinaorg73&Y. Aliorg15&A. Aliciorg10,org54,org28&A.
Alkinorg2&J. Almeorg23&T. Altorg70&L. Altenkamperorg23&I. Altsybeevorg111&M.N.
Anaamorg6&C. Andreiorg48&D. Andreouorg35&H.A. Andrewsorg108&A.
Andronicorg142,org104&M. Angelettiorg35&V. Anguelovorg102&C. Ansonorg16&T.
Antičićorg105&F. Antinoriorg57&P. Antonioliorg54&R. Anwarorg125&N.
Apadulaorg80&L. Aphecetcheorg113&H. Appelshäuserorg70&S. Arcelliorg28&R.
Arnaldiorg59&O.W. Arnoldorg103,org116&I.C. Arseneorg22&M. Arslandokorg102&B.
Audurierorg113&A. Augustinusorg35&R. Averbeckorg104&M.D. Azmiorg17&A.
Badalàorg56&Y.W. Baekorg61,org41&S. Bagnascoorg59&R. Bailhacheorg70&R.
Balaorg99&A. Baldisseriorg135&M. Ballorg43&R.C. Baralorg86&A.M.
Barbanoorg27&R. Barberaorg29&F. Barileorg53&L. Barioglioorg27&G.G.
Barnaföldiorg143&L.S. Barnbyorg93&V. Barretorg132&P. Bartaliniorg6&K.
Barthorg35&E. Bartschorg70&N. Bastidorg132&S. Basuorg141&G. Batigneorg113&B.
Batyunyaorg76&P.C. Batzingorg22&J.L. Bazo Albaorg109&I.G. Beardenorg89&H.
Beckorg102&C. Beddaorg64&N.K. Beheraorg61&I. Belikovorg134&F. Belliniorg35&H.
Bello Martinezorg45&R. Bellwiedorg125&L.G.E. Beltranorg119&V. Belyaevorg92&G.
Bencediorg143&S. Beoleorg27&A. Bercuciorg48&Y. Berdnikovorg96&D.
Berenyiorg143&R.A. Bertensorg128&D. Berzanoorg35,org59&L. Betevorg35&P.P.
Bhaduriorg139&A. Bhasinorg99&I.R. Bhatorg99&H. Bhattorg49&B.
Bhattacharjeeorg42&J. Bhomorg117&A. Bianchiorg27&L. Bianchiorg125&N.
Bianchiorg52&J. Bielčíkorg38&J. Bielčíkováorg94&A. Bilandzicorg116,org103&G.
Biroorg143&R. Biswasorg3&S. Biswasorg3&J.T. Blairorg118&D. Blauorg88&C.
Blumeorg70&G. Bocaorg137&F. Bockorg35&A. Bogdanovorg92&L. Boldizsárorg143&M.
Bombaraorg39&G. Bonomiorg138&M. Bonoraorg35&H. Borelorg135&A.
Borissovorg19,org142&M. Borriorg127&E. Bottaorg27&C. Bourjauorg89&L.
Bratrudorg70&P. Braun-Munzingerorg104&M. Bregantorg120&T.A. Brokerorg70&M.
Brozorg38&E.J. Bruckenorg44&E. Brunaorg59&G.E. Brunoorg35,org34&D.
Budnikovorg106&H. Bueschingorg70&S. Bufalinoorg32&P. Buhlerorg112&P.
Buncicorg35&O. Buschorg131org*&Z. Butheleziorg74&J.B. Buttorg15&J.T.
Buxtonorg18&J. Cabalaorg115&D. Caffarriorg90&H. Cainesorg144&A.
Calivaorg104&E. Calvo Villarorg109&R.S. Camachoorg45&P. Cameriniorg26&A.A.
Caponorg112&F. Carenaorg35&W. Carenaorg35&F. Carnesecchiorg28,org10&J.
Castillo Castellanosorg135&A.J. Castroorg128&E.A.R. Casulaorg55&C. Ceballos
Sanchezorg8&S. Chandraorg139&B. Changorg126&W. Changorg6&S. Chapelandorg35&M.
Chartierorg127&S. Chattopadhyayorg139&S. Chattopadhyayorg107&A.
Chauvinorg103,org116&C. Cheshkovorg133&B. Cheynisorg133&V. Chibante
Barrosoorg35&D.D. Chinellatoorg121&S. Choorg61&P. Chochulaorg35&T.
Chowdhuryorg132&P. Christakoglouorg90&C.H. Christensenorg89&P.
Christiansenorg81&T. Chujoorg131&S.U. Chungorg19&C. Cicaloorg55&L.
Cifarelliorg10,org28&F. Cindoloorg54&J. Cleymansorg124&F. Colamariaorg53&D.
Colellaorg66,org35,org53&A. Colluorg80&M. Colocciorg28&M. Concasorg59orgI&G.
Conesa Balbastreorg79&Z. Conesa del Valleorg62&J.G. Contrerasorg38&T.M.
Cormierorg95&Y. Corrales Moralesorg59&P. Corteseorg33&M.R. Cosentinoorg122&F.
Costaorg35&S. Costanzaorg137&J. Crkovskáorg62&P. Crochetorg132&E.
Cuautleorg71&L. Cunqueiroorg142,org95&T. Dahmsorg103,org116&A. Daineseorg57&S.
Daniorg67&M.C. Danischorg102&A. Danuorg69&D. Dasorg107&I. Dasorg107&S.
Dasorg3&A. Dashorg86&S. Dashorg49&S. Deorg50&A. De Caroorg31&G. de
Cataldoorg53&C. de Contiorg120&J. de Cuvelandorg40&A. De Falcoorg25&D. De
Gruttolaorg10,org31&N. De Marcoorg59&S. De Pasqualeorg31&R.D. De
Souzaorg121&H.F. Degenhardtorg120&A. Deistingorg104,org102&A. Delofforg85&S.
Delsantoorg27&C. Deplanoorg90&P. Dhankherorg49&D. Di Bariorg34&A. Di
Mauroorg35&B. Di Ruzzaorg57&R.A. Diazorg8&T. Dietelorg124&P.
Dillensegerorg70&Y. Dingorg6&R. Diviàorg35&Ø. Djuvslandorg23&A. Dobrinorg35&D.
Domenicis Gimenezorg120&B. Dönigusorg70&O. Dordicorg22&L.V.R.
Doremalenorg64&A.K. Dubeyorg139&A. Dublaorg104&L. Ducrouxorg133&S.
Dudiorg98&A.K. Duggalorg98&M. Dukhishyamorg86&P. Dupieuxorg132&R.J.
Ehlersorg144&D. Eliaorg53&E. Endressorg109&H. Engelorg75&E. Eppleorg144&B.
Erazmusorg113&F. Erhardtorg97&M.R. Ersdalorg23&B. Espagnonorg62&G.
Eulisseorg35&J. Eumorg19&D. Evansorg108&S. Evdokimovorg91&L.
Fabbiettiorg103,org116&M. Fagginorg30&J. Faivreorg79&A. Fantoniorg52&M.
Faselorg95&L. Feldkamporg142&A. Felicielloorg59&G. Feofilovorg111&A. Fernández
Téllezorg45&A. Ferrettiorg27&A. Festantiorg30,org35&V.J.G. Feuillardorg102&J.
Figielorg117&M.A.S. Figueredoorg120&S. Filchaginorg106&D. Finogeevorg63&F.M.
Fiondaorg23&G. Fiorenzaorg53&F. Flororg125&M. Florisorg35&S. Foertschorg74&P.
Fokaorg104&S. Fokinorg88&E. Fragiacomoorg60&A. Francesconorg35&A.
Franciscoorg113&U. Frankenfeldorg104&G.G. Fronzeorg27&U. Fuchsorg35&C.
Furgetorg79&A. Fursorg63&M. Fusco Girardorg31&J.J. Gaardhøjeorg89&M.
Gagliardiorg27&A.M. Gagoorg109&K. Gajdosovaorg89&M. Gallioorg27&C.D.
Galvanorg119&P. Ganotiorg84&C. Garabatosorg104&E. Garcia-Solisorg11&K.
Gargorg29&C. Gargiuloorg35&P. Gasikorg116,org103&E.F. Gaugerorg118&M.B. Gay
Ducatiorg72&M. Germainorg113&J. Ghoshorg107&P. Ghoshorg139&S.K. Ghoshorg3&P.
Gianottiorg52&P. Giubellinoorg104,org59&P. Giubilatoorg30&P.
Glässelorg102&D.M. Goméz Coralorg73&A. Gomez Ramirezorg75&V. Gonzalezorg104&P.
González-Zamoraorg45&S. Gorbunovorg40&L. Görlichorg117&S. Gotovacorg36&V.
Grabskiorg73&L.K. Graczykowskiorg140&K.L. Grahamorg108&L. Greinerorg80&A.
Grelliorg64&C. Grigorasorg35&V. Grigorievorg92&A. Grigoryanorg1&S.
Grigoryanorg76&J.M. Gronefeldorg104&F. Grosaorg32&J.F. Grosse-
Oetringhausorg35&R. Grossoorg104&R. Guernaneorg79&B. Guerzoniorg28&M.
Guittiereorg113&K. Gulbrandsenorg89&T. Gunjiorg130&A. Guptaorg99&R.
Guptaorg99&I.B. Guzmanorg45&R. Haakeorg35&M.K. Habiborg104&C.
Hadjidakisorg62&H. Hamagakiorg82&G. Hamarorg143&M. Hamidorg6&J.C.
Hamonorg134&R. Hanniganorg118&M.R. Haqueorg64&J.W. Harrisorg144&A.
Hartonorg11&H. Hassanorg79&D. Hatzifotiadouorg54,org10&S. Hayashiorg130&S.T.
Heckelorg70&E. Hellbärorg70&H. Helstruporg37&A. Herghelegiuorg48&E.G.
Hernandezorg45&G. Herrera Corralorg9&F. Herrmannorg142&K.F. Hetlandorg37&T.E.
Hildenorg44&H. Hillemannsorg35&C. Hillsorg127&B. Hippolyteorg134&B.
Hohlwegerorg103&D. Horakorg38&S. Hornungorg104&R. Hosokawaorg131,org79&J.
Hotaorg67&P. Hristovorg35&C. Huangorg62&C. Hughesorg128&P. Huhnorg70&T.J.
Humanicorg18&H. Hushnudorg107&N. Hussainorg42&T. Hussainorg17&D.
Hutterorg40&D.S. Hwangorg20&J.P. Iddonorg127&S.A. Iga Buitronorg71&R.
Ilkaevorg106&M. Inabaorg131&M. Ippolitovorg88&M.S. Islamorg107&M.
Ivanovorg104&V. Ivanovorg96&V. Izucheevorg91&B. Jacakorg80&N.
Jacazioorg28&P.M. Jacobsorg80&M.B. Jadhavorg49&S. Jadlovskaorg115&J.
Jadlovskyorg115&S. Jaelaniorg64&C. Jahnkeorg120,org116&M.J.
Jakubowskaorg140&M.A. Janikorg140&C. Jenaorg86&M. Jercicorg97&O.
Jevonsorg108&R.T. Jimenez Bustamanteorg104&M. Jinorg125&P.G. Jonesorg108&A.
Juskoorg108&P. Kalinakorg66&A. Kalweitorg35&J.H. Kangorg145&V. Kaplinorg92&S.
Karorg6&A. Karasu Uysalorg78&O. Karavichevorg63&T. Karavichevaorg63&P.
Karczmarczykorg35&E. Karpechevorg63&U. Kebschullorg75&R. Keidelorg47&D.L.D.
Keijdenerorg64&M. Keilorg35&B. Ketzerorg43&Z. Khabanovaorg90&A.M. Khanorg6&S.
Khanorg17&S.A. Khanorg139&A. Khanzadeevorg96&Y. Kharlovorg91&A. Khatunorg17&A.
Khuntiaorg50&M.M. Kielbowiczorg117&B. Kilengorg37&B. Kimorg131&D.
Kimorg145&D.J. Kimorg126&E.J. Kimorg13&H. Kimorg145&J.S. Kimorg41&J.
Kimorg102&M. Kimorg102,org61&S. Kimorg20&T. Kimorg145&T. Kimorg145&S.
Kirschorg40&I. Kiselorg40&S. Kiselevorg65&A. Kisielorg140&J.L. Klayorg5&C.
Kleinorg70&J. Kleinorg35,org59&C. Klein-Bösingorg142&S. Klewinorg102&A.
Klugeorg35&M.L. Knichelorg35&A.G. Knospeorg125&C. Kobdajorg114&M.
Kofaragoorg143&M.K. Köhlerorg102&T. Kolleggerorg104&N. Kondratyevaorg92&E.
Kondratyukorg91&A. Konevskikhorg63&M. Konyushikhinorg141&O. Kovalenkoorg85&V.
Kovalenkoorg111&M. Kowalskiorg117&I. Králikorg66&A. Kravčákováorg39&L.
Kreisorg104&M. Krivdaorg66,org108&F. Krizekorg94&M. Krügerorg70&E.
Kryshenorg96&M. Krzewickiorg40&A.M. Kuberaorg18&V. Kučeraorg61,org94&C.
Kuhnorg134&P.G. Kuijerorg90&J. Kumarorg49&L. Kumarorg98&S. Kumarorg49&S.
Kunduorg86&P. Kurashviliorg85&A. Kurepinorg63&A.B. Kurepinorg63&A.
Kuryakinorg106&S. Kushpilorg94&J. Kvapilorg108&M.J. Kweonorg61&Y.
Kwonorg145&S.L. La Pointeorg40&P. La Roccaorg29&Y.S. Laiorg80&I.
Lakomovorg35&R. Langoyorg123&K. Lapidusorg144&A. Lardeuxorg22&P.
Larionovorg52&E. Laudiorg35&R. Lavickaorg38&R. Leaorg26&L. Leardiniorg102&S.
Leeorg145&F. Lehasorg90&S. Lehnerorg112&J. Lehrbachorg40&R.C. Lemmonorg93&I.
León Monzónorg119&P. Lévaiorg143&X. Liorg12&X.L. Liorg6&J. Lienorg123&R.
Lietavaorg108&B. Limorg19&S. Lindalorg22&V. Lindenstruthorg40&S.W.
Lindsayorg127&C. Lippmannorg104&M.A. Lisaorg18&V. Litichevskyiorg44&A.
Liuorg80&H.M. Ljunggrenorg81&W.J. Llopeorg141&D.F. Lodatoorg64&V.
Loginovorg92&C. Loizidesorg95,org80&P. Loncarorg36&X. Lopezorg132&E. López
Torresorg8&A. Loweorg143&P. Luettigorg70&J.R. Luhderorg142&M. Lunardonorg30&G.
Luparelloorg60&M. Lupiorg35&A. Maevskayaorg63&M. Magerorg35&S.M.
Mahmoodorg22&A. Maireorg134&R.D. Majkaorg144&M. Malaevorg96&Q.W. Malikorg22&L.
Malininaorg76orgII&D. Mal’Kevichorg65&P. Malzacherorg104&A. Mamonovorg106&V.
Mankoorg88&F. Mansoorg132&V. Manzariorg53&Y. Maoorg6&M.
Marchisoneorg129,org74,org133&J. Marešorg68&G.V. Margagliottiorg26&A.
Margottiorg54&J. Marguttiorg64&A. Marínorg104&C. Markertorg118&M.
Marquardorg70&N.A. Martinorg104&P. Martinengoorg35&J.L. Martinezorg125&M.I.
Martínezorg45&G. Martínez Garcíaorg113&M. Martinez Pedreiraorg35&S.
Masciocchiorg104&M. Maseraorg27&A. Masoniorg55&L. Massacrierorg62&E.
Massonorg113&A. Mastroserioorg53,org136&A.M. Mathisorg116,org103&P.F.T.
Matuokaorg120&A. Matyjaorg117,org128&C. Mayerorg117&M. Mazzilliorg34&M.A.
Mazzoniorg58&F. Meddiorg24&Y. Melikyanorg92&A. Menchaca-Rochaorg73&E.
Meninnoorg31&J. Mercado Pérezorg102&M. Meresorg14&C.S. Mezaorg109&S.
Mhlangaorg124&Y. Miakeorg131&L. Michelettiorg27&M.M. Mieskolainenorg44&D.L.
Mihaylovorg103&K. Mikhaylovorg65,org76&A. Mischkeorg64&A.N. Mishraorg71&D.
Miśkowiecorg104&J. Mitraorg139&C.M. Mituorg69&N. Mohammadiorg35&A.P.
Mohantyorg64&B. Mohantyorg86&M. Mohisin Khanorg17orgIII&D.A. Moreira De
Godoyorg142&L.A.P. Morenoorg45&S. Morettoorg30&A. Morrealeorg113&A.
Morschorg35&V. Mucciforaorg52&E. Mudnicorg36&D. Mühlheimorg142&S.
Muhuriorg139&M. Mukherjeeorg3&J.D. Mulliganorg144&M.G. Munhozorg120&K.
Münningorg43&M.I.A. Munozorg80&R.H. Munzerorg70&H. Murakamiorg130&S.
Murrayorg74&L. Musaorg35&J. Musinskyorg66&C.J. Myersorg125&J.W.
Myrchaorg140&B. Naikorg49&R. Nairorg85&B.K. Nandiorg49&R. Naniaorg54,org10&E.
Nappiorg53&A. Narayanorg49&M.U. Naruorg15&A.F. Nassirpourorg81&H. Natal da
Luzorg120&C. Nattrassorg128&S.R. Navarroorg45&K. Nayakorg86&R. Nayakorg49&T.K.
Nayakorg139&S. Nazarenkoorg106&R.A. Negrao De Oliveiraorg70,org35&L.
Nellenorg71&S.V. Nesboorg37&G. Neskovicorg40&F. Ngorg125&M. Nicassioorg104&J.
Niedzielaorg140,org35&B.S. Nielsenorg89&S. Nikolaevorg88&S. Nikulinorg88&V.
Nikulinorg96&F. Noferiniorg10,org54&P. Nomokonovorg76&G. Noorenorg64&J.C.C.
Norisorg45&J. Normanorg79&A. Nyaninorg88&J. Nystrandorg23&H. Ohorg145&A.
Ohlsonorg102&J. Oleniaczorg140&A.C. Oliveira Da Silvaorg120&M.H.
Oliverorg144&J. Onderwaaterorg104&C. Oppedisanoorg59&R. Oravaorg44&M.
Oravecorg115&A. Ortiz Velasquezorg71&A. Oskarssonorg81&J. Otwinowskiorg117&K.
Oyamaorg82&Y. Pachmayerorg102&V. Pacikorg89&D. Paganoorg138&G. Paićorg71&P.
Palniorg6&J. Panorg141&A.K. Pandeyorg49&S. Panebiancoorg135&V. Papikyanorg1&P.
Pareekorg50&J. Parkorg61&J.E. Parkkilaorg126&S. Parmarorg98&A.
Passfeldorg142&S.P. Pathakorg125&R.N. Patraorg139&B. Paulorg59&H. Peiorg6&T.
Peitzmannorg64&X. Pengorg6&L.G. Pereiraorg72&H. Pereira Da Costaorg135&D.
Peresunkoorg88&E. Perez Lezamaorg70&V. Peskovorg70&Y. Pestovorg4&V.
Petráčekorg38&M. Petroviciorg48&C. Pettaorg29&R.P. Pezziorg72&S. Pianoorg60&M.
Piknaorg14&P. Pillotorg113&L.O.D.L. Pimentelorg89&O. Pinazzaorg54,org35&L.
Pinskyorg125&S. Pisanoorg52&D.B. Piyarathnaorg125&M. Płoskońorg80&M.
Planinicorg97&F. Pliquettorg70&J. Plutaorg140&S. Pochybovaorg143&P.L.M.
Podesta-Lermaorg119&M.G. Poghosyanorg95&B. Polichtchoukorg91&N. Poljakorg97&W.
Poonsawatorg114&A. Poporg48&H. Poppenborgorg142&S. Porteboeuf-
Houssaisorg132&V. Pozdniakovorg76&S.K. Prasadorg3&R. Preghenellaorg54&F.
Prinoorg59&C.A. Pruneauorg141&I. Pshenichnovorg63&M. Puccioorg27&V.
Puninorg106&J. Putschkeorg141&S. Rahaorg3&S. Rajputorg99&J. Rakorg126&A.
Rakotozafindrabeorg135&L. Ramelloorg33&F. Ramiorg134&R. Raniwalaorg100&S.
Raniwalaorg100&S.S. Räsänenorg44&B.T. Rascanuorg70&V. Ratzaorg43&I.
Ravasengaorg32&K.F. Readorg128,org95&K. Redlichorg85orgIV&A. Rehmanorg23&P.
Reicheltorg70&F. Reidtorg35&X. Renorg6&R. Renfordtorg70&A. Reshetinorg63&J.-P.
Revolorg10&K. Reygersorg102&V. Riabovorg96&T. Richertorg64,org81&M.
Richterorg22&P. Riedlerorg35&W. Rieglerorg35&F. Riggiorg29&C. Risteaorg69&S.P.
Rodeorg50&M. Rodríguez Cahuantziorg45&K. Røedorg22&R. Rogalevorg91&E.
Rogochayaorg76&D. Rohrorg35&D. Röhrichorg23&P.S. Rokitaorg140&F.
Ronchettiorg52&E.D. Rosasorg71&K. Roslonorg140&P. Rosnetorg132&A.
Rossiorg30&A. Rotondiorg137&F. Roukoutakisorg84&C. Royorg134&P. Royorg107&O.V.
Ruedaorg71&R. Ruiorg26&B. Rumyantsevorg76&A. Rustamovorg87&E.
Ryabinkinorg88&Y. Ryabovorg96&A. Rybickiorg117&S. Saarinenorg44&S.
Sadhuorg139&S. Sadovskyorg91&K. Šafaříkorg35&S.K. Sahaorg139&B. Sahooorg49&P.
Sahooorg50&R. Sahooorg50&S. Sahooorg67&P.K. Sahuorg67&J. Sainiorg139&S.
Sakaiorg131&M.A. Salehorg141&S. Sambyalorg99&V. Samsonovorg96,org92&A.
Sandovalorg73&A. Sarkarorg74&D. Sarkarorg139&N. Sarkarorg139&P.
Sarmaorg42&M.H.P. Sasorg64&E. Scapparoneorg54&F. Scarlassaraorg30&B.
Schaeferorg95&H.S. Scheidorg70&C. Schiauaorg48&R. Schickerorg102&C.
Schmidtorg104&H.R. Schmidtorg101&M.O. Schmidtorg102&M. Schmidtorg101&N.V.
Schmidtorg95,org70&J. Schukraftorg35&Y. Schutzorg35,org134&K. Schwarzorg104&K.
Schwedaorg104&G. Scioliorg28&E. Scomparinorg59&M. Šefčíkorg39&J.E.
Segerorg16&Y. Sekiguchiorg130&D. Sekihataorg46&I. Selyuzhenkovorg104,org92&K.
Senosiorg74&S. Senyukovorg134&E. Serradillaorg73&P. Settorg49&A.
Sevcencoorg69&A. Shabanovorg63&A. Shabetaiorg113&R. Shahoyanorg35&W.
Shaikhorg107&A. Shangaraevorg91&A. Sharmaorg98&A. Sharmaorg99&M.
Sharmaorg99&N. Sharmaorg98&A.I. Sheikhorg139&K. Shigakiorg46&M.
Shimomuraorg83&S. Shirinkinorg65&Q. Shouorg6,org110&K. Shtejerorg27&Y.
Sibiriakorg88&S. Siddhantaorg55&K.M. Sielewiczorg35&T. Siemiarczukorg85&D.
Silvermyrorg81&G. Simatovicorg90&G. Simonettiorg35,org103&R.
Singarajuorg139&R. Singhorg86&R. Singhorg99&V. Singhalorg139&T. Sinhaorg107&B.
Sitarorg14&M. Sittaorg33&T.B. Skaaliorg22&M. Slupeckiorg126&N.
Smirnovorg144&R.J.M. Snellingsorg64&T.W. Snellmanorg126&J. Songorg19&F.
Soramelorg30&S. Sorensenorg128&F. Sozziorg104&I. Sputowskaorg117&J.
Stachelorg102&I. Stanorg69&P. Stankusorg95&E. Stenlundorg81&D.
Stoccoorg113&M.M. Storetvedtorg37&P. Strmenorg14&A.A.P. Suaideorg120&T.
Sugitateorg46&C. Suireorg62&M. Suleymanovorg15&M. Suljicorg35,org26&R.
Sultanovorg65&M. Šumberaorg94&S. Sumowidagdoorg51&K. Suzukiorg112&S.
Swainorg67&A. Szaboorg14&I. Szarkaorg14&U. Tabassamorg15&J.
Takahashiorg121&G.J. Tambaveorg23&N. Tanakaorg131&M. Tarhiniorg113&M.
Tariqorg17&M.G. Tarzilaorg48&A. Tauroorg35&G. Tejeda Muñozorg45&A.
Telescaorg35&C. Terrevoliorg30&B. Teyssierorg133&D. Thakurorg50&S.
Thakurorg139&D. Thomasorg118&F. Thoresenorg89&R. Tieulentorg133&A.
Tikhonovorg63&A.R. Timminsorg125&A. Toiaorg70&N. Topilskayaorg63&M.
Toppiorg52&S.R. Torresorg119&S. Tripathyorg50&S. Trogoloorg27&G.
Trombettaorg34&L. Tropporg39&V. Trubnikovorg2&W.H. Trzaskaorg126&T.P.
Trzcinskiorg140&B.A. Trzeciakorg64&T. Tsujiorg130&A. Tumkinorg106&R.
Turrisiorg57&T.S. Tveterorg22&K. Ullalandorg23&E.N. Umakaorg125&A.
Urasorg133&G.L. Usaiorg25&A. Utrobicicorg97&M. Valaorg115&J.W. Van
Hoorneorg35&M. van Leeuwenorg64&P. Vande Vyvreorg35&D. Vargaorg143&A.
Vargasorg45&M. Vargyasorg126&R. Varmaorg49&M. Vasileiouorg84&A.
Vasilievorg88&A. Vauthierorg79&O. Vázquez Doceorg103,org116&V.
Vecherninorg111&A.M. Veenorg64&E. Vercellinorg27&S. Vergara Limónorg45&L.
Vermuntorg64&R. Vernetorg7&R. Vértesiorg143&L. Vickovicorg36&J.
Viinikainenorg126&Z. Vilakaziorg129&O. Villalobos Baillieorg108&A. Villatoro
Telloorg45&A. Vinogradovorg88&T. Virgiliorg31&V. Vislaviciusorg89,org81&A.
Vodopyanovorg76&M.A. Völklorg101&K. Voloshinorg65&S.A. Voloshinorg141&G.
Volpeorg34&B. von Hallerorg35&I. Vorobyevorg116,org103&D. Voscekorg115&D.
Vranicorg104,org35&J. Vrlákováorg39&B. Wagnerorg23&H. Wangorg64&M. Wangorg6&Y.
Watanabeorg131&M. Weberorg112&S.G. Weberorg104&A. Wegrzynekorg35&D.F.
Weiserorg102&S.C. Wenzelorg35&J.P. Wesselsorg142&U. Westerhofforg142&A.M.
Whiteheadorg124&J. Wiechulaorg70&J. Wikneorg22&G. Wilkorg85&J.
Wilkinsonorg54&G.A. Willemsorg142,org35&M.C.S. Williamsorg54&E.
Willsherorg108&B. Windelbandorg102&W.E. Wittorg128&R. Xuorg6&S. Yalcinorg78&K.
Yamakawaorg46&S. Yanoorg46&Z. Yinorg6&H. Yokoyamaorg79,org131&I.-K.
Yooorg19&J.H. Yoonorg61&V. Yurchenkoorg2&V. Zaccoloorg59&A. Zamanorg15&C.
Zampolliorg35&H.J.C. Zanoliorg120&N. Zardoshtiorg108&A. Zarochentsevorg111&P.
Závadaorg68&N. Zaviyalovorg106&H. Zbroszczykorg140&M. Zhalovorg96&X.
Zhangorg6&Y. Zhangorg6&Z. Zhangorg6,org132&C. Zhaoorg22&V.
Zherebchevskiiorg111&N. Zhigarevaorg65&D. Zhouorg6&Y. Zhouorg89&Z.
Zhouorg23&H. Zhuorg6&J. Zhuorg6&Y. Zhuorg6&A. Zichichiorg28,org10&M.B.
Zimmermannorg35&G. Zinovjevorg2&J. Zmeskalorg112&S. Zouorg6&

## Affiliation notes

org*Deceased

orgIDipartimento DET del Politecnico di Torino, Turin, Italy

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

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

orgIVInstitute of Theoretical Physics, University of Wroclaw, Poland

## Collaboration Institutes

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

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

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

org4Budker Institute for Nuclear Physics, Novosibirsk, Russia

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

org6Central China Normal University, Wuhan, China

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

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

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

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

org11Chicago State University, Chicago, Illinois, United States

org12China Institute of Atomic Energy, Beijing, China

org13Chonbuk National University, Jeonju, Republic of Korea

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

org15COMSATS Institute of Information Technology (CIIT), Islamabad, Pakistan

org16Creighton University, Omaha, Nebraska, United States

org17Department of Physics, Aligarh Muslim University, Aligarh, India

org18Department of Physics, Ohio State University, Columbus, Ohio, United
States

org19Department of Physics, Pusan National University, Pusan, Republic of
Korea

org20Department of Physics, Sejong University, Seoul, Republic of Korea

org21Department of Physics, University of California, Berkeley, California,
United States

org22Department of Physics, University of Oslo, Oslo, Norway

org23Department of Physics and Technology, University of Bergen, Bergen,
Norway

org24Dipartimento di Fisica dell’Università ’La Sapienza’ and Sezione INFN,
Rome, Italy

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

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

org27Dipartimento di Fisica dell’Università and Sezione INFN, Turin, Italy

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

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

org30Dipartimento di Fisica e Astronomia dell’Università and Sezione INFN,
Padova, Italy

org31Dipartimento di Fisica ‘E.R. Caianiello’ dell’Università and Gruppo
Collegato INFN, Salerno, Italy

org32Dipartimento DISAT del Politecnico and Sezione INFN, Turin, Italy

org33Dipartimento di Scienze e Innovazione Tecnologica dell’Università del
Piemonte Orientale and INFN Sezione di Torino, Alessandria, Italy

org34Dipartimento Interateneo di Fisica ‘M. Merlin’ and Sezione INFN, Bari,
Italy

org35European Organization for Nuclear Research (CERN), Geneva, Switzerland

org36Faculty of Electrical Engineering, Mechanical Engineering and Naval
Architecture, University of Split, Split, Croatia

org37Faculty of Engineering and Science, Western Norway University of Applied
Sciences, Bergen, Norway

org38Faculty of Nuclear Sciences and Physical Engineering, Czech Technical
University in Prague, Prague, Czech Republic

org39Faculty of Science, P.J. Šafárik University, Košice, Slovakia

org40Frankfurt Institute for Advanced Studies, Johann Wolfgang Goethe-
Universität Frankfurt, Frankfurt, Germany

org41Gangneung-Wonju National University, Gangneung, Republic of Korea

org42Gauhati University, Department of Physics, Guwahati, India

org43Helmholtz-Institut für Strahlen- und Kernphysik, Rheinische Friedrich-
Wilhelms-Universität Bonn, Bonn, Germany

org44Helsinki Institute of Physics (HIP), Helsinki, Finland

org45High Energy Physics Group, Universidad Autónoma de Puebla, Puebla, Mexico

org46Hiroshima University, Hiroshima, Japan

org47Hochschule Worms, Zentrum für Technologietransfer und Telekommunikation
(ZTT), Worms, Germany

org48Horia Hulubei National Institute of Physics and Nuclear Engineering,
Bucharest, Romania

org49Indian Institute of Technology Bombay (IIT), Mumbai, India

org50Indian Institute of Technology Indore, Indore, India

org51Indonesian Institute of Sciences, Jakarta, Indonesia

org52INFN, Laboratori Nazionali di Frascati, Frascati, Italy

org53INFN, Sezione di Bari, Bari, Italy

org54INFN, Sezione di Bologna, Bologna, Italy

org55INFN, Sezione di Cagliari, Cagliari, Italy

org56INFN, Sezione di Catania, Catania, Italy

org57INFN, Sezione di Padova, Padova, Italy

org58INFN, Sezione di Roma, Rome, Italy

org59INFN, Sezione di Torino, Turin, Italy

org60INFN, Sezione di Trieste, Trieste, Italy

org61Inha University, Incheon, Republic of Korea

org62Institut de Physique Nucléaire d’Orsay (IPNO), Institut National de
Physique Nucléaire et de Physique des Particules (IN2P3/CNRS), Université de
Paris-Sud, Université Paris-Saclay, Orsay, France

org63Institute for Nuclear Research, Academy of Sciences, Moscow, Russia

org64Institute for Subatomic Physics, Utrecht University/Nikhef, Utrecht,
Netherlands

org65Institute for Theoretical and Experimental Physics, Moscow, Russia

org66Institute of Experimental Physics, Slovak Academy of Sciences, Košice,
Slovakia

org67Institute of Physics, Homi Bhabha National Institute, Bhubaneswar, India

org68Institute of Physics of the Czech Academy of Sciences, Prague, Czech
Republic

org69Institute of Space Science (ISS), Bucharest, Romania

org70Institut für Kernphysik, Johann Wolfgang Goethe-Universität Frankfurt,
Frankfurt, Germany

org71Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México,
Mexico City, Mexico

org72Instituto de Física, Universidade Federal do Rio Grande do Sul (UFRGS),
Porto Alegre, Brazil

org73Instituto de Física, Universidad Nacional Autónoma de México, Mexico
City, Mexico

org74iThemba LABS, National Research Foundation, Somerset West, South Africa

org75Johann-Wolfgang-Goethe Universität Frankfurt Institut für Informatik,
Fachbereich Informatik und Mathematik, Frankfurt, Germany

org76Joint Institute for Nuclear Research (JINR), Dubna, Russia

org77Korea Institute of Science and Technology Information, Daejeon, Republic
of Korea

org78KTO Karatay University, Konya, Turkey

org79Laboratoire de Physique Subatomique et de Cosmologie, Université
Grenoble-Alpes, CNRS-IN2P3, Grenoble, France

org80Lawrence Berkeley National Laboratory, Berkeley, California, United
States

org81Lund University Department of Physics, Division of Particle Physics,
Lund, Sweden

org82Nagasaki Institute of Applied Science, Nagasaki, Japan

org83Nara Women’s University (NWU), Nara, Japan

org84National and Kapodistrian University of Athens, School of Science,
Department of Physics , Athens, Greece

org85National Centre for Nuclear Research, Warsaw, Poland

org86National Institute of Science Education and Research, Homi Bhabha
National Institute, Jatni, India

org87National Nuclear Research Center, Baku, Azerbaijan

org88National Research Centre Kurchatov Institute, Moscow, Russia

org89Niels Bohr Institute, University of Copenhagen, Copenhagen, Denmark

org90Nikhef, National institute for subatomic physics, Amsterdam, Netherlands

org91NRC Kurchatov Institute IHEP, Protvino, Russia

org92NRNU Moscow Engineering Physics Institute, Moscow, Russia

org93Nuclear Physics Group, STFC Daresbury Laboratory, Daresbury, United
Kingdom

org94Nuclear Physics Institute of the Czech Academy of Sciences, Řež u Prahy,
Czech Republic

org95Oak Ridge National Laboratory, Oak Ridge, Tennessee, United States

org96Petersburg Nuclear Physics Institute, Gatchina, Russia

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

org98Physics Department, Panjab University, Chandigarh, India

org99Physics Department, University of Jammu, Jammu, India

org100Physics Department, University of Rajasthan, Jaipur, India

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

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

org103Physik Department, Technische Universität München, Munich, Germany

org104Research Division and ExtreMe Matter Institute EMMI, GSI
Helmholtzzentrum für Schwerionenforschung GmbH, Darmstadt, Germany

org105Rudjer Bošković Institute, Zagreb, Croatia

org106Russian Federal Nuclear Center (VNIIEF), Sarov, Russia

org107Saha Institute of Nuclear Physics, Homi Bhabha National Institute,
Kolkata, India

org108School of Physics and Astronomy, University of Birmingham, Birmingham,
United Kingdom

org109Sección Física, Departamento de Ciencias, Pontificia Universidad
Católica del Perú, Lima, Peru

org110Shanghai Institute of Applied Physics, Shanghai, China

org111St. Petersburg State University, St. Petersburg, Russia

org112Stefan Meyer Institut für Subatomare Physik (SMI), Vienna, Austria

org113SUBATECH, IMT Atlantique, Université de Nantes, CNRS-IN2P3, Nantes,
France

org114Suranaree University of Technology, Nakhon Ratchasima, Thailand

org115Technical University of Košice, Košice, Slovakia

org116Technische Universität München, Excellence Cluster ’Universe’, Munich,
Germany

org117The Henryk Niewodniczanski Institute of Nuclear Physics, Polish Academy
of Sciences, Cracow, Poland

org118The University of Texas at Austin, Austin, Texas, United States

org119Universidad Autónoma de Sinaloa, Culiacán, Mexico

org120Universidade de São Paulo (USP), São Paulo, Brazil

org121Universidade Estadual de Campinas (UNICAMP), Campinas, Brazil

org122Universidade Federal do ABC, Santo Andre, Brazil

org123University College of Southeast Norway, Tonsberg, Norway

org124University of Cape Town, Cape Town, South Africa

org125University of Houston, Houston, Texas, United States

org126University of Jyväskylä, Jyväskylä, Finland

org127University of Liverpool, Liverpool, United Kingdom

org128University of Tennessee, Knoxville, Tennessee, United States

org129University of the Witwatersrand, Johannesburg, South Africa

org130University of Tokyo, Tokyo, Japan

org131University of Tsukuba, Tsukuba, Japan

org132Université Clermont Auvergne, CNRS/IN2P3, LPC, Clermont-Ferrand, France

org133Université de Lyon, Université Lyon 1, CNRS/IN2P3, IPN-Lyon,
Villeurbanne, Lyon, France

org134Université de Strasbourg, CNRS, IPHC UMR 7178, F-67000 Strasbourg,
France, Strasbourg, France

org135 Université Paris-Saclay Centre d¿Études de Saclay (CEA), IRFU,
Department de Physique Nucléaire (DPhN), Saclay, France

org136Università degli Studi di Foggia, Foggia, Italy

org137Università degli Studi di Pavia, Pavia, Italy

org138Università di Brescia, Brescia, Italy

org139Variable Energy Cyclotron Centre, Homi Bhabha National Institute,
Kolkata, India

org140Warsaw University of Technology, Warsaw, Poland

org141Wayne State University, Detroit, Michigan, United States

org142Westfälische Wilhelms-Universität Münster, Institut für Kernphysik,
Münster, Germany

org143Wigner Research Centre for Physics, Hungarian Academy of Sciences,
Budapest, Hungary

org144Yale University, New Haven, Connecticut, United States

org145Yonsei University, Seoul, Republic of Korea