Anisotropic Flow of Charged Particles in Pb-Pb Colli sions at
ffiffiffiffiffiffiffiffi
s
NN
p
¼ 5.02 TeV
J. Adam et al.
*
(The ALICE Collaboration)
(Received 4 February 2016; published 1 April 2016)
We report the first results of elliptic (v
2
), triangular (v
3
), and quadrangular (v
4
) flow of charged particles
in Pb-Pb coll isions at a center-of-mass energy per nucleon pair of
ffiffiffiffiffiffiffiffi
s
NN
p
¼ 5.02 TeV with the ALICE
detector at the CERN Large Hadron Collider. The measurements are performed in the central
pseudorapidity region jηj < 0.8 and for the transverse momentum range 0 . 2 <p
T
< 5 GeV=c.
The anisotropic flow is measured using two-particle correlations with a pseudorapidity gap greater than
one unit and with the multiparticle cumula nt method. Compared to results from Pb-Pb collisions at
ffiffiffiffiffiffiffiffi
s
NN
p
¼ 2.76 TeV, the anisotropic flow coefficients v
2
, v
3
, and v
4
are found to increase by ð3.0 0.6Þ%,
ð4.3 1.4Þ%, and ð 10.2 3.8Þ%, respectively, in the centrality range 0%–50%. This increase can be
attributed mostly to an increase of the average transverse momentum between the two energies. The
measurements are found to be compatible with hydrody namic model calculations. This comparison
provides a unique opportunity to test the validity of the hydrodynamic picture and the power to further
discriminate between various possibilities for the temperature dependence of shear viscosity to entropy
density ratio of the produced matter in heavy-ion collisions at the highest energies.
DOI: 10.1103/PhysRevLett.116.132302
The goal of studies with relativistic heavy-ion collisions is to
in v estigate the quark-gluon plasma (QGP), a state of matter
where quarks and gluons mov e freely o v er distances that are
large in comparison to the typical size of a hadron. The
transition from normal nuclear matter to the QGP state is
expected to occur at extreme values of energy density
(0.2–0.5 GeV=fm
3
, according to lattice quantum chromody-
namics calculations [1,2]), which are accessible in ultrarela-
ti vistic heavy-ion collisions at the Large Hadron Collider
(LHC) [3,4]. The study of such collisions provides a unique
opportunity to probe the properties of the QGP in a region of
the QCD phase diagram where a crossover between the
deconfined phase and normal nuclear matter is expected [5–9].
Studies of the azimuthal anisotropy of particle produc-
tion have contributed significantly to the characterization of
the system created in heavy-ion collisions [10,11].
Anisotropic flow, which measures the momentum
anisotropy of the final-state particles, is sensitive both to
the initial geometry of the overlap region and to the
transport properties and equation of state of the system.
By using a general Fourier series decomposition of the
azimuthal distribution of produced particles,
dN
dφ
∝ 1 þ 2
X
∞
n¼1
v
n
cos½nðφ − Ψ
n
Þ; ð1Þ
anisotropic flow is quantified with coefficients v
n
and
corresponding symmetry planes Ψ
n
[12]. Because of the
approximately ellipsoidal shape of the overlap region in
noncentral heavy-ion collisions (i.e., collisions that corre-
spond to a large impact parameter), the dominant flow
coefficient is v
2
, referred to as elliptic flow. In the transition
from highest RHIC to LHC energies, elliptic flow increases
by 30% [13], as predicted by hydrodynamic models that
include viscous corrections [14–18]. Nonvanishing values
of higher anisotropic flow harmonics v
3
–v
6
at the LHC are
ascribed primarily to the response of the produced QGP to
fluctuations of the initial energy density profile of the
colliding nucleons [19–22]. Moreover, because of such
fluctuations, each flow harmonic v
n
has a distinct sym-
metry plane Ψ
n
and recent measurements of their inter-
correlations provide independent constraints on the QGP
properties [23]. The combination of all such results
demonstrates that the shear viscosity to entropy density
ratio (η=s) of the QGP produced in ultrarelativistic heavy-
ion collisions at RHIC and LHC has a value close to 1=4π,
a lower bound obtained in strong-coupling calculations
based on the AdS=CFT conjecture [24].
Recently, predictions from Niemi et al. on anisotropic
flow coefficients for Pb–Pb
ffiffiffiffiffiffiffiffi
s
NN
p
¼ 5.02 TeV collisions
using the Eskola-Kajantie-Ruuskanen-Tuominen model
were reported in Ref. [25]. These predictions have a special
emphasis on the discriminating power between various
parametrizations of the temperature dependence of η=s.It
was argued that in the transition from 2.76 to 5.02 TeV, the
elliptic flow estimated from two-particle correlations
(denoted further in the text as v
2
f2g, where the number
in the curly brackets indicates the number of particles that
*
Full author list given at the end of the article.
Published by the American Physical Society under the terms of
the Creative Commons Attribution 3.0 License. Further distri-
bution of this work must maintain attribution to the author(s) and
the published article’s title, journal citation, and DOI.
PRL 116, 132302 (2016)
PHYSICAL REVIEW LETTERS
week ending
1 APRIL 2016
0031-9007=16=116(13)=132302(12) 132302-1 © 2016 CERN, for the ALICE Collaboration
are used in correlation [26]) can increase, at most, ∼5% for
all centrality classes. Details of the increase depend on the
parametrization of η=sðTÞ. On the other hand, higher flow
harmonic observables, like v
3
f2g and v
4
f2g, are predicted
to increase more rapidly, 10%–30%. With a different
approach, where previously measured values of flow
harmonics at lower LHC energies are taken as a baseline,
Noronha-Hostler et al. [27] predict a larger increase for
both elliptic and triangular flow in peripheral compared to
central collisions in transition from 2.76 to 5.02 TeV. They
conclude that the anisotropic flow already reaches satu-
ration and its maximum value in central collisions at
2.76 TeV.
A necessary condition for the development of aniso-
tropic flow is the initial anisotropy in the interaction region
of the two colliding ions. These coordinate space anisot-
ropies are described in terms of eccentricities, which are not
directly accessible experimentally. Nonetheless, the theo-
retical modeling of such eccentricities is actively being
studied. For instance, hydrodynamic calculations based on
a MC-Glauber model and MC–Kharzeev-Levin-Nardi ini-
tial conditions do not agree on the details of the saturation
of elliptic flow at LHC energies [28]. However, with these
two initial state models, it was shown that the final spatial
eccentricity decreases monotonically as the collision
energy increases [28], and is expected to become negative
only at the very large collision energies available at the
LHC (see Fig. 9 in Ref. [28]).
In addition to the initial conditions, various other stages
of evolution of the system in a heavy-ion collision may
contribute to the development of anisotropic flow. At lower
energies, the state of the system will primarily resemble a
hadronic gas, and hadron rescattering is the dominant
contribution to the anisotropic flow. At higher energies,
anisotropic flow mostly develops in the thermalized color-
deconfined QGP phase. However, even at these higher
energies, the contribution from the hadronic phase can be
significant. The relative amount of time the system spends
in different phases varies with collision energy [28,29].
Radial flow, a measure for the average velocity of the
system’s collective radial expansion, also increases as a
function of collision energy, which translates into more
particles being transferred to a higher transverse momen-
tum (p
T
) region, thus leading to an increase in average
anisotropic flow values. On the other hand, the opposite
dependence of differential v
2
ðp
T
Þ is expected for light (an
increase at low p
T
) and heavy particles (a decrease at low
p
T
) as a function of collision energy, which might yield to
the saturation of the elliptic flow signal [28]. Finally, the
relative importance of various stages in the system evolu-
tion as a function of collision energy can also vary for each
flow coefficient [29].
The data used in this Letter were recorded with the
ALICE detector [30,31] in November 2015 in run 2 at the
LHC with Pb-Pb collisions at
ffiffiffiffiffiffiffiffi
s
NN
p
¼5.02 TeV. Minimum
bias Pb–Pb events were triggered by the coincidence of
signals from the V0 detector. The V0 detector is composed
of two arrays of scintillator counters, V0-A and V0-C,
which cover the pseudorapidity ranges 2.8 < η < 5.1 and
−3.7 < η < −1.7, respectively [30]. Centrality quantifies
the fraction of a geometrical cross section of the colliding
nuclei. It is determined using the sum of the amplitudes of
the V0-A and -C signals, which provides a resolution better
than 0.5% and up to 20% for central Pb-Pb collisions, and
better than 2% for peripheral collisions [32]. The off-line
event selection employs the information from two zero
degree calorimeters (ZDCs) [30] positioned 112.5 m from
the interaction point on either side. Beam background
events are removed using timing information from the V0
and the ZDCs, respectively. To ensure a uniform acceptance
and reconstruction efficiency in the pseudorapidity region
jηj < 0.8, only events with a reconstructed vertex within
10 cm from the center of the detector along the beam
direction were used. A sample of 140 k Pb-Pb collision
events passed the selection criteria. Only one low lumi-
nosity run (with a trigger rate of 27 Hz) was used, being
least affected by pileup and distortions from space charge in
the main tracking detector, the time projection cham-
ber (TPC).
Charged tracks are reconstructed using the ALICE inner
tracking system (ITS) and the TPC [30]. This combination
ensures a high detection efficiency, optimum momentum
resolution, and a minimum contribution from photon
conversions and secondary charged particles produced
either from the detector material or from weak decays.
In order to reduce the contamination from secondary
particles, only tracks with a distance of closest approach
to the interaction point of less than 3 cm, both in the
longitudinal and transverse directions, are accepted. The
tracking efficiency is calculated from a Monte Carlo
simulation that uses
HIJING
[33] to simulate particle
production.
GEANT
3 [34] is then used for transporting
simulated particles, followed by a full calculation of the
detector response (including the production of secondary
particles) and track reconstruction performed with the
ALICE reconstruction framework. The tracking efficiency
is ∼70% at p
T
∼ 0.2 GeV=c and increases to an approx-
imately constant value of ∼80% for p
T
> 1 GeV =c. The
p
T
resolution is better than 5% for the region presented in
this Letter. The systematic uncertainty related to the
nonuniform reconstruction efficiency was found to be at
the level of 1%. The flow coefficients from tracks that are
reconstructed from TPC space points alone were compared
to coefficients extracted from particles that used both
TPC clusters and ITS hits, which were found to agree
within ∼2%. This difference was taken into account in
the estimation of the systematic uncertainty. Altering the
selection criteria for the tracks reconstructed with the TPC
resulted in a variation of the results of 0.5%, at most. Other
selection criteria that have been scrutinized are the
PRL 116, 132302 (2016)
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centrality determination, e.g., using the silicon pixel detec-
tor (SPD), which contributed by less than 1%, the polarity
of the magnetic field of the ALICE detector and the
position of the reconstructed primary vertex, whose con-
tributions were found to be negligible. The systematic
uncertainties evaluated for each of the sources mentioned
above were added in quadrature to obtain the total
systematic uncertainty of the measurements.
In this Letter, we report the anisotropic flow measure-
ments obtained from two- and multiparticle cumulants,
using the approach proposed in Refs. [35–37]. These two
measurements have different sensitivities to flow fluctua-
tions and nonflow effects. Nonflow effects are azimuthal
correlations not associated with the symmetry planes and
usually arise from resonance decays and jets. Their con-
tributions are expected to be suppressed when using a large
pseudorapidity gap between particle pairs. Thus, in this
study, we require a pseudorapidity gap of jΔηj > 1. This
observable is denoted as v
n
f2; jΔηj > 1g. On the other
hand, nonflow contributions to multiparticle cumulants
v
n
f4g, v
n
f6g, v
n
f8g are found to be negligible in events
with large multiplicities characteristic of heavy-ion
collisions [38].
Figure 1(a) presents the centrality dependence of v
2
, v
3
,
and v
4
from two- and multiparticle cumulants, integrated
over the p
T
range 0.2 <p
T
< 5.0 GeV=c, for 2.76 and
5.02 TeV Pb-Pb collisions. To elucidate the energy evo-
lution of v
2
, v
3
, and v
4
, the ratios of anisotropic flow
measured at 5.02 to 2.76 TeVare presented in Figs. 1(b) and
1(c). Assuming that nonflow effects are suppressed by the
pseudorapidity gap, the remaining differences between
two- and multiparticle cumulants of v
2
can be related to
the strength of elliptic flow fluctuations, which are
expected to give a positive and a negative contribution
to the two- and multiparticle cumulant estimates, respec-
tively [11]. Moreover, the multiparticle cumulants v
2
f4g,
v
2
f6g, and v
2
f8g are all observed to agree within 1%,
which indicates that nonflow effects are largely suppressed.
It is seen that v
2
f2; jΔηj > 1g increases from central to
peripheral collisions and reaches a maximum value of
0.104 0.001 ðstatÞ0.002 ðsystÞ in the 40%–50% cen-
trality class. For the higher harmonics, i.e., v
3
and v
4
, the
values are smaller and the centrality dependence is much
weaker.
Furthermore, the predictions of anisotropic flow coef-
ficients v
n
from the previously mentioned hydrodynamic
model [27] are compared to the measurements in Fig. 1(a).
These predictions combine the changes in initial spatial
anisotropy and the hydrodynamic response (treated as
systematic uncertainty and shown by the width of the
bands). The predictions are compatible with the measured
anisotropic flow v
n
coefficients. At the same time, a
different hydrodynamic calculation [25], which employs
both constant η=s ¼ 0.20 and temperature dependent
η=s, can also describe the increase in anisotropic flow
measurements of v
2
[shown in Fig. 1(b)], v
3
and v
4
[see Fig. 1(c)]. In particular, among the different scenarios
proposed in Ref. [25], the measurements seem to favor a
constant η=s going from
ffiffiffiffiffiffiffiffi
s
NN
p
¼ 2.76 to 5.02 TeV Pb-Pb
collisions.
The increase of v
2
and v
3
from the two energies is rather
moderate, while for v
4
it is more pronounced. In addition,
none of the ratios of flow harmonics exhibit a significant
centrality dependence in the centrality range 0%–50%,
and thus the results of a fit with a constant value over
these ratios are reported. An increase of ð3.0 0.6Þ%,
ð4.3 1.4Þ%, and ð10.2 3.8Þ% is obtained for elliptic,
triangular, and quadrangular flow, respectively, over the
centrality range 0%–50% in Pb-Pb collisions when going
from 2.76 to 5.02 TeV. This increase of anisotropic flow is
compatible with theoretical predictions described in
Refs. [25,27]. Overall, these measurements support a
low value of η=s for the system created in Pb-Pb collisions
at
ffiffiffiffiffiffiffiffi
s
NN
p
¼ 5.02 TeV and seem to indicate that it does not
0.05
0.1
0.15
5.02 TeV
|>1}ηΔ{2, |
2
v
|>1}ηΔ{2, |
3
v
|>1}ηΔ{2, |
4
v
{4}
2
v
{6}
2
v
{8}
2
v
2.76 TeV
|>1}ηΔ{2, |
2
v
|>1}ηΔ{2, |
3
v
|>1}ηΔ{2, |
4
v
{4}
2
v
5.02 TeV, Ref. [27]
|>1}ηΔ{2, |
2
v
|>1}ηΔ{2, |
3
v
ALICE Pb-Pb Hydrodynamics
(a)
1
1.1
1.2
/s(T), param1η
/s = 0.20η
(b)
Hydrodynamics, Ref. [25]
2
v
3
v
4
v
0 1020304050607080
1
1.1
1.2
(c)
Ratio
Centrality percentile
n
v
Ratio
FIG. 1. (a) Anisotropic flow v
n
integrated over the p
T
range
0.2 <p
T
< 5.0 GeV=c, as a function of event centrality, for the
two-particle (with jΔηj > 1) and multiparticle cumulant methods.
Measurements for Pb-Pb collisions at
ffiffiffiffiffiffiffiffi
s
NN
p
¼ 5.02 (2.76) TeV
are shown by solid (open) markers [20]. The ratios of
v
2
f2; jΔηj > 1g (red), v
2
f4g (gray) and v
3
f2; jΔηj > 1g (blue),
v
4
f2; jΔηj > 1g (green) between Pb-Pb collisions at 5.02 and
2.76 TeV are presented in Figs. 1(b) and 1(c). Various hydro-
dynamic calculations are also presented [25,27]. The statistical
and systematical uncertainties are summed in quadrature (the
systematic uncertainty is smaller than the statistical uncertainty,
which is typically within 5%). Data points are shifted for
visibility.
PRL 116, 132302 (2016)
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132302-3
increase significantly with respect to Pb-Pb collisions
at
ffiffiffiffiffiffiffiffi
s
NN
p
¼ 2.76 TeV.
The anisotropic flow coefficients v
2
f2; jΔηj > 1g,
v
3
f2; jΔηj > 1g, and v
4
f2; jΔηj > 1g as a function of
transverse momentum (p
T
) are presented in Fig. 2 for
the 0% –5% and 30%–40% centrality classes. For the
0%–5% centrality class, at p
T
>2 GeV=c v
3
f2gis observed
to become larger than v
2
f2g, while v
4
f2g is compatible
with v
2
f2g, within uncertainties. For the 30%–40% central-
ity class, we see that v
2
f2g is higher than v
3
f2g and v
4
f2g
for the entire p
T
range measured, with no crossing of the
different order flow coefficients observed. Figure 2(c)
presents the p
T
differential v
2
f4g for the 10%–20%,
20%–30% and 30%–40% centrality classes. The v
2
f4g
decreases from midcentral to central collisions over the p
T
range measured. The comparison with the corresponding
measurements from Pb-Pb collisions at
ffiffiffiffiffiffiffiffi
s
NN
p
¼ 2.76 TeV
exhibits comparable values, as illustrated by the ratio of
v
2
f4g for the two energies in Fig. 2(d). This indicates
that the increase observed in the p
T
integrated flow results
seen in Fig. 1 can be attributed to an increase of mean
transverse momentum hp
T
i. The measurements of p
T
-
differential flow are more sensitive to initial conditions and
η=s, and they are expected to provide important informa-
tion to constrain further details of the theoretical calcu-
lations, e.g., determination of radial flow and freeze-out
conditions.
Figure 3 presents the comparison of the fully p
T
integrated v
2
measured in the 20%–30% centrality in
Pb-Pb collisions at the LHC with results at lower energies.
This integrated value in the full p
T
range is determined
using two methods. The first uses fits to the efficiency-
corrected charged-particle spectra and the p
T
differential
v
2
f4g presented in Fig. 2, extrapolated to p
T
¼ 0.
The error on the integrated v
2
is estimated both from the
uncertainty on the p
T
-differential measurements and from
different parametrizations that provide a good fit of the
data. The second calculates v
2
f4g using tracklets formed
from SPD hits in the ITS, which have an acceptance of
p
T
≳ 50 MeV=c. As each method uses different ALICE
subdetectors, they can provide independent measurements
of v
2
coefficients. For this centrality range, they agree
within 1% for both energies. The values presented in the
0
0.1
0.2
5.02 TeV
|>1}ηΔ{2, |
2
v
|>1}ηΔ{2, |
3
v
|>1}ηΔ{2, |
4
v
2.76 TeV
|>1}ηΔ{2, |
2
v
|>1}ηΔ{2, |
3
v
|>1}ηΔ{2, |
4
v
ALICE Pb-Pb 0%-5% (a)
012345
0
0.1
0.2
30%-40% (b)
0.1
0.2
0.3
0.4
(c)
2.76 TeV
10%-20%
20%-30%
30%-40%
5.02 TeV
10%-20%
20%-30%
30%-40%
ALICE Pb-Pb
)c (GeV/
T
p
012345
Ratio
0.9
1
1.1
(d)
(2.76 TeV){4}
2
v (5.02 TeV) / {4}
2
v
20%-30%
| > 1.0}ηΔ{2, |
n
v| > 1.0}ηΔ{2, |
n
v
)c (GeV/
T
p
{4}
2
v
FIG. 2. v
n
ðp
T
Þ using the two-particle cumulant method with jΔηj > 1 for (a) 0%–5% and (b) 30%–40% centrality classes; (c) v
2
ðp
T
Þ
using four-particle cumulant method for the centrality 10%–20%, 20%– 30%, and 30%–40%. Measurements for Pb-Pb collisions at
ffiffiffiffiffiffiffiffi
s
NN
p
¼ 2.76 TeV are also presented as shading. (d) The ratio of v
2
f4g in 20%–30% from two collision energies is also shown here.
The statistical and systematical uncertainties are summed in quadrature (the systematic uncertainty is smaller than the statistical
uncertainty, which is typically within 5%).
(GeV)
NN
s
1 10
2
10
3
10
4
10
2
v
0.08−
0.06−
0.04−
0.02−
0
0.02
0.04
0.06
0.08
ALICE
STAR
PHOBOS
PHENIX
NA49
CERES
E877
EOS
E895
FOPI
FIG. 3. Integrated elliptic flow (v
2
f4g) for the 20%–30% most
central Pb-Pb collisions at
ffiffiffiffiffiffiffiffi
s
NN
p
¼ 5.02 TeV compared with v
2
measurements at lower energies with similar centralities (see
Ref. [13] for references to all data points).
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figure are weighted averages of these two measurements,
using the inverse of the variance of each of them as weights.
A continuous increase of anisotropic flow for this centrality
has been observed from SPS and RHIC to LHC energies.
For these fully p
T
integrated coefficients, an increase of
ð4.9 1.9Þ% is observed going from
ffiffiffiffiffiffiffiffi
s
NN
p
¼ 2.76 to
5.02 TeV, which is close to the values of the previously
mentioned hydrodynamic calculations [25,27].
In summary, we have presented the first anisotropic
flow measurements of charged particles in Pb-Pb collisions
at
ffiffiffiffiffiffiffiffi
s
NN
p
¼ 5.02 TeV at the LHC. An average increase
of ð3.0 0.6Þ%, ð4.3 1.4Þ%, and ð10.2 3.8Þ% is
observed for the transverse momentum integrated elliptic,
triangular, and quadrangular flow, respectively, over the
centrality range 0%–50%, going from 2.76 to 5.02 TeV.
The transverse momentum dependence of anisotropic flow
has also been investigated, and it does not change appreci-
ably between the two LHC energies. Therefore, the
increase in integrated flow coefficients can be attributed
mostly to an increase in average transverse momentum. The
measurements are found to be compatible with predictions
from hydrodynamic models [25,27]. Further comparisons
of p
T
-differential flow measurements and theoretical cal-
culations, which are not available at this time, will provide
extra constraints on the initial conditions and the transport
properties of the QGP.
The ALICE Collaboration would like to thank all of 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 centers 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: the
State Committee of Science, the World Federation of
Scientists (WFS), and Swiss Fonds Kidagan, Armenia;
Conselho Nacional de Desenvolvimento Científico e
Tecnológico (CNPq), Financiadora de Estudos e Projetos
(FINEP), Fundação de Amparo à Pesquisa do Estado de Sáo
Paulo (FAPESP); the National Natural Science Foundation
of China (NSFC), the Chinese Ministry of Education
(CMOE), and the Ministry of Science and Technology of
China (MSTC); the Ministry of Education and Youth of the
Czech Republic; the Danish Natural Science Research
Council, the Carlsberg Foundation, and the Danish
National Research Foundation; the European Research
Council under the European Community’s Seventh
Framework Programme; the Helsinki Institute of Physics
and the Academy of Finland; French CNRS-IN2P3, the
“Region Pays de Loire,” the “Region Alsace,” the “Region
Auvergne,” and CEA, France; German Bundesministerium
fur Bildung, Wissenschaft, Forschung und Technologie
(BMBF), and the Helmholtz Association; the General
Secretariat for Research and Technology, Ministry
of Development, Greece; the National Research,
Development and Innovation Office (NKFIH), Hungary;
the Department of Atomic Energy and Department of
Science and Technology of the Government of India;
Istituto Nazionale di Fisica Nucleare (INFN) and Centro
Fermi—Museo Storico della Fisica e Centro Studi e
Ricerche “Enrico Fermi,” Italy; the Japan Society for the
Promotion of Science (JSPS) KAKENHI and MEXT, Japan;
the Joint Institute for Nuclear Research, Dubna; the National
Research Foundation of Korea (NRF); Consejo Nacional de
Cienca y Tecnologia (CONACYT), Direccion General de
Asuntos del Personal Academico(DGAPA), México,
Amerique Latine Formation academique–European
Commission (ALFA-EC), and the EPLANET Program
(European Particle Physics Latin American Network);
Stichting voor Fundamenteel Onderzoek der Materie
(FOM) and the Nederlandse Organisatie voor
Wetenschappelijk Onderzoek (NWO), Netherlands;
Research Council of Norway (NFR); National Science
Centre, Poland; Ministry of National Education and
Institute for Atomic Physics and National Council of
Scientific Research in Higher Education (CNCSI-
UEFISCDI), Romania; the Ministry of Education and
Science of Russian Federation, the Russian Academy of
Sciences, the Russian Federal Agency of Atomic Energy,
the Russian Federal Agency for Science and Innovations,
and the Russian Foundation for Basic Research; the
Ministry of Education of Slovakia; the Department of
Science and Technology, South Africa; Centro de
Investigaciones Energeticas, Medioambientales y
Tecnologicas (CIEMAT), E-Infrastructure shared between
Europe and Latin America (EELA), Ministerio de
Economía y Competitividad (MINECO) of Spain, Xunta
de Galicia (Consellería de Educación), Centro de
Aplicaciones Tecnológicas y Desarrollo Nuclear
(CEADEN), Cubaenergía, Cuba, and IAEA (International
Atomic Energy Agency); the Swedish Research Council
(VR) and the Knut and Alice Wallenberg Foundation
(KAW); the Ukraine Ministry of Education and Science;
the United Kingdom Science and Technology Facilities
Council (STFC); the United States Department of Energy,
the United States National Science Foundation; Ministry of
Science, Education and Sports of Croatia and Unity through
Knowledge Fund, Croatia; Council of Scientific and
Industrial Research (CSIR), New Delhi, India; and
Pontificia Universidad Católica del Perú.
[1] S. Borsanyi, G. Endrodi, Z. Fodor, A. Jakovac, S. D. Katz,
S. Krieg, C. Ratti, and K. K. Szabo, The QCD equation of
state with dynamical qua rks, J. Hi gh Energy Phys. 11 (2010)
077.
PRL 116, 132302 (2016)
PHYSICAL REVIEW LETTERS
week ending
1 APRIL 2016
132302-5