2016 159 15 June

Higher harmonic flow coefficients of identified hadrons in Pb–Pb collisions at
$\mathbf{\sqrt{s_{\mathrm{{\mathbf{NN}}}}}}$ = 2.76 TeV Higher harmonic flow
at the LHC

ALICE CollaborationSee Appendix B for the list of collaboration members ALICE
Collaboration

The elliptic, triangular, quadrangular and pentagonal anisotropic flow
coefficients for $\pi^{\pm}$, $\mathrm{K}^{\pm}$ and p+$\overline{\mathrm{p}}$
in Pb–Pb collisions at $\sqrt{s_{\mathrm{{NN}}}}=2.76$ TeV were measured with
the ALICE detector at the Large Hadron Collider. The results were obtained
with the Scalar Product method, correlating the identified hadrons with
reference particles from a different pseudorapidity region. Effects not
related to the common event symmetry planes (non-flow) were estimated using
correlations in pp collisions and were subtracted from the measurement. The
obtained flow coefficients exhibit a clear mass ordering for transverse
momentum ($p_{\mathrm{T}}$) values below $\approx$ 3 GeV/$c$. In the
intermediate $p_{\mathrm{T}}$ region ($3<p_{\mathrm{T}}<6$ GeV/$c$), particles
group at an approximate level according to the number of constituent quarks,
suggesting that coalescence might be the relevant particle production
mechanism in this region. The results for $p_{\mathrm{T}}<3$ GeV/$c$ are
described fairly well by a hydrodynamical model (iEBE-VISHNU) that uses
initial conditions generated by A Multi-Phase Transport model (AMPT) and
describes the expansion of the fireball using a value of 0.08 for the ratio of
shear viscosity to entropy density ($\eta/s$), coupled to a hadronic cascade
model (UrQMD). Finally, expectations from AMPT alone fail to quantitatively
describe the measurements for all harmonics throughout the measured transverse
momentum region. However, the comparison to the AMPT model highlights the
importance of the late hadronic rescattering stage to the development of the
observed mass ordering at low values of $p_{\mathrm{T}}$ and of coalescence as
a particle production mechanism for the particle type grouping at intermediate
values of $p_{\mathrm{T}}$ for all harmonics.

###### Contents

  1. 1 Introduction
  2. 2 Experimental setup
  3. 3 Event sample, track selection and particle identification
    1. 3.1 Trigger selection and data sample
    2. 3.2 Track selection
    3. 3.3 Identification of $\pi^{\pm}$, $\mathrm{K}^{\pm}$ and $\mathrm{p}$+$\overline{\mathrm{p}}$
  4. 4 Analysis technique
    1. 4.1 Scalar Product method
    2. 4.2 Estimation of non-flow correlations
  5. 5 Systematic uncertainties
  6. 6 Results and discussion
    1. 6.1 Centrality dependence of flow harmonics
    2. 6.2 Evolution of flow harmonics in ultra-central Pb–Pb collisions
    3. 6.3 Mass ordering
    4. 6.4 Test of scaling properties
    5. 6.5 Comparison with models
      1. 6.5.1 Comparison with iEBE-VISHNU
      2. 6.5.2 Comparison with AMPT
  7. 7 Conclusions
  8. A Additional figures
    1. A.1 Integrated $v_{n}$
    2. A.2 NCQ scaling
    3. A.3 $KE_{\mathrm{T}}$ scaling
  9. B The ALICE Collaboration

##  1 Introduction

Quantum chromodynamics (QCD) calculations on the lattice [1, 2] suggest that
at high values of temperature and energy density a transition takes place from
ordinary nuclear matter to a state where the constituents, the quarks and the
gluons, are deconfined. This state of matter is called the quark-gluon plasma
(QGP) [3, 4, 5]. The aim of the heavy-ion program at the Large Hadron Collider
(LHC) is to study the QGP properties, such as the equation of state, the speed
of sound in the medium, and the value of the ratio of shear viscosity to
entropy density ($\eta/s$).

One of the important observables sensitive to the properties of the QGP is the
azimuthal distribution of particles emitted in the plane transverse to the
beam direction. In non-central collisions between two heavy ions the overlap
region is not isotropic. This spatial anisotropy of the overlap region is
transformed into an anisotropy in momentum space initially through
interactions between partons and at later stages between the produced
particles. The resulting anisotropy is usually expressed in terms of a Fourier
series in azimuthal angle $\varphi$ [6, 7] according to

$E\frac{\mathrm{d}^{3}N}{\mathrm{d}p^{3}}=\frac{1}{2\pi}\frac{\mathrm{d}^{2}N}{p_{\mathrm{T}}\mathrm{d}p_{\mathrm{T}}\mathrm{d}\eta}\Big{\\{}1+2\sum_{n=1}^{\infty}v_{n}(p_{\mathrm{T}},\eta)\cos[n(\varphi-\Psi_{n})]\Big{\\}},$
(1)

where $E$, $N$, $p$, $p_{\mathrm{T}}$, $\varphi$ and $\eta$ are the energy,
particle yield, total momentum, transverse momentum, azimuthal angle and
pseudorapidity of particles, respectively, and $\Psi_{n}$ is the azimuthal
angle of the symmetry plane of the $n^{\mathrm{th}}$-order harmonic [8, 9, 10,
11]. The $n^{\mathrm{th}}$-order flow coefficients are denoted as $v_{n}$ and
can be calculated as

$v_{n}=\langle{\cos[n(\varphi-\Psi_{n})]}\rangle,$ (2)

where the brackets denote an average over all particles in all events. Since
the symmetry planes are not accessible experimentally, the flow coefficients
are estimated solely from the azimuthal angles of the produced particles. The
second Fourier coefficient, $v_{2}$, measures the elliptic flow, i.e. the
momentum space azimuthal anisotropy of particle emission relative to the
second harmonic symmetry plane. The study of $v_{2}$ at both the Relativistic
Heavy Ion Collider (RHIC) and the LHC contributed significantly to the
realisation that the produced system can be described as a strongly-coupled
quark-gluon plasma (sQGP) with a small value of $\eta/s$, very close to the
conjectured lower limit of $1/4\pi$ from AdS/CFT [12].

In addition, the overlap region of the colliding nuclei exhibits an irregular
shape [13, 8, 9, 10, 11]. The irregularities originate from the initial
density profile of nucleons participating in the collision, which is not
isotropic and differs from one event to the other. This, in turn, causes the
symmetry plane of the irregular shape to fluctuate in every event around the
reaction plane, defined by the impact parameter vector and the beam axis, and
also gives rise to the additional higher harmonic symmetry planes $\Psi_{n}$.
The initial state fluctuations yield higher order flow harmonics such as
$v_{3}$, $v_{4}$, and $v_{5}$ that are usually referred to as triangular,
quadrangular, and pentagonal flow, respectively. Recent calculations [14, 15]
suggest that their transverse momentum dependence is a more sensitive probe
than elliptic flow not only of the initial geometry and its fluctuations, but
also of $\eta/s$. The first measurements of the $p_{\mathrm{T}}$-differential
$v_{n}$, denoted as $v_{n}(p_{\mathrm{T}})$, of charged particles at the LHC
[16, 17, 18] provided a strong testing ground for hydrodynamical calculations
that attempt to describe the dynamical evolution of the system created in
heavy-ion collisions.

An additional challenge for hydrodynamical calculations and a constraint on
both the initial conditions and $\eta/s$ can be provided by studying the flow
coefficients of Eq. 2 as a function of collision centrality and transverse
momentum for different particle species. The first results of such studies at
RHIC [19, 20, 21, 22] and the LHC [23, 24] revealed that an interplay of
radial flow (the average velocity of the system’s collective radial expansion)
and anisotropic flow leads to a characteristic mass dependence of
$v_{2}(p_{\mathrm{T}})$ [25, 26, 27] for $p_{\mathrm{T}}<3$ GeV/$c$. For
higher values of transverse momentum up to $p_{\mathrm{T}}\approx 6$ GeV/$c$
these results indicate that the $v_{2}$ of baryons is larger than that of
mesons. This behaviour was explained in a dynamical model where flow develops
at the partonic level followed by quark coalescence into hadrons [28, 29].
This mechanism leads to the observed hierarchy in the values of
$v_{2}(p_{\mathrm{T}})$, referred to as number of constituent quarks (NCQ)
scaling. New results from ALICE [23] and PHENIX [30] exhibit deviations from
the NCQ scaling at the level of $\pm$20$\%$ for $p_{\mathrm{T}}>3$ GeV/$c$. In
addition, the LHC results showed also that the $v_{2}$ of the $\phi$-meson at
intermediate values of transverse momentum follows the baryon rather than the
meson scaling for central Pb–Pb collisions [23]. Recently, the first results
of $v_{2}(p_{\mathrm{T}})$, $v_{3}(p_{\mathrm{T}})$, and
$v_{4}(p_{\mathrm{T}})$ for $\pi^{\pm}$, $\mathrm{K}^{\pm}$ and
p+$\overline{\mathrm{p}}$ for 50$\%$ most central Au–Au collisions at
$\sqrt{s_{\mathrm{NN}}}=200$ GeV were reported [31]. The higher harmonic flow
coefficients exhibit similar mass and particle-type dependences as $v_{2}$ up
to intermediate values of $p_{\mathrm{T}}$.

In this article, we report the results for the $p_{\mathrm{T}}$-differential
elliptic, triangular, quadrangular and pentagonal flow for $\pi^{\pm}$,
$\mathrm{K}^{\pm}$ and p+$\overline{\mathrm{p}}$ measured in Pb–Pb collisions
at the centre of mass energy per nucleon pair $\sqrt{s_{\mathrm{{NN}}}}=2.76$
TeV with the ALICE detector [32, 33] at the LHC. The particles are identified
using signals from both the Time Projection Chamber (TPC) and the Time Of
Flight (TOF) detectors, described in Section 2, with a procedure that is
discussed in Section 3. The results are obtained with the Scalar Product
method described in Section 4, and in detail in Refs. [23, 34, 35, 36]. In
this article, the identified hadron under study and the charged reference
particles are obtained from different, non-overlapping pseudorapidity regions.
A correction for correlations not related to the common symmetry plane (non-
flow), like those arising from jets, resonance decays and quantum statistics
correlations, is presented in Section 4. This procedure relies on measuring
the corresponding correlations in pp collisions and subtracting them from the
$v_{n}$ coefficients measured in Pb–Pb collisions to form the reported
$v_{n}^{\textrm{sub}}(p_{\mathrm{T}})$, where the superscript ‘sub’ is used to
stress the subtraction procedure. The systematic uncertainties of the
measurements are described in Section 5. All harmonics were measured
separately for particles and anti-particles and were found to be compatible
within the statistical uncertainties. Therefore, the
$v_{n}^{\textrm{sub}}(p_{\mathrm{T}})$ for the average of the results for the
opposite charges is reported. The results are reported in Section 6 for the
0–50$\%$ centrality range of Pb–Pb collisions. Finally, results are also
reported separately for ultra-central events, i.e. the 0–1$\%$ centrality
range, where the role of the collision geometry is reduced and one expects
that $v_{n}^{\textrm{sub}}(p_{\mathrm{T}})$ is mainly driven by the initial
state fluctuations.

##  2 Experimental setup

ALICE [32, 33] is one of the four large experiments at the LHC, particularly
designed to cope with the large charged-particle densities present in central
Pb–Pb collisions [37]. By convention, the beam direction defines the $z$-axis,
the $x$-axis is horizontal and points towards the centre of the LHC, and the
$y$-axis is vertical and points upwards. The apparatus consists of a set of
detectors located in the central barrel, positioned inside a solenoidal magnet
which generates a $0.5$ T field parallel to the beam direction, and a set of
forward detectors.

The Inner Tracking System (ITS) [32] and the TPC [38] are the main tracking
detectors of the central barrel. The ITS consists of six layers of silicon
detectors employing three different technologies. The two innermost layers,
positioned at $r=3.9$ cm and 7.6 cm, are Silicon Pixel Detectors (SPD),
followed by two layers of Silicon Drift Detectors (SDD) ($r=15$ cm and 23.9
cm). Finally, the two outermost layers are double-sided Silicon Strip
Detectors (SSD) at $r=38$ cm and 43 cm. The TPC surrounds the ITS and provides
full azimuthal coverage in the pseudorapidity range $|\eta|<0.9$.

Charged pions, kaons and protons were identified using the information from
the TPC and the TOF detectors [32]. The TPC allows for a simultaneous
measurement of the momentum of a particle and its specific energy loss
$\langle\mathrm{d}E/\mathrm{d}x\rangle$ in the gas. The detector provides a
separation by at least 2 standard deviations for the hadron species at
$p_{\mathrm{T}}<0.7$ GeV/$c$ and the possibility to identify particles in the
relativistic rise region of $\mathrm{d}E/\mathrm{d}x$ (i.e. $2<p_{\rm{T}}<20$
GeV/$c$) [33]. The $\mathrm{d}E/\mathrm{d}x$ resolution for the 5$\%$ most
central Pb–Pb collisions is 6.5$\%$ and improves for more peripheral
collisions. The TOF detector is placed around the TPC and provides a $3\sigma$
separation between $\pi$–K and K–$\rm{p}$ up to $p_{\mathrm{T}}=$ 2.5 GeV/$c$
and $p_{\mathrm{T}}=4$ GeV/$c$, respectively [33]. This is done by measuring
the flight time of particles from the collision point with a resolution of
about $80$ ps. The start time for the TOF measurement is provided by the T0
detectors, two arrays of Cherenkov counters positioned at opposite sides of
the interaction points covering $4.6<\eta<4.9$ (T0A) and $-3.3<\eta<-3.0$
(T0C). The start time is also determined using a combinatorial algorithm that
compares the timestamps of particle hits measured by the TOF to the expected
times of the tracks, assuming a common event time $t_{ev}$ [33]. Both methods
of estimating the start time are fully efficient for the 50$\%$ most central
Pb–Pb collisions.

A set of forward detectors, the V0 scintillator arrays [39], were used in the
trigger logic and for the determination of the collision centrality, discussed
in the next section. The V0 consists of two systems, the V0A and the V0C, that
are positioned on each side of the interaction point and cover the
pseudorapidity ranges of $2.8<\eta<5.1$ and $-3.7<\eta<-1.7$, respectively.

For more details on the ALICE experimental setup and the performance of the
detectors, see Refs. [32, 33].

##  3 Event sample, track selection and particle identification

###  3.1 Trigger selection and data sample

The analysis is performed on data from pp and Pb–Pb collisions at
$\sqrt{s_{\mathrm{NN}}}=2.76$ TeV collected with the ALICE detector in 2011.
The minimum bias trigger in pp collisions required at least one hit in either
of the V0 detectors or the SPD. In Pb–Pb collisions, minimum bias events were
triggered by the coincidence between signals from the two sides of the V0
detector. In addition, in Pb–Pb collisions, an online selection based on the
V0 detectors was used to increase the number of central (i.e. 0–10$\%$
centrality range) and semi-central (i.e. 10–50$\%$ centrality range) events.
An offline event selection, exploiting the signal arrival time in V0A and V0C,
measured with a 1 ns resolution, was used to discriminate background (e.g.
beam–gas) from collision events. This led to a reduction of background events
in the analysed samples to a negligible fraction ($<0.1\%$) [33]. All events
selected for the analysis had a reconstructed primary vertex position along
the beam axis ($z_{\textrm{vtx}}$) within 10 cm from the nominal interaction
point. Finally, events with multiple reconstructed vertices were rejected,
leading to a negligible amount of pile–up events for all systems [33]. After
all the selection criteria, a filtered data sample of approximately
$25~{}\times$ $10^{6}$ Pb–Pb and $20~{}\times$ $10^{6}$ pp events were
analysed to produce the results presented in this article.

Events were classified according to fractions of the inelastic cross section
and correspond to the 50$\%$ most central Pb–Pb collisions. The 0–1$\%$
interval represents the most central interactions (i.e. smallest impact
parameter) and will be referred to as ultra-central collisions in the
following. On the other hand, the 40–50$\%$ interval corresponds to the most
peripheral (i.e. largest impact parameter) collisions in the analysed sample,
imposed by the usage of the semi-central trigger for the collected sample in
2011. The centrality of the collision was estimated using the distribution of
signal amplitudes from the V0 detectors. The systematic uncertainty due to the
centrality estimation is determined using the charged particle multiplicity
distribution of TPC tracks and the number of SPD clusters, and will be
discussed in Section 5. Details about the centrality determination can be
found in Ref. [40].

###  3.2 Track selection

In this analysis, tracks are reconstructed using the information from the TPC
and the ITS detectors. The tracking algorithm, based on the Kalman filter [41,
42], starts from a collection of space points (referred to as clusters) inside
the TPC, and provides the quality of the fit by calculating its $\chi^{2}$
value. Each space point is reconstructed at one of the TPC padrows, where the
deposited ionisation energy is also measured. The specific ionisation energy
loss $\langle\mathrm{d}E/\mathrm{d}x\rangle$ is estimated using a truncated
mean, excluding the 40% highest-charge clusters associated to the track. The
obtained $\langle\mathrm{d}E/\mathrm{d}x\rangle$ has a resolution, which we
later refer to as $\sigma_{\mathrm{TPC}}$. The tracks are propagated to the
outer layer of the ITS, and the tracking algorithm attempts to identify space
points in each one of the consecutive layers, reaching the innermost ones
(i.e. SPD). The track parameters are then updated using the combined
information from both the TPC and the ITS detectors. If the algorithm is
unable to match the track reconstructed in the TPC with associated ITS
clusters (e.g. due to inefficiencies caused by dead channels in some of the
ITS layers), the track parameters calculated from the TPC tracking algorithm
are used instead. This tracking mode will be referred to as hybrid tracking in
the rest of the text, and is used as the default in this analysis since it
also provides uniform $\varphi$ distribution.

Primary charged pions, kaons and (anti-)protons were required to have at least
70 reconstructed space points out of the maximum of 159 in the TPC. The
average $\chi^{2}$ of the track fit per TPC space point per degree of freedom
(see [33] for details) was required to be below $2$. These selections reduce
the contribution from short tracks, which are unlikely to originate from the
primary vertex. To further reduce the contamination by secondary tracks from
weak decays or from the interaction with the material, only particles within a
maximum distance of closest approach (DCA) between the tracks and the primary
vertex in both the transverse plane ($\mathrm{DCA}_{xy}<2.4$ cm) and the
longitudinal direction ($\mathrm{DCA}_{z}<3.2$ cm) were analysed. Moreover,
the tracks were required to have at least two associated ITS clusters in
addition to having a hit in either of the two SPD layers. This selection leads
to an efficiency of about $80\%$ for primary tracks at $p_{\mathrm{T}}>0.6$
GeV/$c$ and a contamination from secondaries of about $5\%$ at $p_{\rm{T}}=1$
GeV/$c$ [43]. These values depend on particle species and transverse momentum
[43].

The systematic uncertainty due to the track reconstruction mode was estimated
using two additional tracking modes, one relying on the so-called standalone
TPC tracking with the same parameters described before, and a second that
relies on the combination of the TPC and the ITS detectors (i.e. global
tracking) with tighter selection criteria. In the latter case, the maximum
value of DCA was 0.3 cm in both the transverse plane and the longitudinal
direction, thus further reducing the amount of secondary particles in the
track sample.

The results are reported for all identified hadrons in $|\eta|<0.8$ and for
the transverse momentum range $0.3<$ $p_{\mathrm{T}}$ $<6.0$ $\mathrm{GeV}/c$
for $\pi^{\pm}$ and $0.3<$ $p_{\mathrm{T}}$ $<4.0$ $\mathrm{GeV}/c$ for
$\mathrm{K}^{\pm}$. Finally, since the contamination from secondary protons
created through the interaction of particles with the detector material can
reach values larger than 5$\%$ for $p_{\rm{T}}<1$ GeV/$c$, only
$\overline{\mathrm{p}}$ were considered for $0.4<p_{\rm{T}}<1$ GeV/$c$, while
for higher values (i.e. $1<p_{\rm{T}}<6$ GeV/$c$) a combined measurement of p
and $\overline{\mathrm{p}}$ is reported.

###  3.3 Identification of $\pi^{\pm}$, $\mathrm{K}^{\pm}$ and
$\mathrm{p}$+$\overline{\mathrm{p}}$

The particle identification (PID) for pions ($\pi^{\pm}$), kaons
($\mathrm{K}^{\pm}$) and protons (p+$\overline{\mathrm{p}}$) used in this
analysis is based on a Bayesian technique described in detail in [44], with
the time-of-flight $t_{\mathrm{TOF}}$ and the specific energy loss in the TPC
$\langle\mathrm{d}E/\mathrm{d}x\rangle$ as the input quantities. Different
particle species are identified by requiring a minimum probability of 90%. The
PID efficiency of this method is higher than 95% both for pions and protons up
to $p_{\mathrm{T}}$ $\approx 2.5$ $\mathrm{GeV}/c$ while for kaons it exhibits
a stronger $p_{\mathrm{T}}$ dependence, reaching 60% at 2.5 $\mathrm{GeV}/c$
with a minimum of 25% at 4 $\mathrm{GeV}/c$. Furthermore, the contamination is
below 5% both for pions and protons, while for kaons it remains below 10%
throughout the entire transverse momentum range considered in this analysis.

In addition, a different PID procedure that relied on the two-dimensional
correlation between the number of standard deviations in units of the
resolution from the expected signals of the TPC and the TOF detectors was also
investigated, similar to what was reported in [23]. In this approach particles
were selected by requiring their signal to lie within maximum three standard
deviations from the $\langle\mathrm{d}E/\mathrm{d}x\rangle$ and $t_{\rm{TOF}}$
values expected for a given particle species and transverse momentum. In
addition, the purity was required to be at least 80%, a condition that becomes
essential with increasing transverse momentum where the relevant detector
response for different particle species starts to overlap.

##  4 Analysis technique

In this article, higher flow harmonics for charged pions, charged kaons,
protons and anti-protons are reported. In the following paragraphs, the
technique used for the measurement of flow harmonics is discussed and an
approach to estimate the contribution of non-flow correlations, applied to
obtain the final results, is presented. For the estimation of these higher
flow harmonics, the symmetry planes are not reconstructed on an event-by-event
basis and thus the azimuthal angles of particles are not directly correlated
to them. Instead, they are estimated with correlation techniques, where only
the azimuthal angles of produced particles are required.

###  4.1 Scalar Product method

In this article, the flow harmonics are calculated with the Scalar Product
(SP) method [34, 35] in which the identified particle of interest (POI) and
the charged reference particles (RP) are both selected within the acceptance
of the TPC detector. This method is based on the calculation of the $Q$-vector
from a sample of RP [45], according to

$\vec{Q}_{n}=\sum_{k\in{RP}}^{M}e^{in\varphi_{k}},$ (3)

where $M$ is the multiplicity of RPs, $\varphi_{k}$ is the azimuthal angle of
the $k^{\mathrm{th}}$ reference particle and $n$ is the order of the flow
harmonic.

In this study, each event is divided into two subevents “$a$” and “$b$”,
covering the ranges $-0.8<\eta<0.0$ and $0.0<\eta<0.8$, respectively. The
measured $v_{n}^{a}$ ($v_{n}^{b}$) coefficients are calculated by selecting
the identified hadrons (POIs) from subevent “$a$” (“$b$”) and the reference
particles from subevent “$b$” (“$a$”) according to

$v_{n}^{a}(p_{\mathrm{T}})=\frac{\Big{\langle}{\Big{\langle}{\vec{u}_{n}^{k}(p_{\mathrm{T}})\cdot\frac{\vec{Q}_{n}^{b*}}{M^{b}}}\Big{\rangle}}_{k\in
a}\Big{\rangle}}{\sqrt{\Big{\langle}{\frac{\vec{Q}_{n}^{a}}{M^{a}}\cdot\frac{\vec{Q}_{n}^{b*}}{M^{b}}}\Big{\rangle}}}\,.$
(4)

In Eq. 4, the brackets denote an average over all particles and all events,
$M^{a}$ and $M^{b}$ are the measured multiplicities of RPs from each subevent
in the TPC detector, $\vec{u}_{n}^{k}=e^{in\varphi_{k}}$, $k\in a$, is the
unit vector of the $k^{\mathrm{th}}$ POI in subevent “$a$”, $\vec{Q}_{n}^{a}$
is the $Q$-vector calculated in subevent “$a$” and $\vec{Q}_{n}^{b*}$ is the
complex conjugate of the $Q$-vector calculated in subevent “$b$”. The
denominator in Eq. 4 is referred to further in the text as reference flow. The
final measured $v_{n}^{\mathrm{AA}}$ coefficients are calculated as a weighted
average of $v_{n}^{a}$ and $v_{n}^{b}$ with the inverse of the square of the
statistical uncertainty being the weight.

The Scalar Product method, used in this article, as well as in [23], requires
less statistics than multi-particle methods, since it is essentially based on
two-particle correlations. In addition, it does not introduce any bias
originating from multiplicity fluctuations since all $Q$-vectors in Eq. 4 are
normalised by the relevant multiplicities [36].

###  4.2 Estimation of non-flow correlations

Even after selecting particles from two non-overlapping subevents, a
significant residual non-flow contribution remains in the measured flow
coefficients. These non-flow contributions are mainly few-particle effects and
scale roughly with the inverse of the multiplicity for methods which rely on
two-particle correlations, such as the SP. These include correlations
originating from jets, resonance decays and quantum statistics correlations
which contribute additively to the value of $v_{n}^{\mathrm{AA}}$. We assume
that they do not drastically change with the centrality interval, as discussed
in [35, 46] and shown in [47]. The corresponding contributions can be
estimated using minimum bias pp collisions [35] and in this article this
estimate, denoted as $\delta_{n}^{AA,pp}$, is subtracted from the measured
flow coefficients according to

$v_{n}^{\textrm{sub}}(p_{\mathrm{T}})=v_{n}^{\textrm{AA}}(p_{\mathrm{T}})-\delta_{n}^{\textrm{AA,pp}}(p_{\mathrm{T}}),$
(5)

$\delta_{n}^{\textrm{(a)AA,pp}}(p_{\mathrm{T}})=\frac{\langle{M}\rangle^{\textrm{pp}}\Big{\langle}{\Big{\langle}{\vec{u}_{n}^{k}(p_{\mathrm{T}})\cdot\frac{\vec{Q}^{b*}_{n}}{M^{b}}}\Big{\rangle}}_{k\in
a}\Big{\rangle}^{\textrm{pp}}}{\langle{M}\rangle^{\textrm{AA}}\sqrt{\Big{\langle}{\frac{\vec{Q}_{n}^{a}}{M^{a}}\cdot\frac{\vec{Q}^{b*}_{n}}{M^{b}}}\Big{\rangle}^{\textrm{AA}}}},$
(6)

Figure 1: The $p_{\mathrm{T}}$-differential
$\langle{M}\rangle\langle{\langle{\vec{u}_{n}\cdot\frac{\vec{Q}^{*}_{n}}{M}}\rangle}\rangle$
of pions (left column), kaons (middle column) and protons (right column) for
minimum bias pp and 0–1%, 20–30% and 40–50% centralities in Pb–Pb collisions
at $\sqrt{s_{\mathrm{NN}}}=2.76$ TeV. The rows represent different harmonics.

where the final $\delta_{n}^{\textrm{AA,pp}}$ is calculated as a weighted
average of $\delta_{n}^{\textrm{(a)AA,pp}}$ and
$\delta_{n}^{\textrm{(b)AA,pp}}$ with the inverse of the square of the
statistical uncertainty as the weight. The term
$\delta_{n}^{\textrm{(a)AA,pp}}$ is given by Eq. 6 (similarly for
$\delta_{n}^{\textrm{(b)AA,pp}}$). In Eq. 6, $\langle{M}\rangle^{\textrm{pp}}$
and $\langle{M}\rangle^{\textrm{AA}}$ are the average multiplicities of RPs
calculated in pp and Pb–Pb collisions, respectively. In this article, we
report the results of $v_{n}^{\textrm{sub}}$, defined in Eq. 5, with the
superscript ‘sub’ added to stress the applied subtraction procedure. This
approach is different compared to previous measurements [23, 48], where a
large pseudorapidity gap $\Delta\eta$ between the POIs and the RPs was used to
significantly reduce the contribution from non-flow correlations. The
$v_{2}^{\mathrm{sub}}$ results reported in this article are 2–6% below the
$v_{2}$ measurements reported in [23]. This is probably due to the fact that
the subtraction procedure using pp collisions accounts for the recoil
(away–side) jet which is not accounted for by applying a large $\eta$–gap. On
the other hand, it does not account for known medium-induced modifications of
jet-like correlations. This could lead to an over-estimation of the non-flow
component in high $p_{\mathrm{T}}$ values.

Figure 1 presents the $p_{\mathrm{T}}$-differential
$\langle{M}\rangle\langle{\langle{\vec{u}_{n}\cdot\frac{\vec{Q}^{*}_{n}}{M}}\rangle}\rangle$,
i.e. the azimuthal correlations scaled by the relevant multiplicities, in pp
and Pb–Pb in three centrality intervals (i.e. 0–1%, 20–30% and 40–50%) for all
flow harmonics reported in this article for pions, kaons and protons, in the
appropriate kinematic range for each species. The data points are drawn with
statistical and systematic uncertainties, represented by the error bars and
the boxes, respectively. This representation is used in all plots of this
article. It is seen that
$\langle{M}\rangle^{\textrm{pp}}\langle{\langle{\vec{u}_{2}\cdot\frac{\vec{Q}^{*}_{2}}{M}}\rangle}\rangle^{\textrm{pp}}$
increases monotonically with $p_{\mathrm{T}}$, reaching the magnitude of
$\langle{M}\rangle^{\textrm{AA}}\langle{\langle{\vec{u}_{2}\cdot\frac{\vec{Q}^{*}_{2}}{M}}\rangle}\rangle^{\textrm{AA}}$
in ultra-central collisions at high values of $p_{\mathrm{T}}$, where non-flow
correlations are expected to become significant.

##  5 Systematic uncertainties

The systematic uncertainties are estimated by varying the event and track
selection criteria and by studying the detector effects with Monte Carlo (MC)
simulations for all particle species, centrality intervals and flow harmonics
separately. The contributions from different sources, described below, were
extracted from the difference of the $p_{\mathrm{T}}$-differential
$v_{n}^{\mathrm{AA}}$ (for Pb–Pb collisions) and
$\langle{M}\rangle^{\textrm{pp}}\langle{\langle{\vec{u}_{n}\cdot\frac{\vec{Q}^{*}_{n}}{M}}\rangle}\rangle^{\rm{pp}}$
(for pp collisions) between the default selection criteria described in
Section 3 and their variations summarised in Table 1. All sources with a
statistically significant contribution (i.e. larger than 3$\sigma$, where
$\sigma$ is the uncertainty of the difference between the default results and
the ones obtained from the variation of the selection criteria, assuming the
two are fully correlated) were then added in quadrature to form the final
value of the systematic uncertainty on $v_{n}^{\mathrm{AA}}$ (or
$\langle{M}\rangle^{\textrm{pp}}\langle{\langle{\vec{u}_{n}\cdot\frac{\vec{Q}^{*}_{n}}{M}}\rangle}\rangle^{\rm{pp}}$)
that was propagated to the uncertainty on $v_{n}^{\mathrm{sub}}$.

Error source | Default | Variations
---|---|---
Primary $z_{vtx}$ |  $\pm$10 cm |  $\pm$6 cm, $\pm$8 cm
Centrality estimator | V0 amplitude | SPD clusters, TPC tracks
Magnetic field polarity | both fields | positive, negative
Number of TPC space points | 70 | 50, 80, 90, 100
$\chi^{2}/\mathrm{ndf}$ per TPC space point | 2 | 1, 1.5
$\mathrm{DCA}_{xy}$ ($\mathrm{DCA}_{z}$) cm | 2.4 (3.2) | 0.3, 0.6, 0.9, 1.2
Tracking mode | hybrid | TPC standalone, global
PID probability | 90% | 94%, 98%
MC closure test | — | —
Non-flow estimate from pp | — | —
Table 1: List of the selection criteria and the corresponding variations used
for the estimation of the systematic uncertainties.

Table 2 summarises the maximum absolute value, over all transverse momentum
and centrality intervals, of the systematic uncertainties from each individual
source. These maximum values are obtained for $p_{\mathrm{T}}>3$ GeV/$c$ where
the typical $v_{n}^{\mathrm{sub}}$ values are between 0.1 and 0.2 for
$v_{2}^{\mathrm{sub}}$ (for centrality intervals above the 10–20$\%$ range),
0.07–0.15 for $v_{3}^{\mathrm{sub}}$, 0.05–0.1 for $v_{4}^{\mathrm{sub}}$, and
around 0.05 for $v_{5}^{\mathrm{sub}}$, for all sources apart from the DCA
variations. In the latter case, the maximum values are obtained for
$p_{\mathrm{T}}<1$ GeV/$c$, where the $v_{n}^{\mathrm{sub}}$ values are
significantly smaller.

| $v_{2}^{\mathrm{sub}}$ | $v_{3}^{\mathrm{sub}}$ | $v_{4}^{\mathrm{sub}}$ | $v_{5}^{\mathrm{sub}}$
---|---|---|---|---
Error source | $\pi^{\pm}$ | $\mathrm{K}^{\pm}$ | p+$\overline{\mathrm{p}}$ | $\pi^{\pm}$ | $\mathrm{K}^{\pm}$ | p+$\overline{\mathrm{p}}$ | $\pi^{\pm}$ | $\mathrm{K}^{\pm}$ | p+$\overline{\mathrm{p}}$ | $\pi^{\pm}$ | $\mathrm{K}^{\pm}$ | p+$\overline{\mathrm{p}}$
Centrality estimator | 0.003 | 0.001 | 0.002  | 0.003 | 0.001 | 0.002  | 0.001 | 0.002 | 0.003  | 0.002 | 0.003 | 0.006
Magnetic field polarity | \-  | 0.002 | 0.002 | 0.002  | 0.002 | 0.002 | 0.002  | 0.004 | 0.005 | 0.004
$\mathrm{DCA}_{xy}$ ($\mathrm{DCA}_{z}$) | $10^{-4}$ | – |  $10^{-4}$ | $10^{-4}$ | – |  $10^{-4}$ | $10^{-4}$ | – |  $2\times 10^{-4}$ | $10^{-4}$ | – | $2\times 10^{-4}$
Tracking mode | 0.005 | 0.003 | 0.005  | 0.005 | 0.004 | 0.004  | 0.005 | 0.004 | 0.005  | 0.005 | 0.006 | 0.01
PID probability | \-  | \-  | \-  | 0.001 | 0.001 | 0.001
MC closure test | 0.006 | 0.002 | 0.001  | 0.003 | 0.004 | 0.003  | 0.002 | 0.006 | 0.003  | 0.002 | 0.006 | 0.003
Non-flow estimate from pp | \-  | \-  | 0.001 | 0.001 | 0.003  | 0.001 | 0.001 | 0.003

Table 2: List of the maximum value of systematic uncertainties from each
individual source for each flow harmonic $v_{n}^{\mathrm{sub}}$ and particle
species. Sources that do not contribute to the systematic uncertainty are not
reported in this table.

In order to study the effect of the position of the primary vertex along the
beam axis ($z_{vtx}$) on the measurements, the event sample was varied by
changing this selection criterium from $\pm$10 cm to $\pm$8 cm and finally to
$\pm$6 cm. For all species and centralities, the resulting
$v_{n}^{\mathrm{sub}}$($p_{\mathrm{T}}$) were consistent with results obtained
with the default selection. In addition, changing the centrality selection
criteria from the signal amplitudes in the V0 scintillator detectors to the
multiplicity of TPC tracks or the number of SPD clusters resulted in maximum
contribution of 0.003 ($\pi^{\pm}$), 0.003 ($\mathrm{K}^{\pm}$), 0.006
(p+$\overline{\mathrm{p}}$) for all flow harmonics in $p_{\mathrm{T}}>3$
GeV/$c$. For $p_{\mathrm{T}}<3$ GeV/$c$, the corresponding contributions from
this source were significantly smaller in absolute value. Finally, results
from runs with different magnetic field polarities did not exhibit any
systematic change in $v_{2}^{\mathrm{sub}}$($p_{\mathrm{T}}$) for any particle
species or any centrality. For higher harmonics and for $p_{\mathrm{T}}>3$
GeV/$c$, the corresponding contributions were at maximum 0.002 for all species
and centralities in $v_{3}^{\mathrm{sub}}$($p_{\mathrm{T}}$) and
$v_{4}^{\mathrm{sub}}$($p_{\mathrm{T}}$), and 0.005 in
$v_{5}^{\mathrm{sub}}$($p_{\mathrm{T}}$), with significantly smaller values
for $p_{\mathrm{T}}<3$ GeV/$c$.

In addition, the track selection criteria, such as the number of TPC space
points and the $\chi^{2}$ per TPC space point per degree of freedom were
varied, for all particle species presented in this article. No systematic
deviations in the values of $v_{n}^{\mathrm{sub}}$($p_{\mathrm{T}}$) relative
to the results obtained with the default selections were found. The impact of
secondary particles on the measured $v_{n}^{\mathrm{sub}}$, including products
of weak decays, was estimated by varying the selection criteria on both the
longitudinal and transverse components of the DCA. This resulted in a non-
negligible uncertainty only for pions and anti-protons mainly at low values of
transverse momentum (i.e. $p_{\mathrm{T}}<1$ GeV/$c$) as indicated in Table 2
for all harmonics and centralities. Uncertainties originating from the
selected tracking procedure were estimated by using the global or the
standalone TPC tracking modes (see the discussion in Section 3.2 for details).
For all harmonics, differences that contribute to the final systematic
uncertainty were found for $p_{\mathrm{T}}>3$ GeV/$c$ and their maximum values
over all centralities are summarised in Table 2. Systematic uncertainties
associated with the particle identification procedure were studied by varying
the value of the minimum probability of identifying a particle with the
Bayesian approach from 90% to 94%, and eventually 98%, but also using an
independent technique relying on the number of standard deviations of both the
$dE/dx$ ($\sigma_{\mathrm{TPC}}$) and the $t_{\rm{TOF}}$
($\sigma_{\mathrm{TOF}}$) as described in Section 3.3 and in detail in Ref.
[23]. These variations did not reveal any systematic differences in the
results for $v_{2}^{\mathrm{sub}}$($p_{\mathrm{T}}$),
$v_{3}^{\mathrm{sub}}$($p_{\mathrm{T}}$) and
$v_{4}^{\mathrm{sub}}$($p_{\mathrm{T}}$) relative to the results with the
default identification requirements. For
$v_{5}^{\mathrm{sub}}$($p_{\mathrm{T}}$) and for $p_{\mathrm{T}}>3$ GeV/$c$
the systematic uncertainty was below 0.001 for all particle species.
Systematic uncertainties due to detector inefficiencies were studied using
Monte Carlo samples. In particular, the results of the analysis of a sample at
the event generator level (i.e. without invoking either the detector geometry
or the reconstruction algorithm) were compared with the results of the
analysis over the output of the full reconstruction chain, in a procedure
referred to as “MC closure test”. Table 2 summarises the maximum contributions
over all transverse momenta and centralities, found for $p_{\mathrm{T}}>3$
GeV/$c$, for each particle species and harmonic. On the other hand, for
$p_{\mathrm{T}}<3$ GeV/$c$ the corresponding contributions were significantly
smaller.

Furthermore, the contribution from the estimation of non-flow effects
extracted with the procedure described in Section 4.2 was studied by
investigating the same list of variations of the event and track selection
criteria summarised in Table 1, coherently in pp and Pb–Pb collisions. These
uncertainties do not account for contributions related to jet quenching
effects in Pb–Pb collisions. The maximum differences were negligible for
$v_{2}^{\mathrm{sub}}$($p_{\mathrm{T}}$) and
$v_{3}^{\mathrm{sub}}$($p_{\mathrm{T}}$), and were up to 0.001 for pions and
kaons and 0.003 for protons with $p_{\mathrm{T}}>3$ GeV/$c$ for
$v_{4}^{\mathrm{sub}}$($p_{\mathrm{T}}$) and
$v_{5}^{\mathrm{sub}}$($p_{\mathrm{T}}$).

Moreover, the analysis was repeated using different charge combinations (i.e.
positive–positive and negative–negative) for the identified hadrons and the
reference particles in both Pb–Pb and pp collisions. The results, after the
correction of Eq. 5, were compatible with the default ones. Finally, the two
subevents used to select POIs and RPs were further separated, by applying a
pseudorapidity gap ($\Delta\eta$) between them, from no-gap (default analysis)
to $|\Delta\eta|>0.4$ and eventually reaching $|\Delta\eta|>0.8$. Both
$v_{\textrm{n}}^{\textrm{AA}}$ and $\delta_{n}^{\textrm{AA,pp}}$ were
calculated using the same gap and the results after the subtraction did not
exhibit any systematic change in $v_{n}^{\mathrm{sub}}$($p_{\mathrm{T}}$) for
any particle species or any centrality.

##  6 Results and discussion

In this section, the results for the $p_{\mathrm{T}}$-differential
$v_{2}^{\mathrm{sub}}$, $v_{3}^{\mathrm{sub}}$, $v_{4}^{\mathrm{sub}}$ and
$v_{5}^{\mathrm{sub}}$ measured in Pb–Pb collisions at
$\sqrt{s_{\mathrm{NN}}}=2.76$ TeV for 0–1% up to 40–50% centrality intervals
for pions, kaons and protons are presented. We first present, in Sec. 6.1, the
centrality dependence of $v_{n}^{\mathrm{sub}}$($p_{\mathrm{T}}$) and the
relevant contribution of the subtraction terms used to measure
$v_{n}^{\mathrm{sub}}$. Section 6.2 focuses on the development of
$v_{n}^{\mathrm{sub}}$($p_{\mathrm{T}}$) for different harmonics in ultra-
central collisions. Section 6.3 presents the mass dependence of
$v_{n}^{\mathrm{sub}}$($p_{\mathrm{T}}$) which is followed by a discussion
about the scaling properties of different flow harmonics in different
centrality intervals. In Section 6.5, two models, namely iEBE-VISHNU [49] and
A Multi Phase Transport model (AMPT) [50, 51, 52], are compared with the
experimental measurements. Note that the same data will be shown in different
representations in the following sections to highlight the various physics
implications of the measurements.

###  6.1 Centrality dependence of flow harmonics

Figure 2 presents the $p_{\mathrm{T}}$-differential $v_{2}^{\mathrm{sub}}$ (in
the top row) and the corresponding subtracted terms denoted as
$\delta_{2}^{\textrm{AA,pp}}$($p_{\mathrm{T}}$) (bottom row) for $\pi^{\pm}$,
$\mathrm{K}^{\pm}$ and p+$\overline{\mathrm{p}}$ measured in different
centrality intervals (0–1% up to 40–50%) in Pb–Pb collisions at
$\sqrt{s_{\mathrm{NN}}}=2.76$ TeV. The results are grouped in each panel
according to particle species to show the dependence of
$v_{2}^{\mathrm{sub}}$($p_{\mathrm{T}}$) on centrality.

This figure illustrates how the value of
$v_{2}^{\mathrm{sub}}$($p_{\mathrm{T}}$) increases with centrality (top row)
from ultra-central (0–1%) to the most peripheral collisions (40–50%). This is
in agreement with the interpretation that the final-state ellipticity of the
system originates from the initial-state ellipsoidal geometry in non-central
collisions. As illustrated in this figure, this increase for
$v_{2}^{\mathrm{sub}}$($p_{\mathrm{T}}$) is smaller for more peripheral
collisions: the value of $v_{2}^{\mathrm{sub}}$($p_{\mathrm{T}}$) does not
increase significantly from the 30–40% to the 40–50% centrality interval
despite an increase in the geometrical eccentricity. This feature, which is
also observed and discussed in [23], might originate from several effects,
such as i) the smaller lifetime of the fireball (the hot, dense and rapidly
expanding medium) in peripheral compared to more central collisions that does
not allow $v_{2}^{\mathrm{sub}}$ to develop further, ii) a reduced
contribution of eccentricity fluctuations in these centrality intervals
compared to more central events or iii) final-state hadronic effects [53]. In
addition, a significant $v_{2}^{\mathrm{sub}}$($p_{\mathrm{T}}$) develops in
ultra-central collisions where the collision geometry is almost isotropic and
therefore $v_{2}^{\mathrm{sub}}$ reflects only the contribution from initial-
state fluctuations. In summary, the results in Fig. 2 confirm that the
geometry of the collision plays a crucial role in the development of
$v_{2}^{\mathrm{sub}}$ as a function of centrality for all particle species.
It is also confirmed that the initial-state fluctuations contribute
significantly as well.

Figure 2: The $p_{\mathrm{T}}$-differential $v_{2}^{\mathrm{sub}}$ (top row)
and $\delta_{2}^{\textrm{AA,pp}}$ (bottom row) for different centralities in
Pb–Pb collisions at $\sqrt{s_{\mathrm{NN}}}=2.76$ TeV grouped by particle
species. Figure 3: The $p_{\mathrm{T}}$-differential $v_{3}^{\mathrm{sub}}$
(top row) and $\delta_{3}^{\textrm{AA,pp}}$ (bottom row) for different
centralities in Pb–Pb collisions at $\sqrt{s_{\mathrm{NN}}}=2.76$ TeV grouped
by particle species. Figure 4: The $p_{\mathrm{T}}$-differential
$v_{4}^{\mathrm{sub}}$ (top row) and $\delta_{4}^{\textrm{AA,pp}}$ (bottom
row) for different centralities in Pb–Pb collisions at
$\sqrt{s_{\mathrm{NN}}}=2.76$ TeV grouped by particle species. Figure 5: The
$p_{\mathrm{T}}$-differential $v_{5}^{\mathrm{sub}}$ (top row) and
$\delta_{5}^{\textrm{AA,pp}}$ (bottom row) for different centralities in Pb–Pb
collisions at $\sqrt{s_{\mathrm{NN}}}=2.76$ TeV grouped by particle species.

Figure 2 additionally illustrates how $\delta_{2}^{\textrm{AA,pp}}$ develops
with centrality (bottom row). This figure also shows that the value of
$\delta_{2}^{\textrm{AA,pp}}$ becomes larger with increasing transverse
momentum, in a $p_{\mathrm{T}}$ range where non-flow is believed to be a
significant contributor to the azimuthal correlations. Furthermore, the
relative contribution of $\delta_{2}^{\textrm{AA,pp}}$ to
$v_{2}^{\mathrm{AA}}$ changes as a function of centrality. In particular, the
relative value of $\delta_{2}^{\textrm{AA,pp}}$ is largest for ultra-central
collisions (0–1%) where it is 20% of $v_{2}^{\mathrm{AA}}$. This percentage
drops to 3% in the 10–20% centrality interval and increases to 7% for the most
peripheral collisions (40–50%). This change is also reflected in the absolute
value of $\delta_{2}^{\textrm{AA,pp}}$. The magnitude of
$\delta_{2}^{\textrm{AA,pp}}$ decreases from ultra-central events (0–1%) to
the 10–20% centrality interval and increases from this centrality interval up
to the most peripheral events (40–50%). This trend as a function of centrality
is observed for all particle species and it is due to the interplay between
the decrease in multiplicity and the corresponding increase in reference flow
as one goes towards more peripheral collisions.

Similar to Fig. 2, Figs. 3, 4 and 5 present the $p_{\mathrm{T}}$-differential
$v_{3}^{\mathrm{sub}}$, $v_{4}^{\mathrm{sub}}$ and $v_{5}^{\mathrm{sub}}$ (top
rows), respectively, and the corresponding subtracted terms (bottom rows) for
pions, kaons and protons measured in different centrality intervals. One
observes that all $v_{n}^{\mathrm{sub}}$ have significant non-zero values
throughout the entire measured $p_{\mathrm{T}}$ range for ultra-central
collisions, where the main contributors to the initial coordinate-space
anisotropies, which are necessary for the development of
$v_{n}^{\mathrm{sub}}$, are supposed to be the fluctuations of the initial
density profile [16]. In addition, the values of the higher flow harmonics
increase from ultra-central collisions (0–1%) to the most peripheral
collisions (40–50%). However, this increase as a function of centrality is
smaller in comparison to $v_{2}^{\mathrm{sub}}$. Thus, $v_{2}^{\mathrm{sub}}$
seems to mainly reflect the initial geometry of the system while the higher-
order flow harmonics are affected less. The non-vanishing values of these
higher-order flow harmonics are consistent with the notion in which they are
generated primarily from the event-by-event fluctuations of the initial energy
density profile.

In addition, all flow harmonics show a monotonic increase with increasing
$p_{\mathrm{T}}$ up to 3 $\mathrm{GeV}/c$ reaching a maximum that depends on
the particle species and on the collision centrality. In particular, the
position of this maximum of $v_{n}^{\mathrm{sub}}$($p_{\mathrm{T}}$) exhibits
a centrality dependence due to the change in radial flow which becomes larger
for central compared to peripheral collisions. Moreover, this maximum seems to
have a particle mass dependence as well, since it takes place at a higher
$p_{\mathrm{T}}$ value for heavier particles in each centrality interval.

The lower panel of Figs. 3, 4 and 5 also illustrate the magnitude of
$\delta_{n}^{\textrm{AA,pp}}$ as a function of $p_{\mathrm{T}}$. In these
cases, $\delta_{3}^{\textrm{AA,pp}}$ varies between 5% and 8% relative to
$v_{3}^{\mathrm{AA}}$, $\delta_{4}^{\textrm{AA,pp}}$ between 12% and 18% with
respect to $v_{4}^{\mathrm{AA}}$, and $\delta_{5}^{\textrm{AA,pp}}$ between
12% and 20% with respect to $v_{5}^{\mathrm{AA}}$. Similar to
$\delta_{2}^{\textrm{AA,pp}}$, the variation in the value of higher harmonic
$\delta_{n}^{\textrm{AA,pp}}$ is derived from the decrease in multiplicity and
the increasing reference flow in the transition from central to more
peripheral collisions.

###  6.2 Evolution of flow harmonics in ultra-central Pb–Pb collisions

Figure 6 shows the evolution of different flow harmonics for $\pi^{\pm}$ (left
column), $\mathrm{K}^{\pm}$ (middle column) and p+$\overline{\mathrm{p}}$
(right column) for ultra-central (i.e. 0–1%) collisions in comparison to the
other centrality intervals.

Figure 6: The evolution of the $p_{\mathrm{T}}$-differential
$v_{n}^{\mathrm{sub}}$ for $\pi^{\pm}$, $\mathrm{K}^{\pm}$ and
p+$\overline{\mathrm{p}}$, in the left, middle and right columns,
respectively, grouped by centrality interval in Pb–Pb collisions at
$\sqrt{s_{\mathrm{NN}}}=2.76$ TeV.

For ultra-central Pb–Pb collisions one expects the influence of the collision
geometry to the development of $v_{n}^{\mathrm{sub}}$ to be reduced compared
to the contribution of initial energy-density fluctuations. Figure 6 shows
that for pions the value of $v_{3}^{\mathrm{sub}}$ is equal to
$v_{2}^{\mathrm{sub}}$ at around $p_{\mathrm{T}}$ $\approx 1$ $\mathrm{GeV}/c$
and becomes the dominant harmonic for higher transverse momenta. Furthermore,
$v_{4}^{\mathrm{sub}}$ at $p_{\mathrm{T}}$ $\approx 2$ $\mathrm{GeV}/c$ and
$v_{5}^{\mathrm{sub}}$ at around $p_{\mathrm{T}}$ $\approx 3$ $\mathrm{GeV}/c$
become equal to $v_{2}^{\mathrm{sub}}$. For higher transverse momentum values,
$v_{4}^{\mathrm{sub}}$ becomes gradually larger than $v_{2}^{\mathrm{sub}}$
reaching a similar magnitude as $v_{3}^{\mathrm{sub}}$ at around 3.5
$\mathrm{GeV}/c$, while $v_{5}^{\mathrm{sub}}$ remains equal to
$v_{2}^{\mathrm{sub}}$.

As the collisions become more peripheral, one expects that geometry becomes a
significant contributor to the development of azimuthal anisotropy. As a
result, $v_{2}^{\mathrm{sub}}$ is the dominant harmonic for peripheral
collisions throughout the entire measured momentum range. Furthermore,
$v_{3}^{\mathrm{sub}}$, $v_{4}^{\mathrm{sub}}$ and $v_{5}^{\mathrm{sub}}$ seem
to have similar magnitudes and $p_{\mathrm{T}}$ evolution as observed in
ultra-central Pb–Pb events, indicating a smaller influence of the collision
geometry in their development than for $v_{2}^{\mathrm{sub}}$.

For kaons and protons, one observes a similar trend in the $p_{\mathrm{T}}$
evolution of $v_{2}^{\mathrm{sub}}$, $v_{3}^{\mathrm{sub}}$,
$v_{4}^{\mathrm{sub}}$ and $v_{5}^{\mathrm{sub}}$ as for pions. However, the
flow harmonics for ultra-central collisions (top middle and right plots of
Fig. 6 respectively) exhibit a crossing that takes place at $p_{\mathrm{T}}$
values that change as a function of the particle mass. For kaons, the crossing
between $v_{2}^{\mathrm{sub}}$ and $v_{3}^{\mathrm{sub}}$ occurs at higher
$p_{\mathrm{T}}$ ($\approx$1.4 $\mathrm{GeV}/c$) compared to pions while for
protons it occurs at an even higher $p_{\mathrm{T}}$ value ($\approx$1.8
$\mathrm{GeV}/c$). Similarly, the $v_{2}^{\mathrm{sub}}$ and
$v_{4}^{\mathrm{sub}}$ crossing occurs higher in $p_{\mathrm{T}}$ for kaons
($\approx$2.2 $\mathrm{GeV}/c$) and protons ($\approx$2.8 $\mathrm{GeV}/c$) as
compared to pions. The values of $v_{4}^{\mathrm{sub}}$ for kaons reach a
similar magnitude to $v_{3}^{\mathrm{sub}}$ at around 3.5 $\mathrm{GeV}/c$ and
this takes place at around 4 $\mathrm{GeV}/c$ for protons. The dependence of
the crossing between different flow harmonics, and thus the range where a
given harmonic becomes dominant, on the particle mass can be attributed to the
interplay of not only elliptic but also triangular and quadrangular flow with
radial flow.

Figure 7: The $p_{\mathrm{T}}$-differential $v_{2}^{\mathrm{sub}}$ (left
figure) and $v_{3}^{\mathrm{sub}}$ (right figure) for different particle
species grouped by centrality class in Pb–Pb collisions at
$\sqrt{s_{\mathrm{NN}}}=2.76$ TeV.

Figure 8: The $p_{\mathrm{T}}$-differential $v_{4}^{\mathrm{sub}}$ (left
figure) and $v_{5}^{\mathrm{sub}}$ (right figure) for different particle
species grouped by centrality class in Pb–Pb collisions at
$\sqrt{s_{\mathrm{NN}}}=2.76$ TeV.

###  6.3 Mass ordering

The interplay between the different flow harmonics and radial flow can be
further probed by studying how $v_{n}^{\mathrm{sub}}$($p_{\mathrm{T}}$)
develops as a function of the particle mass for various centralities. In Ref.
[23], it was clearly demonstrated that the interplay between radial and
elliptic flow leads to a characteristic mass ordering at $p_{\mathrm{T}}$ $<$
2–3 $\mathrm{GeV}/c$. This mass ordering originates from the fact that radial
flow creates a depletion in the particle spectrum at low $p_{\mathrm{T}}$
values, which increases with increasing particle mass and transverse velocity.
When this effect is embedded in an environment where azimuthal anisotropy
develops, it leads to heavier particles having smaller $v_{n}^{\mathrm{sub}}$
values compared to lighter ones at given values of $p_{\mathrm{T}}$. It is
thus interesting to study whether the interplay between the anisotropic flow
harmonics and radial flow leads also to a mass ordering in
$v_{n}^{\mathrm{sub}}$($p_{\mathrm{T}}$) for $n>2$.

Figure 7–left presents the $p_{\mathrm{T}}$-differential
$v_{2}^{\mathrm{sub}}$ for charged pions, kaons and protons starting from
ultra-central collisions up to the 40–50% centrality interval. The observed
evolution of $v_{2}^{\mathrm{sub}}$ with mass confirms that the interplay
between elliptic and radial flow leads to lower $v_{2}^{\mathrm{sub}}$ values
at fixed $p_{\mathrm{T}}$ for heavier particles for $p_{\mathrm{T}}$ $<$ 2–3
$\mathrm{GeV}/c$, depending on the centrality interval.

Similarly, Figs. 7–right, 8–left and 8–right show the
$p_{\mathrm{T}}$-differential $v_{3}^{\mathrm{sub}}$, $v_{4}^{\mathrm{sub}}$
and $v_{5}^{\mathrm{sub}}$, respectively, for different particle species and
for each centrality interval. A clear mass ordering is seen in the low
$p_{\mathrm{T}}$ region, i.e. for $p_{\mathrm{T}}$ $<$ 2–3 $\mathrm{GeV}/c$,
for $v_{3}^{\mathrm{sub}}$($p_{\mathrm{T}}$),
$v_{4}^{\mathrm{sub}}$($p_{\mathrm{T}}$) and
$v_{5}^{\mathrm{sub}}$($p_{\mathrm{T}}$), which arises from the interplay
between the anisotropic flow harmonics and radial flow.

Furthermore, the $v_{n}^{\mathrm{sub}}$($p_{\mathrm{T}}$) values show a
crossing between pions, kaons and protons, that, depending on the centrality
and the order of the flow harmonic, takes place at different $p_{\mathrm{T}}$
values. In Figs. 7 and 8 it is seen that the crossing between, e.g.
$\pi^{\pm}$ and p+$\overline{\mathrm{p}}$ occurs at lower $p_{\mathrm{T}}$ for
more peripheral collisions in comparison to more central events. The crossing
point for central collisions occurs at higher $p_{\mathrm{T}}$ values for
$v_{n}^{\mathrm{sub}}$ since the common velocity field, which exhibits a
significant centrality dependence, affects heavy particles more. The current
study shows that this occurs not only in the case of elliptic flow but also
for higher flow harmonics. Finally, beyond the crossing point for each
centrality and for every harmonic, it is seen that particles tend to group
based on their number of constituent quarks. This apparent grouping will be
discussed in the next subsection.

Figure 9: The $p_{\mathrm{T}}/n_{q}$ dependence of
$v_{2}^{\mathrm{sub}}/n_{q}$ (left figure) and $v_{3}^{\mathrm{sub}}/n_{q}$
(right figure) for $\pi^{\pm}$, $\mathrm{K}^{\pm}$and
p+$\overline{\mathrm{p}}$ for Pb–Pb collisions in various centrality intervals
at $\sqrt{s_{\mathrm{NN}}}=2.76$ TeV.

Figure 10: The $p_{\mathrm{T}}/n_{q}$ dependence of
$v_{4}^{\mathrm{sub}}/n_{q}$ (left figure) and $v_{5}^{\mathrm{sub}}/n_{q}$
(right figure) for $\pi^{\pm}$, $\mathrm{K}^{\pm}$and
p+$\overline{\mathrm{p}}$ for Pb–Pb collisions in various centrality intervals
at $\sqrt{s_{\mathrm{NN}}}=2.76$ TeV.

###  6.4 Test of scaling properties

It was first observed at RHIC that at intermediate values of transverse
momentum ($3<$ $p_{\mathrm{T}}$ $<6$ $\mathrm{GeV}/c$) the value of $v_{2}$
for baryons is larger than that of mesons [19, 20, 21, 22]. As a result it was
suggested that if both $v_{n}$ and $p_{\mathrm{T}}$ are scaled by the number
of constituent quarks ($n_{q}$), the resulting $p_{\mathrm{T}}/n_{q}$
dependence of the scaled values for all particle species will have an
approximate similar magnitude and dependence on scaled transverse momentum.
This scaling, known as number of constituent quark scaling (NCQ), worked
fairly well at RHIC energies, although later measurements revealed sizeable
deviations from a perfect scaling [30]. Recently, ALICE measurements [23]
showed that the NCQ scaling at LHC energies holds at an approximate level of
$\pm$20% for $v_{2}^{\mathrm{AA}}$.

Although the scaling is only approximate, it stimulated various theoretical
ideas that attempted to address its origin. As a result, several models [28,
29] attempted to explain this observed effect by requiring quark coalescence
to be the dominant particle production mechanism in the intermediate
$p_{\mathrm{T}}$ region, where the hydrodynamic evolution of the fireball is
not the driving force behind the development of anisotropic flow.

Figures 9 and 10 present $v_{2}^{\mathrm{sub}}$ and $v_{3}^{\mathrm{sub}}$, as
well as $v_{4}^{\mathrm{sub}}$ and $v_{5}^{\mathrm{sub}}$, respectively,
scaled by the number of constituent quarks ($n_{q}$) as a function of
$p_{\mathrm{T}}/n_{q}$ for $\pi^{\pm}$, $\mathrm{K}^{\pm}$ and
p+$\overline{\mathrm{p}}$ grouped in centrality bins. Figure 9–left is
consistent with the observation reported in [23] related to the elliptic flow.
For higher harmonics this scaling holds at the same level ($\pm$20%) within
the current statistical and systematic uncertainties.

###  6.5 Comparison with models

Measurements of $v_{n}^{\mathrm{AA}}$ at RHIC and LHC have been successfully
described by hydrodynamical calculations. In particular in [23] it was shown
that a hybrid model that couples the hydrodynamical expansion of the fireball
to a hadronic cascade model describing the final-state hadronic interactions
is able to reproduce the basic features of the measurements at low values of
$p_{\mathrm{T}}$. In parallel, various other models that incorporate a
different description of the dynamical evolution of the system, such as AMPT,
are also able to describe some of the main features of measurements of
azimuthal anisotropy [50, 51, 52]. In this section, these two different
theoretical approaches will be confronted with the experimental measurements.

####  6.5.1 Comparison with iEBE-VISHNU

Figure 11: The $p_{\mathrm{T}}$-differential $v_{2}^{\mathrm{sub}}$ for pions,
kaons and protons measured with the Scalar Product method in Pb–Pb collisions
at $\sqrt{s_{\mathrm{NN}}}=2.76$ TeV compared to $v_{2}$ measured with iEBE-
VISHNU. The upper panels present the comparison for 10–20% up to 40–50%
centrality intervals. The thickness of the curves reflect the uncertainties of
the hydrodynamical calculations. The differences between
$v_{2}^{\mathrm{sub}}$ from data and $v_{2}$ from iEBE-VISHNU are presented in
the lower panels. Figure 12: The $p_{\mathrm{T}}$-differential
$v_{3}^{\mathrm{sub}}$ for pions, kaons and protons measured with the Scalar
Product method in Pb–Pb collisions at $\sqrt{s_{\mathrm{NN}}}=2.76$ TeV
compared to $v_{3}$ measured with iEBE-VISHNU. The upper panels present the
comparison for 10–20% up to 40–50% centrality intervals. The thickness of the
curves reflect the uncertainties of the hydrodynamical calculations. The
differences between $v_{3}^{\mathrm{sub}}$ from data and $v_{3}$ from iEBE-
VISHNU are presented in the lower panels. Figure 13: The
$p_{\mathrm{T}}$-differential $v_{4}^{\mathrm{sub}}$ for pions, kaons and
protons measured with the Scalar Product method in Pb–Pb collisions at
$\sqrt{s_{\mathrm{NN}}}=2.76$ TeV compared to $v_{4}$measured with iEBE-
VISHNU. The upper panels present the comparison for 10–20% up to 40–50%
centrality intervals. The thickness of the curves reflect the uncertainties of
the hydrodynamical calculations. The differences between
$v_{4}^{\mathrm{sub}}$ from data and $v_{4}$ from iEBE-VISHNU are presented in
the lower panels.

Figures 11, 12 and 13 present the comparison between the ALICE measurements of
$v_{n}^{\mathrm{sub}}$ and recent $v_{n}$ hydrodynamical calculations from
[49]. These calculations are based on iEBE-VISHNU, an event-by-event version
of the VISHNU hybrid model [54] which couples 2+1 dimensional viscous
hydrodynamics (VISH2+1) to a hadron cascade model (UrQMD) [55] and uses a set
of fluctuating initial conditions generated with AMPT. The iEBE-VISHNU model
makes it possible to study the influence of the hadronic stage on the
development of elliptic flow and higher harmonics for different particles. In
this model, the initial time after which the hydrodynamic evolution begins is
set to $\tau_{0}=0.4$ $\mathrm{fm}/c$ and the transition between the
macroscopic and microscopic approaches takes place at a temperature of $T=165$
MeV. Finally, the value of the shear viscosity to entropy density ratio is
chosen to be $\eta/s=0.08$, corresponding to the conjectured lower limit
discussed in the introduction. These input parameters were chosen to best fit
the multiplicity and transverse momentum spectra of charged particles in most
central Pb–Pb collisions as well as the $p_{\mathrm{T}}$-differential $v_{2}$,
$v_{3}$, and $v_{4}$ for charged particles for various centrality intervals.

These figures show that this hydrodynamical calculation can reproduce the
observed mass ordering in the experimental data for pions, kaons and protons.
In particular, it is seen that for the range $1<$ $p_{\mathrm{T}}$ $<2$
$\mathrm{GeV}/c$ in the 10–20% centrality interval the model overpredicts the
pion $v_{2}^{\mathrm{sub}}$($p_{\mathrm{T}}$) values by an average of 10%,
however for more peripheral collisions the curve describes the data points
relatively well. In addition, the model describes $v_{3}^{\mathrm{sub}}$ and
$v_{4}^{\mathrm{sub}}$ for charged pions within 5%, i.e. better than
$v_{2}^{\mathrm{sub}}$. Furthermore, it is seen that iEBE-VISHNU overpredicts
the $v_{2}^{\mathrm{sub}}$($p_{\mathrm{T}}$) values of $\mathrm{K}^{\pm}$
(i.e. 10–15% deviations) and does not describe p+$\overline{\mathrm{p}}$ in
more central collisions (i.e. by 10% with a different transverse momentum
dependence compared to data), but in more peripheral collisions the agreement
with the data points is better. Finally, the model describes the
$v_{3}^{\mathrm{sub}}$($p_{\mathrm{T}}$) and
$v_{4}^{\mathrm{sub}}$($p_{\mathrm{T}}$) values for $\mathrm{K}^{\pm}$ and
p+$\overline{\mathrm{p}}$ with a reasonable accuracy (i.e. within 5%) in all
centrality intervals up to $p_{\mathrm{T}}$ around 2 $\mathrm{GeV}/c$. These
observations are also illustrated in the lower plots of each panel in Figs.
11, 12 and 13 that present the difference between the measured
$v_{n}^{\mathrm{sub}}$ relative to a fit to the hydrodynamical calculation.

Figure 14: The $v_{2}^{\mathrm{AA}}$($p_{\mathrm{T}}$),
$v_{3}^{\mathrm{AA}}$($p_{\mathrm{T}}$) and
$v_{4}^{\mathrm{AA}}$($p_{\mathrm{T}}$) in 20–30% central Pb–Pb collisions at
$\sqrt{s_{\mathrm{NN}}}=2.76$ TeV, obtained using the string melting, with
(left) and without (middle) hadronic rescattering, and the default (right)
versions.

####  6.5.2 Comparison with AMPT

Figure 15: The $v_{2}^{\mathrm{sub}}$($p_{\mathrm{T}}$),
$v_{3}^{\mathrm{sub}}$($p_{\mathrm{T}}$) and
$v_{4}^{\mathrm{sub}}$($p_{\mathrm{T}}$) for $\pi^{\pm}$, $\mathrm{K}^{\pm}$
and p+$\overline{\mathrm{p}}$ measured in Pb–Pb collisions at
$\sqrt{s_{\mathrm{NN}}}=2.76$ TeV compared to AMPT (with the string melting
option) in the 20–30% centrality range.

In addition to the hydrodynamical calculations discussed in the previous
paragraphs, three different versions of AMPT [50, 51, 52] are studied in this
article. The AMPT model can be run in two main configurations: the default and
the string melting. In the default version, partons are recombined with the
parent strings when they stop interacting. The resulting strings are later
converted into hadrons using the Lund string fragmentation model [56, 57]. In
the string melting version, the initial strings are melted into partons whose
interactions are described by a parton cascade model [58]. These partons are
then combined into the final-state hadrons via a quark coalescence model. In
both configurations a final-state hadronic rescattering is implemented which
also includes resonance decays. The third version presented in this article is
based on the string melting configuration, in which the hadronic rescattering
phase is switched off to study its influence to the development of anisotropic
flow. The input parameters used in all cases are: $\alpha_{s}=0.33$, a
partonic cross-section of 1.5 mb, while the Lund string fragmentation
parameters were set to $\alpha=0.5$ and $b=0.9$ GeV-2.

Figure 14 presents the $p_{\mathrm{T}}$-differential $v_{2}$ (first row),
$v_{3}$ (middle row) and $v_{4}$ (bottom row) for pions, kaons and protons for
the 20–30% centrality interval. Each column presents the results of one of the
three AMPT versions discussed above. The string melting AMPT version (left
column) predicts a distinct mass ordering at low values of transverse momentum
as well as a lower value of $v_{n}$ for mesons compared to baryons in the
intermediate $p_{\mathrm{T}}$ region for all harmonics, similar to what is
observed in the experimental measurements. On the other hand, the version with
string melting but without the hadronic rescattering contribution (middle
column) can only reproduce the particle type grouping at intermediate
$p_{\mathrm{T}}$ values. Finally, the default AMPT version is only able to
reproduce the mass ordering in the low $p_{\mathrm{T}}$ region. These
observations suggest that the string melting and the final-state hadronic
rescattering are responsible for the particle type grouping at intermediate
$p_{\mathrm{T}}$ and the mass ordering at low $p_{\mathrm{T}}$, respectively.

Since the AMPT string melting version is able to reproduce the main features
of the experimental measurement throughout the reported $p_{\mathrm{T}}$
range, the corresponding results are compared with the data points in Fig. 15.
It is seen that although this version of AMPT reproduces both the mass
ordering and the particle type grouping at low and intermediate
$p_{\mathrm{T}}$ for all harmonics, it fails to quantitatively reproduce the
measurements. In order to understand the origin of this discrepancy both
spectra and the $p_{\mathrm{T}}$-differential $v_{2}^{\mathrm{sub}}$ for
different particle species for the 20–30% centrality interval in AMPT were
fitted with a blast-wave parametrisation [59]. The results were compared to
the analogous parameters obtained from the experiment [43]. It turns out that
the radial flow in AMPT is around 25% lower than the measured value at the
LHC. As the radial flow is essential in shaping the $p_{\mathrm{T}}$
dependence of $v_{n}^{\mathrm{sub}}$ we suppose that the unrealistically low
radial flow in AMPT is responsible for the quantitative disagreement.

##  7 Conclusions

In this article, a measurement of non-flow subtracted flow harmonics,
$v_{2}^{\mathrm{sub}}$, $v_{3}^{\mathrm{sub}}$, $v_{4}^{\mathrm{sub}}$ and
$v_{5}^{\mathrm{sub}}$ as a function of transverse momentum for $\pi^{\pm}$,
$\mathrm{K}^{\pm}$ and p+$\overline{\mathrm{p}}$ for different centrality
intervals (0–1% up to 40–50%) in Pb–Pb collisions at
$\sqrt{s_{\mathrm{NN}}}=2.76$ TeV are reported. The $v_{n}^{\mathrm{sub}}$
coefficients are calculated with the Scalar Product method, selecting the
identified hadron under study and the reference flow particles from different,
non-overlapping pseudorapidity regions. Correlations not related to the common
symmetry planes (i.e. non-flow) were estimated based on pp collisions and were
subtracted from the measurements.

The validity of this subtraction procedure was checked by repeating the
analysis using different charge combinations (i.e. positive–positive and
negative–negative) for the identified hadrons and the reference particles
collisions as well as applying different pseudorapidity gaps ($\Delta\eta$)
between them, in both Pb–Pb and pp collisions. The results after the
subtraction in both cases did not exhibit any systematic change in
$v_{n}^{\mathrm{sub}}$($p_{\mathrm{T}}$) with respect to the default ones for
any particle species or centrality.

All flow harmonics exhibit an increase in peripheral compared to central
collisions. This increase is more pronounced for $v_{2}^{\mathrm{sub}}$ than
for the higher harmonics. This indicates that $v_{2}^{\mathrm{sub}}$ reflects
mainly the geometry of the system, while higher order flow harmonics are
primarily generated by event-by-event fluctuations of the initial energy
density profile. This is also supported by the observation of a significant
non-zero value of $v_{n}^{\mathrm{sub}}$$>0$ in ultra-central (i.e. 0–1$\%$)
collisions. In this centrality interval of Pb–Pb collisions,
$v_{3}^{\mathrm{sub}}$ and $v_{4}^{\mathrm{sub}}$ become gradually larger than
$v_{2}^{\mathrm{sub}}$ at a transverse momentum value which increases with
increasing order of the flow harmonics and particle mass. In addition, a
distinct mass ordering is observed for all $v_{n}^{\mathrm{sub}}$ coefficients
in all centrality intervals in the low transverse momentum region, i.e. for
$p_{\mathrm{T}}<3$ GeV/$c$. Furthermore, the
$v_{n}^{\mathrm{sub}}$($p_{\mathrm{T}}$) values show a crossing between
$\pi^{\pm}$, $\mathrm{K}^{\pm}$ and p+$\overline{\mathrm{p}}$, that takes
place at different $p_{\mathrm{T}}$ values depending on the centrality and the
order of the flow harmonic. These observations are attributed to the interplay
between not only $v_{2}^{\mathrm{sub}}$ but also the higher flow harmonics and
radial flow. For transverse momentum values beyond the crossing point between
different particle species (i.e. for $p_{\mathrm{T}}>3$ GeV/$c$), the values
of $v_{n}^{\mathrm{sub}}$ for baryons are larger than for mesons. The NCQ
scaling holds for $v_{2}^{\mathrm{sub}}$ at an approximate level of $\pm$20%
which is in agreement with [23]. For higher harmonics this scaling holds at a
similar level within the current level of statistical and systematic
uncertainties.

In the low momentum region, hydrodynamic calculations based on iEBE-VISHNU
describe $v_{2}^{\mathrm{sub}}$ for all three particle species and
$v_{3}^{\mathrm{sub}}$ and $v_{4}^{\mathrm{sub}}$ of pions fairly well. For
kaons and protons the model seems to overpredict $v_{3}^{\mathrm{sub}}$ and
$v_{4}^{\mathrm{sub}}$ in almost all centrality intervals. Finally, the
comparison of different AMPT configurations with the measurements highlights
the importance of the final state hadronic rescattering stage and of particle
production via the coalescence mechanism to the development of the mass
ordering and the particle type grouping at low and intermediate transverse
momentum values, respectively. The AMPT with string melting is able to
describe qualitatively both of these features that the experimental data
exhibit. However, it fails to quantitatively describe the measurements,
probably due to a significantly smaller radial flow compared to the
experiment.

## Acknowledgements

The ALICE Collaboration would like to thank all its engineers and technicians
for their invaluable contributions to the construction of the experiment and
the CERN accelerator teams for the outstanding performance of the LHC complex.
The ALICE Collaboration gratefully acknowledges the resources and support
provided by all Grid centres and the Worldwide LHC Computing Grid (WLCG)
collaboration. The ALICE Collaboration acknowledges the following funding
agencies for their support in building and running the ALICE detector: State
Committee of Science, 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 São Paulo (FAPESP); National Natural Science
Foundation of China (NSFC), the Chinese Ministry of Education (CMOE) and the
Ministry of Science and Technology of China (MSTC); Ministry of Education and
Youth of the Czech Republic; 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;
Helsinki Institute of Physics and the Academy of Finland; French CNRS-IN2P3,
the ‘Region Pays de Loire’, ‘Region Alsace’, ‘Region Auvergne’ and CEA,
France; German BMBF and the Helmholtz Association; General Secretariat for
Research and Technology, Ministry of Development, Greece; Hungarian OTKA and
National Office for Research and Technology (NKTH); 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; MEXT Grant-in-
Aid for Specially Promoted Research, Japan; Joint Institute for Nuclear
Research, Dubna; National Research Foundation of Korea (NRF); CONACYT, DGAPA,
México, 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); Polish Ministry of Science and
Higher Education; National Science Centre, Poland; Ministry of National
Education/Institute for Atomic Physics and CNCS-UEFISCDI - Romania; Ministry
of Education and Science of Russian Federation, Russian Academy of Sciences,
Russian Federal Agency of Atomic Energy, Russian Federal Agency for Science
and Innovations and The Russian Foundation for Basic Research; Ministry of
Education of Slovakia; Department of Science and Technology, South Africa;
CIEMAT, EELA, Ministerio de Economía y Competitividad (MINECO) of Spain, Xunta
de Galicia (Consellería de Educación), CEADEN, Cubaenergía, Cuba, and IAEA
(International Atomic Energy Agency); Swedish Research Council (VR) and Knut
$\&$ Alice Wallenberg Foundation (KAW); Ukraine Ministry of Education and
Science; United Kingdom Science and Technology Facilities Council (STFC); The
United States Department of Energy, the United States National Science
Foundation, the State of Texas, and the State of Ohio.

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##  Appendix A Additional figures

###  A.1 Integrated $v_{n}$

Figure 16: The $v_{2}$, $v_{3}$ and $v_{4}$ integrated over the
$p_{\mathrm{T}}$ range $0.3<$$p_{\mathrm{T}}$$<6$ $\mathrm{GeV}/c$ for
$\pi^{\pm}$ (left), $0.3<$$p_{\mathrm{T}}$$<4$ $\mathrm{GeV}/c$ for
$\mathrm{K}^{\pm}$ (middle) and $0.4<$$p_{\mathrm{T}}$$<6$ $\mathrm{GeV}/c$
for p+$\overline{\mathrm{p}}$ (right) as a function of centrality intervals in
Pb–Pb collisions at $\sqrt{s_{\mathrm{NN}}}=2.76$ TeV.

###  A.2 NCQ scaling

Figure 17: Left: the $p_{\mathrm{T}}/n_{q}$ dependence of the double ratio of
$v_{2}^{\mathrm{sub}}/n_{q}$ for $\mathrm{K}^{\pm}$ and
p+$\overline{\mathrm{p}}$ relative to a fit to $v_{2}^{\mathrm{sub}}/n_{q}$ of
$\pi^{\pm}$ for Pb–Pb collisions in various centrality intervals at
$\sqrt{s_{\mathrm{NN}}}=2.76$ TeV. Right: the same for
$v_{3}^{\mathrm{sub}}/n_{q}$.

Figure 18: Left: the $p_{\mathrm{T}}/n_{q}$ dependence of the double ratio of
$v_{4}^{\mathrm{sub}}/n_{q}$ for $\mathrm{K}^{\pm}$ and
p+$\overline{\mathrm{p}}$ relative to a fit to $v_{4}^{\mathrm{sub}}/n_{q}$ of
$\pi^{\pm}$ for Pb–Pb collisions in various centrality intervals at
$\sqrt{s_{\mathrm{NN}}}=2.76$ TeV. Right: the same for
$v_{5}^{\mathrm{sub}}/n_{q}$.

###  A.3 $KE_{\mathrm{T}}$ scaling

It was suggested at RHIC to extend the scaling to lower $p_{\mathrm{T}}$
values by studying the transverse kinetic energy dependence of anisotropic
flow harmonics. Transverse kinetic energy is defined as
$KE_{\mathrm{T}}=m_{\mathrm{T}}-m_{0}$, where
$m_{\mathrm{T}}=\sqrt{m_{0}^{2}+p_{\mathrm{T}}^{2}}$ is the transverse mass.

Figure 19: The $(m_{\mathrm{T}}-m_{0})/n_{q}$-dependence of
$v_{2}^{\mathrm{sub}}/n_{q}$ (left) and $v_{3}^{\mathrm{sub}}/n_{q}$ (right)
for $\pi^{\pm}$, $\mathrm{K}^{\pm}$ and p+$\overline{\mathrm{p}}$ for Pb-Pb
collisions in various centrality intervals at $\sqrt{s_{\mathrm{NN}}}=2.76$
TeV.

Figure 20: The $(m_{\mathrm{T}}-m_{0})/n_{q}$-dependence of
$v_{4}^{\mathrm{sub}}/n_{q}$ (left) and $v_{5}^{\mathrm{sub}}/n_{q}$ (right)
for $\pi^{\pm}$, $\mathrm{K}^{\pm}$ and p+$\overline{\mathrm{p}}$ for Pb-Pb
collisions in various centrality intervals at $\sqrt{s_{\mathrm{NN}}}=2.76$
TeV.

Figure 21: Left: the $(m_{\mathrm{T}}-m_{0})/n_{q}$ dependence of the double
ratio of $v_{2}^{\mathrm{sub}}/n_{q}$ for $\mathrm{K}^{\pm}$ and
p+$\overline{\mathrm{p}}$ relative to a fit to $v_{2}^{\mathrm{sub}}/n_{q}$ of
$\pi^{\pm}$ for Pb–Pb collisions in various centrality intervals at
$\sqrt{s_{\mathrm{NN}}}=2.76$ TeV. Right: the same for
$v_{3}^{\mathrm{sub}}/n_{q}$.

Figure 22: Left: the $(m_{\mathrm{T}}-m_{0})/n_{q}$ dependence of the double
ratio of $v_{4}^{\mathrm{sub}}/n_{q}$ for $\mathrm{K}^{\pm}$ and
p+$\overline{\mathrm{p}}$ relative to a fit to $v_{4}^{\mathrm{sub}}/n_{q}$ of
$\pi^{\pm}$ for Pb–Pb collisions in various centrality intervals at
$\sqrt{s_{\mathrm{NN}}}=2.76$ TeV. Right: the same for
$v_{5}^{\mathrm{sub}}/n_{q}$.

##  Appendix B The ALICE Collaboration

J. Adam${}^{\textrm{\scriptsize 39}}$, D. Adamová${}^{\textrm{\scriptsize
85}}$, M.M. Aggarwal${}^{\textrm{\scriptsize 89}}$, G. Aglieri
Rinella${}^{\textrm{\scriptsize 35}}$, M. Agnello${}^{\textrm{\scriptsize
112}}$,${}^{\textrm{\scriptsize 31}}$, N. Agrawal${}^{\textrm{\scriptsize
48}}$, Z. Ahammed${}^{\textrm{\scriptsize 136}}$, S.
Ahmad${}^{\textrm{\scriptsize 18}}$, S.U. Ahn${}^{\textrm{\scriptsize 69}}$,
S. Aiola${}^{\textrm{\scriptsize 140}}$, A. Akindinov${}^{\textrm{\scriptsize
55}}$, S.N. Alam${}^{\textrm{\scriptsize 136}}$, D.S.D.
Albuquerque${}^{\textrm{\scriptsize 123}}$, D.
Aleksandrov${}^{\textrm{\scriptsize 81}}$, B.
Alessandro${}^{\textrm{\scriptsize 112}}$, D.
Alexandre${}^{\textrm{\scriptsize 103}}$, R. Alfaro
Molina${}^{\textrm{\scriptsize 64}}$, A. Alici${}^{\textrm{\scriptsize
12}}$,${}^{\textrm{\scriptsize 106}}$, A. Alkin${}^{\textrm{\scriptsize 3}}$,
J. Alme${}^{\textrm{\scriptsize 37}}$,${}^{\textrm{\scriptsize 22}}$, T.
Alt${}^{\textrm{\scriptsize 42}}$, S. Altinpinar${}^{\textrm{\scriptsize
22}}$, I. Altsybeev${}^{\textrm{\scriptsize 135}}$, C. Alves Garcia
Prado${}^{\textrm{\scriptsize 122}}$, M. An${}^{\textrm{\scriptsize 7}}$, C.
Andrei${}^{\textrm{\scriptsize 79}}$, H.A. Andrews${}^{\textrm{\scriptsize
103}}$, A. Andronic${}^{\textrm{\scriptsize 99}}$, V.
Anguelov${}^{\textrm{\scriptsize 95}}$, T. Antičić${}^{\textrm{\scriptsize
100}}$, F. Antinori${}^{\textrm{\scriptsize 109}}$, P.
Antonioli${}^{\textrm{\scriptsize 106}}$, L.
Aphecetche${}^{\textrm{\scriptsize 115}}$, H.
Appelshäuser${}^{\textrm{\scriptsize 61}}$, S. Arcelli${}^{\textrm{\scriptsize
27}}$, R. Arnaldi${}^{\textrm{\scriptsize 112}}$, O.W.
Arnold${}^{\textrm{\scriptsize 36}}$,${}^{\textrm{\scriptsize 96}}$, I.C.
Arsene${}^{\textrm{\scriptsize 21}}$, M. Arslandok${}^{\textrm{\scriptsize
61}}$, B. Audurier${}^{\textrm{\scriptsize 115}}$, A.
Augustinus${}^{\textrm{\scriptsize 35}}$, R. Averbeck${}^{\textrm{\scriptsize
99}}$, M.D. Azmi${}^{\textrm{\scriptsize 18}}$, A.
Badalà${}^{\textrm{\scriptsize 108}}$, Y.W. Baek${}^{\textrm{\scriptsize
68}}$, S. Bagnasco${}^{\textrm{\scriptsize 112}}$, R.
Bailhache${}^{\textrm{\scriptsize 61}}$, R. Bala${}^{\textrm{\scriptsize
92}}$, S. Balasubramanian${}^{\textrm{\scriptsize 140}}$, A.
Baldisseri${}^{\textrm{\scriptsize 15}}$, R.C. Baral${}^{\textrm{\scriptsize
58}}$, A.M. Barbano${}^{\textrm{\scriptsize 26}}$, R.
Barbera${}^{\textrm{\scriptsize 28}}$, F. Barile${}^{\textrm{\scriptsize
33}}$, G.G. Barnaföldi${}^{\textrm{\scriptsize 139}}$, L.S.
Barnby${}^{\textrm{\scriptsize 35}}$,${}^{\textrm{\scriptsize 103}}$, V.
Barret${}^{\textrm{\scriptsize 71}}$, P. Bartalini${}^{\textrm{\scriptsize
7}}$, K. Barth${}^{\textrm{\scriptsize 35}}$, J.
Bartke${}^{\textrm{\scriptsize 119}}$0, E. Bartsch${}^{\textrm{\scriptsize
61}}$, M. Basile${}^{\textrm{\scriptsize 27}}$, N.
Bastid${}^{\textrm{\scriptsize 71}}$, S. Basu${}^{\textrm{\scriptsize 136}}$,
B. Bathen${}^{\textrm{\scriptsize 62}}$, G. Batigne${}^{\textrm{\scriptsize
115}}$, A. Batista Camejo${}^{\textrm{\scriptsize 71}}$, B.
Batyunya${}^{\textrm{\scriptsize 67}}$, P.C. Batzing${}^{\textrm{\scriptsize
21}}$, I.G. Bearden${}^{\textrm{\scriptsize 82}}$, H.
Beck${}^{\textrm{\scriptsize 61}}$,${}^{\textrm{\scriptsize 95}}$, C.
Bedda${}^{\textrm{\scriptsize 112}}$, N.K. Behera${}^{\textrm{\scriptsize
51}}$, I. Belikov${}^{\textrm{\scriptsize 65}}$, F.
Bellini${}^{\textrm{\scriptsize 27}}$, H. Bello
Martinez${}^{\textrm{\scriptsize 2}}$, R. Bellwied${}^{\textrm{\scriptsize
125}}$, R. Belmont${}^{\textrm{\scriptsize 138}}$, E. Belmont-
Moreno${}^{\textrm{\scriptsize 64}}$, L.G.E. Beltran${}^{\textrm{\scriptsize
121}}$, V. Belyaev${}^{\textrm{\scriptsize 76}}$, G.
Bencedi${}^{\textrm{\scriptsize 139}}$, S. Beole${}^{\textrm{\scriptsize
26}}$, I. Berceanu${}^{\textrm{\scriptsize 79}}$, A.
Bercuci${}^{\textrm{\scriptsize 79}}$, Y. Berdnikov${}^{\textrm{\scriptsize
87}}$, D. Berenyi${}^{\textrm{\scriptsize 139}}$, R.A.
Bertens${}^{\textrm{\scriptsize 54}}$, D. Berzano${}^{\textrm{\scriptsize
35}}$, L. Betev${}^{\textrm{\scriptsize 35}}$, A.
Bhasin${}^{\textrm{\scriptsize 92}}$, I.R. Bhat${}^{\textrm{\scriptsize 92}}$,
A.K. Bhati${}^{\textrm{\scriptsize 89}}$, B.
Bhattacharjee${}^{\textrm{\scriptsize 44}}$, J. Bhom${}^{\textrm{\scriptsize
119}}$, L. Bianchi${}^{\textrm{\scriptsize 125}}$, N.
Bianchi${}^{\textrm{\scriptsize 73}}$, C. Bianchin${}^{\textrm{\scriptsize
138}}$, J. Bielčík${}^{\textrm{\scriptsize 39}}$, J.
Bielčíková${}^{\textrm{\scriptsize 85}}$, A. Bilandzic${}^{\textrm{\scriptsize
82}}$,${}^{\textrm{\scriptsize 36}}$,${}^{\textrm{\scriptsize 96}}$, G.
Biro${}^{\textrm{\scriptsize 139}}$, R. Biswas${}^{\textrm{\scriptsize 4}}$,
S. Biswas${}^{\textrm{\scriptsize 80}}$,${}^{\textrm{\scriptsize 4}}$, S.
Bjelogrlic${}^{\textrm{\scriptsize 54}}$, J.T. Blair${}^{\textrm{\scriptsize
120}}$, D. Blau${}^{\textrm{\scriptsize 81}}$, C.
Blume${}^{\textrm{\scriptsize 61}}$, F. Bock${}^{\textrm{\scriptsize
75}}$,${}^{\textrm{\scriptsize 95}}$, A. Bogdanov${}^{\textrm{\scriptsize
76}}$, H. Bøggild${}^{\textrm{\scriptsize 82}}$, L.
Boldizsár${}^{\textrm{\scriptsize 139}}$, M. Bombara${}^{\textrm{\scriptsize
40}}$, M. Bonora${}^{\textrm{\scriptsize 35}}$, J.
Book${}^{\textrm{\scriptsize 61}}$, H. Borel${}^{\textrm{\scriptsize 15}}$, A.
Borissov${}^{\textrm{\scriptsize 98}}$, M. Borri${}^{\textrm{\scriptsize
127}}$,${}^{\textrm{\scriptsize 84}}$, F. Bossú${}^{\textrm{\scriptsize 66}}$,
E. Botta${}^{\textrm{\scriptsize 26}}$, C. Bourjau${}^{\textrm{\scriptsize
82}}$, P. Braun-Munzinger${}^{\textrm{\scriptsize 99}}$, M.
Bregant${}^{\textrm{\scriptsize 122}}$, T. Breitner${}^{\textrm{\scriptsize
60}}$, T.A. Broker${}^{\textrm{\scriptsize 61}}$, T.A.
Browning${}^{\textrm{\scriptsize 97}}$, M. Broz${}^{\textrm{\scriptsize 39}}$,
E.J. Brucken${}^{\textrm{\scriptsize 46}}$, E. Bruna${}^{\textrm{\scriptsize
112}}$, G.E. Bruno${}^{\textrm{\scriptsize 33}}$, D.
Budnikov${}^{\textrm{\scriptsize 101}}$, H. Buesching${}^{\textrm{\scriptsize
61}}$, S. Bufalino${}^{\textrm{\scriptsize 31}}$,${}^{\textrm{\scriptsize
26}}$, S.A.I. Buitron${}^{\textrm{\scriptsize 63}}$, P.
Buncic${}^{\textrm{\scriptsize 35}}$, O. Busch${}^{\textrm{\scriptsize 131}}$,
Z. Buthelezi${}^{\textrm{\scriptsize 66}}$, J.B. Butt${}^{\textrm{\scriptsize
16}}$, J.T. Buxton${}^{\textrm{\scriptsize 19}}$, J.
Cabala${}^{\textrm{\scriptsize 117}}$, D. Caffarri${}^{\textrm{\scriptsize
35}}$, X. Cai${}^{\textrm{\scriptsize 7}}$, H. Caines${}^{\textrm{\scriptsize
140}}$, L. Calero Diaz${}^{\textrm{\scriptsize 73}}$, A.
Caliva${}^{\textrm{\scriptsize 54}}$, E. Calvo Villar${}^{\textrm{\scriptsize
104}}$, P. Camerini${}^{\textrm{\scriptsize 25}}$, F.
Carena${}^{\textrm{\scriptsize 35}}$, W. Carena${}^{\textrm{\scriptsize 35}}$,
F. Carnesecchi${}^{\textrm{\scriptsize 12}}$,${}^{\textrm{\scriptsize 27}}$,
J. Castillo Castellanos${}^{\textrm{\scriptsize 15}}$, A.J.
Castro${}^{\textrm{\scriptsize 128}}$, E.A.R. Casula${}^{\textrm{\scriptsize
24}}$, C. Ceballos Sanchez${}^{\textrm{\scriptsize 9}}$, J.
Cepila${}^{\textrm{\scriptsize 39}}$, P. Cerello${}^{\textrm{\scriptsize
112}}$, J. Cerkala${}^{\textrm{\scriptsize 117}}$, B.
Chang${}^{\textrm{\scriptsize 126}}$, S. Chapeland${}^{\textrm{\scriptsize
35}}$, M. Chartier${}^{\textrm{\scriptsize 127}}$, J.L.
Charvet${}^{\textrm{\scriptsize 15}}$, S.
Chattopadhyay${}^{\textrm{\scriptsize 136}}$, S.
Chattopadhyay${}^{\textrm{\scriptsize 102}}$, A.
Chauvin${}^{\textrm{\scriptsize 96}}$,${}^{\textrm{\scriptsize 36}}$, V.
Chelnokov${}^{\textrm{\scriptsize 3}}$, M. Cherney${}^{\textrm{\scriptsize
88}}$, C. Cheshkov${}^{\textrm{\scriptsize 133}}$, B.
Cheynis${}^{\textrm{\scriptsize 133}}$, V. Chibante
Barroso${}^{\textrm{\scriptsize 35}}$, D.D. Chinellato${}^{\textrm{\scriptsize
123}}$, S. Cho${}^{\textrm{\scriptsize 51}}$, P.
Chochula${}^{\textrm{\scriptsize 35}}$, K. Choi${}^{\textrm{\scriptsize 98}}$,
M. Chojnacki${}^{\textrm{\scriptsize 82}}$, S.
Choudhury${}^{\textrm{\scriptsize 136}}$, P.
Christakoglou${}^{\textrm{\scriptsize 83}}$, C.H.
Christensen${}^{\textrm{\scriptsize 82}}$, P.
Christiansen${}^{\textrm{\scriptsize 34}}$, T. Chujo${}^{\textrm{\scriptsize
131}}$, S.U. Chung${}^{\textrm{\scriptsize 98}}$, C.
Cicalo${}^{\textrm{\scriptsize 107}}$, L. Cifarelli${}^{\textrm{\scriptsize
12}}$,${}^{\textrm{\scriptsize 27}}$, F. Cindolo${}^{\textrm{\scriptsize
106}}$, J. Cleymans${}^{\textrm{\scriptsize 91}}$, F.
Colamaria${}^{\textrm{\scriptsize 33}}$, D. Colella${}^{\textrm{\scriptsize
56}}$,${}^{\textrm{\scriptsize 35}}$, A. Collu${}^{\textrm{\scriptsize 75}}$,
M. Colocci${}^{\textrm{\scriptsize 27}}$, G. Conesa
Balbastre${}^{\textrm{\scriptsize 72}}$, Z. Conesa del
Valle${}^{\textrm{\scriptsize 52}}$, M.E. Connors${}^{\textrm{\scriptsize
140}}$idp1832880, J.G. Contreras${}^{\textrm{\scriptsize 39}}$, T.M.
Cormier${}^{\textrm{\scriptsize 86}}$, Y. Corrales
Morales${}^{\textrm{\scriptsize 26}}$,${}^{\textrm{\scriptsize 112}}$, I.
Cortés Maldonado${}^{\textrm{\scriptsize 2}}$, P.
Cortese${}^{\textrm{\scriptsize 32}}$, M.R. Cosentino${}^{\textrm{\scriptsize
122}}$,${}^{\textrm{\scriptsize 124}}$, F. Costa${}^{\textrm{\scriptsize
35}}$, J. Crkovská${}^{\textrm{\scriptsize 52}}$, P.
Crochet${}^{\textrm{\scriptsize 71}}$, R. Cruz Albino${}^{\textrm{\scriptsize
11}}$, E. Cuautle${}^{\textrm{\scriptsize 63}}$, L.
Cunqueiro${}^{\textrm{\scriptsize 35}}$,${}^{\textrm{\scriptsize 62}}$, T.
Dahms${}^{\textrm{\scriptsize 36}}$,${}^{\textrm{\scriptsize 96}}$, A.
Dainese${}^{\textrm{\scriptsize 109}}$, M.C. Danisch${}^{\textrm{\scriptsize
95}}$, A. Danu${}^{\textrm{\scriptsize 59}}$, D. Das${}^{\textrm{\scriptsize
102}}$, I. Das${}^{\textrm{\scriptsize 102}}$, S. Das${}^{\textrm{\scriptsize
4}}$, A. Dash${}^{\textrm{\scriptsize 80}}$, S. Dash${}^{\textrm{\scriptsize
48}}$, S. De${}^{\textrm{\scriptsize 122}}$, A. De
Caro${}^{\textrm{\scriptsize 30}}$, G. de Cataldo${}^{\textrm{\scriptsize
105}}$, C. de Conti${}^{\textrm{\scriptsize 122}}$, J. de
Cuveland${}^{\textrm{\scriptsize 42}}$, A. De Falco${}^{\textrm{\scriptsize
24}}$, D. De Gruttola${}^{\textrm{\scriptsize 30}}$,${}^{\textrm{\scriptsize
12}}$, N. De Marco${}^{\textrm{\scriptsize 112}}$, S. De
Pasquale${}^{\textrm{\scriptsize 30}}$, R.D. De Souza${}^{\textrm{\scriptsize
123}}$, A. Deisting${}^{\textrm{\scriptsize 99}}$,${}^{\textrm{\scriptsize
95}}$, A. Deloff${}^{\textrm{\scriptsize 78}}$, E.
Dénes${}^{\textrm{\scriptsize 139}}$0, C. Deplano${}^{\textrm{\scriptsize
83}}$, P. Dhankher${}^{\textrm{\scriptsize 48}}$, D. Di
Bari${}^{\textrm{\scriptsize 33}}$, A. Di Mauro${}^{\textrm{\scriptsize 35}}$,
P. Di Nezza${}^{\textrm{\scriptsize 73}}$, B. Di Ruzza${}^{\textrm{\scriptsize
109}}$, M.A. Diaz Corchero${}^{\textrm{\scriptsize 10}}$, T.
Dietel${}^{\textrm{\scriptsize 91}}$, P. Dillenseger${}^{\textrm{\scriptsize
61}}$, R. Divià${}^{\textrm{\scriptsize 35}}$, Ø.
Djuvsland${}^{\textrm{\scriptsize 22}}$, A. Dobrin${}^{\textrm{\scriptsize
83}}$,${}^{\textrm{\scriptsize 35}}$, D. Domenicis
Gimenez${}^{\textrm{\scriptsize 122}}$, B. Dönigus${}^{\textrm{\scriptsize
61}}$, O. Dordic${}^{\textrm{\scriptsize 21}}$, T.
Drozhzhova${}^{\textrm{\scriptsize 61}}$, A.K. Dubey${}^{\textrm{\scriptsize
136}}$, A. Dubla${}^{\textrm{\scriptsize 99}}$,${}^{\textrm{\scriptsize 54}}$,
L. Ducroux${}^{\textrm{\scriptsize 133}}$, P. Dupieux${}^{\textrm{\scriptsize
71}}$, R.J. Ehlers${}^{\textrm{\scriptsize 140}}$, D.
Elia${}^{\textrm{\scriptsize 105}}$, E. Endress${}^{\textrm{\scriptsize
104}}$, H. Engel${}^{\textrm{\scriptsize 60}}$, E.
Epple${}^{\textrm{\scriptsize 140}}$, B. Erazmus${}^{\textrm{\scriptsize
115}}$, I. Erdemir${}^{\textrm{\scriptsize 61}}$, F.
Erhardt${}^{\textrm{\scriptsize 132}}$, B. Espagnon${}^{\textrm{\scriptsize
52}}$, M. Estienne${}^{\textrm{\scriptsize 115}}$, S.
Esumi${}^{\textrm{\scriptsize 131}}$, G. Eulisse${}^{\textrm{\scriptsize
35}}$, J. Eum${}^{\textrm{\scriptsize 98}}$, D. Evans${}^{\textrm{\scriptsize
103}}$, S. Evdokimov${}^{\textrm{\scriptsize 113}}$, G.
Eyyubova${}^{\textrm{\scriptsize 39}}$, L. Fabbietti${}^{\textrm{\scriptsize
36}}$,${}^{\textrm{\scriptsize 96}}$, D. Fabris${}^{\textrm{\scriptsize
109}}$, J. Faivre${}^{\textrm{\scriptsize 72}}$, A.
Fantoni${}^{\textrm{\scriptsize 73}}$, M. Fasel${}^{\textrm{\scriptsize 75}}$,
L. Feldkamp${}^{\textrm{\scriptsize 62}}$, A.
Feliciello${}^{\textrm{\scriptsize 112}}$, G. Feofilov${}^{\textrm{\scriptsize
135}}$, J. Ferencei${}^{\textrm{\scriptsize 85}}$, A. Fernández
Téllez${}^{\textrm{\scriptsize 2}}$, E.G. Ferreiro${}^{\textrm{\scriptsize
17}}$, A. Ferretti${}^{\textrm{\scriptsize 26}}$, A.
Festanti${}^{\textrm{\scriptsize 29}}$, V.J.G.
Feuillard${}^{\textrm{\scriptsize 71}}$,${}^{\textrm{\scriptsize 15}}$, J.
Figiel${}^{\textrm{\scriptsize 119}}$, M.A.S.
Figueredo${}^{\textrm{\scriptsize 122}}$, S. Filchagin${}^{\textrm{\scriptsize
101}}$, D. Finogeev${}^{\textrm{\scriptsize 53}}$, F.M.
Fionda${}^{\textrm{\scriptsize 24}}$, E.M. Fiore${}^{\textrm{\scriptsize
33}}$, M. Floris${}^{\textrm{\scriptsize 35}}$, S.
Foertsch${}^{\textrm{\scriptsize 66}}$, P. Foka${}^{\textrm{\scriptsize 99}}$,
S. Fokin${}^{\textrm{\scriptsize 81}}$, E. Fragiacomo${}^{\textrm{\scriptsize
111}}$, A. Francescon${}^{\textrm{\scriptsize 35}}$, A.
Francisco${}^{\textrm{\scriptsize 115}}$, U.
Frankenfeld${}^{\textrm{\scriptsize 99}}$, G.G. Fronze${}^{\textrm{\scriptsize
26}}$, U. Fuchs${}^{\textrm{\scriptsize 35}}$, C.
Furget${}^{\textrm{\scriptsize 72}}$, A. Furs${}^{\textrm{\scriptsize 53}}$,
M. Fusco Girard${}^{\textrm{\scriptsize 30}}$, J.J.
Gaardhøje${}^{\textrm{\scriptsize 82}}$, M. Gagliardi${}^{\textrm{\scriptsize
26}}$, A.M. Gago${}^{\textrm{\scriptsize 104}}$, K.
Gajdosova${}^{\textrm{\scriptsize 82}}$, M. Gallio${}^{\textrm{\scriptsize
26}}$, C.D. Galvan${}^{\textrm{\scriptsize 121}}$, D.R.
Gangadharan${}^{\textrm{\scriptsize 75}}$, P. Ganoti${}^{\textrm{\scriptsize
90}}$, C. Gao${}^{\textrm{\scriptsize 7}}$, C.
Garabatos${}^{\textrm{\scriptsize 99}}$, E. Garcia-
Solis${}^{\textrm{\scriptsize 13}}$, K. Garg${}^{\textrm{\scriptsize 28}}$, C.
Gargiulo${}^{\textrm{\scriptsize 35}}$, P. Gasik${}^{\textrm{\scriptsize
96}}$,${}^{\textrm{\scriptsize 36}}$, E.F. Gauger${}^{\textrm{\scriptsize
120}}$, M. Germain${}^{\textrm{\scriptsize 115}}$, M.
Gheata${}^{\textrm{\scriptsize 59}}$,${}^{\textrm{\scriptsize 35}}$, P.
Ghosh${}^{\textrm{\scriptsize 136}}$, S.K. Ghosh${}^{\textrm{\scriptsize 4}}$,
P. Gianotti${}^{\textrm{\scriptsize 73}}$, P.
Giubellino${}^{\textrm{\scriptsize 35}}$,${}^{\textrm{\scriptsize 112}}$, P.
Giubilato${}^{\textrm{\scriptsize 29}}$, E. Gladysz-
Dziadus${}^{\textrm{\scriptsize 119}}$, P. Glässel${}^{\textrm{\scriptsize
95}}$, D.M. Goméz Coral${}^{\textrm{\scriptsize 64}}$, A. Gomez
Ramirez${}^{\textrm{\scriptsize 60}}$, A.S. Gonzalez${}^{\textrm{\scriptsize
35}}$, V. Gonzalez${}^{\textrm{\scriptsize 10}}$, P. González-
Zamora${}^{\textrm{\scriptsize 10}}$, S. Gorbunov${}^{\textrm{\scriptsize
42}}$, L. Görlich${}^{\textrm{\scriptsize 119}}$, S.
Gotovac${}^{\textrm{\scriptsize 118}}$, V. Grabski${}^{\textrm{\scriptsize
64}}$, O.A. Grachov${}^{\textrm{\scriptsize 140}}$, L.K.
Graczykowski${}^{\textrm{\scriptsize 137}}$, K.L.
Graham${}^{\textrm{\scriptsize 103}}$, A. Grelli${}^{\textrm{\scriptsize
54}}$, A. Grigoras${}^{\textrm{\scriptsize 35}}$, C.
Grigoras${}^{\textrm{\scriptsize 35}}$, V. Grigoriev${}^{\textrm{\scriptsize
76}}$, A. Grigoryan${}^{\textrm{\scriptsize 1}}$, S.
Grigoryan${}^{\textrm{\scriptsize 67}}$, B. Grinyov${}^{\textrm{\scriptsize
3}}$, N. Grion${}^{\textrm{\scriptsize 111}}$, J.M.
Gronefeld${}^{\textrm{\scriptsize 99}}$, J.F. Grosse-
Oetringhaus${}^{\textrm{\scriptsize 35}}$, R. Grosso${}^{\textrm{\scriptsize
99}}$, L. Gruber${}^{\textrm{\scriptsize 114}}$, F.
Guber${}^{\textrm{\scriptsize 53}}$, R. Guernane${}^{\textrm{\scriptsize
72}}$, B. Guerzoni${}^{\textrm{\scriptsize 27}}$, K.
Gulbrandsen${}^{\textrm{\scriptsize 82}}$, T. Gunji${}^{\textrm{\scriptsize
130}}$, A. Gupta${}^{\textrm{\scriptsize 92}}$, R.
Gupta${}^{\textrm{\scriptsize 92}}$, I.B. Guzman${}^{\textrm{\scriptsize 2}}$,
R. Haake${}^{\textrm{\scriptsize 35}}$,${}^{\textrm{\scriptsize 62}}$, C.
Hadjidakis${}^{\textrm{\scriptsize 52}}$, M. Haiduc${}^{\textrm{\scriptsize
59}}$, H. Hamagaki${}^{\textrm{\scriptsize 130}}$, G.
Hamar${}^{\textrm{\scriptsize 139}}$, J.C. Hamon${}^{\textrm{\scriptsize
65}}$, J.W. Harris${}^{\textrm{\scriptsize 140}}$, A.
Harton${}^{\textrm{\scriptsize 13}}$, D. Hatzifotiadou${}^{\textrm{\scriptsize
106}}$, S. Hayashi${}^{\textrm{\scriptsize 130}}$, S.T.
Heckel${}^{\textrm{\scriptsize 61}}$, E. Hellbär${}^{\textrm{\scriptsize
61}}$, H. Helstrup${}^{\textrm{\scriptsize 37}}$, A.
Herghelegiu${}^{\textrm{\scriptsize 79}}$, G. Herrera
Corral${}^{\textrm{\scriptsize 11}}$, F. Herrmann${}^{\textrm{\scriptsize
62}}$, B.A. Hess${}^{\textrm{\scriptsize 94}}$, K.F.
Hetland${}^{\textrm{\scriptsize 37}}$, H. Hillemanns${}^{\textrm{\scriptsize
35}}$, B. Hippolyte${}^{\textrm{\scriptsize 65}}$, D.
Horak${}^{\textrm{\scriptsize 39}}$, R. Hosokawa${}^{\textrm{\scriptsize
131}}$, P. Hristov${}^{\textrm{\scriptsize 35}}$, C.
Hughes${}^{\textrm{\scriptsize 128}}$, T.J. Humanic${}^{\textrm{\scriptsize
19}}$, N. Hussain${}^{\textrm{\scriptsize 44}}$, T.
Hussain${}^{\textrm{\scriptsize 18}}$, D. Hutter${}^{\textrm{\scriptsize
42}}$, D.S. Hwang${}^{\textrm{\scriptsize 20}}$, R.
Ilkaev${}^{\textrm{\scriptsize 101}}$, M. Inaba${}^{\textrm{\scriptsize
131}}$, E. Incani${}^{\textrm{\scriptsize 24}}$, M.
Ippolitov${}^{\textrm{\scriptsize 81}}$,${}^{\textrm{\scriptsize 76}}$, M.
Irfan${}^{\textrm{\scriptsize 18}}$, V. Isakov${}^{\textrm{\scriptsize 53}}$,
M. Ivanov${}^{\textrm{\scriptsize 35}}$,${}^{\textrm{\scriptsize 99}}$, V.
Ivanov${}^{\textrm{\scriptsize 87}}$, V. Izucheev${}^{\textrm{\scriptsize
113}}$, B. Jacak${}^{\textrm{\scriptsize 75}}$, N.
Jacazio${}^{\textrm{\scriptsize 27}}$, P.M. Jacobs${}^{\textrm{\scriptsize
75}}$, M.B. Jadhav${}^{\textrm{\scriptsize 48}}$, S.
Jadlovska${}^{\textrm{\scriptsize 117}}$, J. Jadlovsky${}^{\textrm{\scriptsize
56}}$,${}^{\textrm{\scriptsize 117}}$, C. Jahnke${}^{\textrm{\scriptsize
122}}$,${}^{\textrm{\scriptsize 36}}$, M.J. Jakubowska${}^{\textrm{\scriptsize
137}}$, M.A. Janik${}^{\textrm{\scriptsize 137}}$, P.H.S.Y.
Jayarathna${}^{\textrm{\scriptsize 125}}$, C. Jena${}^{\textrm{\scriptsize
29}}$, S. Jena${}^{\textrm{\scriptsize 125}}$, R.T. Jimenez
Bustamante${}^{\textrm{\scriptsize 99}}$, P.G. Jones${}^{\textrm{\scriptsize
103}}$, A. Jusko${}^{\textrm{\scriptsize 103}}$, P.
Kalinak${}^{\textrm{\scriptsize 56}}$, A. Kalweit${}^{\textrm{\scriptsize
35}}$, J.H. Kang${}^{\textrm{\scriptsize 141}}$, V.
Kaplin${}^{\textrm{\scriptsize 76}}$, S. Kar${}^{\textrm{\scriptsize 136}}$,
A. Karasu Uysal${}^{\textrm{\scriptsize 70}}$, O.
Karavichev${}^{\textrm{\scriptsize 53}}$, T.
Karavicheva${}^{\textrm{\scriptsize 53}}$, L. Karayan${}^{\textrm{\scriptsize
95}}$,${}^{\textrm{\scriptsize 99}}$, E. Karpechev${}^{\textrm{\scriptsize
53}}$, U. Kebschull${}^{\textrm{\scriptsize 60}}$, R.
Keidel${}^{\textrm{\scriptsize 142}}$, D.L.D.
Keijdener${}^{\textrm{\scriptsize 54}}$, M. Keil${}^{\textrm{\scriptsize
35}}$, M. Mohisin Khan${}^{\textrm{\scriptsize 18}}$idp3268336, P.
Khan${}^{\textrm{\scriptsize 102}}$, S.A. Khan${}^{\textrm{\scriptsize 136}}$,
A. Khanzadeev${}^{\textrm{\scriptsize 87}}$, Y.
Kharlov${}^{\textrm{\scriptsize 113}}$, A. Khatun${}^{\textrm{\scriptsize
18}}$, B. Kileng${}^{\textrm{\scriptsize 37}}$, D.W.
Kim${}^{\textrm{\scriptsize 43}}$, D.J. Kim${}^{\textrm{\scriptsize 126}}$, D.
Kim${}^{\textrm{\scriptsize 141}}$, H. Kim${}^{\textrm{\scriptsize 141}}$,
J.S. Kim${}^{\textrm{\scriptsize 43}}$, J. Kim${}^{\textrm{\scriptsize 95}}$,
M. Kim${}^{\textrm{\scriptsize 51}}$, M. Kim${}^{\textrm{\scriptsize 141}}$,
S. Kim${}^{\textrm{\scriptsize 20}}$, T. Kim${}^{\textrm{\scriptsize 141}}$,
S. Kirsch${}^{\textrm{\scriptsize 42}}$, I. Kisel${}^{\textrm{\scriptsize
42}}$, S. Kiselev${}^{\textrm{\scriptsize 55}}$, A.
Kisiel${}^{\textrm{\scriptsize 137}}$, G. Kiss${}^{\textrm{\scriptsize 139}}$,
J.L. Klay${}^{\textrm{\scriptsize 6}}$, C. Klein${}^{\textrm{\scriptsize
61}}$, J. Klein${}^{\textrm{\scriptsize 35}}$, C. Klein-
Bösing${}^{\textrm{\scriptsize 62}}$, S. Klewin${}^{\textrm{\scriptsize 95}}$,
A. Kluge${}^{\textrm{\scriptsize 35}}$, M.L. Knichel${}^{\textrm{\scriptsize
95}}$, A.G. Knospe${}^{\textrm{\scriptsize 120}}$,${}^{\textrm{\scriptsize
125}}$, C. Kobdaj${}^{\textrm{\scriptsize 116}}$, M.
Kofarago${}^{\textrm{\scriptsize 35}}$, T. Kollegger${}^{\textrm{\scriptsize
99}}$, A. Kolojvari${}^{\textrm{\scriptsize 135}}$, V.
Kondratiev${}^{\textrm{\scriptsize 135}}$, N.
Kondratyeva${}^{\textrm{\scriptsize 76}}$, E.
Kondratyuk${}^{\textrm{\scriptsize 113}}$, A.
Konevskikh${}^{\textrm{\scriptsize 53}}$, M. Kopcik${}^{\textrm{\scriptsize
117}}$, M. Kour${}^{\textrm{\scriptsize 92}}$, C.
Kouzinopoulos${}^{\textrm{\scriptsize 35}}$, O.
Kovalenko${}^{\textrm{\scriptsize 78}}$, V. Kovalenko${}^{\textrm{\scriptsize
135}}$, M. Kowalski${}^{\textrm{\scriptsize 119}}$, G. Koyithatta
Meethaleveedu${}^{\textrm{\scriptsize 48}}$, I. Králik${}^{\textrm{\scriptsize
56}}$, A. Kravčáková${}^{\textrm{\scriptsize 40}}$, M.
Krivda${}^{\textrm{\scriptsize 56}}$,${}^{\textrm{\scriptsize 103}}$, F.
Krizek${}^{\textrm{\scriptsize 85}}$, E. Kryshen${}^{\textrm{\scriptsize
87}}$,${}^{\textrm{\scriptsize 35}}$, M. Krzewicki${}^{\textrm{\scriptsize
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Kučera${}^{\textrm{\scriptsize 85}}$, C. Kuhn${}^{\textrm{\scriptsize 65}}$,
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