2018 103 10 May

Anisotropic flow of identified particles

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

The elliptic ($v_{2}$), triangular ($v_{3}$), and quadrangular ($v_{4}$) flow
coefficients of $\pi^{\pm}$, ${\rm K}^{\pm}$, ${\rm p+\overline{p}}$,
${\Lambda+\overline{\Lambda}}$, ${\rm K}^{\rm 0}_{\rm S}$, and the
$\phi$-meson are measured in Pb–Pb collisions at $\sqrt{s_{\rm NN}}=5.02$ TeV.
Results obtained with the scalar product method are reported for the rapidity
range $|y|<$ 0.5 as a function of transverse momentum, $p_{\text{T}}$, at
different collision centrality intervals between 0–70%, including ultra-
central (0–1%) collisions for $\pi^{\pm}$, ${\rm K}^{\pm}$, and ${\rm
p+\overline{p}}$. For $p_{\text{T}}~{}<~{}3$
GeV$\kern-0.50003pt/\kern-0.20004ptc$, the flow coefficients exhibit a
particle mass dependence. At intermediate transverse momenta
($3<p_{\text{T}}<$ 8-10 GeV$\kern-0.50003pt/\kern-0.20004ptc$), particles show
an approximate grouping according to their type (i.e., mesons and baryons).
The $\phi$-meson $v_{2}$, which tests both particle mass dependence and type
scaling, follows ${\rm p+\overline{p}}$ $v_{2}$ at low $p_{\text{T}}$ and
$\pi^{\pm}$ $v_{2}$ at intermediate $p_{\text{T}}$. The evolution of the shape
of $v_{\rm n}(p_{\mathrm{T}})$ as a function of centrality and harmonic number
$n$ is studied for the various particle species. Flow coefficients of
$\pi^{\pm}$, ${\rm K}^{\pm}$, and ${\rm p+\overline{p}}$ for $p_{\text{T}}<3$
GeV$\kern-0.50003pt/\kern-0.20004ptc$ are compared to iEBE-VISHNU and MUSIC
hydrodynamical calculations coupled to a hadronic cascade model (UrQMD). The
iEBE-VISHNU calculations describe the results fairly well for
$p_{\text{T}}~{}<~{}2.5$ GeV$\kern-0.50003pt/\kern-0.20004ptc$, while MUSIC
calculations reproduce the measurements for $p_{\text{T}}~{}<~{}1$
GeV$\kern-0.50003pt/\kern-0.20004ptc$. A comparison to $v_{\rm n}$
coefficients measured in Pb–Pb collisions at $\sqrt{s_{\rm NN}}$ = 2.76 TeV is
also provided.

##  1 Introduction

Ultra-relativistic heavy-ion collisions are used to study the properties of
the quark-gluon plasma (QGP), a state of deconfined quarks and gluons expected
at high temperatures or baryon densities [1]. Measurements of anisotropies in
particle azimuthal distributions relative to the collision symmetry planes at
the Relativistic Heavy Ion Collider (RHIC) [2, 3, 4, 5] and the Large Hadron
Collider (LHC) [6, 7, 8] have shown that the produced hot and dense matter
behaves as a strongly-interacting QGP. Comparisons to predictions from
hydrodynamic models indicate that the QGP has a shear viscosity to entropy
density ratio $(\eta/s)$ close to the theoretical lower limit from the anti-de
Sitter/conformal field theory (AdS/CFT) correspondence of $1/4\pi$ for
$\hbar=k_{\rm B}=1$ [9].

Azimuthal anisotropies in particle production relative to the collision
symmetry planes, often referred to as anisotropic flow, arise from the
asymmetry in the initial geometry of the collision combined with the initial
inhomogeneities of the system’s energy density [10]. Anisotropic flow depends
on the equation of state and transport coefficients of the system, such as
$\eta/s$ and bulk viscosity to entropy density ratio ($\zeta/s$). Its
magnitude is quantified via the coefficients $v_{\rm n}$ in a Fourier
decomposition of the particle azimuthal distribution [11]

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

where $E$ is the energy, ${p}$ the momentum, $p_{\mathrm{T}}$ the transverse
momentum, $\varphi$ the azimuthal angle, $\eta$ the pseudorapidity of the
particle, and $\Psi_{\rm n}$ the $n$-th harmonic symmetry plane angle. The
second order flow coefficient $v_{2}$, called _elliptic flow_ , is the largest
contribution to the asymmetry of non-central collisions because of the almond-
like geometry of the overlap region between the colliding nuclei in the plane
perpendicular to the beam direction. The third-order flow coefficient $v_{3}$,
named _triangular flow_ , is generated by fluctuations in the initial
distribution of nucleons and gluons in the overlap region [12, 13, 14, 15].
The fourth-order flow coefficient $v_{4}$, called _quandrangular flow_ , is
generated both by initial geometry, fluctuations, and is in addition sensitive
to the non-linear hydrodynamic response of the medium [16, 17]. It has been
shown that higher-order flow coefficients are more sensitive to $\eta/s$ than
$v_{2}$ [18, 19].

In addition to probing $\eta/s$ and $\zeta/s$, anisotropic flow constrains the
initial spatial density (e.g. energy and entropy density), freeze-out
conditions of the system, and particle production mechanisms in different
$p_{\mathrm{T}}$ regions. Stronger constraints are achieved by studying
anisotropic flow of identified particles. To guide interpretation of the
results in the context of these processes, three kinematic ‘regions of
interest’ are defined in the $p_{\mathrm{T}}$-differential $v_{\rm n}$
measurements, $v_{\rm n}(p_{\mathrm{T}})$. For $p_{\mathrm{T}}\lesssim$ 3
$\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc$, anisotropic flow is a remnant
of the collective dynamics during the hydrodynamic expansion of the system.
The interplay between the isotropic expansion (radial flow) and anisotropic
flow leads to a characteristic mass ordering of $v_{\rm n}(p_{\mathrm{T}})$
[20, 21, 22, 23, 24, 25, 26, 27, 28], meaning that heavier particles have
smaller $v_{\rm n}(p_{\mathrm{T}})$. At intermediate $p_{\mathrm{T}}$ (3
$\lesssim p_{\mathrm{T}}{}\lesssim$ 8
$\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc$), the values of $v_{\rm n}$ for
different particles tend to separate mesons and baryons [29, 30, 31, 32, 33,
27, 28]. The flow of baryons is larger than that of mesons in this
$p_{\mathrm{T}}$ range, supporting the hypothesis of hadronization through
quark coalescence [34], where it is assumed that the invariant spectrum of
produced particles is proportional to the product of the spectra of their
constituents [35, 36]. However, the scaling only holds approximately at RHIC
[32] and at the level of $\pm 20\%$ in Pb–Pb collisions at
$\sqrt{s_{\mathrm{NN}}}$ = 2.76 TeV [27, 28]. This behaviour is also
qualitatively consistent with a scenario in which particle production includes
interactions of jet fragments with bulk matter [37, 38]. For $p_{\mathrm{T}}$
$\gtrsim$ 8 $\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc$, anisotropic flow
is generated when hard partons that propagate through the system lose energy
via (multiple) scattering and gluon radiation [39, 40], resulting in $v_{\rm
n}$ that remain non-zero up to very high $p_{\mathrm{T}}$ [41, 42, 43, 44].

Anisotropic flow of identified particles is an important observable when
studying the characteristics of the QGP. However, since particles can scatter
and be regenerated in between the chemical and kinetic freeze-out of a
collision (the _hadronic phase_), information about the QGP phase imprinted in
$v_{\rm n}(p_{\mathrm{T}})$ can be altered by late-stage interactions and
resonance decays, which can affect both $v_{\rm n}$ and $\langle
p_{\mathrm{T}}{}\rangle$ [45], leading to a deviation in mass ordering in
$v_{\rm n}(p_{\mathrm{T}})$ at low $p_{\mathrm{T}}$ [46]. The $\phi$-meson has
been suggested as a particularly sensitive probe of the early collision phase
as its production rate via regeneration in the hadronic phase is negligible
[47] and it is theorized to have a low hadronic cross section [48, 49, 50],
making it insensitive to the dissipative effects of the hadronic phase of the
collision (although it should be noted that there is no consensus on the exact
value of the cross section between the $\phi$-meson and nucleons in heavy-ion
collisions [51, 52, 53, 54]). Recent experimental studies [27, 55, 56] suggest
that the $\phi$-meson may be more sensitive to the hadronic phase than
anticipated.

In this article, we present measurements of $p_{\mathrm{T}}$-differential
elliptic, triangular, and quadrangular flow coefficients of $\pi^{\pm}$, ${\rm
K}^{\pm}$, p+$\rm\overline{p}$, $\Lambda$+$\overline{\Lambda}$, ${\rm K}^{\rm
0}_{\rm S}$, and the $\phi$-meson in Pb–Pb collisions at $\sqrt{s_{\rm NN}}$ =
5.02 TeV, extending greatly, and improving in precision upon, the previous
measurements of identified particle $v_{\rm n}$ in Pb–Pb collisions at
$\sqrt{s_{\rm NN}}$ = 2.76 TeV as carried out by ALICE [27, 28, 33]. The
results are reported for a wide range of particle transverse momenta within
the rapidity range $|y|<$ 0.5 at different collision centralities between
0–70% range. To isolate the fraction of anisotropic flow that is generated by
initial-state fluctuations rather than geometry, the flow coefficients are
also studied in ultra-central collisions (0–1% collision centrality).
Centrality estimates the degree of overlap between the two colliding nuclei
and is expressed as percentiles of the inelastic hadronic cross section, with
low percentage values corresponding to head-on collisions. The measurements
are performed using the scalar product method [57, 58, 59] with a
(pseudo-)rapidity gap of $|\Delta\eta|>2.0$ between the identified particles
under study and the charged reference particles. The flow coefficients are
measured separately for particles and anti-particles and are found to be
compatible within the statistical uncertainties for most $p_{\mathrm{T}}$ and
centrality intervals. Any residual differences are included in the systematic
uncertainties, and $v_{\rm n}$ denotes the average between results for
particles and anti-particles.

This paper is organized as follows. Analysis details, particle identification,
reconstruction methods, and flow measurement techniques are outlined in Sec.
2. The evaluation of systematic uncertainties is discussed in Sec. 3. The flow
coefficients of $\pi^{\pm}$, ${\rm K}^{\pm}$, p+$\rm\overline{p}$ ($v_{2}$,
$v_{3}$, and $v_{4}$), $\Lambda$+$\overline{\Lambda}$, ${\rm K}^{\rm 0}_{\rm
S}$ ($v_{2}$ and $v_{3}$), and the $\phi$-meson ($v_{2}$) are reported and
compared to model calculations in Sec. 4. Finally, the results are summarized
in Sec. 5.

##  2 Experimental setup and data analysis

ALICE [60, 61, 62] is a dedicated heavy-ion experiment at the LHC optimized to
study the properties of strongly interacting matter produced in heavy-ion
collisions. A full overview of the detector layout and its performance can be
found in [62, 63]. The main subsystems used in this analysis are the Inner
Tracking System (ITS) [64], Time Projection Chamber (TPC) [65], Time Of Flight
detector (TOF) [66], and V0 [67]. The ITS, TPC, and TOF detectors cover full
azimuth within pseudorapidity range $|\eta|<$ 0.9 and lie within a homogeneous
magnetic field of up to 0.5 T. The ITS consists of six layers of silicon
detectors used for tracking and vertex reconstruction. The TPC is the main
tracking detector and is also used to identify particles via specific
ionization energy loss, $\mathrm{d}E/\mathrm{d}x$. The TOF in conjunction with
the timing information from the T0 detector [68] provide particle
identification based on flight time. The T0 is made up of two arrays of
Cherenkov counters T0C and T0A, located at -3.3 $<\eta<$ -3.0 and 4.5 $<\eta<$
4.9, respectively. Two scintillator arrays (V0), which cover the
pseudorapidity ranges $-3.7<\eta<-1.7$ (V0C) and $2.8<\eta<5.1$ (V0A), are
used for triggering, event selection, and the determination of centrality [69]
and $\textbf{Q}_{\rm n}$-vectors (see Sec. 2.5). Both V0 detectors are
segmented in four rings in the radial direction with each ring divided into
eight sectors in the azimuthal direction. In addition, two tungsten-quartz
neutron Zero Degree Calorimeters (ZDCs), installed 112.5 meters from the
interaction point on each side, are used for event selection.

###  2.1 Event and track selection

The data sample recorded by ALICE during the 2015 LHC Pb–Pb run at
$\sqrt{s_{\mathrm{NN}}}$ = 5.02 TeV is used for this analysis. The minimum-
bias trigger requires signals in both V0A and V0C detectors. An offline event
selection is applied to remove beam-induced background (i.e. beam-gas events)
and pileup events. The former is rejected utilizing the V0 and ZDC timing
information. The remaining contribution of such interactions is found to be
smaller than 0.02% [63]. Pileup events, which constitute about 0.25% of the
recorded sample, are removed by comparing multiplicity estimates from the V0
detector to those of tracking detectors at mid-rapidity, exploiting the
difference in readout times between the systems. The fraction of pileup events
left after applying the dedicated pileup removal criteria is found to be
negligible. The primary vertex position is determined from tracks
reconstructed in the ITS and TPC as described in Ref. [63]. Only events with a
primary vertex position within $\pm 10$ cm from the nominal interaction point
along the beam direction are used in the analysis. Approximately $67\times
10^{6}$ Pb–Pb events in the 0–70% centrality interval pass these selection
criteria. Centrality is estimated from the energy deposition measured in the
V0 detector [69].

Charged-particle tracks, used to measure the $v_{\rm n}$ of $\pi^{\pm}$, ${\rm
K}^{\pm}$, p+$\rm\overline{p}$ and the $\phi$-meson, are reconstructed using
the ITS and TPC within $|\eta|<0.8$ and $0.5<p_{\mathrm{T}}<16.0$ GeV/$c$ with
a track-momentum resolution better than 4% for the considered range [63].
Additional quality criteria are used to reduce the contamination from
secondary charged particles (i.e., particles originating from weak decays,
$\gamma$-conversions, and secondary hadronic interactions in the detector
material) and fake tracks (random associations of space points). Only tracks
with at least 70 space points, out of a maximum of 159, with a $\chi^{2}$ per
degree-of-freedom for the track fit lower than 2, are accepted. Moreover, each
track is required to cross at least 70 TPC pad rows and to be reconstructed
from at least 80% of the number of expected TPC space points, in addition to
having at least one hit in the two innermost layers of the ITS. Furthermore,
tracks with a distance of closest approach (DCA) to the reconstructed event
vertex smaller than 2 cm in the longitudinal direction ($z$) and (0.0105 +
0.0350 ($p_{\mathrm{T}}$ $c$/GeV)-1.1) cm in the transverse plane ($xy$) are
selected. Relevant selection criteria for tracks used for the reconstruction
of ${\rm K}^{\rm 0}_{\rm S}$ and $\Lambda$+$\overline{\Lambda}$ are given in
Sec. 2.3.

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

Particle identification is performed using the specific ionization energy
loss, $\mathrm{d}E/\mathrm{d}x$, measured in the TPC and the time of flight
obtained from the TOF. A truncated-mean procedure is used to estimate the
$\mathrm{d}E/\mathrm{d}x$ (where the 40% highest-charge clusters are
discarded), which yields a $\mathrm{d}E/\mathrm{d}x$ resolution around 6.5% in
the 0–5% centrality class [63]. At least 70 clusters are used for the
$\mathrm{d}E/\mathrm{d}x$ estimation. The TOF measures the time that a
particle needs to travel from the primary vertex to the detector itself with a
time resolution of $\approx$ 80 ps [63]. The start time for the TOF
measurement is provided by the T0 detector or from a combinatorial algorithm
which uses the particle arrival times at the TOF detector itself [63, 66].

Expressing the difference between the expected $\mathrm{d}E/\mathrm{d}x$ and
the time of flight for $\pi^{\pm}$, ${\rm K}^{\pm}$ and p+$\rm\overline{p}$,
and the measured signals in both TPC and TOF, in units of the standard
deviations from the most probable value for both detectors (n$\sigma_{\rm
TPC},~{}$n$\sigma_{\rm TOF}$), and applying a selection on the number of
accepted n$\sigma$, allows for particle identification on a track-by-track
basis. The TPC $\mathrm{d}E/\mathrm{d}x$ of different particle species are
separated by at least 4$\sigma$ for $p_{\mathrm{T}}$ $<$ 0.7
$\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc$, while in the relativistic rise
region of the $\mathrm{d}E/\mathrm{d}x$ ($p_{\mathrm{T}}>$ 2
$\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc$) particle identification is
still possible but only on a statistical basis [63]. The TOF detector provides
3$\sigma$ separation between $\pi^{\pm}$ and ${\rm K}^{\pm}$ for
$p_{\mathrm{T}}$ $<$ 2.5 $\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc$, and
between ${\rm K}^{\pm}$ and p+$\rm\overline{p}$ for $p_{\mathrm{T}}$ $<$ 4
$\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc$ [63].

The information from the TPC and TOF is combined using a quadratic sum ${\rm
n}\sigma_{\rm PID}=\sqrt{{\rm n}\sigma_{\rm TPC}^{2}+{\rm n}\sigma_{\rm
TOF}^{2}}$ for 0.5 $<$ $p_{\mathrm{T}}$ $\leq$ 4
$\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc$. Particles are selected by
requiring ${\rm n}\sigma_{\rm PID}<3$ for each species. The smallest ${\rm
n}\sigma_{\rm PID}$ is used to assign the identity when the selection
criterion is fulfilled by more than one species. When measuring
p+$\rm\overline{p}$ $v_{\rm n}(p_{\mathrm{T}})$, only $\rm\overline{p}$ are
considered for $p_{\mathrm{T}}$ $<$ 2
$\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc$ to exclude secondary protons
from detector material. At high transverse momenta ($p_{\mathrm{T}}$ $>$ 4
$\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc$), ${\rm K}^{\pm}$ cannot
reliably be identified. Identification of $\pi^{\pm}$ and p+$\rm\overline{p}$
for $p_{\mathrm{T}}$ $>4$ $\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc$ is
done utilizing the TPC $\mathrm{d}E/\mathrm{d}x$ signal only. Pions (protons)
are selected from the upper (lower) part of the expected pion (proton)
$\mathrm{d}E/\mathrm{d}x$ distribution. For example, proton selection
typically varies in the range from 0 to $-3\sigma_{\rm TPC}$ or from
$-1.5\sigma_{\rm TPC}$ to $-4.5\sigma_{\rm TPC}$ depending on the momentum.

Secondary contamination from weak decays, studied using the procedure outlined
in [70], decreases from about 30% to 5% for p+$\rm\overline{p}$ in the
$p_{\mathrm{T}}$ range 0.7-4.0 GeV/$c$ and from about 5% to 0.5% for
$\pi^{\pm}$ in the $p_{\mathrm{T}}$ range 0.5-4.0 GeV/$c$, while it is
negligible for ${\rm K}^{\pm}$. The $v_{\rm n}$ coefficients are not corrected
for these contaminations; their effect on $v_{\rm n}$ is at maximum $\approx$
8%, for $\rm p+\overline{p}$ $v_{2}$ at $p_{\mathrm{T}}$ $<$ 1
$\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc$ for central collisions, and
negligible for ${\rm K}^{\pm}$, $\pi^{\pm}$ $v_{\rm n}$. The contamination
from other particle species is below 3% and 20% at $p_{\mathrm{T}}$ $>$ 4.0
$\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc$ for $\pi^{\pm}$ and
p+$\rm\overline{p}$, respectively, and contamination from fake tracks is
negligible. The $v_{\rm n}$ results are reported for
$0.5<p_{\mathrm{T}}<16.0(12.0,6.0)$
$\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc$ for $\pi^{\pm}$ $v_{2}$
($v_{3}$, $v_{4}$), $0.7<p_{\mathrm{T}}<16.0(12.0,6.0)$
$\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc$ for p+$\rm\overline{p}$ $v_{2}$
($v_{3}$, $v_{4}$), and $0.5<p_{\mathrm{T}}<4.0$
$\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc$ for ${\rm K}^{\pm}$ $v_{\rm
n}$, all within $|y|<$ 0.5.

###  2.3 Reconstruction of ${\rm K}^{\rm 0}_{\rm S}$ and
$\Lambda+\overline{\Lambda}$

The ${\rm K}^{\rm 0}_{\rm S}$ and $\Lambda$+$\overline{\Lambda}$ are
reconstructed in the ${\rm K}^{\rm 0}_{\rm S}$ $\rightarrow$ $\pi^{+}$ \+
$\pi^{-}$ and $\Lambda{}$ $\rightarrow$ p + $\pi^{-}$
($\overline{\Lambda}\rightarrow\rm\overline{p}{}+\pi^{+}{}$) channels with
branching ratios of 69.2% [71] and 63.9% [71] respectively. Reconstruction of
${\rm K}^{\rm 0}_{\rm S}$ and $\Lambda$+$\overline{\Lambda}$ is based on
identifying secondary vertices from which two oppositely-charged particles
originate, called V0s. Topological selection criteria pertaining to the shape
of the ${\rm V}^{\rm 0}$ decay can be imposed, as well as requirements on the
species identity of the decay products (called _daughter particles_).

The ${\rm V}^{\rm 0}$ candidates are selected to have an invariant mass
between 0.4 and 0.6 GeV/$c^{2}$ and 1.07 and 1.17 GeV/$c^{2}$ for ${\rm
K}^{\rm 0}_{\rm S}$ and $\Lambda$+$\overline{\Lambda}$, respectively. The
invariant mass of the ${\rm V}^{\rm 0}$ is calculated based on the assumption
that the daughter particles are either a $\pi^{+}$$\pi^{-}$ pair, or a
p$\pi^{-}$ ($\rm\overline{p}$$\pi^{+}$) pair. The daughter particles have been
identified over the entire $p_{\mathrm{T}}$ range using the TPC following the
n$\sigma$ approach detailed in Sec. 2.2 ($|{\rm n}\sigma_{\rm TPC}|<3$). The
daughter tracks were reconstructed within $|\eta|<0.8$, while the criteria on
the number of TPC space points, the $\chi^{2}$ per TPC space point per degree-
of-freedom, the number of crossed TPC pad rows, and the percentage of the
expected TPC space points used to reconstruct a track are identical to those
applied for primary particles. In addition, the minimum DCA of daughter tracks
to the primary vertex is 0.1 cm. Furthermore, the maximum DCA of daughter
tracks to the secondary vertex is 0.5 cm to ensure that they are products of
the same decay.

To reject secondary vertices arising from decays into more than two particles,
the cosine of the pointing angle $\theta_{p}$ is required to be larger than
0.998. This angle is defined as the angle between the momentum-vector of the
${\rm V}^{\rm 0}$ assessed at its decay position and the line connecting the
${\rm V}^{\rm 0}$ decay vertex to the primary vertex and has to be close to 0
as a result of momentum conservation. In addition, the ${\rm V}^{\rm 0}$
candidates are only accepted when they are produced at a distance between 5
and 100 cm from the nominal primary vertex in the radial direction. The lower
value is chosen to avoid any bias from the efficiency loss when secondary
tracks are being wrongly matched to clusters in the first layer of the ITS. To
assess the systematic uncertainty related to contaminations from
$\Lambda$+$\overline{\Lambda}$ and electron–positron pairs coming from
$\gamma$-conversions to the ${\rm K}^{\rm 0}_{\rm S}$ sample, a selection in
the Armenteros-Podolanski variables [72] is applied for the ${\rm K}^{\rm
0}_{\rm S}$ candidates, rejecting ones with $q\leq|\alpha|/5$. Here $q$ is the
momentum projection of the positively charged daughter track in the plane
perpendicular to the ${\rm V}^{\rm 0}$ momentum and $\alpha$ = ($p_{\rm
L}^{+}-p_{\rm L}^{-})/(p_{\rm L}^{+}+p_{\rm L}^{-}$), with $p_{\rm L}^{\pm}$
the projection of the positive or negative daughter tracks’ momentum onto the
momentum of the ${\rm V}^{\rm 0}$.

To obtain the $p_{\mathrm{T}}$-differential yield of ${\rm K}^{\rm 0}_{\rm S}$
and $\Lambda$+$\overline{\Lambda}$ (which, together with background yields,
are used for the $v_{\rm n}$ extraction cf. Eq. 4), invariant mass
distributions at various $p_{\mathrm{T}}$ intervals are parametrized as a sum
of a Gaussian distribution and a second-order polynomial function. The latter
is introduced to account for residual contaminations (_background yield_) that
are present in the ${\rm K}^{\rm 0}_{\rm S}$ and
$\Lambda$+$\overline{\Lambda}$ signals after the topological and daughter
track selections. The ${\rm K}^{\rm 0}_{\rm S}$ and
$\Lambda$+$\overline{\Lambda}$ yields are extracted by integration of the
Gaussian distribution. Obtained yields have not been corrected for feed-down
from higher mass baryons ($\Xi^{\pm}$, $\Omega^{\pm}$) as earlier studies have
shown that these have a negligible effect on the measured $v_{\rm n}$ [27].
The $v_{\rm n}(p_{\mathrm{T}})$ results are reported within $|y|<$ 0.5 and
$0.5<p_{\mathrm{T}}<10$ $\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc$ for
${\rm K}^{\rm 0}_{\rm S}$ and $0.8<p_{\mathrm{T}}<10$
$\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc$ for
$\Lambda$+$\overline{\Lambda}$.

###  2.4 Reconstruction of $\phi$-mesons

The $\phi$-meson is reconstructed in the $\phi\rightarrow$ K++K- channel with
a branching ratio of 48.9% [71]. Its reconstruction proceeds by first
identifying all primary ${\rm K}^{\pm}$ tracks in an event, following the
procedure for primary charged ${\rm K}^{\pm}$ outlined in Sec. 2.2. The ${\rm
K}^{\pm}$ identification criterion ${\rm n}\sigma_{\rm PID}<3$ is chosen as it
improves the significance of the $\phi$-meson yield, while retaining a
sufficient reconstruction efficiency. The vector sums of all possible ${\rm
K}^{\pm}$ pairs are called $\phi$-meson _candidates_ , the yield of which is
obtained as function of invariant mass M${}_{\rm K^{+}K^{-}}$ in various
$p_{\mathrm{T}}$ intervals. The $p_{\mathrm{T}}$-differential $\phi$-meson
yield is obtained by first subtracting a _background_ yield from the candidate
yield. This background yield is estimated using an event-mixing technique
[73], in which ${\rm K}^{\pm}$ from different collisions are paired into
background tracks, and is normalized to the candidate yield for 1.04 $<$
M${}_{\rm K^{+}K^{-}}<$ 1.09
$\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc^{2}$. Collisions with similar
characteristics (vertex position, centrality) are used for this mixing. To
obtain the $p_{\mathrm{T}}$-differential yield of $\phi$-mesons, the invariant
mass distributions of the candidate yield is, after the aforementioned
subtraction, parametrized as a sum of a Breit-Wigner distribution and a
second-order polynomial function, the latter introduced to account for
residual contaminations. The $\phi$-meson yields are extracted by integration
of the Breit-Wigner distribution and, together with background yields, used
for the $v_{\rm n}$ extraction (see Eq. 4). The $v_{\rm 2}(p_{\mathrm{T}})$
results are reported for $0.9<p_{\mathrm{T}}<6.5$
$\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc$ within $|y|<$ 0.5.

###  2.5 Flow analysis techniques

The flow coefficients $v_{\rm n}$ are measured using the scalar product method
[57, 58, 59], written as

$v_{\rm n}\\{{\rm SP}\\}=\langle\langle{\bf u}_{\rm n,k}{\bf Q}_{\rm
n}^{*}\rangle\rangle\Bigg{/}\sqrt{\frac{\langle{\bf Q}_{\rm n}{\bf Q}_{\rm
n}^{\rm A*}\rangle\langle{\bf Q}_{\rm n}{\bf Q}_{\rm n}^{\rm
B*}\rangle}{\langle{\bf Q}_{\rm n}^{\rm A}{\bf Q}_{\rm n}^{\rm B*}\rangle}},$
(2)

where ${\bf u}_{\rm n,k}=\exp(in\varphi_{k})$ is the unit flow vector of the
particle of interest $k$ with azimuthal angle $\varphi_{k}$, ${\bf Q}_{\rm n}$
is the event flow vector, and $n$ is the harmonic number. Brackets
$\langle\cdots\rangle$ denote an average over all events, the double brackets
$\langle\langle\cdots\rangle\rangle$ an average over all particles in all
events, and ∗ the complex conjugate.

The vector ${\bf Q}_{\rm n}$ is calculated from the azimuthal distribution of
the energy deposition measured in the V0A. Its $x$ and $y$ components are
given by

$Q_{\rm n,x}=\sum_{j}w_{j}\cos({\rm n}\varphi_{j}),\;Q_{\rm
n,y}=\sum_{j}w_{j}\sin({\rm n}\varphi_{j}),$ (3)

where the sum runs over the 32 channels $j$ of the V0A detector, $\varphi_{j}$
is the azimuthal angle of channel $j$ defined by the geometric center, and
$w_{j}$ is the amplitude measured in channel $j$. The vectors ${\bf Q}_{\rm
n}^{\rm A}$ and ${\bf Q}_{\rm n}^{\rm B}$ are determined from the azimuthal
distribution of the energy deposition measured in the V0C and the azimuthal
distribution of the tracks reconstructed in the ITS and TPC, respectively. The
amplitude measured in each channel of the V0C (32 channels as for the V0A) is
used as weight in the case of ${\bf Q}_{\rm n}^{\rm A}$, while unity weights
are applied for ${\bf Q}_{\rm n}^{\rm B}$. Tracks used for ${\bf Q}_{\rm
n}^{\rm B}$ are selected following the procedure for primary charged tracks
outlined in Sec. 2.1 for $0.2~{}<~{}p_{\mathrm{T}}{}~{}<~{}5.0$
$\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc$. In order to account for a non-
uniform detector response, the components of the ${\bf Q}_{\rm n}$ and ${\bf
Q}_{\rm n}^{\rm A}$ vectors are recalibrated using a recentering procedure
(i.e. subtraction of the ${\bf Q}_{\rm n}$-vector averaged over many events
from the ${\bf Q}_{\rm n}$-vector of each event) [74]. The large gap in
pseudorapidity between un,k and ${\bf Q}_{\rm n}$ ($|\Delta\eta|>2.0$) greatly
suppresses short-range correlations unrelated to the azimuthal asymmetry in
the initial geometry, commonly referred to as ‘non-flow’. These correlations
largely come from the inter-jet correlations and resonance decays.

The $v_{\rm n}$ of the ${\rm K}^{\rm 0}_{\rm S}$,
$\Lambda$+$\overline{\Lambda}$, and $\phi$-meson cannot directly be measured
using Eq. 2 as ${\rm K}^{\rm 0}_{\rm S}$, $\Lambda$+$\overline{\Lambda}$ and
the $\phi$-meson cannot be identified on a particle-by-particle basis.
Therefore, the $v_{n}^{\rm{tot}}$ of ${\rm V}^{\rm 0}$s and $\phi$-meson
candidates is measured as function of both invariant mass, M${}_{\rm
d^{+}d^{-}}$, and candidate $p_{\mathrm{T}}$. This $v_{n}^{\rm{tot}}$ can be
written [75] as the weighted sum of $v_{\rm n}(p_{\mathrm{T}})$ of the
particle of interest, $v_{n}^{\rm{sig}}$, and that of background tracks,
$v_{n}^{\rm{bg}}({\rm{M}_{\rm{d}^{+}\rm{d}^{-}}})$, as

$v_{\rm n}^{\rm{tot}}({\rm{M}_{\rm{d}^{+}\rm{d}^{-}}})=v_{\rm
n}^{\rm{sig}}\frac{N^{\rm{sig}}}{N^{\rm{sig}}+N^{\rm{bg}}}({\rm{M}_{\rm{d}^{+}\rm{d}^{-}}})+v_{\rm
n}^{\rm{bg}}({\rm{M}_{\rm{d}^{+}\rm{d}^{-}}})\frac{N^{\rm{bg}}}{N^{\rm{sig}}+N^{\rm{bg}}}({\rm{M}_{\rm{d}^{+}\rm{d}^{-}}}),$
(4)

where _signal_ and _background_ yields $N^{\rm sig}$ and $N^{\rm bg}$ are
obtained for each $p_{\mathrm{T}}$ interval from the ${\rm K}^{\rm 0}_{\rm
S}$, $\Lambda$+$\overline{\Lambda}$ and $\phi$-meson reconstruction procedures
outlined in Secs 2.3 and 2.4. The formalism of Eq. 2 is used to measure
$v_{\rm n}^{\rm{tot}}(\rm{M}_{\rm{d}^{+}\rm{d}^{-}})$, $v_{\rm n}^{\rm{sig}}$
is obtained by parametrizing $v_{\rm
n}^{\rm{bg}}({\rm{M}_{\rm{d}^{+}\rm{d}^{-}}})$ as a second-order polynomial
function and fitting Eq. 4 to the data. Figure 1 illustrates this procedure
for the $\phi$-meson, showing the invariant mass spectrum of the $\phi$-meson
in the upper panel, and a fit of Eq. 4 to
$v_{2}^{\rm{tot}}({\rm{M}_{\rm{d}^{+}\rm{d}^{-}}})$ data in the lower panel.

Figure 1: (Colour online) Illustration of reconstruction and $v_{2}$
measurement for the $\phi$-meson. The reconstruction of the $\phi$-meson and
extraction of $N^{\rm sig}$ and $N^{\rm bg}$ are shown in the upper panel. A
fit of Eq. 4 to data is presented in the lower panel.

##  3 Systematic uncertainties

The systematic uncertainties on $v_{\rm n}$ fall into the following
categories: those arising from event selection, those arising from charged
particle tracking, uncertainties in particle identification, uncertainties in
${\rm V}^{\rm 0}$ finding, and those coming from the extraction of $v_{\rm
n}(p_{\mathrm{T}})$.

For $p_{\mathrm{T}}\leq 4$ $\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc$, a
$p_{\mathrm{T}}$-dependent systematic uncertainty is assigned to $v_{2}$,
$v_{3}$, and $v_{4}$ of $\pi^{\pm}$, ${\rm K}^{\pm}$, p+$\rm\overline{p}$,
$\Lambda$+$\overline{\Lambda}$, ${\rm K}^{\rm 0}_{\rm S}$ and the
$\phi$-meson. Per measured point, the difference between the nominal
measurement and a variation on the nominal measurement is calculated. If this
difference between the nominal data point and the systematic variation is
significant (where significance is evaluated based on the recommendations in
[76]), it is considered to be a systematic uncertainty. When various checks
are performed to quantify the effect of one systematic uncertainty (e.g. using
three different centrality estimators to estimate the uncertainty in
centrality determination), the maximum significant deviation that is found
between the nominal measurement and the systematic variations is assigned as a
systematic uncertainty. For each particle species, a
$p_{\mathrm{T}}$-independent average uncertainty is reported for
$p_{\mathrm{T}}{}>4$ $\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc$ in order
to suppress sensitivity to statistical fluctuations. The uncertainty is
obtained by fitting a zeroth-order polynomial to the significant
$p_{\mathrm{T}}$-dependent relative uncertainties.

The systematic uncertainties are evaluated (if applicable) for each particle
species, $v_{\rm n}(p_{\mathrm{T}})$ and centrality intervals. A quadratic sum
of the systematic uncertainties from the independent sources is reported as
final systematic uncertainty on the measurements. An overview of the magnitude
of the relative systematic uncertainties per particle species is given in
Tabs. 1, 2, and 3 for $v_{2}$, $v_{3}$, and $v_{4}$, respectively.

Error source | $\pi^{\pm}$ | ${\rm K}^{\pm}$ | p+$\rm\overline{p}$ | ${\rm K}^{\rm 0}_{\rm S}$ |  $\Lambda$+$\overline{\Lambda}$ | $\phi$
---|---|---|---|---|---|---
Vertex position | 0–1% | 0–1% | 0–2% | 0–2% | 0–4% | 1–6%
1% wide centrality intervals | 0–3% | 0–4% | 0–4% |  |  |
Centrality estimator | 0–3% | 0–2% | 0–3% | 0–4% | 0–5% | 1–5%
Magnetic field polarity | 0–2% | 0–1% | 0–2% | 0–3% | 0–3% | 1–3%
Interaction rate | 0–2% | 0–1% | 1–2% | _negl_ | _negl_ | _negl_
Pileup rejection | 0–1% | 0–1% | 0–2% | 0–1% | 0–2% | 0–1%
Tracking mode | 0–4% | 0–8% | 0–10% |  |  | 0–5%
Number of TPC space points | 0–2% | 0–2% | 0–2% | 0–4% | 0–2% | _negl_
Track quality | 0–3% | 0–2% | 0–3% | 0–4% | 0–3% | _negl_
Particle identification purity | 0–5% | 0–7% | 0–5% | 0–3% | 0–8% | 0–6%
Number of TPC clusters used for $\mathrm{d}E/\mathrm{d}x$ | 0–6% | 0–5% | 0–5% | 0–5% | 0% | _negl_
Exclusive particle identification | 0–2% | 0–3% | 0–3% |  |  |
Decay vertex (radial position) |  |  |  | 0–10% | 0–11% |
Armenteros-Podolanski variables |  |  |  | 0–2% |  |
DCA decay products to primary vertex |  |  |  | 0–3% | 0–5% |
DCA between decay products |  |  |  | 0–2% | 0–7% |
Pointing angle $\cos\theta_{\rm{p}}$ |  |  |  | 0–4% | 0–9% |
Minimum $p_{\mathrm{T}}$ of daughter tracks |  |  |  | 0–4% | 0–5% |
Peak shape |  |  |  | _negl_ | _negl_ | _negl_
Residual background in yield |  |  |  | _negl_ | _negl_ | _negl_
Event mixing |  |  |  |  |  | 1–3%
Positive and negative rapidities | 0–3% | 0–2% | 0–2% | 0–4% | 0–7% | _negl_
Opposite charges | 0–2% | 0–2% | 0–2% |  |  |
Channel removal from V0A | 0–5% | 0–5% | 0–8% | 0–3% | 0–5% | 0–4%
$v_{\rm n}$ from V0A or V0C | 0–2% | 0–2% | 0–2% | _negl_ | _negl_ | _negl_
$v_{\rm n}^{\rm bg}$ parametrization |  |  |  | _negl_ | _negl_ | _negl_
$v_{n}^{\rm{tot}}$ fit ranges |  |  |  | 0-1% | 0-2% | 0-1%
Table 1:  Summary of systematic uncertainties for the $v_{2}$ of $\pi^{\pm}$, ${\rm K}^{\pm}$, p+$\rm\overline{p}$, $\Lambda$+$\overline{\Lambda}$, ${\rm K}^{\rm 0}_{\rm S}$, and the $\phi$-meson. The uncertainties depend on $p_{\mathrm{T}}$ and centrality range; minimum and maximum values are listed here. Empty fields indicate that a given check does not apply to the particle of interest. If an uncertainty has been tested but cannot be resolved within statistical precision, the field is marked _negl_ for negligible. Horizontal lines are used to separate the different categories of systematic uncertainties as explained in Sec. 3. Error source | $\pi^{\pm}$ | ${\rm K}^{\pm}$ | p+$\rm\overline{p}$ | ${\rm K}^{\rm 0}_{\rm S}$ |  $\Lambda$+$\overline{\Lambda}$
---|---|---|---|---|---
Vertex position | 0–2% | 0–1% | 0–2% | 0–3% | 0–9%
1% wide centrality intervals | 0–2% | 0–2% | 0–2% |  |
Centrality estimator | 0–2% | 0–2% | 0–2% | 0–4% | 0–9%
Magnetic field polarity | 0–2% | 0–1% | 0–3% | 0–3% | 0–3%
Interaction rate | 1–2% | 1–2% | 1–3% | _negl_ | _negl_
Pileup rejection | 0–2% | 0–1% | 0–3% | 0–1% | 0–2%
Tracking mode | 0–3% | 1–5% | 0–10% |  |
Number of TPC space points | 0–1% | 0–2% | 0–5% | 0–3% | 0–6%
Track quality | 1–3% | 1–2% | 1–3% | 0–3% | 0–6%
Particle identification purity | 0–4% | 1–3% | 0–10% | 0–4% | 0–4%
Number of TPC clusters used for $\mathrm{d}E/\mathrm{d}x$ | 0–5% | 0–5% | 0–5% |  |
Exclusive particle identification | 0–1% | 0–2% | 0–1% |  |
Decay vertex (radial position) |  |  |  | 0–9% | 0–11%
Armenteros-Podolanski variables |  |  |  | 0–4% |
DCA decay products to primary vertex |  |  |  | 0–3% | 0–5%
DCA between decay products |  |  |  | 0–5% | 0–8%
Pointing angle $\cos\theta_{\rm{p}}$ |  |  |  | 0–5% | 0–1%
Minimum $p_{\mathrm{T}}$ of daughter tracks |  |  |  | 0–4% | _negl_
Peak shape |  |  |  | _negl_ | _negl_
Residual background in yield |  |  |  | _negl_ | _negl_
Positive and negative rapidities | 0–2% | 0–1% | 0–3% | 0–5% | 0–4%
Opposite charges | 0–2% | 0–2% | 0–2% |  |
$v_{\rm n}$ from V0A or V0C | 0–2% | 0–1% | 0–2% | 0–4% | 0–3%
Channel removal from V0A | 0–8% | 1–8% | 1–8% | 0–4% | 0–5%
$v_{\rm n}^{\rm bg}$ parametrization |  |  |  | _negl_ | _negl_
$v_{n}^{\rm{tot}}$ fit ranges |  |  |  | 0-2% | 0-2%
Table 2:  Summary of systematic uncertainties for the $v_{3}$ of $\pi^{\pm}$, ${\rm K}^{\pm}$, p+$\rm\overline{p}$, $\Lambda$+$\overline{\Lambda}$, and ${\rm K}^{\rm 0}_{\rm S}$. The uncertainties depend on $p_{\mathrm{T}}$ and centrality range; minimum and maximum values are listed here. Empty fields indicate that a given check does not apply to the particle of interest. If an uncertainty has been tested but cannot be resolved within statistical precision, the field is marked _negl_ for negligible. Horizontal lines are used to separate the different categories of systematic uncertainties as explained in Sec. 3. Error source | $\pi^{\pm}$ | ${\rm K}^{\pm}$ | p+$\rm\overline{p}$
---|---|---|---
Vertex position | 1–3% | 1–3% | 1–3%
1% wide centrality intervals | 0–1% | 0–1% | 0–1%
Centrality estimator | 1–3% | 1–3% | 2–3%
Magnetic field polarity | 1–2% | 1–3% | 1–3%
Interaction rate | 1–2% | 2–3% | 2–3%
Pileup rejection | 0–2% | 1–2% | 2–3%
Tracking mode | 0–2% | 1–5% | 1–10%
Number of TPC space points | 0–1% | 0–1% | 0–1%
Track quality | 3–4% | 2–3% | 3–4%
Particle identification purity | 1–4% | 2–4% | 2–5%
Number of TPC clusters used for $\mathrm{d}E/\mathrm{d}x$ | 0–2% | 0–1% | 0–1%
Exclusive particle identification | 0–1% | 0–2% | 0–1%
Positive and negative rapidities | 1–3% | 1–2% | 2–3%
Opposite charges | 2–3% | 2–3% | 2–3%
$v_{\rm n}$ from V0A or V0C | 1–3% | 2–4% | 2–4%
Channel removal from V0A | 6–14% | 6–14% | 5–15%
Table 3:  Summary of systematic uncertainties for the $v_{4}$ of $\pi^{\pm}$,
${\rm K}^{\pm}$, and p+$\rm\overline{p}$. The uncertainties depend on
$p_{\mathrm{T}}$ and centrality range; minimum and maximum values are listed
here. Horizontal lines are used to separate the different categories of
systematic uncertainties as explained in Sec. 3.

#### Event selection

The nominal event selection criteria and centrality determination are
discussed in Sec. 2.1. Event selection criteria are varied by (i) changing the
default centrality estimator from energy deposition in the V0 scintillator to
either an estimate based on the number of hits in the first or second layer of
the ITS; (ii) performing the $v_{\rm n}$ analysis of $\pi^{\pm}$, ${\rm
K}^{\pm}$, and p+$\rm\overline{p}$ in 1% wide centrality intervals to test the
effect of multiplicity fluctuations (a test not possible for ${\rm K}^{\rm
0}_{\rm S}$, $\Lambda$+$\overline{\Lambda}$ $v_{3}$); (iii) not rejecting
events with tracks caused by pileup or imposing a stricter than default pileup
rejection by requiring a tighter correlation between the V0 and central barrel
multiplicities; (iv) requiring the reconstructed primary vertex of a collision
to lie alternatively within $\pm$12 cm and $\pm$5 cm from the nominal
interaction point along the beam axis; (v) analyzing events recorded under
different magnetic field polarities independently; (v) analyzing events
recorded at different collision rates independently.

#### Charged particle tracking

The nominal charged particle track selection criteria are outlined in Sec.
2.1. Charged particle track selection criteria are varied by (i) requiring the
third layer of the ITS to be part of the track reconstruction rather than the
first two layers only; (ii) using only tracks that have at least three hits
per track in the ITS, complemented by tracks without hits in the first two
layers of the ITS (in which case the primary interaction vertex is used as an
additional constraint for the momentum determination); (iii) changing the
requirement on the minimum number of TPC space points that are used in the
reconstruction from 70 to 60, 80, and 90; (iv) an additional systematic
uncertainty is evaluated combining the following checks of the track quality:
rejecting tracks that are reconstructed close to the sector boundaries of the
TPC to which the sensitive pad rows do not extend, varying the minimum number
of crossed TPC pad rows from 70 to 120, and requesting at least 90% instead of
80% of the expected TPC space points to reconstruct a track. Variations (i)
and (ii) are referred to as _tracking mode_ in Tabs. 1, 2, and 3.

#### Particle identification

The nominal particle identification approach for $\pi^{\pm}$, ${\rm K}^{\pm}$,
and p+$\rm\overline{p}$ is outlined in Sec. 2.2. Particle identification
criteria are varied by (i) changing the minimum number of clusters in the TPC
that are used to estimate the $\mathrm{d}E/\mathrm{d}x$ from 70 to 60, 80, and
90; (ii) rejecting tracks that satisfy the particle identification criterion
for more than one particle species simultaneously for $p_{\mathrm{T}}$ $<$ 4
$\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc$; (iii) varying the particle
identification criterion from ${\rm n}\sigma_{\rm PID}<3$ to ${\rm
n}\sigma_{\rm PID}<1$, ${\rm n}\sigma_{\rm PID}<2$, and ${\rm n}\sigma_{\rm
PID}<4$; (iv) varying the ${\rm n}\sigma_{\rm TPC}$ ranges that are used for
particle identification for $p_{\mathrm{T}}$ $>$ 4
$\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc$.

#### The ${\rm V}^{\rm 0}$ finding and $\phi$-meson reconstruction

The nominal ${\rm V}^{\rm 0}$ finding strategy is described in Sec. 2.3. The
${\rm V}^{\rm 0}$ finding criteria fall into two categories: topological
requirements on the ${\rm V}^{\rm 0}$s themselves, and selection imposed on
their daughter tracks. These criteria are varied by (i) requiring a minimum
$p_{\mathrm{T}}$ of the ${\rm V}^{\rm 0}$ daughter tracks of 0.2
$\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc$; (ii) changing the requirement
on the minimum number of TPC space points that are used in the reconstruction
of the ${\rm V}^{\rm 0}$ daughter tracks form 70 to 60 and 80; (iii) varying
the minimum number of TPC padrows crossed by the ${\rm V}^{\rm 0}$ daughter
tracks from 70 to 60 and 80; (iv) requesting at least 90% or 70% instead of
80% of the expected TPC space points to reconstruct the ${\rm V}^{\rm 0}$
daughter tracks; (v) changing the maximum DCA of the ${\rm V}^{\rm 0}$
daughter tracks to the secondary vertex from 0.5 cm to 0.3 cm and 0.7 cm; (vi)
changing the minimum DCA of the ${\rm V}^{\rm 0}$ daughter tracks to the
primary vertex from 0.1 cm to 0.05 cm and 0.3 cm; (vii) varying the number of
clusters in the TPC that are used to estimate the $\mathrm{d}E/\mathrm{d}x$ of
the ${\rm V}^{\rm 0}$ daughter tracks from 70 to 60 and 90; (viii) varying the
particle identification criterion of the ${\rm V}^{\rm 0}$ daughter tracks
from $|{\rm n}\sigma_{\rm TPC}|<3$ to $|{\rm n}\sigma_{\rm TPC}|<1$ and $|{\rm
n}\sigma_{\rm TPC}|<4$; (ix) changing the minimum value of the
$\cos\theta_{p}$ from 0.998 to 0.98; (x) varying the minimum radial distance
to the primary vertex at which the ${\rm V}^{\rm 0}$ can be produced from 5 cm
to 1 cm and 15 cm; (xi) varying the maximum radial distance to the beam pipe
at which the ${\rm V}^{\rm 0}$ can be produced from 100 cm to 50 cm and 150
cm; (xii) the contamination from $\Lambda$+$\overline{\Lambda}$ decays and
$\gamma$-conversions to the ${\rm K}^{\rm 0}_{\rm S}$ sample is checked by
only selecting ${\rm V}^{\rm 0}$ daughter tracks with a
$\mathrm{d}E/\mathrm{d}x$ value 2$\sigma$ away from the expected electron
$\mathrm{d}E/\mathrm{d}x$, effectively excluding electrons, and limiting the
value of the Armenteros-Podolanski variables $\alpha$ and $q$.

The yield extraction, as explained in Sec 2.3 for the ${\rm K}^{\rm 0}_{\rm
S}$ and $\Lambda$+$\overline{\Lambda}$, and Sec 2.4 for the $\phi$-meson, is
varied by: (i) using a third-order polynomial as parametrization of residual
background in the invariant mass spectra; (ii) using for the $\phi$-meson a
Voigtian distribution (a convolution of a Gaussian distribution and Breit-
Wigner distribution, where the width of the Breit-Wigner distribution is set
to the natural width of the $\phi$-meson, allowing for the Gaussian
distribution to describe the smearing of the $\phi$-meson width due to the
detector resolution) for the parametrization of the $\phi$-meson invariant
mass yield; using for the ${\rm K}^{\rm 0}_{\rm S}$ and
$\Lambda$+$\overline{\Lambda}$ a sum of two Gaussian distributions with the
same mean for the parametrization of the ${\rm K}^{\rm 0}_{\rm S}$,
$\Lambda$+$\overline{\Lambda}$ invariant mass yield; (iii, for the
$\phi$-meson only) using the yield of like-sign kaon pairs, in which two kaons
with equal charge from the same event are used as candidate, for background
yield description instead of event mixing.

#### Extraction of the $v_{\rm n}(p_{\mathrm{T}})$

The nominal approach of measuring $v_{\rm n}(p_{\mathrm{T}})$ is outlined in
Sec. 2.5, and is varied by: (i) performing flow analysis for $\pi^{\pm}$,
${\rm K}^{\pm}$, and p+$\rm\overline{p}$ for positive and negative charges
independently; (ii) performing flow analysis for positive and negative
rapidities independently; (iii) performing flow analysis for $\pi^{\pm}$,
${\rm K}^{\pm}$, and p+$\rm\overline{p}$ in 1% centrality intervals and
merging the result rather than measuring in wider centrality intervals
directly; (iv) suppressing the signal from a specific V0A channel in the
evaluation of the Qn-vector (see Eq. 3), which, on average, measures a lower
energy deposition with respect to the ones reported by the other channels from
the same ring; (v) performing flow analysis with the ${\bf Q}_{\rm n}$-vector
calculated from the V0A or V0C separately; (vi) testing various M${}_{\rm
d^{+}d^{-}}$ intervals over which
$v_{n}^{\rm{bg}}({\rm{M}_{\rm{d}^{+}\rm{d}^{-}}})$ is fitted; (vii) testing
the assumption made on $v_{\rm n}^{\rm bg}$ by changing the parametrization
from a second-order polynomial to a first-order polynomial function.

##  4 Results and discussion

The flow coefficients $v_{2}$, $v_{3}$, and $v_{4}$ of identified particles
are presented for various centrality classes in Sec. 4.1; scaling properties
are discussed in Sec. 4.2. Comparisons to various model calculations, studies
on the shape evolution of $v_{\rm n}(p_{\mathrm{T}})$ with centrality, and
comparisons to $v_{\rm n}$ measured at $\sqrt{s_{\mathrm{NN}}}$ = 2.76 TeV are
shown in Secs. 4.3, 4.4, and 4.5, respectively.

###  4.1 Centrality and $p_{\mathrm{T}}$ dependence of flow coefficients

Figure 2: (Colour online) Centrality dependence of $v_{\rm 2}(p_{\mathrm{T}})$
for $\pi^{\pm}$, ${\rm K}^{\pm}$, p+$\rm\overline{p}$,
$\Lambda$+$\overline{\Lambda}$, ${\rm K}^{\rm 0}_{\rm S}$, and the
$\phi$-meson. Statistical and systematic uncertainties are shown as bars and
boxes, respectively. Figure 3: (Colour online) Centrality dependence of
$v_{\rm 3}(p_{\mathrm{T}})$ for $\pi^{\pm}$, ${\rm K}^{\pm}$,
p+$\rm\overline{p}$, $\Lambda$+$\overline{\Lambda}$, and ${\rm K}^{\rm 0}_{\rm
S}$. Statistical and systematic uncertainties are shown as bars and boxes,
respectively. Figure 4: (Colour online) Centrality dependence of $v_{\rm
4}(p_{\mathrm{T}})$ for $\pi^{\pm}$, ${\rm K}^{\pm}$, and p+$\rm\overline{p}$.
Statistical and systematic uncertainties are shown as bars and boxes,
respectively.

Figure 2 shows the $v_{\rm 2}(p_{\mathrm{T}})$ of $\pi^{\pm}$, ${\rm
K}^{\pm}$, p+$\rm\overline{p}$, $\Lambda$+$\overline{\Lambda}$, ${\rm K}^{\rm
0}_{\rm S}$, and the $\phi$-meson for various centrality classes in the range
0–70%. For the $\pi^{\pm}$, ${\rm K}^{\pm}$ and p+$\rm\overline{p}$,
measurements performed in ultra-central collisions (0–1%) are also presented.
For the $\phi$-meson, the results are reported in the 5–60% centrality range,
where $v_{2}$ can be measured accurately. The magnitude of $v_{2}$ increases
strongly with decreasing centrality up to the 40–50% centrality interval for
all particle species. This evolution is expected, since the eccentricity of
the overlap zone of the colliding nuclei increases for peripheral collisions
and $v_{2}$ scales approximately linearly with eccentricity [77]. For more
peripheral collisions (i.e. 50–60% and 60–70%), the value of $v_{2}$ is
smaller than in the previous centrality intervals for all particle species
except the $\phi$-meson. This suggests that the system has a shorter lifetime
in more peripheral collisions, which does not allow for the generation of
large $v_{2}$ [78]. Furthermore, the reduced contribution of eccentricity
fluctuations and hadronic interactions might play an important role in these
centrality ranges [79]. A non-zero, positive $v_{2}$ is found in the 0–1%
centrality interval for $p_{\mathrm{T}}<6$
$\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc$ for $\pi^{\pm}$, ${\rm
K}^{\pm}$, and p+$\rm\overline{p}$, which mostly reflects the contribution
from event-by-event fluctuations in the initial nucleon and gluon density as
the system shape is almost spherical at vanishing impact parameter.

The third-order flow coefficent $v_{3}$ is generated by inhomogeneities in the
initial nucleon and gluon density and not by the collision geometry [12, 13,
14, 15], while $v_{4}$ arises from initial collision geometry, fluctuations,
and the non-linear hydrodynamic response of the medium [16, 17]. Higher-order
flow harmonics are more sensitive to transport coefficients than $v_{2}$ [15],
as the dampening effect of $\eta/s$ leads to a stronger decrease of these
coefficients [18, 19]. Figures 3 and 4 present the $v_{\rm 3}(p_{\mathrm{T}})$
of $\pi^{\pm}$, ${\rm K}^{\pm}$, p+$\rm\overline{p}$,
$\Lambda$+$\overline{\Lambda}$, and ${\rm K}^{\rm 0}_{\rm S}$ and $v_{\rm
4}(p_{\mathrm{T}})$ of $\pi^{\pm}$, ${\rm K}^{\pm}$, and p+$\rm\overline{p}$
for various centrality classes in the 0–50% range. Statistical precision
limits extending the $v_{4}$ measurement to more peripheral collisions or
carrying it out for $\Lambda$+$\overline{\Lambda}$, ${\rm K}^{\rm 0}_{\rm S}$,
and the $\phi$-meson. Non-zero, positive $v_{3}$ and $v_{4}$ are observed for
particle species throughout the entire $p_{\mathrm{T}}$ ranges up to $\approx$
8 $\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc$. Unlike $v_{2}$, the
coefficients $v_{3}$ and $v_{4}$ increase weakly from ultra-central to
peripheral collisions. This observation illustrates that higher-order flow
coefficients are mainly generated by event-by-event fluctuations in the
initial nucleon and gluon density.

All flow coefficients increase monotonically with increasing $p_{\mathrm{T}}$
up to 3-4 $\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc$ where a maximum is
reached. The position of this maximum depends on centrality and particle
species as it takes place at higher $p_{\mathrm{T}}$ for heavier particles for
various centrality classes. This behaviour can be explained by the centrality
dependence of radial flow combined with the parton density, which will be
detailed in Sec. 4.4.

Figure 5 presents the evolution of $v_{\rm n}(p_{\mathrm{T}})$ of different
particle species for various centrality classes. In the most central
collisions, initial nucleon-density fluctuations are expected to be the main
contributor to the generation of $v_{\rm n}$. For the 0–1% centrality
interval, $v_{3}$ is the dominant flow coefficient for
$1.5<p_{\mathrm{T}}<6.0$ $\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc$,
$2.0<p_{\mathrm{T}}<4$ $\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc$, and
$2.5<p_{\mathrm{T}}<6$ $\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc$ for
$\pi^{\pm}$, ${\rm K}^{\pm}$, and p+$\rm\overline{p}$, respectively.
Furthermore, $v_{4}$ becomes equal to $v_{2}$ at $p_{\mathrm{T}}\approx$ 2.0
$\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc$ (2.2, 2.5) for $\pi^{\pm}$
(${\rm K}^{\pm}$, p+$\rm\overline{p}$), after which it increases gradually and
reaches a magnitude similar to $v_{3}$ at around 3.5 GeV/$c$. A similar trend
is observed in the 0–5% centrality class for all particle species. However,
the crossing between flow coefficients (the $p_{\mathrm{T}}$ value at which
they reach a similar magnitude), which also depends on the particle mass,
takes place at different $p_{\mathrm{T}}$ values than for the 0–1% centrality
interval. This dependence of the crossing between different flow coefficients
can be attributed to the interplay of elliptic, triangular, and quadrangular
flow with radial flow. Upwards of 5% collision centrality, $v_{2}$ is larger
than $v_{3}$ and $v_{4}$, confirming the hypothesis that collision geometry
dominates the generation of flow coefficients.

Figure 5: (Colour online) The evolution of $v_{\rm n}(p_{\mathrm{T}})$ of
$\pi^{\pm}$, ${\rm K}^{\pm}$, p+$\rm\overline{p}$,
$\Lambda$+$\overline{\Lambda}$, and ${\rm K}^{\rm 0}_{\rm S}$ for various
centrality classes. Statistical and systematic uncertainties are shown as bars
and boxes, respectively.

Figure 6 shows the $v_{\rm 2}(p_{\mathrm{T}})$ of $\pi^{\pm}$, ${\rm
K}^{\pm}$, p+$\rm\overline{p}$, $\Lambda$+$\overline{\Lambda}$, ${\rm K}^{\rm
0}_{\rm S}$, and the $\phi$-meson in a given centrality interval arranged into
panels of various centrality classes, which allows for further illustration of
the interplay between elliptic and radial flow. For $p_{\mathrm{T}}<$ 2-3
$\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc$, $v_{2}$ of the different
particle species is mass-ordered, meaning that lighter particles have a larger
$v_{2}$ than heavier particles at the same $p_{\mathrm{T}}$. This behaviour is
indicative of strong radial flow which imposes an equal, isotropic velocity
boost to all particles in addition to the anisotropic expansion of the medium
[20, 21, 22]. For $3<p_{\mathrm{T}}<$ 8-10
$\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc$, particles are grouped
according to their number of constituent quarks, which supports the hypothesis
of particle production via quark coalescence [34]. Particle type scaling and
mass ordering are most directly tested by the $\phi$-meson $v_{2}$, as its
mass is close to the proton mass. Figure 6 demonstrates that the $\phi$-meson
$v_{2}$ follows proton $v_{2}$ at low $p_{\mathrm{T}}$, but pion $v_{2}$ at
intermediate $p_{\mathrm{T}}$ in all centrality classes. The crossing between
meson and baryon $v_{2}$, which depends on the particle species, happens at
higher $p_{\mathrm{T}}$ values for central than peripheral collisions as a
result of the larger radial flow in the former. Lastly, it is seen that the
$v_{2}$ of baryons is higher than that of mesons up to $p_{\mathrm{T}}$
$\approx$ 10 $\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc$, indicating that
particle type dependence of $v_{2}$ persists up to high $p_{\mathrm{T}}$. For
$p_{\mathrm{T}}>10$ $\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc$, where
$v_{2}$ depends only weakly on transverse momentum, the magnitude of
p+$\rm\overline{p}$ $v_{2}$ is compatible with that for $\pi^{\pm}$ within
statistical and systematic uncertainties. Furthermore, the nuclear
modification factor in this high $p_{\mathrm{T}}$ region is found to be the
same for the two particle species within uncertainties [80].

Figures 7 and 8 present the $v_{\rm 3}(p_{\mathrm{T}})$ and $v_{\rm
4}(p_{\mathrm{T}})$ for different particle species in a given centrality
interval. Both $v_{3}$ and $v_{4}$ show a clear mass ordering at
$p_{\mathrm{T}}<$ 2-3 $\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc$,
confirming the interplay between triangular and quadrangular flow and radial
flow. For $3<p_{\mathrm{T}}<8$ $\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc$,
particles are grouped into mesons and baryons and, analogous to the trend of
$v_{2}$ in this $p_{\mathrm{T}}$ region, the flow of baryons is larger than
that of mesons. The crossing between meson and baryon $v_{3}$ and $v_{4}$ also
exhibits a centrality and particle mass dependence.

Figure 6: (Colour online) The $p_{\mathrm{T}}$-differential $v_{2}$ of
$\pi^{\pm}$, ${\rm K}^{\pm}$, p+$\rm\overline{p}$,
$\Lambda$+$\overline{\Lambda}$, ${\rm K}^{\rm 0}_{\rm S}$, and the
$\phi$-meson for various centrality classes. Statistical and systematic
uncertainties are shown as bars and boxes, respectively. Figure 7: (Colour
online) The $p_{\mathrm{T}}$-differential $v_{3}$ of $\pi^{\pm}$, ${\rm
K}^{\pm}$, p+$\rm\overline{p}$, $\Lambda$+$\overline{\Lambda}$, and ${\rm
K}^{\rm 0}_{\rm S}$ for various centrality classes. Statistical and systematic
uncertainties are shown as bars and boxes, respectively. Figure 8: (Colour
online) The $p_{\mathrm{T}}$-differential $v_{4}$ of $\pi^{\pm}$, ${\rm
K}^{\pm}$, and p+$\rm\overline{p}$ for various centrality classes. Statistical
and systematic uncertainties are shown as bars and boxes, respectively.

Figures 6 and 7 also show a comparison between ${\rm K}^{\pm}$ and ${\rm
K}^{\rm 0}_{\rm S}$ $v_{2}$ and $v_{3}$ as a function of $p_{\mathrm{T}}$ for
various centrality classes. A difference in $v_{\rm n}(p_{\mathrm{T}})$ is
found between the ${\rm K}^{\pm}$ and ${\rm K}^{\rm 0}_{\rm S}$ measurements:
the magnitude of ${\rm K}^{\rm 0}_{\rm S}$ $v_{\rm n}$ is systematically
smaller than the magnitude of ${\rm K}^{\pm}$ $v_{\rm n}$. This difference in
$v_{\rm n}$ exhibits no $p_{\mathrm{T}}$ dependence, but changes with
centrality for $v_{2}$. For $0.8<p_{\mathrm{T}}{}<4.0$
$\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc$, the difference in $v_{2}$
ranges from $7\%\pm 3.5\%({\rm syst})\pm 0.7\%({\rm stat})$ in the most
central collisions to $1.5\%\pm 1.5\%({\rm syst})\pm 0.4\%({\rm stat})$ in
peripheral collisions. In the same kinematic range, a deviation in $v_{3}$ of
$6.5\%\pm 5\%({\rm syst})\pm 1.7\%({\rm stat})$ is found in the most central
collisions and of $6\%\pm 4.5\%({\rm syst})\pm 1\%({\rm stat})$ in peripheral
collisions. This difference is similar in magnitude and centrality dependence
as the one reported by ALICE in Pb–Pb collisions at $\sqrt{s_{\mathrm{NN}}}$ =
2.76 TeV in [27].

###  4.2 Scaling properties

To test the hypothesis of particle production via quark coalescence [34],
which would lead to a grouping of $v_{\rm n}$ of mesons and baryons at
intermediate $p_{\mathrm{T}}$, both $v_{\rm n}$ and $p_{\mathrm{T}}$ are
divided by the number of constituent quarks ($n_{\rm q}$) independently for
each particle species. The $v_{2}/n_{\rm q}$, $v_{3}/n_{\rm q}$, and
$v_{4}/n_{\rm q}$ of $\pi^{\pm}$, ${\rm K}^{\pm}$, p+$\rm\overline{p}$,
$\Lambda$+$\overline{\Lambda}$, ${\rm K}^{\rm 0}_{\rm S}$, and the
$\phi$-meson, plotted as a function of $p_{\mathrm{T}}/n_{\rm q}$, are
reported in Figs. 9, 10, and 11 for various centrality classes.

For $p_{\mathrm{T}}$$/n_{\rm q}>$ 1
$\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc$, the scaling is only
approximate. To quantify the degree to which the measurements deviate from the
$n_{\rm q}$ scaling, the $p_{\mathrm{T}}/n_{\rm q}$ dependence of $v_{\rm
n}/n_{\rm q}$ has been divided by a cubic spline fit to the
p+$\rm\overline{p}$ $v_{\rm n}/n_{\rm q}$. In the region where quark
coalescence is hypothesized to be the dominant process ($\approx
1<p_{\mathrm{T}}/n_{\rm q}<3$ $\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc$)
[34, 81], a deviation from the exact scaling of $\pm$ 20% is found for $v_{2}$
for central collisions, which decreases to $\pm 15\%$ for the most peripheral
collisions. For higher harmonics, a $\pm 20\%$ deviation is found for all
centrality classes. This deviation is in agreement with earlier observations
[32, 27, 28].

Figure 9: (Colour online) The $p_{\mathrm{T}}/n_{\rm q}$ dependence of
$v_{2}/n_{\rm q}$ of $\pi^{\pm}$, ${\rm K}^{\pm}$, p+$\rm\overline{p}$,
$\Lambda$+$\overline{\Lambda}$, ${\rm K}^{\rm 0}_{\rm S}$, and the
$\phi$-meson for various centrality classes. Statistical and systematic
uncertainties are shown as bars and boxes, respectively. Figure 10: (Colour
online) The $p_{\mathrm{T}}/n_{\rm q}$ dependence of $v_{3}/n_{\rm q}$ of
$\pi^{\pm}$, ${\rm K}^{\pm}$, p+$\rm\overline{p}$,
$\Lambda$+$\overline{\Lambda}$, and ${\rm K}^{\rm 0}_{\rm S}$ for various
centrality classes. Statistical and systematic uncertainties are shown as bars
and boxes, respectively. Figure 11: (Colour online) The $p_{\mathrm{T}}/n_{\rm
q}$ dependence of $v_{4}/n_{\rm q}$ of $\pi^{\pm}$, ${\rm K}^{\pm}$, and
p+$\rm\overline{p}$ for various centrality classes. Statistical and systematic
uncertainties are shown as bars and boxes, respectively.

###  4.3 Comparison with model calculations

Figure 12: (Colour online) The $p_{\mathrm{T}}$-differential $v_{2}$ (top),
$v_{3}$ (middle), and $v_{4}$ (bottom) of $\pi^{\pm}$ for the 0–5%, 10–20%,
and 40–50% centrality classes compared to hydrodynamical calculations from
MUSIC model using IP-Glasma initial conditions (magenta) [82] and the iEBE-
VISHNU hybrid model using AMPT (orange) or TRENTo (cyan) initial conditions
[83]. Statistical and systematic uncertainties of the data points are shown as
bars and boxes, respectively. The uncertainties of the hydrodynamical
calculations are depicted by the thickness of the curves. The ratios of the
measured $v_{\rm n}$ to a fit to the hydrodynamical calculations are also
presented for clarity. Figure 13: (Colour online) The
$p_{\mathrm{T}}$-differential $v_{2}$ (top), $v_{3}$ (middle), and $v_{4}$
(bottom) of ${\rm K}^{\pm}$ for the 0–5%, 10–20%, and 40–50% centrality
classes compared to hydrodynamical calculations from MUSIC model using IP-
Glasma initial conditions (magenta) [82] and the iEBE-VISHNU hybrid model
using AMPT (orange) or TRENTo (cyan) initial conditions [83]. Statistical and
systematic uncertainties of the data points are shown as bars and boxes,
respectively. The uncertainties of the hydrodynamical calculations are
depicted by the thickness of the curves. The ratios of the measured $v_{\rm
n}$ to a fit to the hydrodynamical calculations are also presented for
clarity. Figure 14: (Colour online) The $p_{\mathrm{T}}$-differential $v_{2}$
(top), $v_{3}$ (middle), and $v_{4}$ (bottom) of p+$\rm\overline{p}$ for the
0–5%, 10–20%, and 40–50% centrality classes compared to hydrodynamical
calculations from MUSIC model using IP-Glasma initial conditions (magenta)
[82] and the iEBE-VISHNU hybrid model using AMPT (orange) or TRENTo (cyan)
initial conditions [83]. Statistical and systematic uncertainties of the data
points are shown as bars and boxes, respectively. The uncertainties of the
hydrodynamical calculations are depicted by the thickness of the curves. The
ratios of the measured $v_{\rm n}$ to a fit to the hydrodynamical calculations
are also presented for clarity.

To test the validity of the hydrodynamic description of the QGP evolution, the
$v_{\rm n}$ measurements in the 0–5%, 10–20% and 40–50% centrality intervals
are compared to hydrodynamical calculations in Figs. 12, 13, and 14 for
$\pi^{\pm}$, ${\rm K}^{\pm}$, and p+$\rm\overline{p}$, respectively.
Predictions from MUSIC [82] and iEBE-VISHNU [83] simulations are depicted by
the different coloured curves. The first calculation is based on MUSIC [84],
an event-by-event 3+1 dimensional viscous hydrodynamic model, coupled to a
hadronic cascade model (UrQMD) [85, 86], which allows the influence of the
hadronic phase on the anisotropic flow to be studied for different particle
species. The IP-Glasma model [87, 88] is used to simulate the initial
conditions of the collision. MUSIC uses a starting time for the hydrodynamic
evolution of $\tau_{0}=0.4$ fm/$c$, a switching temperature between the
macroscopic hydrodynamic description and the microscopic transport evolution
of $T_{\rm sw}=145$ MeV, a value of $\eta/s$ = 0.095, and a temperature
dependent $\zeta/s$. The second calculation employs the iEBE-VISHNU hybrid
model [89], which is an event-by-event version of the VISHNU hybrid model
[90], and couples 2+1 dimensional viscous hydrodynamics VISH2+1 [78] to UrQMD.
The TRENTo [91] and AMPT [92] models are used to describe the initial
conditions. For both configurations, $\tau_{0}=0.6$ fm/$c$ and $T_{\rm
sw}=148$ MeV are set from [93], where these values have been obtained
utilizing Bayesian statistics from a simultaneous fit of final charged-
particle density, mean transverse momentum, and integrated flow coefficients
$v_{\rm n}$ in Pb–Pb collisions at $\sqrt{s_{\mathrm{NN}}}$ = 2.76 TeV. The
temperature-dependent $\eta/s$ and $\zeta/s$ extracted in [93] are used for
TRENTo initial conditions, while $\eta/s=0.08$ and $\zeta/s=0$ are taken for
AMPT.

Figures 12, 13, and 14 show that the hydrodynamical calculations qualitatively
reproduce the $v_{\rm n}$ measurements. The differences between the data
points and models are visualized in Figs. 12, 13, and 14 as the ratios of the
measured $v_{\rm n}$ to a fit to the theoretical calculations. The iEBE-VISHNU
calculations using AMPT initial conditions describe the
$p_{\mathrm{T}}$-differential $v_{\rm n}$ of $\pi^{\pm}$, ${\rm K}^{\pm}$, and
p+$\rm\overline{p}$ more accurately than TRENTo based and MUSIC calculations
for $p_{\mathrm{T}}>1$ GeV/$c$. Using AMPT initial conditions, there is good
agreement between $\pi^{\pm}$ and ${\rm K}^{\pm}$ $v_{\rm n}$ and iEBE-VISHNU
calculations for $p_{\mathrm{T}}<2$
$\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc$, while p+$\rm\overline{p}$
$v_{\rm n}$ is described fairly well up to $p_{\mathrm{T}}=3$
$\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc$. The TRENTo based predictions
follow $\pi^{\pm}$ and ${\rm K}^{\pm}$ $v_{\rm n}$ up to slightly lower
transverse momenta ($p_{\mathrm{T}}<$1-2
$\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc$) and to $p_{\mathrm{T}}{}<3$
$\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc$ for p+$\rm\overline{p}$,
depending on the considered centrality interval. The MUSIC calculations are in
agreement with the measured $v_{\rm n}$ for $p_{\mathrm{T}}{}<1$
$\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc$ in central collisions, however
they overestimate $v_{2}$ at lower $p_{\mathrm{T}}$ in more peripheral
collisions.

###  4.4 Shape evolution of $v_{\rm n}(p_{\mathrm{T}})$ as function of
centrality

The evolution of the shape of $v_{\rm n}(p_{\mathrm{T}})$ as function of
centrality is quantified by taking the ratio of $v_{\rm n}(p_{\mathrm{T}})$ in
a given centrality interval to the $v_{\rm n}(p_{\mathrm{T}})$ measured in the
20–30% centrality interval

$v_{\rm n}(p_{\mathrm{T}}){}_{\rm ratio~{}to~{}20-30\%}=\frac{v_{\rm
n}(p_{\mathrm{T}}){}}{v_{\rm n}(p_{\mathrm{T}}){}|_{20-30\%}}\frac{v_{\rm
n}{}|_{20-30\%}}{v_{\rm n}{}},$ (5)

where the second fraction on the right-hand side of the equation serves as a
normalization factor which is constructed from the $p_{\mathrm{T}}$-integrated
$v_{\rm n}$ values obtained in the 20–30% centrality interval ($v_{\rm
n}$$|_{20-30\%}$) and the centrality interval of interest ($v_{\rm n}$).
Centrality-dependent variations in the shape of $v_{\rm n}(p_{\mathrm{T}})$
will present themselves as deviations from unity of the observed $v_{\rm
n}(p_{\mathrm{T}}){}_{\rm ratio~{}to~{}20-30\%}$.

The shape evolution of elliptic and triangular flow is shown in Figs. 15 and
16 for $\pi^{\pm}$, ${\rm K}^{\pm}$, p+$\rm\overline{p}$, and inclusive
charged particles (the latter taken from [44]). For inclusive charged
particles, variations in shape of about 10% are observed for
$p_{\mathrm{T}}<3$ $\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc$, which
increase to about 30% for $p_{\mathrm{T}}<6$
$\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc$. The shape evolution of $v_{\rm
2}(p_{\mathrm{T}})$ shows different trends for $\pi^{\pm}$, ${\rm K}^{\pm}$,
and p+$\rm\overline{p}$. While $\pi^{\pm}$ $v_{2}(p_{\mathrm{T}})_{\rm
ratio~{}to~{}20-30\%}$ follows inclusive charged particle over the considered
$p_{\mathrm{T}}$ range, the elliptic flow of p+$\rm\overline{p}$ (${\rm
K}^{\pm}$) varies between 20% (10%) to 250% (55%) at low $p_{\mathrm{T}}$ from
most central to peripheral collisions. The variations are more pronounced for
$v_{\rm 3}(p_{\mathrm{T}})$, in particular for central collisions. The mass
dependence found in the shape evolution of both $v_{2}$ and $v_{3}$ for
$p_{\mathrm{T}}<4$ $\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc$ can be
attributed to variations of the magnitude of radial flow and quark density,
both being larger for central than peripheral collisions. Radial flow has a
stronger effect on the $v_{\rm n}$ of heavier particles than that of lighter
particles at low $p_{\mathrm{T}}$, while the quark density influences the peak
value of $v_{\rm n}(p_{\mathrm{T}})$ in the coalescence model picture [35, 36,
94]. For $p_{\mathrm{T}}>4$ $\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc$,
the shape evolution shows little (if any) particle type dependence.

Figure 15: (Colour online) Centrality dependence of $v_{\rm
2}(p_{\mathrm{T}}){}_{\rm ratio~{}to~{}20-30\%}$ for $\pi^{\pm}$, ${\rm
K}^{\pm}$, p+$\rm\overline{p}$, and inclusive charged particles [44].
Statistical and systematic uncertainties are shown as bars and boxes,
respectively. Figure 16: (Colour online) Centrality dependence of $v_{\rm
3}(p_{\mathrm{T}}){}_{\rm ratio~{}to~{}20-30\%}$ for $\pi^{\pm}$, ${\rm
K}^{\pm}$, p+$\rm\overline{p}$, and inclusive charged particles [44].
Statistical and systematic uncertainties are shown as bars and boxes,
respectively.

The shape evolution of $v_{\rm 2}(p_{\mathrm{T}})$ for $\pi^{\pm}$, ${\rm
K}^{\pm}$, and p+$\rm\overline{p}$ is compared to calculations from the MUSIC
and iEBE-VISHNU hybrid models in Fig. 17. Both models describe the shape
evolution for p+$\rm\overline{p}$ over the $p_{\mathrm{T}}$ range
$0.7<p_{\mathrm{T}}<3$ $\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc$. The
iEBE-VISHNU model reproduces the shape evolution for $\pi^{\pm}$ and ${\rm
K}^{\pm}$ for $p_{\mathrm{T}}<1.5$
$\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc$. Calculations from the MUSIC
model deviate strongly from the observed shape evolution for $\pi^{\pm}$ and
${\rm K}^{\pm}$ in peripheral collisions.

Figure 17: (Colour online) Centrality dependence of $v_{\rm
2}(p_{\mathrm{T}}){}_{\rm ratio~{}to~{}20-30\%}$ for $\pi^{\pm}$ (upper
panels), ${\rm K}^{\pm}$ (middle panels), and p+$\rm\overline{p}$ (lower
panels) compared to hydrodynamical calculations from the MUSIC model using IP-
Glasma initial conditions (magenta) [82], the iEBE-VISHNU hybrid model using
AMPT (orange) or TRENTo (cyan) initial conditions [83]. Statistical and
systematic uncertainties of the data points are shown as bars and boxes,
respectively.

As quark density depends on centrality, the maximum $v_{\rm n}$ is expected to
be found at higher $p_{\mathrm{T}}$ in more central collisions. To further
quantify this aspect of the shape evolution of $v_{\rm n}(p_{\mathrm{T}})$,
the $p_{\mathrm{T}}$ of $\pi^{\pm}$, p+$\rm\overline{p}$,
$\Lambda$+$\overline{\Lambda}$, and ${\rm K}^{\rm 0}_{\rm S}$ where $v_{\rm
2}(p_{\mathrm{T}})$ and $v_{\rm 3}(p_{\mathrm{T}})$ reach a maximum, divided
by number of constituent quarks $n_{\rm q}$, is reported in Fig. 18 as a
function of centrality. The $\phi$-meson and ${\rm K}^{\pm}$ are not included
since the kinematic range and granularity of the measurements do not allow for
a reliable extraction of a maximum. The left panel of Fig. 18 shows that the
$p_{\mathrm{T}}$$/n_{\rm q}$ at which $v_{\rm 2}(p_{\mathrm{T}})$ reaches a
maximum, denoted as $p_{\mathrm{T}}{}|_{v_{2}^{\mathrm{max}}}/n_{\rm q}$,
decreases with increasing centrality percentile for collision centralities
larger than 5–10%, following the expectations from the hypothesis of
hadronization through coalescence. The systematic uncertainties as presented
in Fig. 18 have been evaluated directly on $p_{\mathrm{T}}{}|_{v_{\rm
n}^{\mathrm{max}}}/n_{\rm q}$ to accurately take into account that some
systematic uncertainties can be point-by-point correlated in $p_{\mathrm{T}}$.
In the 0–5% centrality interval, there is a hint of a lower
$p_{\mathrm{T}}{}|_{v_{2}^{\mathrm{max}}}/n_{\rm q}$ than in the 5–10%
centrality class for all particle species. The observed
$p_{\mathrm{T}}{}|_{v_{2}^{\mathrm{max}}}/n_{\rm q}$ is compatible among all
particle species with the exception of the p+$\rm\overline{p}$
$p_{\mathrm{T}}{}|_{v_{2}^{\mathrm{max}}}/n_{\rm q}$, which is slightly lower
in the 0–20% centrality range. The right panel of Fig. 18 presents
$p_{\mathrm{T}}{}|_{v_{3}^{\mathrm{max}}}/n_{\rm q}$, which shows, within the
large uncertainties, a weak (if any) centrality dependence for $\pi^{\pm}$ and
${\rm K}^{\rm 0}_{\rm S}$ and no centrality dependence for p+$\rm\overline{p}$
and $\Lambda$+$\overline{\Lambda}$. The
$p_{\mathrm{T}}{}|_{v_{3}^{\mathrm{max}}}/n_{\rm q}$ is the same for the
different particle species within uncertainties.

Figure 18: (Colour online) Centrality dependence of
$p_{\mathrm{T}}{}|_{v_{2}^{\mathrm{max}}}/n_{\rm q}$ (left) and
$p_{\mathrm{T}}{}|_{v_{3}^{\mathrm{max}}}/n_{\rm q}$ (right) divided by number
of constituent quarks, $n_{\rm q}$, for $\pi^{\pm}$, p+$\rm\overline{p}$,
$\Lambda$+$\overline{\Lambda}$, and ${\rm K}^{\rm 0}_{\rm S}$. Points are
slightly shifted along the horizontal axis for better visibility in both
panels. Statistical and systematic uncertainties are shown as bars and boxes,
respectively.

In the scenario of ideal hydrodynamics, $v_{\rm n}$ is a power law function of
the radial expansion velocity of the medium [95, 96] so that $v_{\rm n}\propto
p_{\mathrm{T}}{}^{\rm n}$ up to $p_{\mathrm{T}}{}\sim M$ for particles with
mass $M$. Figure 19 shows $|v_{\rm n}|^{1/{\rm n}}/p_{\mathrm{T}}{}$ as
function of $p_{\mathrm{T}}$ for $n=2$ and $n=3$ in various centrality
intervals for inclusive charged particles [44], $\pi^{\pm}$, ${\rm K}^{\pm}$,
p+$\rm\overline{p}$, $\Lambda$+$\overline{\Lambda}$, ${\rm K}^{\rm 0}_{\rm
S}$, and the $\phi$-meson ($n=2$ only). When $v_{\rm n}\propto
p_{\mathrm{T}}{}^{\rm n}$, the observable $|v_{\rm n}|^{1/{\rm
n}}/p_{\mathrm{T}}{}$ should be a constant. For $\pi^{\pm}$ and the inclusive
charged particles, the $v_{\rm n}\propto p_{\mathrm{T}}{}^{\rm n}$ scaling is
broken both for $v_{2}$ and $v_{3}$ for all centrality intervals, as is also
hypothesized in [97]. It should be noted however that the kinematic
constraints imposed on the measurement preclude testing the scaling hypothesis
in the full relevant momentum region. The scaling holds up to
$p_{\mathrm{T}}{}~{}\approx~{}1~{}\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc{}$
for ${\rm K}^{\pm}$ and ${\rm K}^{\rm 0}_{\rm S}$, and up to
$p_{\mathrm{T}}{}~{}\approx~{}2~{}\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc{}$
for p+$\rm\overline{p}$, $\Lambda$+$\overline{\Lambda}$, and the $\phi$-meson
for the 0–5% and 10–20% centrality intervals. Similar qualitative observations
are found in the three hydrodynamical calculations [82, 83].

Figure 19: (Colour online) Centrality dependence of $|v_{\rm n}|^{1/{\rm
n}}/p_{\mathrm{T}}{}$ of inclusive charged particles [44], $\pi^{\pm}$, ${\rm
K}^{\pm}$, p+$\rm\overline{p}$, $\Lambda$+$\overline{\Lambda}$, ${\rm K}^{\rm
0}_{\rm S}$, and the $\phi$-meson for $n=2$ (upper panels) and $n=3$ (lower
panels). Statistical and systematic uncertainties are shown as bars and boxes,
respectively.

If $v_{\rm n}$ indeed exhibits a power law dependence on
$p_{\mathrm{T}}{}^{\rm n}$, ratios of the form of $v_{\rm n}^{1/{\rm
n}}/v_{\rm m}^{1/{\rm m}}$ are $p_{\mathrm{T}}$-independent. Previous
measurements at RHIC [98, 99] and the LHC [100, 101] have shown that the
ratios $v_{\rm n}^{1/{\rm n}}/v_{\rm m}^{1/{\rm m}}$ show little to no
$p_{\mathrm{T}}$ dependence up to about 6
$\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc$ independent of the harmonic $n$
and $m$ for peripheral and semi-central collisions. However, a
$p_{\mathrm{T}}$ dependence is observed for central collisions, which might be
due to fluctuations in the initial geometry [99].

Figure 20: (Colour online) Centrality dependence of $v_{3}/|v_{2}|^{3/2}$ for
inclusive charged particles [44], $\pi^{\pm}$, ${\rm K}^{\pm}$, and
p+$\rm\overline{p}$. Statistical and systematic uncertainties are shown as
bars and boxes, respectively. Figure 21: (Colour online) Centrality dependence
of $v_{4}/|v_{2}|^{4/2}$ for inclusive charged particles [44], $\pi^{\pm}$,
${\rm K}^{\pm}$, and p+$\rm\overline{p}$. Statistical and systematic
uncertainties are shown as bars and boxes, respectively. Figure 22: (Colour
online) Centrality dependence of $v_{4}/|v_{3}|^{4/3}$ for inclusive charged
particles [44], $\pi^{\pm}$, ${\rm K}^{\pm}$, and p+$\rm\overline{p}$.
Statistical and systematic uncertainties are shown as bars and boxes,
respectively.

The ratios $v_{3}/|v_{2}|^{3/2}$, $v_{4}/|v_{2}|^{4/2}$, and
$v_{4}/|v_{3}|^{4/3}$, which probe the same scaling but are in practice more
sensitive, are shown in Figs. 20, 21, and 22, respectively. For each figure,
$v_{\rm n}/|v_{\rm m}|^{\rm n/m}$ is shown for inclusive charged particles
[44], $\pi^{\pm}$, ${\rm K}^{\pm}$ and p+$\rm\overline{p}$ in various
centrality intervals. For $v_{3}/|v_{2}|^{3/2}$ and $v_{4}/|v_{2}|^{4/2}$, no
obvious $p_{\mathrm{T}}$ dependence is found for inclusive charged particles
between 5–50% collision centrality. For the 0–5% centrality class, the ratios
are flat for $p_{\mathrm{T}}<3$ $\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc$
and rise monotonically for higher momenta. No particle type dependence of the
ratios is found for $p_{\mathrm{T}}{}>$ 1.5
$\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc$, below which the ratios for
p+$\rm\overline{p}$ $v_{\rm n}$ rise. This rise of the p+$\rm\overline{p}$
$v_{\rm n}$ ratios can be attributed to an increase of radial flow which
affects the independent harmonics differently. For the ratio
$v_{4}/|v_{3}|^{4/3}$, no $p_{\mathrm{T}}$ dependence is observed over the
full centrality range. Large statistical uncertainties do not allow
conclusions to be drawn on the behaviour of p+$\rm\overline{p}$ $v_{n}$ in the
$v_{4}/|v_{3}|^{4/3}$ ratio.

###  4.5 Comparison with $v_{\rm n}$ of identified particles at
$\sqrt{s_{\mathrm{NN}}}$ = 2.76 TeV

The transport properties and initial condition models can be further
constrained by studying the energy dependence of anisotropic flow. Figure 23
presents the $v_{\rm 2}(p_{\mathrm{T}})$, $v_{\rm 3}(p_{\mathrm{T}})$, and
$v_{\rm 4}(p_{\mathrm{T}})$ of $\pi^{\pm}$, ${\rm K}^{\pm}$, and
p+$\rm\overline{p}$ compared to ALICE measurements performed at
$\sqrt{s_{\mathrm{NN}}}$ = 2.76 TeV [28].

The $v_{n}$ coefficients at $\sqrt{s_{\mathrm{NN}}}$ = 2.76 TeV have been
measured using the scalar product method, taking the particle of interest
under study and the charged reference particles from different, non-
overlapping pseudorapidity regions between $|\eta|<0.8$. Assuming no
anisotropic flow in minimum bias pp collisions at the same collision energy,
the non-flow contributions are estimated from minimum bias pp collisions and
subtracted from the measured $v_{\rm n}$ coefficients. Ratios of the
measurements presented in this paper to a cubic spline fit to the ones
performed at $\sqrt{s_{\mathrm{NN}}}$ = 2.76 TeV are given in the figure for
each presented centrality interval and flow coefficient. The uncertainties in
these ratios are obtained by summing the statistical and systematic
uncertainties on the independent measurements in quadrature, and propagating
the obtained uncertainties as uncorrelated.

An increase of radial flow with increasing collision energy is expected to
lead to a suppression of $v_{\rm n}$ at low $p_{\mathrm{T}}$, an effect which
would be most pronounced for heavier particles. Although a possible
suppression of p+$\rm\overline{p}$ $v_{\rm n}$ at $\sqrt{s_{\mathrm{NN}}}$ =
5.02 TeV can be seen between
$1~{}\lesssim~{}p_{\mathrm{T}}{}~{}\lesssim~{}3~{}\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc{}$
in central collisions and additionally for $v_{\rm 2}(p_{\mathrm{T}})$ of
$\pi^{\pm}$ and ${\rm K}^{\pm}$ at the same centrality interval, the precision
of the results does not allow for conclusions to be drawn as the measurements
at different collision energies are compatible within uncertainties.

Figure 23: (Colour online) The $p_{\mathrm{T}}$-differential $v_{2}$ (top),
$v_{3}$ (middle), and $v_{4}$ (bottom) of $\pi^{\pm}$, ${\rm K}^{\pm}$, and
p+$\rm\overline{p}$ compared to ALICE measurements performed in Pb–Pb
collisions at $\sqrt{s_{\mathrm{NN}}}$ = 2.76 TeV (coloured bands) [28] for
the 0–5%, 10–20%, and 40–50% centrality classes. For the measurements at
$\sqrt{s_{\mathrm{NN}}}$ = 5.02 TeV, statistical and systematic uncertainties
are shown as bars and boxes, respectively. For the measurements at
$\sqrt{s_{\mathrm{NN}}}$ = 2.76 TeV, the thickness of the bands corresponds to
the quadratic sum of statistical and systematic uncertainties. The ratios of
measurements at $\sqrt{s_{\mathrm{NN}}}$ = 5.02 TeV to a cubic spline fit to
the measurements at $\sqrt{s_{\mathrm{NN}}}$ = 2.76 TeV are also presented for
clarity.

Figure 24 shows the $v_{\rm 2}(p_{\mathrm{T}})$ of
$\Lambda$+$\overline{\Lambda}$, ${\rm K}^{\rm 0}_{\rm S}$, and the
$\phi$-meson compared to ALICE measurements performed at
$\sqrt{s_{\mathrm{NN}}}$ = 2.76 TeV [27], where the $v_{2}$ coefficients at
$\sqrt{s_{\mathrm{NN}}}$ = 2.76 TeV have been measured using the scalar
product method with an $|\Delta\eta|>0.9$ gap to suppress non-flow. No
differences are observed between the ${\rm K}^{\rm 0}_{\rm S}$ and
$\Lambda$+$\overline{\Lambda}$ $v_{\rm 2}(p_{\mathrm{T}})$ measured at two
different collision energies. The strongly improved precision of the
$\phi$-meson measurement at $\sqrt{s_{\mathrm{NN}}}$ = 5.02 TeV, both in terms
of statistical uncertainty and granularity in $p_{\mathrm{T}}$, shows that the
$v_{\rm 2}(p_{\mathrm{T}})$ follows a mass ordering at low $p_{\mathrm{T}}$
and groups with mesons after $p_{\mathrm{T}}$$\approx$ 3
$\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc$ for all centrality intervals.

Figure 24: (Colour online) The $p_{\mathrm{T}}$-differential $v_{2}$ of
$\Lambda$+$\overline{\Lambda}$, ${\rm K}^{\rm 0}_{\rm S}$, and the
$\phi$-meson compared to ALICE measurements performed in Pb–Pb collisions at
$\sqrt{s_{\mathrm{NN}}}$ = 2.76 TeV (coloured bands) [27] for the 0–5%,
10–20%, and 40–50% centrality classes. For the measurements at
$\sqrt{s_{\mathrm{NN}}}$ = 5.02 TeV, statistical and systematic uncertainties
are shown as bars and boxes, respectively. For the measurements at
$\sqrt{s_{\mathrm{NN}}}$ = 2.76 TeV, the thickness of the bands corresponds to
the quadratic sum of statistical and systematic uncertainties. The ratios of
measurements at $\sqrt{s_{\mathrm{NN}}}$ = 5.02 TeV to a cubic spline fit to
the measurements at $\sqrt{s_{\mathrm{NN}}}$ = 2.76 TeV are also presented for
clarity.

##  5 Summary

In summary, the elliptic, triangular, and quadrangular flow coefficients of
$\pi^{\pm}$, ${\rm K}^{\pm}$, p+$\rm\overline{p}$,
$\Lambda$+$\overline{\Lambda}$, ${\rm K}^{\rm 0}_{\rm S}$, and the
$\phi$-meson have been measured in Pb–Pb collisions at $\sqrt{s_{\rm
NN}}=5.02$ TeV over a broad range of transverse momentum and in various
centrality ranges. The precision of these measurements provide constraints for
initial-state fluctuations and transport coefficients of the medium. The
magnitude of $v_{\rm n}$ increases with decreasing centrality up to the 40–50%
centrality interval for all particle species. This increase is stronger for
$v_{2}$ than for $v_{3}$ and $v_{4}$, which indicates that collision geometry
dominates the generation of elliptic flow while higher flow coefficients are
mainly generated by event-by-event fluctuations in the initial nucleon and
gluon densities. This interpretation is also supported by the non-zero,
positive $v_{\rm n}$ found in the 0–1% centrality interval. In most central
collisions (i.e. 0–1% and 0–5%), $v_{3}$ and $v_{4}$ reach a similar magnitude
as $v_{2}$ at different $p_{\mathrm{T}}$ values depending on particle mass,
after which they increase gradually. For $p_{\mathrm{T}}<3$
$\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc$, the $v_{\rm n}$ coefficients
show a mass ordering consistent with an interplay between anisotropic flow and
the isotropic expansion (radial flow) of the collision system. In this
transverse momentum range, the iEBE-VISHNU hydrodynamical calculations
describe the measured $v_{\rm n}$ of $\pi^{\pm}$, ${\rm K}^{\pm}$, and
p+$\rm\overline{p}$ fairly well for $p_{\mathrm{T}}<2.5$
$\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc$, while MUSIC reproduces the
measurements for $p_{\mathrm{T}}<1$
$\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc$. It should be noted that
neither of the presented hydrodynamical models is able to fully describe the
measurements. At intermediate transverse momenta ($3<p_{\mathrm{T}}<$ 8-10
$\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc$), particles show an approximate
grouping by the number of constituent quarks at the level of $\pm 20\%$ for
all flow coefficients in the 0–50% centrality range. The $\phi$-meson $v_{2}$,
which tests both particle mass dependence and type scaling, follows
p+$\rm\overline{p}$ $v_{2}$ at low $p_{\mathrm{T}}$ and $\pi^{\pm}$ $v_{2}$ at
intermediate $p_{\mathrm{T}}$. The baryon $v_{\rm n}$ has a magnitude larger
than that of mesons for $p_{\mathrm{T}}<$ 8-10
$\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc$, indicating that the particle
type dependence persists up to high $p_{\mathrm{T}}$. For $p_{\mathrm{T}}>10$
$\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc$, the $v_{2}$ of
p+$\rm\overline{p}$ is compatible with that of $\pi^{\pm}$ within
uncertainties. The shape evolution of $v_{\rm 2}(p_{\mathrm{T}})$ as function
of centrality shows different trends for $\pi^{\pm}$, ${\rm K}^{\pm}$, and
p+$\rm\overline{p}$ and varies between 20% (10%) to 250% (55%) for
p+$\rm\overline{p}$ (${\rm K}^{\pm}$) at low $p_{\mathrm{T}}$ from most
central to peripheral collisions; variations are more pronounced for $v_{\rm
3}(p_{\mathrm{T}})$, in particular for central collisions. Ratios
$v_{3}/|v_{2}|^{3/2}$ and $v_{4}/|v_{2}|^{4/2}$ are flat for
$p_{\mathrm{T}}<3$ $\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc$ and rise
monotonically for higher momenta for the 0-5% centrality class. No particle
type dependence of the ratios is found for $p_{\mathrm{T}}{}>$ 1.5
$\mathrm{GeV}\kern-0.50003pt/\kern-0.20004ptc$, below which the ratios for
p+$\rm\overline{p}$ $v_{\rm n}$ rise, which can be attributed to an increase
of radial flow which affects the independent harmonics differently. For the
ratio $v_{4}/|v_{3}|^{4/3}$, no $p_{\mathrm{T}}$ dependence is observed over
the full centrality range. The measurements are compatible with those
performed in Pb–Pb collisions at $\sqrt{s_{\mathrm{NN}}}$ = 2.76 TeV within
uncertainties.

## Acknowledgements

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

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##  Appendix A The ALICE Collaboration

S. Acharyaorg139&F.T.-. Acostaorg22&D. Adamováorg94&J. Adolfssonorg81&M.M.
Aggarwalorg98&G. Aglieri Rinellaorg36&M. Agnelloorg33&N. Agrawalorg49&Z.
Ahammedorg139&S.U. Ahnorg77&S. Aiolaorg144&A. Akindinovorg65&M. Al-
Turanyorg104&S.N. Alamorg139&D.S.D. Albuquerqueorg120&D. Aleksandrovorg88&B.
Alessandroorg59&R. Alfaro Molinaorg73&Y. Aliorg16&A. Aliciorg11,org54,org29&A.
Alkinorg3&J. Almeorg24&T. Altorg70&L. Altenkamperorg24&I. Altsybeevorg138&M.N.
Anaamorg7&C. Andreiorg48&D. Andreouorg36&H.A. Andrewsorg108&A.
Andronicorg142,org104&M. Angelettiorg36&V. Anguelovorg102&C. Ansonorg17&T.
Antičićorg105&F. Antinoriorg57&P. Antonioliorg54&R. Anwarorg124&N.
Apadulaorg80&L. Aphecetcheorg112&H. Appelshäuserorg70&S. Arcelliorg29&R.
Arnaldiorg59&O.W. Arnoldorg103,org115&I.C. Arseneorg23&M. Arslandokorg102&B.
Audurierorg112&A. Augustinusorg36&R. Averbeckorg104&M.D. Azmiorg18&A.
Badalàorg56&Y.W. Baekorg61,org42&S. Bagnascoorg59&R. Bailhacheorg70&R.
Balaorg99&A. Baldisseriorg134&M. Ballorg44&R.C. Baralorg86&A.M.
Barbanoorg28&R. Barberaorg30&F. Barileorg53&L. Barioglioorg28&G.G.
Barnaföldiorg143&L.S. Barnbyorg93&V. Barretorg131&P. Bartaliniorg7&K.
Barthorg36&E. Bartschorg70&N. Bastidorg131&S. Basuorg141&G. Batigneorg112&B.
Batyunyaorg76&P.C. Batzingorg23&J.L. Bazo Albaorg109&I.G. Beardenorg89&H.
Beckorg102&C. Beddaorg64&N.K. Beheraorg61&I. Belikovorg133&F. Belliniorg36&H.
Bello Martinezorg2&R. Bellwiedorg124&L.G.E. Beltranorg118&V. Belyaevorg92&G.
Bencediorg143&S. Beoleorg28&A. Bercuciorg48&Y. Berdnikovorg96&D.
Berenyiorg143&R.A. Bertensorg127&D. Berzanoorg36,org59&L. Betevorg36&P.P.
Bhaduriorg139&A. Bhasinorg99&I.R. Bhatorg99&H. Bhattorg49&B.
Bhattacharjeeorg43&J. Bhomorg116&A. Bianchiorg28&L. Bianchiorg124&N.
Bianchiorg52&J. Bielčíkorg39&J. Bielčíkováorg94&A. Bilandzicorg115,org103&G.
Biroorg143&R. Biswasorg4&S. Biswasorg4&J.T. Blairorg117&D. Blauorg88&C.
Blumeorg70&G. Bocaorg136&F. Bockorg36&A. Bogdanovorg92&L. Boldizsárorg143&M.
Bombaraorg40&G. Bonomiorg137&M. Bonoraorg36&H. Borelorg134&A.
Borissovorg20,org142&M. Borriorg126&E. Bottaorg28&C. Bourjauorg89&L.
Bratrudorg70&P. Braun-Munzingerorg104&M. Bregantorg119&T.A. Brokerorg70&M.
Brozorg39&E.J. Bruckenorg45&E. Brunaorg59&G.E. Brunoorg36,org35&D.
Budnikovorg106&H. Bueschingorg70&S. Bufalinoorg33&P. Buhlerorg111&P.
Buncicorg36&O. Buschorg130org*&Z. Butheleziorg74&J.B. Buttorg16&J.T.
Buxtonorg19&J. Cabalaorg114&D. Caffarriorg90&H. Cainesorg144&A.
Calivaorg104&E. Calvo Villarorg109&R.S. Camachoorg2&P. Cameriniorg27&A.A.
Caponorg111&F. Carenaorg36&W. Carenaorg36&F. Carnesecchiorg29,org11&J.
Castillo Castellanosorg134&A.J. Castroorg127&E.A.R. Casulaorg55&C. Ceballos
Sanchezorg9&S. Chandraorg139&B. Changorg125&W. Changorg7&S. Chapelandorg36&M.
Chartierorg126&S. Chattopadhyayorg139&S. Chattopadhyayorg107&A.
Chauvinorg103,org115&C. Cheshkovorg132&B. Cheynisorg132&V. Chibante
Barrosoorg36&D.D. Chinellatoorg120&S. Choorg61&P. Chochulaorg36&T.
Chowdhuryorg131&P. Christakoglouorg90&C.H. Christensenorg89&P.
Christiansenorg81&T. Chujoorg130&S.U. Chungorg20&C. Cicaloorg55&L.
Cifarelliorg11,org29&F. Cindoloorg54&J. Cleymansorg123&F. Colamariaorg53&D.
Colellaorg66,org36,org53&A. Colluorg80&M. Colocciorg29&M. Concasorg59orgI&G.
Conesa Balbastreorg79&Z. Conesa del Valleorg62&J.G. Contrerasorg39&T.M.
Cormierorg95&Y. Corrales Moralesorg59&P. Corteseorg34&M.R. Cosentinoorg121&F.
Costaorg36&S. Costanzaorg136&J. Crkovskáorg62&P. Crochetorg131&E.
Cuautleorg71&L. Cunqueiroorg142,org95&T. Dahmsorg103,org115&A. Daineseorg57&S.
Daniorg67&M.C. Danischorg102&A. Danuorg69&D. Dasorg107&I. Dasorg107&S.
Dasorg4&A. Dashorg86&S. Dashorg49&S. Deorg50&A. De Caroorg32&G. de
Cataldoorg53&C. de Contiorg119&J. de Cuvelandorg41&A. De Falcoorg26&D. De
Gruttolaorg11,org32&N. De Marcoorg59&S. De Pasqualeorg32&R.D. De
Souzaorg120&H.F. Degenhardtorg119&A. Deistingorg104,org102&A. Delofforg85&S.
Delsantoorg28&C. Deplanoorg90&P. Dhankherorg49&D. Di Bariorg35&A. Di
Mauroorg36&B. Di Ruzzaorg57&R.A. Diazorg9&T. Dietelorg123&P.
Dillensegerorg70&Y. Dingorg7&R. Diviàorg36&Ø. Djuvslandorg24&A. Dobrinorg36&D.
Domenicis Gimenezorg119&B. Dönigusorg70&O. Dordicorg23&L.V.R.
Doremalenorg64&A.K. Dubeyorg139&A. Dublaorg104&L. Ducrouxorg132&S.
Dudiorg98&A.K. Duggalorg98&M. Dukhishyamorg86&P. Dupieuxorg131&R.J.
Ehlersorg144&D. Eliaorg53&E. Endressorg109&H. Engelorg75&E. Eppleorg144&B.
Erazmusorg112&F. Erhardtorg97&M.R. Ersdalorg24&B. Espagnonorg62&G.
Eulisseorg36&J. Eumorg20&D. Evansorg108&S. Evdokimovorg91&L.
Fabbiettiorg103,org115&M. Fagginorg31&J. Faivreorg79&A. Fantoniorg52&M.
Faselorg95&L. Feldkamporg142&A. Felicielloorg59&G. Feofilovorg138&A. Fernández
Téllezorg2&A. Ferrettiorg28&A. Festantiorg31,org36&V.J.G. Feuillardorg102&J.
Figielorg116&M.A.S. Figueredoorg119&S. Filchaginorg106&D. Finogeevorg63&F.M.
Fiondaorg24&G. Fiorenzaorg53&F. Flororg124&M. Florisorg36&S. Foertschorg74&P.
Fokaorg104&S. Fokinorg88&E. Fragiacomoorg60&A. Francesconorg36&A.
Franciscoorg112&U. Frankenfeldorg104&G.G. Fronzeorg28&U. Fuchsorg36&C.
Furgetorg79&A. Fursorg63&M. Fusco Girardorg32&J.J. Gaardhøjeorg89&M.
Gagliardiorg28&A.M. Gagoorg109&K. Gajdosovaorg89&M. Gallioorg28&C.D.
Galvanorg118&P. Ganotiorg84&C. Garabatosorg104&E. Garcia-Solisorg12&K.
Gargorg30&C. Gargiuloorg36&P. Gasikorg115,org103&E.F. Gaugerorg117&M.B. Gay
Ducatiorg72&M. Germainorg112&J. Ghoshorg107&P. Ghoshorg139&S.K. Ghoshorg4&P.
Gianottiorg52&P. Giubellinoorg104,org59&P. Giubilatoorg31&P.
Glässelorg102&D.M. Goméz Coralorg73&A. Gomez Ramirezorg75&V. Gonzalezorg104&P.
González-Zamoraorg2&S. Gorbunovorg41&L. Görlichorg116&S. Gotovacorg37&V.
Grabskiorg73&L.K. Graczykowskiorg140&K.L. Grahamorg108&L. Greinerorg80&A.
Grelliorg64&C. Grigorasorg36&V. Grigorievorg92&A. Grigoryanorg1&S.
Grigoryanorg76&J.M. Gronefeldorg104&F. Grosaorg33&J.F. Grosse-
Oetringhausorg36&R. Grossoorg104&R. Guernaneorg79&B. Guerzoniorg29&M.
Guittiereorg112&K. Gulbrandsenorg89&T. Gunjiorg129&A. Guptaorg99&R.
Guptaorg99&I.B. Guzmanorg2&R. Haakeorg36&M.K. Habiborg104&C.
Hadjidakisorg62&H. Hamagakiorg82&G. Hamarorg143&M. Hamidorg7&J.C.
Hamonorg133&R. Hanniganorg117&M.R. Haqueorg64&J.W. Harrisorg144&A.
Hartonorg12&H. Hassanorg79&D. Hatzifotiadouorg54,org11&S. Hayashiorg129&S.T.
Heckelorg70&E. Hellbärorg70&H. Helstruporg38&A. Herghelegiuorg48&E.G.
Hernandezorg2&G. Herrera Corralorg10&F. Herrmannorg142&K.F. Hetlandorg38&T.E.
Hildenorg45&H. Hillemannsorg36&C. Hillsorg126&B. Hippolyteorg133&B.
Hohlwegerorg103&D. Horakorg39&S. Hornungorg104&R. Hosokawaorg130,org79&J.
Hotaorg67&P. Hristovorg36&C. Huangorg62&C. Hughesorg127&P. Huhnorg70&T.J.
Humanicorg19&H. Hushnudorg107&N. Hussainorg43&T. Hussainorg18&D.
Hutterorg41&D.S. Hwangorg21&J.P. Iddonorg126&S.A. Iga Buitronorg71&R.
Ilkaevorg106&M. Inabaorg130&M. Ippolitovorg88&M.S. Islamorg107&M.
Ivanovorg104&V. Ivanovorg96&V. Izucheevorg91&B. Jacakorg80&N.
Jacazioorg29&P.M. Jacobsorg80&M.B. Jadhavorg49&S. Jadlovskaorg114&J.
Jadlovskyorg114&S. Jaelaniorg64&C. Jahnkeorg119,org115&M.J.
Jakubowskaorg140&M.A. Janikorg140&C. Jenaorg86&M. Jercicorg97&O.
Jevonsorg108&R.T. Jimenez Bustamanteorg104&M. Jinorg124&P.G. Jonesorg108&A.
Juskoorg108&P. Kalinakorg66&A. Kalweitorg36&J.H. Kangorg145&V. Kaplinorg92&S.
Karorg7&A. Karasu Uysalorg78&O. Karavichevorg63&T. Karavichevaorg63&P.
Karczmarczykorg36&E. Karpechevorg63&U. Kebschullorg75&R. Keidelorg47&D.L.D.
Keijdenerorg64&M. Keilorg36&B. Ketzerorg44&Z. Khabanovaorg90&A.M. Khanorg7&S.
Khanorg18&S.A. Khanorg139&A. Khanzadeevorg96&Y. Kharlovorg91&A. Khatunorg18&A.
Khuntiaorg50&M.M. Kielbowiczorg116&B. Kilengorg38&B. Kimorg130&D.
Kimorg145&D.J. Kimorg125&E.J. Kimorg14&H. Kimorg145&J.S. Kimorg42&J.
Kimorg102&M. Kimorg61,org102&S. Kimorg21&T. Kimorg145&T. Kimorg145&S.
Kirschorg41&I. Kiselorg41&S. Kiselevorg65&A. Kisielorg140&J.L. Klayorg6&C.
Kleinorg70&J. Kleinorg36,org59&C. Klein-Bösingorg142&S. Klewinorg102&A.
Klugeorg36&M.L. Knichelorg36&A.G. Knospeorg124&C. Kobdajorg113&M.
Kofaragoorg143&M.K. Köhlerorg102&T. Kolleggerorg104&N. Kondratyevaorg92&E.
Kondratyukorg91&A. Konevskikhorg63&M. Konyushikhinorg141&O. Kovalenkoorg85&V.
Kovalenkoorg138&M. Kowalskiorg116&I. Králikorg66&A. Kravčákováorg40&L.
Kreisorg104&M. Krivdaorg66,org108&F. Krizekorg94&M. Krügerorg70&E.
Kryshenorg96&M. Krzewickiorg41&A.M. Kuberaorg19&V. Kučeraorg94,org61&C.
Kuhnorg133&P.G. Kuijerorg90&J. Kumarorg49&L. Kumarorg98&S. Kumarorg49&S.
Kunduorg86&P. Kurashviliorg85&A. Kurepinorg63&A.B. Kurepinorg63&A.
Kuryakinorg106&S. Kushpilorg94&J. Kvapilorg108&M.J. Kweonorg61&Y.
Kwonorg145&S.L. La Pointeorg41&P. La Roccaorg30&Y.S. Laiorg80&I.
Lakomovorg36&R. Langoyorg122&K. Lapidusorg144&A. Lardeuxorg23&P.
Larionovorg52&E. Laudiorg36&R. Lavickaorg39&R. Leaorg27&L. Leardiniorg102&S.
Leeorg145&F. Lehasorg90&S. Lehnerorg111&J. Lehrbachorg41&R.C. Lemmonorg93&I.
León Monzónorg118&P. Lévaiorg143&X. Liorg13&X.L. Liorg7&J. Lienorg122&R.
Lietavaorg108&B. Limorg20&S. Lindalorg23&V. Lindenstruthorg41&S.W.
Lindsayorg126&C. Lippmannorg104&M.A. Lisaorg19&V. Litichevskyiorg45&A.
Liuorg80&H.M. Ljunggrenorg81&W.J. Llopeorg141&D.F. Lodatoorg64&V.
Loginovorg92&C. Loizidesorg95,org80&P. Loncarorg37&X. Lopezorg131&E. López
Torresorg9&A. Loweorg143&P. Luettigorg70&J.R. Luhderorg142&M. Lunardonorg31&G.
Luparelloorg60&M. Lupiorg36&A. Maevskayaorg63&M. Magerorg36&S.M.
Mahmoodorg23&A. Maireorg133&R.D. Majkaorg144&M. Malaevorg96&Q.W. Malikorg23&L.
Malininaorg76orgII&D. Mal’Kevichorg65&P. Malzacherorg104&A. Mamonovorg106&V.
Mankoorg88&F. Mansoorg131&V. Manzariorg53&Y. Maoorg7&M.
Marchisoneorg128,org74,org132&J. Marešorg68&G.V. Margagliottiorg27&A.
Margottiorg54&J. Marguttiorg64&A. Marínorg104&C. Markertorg117&M.
Marquardorg70&N.A. Martinorg104&P. Martinengoorg36&J.L. Martinezorg124&M.I.
Martínezorg2&G. Martínez Garcíaorg112&M. Martinez Pedreiraorg36&S.
Masciocchiorg104&M. Maseraorg28&A. Masoniorg55&L. Massacrierorg62&E.
Massonorg112&A. Mastroserioorg53,org135&A.M. Mathisorg115,org103&P.F.T.
Matuokaorg119&A. Matyjaorg116,org127&C. Mayerorg116&M. Mazzilliorg35&M.A.
Mazzoniorg58&F. Meddiorg25&Y. Melikyanorg92&A. Menchaca-Rochaorg73&E.
Meninnoorg32&J. Mercado Pérezorg102&M. Meresorg15&C.S. Mezaorg109&S.
Mhlangaorg123&Y. Miakeorg130&L. Michelettiorg28&M.M. Mieskolainenorg45&D.L.
Mihaylovorg103&K. Mikhaylovorg65,org76&A. Mischkeorg64&A.N. Mishraorg71&D.
Miśkowiecorg104&J. Mitraorg139&C.M. Mituorg69&N. Mohammadiorg36&A.P.
Mohantyorg64&B. Mohantyorg86&M. Mohisin Khanorg18orgIII&D.A. Moreira De
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