2015 173 9 July

Heavy-flavour decay muon $v_{2}$ in Pb–Pb collisions

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

The elliptic flow, $v_{2}$, of muons from heavy-flavour hadron decays at
forward rapidity ($2.5<y<4$) is measured in Pb–Pb collisions at $\sqrt{s_{\rm
NN}}$ = 2.76 TeV with the ALICE detector at the LHC. The scalar product, two-
and four-particle $Q$ cumulants and Lee-Yang zeros methods are used. The
dependence of the $v_{2}$ of muons from heavy-flavour hadron decays on the
collision centrality, in the range 0–40%, and on transverse momentum, $p_{\rm
T}$, is studied in the interval $3<p_{\rm T}<10$ GeV/$c$. A positive $v_{2}$
is observed with the scalar product and two-particle $Q$ cumulants in semi-
central collisions (10–20% and 20–40% centrality classes) for the $p_{\rm T}$
interval from 3 to about 5 GeV/$c$. The $v_{2}$ magnitude tends to decrease
towards more central collisions and with increasing $p_{\rm T}$. It becomes
compatible with zero in the interval $6<p_{\rm T}<10~{}{\rm GeV/}c$. The
results are compared to models describing the interaction of heavy quarks and
open heavy-flavour hadrons with the high-density medium formed in high-energy
heavy-ion collisions. The model calculations describe the measured $v_{2}$
within uncertainties.

Keywords: LHC, ALICE experiment, Pb–Pb collisions, heavy-flavour decay muons,
elliptic flow
PACS: 25.75.-q, 25.75.Cj, 25.75.Ld, 24.10.Nz

##  1 Introduction

Experiments with ultra-relativistic heavy-ion collisions aim at investigating
the properties of strongly-interacting matter at very high temperatures and
energy densities. Quantum Chromodynamics (QCD) calculations on the lattice
predict, under these conditions, the formation of a Quark-Gluon Plasma (QGP),
where colour confinement vanishes and chiral symmetry is partially restored
[1, 2, 3, 4, 5]. Heavy quarks (charm and beauty) are created in initial hard-
scattering processes on a time scale shorter than the QGP formation time.
Subsequently, they interact with the medium constituents via inelastic [6, 7]
and elastic [8, 9, 10] processes. Therefore, heavy quarks are regarded as
effective probes of the QGP properties.

Heavy-quark energy loss due to in-medium interactions can be studied by means
of the nuclear modification factor $R_{\rm AA}$, defined as the ratio of the
yield of heavy-flavour particles measured in nucleus–nucleus (AA) collisions
to that observed in proton–proton (pp) collisions scaled by the number of
binary nucleon–nucleon collisions. The PHENIX and STAR Collaborations
measured, in central Au–Au collisions at $\sqrt{s_{\rm NN}}$ = 200 GeV, a
strong suppression corresponding to a $R_{\rm AA}$ of about 0.2–0.3 for heavy-
flavour decay electrons at mid-rapidity ($y$) and transverse momentum $p_{\rm
T}>5$ GeV/$c$ [11, 12, 13, 14, 15, 16, 17]. A similar suppression was also
measured by the STAR Collaboration for mid-rapidity ${\rm D}^{0}$ mesons [18].
A significant suppression was also observed by the PHENIX Collaboration at
forward rapidity for muons from heavy-flavour hadron decays in central Cu–Cu
collisions at $\sqrt{s_{\rm NN}}$ = 200 GeV [19]. At the LHC, the ALICE
Collaboration reported a similar effect in central Pb–Pb collisions at
$\sqrt{s_{\rm NN}}$ = 2.76 TeV for D mesons at mid-rapidity [20] and muons
from heavy-flavour hadron decays at forward rapidity [21] in the interval
$2<p_{\rm T}<16$ GeV/$c$ and $4<p_{\rm T}<10$ GeV/$c$, respectively. The CMS
Collaboration measured a significant suppression of non-prompt $\rm J/\psi$
from beauty-hadron decays in the interval $6.5<p_{\rm T}<30$ GeV/$c$
($3<p_{\rm T}<30$ GeV/$c$) and $|y|<2.4$ ($1.6<|y|<2.4$) [22, 23]. A first
measurement of non-prompt ${\rm J}/\psi$ by the ALICE Collaboration at mid-
rapidity ($|y|<0.8$) and in the interval $4.5<p_{\rm T}<10~{}{\rm GeV/}c$ has
been recently published [24].

Further insights into the QGP evolution and the in-medium interactions can be
gained from the study of the azimuthal anisotropy of particles carrying heavy
quarks which, in contrast to light quarks, have experienced the full system
evolution. The study of azimuthal anisotropy is a field of intense
experimental and theoretical investigations (see [25] and references therein).
In non-central collisions, the initial spatial anisotropy of the overlap
region, elongated in the direction perpendicular to the reaction plane,
defined by the beam axis and the impact parameter of the collision, is
converted into an anisotropy in momentum space through rescatterings [26].
Experimentally, the study of the particle azimuthal anisotropy is based on a
Fourier expansion of azimuthal distributions given by:

${{\rm d}^{2}N\over{{\rm d}p_{\rm T}{\rm d}\varphi}}={1\over 2\pi}{{\rm
d}N\over{\rm d}p_{\rm T}}\bigg{(}1+2\sum_{n=1}^{\infty}v_{n}(p_{\rm T}){\rm
cos}[n(\varphi-\Psi_{n})]\bigg{)},$ (1)

where $\varphi$ and $p_{\rm T}$ are the particle azimuthal angle and
transverse momentum, respectively. The Fourier coefficients, $v_{n}$,
characterize the anisotropy of produced particles and $\Psi_{n}$ is the
azimuthal angle of the initial-state symmetry plane for the $n^{\rm th}$
harmonic, introduced to account for the event-by-event fluctuations of the
initial nucleon density profile. The second Fourier coefficient, $v_{2}$,
which can also be expressed as $v_{2}=\langle\rm
cos[2(\varphi-\Psi_{2})]\rangle$, is named elliptic flow.

The $v_{2}$ of heavy-flavour hadrons is expected to provide information on the
collective expansion and degree of thermalization of heavy quarks in the
medium at low $p_{\rm T}$ ($p_{\rm T}<2-3$ GeV/$c$). The participation of
heavy quarks in the collective expansion is expected to give a positive
$v_{2}$ [26]. Moving towards intermediate $p_{\rm T}$ ($3<p_{\rm T}<6$
GeV/$c$), the $v_{2}$ Fourier coefficient is also expected to be sensitive to
the presence of recombination processes in the hadronization of heavy quarks
[27, 28]. At high $p_{\rm T}$ ($p_{\rm T}>6$ GeV/$c$), the $v_{2}$ measurement
can constrain the path-length dependence of the in-medium parton energy loss,
which becomes the dominant contribution to the azimuthal anisotropy and is
also predicted to give a positive $v_{2}$ [29, 30], thus complementing the
$R_{\rm AA}$ measurement.

The PHENIX Collaboration reported a positive $v_{2}$ of heavy-flavour decay
electrons at mid-rapidity in Au–Au collisions at $\sqrt{s_{\rm NN}}$ = 200
GeV, reaching a maximum value of about 0.15 at $p_{\rm T}$ = 1.5 GeV/$c$ in
semi-central collisions [14, 15, 31]. A similar behaviour was also observed by
the STAR Collaboration [32]. Recently, a $v_{2}$ value significantly larger
than zero was measured for D mesons at mid-rapidity in Pb–Pb collisions at
$\sqrt{s_{\rm NN}}$ = 2.76 TeV [33, 34]. A complementary measurement at the
same energy, provided by the heavy-flavour decay muon elliptic flow at forward
rapidity ($2.5<y<4$), is of great interest in order to provide new constraints
for models that implement the heavy-quark interactions with the medium.
Finally, the measurement is also important for the interpretation of the
J/$\psi$ elliptic flow results at forward rapidity [35] in terms of a
regeneration production from deconfined charm quarks in the medium.

In this Letter, we present the measurement of the elliptic flow of muons from
heavy-flavour hadron decays at forward rapidity ($2.5<y<4$) in Pb–Pb
collisions at $\sqrt{s_{\rm NN}}$ = 2.76 TeV recorded with the ALICE detector.
The elliptic flow is measured using different methods: scalar product [36],
two- and four-particle $Q$ cumulants [37, 38] and Lee-Yang zeros [39, 40, 41].
These methods exhibit different sensitivities to flow fluctuations and
correlations not related to the azimuthal asymmetry in the initial geometry
(non-flow effects). The $v_{2}$ coefficient is measured as a function of
$p_{\rm T}$ in the interval $3<p_{\rm T}<10$ GeV/$c$ and in three centrality
classes in the range 0–40%. The centrality dependence of $v_{2}$ is presented
in the interval $3<p_{\rm T}<10$ GeV/$c$.

The Letter is organized as follows. The ALICE detector, with an emphasis on
the muon spectrometer, and the data sample are presented in Section 2. The
analysis details, the methods for the $v_{2}$ measurement, the inclusive muon
$v_{2}$ determination, the procedure for the subtraction of the background of
muons from decays of light-flavour hadrons and the study of systematic
uncertainties, are described in Section 3. The $v_{2}$ results for muons from
heavy-flavour decays are presented in Section 4 and compared to model
calculations in Section 5. Finally, conclusions are given in Section 6.

##  2 ALICE experiment and data sample

The ALICE detector is described in detail in [42, 43]. The apparatus is
composed of a set of central barrel detectors (pseudo-rapidity coverage
$|\eta|<0.9$) located inside a solenoid magnet that generates a field of 0.5 T
parallel to the beam direction, a muon spectrometer ($-4<\eta<-2.5$111In the
ALICE reference frame, the muon spectrometer covers a negative $\eta$ range
and consequently a negative $y$ range. In the following, given that the
colliding system is symmetric, the results are presented with a positive $y$
notation.) and a set of detectors for event characterization and triggering
located in the forward and backward $\eta$ regions. The muon spectrometer
consists of a passive front absorber made of carbon, concrete and steel, a
beam shield, a 3 T$\cdot$m dipole magnet, tracking chambers, a muon filter
(iron wall) and trigger chambers. The muon tracking system is composed of five
stations, each including two planes of cathod pad chambers, with the third
station inside the dipole magnet. The muon tracking system is completed by
four trigger planes of resistive plate chambers downstream of the iron wall,
which absorbs hadrons that punch through the front absorber, as well as
secondary particles produced inside it and low momentum muons ($p<4$ GeV/$c$).
Two scintillator arrays (V0) covering the pseudo-rapidity intervals
$-3.7<\eta<-1.7$ and $2.8<\eta<5.1$ are used for triggering, for collision
centrality determination and for beam-induced background rejection. The Zero
Degree Calorimeters (ZDC), located at 114 m from the centre of the detector on
both sides, can detect spectator protons and neutrons and are also used for
the offline rejection of beam-induced background and electromagnetic
interactions. The Silicon Pixel Detector (SPD), that composes the two
innermost layers of the Inner Tracking System (ITS), is used for the
interaction vertex reconstruction. The Time Projection Chamber (TPC), which
measures charged-particle tracks with full azimuthal coverage in $|\eta|<0.9$,
is used in this analysis for the measurement of the reference particles
(Section 3.1).

The results presented in this Letter are obtained from the data sample
recorded with ALICE during the 2011 Pb–Pb run. The data were collected with a
minimum-bias trigger requiring the coincidence of signals in the two V0 arrays
in synchronization with the passage of two crossing bunches. In addition, the
recorded event sample was enriched with central and semi-central Pb–Pb
collisions by applying thresholds, at the trigger level, on the V0 signal
amplitude. The beam-induced background (beam-gas interactions) was reduced by
using the timing information from the V0 and ZDC detectors. Furthermore, a
minimal energy deposit in the ZDC was required to reject the contribution from
electromagnetic Pb–Pb interactions. Only events with a reconstructed primary
vertex within $\pm$ 10 cm from the nominal position of the interaction vertex
along the beam direction are analyzed. The Pb–Pb collisions are classified
according to their degree of centrality by means of the sum of the amplitudes
of the signals in the V0 detector and the centrality classes are defined as
percentiles of the total hadronic Pb–Pb cross section [44]. The analysis is
carried out in three centrality classes: 0–10%, 10–20% and 20–40%. The
analysed data sample corresponds to an integrated luminosity of 11.3
$\mathchoice{\hbox{\normalsize\textmu}}{\hbox{\normalsize\textmu}}{\hbox{\scriptsize\textmu}}{\hbox{\tiny\textmu}}\rm{b}^{-1}$
in the 0–10% centrality class and of 3.5
$\mathchoice{\hbox{\normalsize\textmu}}{\hbox{\normalsize\textmu}}{\hbox{\scriptsize\textmu}}{\hbox{\tiny\textmu}}\rm{b}^{-1}$
in the other two centrality classes.

##  3 Data analysis

The elliptic flow of muons from heavy-flavour hadron decays,
$v_{2}^{\mu\leftarrow{\rm HF}}$, is obtained from the measurement of the
inclusive muon elliptic flow, $v_{2}^{\mu}$, by subtracting the elliptic flow
of muons from primary charged pion and kaon decays
$v_{2}^{\mu\leftarrow\pi,{\rm K}}$ (Sections 3.1 and 3.4), as:

$v_{2}^{\mu\leftarrow{\rm HF}}={v_{2}^{\mu}-f^{\mu\leftarrow\pi,{\rm K}}\cdot
v_{2}^{\mu\leftarrow\pi,{\rm K}}\over{1-f^{\mu\leftarrow\pi,{\rm K}}}},$ (2)

where $f^{\mu\leftarrow\pi,K}$ is the muon background fraction, defined as the
ratio of the yield of muons from primary charged pion and kaon decays to that
of inclusive muons. The measurement of the $v_{2}^{\mu\leftarrow{\rm HF}}$
coefficient is carried out in the interval $3<p_{\rm T}<10$ GeV/$c$ in order
to limit the systematic uncertainty on the subtraction of the muon background
contribution.

###  3.1 Track selection

The selection criteria for particles of interest, muon tracks, are similar to
those used in the previous analyses of pp collisions at $\sqrt{s}$ = 2.76 TeV
and 7 TeV and Pb–Pb collisions at $\sqrt{s_{\rm NN}}$ = 2.76 TeV [21, 45]. The
tracks are required to be within the geometrical acceptance of the muon
spectrometer, with $-4<\eta<-2.5$ and $170^{\circ}<\theta_{\rm
abs}<178^{\circ}$, where $\theta_{\rm abs}$ is the polar angle measured at the
end of the absorber. In order to improve the muon identification, a
reconstructed track in the tracking chambers is required to match a track
segment in the trigger chambers. This leads to a very efficient rejection of
the background produced by charged hadrons, which are absorbed in the iron
wall. Furthermore, a cut on the product $p\cdot DCA$ of the track momentum $p$
and distance of closest approach ($DCA$) to the primary vertex is applied to
remove the beam-induced background tracks and fake tracks coming from the
superposition of several particles crossing the muon spectrometer. This cut is
set to $6\sigma$, where $\sigma$ is extracted from a Gaussian fit to the
$p\cdot DCA$ distribution measured in two intervals of $\theta_{\rm abs}$,
corresponding to different materials in the front absorber. After the cuts are
applied, in the region $p_{\rm T}>3$ GeV/$c$ the residual background to heavy-
flavour decay muons consists of muons from decays of primary charged pions and
kaons222Note that the contribution of muons from secondary light hadron decays
produced inside the front absorber is negligible for $p_{\rm T}>3$ GeV/$c$
[45]. and it amounts to 5–15%, depending on $p_{\rm T}$ and on collision
centrality (Section 3.4).

The mid-rapidity charged-particle tracks used to determine the flow vector
$\vec{Q}_{n}$ or the generating function (Section 3.2) are called in the
following reference particles. They are defined as tracks measured in the TPC
in $|\eta|<0.8$. These are required to have at least 70 associated space
points out of the maximum of 159, a $\chi^{2}$ per degree of freedom (ndf) for
the momentum fit in the range $\chi^{2}/{\rm ndf}<2$ and a transverse momentum
value in the interval $0.2<p_{\rm T}<5$ GeV/$c$. Additionally, tracks are
rejected if their distance of closest approach to the primary vertex is larger
than 3 cm in the plane transverse to the beam direction or in the longitudinal
direction.

###  3.2 Flow analysis methods

The elliptic flow measurement is carried out using various methods that have
different sensitivities to flow fluctuations and non-flow effects [46]. Flow
fluctuations are mainly due to event-by-event fluctuations of the initial
density profile, while non-flow effects correspond to correlations not related
to the azimuthal anisotropy in the initial state, such as resonance decays,
jets and Bose-Einstein correlations between identical particles. It is worth
mentioning that, in the present analysis, most of these non-flow effects are
strongly suppressed by introducing an $\eta$ gap between reference particles
and particles of interest [47]. In this analysis, the scalar product [36],
two- and four-particle $Q$ cumulants [37, 38] and Lee-Yang zeros [39, 40, 41]
methods are employed. The description of these methods will be limited to the
features specific to the present analysis. The following notations are
introduced: $v_{2}^{\mu(\mu\leftarrow{\rm HF})}\\{{\rm SP}\\}$, refers to the
measurement using the scalar product, $v_{2}^{\mu(\mu\leftarrow{\rm
HF})}\\{{\rm 2}\\}$ and $v_{2}^{\mu(\mu\leftarrow{\rm HF})}\\{{\rm 4}\\}$
correspond to the ones using the two-particle $Q$ cumulants and four-particle
$Q$ cumulants, while $v_{2}^{\mu(\mu\leftarrow{\rm HF})}\\{{\rm LYZ-Prod}\\}$
and $v_{2}^{\mu(\mu\leftarrow{\rm HF})}\\{{\rm LYZ-Sum}\\}$ are obtained using
Lee-Yang zeros with product and sum generating functions. The superscripts
$\mu$ and $\mu\leftarrow{\rm HF}$ refer to inclusive muons and muons from
heavy-flavour hadron decays, respectively. It is worth mentioning that these
methods are more accurate than the standard event plane method, which yields a
measurement lying between the event-averaged mean value and the root-mean-
square value in the presence of flow fluctuations [48, 49]. Moreover, the
multi-particle correlation methods (four-particle $Q$ cumulants and Lee-Yang
zeros) are less affected by non-flow correlations than two-particle
correlation methods, but they cannot be used reliably when the muon flow
magnitude is small and when the number of muons is small in the selected
phase-space region e.g. in central and peripheral collisions, respectively
[37, 39]. Under these conditions, the scalar product and two-particle cumulant
methods provide a $v_{2}$ measurement in a wider centrality range.

The scalar product method [36, 48], derived from the standard event plane
technique [48], is based on the measurement of the flow vector $\vec{Q}_{n}$
[36] computed from reference particles. In order to determine the elliptic
flow, the $\vec{Q}_{2}$ vector in a given event is expressed as:

$\vec{Q}_{2}=\Big{(}\sum_{j=1}^{N}{\rm cos}2\varphi_{j},\sum_{j=1}^{N}{\rm
sin}2\varphi_{j}\Big{)},$ (3)

where $\varphi_{j}$ is the particle azimuthal angle and $N$ is the
multiplicity of reference particles.

With this method the $2^{\rm nd}$ harmonic coefficient is given by:

$v_{2}\\{{\rm SP}\\}={\langle\vec{Q}_{2}\cdot\vec{u}_{2,i}(\eta,p_{\rm
T})\rangle\over{2\sqrt{\langle\vec{Q_{2}^{\rm A}}\cdot\vec{Q_{2}^{\rm
B}}\rangle}}},$ (4)

where the brackets in the numerator indicate the average over muons at forward
rapidity, in all events. The vector $Q_{2}$ is calculated from Eq. (3) and the
vector $\vec{u}_{2,i}=({\rm cos}2\varphi_{i},{\rm sin}2\varphi_{i})$ is the
unit vector of the $i^{\rm th}$ muon. In the denominator, each sample of
reference particles used to compute $\vec{Q}_{2}$ is divided into two sub-
samples of same multiplicity in symmetrical $\eta$ intervals, $-0.8<\eta<-0.5$
and $0.5<\eta<0.8$, separated by a $\eta$ gap of one unit of pseudo-rapidity,
labeled with the superscripts $\rm A$ and ${\rm B}$ and the brackets
correspond to the average over events.

The cumulant technique [37, 38] is based on a cumulant expansion of multi-
particle azimuthal correlations. Different order cumulants have different
sensitivities to flow fluctuations. In the present analysis, two- and four-
particle cumulants are used to extract the muon elliptic flow. The results
presented in the following are obtained from a direct calculation of multi-
particle cumulants performed by using the $Q$-cumulant technique [38], which
is based on the moments of the magnitude of the flow vector $\vec{Q_{2}}$. It
is worth mentioning that in this approach the cumulants are not biased by the
interferences between various harmonics. The reference elliptic flow values
$V_{2}$ evaluated from the 2nd order cumulant $c_{2}\\{2\\}$ and $4^{\rm th}$
order cumulant $c_{2}\\{4\\}$ with reference particles are given by
$V_{2}\\{2\\}=\sqrt{c_{2}\\{2\\}}$ and $V_{2}\\{4\\}=\
^{4}\sqrt{-c_{2}\\{4\\}}$, respectively. Once the reference elliptic flow is
estimated, the muon elliptic flow with respect to the reference elliptic flow
is obtained from the 2nd and 4th order cumulants according to:

$v_{2}\\{2\\}=\frac{d_{2}\\{2\\}}{V_{2}\\{2\\}}\ {\rm and}\
v_{2}\\{4\\}=\frac{d_{2}\\{4\\}}{V_{2}\\{4\\}^{3}},$ (5)

where $d_{2}\\{2\\}$ and $d_{2}\\{4\\}$ are the $2^{\rm nd}$ and $4^{\rm th}$
order cumulants of selected muons [38].

The Lee-Yang zeros method [39, 40, 41] relies on correlations involving all
particles in the event. This is the limit of cumulants when the order of
cumulants goes to infinity. The method is based on the location of the zeros
in the complex plane, of a generating function of azimuthal correlations,
which relates the position of the first minimum of the generating function to
the magnitude of the reference elliptic flow $V_{2}$ defined as:

$V_{2}\equiv\bigg{\langle}\sum_{j=1}^{M}{\rm
cos}[2(\varphi_{j}-\Psi_{2})]\bigg{\rangle}_{\rm events},$ (6)

where $M$ is the multiplicity of reference particles and the average is taken
over all events. For this purpose, the following complex-valued generating
function is evaluated as a function of a positive real variable $r$ and few,
typically five, equally spaced reference angles $\vartheta$ ($\rm{LYZ-Prod}$
method):

$G^{\vartheta}(ir)\equiv\bigg{\langle}\prod_{j=1}^{M}(1+ir{\rm
cos}[2(\varphi_{j}-\vartheta)])\bigg{\rangle}_{\rm events}.$ (7)

The first positive minimum of $|G^{\vartheta}(ir)|$, denoted as
$r_{0}^{\vartheta}$, allows one to estimate $V^{\vartheta}_{2}$, which can be
written as $V_{2}^{\vartheta}=j_{01}/r_{0}^{\vartheta}$, where $j_{01}\simeq
2.405$ is the first root of the Bessel function. Once the first minimum
$r^{\vartheta}_{0}$ is determined, the differential muon elliptic flow is
estimated with respect to the reference flow $V_{2}^{\vartheta}$ as detailed
in [41]. Finally, the result is averaged over all $\vartheta$ angles. An
alternative form of the generating function provided with the $\rm{LYZ-Sum}$
method is:

$G^{\vartheta}(ir)\equiv\bigg{\langle}{\rm exp}\bigg{(}ir\sum_{j=1}^{M}{\rm
cos}[2(\varphi_{j}-\vartheta)]\bigg{)}\bigg{\rangle}_{\rm events}.$ (8)

The version of the method involving a product for the construction of the
generation function (Eq. (7)) was designed to disentangle interferences
between different harmonics, which is not the case with the generating
function using a sum of the individual reference particle contributions. Both
generating functions are used in this analysis.

Note that, for all methods, autocorrelation effects are avoided because the
particles (muons) used in the determination of the flow are not included in
the estimation of the reference flow.

###  3.3 Inclusive muon elliptic flow

The elliptic flow of inclusive muons, $v_{2}^{\mu}$, is studied with two-
particle correlation methods (scalar product and two-particle $Q$ cumulants)
in the centrality intervals 0–10%, 10–20% and 20–40%. In the 20–40% centrality
interval, the multi-particle correlation methods (four-particle $Q$ cumulants
and Lee-Yang zeros) are also used.

Several sources of systematic uncertainty affecting the muon elliptic flow
measurement are considered. These take into account the changes due to the
variations of the reference particle selection criteria as in [33, 34, 50], to
allow us to check the robustness of the $v_{2}^{\mu}$ measurement. Since the
collision impact parameter distribution could slightly depend on the
observable used for the centrality determination, a systematic uncertainty is
estimated by repeating the analysis using the number of clusters in the
outermost layer of the SPD and the number of tracks in the TPC as centrality
estimators, instead of the V0 signal amplitude. The systematic uncertainty due
to the effect of TPC tracks from different Pb–Pb collisions piled-up in the
same recorded event is estimated by applying a tighter cut to remove outliers
in the multiplicity distribution of reference particles. This is done by
requiring that the centrality values determined using the V0 signal amplitude
and the number of TPC tracks do not differ by more than 5%. An additional
systematic uncertainty specific to the scalar product is evaluated by varying
the $\eta$ gap between the two sub-events from 1 to 0.8 $\eta$-units (see Eq.
(4) and [36]). The various systematic uncertainties are added in quadrature.
They tend to increase with increasing $p_{\rm T}$ (see Fig. 1). A summary of
the systematic uncertainties, in the interval $3<p_{\rm T}<4.5$ GeV/$c$, is
presented in Table 1.

$v_{2}^{\mu}$ analysis | Source | Systematic uncertainty ($\%$)
---|---|---
0–10% | 10–20% | 20–40%
$v_{2}^{\mu}\\{{\rm SP}\\}$ | Reference particles | 3 | 1 | 3
| Centrality selection | 6 | 1 | 4
| TPC pile-up | 2 | 4 | 2
|  $\eta$ gap | 13 | 1 | 1
$v_{2}^{\mu}\\{2\\}$ | Reference particles | 13 | 3 | 2
| Centrality selection | 14 | 3 | 6
| TPC pile-up | 8 | 1 | 4
$v_{2}^{\mu}\\{4\\}$ | Reference particles |  |  | 10
| Centrality selection |  |  | 1
| TPC pile-up |  |  | 1
$v_{2}^{\mu}\\{{\rm LYZ-Sum}\\}$ | Reference particles |  |  | 4
| Centrality selection |  |  | 7
| TPC pile-up |  |  | 2
$v_{2}^{\mu}\\{{\rm LYZ-Prod}\\}$ | Reference particles |  |  | 2
| Centrality selection |  |  | 8
| TPC pile-up |  |  | 2
Table 1: Systematic uncertainty sources affecting the inclusive muon elliptic
flow measurement in the 0–10%, 10–20% and 20–40% centrality classes for the
interval $3<p_{\rm T}<4.5$ GeV/$c$. They are given as a percentage of the
$v_{2}$ value.

Figure 1: $p_{\rm T}$-differential inclusive muon $v_{2}$ in $2.5<y<4$ and
various centrality intervals, in Pb–Pb collisions at $\sqrt{s_{\rm NN}}$ =
2.76 TeV. The symbols are placed at the centre of the $p_{\rm T}$ interval
and, for visibility, the points from two-particle $Q$ cumulants and Lee-Yang
zeros with product generating function are shifted horizontally. The vertical
error bars represent the statistical uncertainty, the horizontal error bars
correspond to the width of the bin (not shown for the shifted data points) and
the open boxes are the systematic uncertainties. The $p_{\rm T}$ intervals
used with the Lee-Yang zeros method are different with respect to the other
methods. Upper panels: results from two-particle correlation flow methods
(scalar product and two-particle $Q$ cumulants) in the 0–10% (left) and 10–20%
(right) centrality intervals. Lower panels: results in the 20–40% centrality
interval from two-particle correlation flow methods (scalar product and two-
particle $Q$ cumulants) and from four-particle $Q$ cumulants (left), and from
four-particle $Q$ cumulants and Lee-Yang zeros (right).

Figure 1 shows the $p_{\rm T}$-differential muon elliptic flow ($v_{2}^{\mu}$)
in the 0–10%, 10–20% and 20–40% centrality classes as obtained using the
various methods. The values of $v_{2}^{\mu}$ slightly increase from central to
semi-central collisions and this effect is more pronounced in the $p_{\rm T}$
interval $2<p_{\rm T}<4$ GeV/$c$. The two-particle correlation methods (scalar
product and two-particle $Q$ cumulants) give consistent results over the whole
$p_{\rm T}$ range, indicating that these methods have a similar sensitivity to
non-flow effects333Note that, in this analysis, most non-flow correlations are
suppressed, even with two-particle correlation methods since reference
particles and inclusive muons are separated by at least 1.7 $\eta$-units.
However, it is worth mentioning that the main difference between the two
methods is the $\eta$ gap between the two sub-samples used to compute
$\vec{Q}_{2}$ (Eq. (4)) which also allows to partly remove non-flow effects.
and in particular to flow fluctuations. A similar agreement is found when
comparing the multi-particle correlation methods (four-particle $Q$ cumulants
and Lee-Yang zeros) to each other. No significant difference between the
$v_{2}^{\mu}$ results extracted with Lee-Yang zeros using either the sum or
product generating function is seen, hence indicating that interferences
between harmonics are negligible [51]. The four-particle $Q$ cumulants and
Lee-Yang zeros are expected to be less affected by non-flow effects than
scalar product or two-particle $Q$ cumulants [52]. Moreover, since four-
particle $Q$ cumulants give comparable results as Lee-Yang zeros, one can
conclude that non-flow correlations are almost completely removed at the
$4^{\rm th}$ order. Finally, the central values of $v_{2}^{\mu}$ obtained with
four-particle $Q$ cumulants or Lee-Yang zeros are systematically smaller than
with two-particle correlation methods, although compatible within
uncertainties. Such differences may indicate that initial fluctuations play a
role in the development of the final momentum-space anisotropy.

###  3.4 Muon background subtraction

The subtraction of the muon background contribution to the measured
$v_{2}^{\mu}$ requires an estimate of the elliptic flow of muons from charged
pion and kaon decays, $v_{2}^{\mu\leftarrow{\rm\pi,K}}$, and of the background
fraction, $f^{\mu\leftarrow{\rm\pi,K}}$ (see Eq. (2)). The determination of
the $v_{2}^{\mu\leftarrow{\rm\pi,K}}$ coefficient requires two steps. First,
the $p_{\rm T}$\- and $\eta$-differential $v_{2}$ of charged particles
measured in $|\eta|<2.5$ by the ATLAS Collaboration in Pb–Pb collisions [53]
and the $p_{\rm T}$ distributions of charged pions and kaons measured in
$|y|<0.8$ by the ALICE Collaboration in pp and Pb–Pb collisions [54, 55] are
extrapolated to forward rapidity. Then, the $p_{\rm T}$ distributions of muons
from charged pion and kaon decays, needed to estimate
$f^{\mu\leftarrow{\rm\pi,K}}$ and $v_{2}^{\mu\leftarrow{\rm\pi,K}}$, are
generated according to a simulation taking into account the decay kinematics
and the effect of the front absorber.

The $p_{\rm T}$\- and $\eta$-differential elliptic flow of charged particles
in $|\eta|<2.5$, $v_{2}^{\rm ch}$, is extrapolated to forward rapidity using:

$v_{2}^{\rm ch}(p_{\rm T},\eta)=F(\eta)\cdot v_{2}^{\rm ch}(p_{\rm
T},2<|\eta|<2.5),$ (9)

where $v_{2}^{\rm ch}(p_{\rm T},2<|\eta|<2.5)$ is the measured charged-
particle elliptic flow in $2<|\eta|<2.5$ with the event plane method. Since
the $v_{2}^{\rm ch}(p_{\rm T})$ measured by the ATLAS Collaboration is
affected by statistical fluctuations, it is assumed that in the interval
$10<p_{\rm T}<20$ GeV/$c$, needed to simulate the decay muons up to $p_{\rm
T}$ = 10 GeV/$c$, $v_{2}^{\rm ch}$ remains constant with a value given by the
one measured in the interval $10<p_{\rm T}<12$ GeV/$c$. The extrapolation
factor $F(\eta)$ is calculated by parameterizing the $\eta$-differential
$v_{2}^{\rm ch}$ measured by the ATLAS Collaboration in various $p_{\rm T}$
intervals with a second order polynomial. In the interval $7<p_{\rm T}<20$
GeV/$c$, the ATLAS $v_{2}^{\rm ch}$ does not show a dependence on $\eta$ in
$|\eta|<2.5$. Therefore, for $p_{\rm T}>7$ GeV/$c$, $F(\eta)$ is computed as
the average between a flat extrapolation function and the extrapolation factor
obtained with the parabolic parameterization in $4<p_{\rm T}<7$ GeV/$c$.

The mid-rapidity charged pion and kaon $p_{\rm T}$ distributions measured in
Pb–Pb collisions are extrapolated to forward rapidity using the same strategy
as in [21] and summarized in the following. Assuming that the nuclear
modification factor $R_{\rm AA}^{\pi,\rm K}$ of charged pions and kaons in
Pb–Pb collisions does not depend on rapidity up to $y$ = 4 [21, 56], the
$p_{\rm T}$ distributions of charged pions and kaons at forward rapidity can
be expressed as:

$\ \frac{{\rm d}N_{\rm{PbPb}}^{\pi,{\rm K}}}{{\rm d}p_{\rm T}{\rm d}y}=\langle
T_{\rm AA}\rangle\cdot\frac{{\rm d}\sigma_{\rm{pp}}^{\pi,{\rm K}}}{{\rm
d}p_{\rm T}{\rm d}y}\cdot[R_{\rm AA}^{\pi,{\rm K}}(p_{\rm T})]_{y=0},$ (10)

where $\langle T_{\rm AA}\rangle$ is the average nuclear overlap function in
centrality classes under study, estimated as described in [57]. The systematic
uncertainty introduced by the assumption on $R_{\rm AA}^{\pi,\rm K}$ will be
discussed later. The rapidity extrapolation of the mid-rapidity pion and kaon
$p_{\rm T}$-differential cross sections measured in pp collisions [21, 58] is
done according to:

$\frac{{\rm d^{2}}\sigma_{\rm{pp}}^{\pi,{\rm K}}}{{\rm d}p_{\rm T}{\rm
d}y}=\bigg{[}\frac{{\rm d^{2}}\sigma_{\rm{pp}}^{\pi,{\rm K}}}{{\rm d}p_{\rm
T}{\rm d}y}\bigg{]}_{y=0}\cdot{\rm
exp}\Big{(}{-y^{2}\over{2\sigma^{2}_{y}}}\Big{)},$ (11)

$\sigma_{y}$ being estimated from Monte-Carlo event generators (see [21] for
details).

The elliptic flow of muons from charged pion and kaon decays,
$v_{2}^{\mu\leftarrow\pi,{\rm K}}$, in $2.5<y<4$ and in various centrality
classes444The $v_{2}^{\mu\leftarrow\pi,{\rm K}}$ of muons from charged pion
and kaon decays in the 20–40% centrality class is then obtained from the mean
of the charged-particle $v_{2}$ in 20–30% and 30–40% centrality classes, with
an additional systematic uncertainty provided by the difference with respect
to the results in these two centrality classes., is obtained by means of fast
simulations using $v_{2}^{\rm ch}(\eta,p_{\rm T})$ given by Eq. (9) and
charged pion and kaon $p_{\rm T}$ distributions as obtained from Eq.
(10)–(11). The absorber effect is accounted for by rejecting the pions and
kaons that do not decay within a distance corresponding to one interaction
length from the beginning of the absorber. The simulation was repeated twice,
considering that charged particles are either all pions or all kaons. The
estimated $v_{2}^{\mu\leftarrow\pi,{\rm K}}$ decreases with increasing $p_{\rm
T}$ from about 0.085 at $p_{\rm T}$ = 3 GeV/$c$ to 0.035 at $p_{\rm T}$ = 10
GeV/$c$ in the 10% most central collisions. In the 20–40% centrality interval,
the $v_{2}^{\mu\leftarrow\pi,{\rm K}}$ values vary between 0.19 ($p_{\rm T}$ =
3 GeV/$c$) and 0.08 ($p_{\rm T}$ = 10 GeV/$c$)

The background fraction, $f^{\mu\leftarrow{\rm\pi,K}}$, is calculated as the
ratio of the $p_{\rm T}$-differential yield of muons from charged pion and
kaon decays in $2.5<y<4$ obtained in the simulation to the measured $p_{\rm
T}$-differential yield of inclusive muons. It decreases as $p_{\rm T}$
increases, from about 12% (15%) at $p_{\rm T}$ = 3 GeV/$c$ to 5% (7%) at
$p_{\rm T}$ = 10 GeV/$c$ in the 0–10% (20–40%) centrality class.

The systematic uncertainties affecting the estimated
$v_{2}^{\mu\leftarrow\pi,{\rm K}}$ are summarized in Table 2. They originate
from i) the method used to measure the charged-particle $v_{2}^{\rm ch}$ in
ATLAS, ii) the $\eta$ and $p_{\rm T}$ extrapolation of $v_{2}^{\rm ch}$ and
iii) the treatment of the charged-particle $v_{2}^{\rm ch}$ in the fast
simulation procedure. As the event plane method was used for the $v_{2}^{\rm
ch}$ measurement in ATLAS, the results range between the mean ($\langle
v_{2}^{\rm ch}\rangle$) and R.M.S. ($\sqrt{\langle(v_{2}^{\rm
ch})^{2}\rangle}$) of the true $v_{2}^{\rm ch}$ values due to fluctuations,
depending on the event plane resolution which varies with the collision
centrality [49]. According to a Monte-Carlo Glauber model [49], the ratio
$\sqrt{\langle v_{2}^{2}\rangle}/\langle v_{2}\rangle$ is expected to vary
from about 1.06 to 1.15. Consequently, a conservative systematic uncertainty
of 15% is applied to account for this bias and is propagated to
$v_{2}^{\mu\leftarrow{\rm\pi,K}}$. The systematic uncertainty due to the
$\eta$ extrapolation of $v_{2}^{\rm ch}$ is evaluated using several fit
functions (first and third order polynomials, and Gaussian function) in the
region $p_{\rm T}<7$ GeV/$c$, and for larger $p_{\rm T}$ values an additional
systematic uncertainty due to the extrapolation procedure is considered. The
latter is determined by comparing the results obtained with the two
extrapolation functions used in the interval $p_{\rm T}>7$ GeV/$c$. The
systematic uncertainty due to the assumption on $v_{2}^{\rm ch}$ in the region
$p_{\rm T}>10$ GeV/$c$ is estimated by varying $v_{2}^{\rm ch}$ between 0 and
the value in $10<p_{\rm T}<12$ GeV/$c$ in the fast simulations. Such
uncertainty affects mainly the high $p_{\rm T}$ region ($p_{\rm T}>7$
GeV/$c$). Finally, the systematic uncertainty obtained by treating charged
particles separately as pions and kaons is found to be negligible. The various
systematic uncertainty sources are propagated to the estimated
$v_{2}^{\mu\leftarrow{\rm\pi,K}}$ and added in quadrature.

Source | Systematic uncertainty (%)
---|---
Input $v_{2}^{\rm ch}$ bias | 9
$v_{2}^{\rm ch}$ $\eta$ extrapolation | 9–12
$v_{2}^{\rm ch}$ high $p_{\rm T}$ extrapolation | 13–15
$\pi$ and $\rm K$ in fast simulations |  $<$ 1
Table 2: Systematic uncertainty sources affecting the estimated
$v_{2}^{\mu\leftarrow{\rm\pi,K}}$ for the interval $3<p_{\rm T}<10$ GeV/$c$.
They are stated as a percentage of the $v_{2}$ value. The given range reflects
the dependence on the collision centrality.

The systematic uncertainty on $f^{\mu\leftarrow{\rm\pi,K}}$, detailed in [21],
includes the uncertainty on the generated $p_{\rm T}$ distributions of muons
from charged pion and kaon decays, and the uncertainty on the measured
inclusive muon $p_{\rm T}$ distributions. The former originates from the input
charged pion and kaon distributions, the rapidity extrapolation and the
absorber effect. The systematic uncertainty on the measured inclusive muon
yields contains the systematic uncertainty on detector response, residual mis-
alignment and centrality dependence of the efficiency. This gives a total
systematic uncertainty on $f^{\mu\leftarrow{\rm\pi,K}}$ of about 21% in the
interval $3<p_{\rm T}<4.5$ GeV/$c$ with almost no dependence on the collision
centrality. Finally, as done for the measurement of the heavy-flavour decay
muon $R_{\rm AA}$ [21], the systematic uncertainty due to the unknown
suppression of charged particles at forward rapidity is calculated by varying
$f^{\mu\leftarrow{\rm\pi,K}}$ from 0 to two times the estimated value. This
corresponds to a variation of $R_{\rm AA}^{\pi,{\rm K}}(p_{\rm T})$ at forward
rapidity from 0 up to two times $[R_{\rm AA}^{\pi,{\rm K}}(p_{\rm T})]_{y=0}$.
This systematic uncertainty amounts to 10–30% in the interval $3<p_{\rm
T}<4.5$ GeV/$c$, depending on the collision centrality and the flow analysis
method.

Finally, the systematic uncertainty on the elliptic flow of muons from heavy-
flavour decays, $v_{2}^{\mu\leftarrow{\rm HF}}$, contains two contributions:
the systematic uncertainties on $v_{2}^{\mu}$,
$v_{2}^{\mu\leftarrow{\rm\pi,K}}$ and $f^{\mu\leftarrow{\rm\pi,K}}$ propagated
according to the definition of $v_{2}^{\mu\leftarrow HF}$ given in Eq. (2),
and the systematic uncertainty due to the unknown suppression of charged
particles at forward rapidity. The final systematic uncertainty on
$v_{2}^{\mu\leftarrow{\rm HF}}$ is obtained by adding in quadrature the two
contributions. It amounts to about 12%–36% in the interval $3<p_{\rm T}<4.5$
GeV/$c$, depending on the collision centrality and the flow analysis method.

##  4 Results

Figure 2 presents the $p_{\rm T}$-differential elliptic flow of muons from
heavy-flavour hadron decays, $v_{2}^{\mu\leftarrow{\rm HF}}$, calculated with
Eq. (2). The results are shown for the 0–10% (upper, left), 10–20% (upper,
right) and 20–40% (bottom) centrality classes using the same flow methods as
for the measurement of the inclusive muon elliptic flow (Fig. 1).

Figure 2:  $p_{\rm T}$-differential elliptic flow of muons from heavy-flavour
decays, $v_{2}^{\mu\leftarrow{\rm HF}}$, in $2.5<y<4$ and various centrality
intervals, in Pb–Pb collisions at $\sqrt{s_{\rm NN}}$ = 2.76 TeV. The symbols
are placed at the centre of the $p_{\rm T}$ interval and, for visibility, the
points from two-particle $Q$ cumulants and Lee-Yang zeros with product
generating function are shifted horizontally. The meaning of the symbols is
the same as in Fig. 1. The horizontal error bars are not plotted for shifted
data points. The $p_{\rm T}$ intervals used with the Lee-Yang zeros method are
different with respect to the other methods. Upper panels: results from two-
particle correlation flow methods (scalar product and two-particle $Q$
cumulants) in the 0–10% (left) and 10–20% (right) centrality intervals. Lower
panels: results in the 20–40% centrality interval from two-particle
correlation flow methods (scalar product and two-particle $Q$ cumulants) and
from four-particle $Q$ cumulants (left), and from four-particle $Q$ cumulants
and Lee-Yang zeros (right). See the text for details.

When comparing the results to those obtained for inclusive muons (Fig. 1), one
can notice that $v_{2}^{\mu\leftarrow{\rm HF}}$ and $v_{2}^{\mu}$ are similar
due to the small background fraction (5% to 15%) in the $p_{\rm T}$ interval
3–10 GeV/$c$. The differences between the various methods are similar to those
discussed for the measurement of the inclusive muon $v_{2}^{\mu}$ i.e. i)
scalar product and two-particle $Q$ cumulants give compatible results, ii)
consistent results are also found with four-particle $Q$ cumulants and Lee-
Yang zeros, and iii) the $v_{2}^{\mu\leftarrow{\rm HF}}$ values extracted from
these multi-particle correlation methods are smaller, although still
compatible within uncertainties, than the ones obtained with two-particle
correlation methods. As mentioned in Section 3.3, such differences are
expected if initial-state fluctuations play a role in the development of the
final momentum-space anisotropy.

A positive $v_{2}^{\mu\leftarrow{\rm HF}}$ is observed at intermediate $p_{\rm
T}$ for the 20–40% and 10–20% centrality classes with a significance larger
than $3\sigma$ when combining statistical and systematic uncertainties. In the
20–40% centrality class, the values of the significance in the interval
$3<p_{\rm T}<4$ GeV/$c$ ($4<p_{\rm T}<5.5$ GeV/$c$) are 4 $\sigma$ ( 3.2
$\sigma$) and 4.3 $\sigma$ (3.8 $\sigma$) with scalar product and two-particle
$Q$ cumulants, respectively. In the 10–20% centrality class and in the
interval $3<p_{\rm T}<4.5$ GeV/$c$, the values of the significance correspond
to 4.4$\sigma$ both with scalar product and two-particle $Q$ cumulants. This
behaviour results from the interplay between the significant interaction of
heavy quarks with the expanding medium and the path-length dependence of in-
medium parton energy loss [29, 30]. The $v_{2}^{\mu\leftarrow{\rm HF}}$ of
muons from heavy-flavour hadron decays decreases with increasing $p_{\rm T}$
and becomes compatible with zero in the high $p_{\rm T}$ region.

Figure 3 shows the centrality dependence of the $p_{\rm T}$-integrated
($3<p_{\rm T}<10$ GeV/$c$) elliptic flow of muons from heavy-flavour hadron
decays. It is investigated with scalar product and two-particle $Q$ cumulants,
which can be applied in a wider event-multiplicity (i.e. centrality) interval
compared to multi-particle correlation methods. A significant decrease of the
$v_{2}$ magnitude towards central collisions is observed. This is expected
from the decrease of the initial spatial anisotropy from semi-central to
central collisions.

Figure 3: Elliptic flow of muons from heavy-flavour hadron decays as a
function of the collision centrality in $2.5<y<4$ and $3<p_{\rm T}<10$
GeV/$c$, in Pb–Pb collisions at $\sqrt{s_{\rm NN}}$ = 2.76 TeV. The results
are obtained with scalar product and two-particle $Q$ cumulants. Vertical bars
(open boxes) represent the statistical (systematic) uncertainty, the
horizontal error bars correspond to the width of the centrality bin. For
visibility, the points from scalar product are shifted horizontally and the
horizontal error bars are not plotted

.

ALICE has measured the elliptic flow of prompt D mesons in $|y|<0.8$ in three
centrality classes in the interval 0–50% with various two-particle correlation
methods [33, 34]. Similar trends as those reported here for muons from heavy-
flavour decays are observed, although in different $p_{\rm T}$ and rapidity
intervals. In particular, a positive $v_{2}$ was observed for D mesons in
semi-central collisions in 2 $<$ $p_{\rm T}$ $<$ 6 GeV/$c$.

The positive elliptic flow of muons from heavy-flavour hadron decays has been
observed in a $p_{\rm T}$ interval from 3 to about 5 GeV/$c$ where the charm
contribution is expected to be dominant with respect to the beauty component
according to perturbative QCD calculations [21]. This measurement supports the
interpretation of the ${\rm J}/\psi$ positive $v_{2}$ at forward rapidity [35]
in terms of a significant contribution to $\rm J/\psi$ production from
recombination of flowing charm quarks in the deconfined medium.

##  5 Comparison with models

The results presented in this publication may constrain models describing the
interactions of heavy quarks with the medium via elastic (collisional) and
inelastic (radiative) processes, and in particular the parton energy loss
dependence on the path-length within the medium.

The elliptic flow coefficient and the nuclear modification factor of muons
from heavy-flavour hadron decays [21] are compared to the following three
models. The MC@sHQ + EPOS transport model [59] treats the propagation of heavy
quarks in the medium including collisional and radiative energy loss, within a
3 + 1 dimensional fluid dynamical expansion based on the EPOS model [60, 61].
The hadronization of heavy quarks takes place at the transition temperature
via recombination at low $p_{\rm T}$ and fragmentation at intermediate and
high $p_{\rm T}$. The final-state hadronic interactions are not included in
the model. TAMU [62] is a transport model including only collisional processes
via the Langevin equation. The hydrodynamical expansion is constrained by
$p_{\rm T}$ spectra and elliptic flow data of light-flavour hadrons. The
hadronization is modeled including a component of recombination of heavy
quarks with light-flavour hadrons in the QGP. The diffusion of heavy-flavour
mesons in the hadronic phase is also included. BAMPS [63, 64, 65] is a
partonic transport model based on the Boltzmann approach to multi-parton
scatterings. It includes collisional processes with a running strong coupling
constant. The lack of radiative contributions is accounted for by scaling the
binary cross section with a correction factor, tuned to describe the nuclear
modification factor and elliptic flow results at RHIC energies. Vacuum
fragmentation functions are used for the hadronization.

Figure 4 (left) shows that the $p_{\rm T}$-differential elliptic flow of muons
from heavy-flavour hadron decays in the 20–40% centrality class is described
reasonably well by the three models. However, the BAMPS model tends to
slightly underestimate the $R_{\rm AA}$ of muons from heavy-flavour decays in
the 10% most central collisions, while the MC@sHQ$+$EPOS model tends to
overestimate it. The TAMU model describes the $R_{\rm AA}$ measurement over
the entire $p_{\rm T}$ interval within uncertainties and tends to slightly
underestimates the $v_{2}^{\mu\leftarrow{\rm HF}}$ measurement in the low
$p_{\rm T}$ region. This indicates that it is challenging to simultaneously
describe the strong suppression of high-$p_{\rm T}$ muons from heavy-flavour
hadron decays in central collisions and the azimuthal anisotropy in semi-
central collisions. Similar trends are also observed in the mid-rapidity
region from the comparison of the $R_{\rm AA}$ and $v_{2}$ of D mesons with
model calculations [34].

Figure 4: Left: $p_{\rm T}$-differential elliptic flow of muons from heavy-
flavour hadron decays in $2.5<y<4$, in Pb–Pb collisions at $\sqrt{s_{\rm NN}}$
= 2.76 TeV for the centrality class 20–40% compared to various transport model
predictions: MC@sHQ + EPOS [59, 60, 61], TAMU [62] and BAMPS [63, 64, 65]. The
TAMU model is shown with a theoretical uncertainty band. Right: $p_{\rm
T}$-differential $R_{\rm AA}$ of muons from heavy-flavour hadron decays for
the centrality class 0–10% from [21] compared to the same models as for
$v_{2}^{\mu\leftarrow{\rm HF}}$.

##  6 Conclusions

In summary, we have reported on a measurement of the elliptic flow of muons
from heavy-flavour hadron decays at forward rapidity in central and semi-
central Pb–Pb collisions at $\sqrt{s_{\rm NN}}$ = 2.76 TeV with the ALICE
detector at the LHC.

Measurements have been carried out using several methods which exhibit
different sensitivity to initial-state fluctuations and non-flow correlations.
The systematic comparison of scalar product, two- and four-particle $Q$
cumulants and Lee-Yang zeros helps in understanding the processes that build
up the observed differences between two-particle correlation methods and
multi-particle correlation methods and suggests that flow fluctuations are
significant.

The magnitude of the elliptic flow of muons from heavy-flavour hadron decays
increases from central to semi-central collisions and decreases with
increasing $p_{\rm T}$, becoming compatible with zero at high $p_{\rm T}$ The
results indicate a positive elliptic flow with the scalar product and two-
particle $Q$ cumulants in semi-central collisions (10–20% and 20–40%
centrality classes) for the $p_{\rm T}$ interval from 3 to about 5 GeV/$c$
with a significance larger than $3\sigma$ The data are described by transport
model calculations within uncertainties, although a simultaneous description
of $R_{\rm AA}$ and $v_{2}$ remains a challenge. The results reported in this
Letter in various centrality classes may provide further important constraints
to the models.

## Acknowledgements

The ALICE Collaboration would like to thank all its engineers and technicians
for their invaluable contributions to the construction of the experiment and
the CERN accelerator teams for the outstanding performance of the LHC complex.
The ALICE Collaboration gratefully acknowledges the resources and support
provided by all Grid centres and the Worldwide LHC Computing Grid (WLCG)
collaboration. The ALICE Collaboration acknowledges the following funding
agencies for their support in building and running the ALICE detector: State
Committee of Science, World Federation of Scientists (WFS) and Swiss Fonds
Kidagan, Armenia, Conselho Nacional de Desenvolvimento Científico e
Tecnológico (CNPq), Financiadora de Estudos e Projetos (FINEP), Fundação de
Amparo à Pesquisa do Estado de São Paulo (FAPESP); National Natural Science
Foundation of China (NSFC), the Chinese Ministry of Education (CMOE) and the
Ministry of Science and Technology of China (MSTC); Ministry of Education and
Youth of the Czech Republic; Danish Natural Science Research Council, the
Carlsberg Foundation and the Danish National Research Foundation; The European
Research Council under the European Community’s Seventh Framework Programme;
Helsinki Institute of Physics and the Academy of Finland; French CNRS-IN2P3,
the ‘Region Pays de Loire’, ‘Region Alsace’, ‘Region Auvergne’ and CEA,
France; German Bundesministerium fur Bildung, Wissenschaft, Forschung und
Technologie (BMBF) and the Helmholtz Association; General Secretariat for
Research and Technology, Ministry of Development, Greece; Hungarian Orszagos
Tudomanyos Kutatasi Alappgrammok (OTKA) and National Office for Research and
Technology (NKTH); Department of Atomic Energy and Department of Science and
Technology of the Government of India; Istituto Nazionale di Fisica Nucleare
(INFN) and Centro Fermi - Museo Storico della Fisica e Centro Studi e Ricerche
”Enrico Fermi”, Italy; MEXT Grant-in-Aid for Specially Promoted Research,
Japan; Joint Institute for Nuclear Research, Dubna; National Research
Foundation of Korea (NRF); Consejo Nacional de Cienca y Tecnologia (CONACYT),
Direccion General de Asuntos del Personal Academico(DGAPA), México, :Amerique
Latine Formation academique â€“ European Commission(ALFA-EC) and the EPLANET
Program (European Particle Physics Latin American Network) Stichting voor
Fundamenteel Onderzoek der Materie (FOM) and the Nederlandse Organisatie voor
Wetenschappelijk Onderzoek (NWO), Netherlands; Research Council of Norway
(NFR); National Science Centre, Poland; Ministry of National
Education/Institute for Atomic Physics and Consiliul NaÅ£ional al CercetÄfrii
ÅžtiinÅ£ifice - Executive Agency for Higher Education Research Development and
Innovation Funding (CNCS-UEFISCDI) - Romania; Ministry of Education and
Science of Russian Federation, Russian Academy of Sciences, Russian Federal
Agency of Atomic Energy, Russian Federal Agency for Science and Innovations
and The Russian Foundation for Basic Research; Ministry of Education of
Slovakia; Department of Science and Technology, South Africa; Centro de
Investigaciones Energeticas, Medioambientales y Tecnologicas (CIEMAT),
E-Infrastructure shared between Europe and Latin America (EELA), Ministerio de
Economía y Competitividad (MINECO) of Spain, Xunta de Galicia (Consellería de
Educación), Centro de Aplicaciones TecnolÃ³gicas y Desarrollo Nuclear
(CEADEN), Cubaenergía, Cuba, and IAEA (International Atomic Energy Agency);
Swedish Research Council (VR) and Knut $\&$ Alice Wallenberg Foundation (KAW);
Ukraine Ministry of Education and Science; United Kingdom Science and
Technology Facilities Council (STFC); The United States Department of Energy,
the United States National Science Foundation, the State of Texas, and the
State of Ohio; Ministry of Science, Education and Sports of Croatia and Unity
through Knowledge Fund, Croatia. Council of Scientific and Industrial Research
(CSIR), New Delhi, India

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##  Appendix A The ALICE Collaboration

J. Adamorg40&D. Adamováorg83&M.M. Aggarwalorg87&G. Aglieri Rinellaorg36&M.
Agnelloorg110&N. Agrawalorg48&Z. Ahammedorg131&S.U. Ahnorg68&S. Aiolaorg135&A.
Akindinovorg58&S.N. Alamorg131&D. Aleksandrovorg99&B. Alessandroorg110&D.
Alexandreorg101&R. Alfaro Molinaorg64&A. Aliciorg104,org12&A. Alkinorg3&J.R.M.
Almarazorg118&J. Almeorg38&T. Altorg43&S. Altinpinarorg18&I.
Altsybeevorg130&C. Alves Garcia Pradoorg119&C. Andreiorg78&A. Andronicorg96&V.
Anguelovorg93&J. Anielskiorg54&T. Antičićorg97&F. Antinoriorg107&P.
Antonioliorg104&L. Aphecetcheorg112&H. Appelshäuserorg53&S. Arcelliorg28&N.
Armestoorg17&R. Arnaldiorg110&I.C. Arseneorg22&M. Arslandokorg53&B.
Audurierorg112&A. Augustinusorg36&R. Averbeckorg96&M.D. Azmiorg19&M.
Bachorg43&A. Badalàorg106&Y.W. Baekorg44&S. Bagnascoorg110&R.
Bailhacheorg53&R. Balaorg90&A. Baldisseriorg15&F. Baltasar Dos Santos
Pedrosaorg36&R.C. Baralorg61&A.M. Barbanoorg110&R. Barberaorg29&F.
Barileorg33&G.G. Barnaföldiorg134&L.S. Barnbyorg101&V. Barretorg70&P.
Bartaliniorg7&K. Barthorg36&J. Bartkeorg116&E. Bartschorg53&M. Basileorg28&N.
Bastidorg70&S. Basuorg131&B. Bathenorg54&G. Batigneorg112&A. Batista
Camejoorg70&B. Batyunyaorg66&P.C. Batzingorg22&I.G. Beardenorg80&H.
Beckorg53&C. Beddaorg110&N.K. Beheraorg49,org48&I. Belikovorg55&F.
Belliniorg28&H. Bello Martinezorg2&R. Bellwiedorg121&R. Belmontorg133&E.
Belmont-Morenoorg64&V. Belyaevorg76&G. Bencediorg134&S. Beoleorg27&I.
Berceanuorg78&A. Bercuciorg78&Y. Berdnikovorg85&D. Berenyiorg134&R.A.
Bertensorg57&D. Berzanoorg27,org36&L. Betevorg36&A. Bhasinorg90&I.R.
Bhatorg90&A.K. Bhatiorg87&B. Bhattacharjeeorg45&J. Bhomorg127&L.
Bianchiorg121&N. Bianchiorg72&C. Bianchinorg133,org57&J. Bielčíkorg40&J.
Bielčíkováorg83&A. Bilandzicorg80&R. Biswasorg4&S. Biswasorg79&S.
Bjelogrlicorg57&J.T. Blairorg117&F. Blancoorg10&D. Blauorg99&C. Blumeorg53&F.
Bockorg93,org74&A. Bogdanovorg76&H. Bøggildorg80&L. Boldizsárorg134&M.
Bombaraorg41&J. Bookorg53&H. Borelorg15&A. Borissovorg95&M. Borriorg82&F.
Bossúorg65&E. Bottaorg27&S. Böttgerorg52&P. Braun-Munzingerorg96&M.
Bregantorg119&T. Breitnerorg52&T.A. Brokerorg53&T.A. Browningorg94&M.
Brozorg40&E.J. Bruckenorg46&E. Brunaorg110&G.E. Brunoorg33&D. Budnikovorg98&H.
Bueschingorg53&S. Bufalinoorg27,org36&P. Buncicorg36&O. Buschorg127,org93&Z.
Butheleziorg65&J.B. Buttorg16&J.T. Buxtonorg20&D. Caffarriorg36&X. Caiorg7&H.
Cainesorg135&L. Calero Diazorg72&A. Calivaorg57&E. Calvo Villarorg102&P.
Cameriniorg26&F. Carenaorg36&W. Carenaorg36&F. Carnesecchiorg28&J. Castillo
Castellanosorg15&A.J. Castroorg124&E.A.R. Casulaorg25&C. Cavicchioliorg36&C.
Ceballos Sanchezorg9&J. Cepilaorg40&P. Cerelloorg110&J. Cerkalaorg114&B.
Changorg122&S. Chapelandorg36&M. Chartierorg123&J.L. Charvetorg15&S.
Chattopadhyayorg131&S. Chattopadhyayorg100&V. Chelnokovorg3&M. Cherneyorg86&C.
Cheshkovorg129&B. Cheynisorg129&V. Chibante Barrosoorg36&D.D.
Chinellatoorg120&P. Chochulaorg36&K. Choiorg95&M. Chojnackiorg80&S.
Choudhuryorg131&P. Christakoglouorg81&C.H. Christensenorg80&P.
Christiansenorg34&T. Chujoorg127&S.U. Chungorg95&Z. Chunhuiorg57&C.
Cicaloorg105&L. Cifarelliorg12,org28&F. Cindoloorg104&J. Cleymansorg89&F.
Colamariaorg33&D. Colellaorg36,org33,org59&A. Colluorg25&M. Colocciorg28&G.
Conesa Balbastreorg71&Z. Conesa del Valleorg51&M.E. Connorsorg135&J.G.
Contrerasorg11,org40&T.M. Cormierorg84&Y. Corrales Moralesorg27&I. Cortés
Maldonadoorg2&P. Corteseorg32&M.R. Cosentinoorg119&F. Costaorg36&P.
Crochetorg70&R. Cruz Albinoorg11&E. Cuautleorg63&L. Cunqueiroorg36&T.
Dahmsorg92,org37&A. Daineseorg107&A. Danuorg62&D. Dasorg100&I.
Dasorg100,org51&S. Dasorg4&A. Dashorg120&S. Dashorg48&S. Deorg119&A. De
Caroorg31,org12&G. de Cataldoorg103&J. de Cuvelandorg43&A. De Falcoorg25&D. De
Gruttolaorg12,org31&N. De Marcoorg110&S. De Pasqualeorg31&A.
Deistingorg96,org93&A. Delofforg77&E. Dénesorg1340&G. D’Erasmoorg33&D. Di
Bariorg33&A. Di Mauroorg36&P. Di Nezzaorg72&M.A. Diaz Corcheroorg10&T.
Dietelorg89&P. Dillensegerorg53&R. Diviàorg36&Ø. Djuvslandorg18&A.
Dobrinorg57,org81&T. Dobrowolskiorg770&D. Domenicis Gimenezorg119&B.
Dönigusorg53&O. Dordicorg22&T. Drozhzhovaorg53&A.K. Dubeyorg131&A.
Dublaorg57&L. Ducrouxorg129&P. Dupieuxorg70&R.J. Ehlersorg135&D. Eliaorg103&H.
Engelorg52&E. Eppleorg135&B. Erazmusorg112,org36&I. Erdemirorg53&F.
Erhardtorg128&B. Espagnonorg51&M. Estienneorg112&S. Esumiorg127&J. Eumorg95&D.
Evansorg101&S. Evdokimovorg111&G. Eyyubovaorg40&L. Fabbiettiorg37,org92&D.
Fabrisorg107&J. Faivreorg71&A. Fantoniorg72&M. Faselorg74&L. Feldkamporg54&D.
Feleaorg62&A. Felicielloorg110&G. Feofilovorg130&J. Ferenceiorg83&A. Fernández
Téllezorg2&E.G. Ferreiroorg17&A. Ferrettiorg27&A. Festantiorg30&V.J.G.
Feuillardorg15,org70&J. Figielorg116&M.A.S. Figueredoorg123,org119&S.
Filchaginorg98&D. Finogeevorg56&F.M. Fiondaorg25&E.M. Fioreorg33&M.G.
Fleckorg93&M. Florisorg36&S. Foertschorg65&P. Fokaorg96&S. Fokinorg99&E.
Fragiacomoorg109&A. Francesconorg36,org30&U. Frankenfeldorg96&U. Fuchsorg36&C.
Furgetorg71&A. Fursorg56&M. Fusco Girardorg31&J.J. Gaardhøjeorg80&M.
Gagliardiorg27&A.M. Gagoorg102&M. Gallioorg27&D.R. Gangadharanorg74&P.
Ganotiorg88&C. Gaoorg7&C. Garabatosorg96&E. Garcia-Solisorg13&C.
Gargiuloorg36&P. Gasikorg92,org37&M. Germainorg112&A. Gheataorg36&M.
Gheataorg62,org36&P. Ghoshorg131&S.K. Ghoshorg4&P. Gianottiorg72&P.
Giubellinoorg36&P. Giubilatoorg30&E. Gladysz-Dziadusorg116&P.
Glässelorg93&D.M. Goméz Coralorg64&A. Gomez Ramirezorg52&P. González-
Zamoraorg10&S. Gorbunovorg43&L. Görlichorg116&S. Gotovacorg115&V.
Grabskiorg64&L.K. Graczykowskiorg132&K.L. Grahamorg101&A. Grelliorg57&A.
Grigorasorg36&C. Grigorasorg36&V. Grigorievorg76&A. Grigoryanorg1&S.
Grigoryanorg66&B. Grinyovorg3&N. Grionorg109&J.F. Grosse-
Oetringhausorg36&J.-Y. Grossiordorg129&R. Grossoorg36&F. Guberorg56&R.
Guernaneorg71&B. Guerzoniorg28&K. Gulbrandsenorg80&H. Gulkanyanorg1&T.
Gunjiorg126&A. Guptaorg90&R. Guptaorg90&R. Haakeorg54&Ø. Haalandorg18&C.
Hadjidakisorg51&M. Haiducorg62&H. Hamagakiorg126&G. Hamarorg134&J.W.
Harrisorg135&A. Hartonorg13&D. Hatzifotiadouorg104&S. Hayashiorg126&S.T.
Heckelorg53&M. Heideorg54&H. Helstruporg38&A. Herghelegiuorg78&G. Herrera
Corralorg11&B.A. Hessorg35&K.F. Hetlandorg38&T.E. Hildenorg46&H.
Hillemannsorg36&B. Hippolyteorg55&R. Hosokawaorg127&P. Hristovorg36&M.
Huangorg18&T.J. Humanicorg20&N. Hussainorg45&T. Hussainorg19&D.
Hutterorg43&D.S. Hwangorg21&R. Ilkaevorg98&I. Ilkivorg77&M. Inabaorg127&M.
Ippolitovorg76,org99&M. Irfanorg19&M. Ivanovorg96&V. Ivanovorg85&V.
Izucheevorg111&P.M. Jacobsorg74&S. Jadlovskaorg114&C. Jahnkeorg119&H.J.
Jangorg68&M.A. Janikorg132&P.H.S.Y. Jayarathnaorg121&C. Jenaorg30&S.
Jenaorg121&R.T. Jimenez Bustamanteorg96&P.G. Jonesorg101&H. Jungorg44&A.
Juskoorg101&P. Kalinakorg59&A. Kalweitorg36&J. Kaminorg53&J.H. Kangorg136&V.
Kaplinorg76&S. Karorg131&A. Karasu Uysalorg69&O. Karavichevorg56&T.
Karavichevaorg56&L. Karayanorg93,org96&E. Karpechevorg56&U. Kebschullorg52&R.
Keidelorg137&D.L.D. Keijdenerorg57&M. Keilorg36&M. Mohisin Khanorg19&P.
Khanorg100&S.A. Khanorg131&A. Khanzadeevorg85&Y. Kharlovorg111&B.
Kilengorg38&B. Kimorg136&D.W. Kimorg44&D.J. Kimorg122&H. Kimorg136&J.S.
Kimorg44&M. Kimorg44&M. Kimorg136&S. Kimorg21&T. Kimorg136&S. Kirschorg43&I.
Kiselorg43&S. Kiselevorg58&A. Kisielorg132&G. Kissorg134&J.L. Klayorg6&C.
Kleinorg53&J. Kleinorg93,org36&C. Klein-Bösingorg54&A. Klugeorg36&M.L.
Knichelorg93&A.G. Knospeorg117&T. Kobayashiorg127&C. Kobdajorg113&M.
Kofaragoorg36&T. Kolleggerorg43,org96&A. Kolojvariorg130&V.
Kondratievorg130&N. Kondratyevaorg76&E. Kondratyukorg111&A. Konevskikhorg56&M.
Kopcikorg114&M. Kourorg90&C. Kouzinopoulosorg36&O. Kovalenkoorg77&V.
Kovalenkoorg130&M. Kowalskiorg116&G. Koyithatta Meethaleveeduorg48&J.
Kralorg122&I. Králikorg59&A. Kravčákováorg41&M. Kretzorg43&M.
Krivdaorg59,org101&F. Krizekorg83&E. Kryshenorg36&M. Krzewickiorg43&A.M.
Kuberaorg20&V. Kučeraorg83&T. Kugathasanorg36&C. Kuhnorg55&P.G. Kuijerorg81&A.
Kumarorg90&J. Kumarorg48&L. Kumarorg79,org87&P. Kurashviliorg77&A.
Kurepinorg56&A.B. Kurepinorg56&A. Kuryakinorg98&S. Kushpilorg83&M.J.
Kweonorg50&Y. Kwonorg136&S.L. La Pointeorg110&P. La Roccaorg29&C. Lagana
Fernandesorg119&I. Lakomovorg36&R. Langoyorg42&C. Laraorg52&A. Lardeuxorg15&A.
Lattucaorg27&E. Laudiorg36&R. Leaorg26&L. Leardiniorg93&G.R. Leeorg101&S.
Leeorg136&I. Legrandorg36&F. Lehasorg81&R.C. Lemmonorg82&V. Lentiorg103&E.
Leograndeorg57&I. León Monzónorg118&M. Leoncinoorg27&P. Lévaiorg134&S.
Liorg7,org70&X. Liorg14&J. Lienorg42&R. Lietavaorg101&S. Lindalorg22&V.
Lindenstruthorg43&C. Lippmannorg96&M.A. Lisaorg20&H.M. Ljunggrenorg34&D.F.
Lodatoorg57&P.I. Loenneorg18&V. Loginovorg76&C. Loizidesorg74&X. Lopezorg70&E.
López Torresorg9&A. Loweorg134&P. Luettigorg53&M. Lunardonorg30&G.
Luparelloorg26&P.H.F.N.D. Luzorg119&A. Maevskayaorg56&M. Magerorg36&S.
Mahajanorg90&S.M. Mahmoodorg22&A. Maireorg55&R.D. Majkaorg135&M.
Malaevorg85&I. Maldonado Cervantesorg63&L. Malininaidp3777184,org66&D.
Mal’Kevichorg58&P. Malzacherorg96&A. Mamonovorg98&V. Mankoorg99&F.
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Markertorg117&M. Marquardorg53&N.A. Martinorg96&J. Martin Blancoorg112&P.
Martinengoorg36&M.I. Martínezorg2&G. Martínez Garcíaorg112&M. Martinez
Pedreiraorg36&Y. Martynovorg3&A. Masorg119&S. Masciocchiorg96&M.
Maseraorg27&A. Masoniorg105&L. Massacrierorg112&A. Mastroserioorg33&H.
Masuiorg127&A. Matyjaorg116&C. Mayerorg116&J. Mazerorg124&M.A.
Mazzoniorg108&D. Mcdonaldorg121&F. Meddiorg24&Y. Melikyanorg76&A. Menchaca-
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Miakeorg127&M.M. Mieskolainenorg46&K. Mikhaylovorg66,org58&L. Milanoorg36&J.
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Miśkowiecorg96&J. Mitraorg131&C.M. Mituorg62&N. Mohammadiorg57&B.
Mohantyorg131,org79&L. Molnarorg55&L. Montaño Zetinaorg11&E. Montesorg10&M.
Morandoorg30&D.A. Moreira De Godoyorg112,org54&L.A.P. Morenoorg2&S.
Morettoorg30&A. Morrealeorg112&A. Morschorg36&V. Mucciforaorg72&E.
Mudnicorg115&D. Mühlheimorg54&S. Muhuriorg131&M. Mukherjeeorg131&J.D.
Mulliganorg135&M.G. Munhozorg119&R.H. Munzerorg92,org37&S. Murrayorg65&L.
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Naruorg16&C. Nattrassorg124&K. Nayakorg79&T.K. Nayakorg131&S.
Nazarenkoorg98&A. Nedosekinorg58&L. Nellenorg63&F. Ngorg121&M.
Nicassioorg96&M. Niculescuorg62,org36&J. Niedzielaorg36&B.S. Nielsenorg80&S.
Nikolaevorg99&S. Nikulinorg99&V. Nikulinorg85&F. Noferiniorg104,org12&P.
Nomokonovorg66&G. Noorenorg57&J.C.C. Norisorg2&J. Normanorg123&A.
Nyaninorg99&J. Nystrandorg18&H. Oeschlerorg93&S. Ohorg135&S.K. Ohorg67&A.
Ohlsonorg36&A. Okatanorg69&T. Okuboorg47&L. Olahorg134&J. Oleniaczorg132&A.C.
Oliveira Da Silvaorg119&M.H. Oliverorg135&J. Onderwaaterorg96&C.
Oppedisanoorg110&R. Oravaorg46&A. Ortiz Velasquezorg63&A. Oskarssonorg34&J.
Otwinowskiorg116&K. Oyamaorg93&M. Ozdemirorg53&Y. Pachmayerorg93&P.
Paganoorg31&G. Paićorg63&C. Pajaresorg17&S.K. Palorg131&J. Panorg133&A.K.
Pandeyorg48&D. Pantorg48&P. Papcunorg114&V. Papikyanorg1&G.S.
Pappalardoorg106&P. Pareekorg49&W.J. Parkorg96&S. Parmarorg87&A.
Passfeldorg54&V. Paticchioorg103&R.N. Patraorg131&B. Paulorg100&T.
Peitzmannorg57&H. Pereira Da Costaorg15&E. Pereira De Oliveira Filhoorg119&D.
Peresunkoorg99,org76&C.E. Pérez Laraorg81&E. Perez Lezamaorg53&V.
Peskovorg53&Y. Pestovorg5&V. Petráčekorg40&V. Petrovorg111&M.
Petroviciorg78&C. Pettaorg29&S. Pianoorg109&M. Piknaorg39&P. Pillotorg112&O.
Pinazzaorg104,org36&L. Pinskyorg121&D.B. Piyarathnaorg121&M. Płoskońorg74&M.
Planinicorg128&J. Plutaorg132&S. Pochybovaorg134&P.L.M. Podesta-
Lermaorg118&M.G. Poghosyanorg86,org84&B. Polichtchoukorg111&N. Poljakorg128&W.
Poonsawatorg113&A. Poporg78&S. Porteboeuf-Houssaisorg70&J. Porterorg74&J.
Pospisilorg83&S.K. Prasadorg4&R. Preghenellaorg36,org104&F. Prinoorg110&C.A.
Pruneauorg133&I. Pshenichnovorg56&M. Puccioorg110&G. Pudduorg25&P.
Pujahariorg133&V. Puninorg98&J. Putschkeorg133&H. Qvigstadorg22&A.
Rachevskiorg109&S. Rahaorg4&S. Rajputorg90&J. Rakorg122&A.
Rakotozafindrabeorg15&L. Ramelloorg32&F. Ramiorg55&R. Raniwalaorg91&S.
Raniwalaorg91&S.S. Räsänenorg46&B.T. Rascanuorg53&D. Ratheeorg87&K.F.
Readorg124&J.S. Realorg71&K. Redlichorg77&R.J. Reedorg133&A. Rehmanorg18&P.
Reicheltorg53&F. Reidtorg93,org36&X. Renorg7&R. Renfordtorg53&A.R.
Reolonorg72&A. Reshetinorg56&F. Rettigorg43&J.-P. Revolorg12&K.
Reygersorg93&V. Riabovorg85&R.A. Ricciorg73&T. Richertorg34&M. Richterorg22&P.
Riedlerorg36&W. Rieglerorg36&F. Riggiorg29&C. Risteaorg62&A. Rivettiorg110&E.
Roccoorg57&M. Rodríguez Cahuantziorg2&A. Rodriguez Mansoorg81&K. Røedorg22&E.
Rogochayaorg66&D. Rohrorg43&D. Röhrichorg18&R. Romitaorg123&F.
Ronchettiorg72,org36&L. Ronfletteorg112&P. Rosnetorg70&A. Rossiorg30,org36&F.
Roukoutakisorg88&A. Royorg49&C. Royorg55&P. Royorg100&A.J. Rubio
Monteroorg10&R. Ruiorg26&R. Russoorg27&E. Ryabinkinorg99&Y. Ryabovorg85&A.
Rybickiorg116&S. Sadovskyorg111&K. Šafaříkorg36&B. Sahlmullerorg53&P.
Sahooorg49&R. Sahooorg49&S. Sahooorg61&P.K. Sahuorg61&J. Sainiorg131&S.
Sakaiorg72&M.A. Salehorg133&C.A. Salgadoorg17&J. Salzwedelorg20&S.
Sambyalorg90&V. Samsonovorg85&L. Šándororg59&A. Sandovalorg64&M. Sanoorg127&D.
Sarkarorg131&E. Scapparoneorg104&F. Scarlassaraorg30&R.P. Scharenbergorg94&C.
Schiauaorg78&R. Schickerorg93&C. Schmidtorg96&H.R. Schmidtorg35&S.
Schuchmannorg53&J. Schukraftorg36&M. Schulcorg40&T. Schusterorg135&Y.
Schutzorg112,org36&K. Schwarzorg96&K. Schwedaorg96&G. Scioliorg28&E.
Scomparinorg110&R. Scottorg124&J.E. Segerorg86&Y. Sekiguchiorg126&D.
Sekihataorg47&I. Selyuzhenkovorg96&K. Senosiorg65&J. Seoorg95,org67&E.
Serradillaorg64,org10&A. Sevcencoorg62&A. Shabanovorg56&A. Shabetaiorg112&O.
Shaduraorg3&R. Shahoyanorg36&A. Shangaraevorg111&A. Sharmaorg90&M.
Sharmaorg90&M. Sharmaorg90&N. Sharmaorg124,org61&K. Shigakiorg47&K.
Shtejerorg9,org27&Y. Sibiriakorg99&S. Siddhantaorg105&K.M. Sielewiczorg36&T.
Siemiarczukorg77&D. Silvermyrorg84,org34&C. Silvestreorg71&G.
Simatovicorg128&G. Simonettiorg36&R. Singarajuorg131&R. Singhorg79&S.
Singhaorg131,org79&V. Singhalorg131&B.C. Sinhaorg131&T. Sinhaorg100&B.
Sitarorg39&M. Sittaorg32&T.B. Skaaliorg22&M. Slupeckiorg122&N.
Smirnovorg135&R.J.M. Snellingsorg57&T.W. Snellmanorg122&C. Søgaardorg34&R.
Soltzorg75&J. Songorg95&M. Songorg136&Z. Songorg7&F. Soramelorg30&S.
Sorensenorg124&M. Spacekorg40&E. Spiritiorg72&I. Sputowskaorg116&M.
Spyropoulou-Stassinakiorg88&B.K. Srivastavaorg94&J. Stachelorg93&I.
Stanorg62&G. Stefanekorg77&E. Stenlundorg34&G. Steynorg65&J.H. Stillerorg93&D.
Stoccoorg112&P. Strmenorg39&A.A.P. Suaideorg119&T. Sugitateorg47&C.
Suireorg51&M. Suleymanovorg16&M. Suljicorg260&R. Sultanovorg58&M.
Šumberaorg83&T.J.M. Symonsorg74&A. Szaboorg39&A. Szanto de Toledoorg1190&I.
Szarkaorg39&A. Szczepankiewiczorg36&M. Szymanskiorg132&U. Tabassamorg16&J.
Takahashiorg120&G.J. Tambaveorg18&N. Tanakaorg127&M.A. Tangaroorg33&J.D. Tapia
Takakiidp5932384,org51&A. Tarantola Peloniorg53&M. Tarhiniorg51&M.
Tariqorg19&M.G. Tarzilaorg78&A. Tauroorg36&G. Tejeda Muñozorg2&A.
Telescaorg36&K. Terasakiorg126&C. Terrevoliorg30,org25&B. Teyssierorg129&J.
Thäderorg74,org96&D. Thomasorg117&R. Tieulentorg129&A.R. Timminsorg121&A.
Toiaorg53&S. Trogoloorg110&V. Trubnikovorg3&W.H. Trzaskaorg122&T.
Tsujiorg126&A. Tumkinorg98&R. Turrisiorg107&T.S. Tveterorg22&K.
Ullalandorg18&A. Urasorg129&G.L. Usaiorg25&A. Utrobicicorg128&M.
Vajzerorg83&L. Valencia Palomoorg70&S. Valleroorg27&J. Van Der
Maarelorg57&J.W. Van Hoorneorg36&M. van Leeuwenorg57&T. Vanatorg83&P. Vande
Vyvreorg36&D. Vargaorg134&A. Vargasorg2&M. Vargyasorg122&R. Varmaorg48&M.
Vasileiouorg88&A. Vasilievorg99&A. Vauthierorg71&V. Vecherninorg130&A.M.
Veenorg57&M. Veldhoenorg57&A. Velureorg18&M. Venaruzzoorg73&E.
Vercellinorg27&S. Vergara Limónorg2&R. Vernetorg8&M. Verweijorg133,org36&L.
Vickovicorg115&G. Viestiorg300&J. Viinikainenorg122&Z. Vilakaziorg125&O.
Villalobos Baillieorg101&A. Villatoro Telloorg2&A. Vinogradovorg99&L.
Vinogradovorg130&Y. Vinogradovorg980&T. Virgiliorg31&V. Vislaviciusorg34&Y.P.
Viyogiorg131&A. Vodopyanovorg66&M.A. Völklorg93&K. Voloshinorg58&S.A.
Voloshinorg133&G. Volpeorg134,org36&B. von Hallerorg36&I.
Vorobyevorg92,org37&D. Vranicorg96,org36&J. Vrlákováorg41&B. Vulpescuorg70&A.
Vyushinorg98&B. Wagnerorg18&J. Wagnerorg96&H. Wangorg57&M. Wangorg7,org112&D.
Watanabeorg127&Y. Watanabeorg126&M. Weberorg36&S.G. Weberorg96&J.P.
Wesselsorg54&U. Westerhofforg54&J. Wiechulaorg35&J. Wikneorg22&M.
Wildeorg54&G. Wilkorg77&J. Wilkinsonorg93&M.C.S. Williamsorg104&B.
Windelbandorg93&M. Winnorg93&C.G. Yaldoorg133&H. Yangorg57&P. Yangorg7&S.
Yanoorg47&Z. Yinorg7&H. Yokoyamaorg127&I.-K. Yooorg95&V. Yurchenkoorg3&I.
Yushmanovorg99&A. Zaborowskaorg132&V. Zaccoloorg80&A. Zamanorg16&C.
Zampolliorg104&H.J.C. Zanoliorg119&S. Zaporozhetsorg66&N. Zardoshtiorg101&A.
Zarochentsevorg130&P. Závadaorg60&N. Zaviyalovorg98&H. Zbroszczykorg132&I.S.
Zguraorg62&M. Zhalovorg85&H. Zhangorg18,org7&X. Zhangorg74,org7&Y.
Zhangorg7&Z. Zhangorg7&C. Zhaoorg22&N. Zhigarevaorg58&D. Zhouorg7&Y.
Zhouorg80,org57&Z. Zhouorg18&H. Zhuorg18,org7&J. Zhuorg7,org112&A.
Zichichiorg28,org12&A. Zimmermannorg93&M.B. Zimmermannorg36,org54&G.
Zinovjevorg3&M. Zyzakorg43

## Affiliation notes

0Deceased

idp3777184Also at: M.V. Lomonosov Moscow State University, D.V. Skobeltsyn
Institute of Nuclear, Physics, Moscow, Russia

idp5932384Also at: University of Kansas, Lawrence, Kansas, United States

## Collaboration Institutes

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

org2Benemérita Universidad Autónoma de Puebla, Puebla, Mexico

org3Bogolyubov Institute for Theoretical Physics, Kiev, Ukraine

org4Bose Institute, Department of Physics and Centre for Astroparticle Physics
and Space Science (CAPSS), Kolkata, India

org5Budker Institute for Nuclear Physics, Novosibirsk, Russia

org6California Polytechnic State University, San Luis Obispo, California,
United States

org7Central China Normal University, Wuhan, China

org8Centre de Calcul de l’IN2P3, Villeurbanne, France

org9Centro de Aplicaciones Tecnológicas y Desarrollo Nuclear (CEADEN), Havana,
Cuba

org10Centro de Investigaciones Energéticas Medioambientales y Tecnológicas
(CIEMAT), Madrid, Spain

org11Centro de Investigación y de Estudios Avanzados (CINVESTAV), Mexico City
and Mérida, Mexico

org12Centro Fermi - Museo Storico della Fisica e Centro Studi e Ricerche
“Enrico Fermi”, Rome, Italy

org13Chicago State University, Chicago, Illinois, USA

org14China Institute of Atomic Energy, Beijing, China

org15Commissariat à l’Energie Atomique, IRFU, Saclay, France

org16COMSATS Institute of Information Technology (CIIT), Islamabad, Pakistan

org17Departamento de Física de Partículas and IGFAE, Universidad de Santiago
de Compostela, Santiago de Compostela, Spain

org18Department of Physics and Technology, University of Bergen, Bergen,
Norway

org19Department of Physics, Aligarh Muslim University, Aligarh, India

org20Department of Physics, Ohio State University, Columbus, Ohio, United
States

org21Department of Physics, Sejong University, Seoul, South Korea

org22Department of Physics, University of Oslo, Oslo, Norway

org23Dipartimento di Elettrotecnica ed Elettronica del Politecnico, Bari,
Italy

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

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

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

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

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

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

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

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

org32Dipartimento di Scienze e Innovazione Tecnologica dell’Università del
Piemonte Orientale and Gruppo Collegato INFN, Alessandria, Italy

org33Dipartimento Interateneo di Fisica ‘M. Merlin’ and Sezione INFN, Bari,
Italy

org34Division of Experimental High Energy Physics, University of Lund, Lund,
Sweden

org35Eberhard Karls Universität Tübingen, Tübingen, Germany

org36European Organization for Nuclear Research (CERN), Geneva, Switzerland

org37Excellence Cluster Universe, Technische Universität München, Munich,
Germany

org38Faculty of Engineering, Bergen University College, Bergen, Norway

org39Faculty of Mathematics, Physics and Informatics, Comenius University,
Bratislava, Slovakia

org40Faculty of Nuclear Sciences and Physical Engineering, Czech Technical
University in Prague, Prague, Czech Republic

org41Faculty of Science, P.J. Šafárik University, Košice, Slovakia

org42Faculty of Technology, Buskerud and Vestfold University College,
Vestfold, Norway

org43Frankfurt Institute for Advanced Studies, Johann Wolfgang Goethe-
Universität Frankfurt, Frankfurt, Germany

org44Gangneung-Wonju National University, Gangneung, South Korea

org45Gauhati University, Department of Physics, Guwahati, India

org46Helsinki Institute of Physics (HIP), Helsinki, Finland

org47Hiroshima University, Hiroshima, Japan

org48Indian Institute of Technology Bombay (IIT), Mumbai, India

org49Indian Institute of Technology Indore, Indore (IITI), India

org50Inha University, Incheon, South Korea

org51Institut de Physique Nucléaire d’Orsay (IPNO), Université Paris-Sud,
CNRS-IN2P3, Orsay, France

org52Institut für Informatik, Johann Wolfgang Goethe-Universität Frankfurt,
Frankfurt, Germany

org53Institut für Kernphysik, Johann Wolfgang Goethe-Universität Frankfurt,
Frankfurt, Germany

org54Institut für Kernphysik, Westfälische Wilhelms-Universität Münster,
Münster, Germany

org55Institut Pluridisciplinaire Hubert Curien (IPHC), Université de
Strasbourg, CNRS-IN2P3, Strasbourg, France

org56Institute for Nuclear Research, Academy of Sciences, Moscow, Russia

org57Institute for Subatomic Physics of Utrecht University, Utrecht,
Netherlands

org58Institute for Theoretical and Experimental Physics, Moscow, Russia

org59Institute of Experimental Physics, Slovak Academy of Sciences, Košice,
Slovakia

org60Institute of Physics, Academy of Sciences of the Czech Republic, Prague,
Czech Republic

org61Institute of Physics, Bhubaneswar, India

org62Institute of Space Science (ISS), Bucharest, Romania

org63Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México,
Mexico City, Mexico

org64Instituto de Física, Universidad Nacional Autónoma de México, Mexico
City, Mexico

org65iThemba LABS, National Research Foundation, Somerset West, South Africa

org66Joint Institute for Nuclear Research (JINR), Dubna, Russia

org67Konkuk University, Seoul, South Korea

org68Korea Institute of Science and Technology Information, Daejeon, South
Korea

org69KTO Karatay University, Konya, Turkey

org70Laboratoire de Physique Corpusculaire (LPC), Clermont Université,
Université Blaise Pascal, CNRS–IN2P3, Clermont-Ferrand, France

org71Laboratoire de Physique Subatomique et de Cosmologie, Université
Grenoble-Alpes, CNRS-IN2P3, Grenoble, France

org72Laboratori Nazionali di Frascati, INFN, Frascati, Italy

org73Laboratori Nazionali di Legnaro, INFN, Legnaro, Italy

org74Lawrence Berkeley National Laboratory, Berkeley, California, United
States

org75Lawrence Livermore National Laboratory, Livermore, California, United
States

org76Moscow Engineering Physics Institute, Moscow, Russia

org77National Centre for Nuclear Studies, Warsaw, Poland

org78National Institute for Physics and Nuclear Engineering, Bucharest,
Romania

org79National Institute of Science Education and Research, Bhubaneswar, India

org80Niels Bohr Institute, University of Copenhagen, Copenhagen, Denmark

org81Nikhef, Nationaal instituut voor subatomaire fysica, Amsterdam,
Netherlands

org82Nuclear Physics Group, STFC Daresbury Laboratory, Daresbury, United
Kingdom

org83Nuclear Physics Institute, Academy of Sciences of the Czech Republic, Řež
u Prahy, Czech Republic

org84Oak Ridge National Laboratory, Oak Ridge, Tennessee, United States

org85Petersburg Nuclear Physics Institute, Gatchina, Russia

org86Physics Department, Creighton University, Omaha, Nebraska, United States

org87Physics Department, Panjab University, Chandigarh, India

org88Physics Department, University of Athens, Athens, Greece

org89Physics Department, University of Cape Town, Cape Town, South Africa

org90Physics Department, University of Jammu, Jammu, India

org91Physics Department, University of Rajasthan, Jaipur, India

org92Physik Department, Technische Universität München, Munich, Germany

org93Physikalisches Institut, Ruprecht-Karls-Universität Heidelberg,
Heidelberg, Germany

org94Purdue University, West Lafayette, Indiana, United States

org95Pusan National University, Pusan, South Korea

org96Research Division and ExtreMe Matter Institute EMMI, GSI Helmholtzzentrum
für Schwerionenforschung, Darmstadt, Germany

org97Rudjer Bošković Institute, Zagreb, Croatia

org98Russian Federal Nuclear Center (VNIIEF), Sarov, Russia

org99Russian Research Centre Kurchatov Institute, Moscow, Russia

org100Saha Institute of Nuclear Physics, Kolkata, India

org101School of Physics and Astronomy, University of Birmingham, Birmingham,
United Kingdom

org102Sección Física, Departamento de Ciencias, Pontificia Universidad
Católica del Perú, Lima, Peru

org103Sezione INFN, Bari, Italy

org104Sezione INFN, Bologna, Italy

org105Sezione INFN, Cagliari, Italy

org106Sezione INFN, Catania, Italy

org107Sezione INFN, Padova, Italy

org108Sezione INFN, Rome, Italy

org109Sezione INFN, Trieste, Italy

org110Sezione INFN, Turin, Italy

org111SSC IHEP of NRC Kurchatov institute, Protvino, Russia

org112SUBATECH, Ecole des Mines de Nantes, Université de Nantes, CNRS-IN2P3,
Nantes, France

org113Suranaree University of Technology, Nakhon Ratchasima, Thailand

org114Technical University of Košice, Košice, Slovakia

org115Technical University of Split FESB, Split, Croatia

org116The Henryk Niewodniczanski Institute of Nuclear Physics, Polish Academy
of Sciences, Cracow, Poland

org117The University of Texas at Austin, Physics Department, Austin, Texas,
USA

org118Universidad Autónoma de Sinaloa, Culiacán, Mexico

org119Universidade de São Paulo (USP), São Paulo, Brazil

org120Universidade Estadual de Campinas (UNICAMP), Campinas, Brazil

org121University of Houston, Houston, Texas, United States

org122University of Jyväskylä, Jyväskylä, Finland

org123University of Liverpool, Liverpool, United Kingdom

org124University of Tennessee, Knoxville, Tennessee, United States

org125University of the Witwatersrand, Johannesburg, South Africa

org126University of Tokyo, Tokyo, Japan

org127University of Tsukuba, Tsukuba, Japan

org128University of Zagreb, Zagreb, Croatia

org129Université de Lyon, Université Lyon 1, CNRS/IN2P3, IPN-Lyon,
Villeurbanne, France

org130V. Fock Institute for Physics, St. Petersburg State University, St.
Petersburg, Russia

org131Variable Energy Cyclotron Centre, Kolkata, India

org132Warsaw University of Technology, Warsaw, Poland

org133Wayne State University, Detroit, Michigan, United States

org134Wigner Research Centre for Physics, Hungarian Academy of Sciences,
Budapest, Hungary

org135Yale University, New Haven, Connecticut, United States

org136Yonsei University, Seoul, South Korea

org137Zentrum für Technologietransfer und Telekommunikation (ZTT),
Fachhochschule Worms, Worms, Germany