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Physics
Letters
B
www.elsevier.com/locate/physletb
Elliptic
flow
of
muons
from
heavy-flavour
hadron
decays
at
forward
rapidity
in
Pb–Pb
collisions
at
√
s
NN
=
2
.
76 TeV
.
ALICE
Collaboration
a
r
t
i
c
l
e
i
n
f
o
a
b
s
t
r
a
c
t
Articlehistory: Received15July2015
Receivedinrevisedform19November2015 Accepted20November2015
Availableonline2December2015 Editor: L.Rolandi
Keywords: LHC
ALICEexperiment Pb–Pbcollisions
Heavy-flavourdecaymuons Ellipticflow
The elliptic flow, v2, of muons from heavy-flavour hadron decays atforward rapidity (2.5< y<4)
is measured inPb–Pb collisions at√sNN=2.76 TeV with the ALICE detector atthe LHC. The scalar
product,two- andfour-particleQ cumulantsandLee–Yangzerosmethodsareused.Thedependenceof the v2ofmuonsfromheavy-flavourhadrondecaysonthecollisioncentrality,intherange0–40%,and
ontransversemomentum, pT,isstudiedintheinterval 3<pT<10 GeV/c.Apositive v2is observed
withthe scalarproductandtwo-particle Q cumulantsinsemi-central collisions(10–20%and 20–40% centrality classes) for the pT interval from 3 to about 5 GeV/c with a significance larger than 3
σ
,basedonthecombinationofstatisticalandsystematicuncertainties.Thev2magnitudetendstodecrease
towardsmorecentralcollisionsandwithincreasingpT.Itbecomescompatiblewithzerointheinterval
6<pT<10 GeV/c.Theresultsarecomparedtomodelsdescribingtheinteractionofheavyquarksand
openheavy-flavourhadronswiththehigh-densitymediumformedinhigh-energyheavy-ioncollisions.
©2015CERNforthebenefitoftheALICECollaboration.PublishedbyElsevierB.V.Thisisanopen accessarticleundertheCCBYlicense(http://creativecommons.org/licenses/by/4.0/).FundedbySCOAP3.
1. Introduction
Experimentswith ultra-relativistic heavy-ion collisions aim at investigatingtheproperties ofstrongly-interacting matter atvery hightemperaturesandenergydensities.Quantum Chromodynam-ics (QCD) calculations on the lattice predict, under these con-ditions, the formation of a Quark–Gluon Plasma (QGP), where color confinement vanishes and chiral symmetry is partially re-stored[1–5].Heavyquarks(charmandbeauty)arecreatedin ini-tialhard-scatteringprocessesonatimescaleshorterthantheQGP formationtime.Subsequently,theyinteractwiththemedium con-stituentsviainelastic[6,7]andelastic[8–10]processes.Therefore, heavyquarksare regardedaseffectiveprobes oftheQGP proper-ties.
Heavy-quark energy loss due to in-medium interactions can be studied by means ofthe nuclear modification factor RAA,
de-finedastheratiooftheyieldofheavy-flavourparticles measured in nucleus–nucleus (AA) collisions to that observed in proton– proton (pp) collisions scaled by the number of binary nucleon– nucleoncollisions.ThePHENIXandSTARCollaborationsmeasured, incentralAu–Aucollisions at
√
sNN=
200 GeV, astrongsuppres-sion corresponding to a RAA of about 0.2–0.3 for heavy-flavour
decay electrons at mid-rapidity ( y) and transverse momentum
pT
>
5 GeV/
c[11–17].AsimilarsuppressionwasalsomeasuredbyE-mailaddress:alice-publications@cern.ch.
theSTARCollaborationformid-rapidityD0 mesons[18].A
signif-icantsuppression wasalso observedbythePHENIX Collaboration at forwardrapidity formuons fromheavy-flavour hadron decays in central Cu–Cucollisions at
√
sNN=
200 GeV [19]. At the LHC,theALICECollaborationreportedasimilar effectincentralPb–Pb collisions at
√
sNN=
2.
76 TeV for Dmesons atmid-rapidity [20]and muons from heavy-flavour hadron decays at forward rapid-ity[21]intheinterval 2
<
pT<
16 GeV/
c and4<
pT<
10 GeV/
c,respectively. The CMS Collaboration measured a significant sup-pression of non-prompt J
/ψ
from beauty-hadron decays in the interval 6.
5<
pT<
30 GeV/
c (3<
pT<
30 GeV/
c) and|
y|
<
2.
4(1
.
6<
|
y|
<
2.
4)[22,23]. Afirstmeasurementofnon-prompt J/ψ
by the ALICECollaborationat mid-rapidity(|
y|
<
0.
8) andin the interval4.
5<
pT<
10 GeV/
c hasbeenrecentlypublished[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 andtheoreticalinvestigations(see [25]andreferencestherein).In non-central collisions,the initialspatial anisotropy ofthe overlap region, elongated in the direction perpendicular to the reaction plane, defined by the beam axis and the impact parameter of thecollision,isconvertedintoananisotropy inmomentumspace throughrescatterings[26].Experimentally,thestudyoftheparticle azimuthalanisotropyisbasedonaFourierexpansionofazimuthal distributionsgivenby:
http://dx.doi.org/10.1016/j.physletb.2015.11.059
0370-2693/©2015CERNforthebenefitoftheALICECollaboration.PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense (http://creativecommons.org/licenses/by/4.0/).FundedbySCOAP3.
d2N dpTd
ϕ
=
1 2π
dN dpT 1+
2 ∞ n=1 vn(
pT)
cos[
n(
ϕ
−
n)
]
,
(1)where
ϕ
and pT are the particleazimuthal angle andtransversemomentum,respectively.The Fouriercoefficients, vn,characterize theanisotropyofproducedparticlesand
nistheazimuthalangle of the initial-state symmetry plane for the nth harmonic, intro-ducedtoaccount fortheevent-by-eventfluctuationsoftheinitial nucleondensityprofile. Thesecond Fourier coefficient, v2, which
canalsobe expressedas v2
=
cos[
2(
ϕ
−
2)
]
,isnamed ellipticflow.
The v2 of heavy-flavourhadronsis expectedto provide
infor-mation on the collective expansion anddegree of thermalization ofheavy quarksinthemedium atlow pT (pT
<
2–3 GeV/
c).Theparticipation of heavy quarks in the collective expansion is ex-pected to give a positive v2 [26]. Moving towards intermediate pT (3
<
pT<
6 GeV/
c),the v2 Fouriercoefficient isalsoexpectedtobe sensitiveto thepresenceofrecombinationprocessesinthe hadronizationofheavyquarks[27,28].AthighpT (pT
>
6 GeV/
c),thev2 measurementcanconstrainthepath-lengthdependenceof
thein-medium partonenergyloss, whichbecomes the dominant contributionto theazimuthal anisotropy andis alsopredictedto givea positive v2 [29,30],thuscomplementingthe RAA
measure-ment.
The PHENIX Collaboration reported a positive v2 of
heavy-flavour decay electrons at mid-rapidity in Au–Au collisions at
√
sNN
=
200 GeV, reaching a maximum value of about 0.15 at pT=
1.
5 GeV/
c in semi-central collisions [14,15,31]. A similarbehavior was also observed by the STAR Collaboration [32]. Re-cently,av2valuesignificantlylargerthanzerowasmeasuredforD
mesonsatmid-rapidityinPb–Pbcollisionsat
√
sNN=
2.
76 TeV[33, 34].Acomplementarymeasurementatthesameenergy,provided bytheheavy-flavourdecaymuonellipticflowatforwardrapidity (2.
5<
y<
4), is of great interest in order to provide new con-straints for models that implement the heavy-quark interactions withthemedium. Finally,themeasurement isalsoimportantfor the interpretation of the J/ψ
elliptic flow results at forward ra-pidity[35]intermsofaregenerationproductionfromdeconfined charmquarksinthemedium.InthisLetter, wepresentthemeasurementoftheellipticflow of muons from heavy-flavour hadron decays at forward rapidity (2
.
5<
y<
4) in Pb–Pb collisions at√
sNN=
2.
76 TeV recordedwiththe ALICE detector.The elliptic flow is measured using dif-ferentmethods:scalarproduct[36],two- andfour-particle Q
cu-mulants [37,38] andLee–Yang zeros [39–41]. These methods ex-hibitdifferentsensitivitiestoflowfluctuationsandcorrelationsnot relatedtotheazimuthal asymmetryintheinitial geometry (non-floweffects).The v2 coefficientismeasuredasafunctionofpT in
theinterval 3
<
pT<
10 GeV/
c and inthree centralityclasses intherange0–40%.Thecentralitydependenceofv2 ispresentedin
theinterval3
<
pT<
5 GeV/
c.TheLetterisorganized asfollows.TheALICEdetector,withan emphasisonthemuonspectrometer,andthedatasampleare pre-sentedin Section 2.The analysisdetails, the methods forthe v2
measurement, the inclusive muon v2 determination, the
proce-dureforthesubtractionofthebackgroundofmuonsfromdecays oflight-flavourhadronsandthestudyofsystematicuncertainties, aredescribed inSection3.The v2 resultsformuonsfrom
heavy-flavourdecaysarepresentedinSection4.The v2 measurementin
semi-centralcollisionsaswellasthepublished RAAincentral
col-lisions are compared to model calculations in Section 5. Finally, conclusionsaregiveninSection6.
2. ALICEexperimentanddatasample
The ALICE detector is described in detail in [42,43]. The ap-paratus is composedof aset ofcentral barreldetectors (pseudo-rapidity coverage
|
η
|
<
0.
9)located insideasolenoidmagnetthat generates a field of0.5 T parallelto the beamdirection, amuon spectrometer (−
4<
η
<
−
2.
51) and a set of detectors forevent characterization andtriggering located in the forward and back-wardη
regions.Themuonspectrometerconsistsofapassivefront absorber made of carbon, concrete and steel, a beam shield, a 3 T mdipole magnet,trackingchambers,a muonfilter(ironwall) andtrigger chambers. The muon trackingsystemis composed of five stations, each includingtwo planes ofcathod pad chambers, withthe thirdstationinside thedipole magnet. Themuon track-ing systemis completed by four trigger planes of resistiveplate chambers downstream of the iron wall, which absorbs hadrons thatpunchthroughthefrontabsorber,aswell assecondary parti-clesproducedinsideitandlowmomentummuons(p<
4 GeV/
c).Twoscintillatorarrays(V0)coveringthepseudo-rapidity inter-vals
−
3.
7<
η
<
−
1.
7 and 2.
8<
η
<
5.
1 are used for triggering, forcollision centralitydeterminationandforbeam-induced back-ground rejection.The Zero DegreeCalorimeters (ZDC), located at 114 m fromthecentre ofthe detectoron both sides, can detect spectator protons and neutrons andare also used for the offline rejection ofbeam-inducedbackgroundandelectromagnetic inter-actions. The Silicon PixelDetector (SPD), that composes the two innermost layers of the Inner Tracking System (ITS), is used for theinteractionvertexreconstruction.TheTimeProjectionChamber (TPC), whichmeasurescharged-particletrackswithfullazimuthal coveragein|
η
|
<
0.
9,isusedinthisanalysisforthemeasurement ofthereferenceparticles(Section3.1).TheresultspresentedinthisLetterareobtainedfromthedata sample recordedwithALICEduringthe2011Pb–Pbrun.Thedata were collected withaminimum-biastrigger requiringthe coinci-denceofsignalsinthetwoV0arraysinsynchronizationwiththe passage oftwo crossing bunches.In addition,the recordedevent sample was enriched with central and semi-central Pb–Pb colli-sionsbyapplyingthresholds,atthetriggerlevel,ontheV0signal amplitude.Thebeam-inducedbackground(beam–gasinteractions) was reduced by using the timing information from the V0 and ZDCdetectors.Furthermore,a minimalenergydepositintheZDC was requiredto rejectthe contributionfromelectromagneticPb– Pb interactions. Onlyevents witha reconstructed primary vertex within
±
10 cmfromthenominalpositionofthe interaction ver-texalongthebeamdirectionareanalyzed.ThePb–Pbcollisionsare classified accordingtotheir degree of centralityby means ofthe sum ofthe amplitudesof thesignals inthe V0detectorand the centrality classesare definedaspercentiles ofthe total hadronic Pb–Pb crosssection[44].The analysisiscarriedout inthree cen-trality classes: 0–10% (using the sample with trigger on central collisions),10–20%and20–40%(using thesamplewithtriggeron semi-central collisions).The analyzeddatasample corresponds to anintegratedluminosityof11.3 μb−1 inthe0–10%centralityclass andof3.5 μb−1 intheothertwocentralityclasses.3. Dataanalysis
The elliptic flow of muonsfrom heavy-flavourhadron decays,
vμ2←HF,isobtainedfromthemeasurement oftheinclusivemuon ellipticflow,vμ2,bysubtractingtheellipticflowofmuonsfrom
pri-1 IntheALICEreferenceframe,themuonspectrometercoversanegativeηrange andconsequentlyanegativey range.Inthefollowing,giventhatthecolliding sys-temissymmetric,theresultsarepresentedwithapositivey notation.
marychargedpionandkaondecaysv2μ←π,K(Sections3.1and3.4), as: vμ2←HF
=
v μ 2−
fμ←π,K·
v μ←π,K 2 1−
fμ←π,K,
(2)where f μ←π,K is the muon background fraction, definedas the
ratiooftheyield ofmuonsfromprimary chargedpionandkaon decaystothatofinclusivemuons.Themeasurementofthevμ2←HF
coefficientiscarriedoutintheinterval3
<
pT<
10 GeV/
c inordertolimitthesystematicuncertaintyonthesubtractionofthemuon backgroundcontribution.
3.1.Trackselection
Theselectioncriteriaforparticles ofinterest,muontracks,are similarto those usedin theprevious analyses ofpp collisions at
√
s
=
2.
76 TeV and7TeVandPb–Pbcollisionsat√
sNN=
2.
76 TeV [21,45].The tracks are requiredto be within thegeometrical ac-ceptance of the muon spectrometer, with−
4<
η
<
−
2.
5 and 170◦< θ
abs<
178◦,whereθ
abs isthepolaranglemeasuredattheendoftheabsorber.Inordertoimprovethemuonidentification,a reconstructedtrackinthetrackingchambersisrequiredtomatch atracksegment inthe triggerchambers. Thisleads to avery ef-ficientrejectionofthebackgroundproduced by chargedhadrons, which are absorbed in the iron wall. Furthermore, a cut on the product p
·
DCA of the track momentum p anddistance of clos-estapproach(DCA)totheprimaryvertexisappliedtoremovethe beam-inducedbackgroundtracksandfaketrackscomingfromthe superpositionofseveralparticlescrossingthemuonspectrometer. Due to multiple scatteringin the front absorber, the DCAdistri-bution of tracks coming form the interaction vertex is expected to be described by a Gaussian function, its width being depen-dentontheabsorbermaterialandproportionalto1/p.Background trackshaveaverybroaddistributioninp
·
DCA andareeffectively rejected by a cut at 6σ
, whereσ
is extracted from a Gaussian fit to the p·
DCA distribution measured intwo intervalsofθ
abs,correspondingtodifferentmaterialsinthefrontabsorber.The rel-ative momentum resolution of reconstructed tracks varies from about1%to4%fortrackswithmomentumbetween20 GeV
/
c and100 GeV
/
c.Afterthecutsareapplied,intheregion pT>
3 GeV/
ctheresidualbackgroundtoheavy-flavourdecaymuonsconsistsof muonsfrom decaysof primary charged pions andkaons2 andit amounts to 5–15%, depending on pT and on collision centrality
(Section3.4).
Themid-rapiditycharged-particletracksusedtodeterminethe flowvector Q
n orthegeneratingfunction(Section3.2)are called in the following reference particles. They are defined as tracks measured in the TPCin|
η
|
<
0.
8. These are required to have at least 70 associated space points out of the maximum of 159, aχ
2 per degree of freedom (ndf) for the momentum fit in therange
χ
2/
ndf<
2 and a transverse momentum value in thein-terval0
.
2<
pT<
5 GeV/
c.Additionally,tracksarerejectediftheirdistanceof closest approachto the primary vertex islarger than 3 cmintheplanetransversetothebeamdirectionorinthe lon-gitudinaldirection.
3.2.Flowanalysismethods
The elliptic flow measurement is carried out using various methodsthat havedifferentsensitivities to flow fluctuationsand
2 Notethatthecontributionofmuonsfromsecondarylighthadrondecays pro-ducedinsidethefrontabsorberisnegligibleforpT>3 GeV/c[45].
non-flow effects [46]. Flow fluctuationsare mainlydue to event-by-eventfluctuationsoftheinitial densityprofile,whilenon-flow effects correspond to correlations not related to the azimuthal anisotropy inthe initial state,such asresonance decays,jetsand Bose–Einsteincorrelationsbetweenidentical particles.It isworth mentioning that, inthe present analysis, mostof thesenon-flow effects arestrongly suppressedby introducing an
η
gapbetween reference particles andparticles of interest [47]. In thisanalysis, the scalarproduct [36],two- and four-particle Q cumulants [37, 38] andLee–Yang zeros [39–41] methods are employed. The de-scriptionofthesemethodswill belimitedtothefeaturesspecific to the present analysis. The following notations are introduced:vμ2(μ←HF)
{
SP}
,referstothemeasurementusingthescalarproduct,v2μ(μ←HF)
{
2}
and v2μ(μ←HF){
4}
correspond to the ones using the two-particle Q cumulants andfour-particle Q cumulants, whilev2μ(μ←HF)
{
LYZ-Prod}
and v2μ(μ←HF){
LYZ-Sum}
are obtained using Lee–Yang zeros with product and sum generating functions. The superscriptsμ
andμ
←
HF refer to inclusivemuonsandmuons from heavy-flavourhadron decays, respectively. It is worth men-tioning that thesemethods are more accurate than the standard eventplane method,which yields a measurement lying between the event-averaged mean value and the root-mean-square value inthe presenceofflow fluctuations[48,49].Moreover, the multi-particlecorrelation methods(four-particle Q cumulantsandLee– Yang zeros)are less affected by non-flow correlationsthan two-particle correlation methods, but they cannot be used reliably when the muon flow magnitude is small and when the num-ber of muonsis small in the selected phase-spaceregion e.g. in centralandperipheralcollisions,respectively[37,39].Underthese conditions,thescalarproductandtwo-particlecumulantmethods providea v2 measurementinawidercentralityrange.The scalarproduct method[36,48], derived fromthestandard eventplane technique [48], is basedon the measurement of the flow vector Q
n [36] computed fromreference particles. In order to determine the ellipticflow, the Q2 vector in a givenevent isexpressedas:
Q2=
N j=1 cos2
ϕ
j,
N j=1 sin2ϕ
j,
(3)where
ϕ
jistheparticleazimuthalangleandN isthemultiplicity ofreferenceparticles.Withthismethodthe2ndharmoniccoefficientisgivenby: v2
{
SP} =
Q2
·
u2,i(
η
,
pT)
2Q2A
·
Q2B,
(4)where the brackets in the numerator indicate the average over muonsat forwardrapidity,in all events.The vector Q2 is
calcu-latedfromEq.(3)andthevector
u2,i= (
cos 2ϕ
i,
sin 2ϕ
i)
istheunit vectoroftheithmuon.Inthedenominator,eachsampleof refer-enceparticlesusedtocompute Q2isdividedintotwosub-samplesofsamemultiplicity insymmetrical
η
intervals,−
0.
8<
η
<
−
0.
5 and 0.
5<
η
<
0.
8, separated by aη
gap of one unit of pseudo-rapidity, labeled withthe superscripts A and B and the brackets correspondtotheaverageoverevents.Thecumulanttechnique[37,38]isbasedonacumulant expan-sionofmulti-particleazimuthalcorrelations.Differentorder cumu-lantshavedifferentsensitivitiestoflowfluctuations.Inthepresent analysis, two- andfour-particlecumulantsareusedtoextractthe muonellipticflow. Theresultspresentedinthe followingare ob-tained from a direct calculation of multi-particle cumulants per-formed by usingthe Q -cumulanttechnique [38], whichis based on the moments of the magnitude of the flow vector Q
2. It isworth mentioning that in this approach the cumulants are not biasedby the interferences between various harmonics. The ref-erenceellipticflowvaluesV2evaluatedfromthe2ndorder
cumu-lant c2
{
2}
and4thorder cumulantc2{
4}
withreferenceparticlesare given by V2
{
2}
=
√
c2{
2}
and V2{
4}
=
√
4−
c2{
4}
,respectively.Oncethereferenceellipticflowisestimated,themuonellipticflow withrespecttothereferenceellipticflowisobtainedfromthe2nd and4thordercumulantsaccordingto:
v2
{
2} =
d2{
2}
V2{
2}
and v2{
4} =
d2{
4}
V2{
4}
3,
(5)where d2
{
2}
andd2{
4}
are the 2nd and 4thorder cumulants ofselectedmuons[38].
The Lee–Yangzeros method [39–41] relieson correlations in-volving all particles in the event. This is the limit of cumulants whentheorderofcumulantsgoestoinfinity.Themethodisbased on the location ofthe zeros in thecomplex plane, of a generat-ing functionof azimuthal correlations, whichrelates theposition ofthefirstminimumofthegeneratingfunctiontothemagnitude ofthereferenceellipticflowV2 definedas:
V2
≡
M j=1 cos
[
2(ϕ
j−
2)
]
events
,
(6)whereM isthemultiplicityofreferenceparticlesandtheaverage istakenover allevents.Forthispurpose,thefollowing complex-valuedgeneratingfunctionisevaluatedasafunctionofapositive realvariabler andfew,typicallyfive,equallyspacedreference an-gles
ϑ
(LYZ-Prodmethod):Gϑ
(
ir)
≡
M j=1
(1
+
ir cos[
2(ϕ
j− ϑ)])
events
.
(7)Thefirstpositive minimumof
|
Gϑ(
ir)
|
,denotedasrϑ0,allowsone
to estimate Vϑ
2, which can be written as V2ϑ
=
j01/
r0ϑ, where j012.
405 isthe firstrootofthe Besselfunction. Oncethefirstminimum rϑ
0 is determined, the differential muon elliptic flow
is estimated with respect to the reference flow Vϑ
2 as detailed
in[41].Finally,theresultis averagedover all
ϑ
angles.An alter-nativeformofthegeneratingfunctionprovidedwiththeLYZ-Sum methodis: Gϑ(
ir)
≡
exp ir M j=1 cos[
2(ϕ
j− ϑ)]
events
.
(8)Theversionofthemethodinvolvingaproductfortheconstruction of the generation function (Eq. (7)) was designedto disentangle interferences betweendifferentharmonics, whichis not the case withthegeneratingfunction usinga sumoftheindividual refer-enceparticlecontributions.Both generatingfunctionsareusedin thisanalysis.
Notethat, for all methods, autocorrelationeffects are avoided because the particles (muons) used in the determination of the flowarenotincludedintheestimationofthereferenceflow.
3.3. Inclusivemuonellipticflow
The ellipticflow ofinclusivemuons, vμ2,isstudied with two-particle correlation methods (scalar product and two-particle Q
cumulants)inthecentralityintervals0–10%,10–20%and20–40%. In the 20–40% centrality interval, the multi-particle correlation methods(four-particle Q cumulantsandLee–Yangzeros)arealso used.
Severalsourcesofsystematicuncertaintyaffectingthemuon el-liptic flow measurement are considered. Thesetake into account the changes dueto thevariations ofthe referenceparticle selec-tion criteriaasin[33,34,50],to allowusto check therobustness ofthevμ2 measurement.Sincethecollisionimpactparameter dis-tribution could slightly depend on the observable used for the centralitydetermination,a systematicuncertaintyis estimatedby repeating the analysisusingthe numberofclustersin the outer-most layer of the SPD and the number of tracks in the TPC as centralityestimators,insteadoftheV0signalamplitude. The sys-tematicuncertaintyduetotheeffectofTPCtracksfromdifferent Pb–Pbcollisions piled-upinthesamerecordedeventisestimated byapplyingatightercuttoremoveoutliersinthemultiplicity dis-tribution ofreferenceparticles.Thisisdone byrequiringthat the centralityvaluesdeterminedusingtheV0signalamplitudeandthe numberofTPCtracksdonotdifferbymorethan5%.Anadditional systematic uncertaintyspecific to the scalar product isevaluated by varying the
η
gapbetweenthe two sub-events from1to 0.8η
-units (see Eq. (4) and[36]). The various systematic uncertain-tiesareaddedinquadrature.TheytendtoincreasewithincreasingpT (see Fig. 1).Asummaryofthesystematicuncertainties,inthe
interval3
<
pT<
4.
5 GeV/
c,ispresentedinTable 1.Fig. 1showsthe pT-differentialmuonellipticflow(vμ2) inthe
0–10%, 10–20% and 20–40% centrality classes as obtained using thevariousmethods.Thevaluesofvμ2 slightlyincreasefrom cen-tral tosemi-central collisions andthiseffect ismorepronounced in the pT interval 3
<
pT<
4.
5 GeV/
c. The two-particlecorrela-tion methods(scalarproduct andtwo-particle Q cumulants)give consistent results over the whole pT range,indicating that these
methodshaveasimilarsensitivitytonon-floweffects3andin par-ticular to flow fluctuations. A similar agreement is found when comparingthemulti-particlecorrelation methods(four-particle Q
cumulantsandLee–Yangzeros)toeachother.Nosignificant differ-encebetweenthe vμ2 resultsextractedwithLee–Yangzerosusing either thesum orproduct generatingfunction is seen, hence in-dicating thatinterferencesbetweenharmonicsarenegligible [51]. Moreover, four-particle Q cumulants give comparable results as Lee–Yang zeros.The four-particle Q cumulants andLee–Yang ze-rosareexpectedtobelessaffectedbynon-floweffectsthanscalar productortwo-particle Q cumulants[52].However,asmentioned non-flow effects are expected to be negligible, even with two-particle correlation techniques, due to the large
η
between ref-erenceparticlesandinclusivemuons.Finally,thecentralvaluesofvμ2 obtainedwithfour-particleQ cumulantsorLee–Yangzerosare systematicallysmallerthanwithtwo-particlecorrelationmethods, althoughcompatiblewithinuncertainties.Suchdifferencesmay in-dicatethatinitialfluctuationsplayaroleinthedevelopmentofthe finalmomentum-spaceanisotropy.
3.4. Muonbackgroundsubtraction
The subtraction of the muon background contribution to the measured vμ2 requires an estimate of the elliptic flow of muons from charged pion and kaon decays, v2μ←π,K, and of the back-ground fraction, f μ←π,K (see Eq. (2)). The determination of the vμ2←π,K coefficient requires two steps. First, the pT- and
η
-differential v2 of charged particles measured in|
η
|
<
2.
5 bythe ATLAS Collaboration inPb–Pb collisions [53] andthe pT
dis-tributions of charged pions and kaons measured in
|
y|
<
0.
8 by3 Notethat,inthisanalysis,mostnon-flowcorrelationsaresuppressed,evenwith two-particlecorrelationmethodssincereferenceparticlesandinclusivemuonsare separatedbyatleast1.7 η-units.However,itisworthmentioningthatthemain differencebetweenthetwomethodsistheηgapbetweenthetwosub-samples usedtocomputeQ2(Eq.(4))whichalsoallowstopartlyremovenon-floweffects.
Table 1
Systematicuncertaintysourcesaffectingtheinclusivemuonellipticflowmeasurementinthe0–10%,10–20%and 20–40%centralityclassesfortheinterval3<pT<4.5 GeV/c.Theyaregivenasapercentageofthev2value.
vμ2 analysis Source Systematic uncertainty (%)
0–10% 10–20% 20–40% vμ2{SP} Reference particles 3 1 3 Centrality selection 6 1 4 TPC pile-up 2 4 2 ηgap 13 1 1 vμ2{2} Reference particles 13 3 2 Centrality selection 14 3 6 TPC pile-up 8 1 4 vμ2{4} Reference particles 10 Centrality selection 1 TPC pile-up 1
vμ2{LYZ-Sum} Reference particles 4
Centrality selection 7
TPC pile-up 2
vμ2{LYZ-Prod} Reference particles 2
Centrality selection 8
TPC pile-up 2
Fig. 1. pT-differentialinclusivemuonv2in2.5<y<4 andvariouscentralityintervals,inPb–Pbcollisionsat√sNN=2.76 TeV.Thesymbolsareplacedatthecentreofthe
pTintervaland,forvisibility,thepointsfromtwo-particleQ cumulantsandLee–Yangzeroswithproductgeneratingfunctionareshiftedhorizontally.Theverticalerrorbars representthestatisticaluncertainty,thehorizontalerrorbarscorrespondtothewidthofthebin(notshownfortheshifteddatapoints)andtheopenboxesarethesystematic uncertainties.ThepTintervalsusedwiththeLee–Yangzerosmethodaredifferentwithrespecttotheothermethods.Upperpanels:resultsfromtwo-particlecorrelationflow methods(scalarproductandtwo-particle Q cumulants)inthe0–10%(left)and10–20%(right)centralityintervals.Lowerpanels:resultsinthe20–40%centralityinterval fromtwo-particlecorrelationflowmethods(scalarproductandtwo-particleQ cumulants)andfromfour-particleQ cumulants(left),andfromfour-particleQ cumulants andLee–Yangzeros(right).
the ALICE Collaboration in pp and Pb–Pb collisions [54,55] are extrapolated to forward rapidity. Then, the pT distributions of
muons from charged pion and kaon decays, needed to estimate
f μ←π,Kandvμ←π,K
2 ,aregeneratedaccordingtoasimulation
tak-inginto accountthe decaykinematicsandtheeffectof thefront absorber.
The pT- and
η
-differentialelliptic flowof chargedparticles in|
η
|
<
2.
5,vch2 ,isextrapolatedtoforwardrapidityusing:
vch2
(
pT,
η
)
=
F(
η
)
·
vch2(
pT,2
<
|
η
| <
2.5), (9)where vch2
(
pT,
2<
|
η
|
<
2.
5)
is themeasured charged-particlethe vch2
(
pT)
measured by the ATLAS Collaboration is affected bystatistical fluctuations, it is assumed that in the interval 10
<
pT
<
20 GeV/
c,neededto simulatethedecaymuonsup to pT=
10 GeV
/
c, vch2 remains constant with a value given by the one
measured in the interval 10
<
pT<
12 GeV/
c. The extrapolationfactor F
(
η
)
iscalculated by parameterizingtheη
-differential vch2measuredbytheATLASCollaborationinvarious pT intervalswith
asecondorderpolynomial.Intheinterval7
<
pT<
20 GeV/
c,theATLAS vch2 doesnotshowa dependenceon
η
in|
η
|
<
2.
5. There-fore,for pT>
7 GeV/
c, F(
η
)
iscomputedastheaveragebetweenaflatextrapolationfunctionandtheextrapolationfactorobtained withtheparabolicparameterizationin4
<
pT<
7 GeV/
c.Themid-rapiditychargedpionandkaon pT distributions
mea-suredinPb–Pbcollisionsareextrapolatedtoforwardrapidityusing thesamestrategyasin[21]andsummarizedinthefollowing. As-sumingthatthenuclearmodificationfactorRπAA,K ofchargedpions andkaonsin Pb–Pbcollisions doesnot dependon rapidityup to
y
=
4[21,56],the pT distributionsofchargedpionsandkaons atforwardrapiditycanbeexpressedas:
dNPbPbπ,K dpTd y
=
TAA·
dσ
ppπ,K dpTd y· [
RπAA,K(
pT)
]
y=0,
(10)where
TAA is the average nuclear overlap function incentral-ity classesunder study, estimated asdescribed in [57]. The sys-tematic uncertainty introduced by the assumption on RπAA,K will be discussed later. The rapidity extrapolation ofthe mid-rapidity pionandkaon pT-differentialcrosssectionsmeasuredinpp
colli-sions[21,58]isdoneaccordingto:
d2
σ
ppπ,K dpTd y=
d2σ
ppπ,K dpTd y y=0·
exp−
y 2 2σ
2 y,
(11)σ
y beingestimated fromMonte-Carlo eventgenerators (see [21] fordetails).The elliptic flow of muons from charged pion and kaon de-cays, vμ2←π,K, in 2
.
5<
y<
4 and in various centrality classes,4is obtained by means of fast simulations using vch
2
(
η
,
pT)
givenby Eq. (9) and charged pion and kaon pT distributions as
ob-tained from Eqs. (10)–(11). The absorber effect is accounted for by rejectingthe pionsandkaonsthat donot decaywithin a dis-tancecorrespondingtoone interactionlengthfromthebeginning of the absorber. The simulation was repeated twice, considering thatchargedparticlesareeitherallpionsorallkaons.
Thebackground fraction, f μ←π,K,is calculatedastheratio of
thepT-differentialyieldofmuonsfromchargedpionandkaon
de-cays in 2
.
5<
y<
4 obtained in the simulation to the measuredpT-differentialyieldofinclusivemuons.
The systematic uncertainties affecting the estimated vμ2←π,K
aresummarizedinTable 2.Theyoriginatefromi)themethodused tomeasurethecharged-particle vch2 inATLAS,ii)the
η
andpTex-trapolation of vch2 and iii) the treatment of the charged-particle
vch2 inthe fastsimulation procedure. As theeventplane method was used for the vch2 measurement in ATLAS, the results range betweenthemean (
vch2)and R.M.S.((
vch2)
2) ofthe true vch 2
valuesdue tofluctuations, depending onthe eventplane resolu-tionwhichvarieswiththecollisioncentrality[49].Accordingtoa Monte-CarloGlaubermodel[49],theratio
v22/
v2isexpected 4 Thevμ←π,K2 ofmuonsfromchargedpionandkaondecaysinthe20–40% cen-tralityclassisthenobtainedfromthemeanofthecharged-particlev2in20–30% and30–40%centralityclasses,withanadditionalsystematicuncertaintyprovided bythedifferencewithrespecttotheresultsinthesetwocentralityclasses.
Table 2
Systematicuncertaintysourcesaffectingtheestimatedvμ2←π,Kfortheinterval3<
pT<10 GeV/c.Theyarestatedasapercentageofthev2 value.Thegivenrange reflectsthedependenceonthecollisioncentrality.
Source Systematic uncertainty (%)
Input vch 2 bias 9 vch 2 ηextrapolation 9–12 vch 2 high pTextrapolation 13–15 πand K in fast simulations <1
to varyfromabout1.06 to1.15.Consequently,a conservative sys-tematicuncertaintyof15%isappliedtoaccount forthisbiasand ispropagatedto v2μ←π,K.Thesystematicuncertaintyduetothe
η
extrapolation of vch2 is evaluated using severalfit functions(first
andthirdorderpolynomials,andGaussian function)intheregion
pT
<
7 GeV/
c, andfor larger pT values an additional systematicuncertaintyduetotheextrapolationprocedureisconsidered. The latter is determined by comparing the results obtainedwith the twoextrapolationfunctionsusedintheinterval pT
>
7 GeV/
c.Thesystematic uncertainty due to the assumption on vch
2 in the
re-gion pT
>
10 GeV/
c is estimatedby varying vch2 between0 andthevaluein10
<
pT<
12 GeV/
c inthefastsimulations.Suchun-certaintyaffectsmainlythehighpT region(pT
>
7 GeV/
c).Finally,the systematicuncertainty obtainedby treating charged particles separately aspionsandkaonsisfound tobenegligible.The vari-oussystematicuncertaintysourcesarepropagatedtotheestimated
vμ2←π,Kandaddedinquadrature.
The systematic uncertainty on f μ←π,K, detailed in [21],
in-cludestheuncertaintyonthegenerated pTdistributionsofmuons
from charged pionand kaon decays,and the uncertainty on the measured inclusivemuon pT distributions. The former originates
from theinput chargedpion andkaon distributions, therapidity extrapolation andthe absorber effect.The systematicuncertainty on the measured inclusive muon yields contains the systematic uncertaintyondetectorresponse,residualmis-alignmentand cen-trality dependenceof the efficiency.This givesa total systematic uncertainty on f μ←π,K of about 21% in the interval 3
<
pT<
4
.
5 GeV/
c withalmost nodependenceonthecollision centrality. Finally, asdone forthe measurement of theheavy-flavour decay muon RAA [21], the systematic uncertainty dueto the unknownsuppression of chargedparticles at forwardrapidity is calculated by varying f μ←π,K from 0 to two times the estimated value.
This corresponds to a variation of RAAπ,K
(
pT)
at forward rapidityfrom0uptotwotimes
[
RπAA,K(
pT)
]
y=0.Thissystematicuncertaintyamountsto10–30%intheinterval3
<
pT<
4.
5 GeV/
c,dependingonthecollisioncentralityandtheflowanalysismethod.
Fig. 2presentstheestimatedbackgroundellipticflow(vμ2←π,K, left)andbackgroundfraction( f μ←π,K,right)asafunctionofp
Tin
the0–10%,10–20%and20–40%centralityclasses.Theopenboxes representthesystematicuncertaintiespreviouslydiscussed,except forthesystematicuncertaintyduetotheunknownsuppressionof charged particles atforward rapidity which is treatedseparately. The estimated vμ2←π,K and f μ←π,K decrease withincreasing p
T.
Adecreasingtrendofthemagnitudeofvμ2←π,Kfromsemi-central collisionstowardscentralcollisionsisalsoobserved.
Finally,thesystematicuncertaintyontheellipticflowofmuons fromheavy-flavourdecays,vμ2←HF,containstwocontributions:the systematic uncertainties on vμ2, v2μ←π,K and f μ←π,K propagated
accordingtothedefinitionofv2μ←HF giveninEq.(2),andthe sys-tematic uncertainty due to the unknown suppression of charged particles atforward rapidity. The final systematic uncertainty on
Fig. 2. Estimatedbackgroundv2(vμ2←π,K,left)andbackgroundfraction( fμ←π,K,right)asafunctionofpTin2.5<y<4 andvariouscentralityintervals,inPb–Pbcollisions at√sNN=2.76 TeV.ThesymbolsareplacedatthecentreofthepTintervaland,forvisibility,thepointsforthecentralityclasses10–20%and20–40%areshiftedhorizontally. Thehorizontalerrorbarscorrespondtothewidthofthebin(notshownfortheshiftedvalues)andtheopenboxesarethesystematicuncertainties.Seethetextfordetails.
Fig. 3. pT-differentialellipticflowofmuonsfromheavy-flavourdecays,vμ2←HF,in2.5<y<4 andvariouscentralityintervals,inPb–Pbcollisionsat √s
NN=2.76 TeV.The symbolsareplacedatthecentreofthepTintervaland,forvisibility,thepointsfromtwo-particleQ cumulantsandLee–Yangzeroswithproductgeneratingfunctionare shiftedhorizontally.ThemeaningofthesymbolsisthesameasinFig. 1.Thehorizontalerrorbarsarenotplottedforshifteddatapoints.ThepTintervalsusedwiththe Lee–Yangzerosmethodaredifferentwithrespecttotheothermethods.Upperpanels:resultsfromtwo-particlecorrelationflowmethods(scalarproductandtwo-particle Q cumulants)inthe0–10%(left)and10–20%(right)centralityintervals.Lowerpanels:resultsinthe20–40%centralityintervalfromtwo-particlecorrelationflowmethods (scalarproductandtwo-particle Q cumulants)andfromfour-particleQ cumulants(left),andfromfour-particleQ cumulantsandLee–Yangzeros(right).Seethetextfor details.
Itamountsto about12%–36%inthe interval3
<
pT<
4.
5 GeV/
c,dependingonthecollisioncentralityandtheflowanalysismethod.
4. Results
Fig. 3 presentsthe pT-differential ellipticflow ofmuons from
heavy-flavourhadrondecays, vμ2←HF, calculatedwithEq.(2).The resultsareshownforthe0–10%(upper,left),10–20%(upper,right) and20–40%(bottom)centralityclassesusingthesameflow meth-ods as for the measurement of the inclusive muon elliptic flow
(Fig. 1). When comparing the results to those obtained for in-clusive muons (Fig. 1), one can notice that vμ2←HF and vμ2 are similarduetothesmallbackgroundfraction(5%to15%)inthe pT
interval 3–10 GeV
/
c. The differences betweenthe various meth-ods are similar to those discussed for the measurement of the inclusive muon vμ2 i.e. i) scalar product and two-particle Qcu-mulants give compatible results, ii) consistent results are also found with four-particle Q cumulants and Lee–Yang zeros, and iii) the vμ2←HF values extracted from these multi-particle corre-lation methods are smaller, although still compatible within
un-Fig. 4. Ellipticflow ofmuonsfromheavy-flavourhadron decaysas afunctionofthe collisioncentralityin2.5<y<4 and3<pT<5 GeV/c,inPb–Pbcollisionsat √
sNN=2.76 TeV.Theresultsareobtainedwithscalarproductandtwo-particle Q cumulants.Verticalbars(openboxes)representthestatistical(systematic)uncertainty, thehorizontalerrorbarscorrespondtothewidthofthecentralitybin.Forvisibility,thepointsfromscalarproductareshiftedhorizontallyandthehorizontalerrorbarsare notplotted.
certainties, than the ones obtained with two-particle correlation methods. As mentioned in Section 3.3, such differences are ex-pectedif initial-statefluctuationsplay a role inthe development ofthefinalmomentum-spaceanisotropy.
Apositivevμ2←HFisobservedatintermediatepTforthe20–40%
and10–20% centrality classeswith a significancelarger than 3
σ
when combining statistical and systematic uncertainties. In the 20–40% centrality class, the values of the significance in the in-terval 3
<
pT<
4 GeV/
c (4<
pT<
5.
5 GeV/
c) are4σ
(3.
2σ
) and4
.
3σ
(3.
8σ
) with scalar product and two-particle Q cumulants,respectively. In the 10–20% centrality class and in the interval 3
<
pT<
4.
5 GeV/
c, the valuesof the significancecorrespond to4
.
4σ
bothwithscalarproductandtwo-particle Q cumulants.This behavior resultsfromtheinterplay betweenthesignificant inter-actionofheavyquarkswiththeexpandingmedium andthe path-length dependenceofin-medium partonenergyloss [29,30].Thevμ2←HF ofmuonsfromheavy-flavourhadrondecaysdecreaseswith increasingpTandbecomescompatiblewithzerointhehighpT
re-gion.
Fig. 4shows the centrality dependenceof the ellipticflow of muonsfromheavy-flavourhadrondecaysintheinterval3
<
pT<
5 GeV
/
c.Itisinvestigatedwithscalarproductandtwo-particle Qcumulants,whichcanbeappliedinawiderevent-multiplicity(i.e. centrality)intervalcomparedtomulti-particlecorrelationmethods. Asignificant decrease ofthe v2 magnitude towardscentral
colli-sionsisobserved.Thisisexpectedfromthedecreaseoftheinitial spatialanisotropyfromsemi-centraltocentralcollisions.
ALICEhas measured the ellipticflow of prompt Dmesons in
|
y|
<
0.
8 in three centrality classes in the interval 0–50% with varioustwo-particlecorrelationmethods[33,34].Similartrendsas thosereportedhereformuonsfromheavy-flavourdecaysare ob-served,althoughindifferentpTandrapidityintervals.Inparticular,apositive v2wasobservedforDmesonsinsemi-centralcollisions
in2
<
pT<
6 GeV/
c withasignificanceof5.
7σ
.Thepositive ellipticflow ofmuonsfromheavy-flavourhadron decayshasbeenobservedina pTintervalfrom3toabout5 GeV/c
where the charm contribution is expected to be dominant with respect to the beautycomponent according to perturbative QCD calculations[21].Thismeasurementsupportstheinterpretationof theJ
/ψ
positive v2 atforwardrapidity [35]interms ofasignifi-cantcontributiontoJ
/ψ
productionfromrecombinationofflowing charmquarksinthedeconfinedmedium.5. Comparisonwithmodels
The resultspresented in this publication may constrain mod-els describing theinteractions ofheavy quarks withthemedium via elastic (collisional) and inelastic (radiative) processes, and in particular the partonenergyloss dependenceon the path-length withinthemedium.
The ellipticflow coefficient and the nuclear modification fac-tor of muons from heavy-flavour hadron decays [21] are com-paredtothefollowingthreemodels.TheMC@sHQ
+
EPOS trans-port 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 atlow pTand fragmentation at intermediate and high pT. 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 pT spectraandelliptic flow dataoflight-flavour hadrons. The
hadronization is modeled including a component of recombina-tion of heavy quarks with light-flavourhadrons in the QGP. The diffusionofheavy-flavourmesonsinthehadronicphaseisalso in-cluded.BAMPS[63–65]isapartonictransportmodelbasedonthe Boltzmann approachto multi-partonscatterings. Itincludes colli-sionalprocesseswitharunningstrongcouplingconstant.Thelack of radiative contributions is accounted for by scaling the binary cross section witha correction factor, tuned to describe the nu-clearmodificationfactorandellipticflowresultsatRHICenergies. Vacuumfragmentationfunctionsareusedforthehadronization.
Fig. 5 shows a comparison of the three models with the measurement of the pT-differential elliptic flow of muons from
heavy-flavour hadron decays in the 20–40% centrality class (up-per panel) and of the pT-differential nuclear modification factor
of muons from heavy-flavour hadron decays in the 0–10% cen-tralityclass [21] (lower panel).Inthe interval 3
<
pT<
5 GeV/
c,theBAMPS modeldescribesthe vμ2←HF datawithin uncertainties, while the TAMU andMC@sHQ
+
EPOS models give vμ2←HF values lower than thedata. The three models describe the vμ2←HF data athigher pT,althoughthesizeable experimentaluncertaintiesaf-fectthesignificanceofthecomparison.TheBAMPSmodeltendsto slightly underestimate the RAA of muons fromheavy-flavour
Fig. 5. Upperpanel:pT-differentialellipticflowofmuonsfromheavy-flavourhadron decaysin2.5<y<4,inPb–Pb collisions at √sNN=2.76 TeV for the central-ityclass20–40% compared tovarious transportmodel predictions:MC@sHQ + EPOS[59–61],TAMU[62]andBAMPS [63–65].TheTAMU modelis shownwith atheoretical uncertaintyband.Lowerpanel: pT-differential RAA ofmuonsfrom heavy-flavourhadrondecaysforthecentralityclass0–10%from[21]comparedto thesamemodelsasforvμ2←HF.
model tends to overestimate it. The TAMU model describes the
RAA measurement over the entire pT interval within
uncertain-ties. These comparisons indicate that it is challenging to simul-taneouslydescribethestrongsuppressionofhigh-pT muonsfrom
heavy-flavourhadrondecaysincentralcollisionsandtheazimuthal anisotropy in semi-central collisions. Similar trends are also ob-servedinthemid-rapidityregionfromthecomparisonoftheRAA
andv2ofDmesonswithmodelcalculations[34]. 6. Conclusions
Insummary,wehavereportedonameasurementoftheelliptic flowofmuonsfromheavy-flavourhadrondecaysatforward rapid-ityincentralandsemi-centralPb–Pbcollisionsat
√
sNN=
2.
76 TeVwiththeALICEdetectorattheLHC.
Measurements have been carried out using several methods whichexhibit differentsensitivity toinitial-statefluctuations and non-flow correlations. The systematiccomparison of scalar prod-uct,two- andfour-particleQ cumulantsandLee–Yangzeroshelps inunderstandingtheprocesses thatbuild upthe observed differ-encesbetweentwo-particlecorrelationmethodsandmulti-particle correlationmethodsandsuggeststhatflowfluctuationsare signif-icant.
Themagnitudeoftheellipticflowofmuonsfromheavy-flavour hadrondecaysincreasesfromcentraltosemi-centralcollisionsand
decreases with increasing pT, becoming compatiblewith zero at
highpT. Theresultsindicateapositiveellipticflowwiththescalar
product and two-particle Q cumulants in semi-central collisions (10–20%and20–40%centralityclasses)forthe pT intervalfrom3
to about5 GeV/c with asignificance larger than 3
σ
. The elliptic flow in semi-central collisions and the previously published nu-clear modification factorin the 10% most central collisions were compared with transport model calculations. These comparisons show that a simultaneous description of RAA and v2 over thewhole pTintervalremainsachallenge.Theresultsreportedinthis
Letter invariouscentralityclassesmayprovidefurther important constraintstothemodels.
Acknowledgements
The ALICE Collaboration would like to thank all its engineers andtechniciansfortheir invaluablecontributions tothe construc-tionoftheexperimentandtheCERNacceleratorteamsforthe out-standingperformanceoftheLHCcomplex.TheALICECollaboration gratefully acknowledges the resources and support provided by all Gridcentres andtheWorldwide LHC ComputingGrid (WLCG) collaboration. The ALICE Collaboration acknowledges the follow-ing funding agencies for their support in building and running theALICEdetector:StateCommittee ofScience,WorldFederation of Scientists (WFS)and SwissFonds Kidagan, Armenia; Conselho Nacional de DesenvolvimentoCientífico e Tecnológico (CNPq), Fi-nanciadorade Estudos eProjetos(FINEP),Fundação de Amparoà Pesquisa do Estado de São Paulo (FAPESP); National Natural Sci-enceFoundation ofChina (NSFC), theChinese Ministryof Educa-tion(CMOE)andtheMinistryofScienceandTechnologyofChina (MSTC); Ministry of Education andYouth ofthe Czech Republic; Danish Natural Science Research Council, the Carlsberg Founda-tion andthe DanishNationalResearch Foundation;TheEuropean ResearchCouncilundertheEuropeanCommunity’sSeventh Frame-work Programme; Helsinki Institute of Physics andthe Academy of Finland; French CNRS-IN2P3, the ‘Region Pays de Loire’, ‘Re-gion Alsace’, ‘Region Auvergne’ and CEA, France; German Bun-desministerium für Bildung, Wissenschaft, Forschung und Tech-nologie(BMBF)andtheHelmholtzAssociation;GeneralSecretariat forResearchandTechnology,MinistryofDevelopment,Greece; Na-tionalResearch,DevelopmentandInnovationOffice(NKFIH), Hun-gary;DepartmentofAtomicEnergyandDepartmentofScienceand TechnologyoftheGovernmentofIndia;IstitutoNazionalediFisica Nucleare(INFN) and CentroFermi –Museo Storico dellaFisica e CentroStudieRicerche“EnricoFermi”,Italy;JapanSocietyforthe PromotionofScience(JSPS)KAKENHIandMEXT,Japan;Joint Insti-tuteforNuclearResearch,Dubna;NationalResearchFoundationof Korea(NRF); ConsejoNacionaldeCiencayTecnologia(CONACYT), Direccion General de Asuntos del Personal Academico (DGAPA), México,AmeriqueLatineFormationacademique–European Com-mission (ALFA-EC) and the EPLANET Program (European Particle PhysicsLatinAmericanNetwork);StichtingvoorFundamenteel On-derzoekder Materie(FOM)andtheNederlandseOrganisatievoor WetenschappelijkOnderzoek(NWO),Netherlands; Research Coun-cilof Norway(NFR); NationalScienceCentre, Poland;Ministryof NationalEducation/InstituteforAtomicPhysicsandNational Coun-cil of Scientific Research in Higher Education (CNCSI-UEFISCDI), Romania;MinistryofEducationandScienceofRussianFederation, Russian Academy of Sciences, Russian Federal Agency of Atomic Energy, Russian Federal Agency for Science and Innovations and The RussianFoundation forBasicResearch;Ministry ofEducation ofSlovakia; Departmentof ScienceandTechnology, SouthAfrica; Centro de Investigaciones Energeticas, Medioambientales y Tec-nologicas (CIEMAT), E-Infrastructure shared between Europe and Latin America (EELA), Ministerio de Economía y Competitividad
(MINECO) of Spain, Xunta de Galicia (Consellería de Educación), Centro de Aplicaciones Tecnológicas y Desarrollo Nuclear (CEA-DEN), Cubaenergía, Cuba, and IAEA (International Atomic Energy Agency);SwedishResearchCouncil(VR)andKnut& Alice Wallen-berg Foundation (KAW); Ukraine Ministry of Education and Sci-ence; United Kingdom Science and Technology Facilities Council (STFC);TheUnitedStatesDepartmentofEnergy,theUnitedStates NationalScience Foundation, the State of Texas,and theState of Ohio; Ministry of Science, Education and Sports of Croatia and Unity throughKnowledge Fund, Croatia; Council ofScientific and IndustrialResearch(CSIR),NewDelhi,India;PontificiaUniversidad CatólicadelPerú.
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