Transverse-momentum and event-shape dependence of D-meson flow harmonics in Pb–Pb collisions at $\sqrt {s_{NN}}$ = 5.02 TeV

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Transverse-momentum and event-shape dependence of

D-meson flow harmonics in Pb–Pb collisions at

√

s_N N

= 5.02 TeV

Shreyasi Acharya, Dagmar Adamova, Alexander Adler, Jonatan Adolfsson,

Madan Mohan Aggarwal, Gianluca Aglieri Rinella, Michelangelo Agnello,

Neelima Agrawal, Zubayer Ahammed, Shakeel Ahmad, et al.

To cite this version:

Shreyasi Acharya, Dagmar Adamova, Alexander Adler, Jonatan Adolfsson, Madan Mohan

Ag-garwal, et al..

Transverse-momentum and event-shape dependence of D-meson flow harmonics

in Pb–Pb collisions at

√

s_N N = 5.02 TeV. Physics Letters B, Elsevier, 2021, 813, pp.136054.

Contents lists available atScienceDirect

Physics

Letters

B

www.elsevier.com/locate/physletb

Transverse-momentum

and

event-shape

dependence

of

D-meson

flow

harmonics

in

Pb–Pb

collisions

at

√

s

NN

=

5.02 TeV

.

ALICE

Collaboration



a

r

t

i

c

l

e

i

n

f

o

a

b

s

t

r

a

c

t

Articlehistory:

Received13September2020

Receivedinrevisedform20November2020 Accepted22December2020

Availableonline29December2020 Editor:M.Doser

The elliptic and triangular flow coefficients v2 and v3 of prompt D0, D+, and D∗+ mesons were measuredatmidrapidity(|y|<0.8)inPb–Pbcollisionsatthecentre-of-massenergypernucleonpairof √_s

NN=5.02 TeV withtheALICEdetectorattheLHC.TheDmesonswerereconstructedviatheirhadronic

decays inthe transverse momentuminterval 1<pT<36 GeV/c in central (0–10%)and semi-central (30–50%)collisions.Comparedtopions,protons,and J/ψ mesons, theaverageD-meson vn harmonics arecompatiblewithinuncertaintieswithamasshierarchyforpT3 GeV/c,andaresimilartothoseof charged pions forhigher pT.The coupling ofthe charm quark to the lightquarks inthe underlying medium is further investigated with the application of the event-shape engineering (ESE)technique totheD-meson v2and pT-differential yields.TheD-meson v2 iscorrelatedwithaveragebulkelliptic flowinbothcentralandsemi-centralcollisions.Withinthecurrentprecision,theratiosofper-event D-mesonyieldsintheESE-selectedandunbiasedsamplesarefoundtobecompatiblewithunity.Allthe measurementsarefoundtobereasonablywelldescribedbytheoreticalcalculationsincludingtheeffects ofcharm-quarktransportandtherecombinationofcharmquarkswithlightquarksinahydrodynamically expandingmedium.

©2020TheAuthor(s).PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense (http://creativecommons.org/licenses/by/4.0/).FundedbySCOAP3_.

1. Introduction

Theformationofastronglycoupledcolour-deconfinedmedium inultra-relativisticheavy-ioncollisions,calledquark–gluonplasma (QGP), hasbeenestablished bothatRHIC andLHC energies [1,2]. TheQGPbehavesasanear-perfectfluidwithsmallshearviscosity overentropydensityratio,

η

/

s,undergoinganexpansionthat can bedescribedbyrelativistichydrodynamics [3].

In heavy-ion collisions, heavy quarks (charm and beauty) are predominantly produced via hard-scattering processes on a time scale shorter than the QGP formation time [4,5], and therefore they experience all the stages of the system evolution, interact-ingwiththemediumconstituentsviabothelastic(collisional) [6] andinelastic (gluonradiation) [7–9] processes.The measurement ofthesuppressionoftheyieldofheavy-flavourhadronsincentral nucleus–nucleus collisions relative to pp collisions scaled by the number of nucleon–nucleon collisions at both RHIC [10–14] and LHCenergies [15–21] providescompellingevidenceofheavy-quark energylossindeconfinedstronglyinteractingmatter.

AdditionalinsightsintotheQGPpropertiescanbeobtainedby measuring the azimuthal anisotropy of heavy-flavourhadrons. In non-centralnucleus–nucleuscollisionstheinitialspatialanisotropy

 _{E-mailaddress:alice-publications@cern.ch.}

of the overlap region is converted via multiple interactions into anazimuthallyanisotropicdistributioninthemomentumspaceof theproduced particles [22,23].This anisotropyis characterisedin termsof theFourier coefficients vn

= 

cos

[

n

(

ϕ

− 

n

)

]

, where

ϕ

istheazimuthalangleoftheparticleand



n istheazimuthal

an-gleofthesymmetryplaneforthenth-order harmonic [23,24].The valuesofthe Fouriercoefficientsdepend on thegeometry ofthe collision,thefluctuationsinthedistributionsofnucleonsand glu-onswithinthenuclei [25],andthedynamicsoftheexpansion.The second order flow coefficient v2,called ellipticflow, is relatedto

the almond-shaped geometry of the overlap region betweenthe colliding nuclei and, consequently, is the largest contribution to theanisotropy innon-central collisions.The thirdharmonic coef-ficient v3, named triangularflow, originates from event-by-event

fluctuations in the initial distribution of nucleons andgluons in theoverlapregion [26].Inparticular,themeasurementofthe az-imuthal anisotropy ofheavy-flavour hadrons at low pT can help

quantify the extent to which charm and beauty quarks partici-pate in the collective expansion of the medium [27], as well as thefraction ofheavy-flavourhadrons hadronising via recombina-tion with flowing light quarks [28,29]. At high pT, instead, the

charmhadronazimuthalanisotropy canconstrainthepath-length dependenceofheavy-quarkin-mediumenergyloss [30,31].Precise measurements ofheavy-flavour vn coefficientsare usefulto

con-https://doi.org/10.1016/j.physletb.2020.136054

ALICE Collaboration Physics Letters B 813 (2021) 136054

strain the parametersof modelsthat implementthe heavy-quark transport intheQGP. Inthiscontext,theheavy-quarkspatial dif-fusion coefficient Ds in the QGP is particularlyinteresting, since

itisrelatedtotherelaxation(equilibration)timeofheavy quarks

τ

Q

= (

mQ

/

T

)

Ds,wheremQisthequarkmassandT isthemedium

temperature [32].

Furtherinvestigationintothedynamicsofheavy quarksinthe mediumcanbeperformedwiththeevent-shapeengineering(ESE) technique [33],whichallowsforselectionofeventswiththesame centralitybutdifferentinitialgeometryonthebasisofthe magni-tude ofthe average bulkflow. Infact, hydrodynamic calculations show that the average flow of the bulk of soft hadrons is pro-portionaltotheinitial-stateeccentricities [34] forsmallvaluesof

η

/

s [3,35,36].By classifyingthe eventswiththeESE technique it is possibletoinvestigate thecorrelation betweentheflow coeffi-cients of Dmesons andsoft hadrons. According to the available calculations [34,37,38], the initial system ellipticity is converted into parton flow with a similar efficiency for bulk and charm quarks, despite the different production mechanisms, dynamics, andhadronisation ofheavy quarks andlight partonsforming the bulk ofthe medium.Moreover,themeasurement oftheD-meson spectra in eventswith differentaverage eccentricity provides in-formation about the possible correlation betweenthe radial and ellipticflowsatlow-intermediatepT,andthecharm-quarkenergy

lossandtheellipticflowathighpT.Thecorrelationwiththeradial

flowisexpectedtobepresentfromtheobservationofthescaling oftheflowharmonicswiththeparticlemass [39],whilethe corre-lationwiththein-mediumenergylosswouldbemotivatedbythe differentpathtraversedbythecharmquarkinthemediuminthe caseofanisotropicoraneccentricsystem.

A positive D-meson v2 is observed at both RHIC [10,40,41]

and the LHC [42–48]. The comparison of the D-meson v2 with

thecharged-pion v2andwiththeoreticalmodels [49–57] indicates

that charm quarks participate in the collective expansion of the mediumandthatbothcollisionalprocessesandtherecombination ofcharmandlightquarkscontribute totheobservedellipticflow. Furthermore, a positive D0-meson v3 was measured by the CMS

Collaboration [47].The pT-differentialyields and v2 ofDmesons

weremeasuredbytheALICECollaborationinsamplesofevents se-lected onthebasis oftheaverage bulkellipticflow withtheESE technique [48].AcorrelationbetweentheD-mesonv2 andthe v2

ofthe bulk oflighthadronswas observed, whiletheratio ofthe

pT-differential yields in ESE-selected samplesto the yields

mea-suredwithoutanyESEselectionwas foundtobecompatiblewith unitywithinthelargeuncertainties.

In this Letter, the measurement of the non-strange D-meson flowharmonicsperformedonalargesampleofPb–Pbcollisionsat

√

sNN

=

5

.

02 TeVcollected byALICEin2018isreported.Withthis

datasample,theD-meson v2 ismeasuredwiththeScalarProduct

(SP) methodin an extended pT intervaland withsmaller

uncer-tainties with respect to the previous results obtained with the EventPlane (EP)methoddescribed in [46,48] inthe30–50% cen-tralityclass.TheresultsobtainedwiththeSPandtheEP method were found to be compatiblebetweeneach other,as reportedin previous publications [43]. The measurement of the D-meson v2

coefficient inthe 0–10% centralityclass and v3 coefficientin the

0–10% and 30–50% centrality classes are also presented. In ad-dition, the measurement of the v2 and the modification of the pT distributions in the ESE-selected samples is reported in

nar-rowerclassesofthe averageeventflowwithrespect to [48]. The measurementsarecomparedtotheoreticalcalculationsinorderto assess informationaboutthe participationof thecharm quark in the collective motionofthe systemandits interactions with the QGPconstituents.

2. Detectoranddatasample

AdetaileddescriptionoftheALICEapparatusanddata acquisi-tionframeworkcan befoundin [58,59]. Themaindetectorsused forthisanalysisaretheInnerTrackingSystem(ITS) [60],theTime Projection Chamber (TPC) [61], and the Time-Of-Flight (TOF) de-tector [62]. The ITSis asix-layer silicondetectorwhich provides theevent selection,the reconstruction of primary andsecondary vertices, and the tracking of charged particles. The TPC detector isusedforthetrackreconstruction andtheparticleidentification (PID)viathemeasurementofthespecificenergylossdE

/

dx,while theTOF detector provides PIDvia the measurement ofthe flight timeoftheparticles.Thesedetectorsarelocatedinsideasolenoid providing a uniform magnetic field of 0.5 T parallel to the LHC beam direction and cover the pseudorapidity interval

|

η

|

<

0.9. A minimum-bias interaction trigger was provided by the coinci-dence of signals in the two scintillator arrays of the V0 detec-tor [63], covering the full azimuth in the pseudorapidity regions

−

3

.

7

<

η

<

−

1

.

7 (V0C) and2

.

8

<

η

<

5

.

1 (V0A).Anonline selec-tionbasedontheV0signalamplitudeswasappliedinorderto en-hancethesampleofcentralandmid-centralcollisionsthroughtwo separate triggerclasses.Background eventsfrombeam–gas inter-actionswereremovedofflineusingthetimeinformationprovided by the V0and the neutron Zero-Degree Calorimeters (ZDC) [64]. Onlyeventswith aprimary vertexreconstructedwithin

±

10 cm fromthecentreofthedetectoralong thebeamlinewere consid-eredintheanalysis.

Eventsweredividedintocentralityclasses,definedintermsof percentilesofthe hadronicPb–Pb crosssection, usingthe ampli-tudesofthesignalsintheV0arrays.Thenumberofeventsineach centrality class considered for this analysis (0–10% and 30–50%) isabout100

×

106 and85

×

106,corresponding to an integrated luminosityof



130 μb−1 and



56 μb−1,respectively [65].In or-dertoapplytheESEtechnique,theeventsineach centralityclass were further divided into samples withdifferent average elliptic anisotropy offinal-state particles,selected accordingto the mag-nitudeofthesecond-orderharmonicreducedflowvectorq2 [36],

definedas

q2

= |

QQQ2

|/

√

M

,

(1)

whereM isthenumberoftracksusedinthe

|

QQQ2

|

calculation

se-lectedasdescribedbelow,and

QQQ2

=

M



k=1

ei2ϕk ₍₂₎

isavectorbuiltfromtheazimuthalangles(

ϕ

k)oftheconsidered

particles. The QQQ2 vector was measured using charged tracks

re-constructedinthe TPCwith

|

η

|

<

0

.

8 and 0

.

2

<

pT

<

5 GeV

/

c to

exploit the

ϕ

resolution ofthe TPC andthe large multiplicity at midrapidity, which are crucial to maximise the selectivity of q2

withrespect to the final state flow eccentricity [48,66]. The de-nominator inEq. (1) is introduced to remove the dependenceof

|

QQQ2

|

on

√

M intheabsenceofflow [36].Thetracksusedtoform the D-meson candidateswere excluded fromthe computation of

q2 topartiallyremoveautocorrelationsbetweenDmesonsandq2.

TheeffectofresidualautocorrelationsbetweentheDmesonsand

q2 was studied in [48] by computingq2 fromtheazimuthal

dis-tributionofthe energydeposition measured intheV0Adetector, andhenceintroducingapseudorapiditygapoftwounitsbetween theDmesonsandq2.The v2 valuesobtainedwiththe q2

repeatedforthedatasample usedforthisanalysis, leadingtothe sameconclusions.

The selection of the events according to the average elliptic flow of the event was performed by defining q2 percentiles in

1%-widecentralityintervalsasdescribedin [48] and [67] toavoid theintroduction ofbiasesinthecentrality(multiplicity) distribu-tionoftheselectedevents.TheESE-selectedclassesdefinedforthe analyses presentedinthispapercorrespond tothe20% ofevents with smallest and largest q2, respectively, and will be indicated

as“small-q2”and“large-q2”.IncaseofnoESEselection,theterm

“unbiased”willbeused. 3. Analysistechnique

Thecharmedmesonswerereconstructedatmidrapidityviathe decay channels D0

_→

_K−

_π

+ _{(with branching ratio, BR}

₌

₃

_.

₈₉

_±

0

.

04%), D+

→

K−

π

+

π

+ (BR

=

8

.

98

±

0

.

28%), and D∗+

→

D0

_π

+

(BR

=

67

.

7

±

0

.

5%) and their charge conjugates [68]. D0 _and

D+ candidates were built combining pairs and triplets of tracks with the proper charge, pT

>

0

.

4 GeV

/

c,

|

η

|

<

0.8, a fit quality

χ

2_/ndf

_<

_{2 in the TPC (where ndf is the number of degrees of}

freedom involved in the track fit procedure), at least 70 (out of 159) associatedspacepoints intheTPC, andaminimumnumber oftwohitsintheITS,withatleastoneinthetwoinnermost lay-ers.D∗+candidateswereformedbycombiningD0_{candidateswith}

low-pTtracks,referredtohereas“softpions”,whichwererequired

to have pT

>

0.1 GeV

/

c,

|

η

|

<

0.8, andat least three associated

hitsin theITS. These selectionslimitthe D-meson acceptancein rapidity,which drops tozero for

|

y

|

>

0

.

6 for pT

=

1 GeV

/

c and

|

y

|

>

0

.

8 for pT

>

5 GeV

/

c. A pT-dependent fiducial acceptance

cut,

|

yD

|

<

yfid

(

pT

)

, was therefore applied, defined as a

second-orderpolynomial functionincreasingfrom0.6to0.8intherange 1

<

pT

<

5 GeV

/

c,andfixedto0.8forpT

>

5 GeV

/

c.

The D-meson candidate selection approach adoptedto reduce the combinatorial backgroundis similar to that used inprevious analyses [43,46].Theanalysisproceduresearchesfordecayvertices displacedfromtheprimaryvertex,exploitingthemeanproper de-cay lengths of about 123 and 312 μm for D0 and D+ mesons, respectively [68].Thevariablesmainlyusedtodistinguishbetween signalandbackgroundcandidatesarebasedontheseparation be-tween the primary and decay vertices, the displacement of the tracksfromtheprimary vertex, andthepointingangleofthe re-constructed D-meson momentum to the primary vertex, and are the sameasdescribed in [21,69].In thestrong decayoftheD∗+ mesonthe primary vertexcannot be differentiated fromthe sec-ondary vertex. Therefore the geometrical selectionswere applied onthesecondaryvertextopologyoftheproducedD0mesons.The optimisationoftheselectioncriteriaforeachD-mesonspecieswas performedasafunctionofpT andindependentlyforthetwo

cen-tralityclasses.Furtherreduction ofthe combinatorialbackground wasobtainedbyapplyingPIDforthedaughtertrackswiththeTPC and TOF detectors.A selection in units ofresolution (

±

3

σ

) was appliedonthedifferencebetweenthemeasuredandexpected sig-nals of pions and kaons for both dE

/

dx and time-of-flight. The same selections are applied both forthe unbiased and the ESE-selectedmeasurements.

TheD-mesonellipticandtriangularflowcoefficients,v2 andv3,

were measured using the Scalar Product(SP) method [36,70,71]. ForeachD-mesoncandidate,thevn coefficientscanbe expressed

intermsofthe Qnvectors,introducedinSec.2,as

vn

{

SP

} = 

uuun

·

Q Q QA_n∗ MA











_





QQQAn MA

·

Q Q QBn∗ MB



Q QQAn MA

·

Q Q QCn∗ MC





QQQBn MB

·

Q Q QCn∗ MC



,

(3)

where un

=

einϕD istheunitflowvectoroftheD-mesoncandidate

withazimuthalangle

ϕ

Dandthesymbol“*” denotesthecomplex

conjugation.The denominatoris calledthe resolution(Rn) andis

calculated withthe formulaintroduced in [36], where the three subevents, indicated as A, B, andC, are defined by the particles measuredinthe V0C,V0A,andTPCdetectors,respectively. QQQk

nis

thesubeventflowvectorcorrespondingtothenth-order harmonic forthe subevent k, and Mk _{represents the subevent multiplicity.}

This is defined as the sum of the amplitudes measured in each channelfortheV0AandtheV0C.FortheV0AandV0Cdetectors, the Qnvectorswerecalculatedfromtheazimuthaldistributionof

theenergydeposition,andtheircomponentsaregivenby

Q_nV0A or V0C_,x

=

N



sectors k=1 wkcos

(

n

ϕ

k

),

Q_nV0A or V0C_,y

=

N



sectors k=1 wksin

(

n

ϕ

k

),

(4)

wherethe sumruns over the32 sectors(Nsectors) ofthe V0A or

V0Cdetector,

ϕ

k isthe azimuthal angleofthe centreof the

sec-tor k, and wk is the amplitude measured in sector k, once the

gainofthesingle channelsisequalisedandtherecenteringis ap-pliedtocorrecteffectsofnon-uniformacceptance [72].FortheTPC detector,the Qn vectorswerecomputedusingEq. (2).The single

bracket



inEq. (3) refers toanaverageoveralltheevents,while the double brackets



denote the average over all particles in theconsidered pT intervalandall events.The Rnisobtainedasa

functionofthecollisioncentrality.

The vn of the D mesons cannot be directly measured using

Eq. (3) asD0_,D+_,andD∗+ _{cannot beidentified ona}

particle-by-particlebasis. Therefore,a simultaneous fit tothe invariant-mass spectrum and the vtot

n distribution as a function of the

invari-ant mass (MD) was performed in each pT interval for D0 and

D+ candidates separatelyin ordertomeasure therawyields and theflowcoefficients. FortheD∗+ casethedistributions are stud-ied asa function ofthe massdifference



M

=

M

(

K

π π

)

− (

K

π

)

. Themeasuredanisotropicflowcoefficient,vtot

n ,canbewrittenasa

weightedsumofthe vn oftheD-mesoncandidate,vsign ,andthat

ofbackground,vbkgn [73] as vtot_n

(

MD

)

=

vsign Nsig Nsig

₊

_Nbkg

(

MD

)

+

v bkg n

(

MD

)

Nbkg Nsig

₊

_Nbkg

(

MD

),

(5)

where Nsig and Nbkg are the raw signal and background yields, respectively. The fit function for the invariant-mass distributions was composed of a Gaussian termto describe the signal and an exponentialdistributionforthebackgroundforD0 _andD+ candi-dates,whilefortheD∗+candidatesthebackgroundwasdescribed by the function a

√



M

−

mπ eb(M−mπ)_{, where a and b are free} parameters.InthecaseoftheD0 _{invariantmassthecontribution}

ofsignalcandidates withthe reflectedK-

π

massassignment was takenintoaccountwithanadditionalterm.Itsinvariant-mass dis-tribution was parameterised witha double-Gaussian distribution based on Monte Carlo (MC) simulations [43,46,48,69,74]. In the MC simulation, the underlying Pb–Pb events at

√

sNN

=

5

.

02 TeV

weresimulated usingtheHIJING v1.383generator [75] and cc or bb pairswere addedwiththePYTHIA6.4.25 generator [76] with Perugia-2011tune [77].Inthesimultaneousfit,the vnparameter

forthecandidateswithwrongK-

π

massassignmentwassettobe equalto vsign ,providedthattheoriginofthesecandidatesarereal

D0 mesons.The vsign ismeasuredfromthefittothe vtotn

ALICE Collaboration Physics Letters B 813 (2021) 136054

Fig. 1. Simultaneousfitstotheinvariant-massspectrumandv2(MD)ofD0(leftpanel),D+(middlepanel),andD∗+(rightpanel)mesoncandidatesinthe3<pT<4 GeV/c, 5<pT<6 GeV/c,and8<pT<10 GeV/c intervals,respectively,for the30–50%centralityclass.Thesolidblueandthedottedredcurvesrepresentthetotalandthe combinatorial-backgroundfitfunctions,respectively.FortheD0_{candidates,thegreendashedcurverepresentsthecontributionofthereflectedsignal.}

forD+ andD∗+ mesons,andD0 _{mesonswith p}

T

>

4 GeV

/

c.For

the D0 _{candidateswith p}

T

<

4 GeV

/

c, asecond-orderpolynomial

function was used instead. Fig. 1 shows the simultaneous fit to theinvariant-massspectrumandvtot

2

(

MD

)

inthe pT intervals3–4

GeV

/

c forD0,5–6GeV

/

c forD+,and8–10GeV

/

c forD∗+ inthe 30–50%centralityclass.

The reconstructed D-meson signal is a mixture of prompt D mesons from c-quark hadronisation or strong decays of excited charmonium or open-charm states, and D mesons from beauty-hadron decays, called “feed-down” in the following. The vsign is

thereforealinearcombinationofprompt(vpromptn )andfeed-down

(vfeed-down

n )contributions,andcanbeexpressedas

vsign

=

fpromptvpromptn

+ (

1

−

fprompt

)

vfeed-downn

,

(6)

where fprompt isthefractionofpromptlyproducedDmesons

es-timated as a function of pT with the theory-driven method

de-scribed in [21]. This method uses (i) FONLL calculations [78,79] fortheproductioncrosssectionofbeautyhadrons,(ii)the beauty-hadron decaykinematics from the EvtGen package [80], (iii) the product ofefficiency andacceptance

(

Acc

×

ε

)

fromMonteCarlo simulations,and(iv)ahypothesisonthenuclearmodification fac-toroffeed-downDmesons.

The anisotropic flow coefficients of promptly produced D mesons were obtained assuming vfeed-down_n

=

vpromptn

/

2. The

hy-pothesis is based on the measurement of the non-prompt J

/ψ

performed by CMS[19] and on the available model calculations [49,81,82],thatindicate0

<

vfeed-down_n

<

vpromptn .

Forthemeasurementofthemodificationofthe pT-differential

distributionsofDmesonsintheESE-selectedsamplescomparedto theunbiasedsample,therawyields wereextractedvia fitstothe invariant-mass distributions of D0, D+, and D∗+ candidates and normalised to the corresponding numberof events inthe corre-spondingESE-selectedsample.Thesamefunctionsadoptedinthe simultaneous fits forthe invariant-mass distributions were used. The extractedraw yields were not corrected forthe efficiencyin theratiocalculation,undertheassumptionthatthereconstruction

andselection efficiencies do not depend on q2. This assumption

waspreviouslyverifiedin [48].

4. Systematicuncertainties

TheD-meson vncoefficientsareaffectedbythesystematic

un-certaintiesdueto(i)thesignalextractionfromtheinvariant-mass andvtot

n distributions,(ii)thebeautyfeed-downcontribution,(iii)

on the selection of the centrality interval in which Rn is

calcu-lated,and(iv),fortheESE-selectedsamples,theuncertaintiesdue topossiblebiascausedbythepresenceofauto-correlationeffects betweenthesubeventsusedforRnandq2 calculations.

Theuncertainty duetothe simultaneousfit was estimatedby repeatingthefitseveraltimeswithdifferentconfigurations.In par-ticular,thelower andupperlimitsofthefitrange,thebinwidth, andthe backgroundfitfunctionsusedfortheinvariant-mass and

vtot

n distributionswerevaried.ForeachconfigurationtheD-meson vnwascalculatedandtheabsolutesystematicuncertaintyforeach pT interval was assigned asthe r.m.s. of the vn distribution

ob-tained from the different trials. The absolute systematic uncer-tainty valuesonthe vn are reportedinTable 1andthey depend

ontheD-mesonspecies,thepTintervalandtheESE-selectedclass.

Thissourceofuncertaintywasconsidered asuncorrelatedamong the pT intervalsandthecentralityclassesforthetwoharmonics.

The correlation between the small-q2/large-q2 and the unbiased

case was investigated and the outcome indicated that this un-certaintysourceisuncorrelatedbetweenthedifferentq2-selected

samples.

Forthe pT-differentialyieldratiosinESE-selectedsamples,the

uncertaintyforthesignalextractionwasestimatedusingthesame approach described above, directly on the ratio of the yields in the ESE-selected and unbiased samples, leading to a systematic uncertaintyvalue from0.7% to 5%, depending onthe pT andthe

D-mesonspecies.

The systematicuncertaintysource related tothe beauty feed-downcorrectionhastwomaincontributions.Thefirstisduetothe

Table 1

SummaryofsystematicuncertaintiesonthemeasurementoftheD-mesonv2,intheunbiasedand ESE-selectedsamples,andv3inPb–Pbcollisionsat√sNN=5.02 TeV.Therangeoftheuncertaintieson

thefittingprocedureandfeed-downsubtractionarequotedasabsoluteuncertainties,whilethoseon theRnasrelativeuncertainty.

Systematic uncertainty source v2 v3 v2small-q2 v2large-q2 0–10% M and vnfits 0.005–0.03 0.006–0.03 0.006–0.01 0.006–0.01 Feed-down 0.002–0.01 0.0007–0.01 0.0003–0.006 0.003–0.016 Rndetermination 3.5% negl. 3.5% 3.5% Autocorrelations on R2and q2 - - 3.5% 1% 30–50% M and vnfits 0.006–0.025 0.01–0.05 0.006–0.015 0.004–0.015 Feed-down 0.0004–0.02 0.003–0.018 0.003–0.01 0.004–0.029 Rndetermination 0.5% 0.5% 0.5% 0.5% Autocorrelations on R2and q2 - - 0.5% 0.5%

andtherenormalisationandfactorisationscalesintheFONLL cal-culations,theRfeed-down_AA hypothesisasreportedin [21].Thesecond contribution is due to the assumption of vfeed-down

n = v

prompt n /2,

previously described in Sec.3,and was estimatedby assuminga flatdistributionofvfeed-down

n between0andv prompt

n andbyvarying

thecentralvalueofvfeed-down n by

±

v

prompt n /

√

12.Thevaluesofthe absolute systematic uncertainty fromthe beautyfeed-down cor-rectionare reportedinTable1andthey dependontheD-meson species,thepT intervalandtheESE-selectedclass.Theuncertainty

dueto thebeautyfeed-downcorrection was assumedtobe fully correlatedamongthe pT binsforthemeasured vncoefficientsin

thesamecentralityclass.

The non-flow effects are naturally suppressed because of the pseudorapiditygapofatleast0.9unitsbetweenthe pseudorapid-ityintervalusedfortheD-mesonreconstruction,andtheV0Cused fortheQn-vectordetermination.Furthermore,theauto-correlation

effectdueto theusage oftheTPCtracks fortheq2 estimate has

been discussed in Sec. 2 and the related systematic uncertainty wasfoundtobenegligible,asdescribedin [48].

Thecontributionofthe Rntothesystematicuncertaintyisdue

to the centrality dependence. The central value of Rn was

esti-mated using the three subevent formula, as described in Sec. 3, averaged overtheeventsinthe 0–10%and30–50%intervals.The uncertaintywas evaluatedasthedifference ofthecentrality inte-grated Rn valueswiththoseobtainedasweightedaverages ofRn

valuesin narrowcentralityintervalsusingthe D-mesonyields as weights. A systematicuncertaintyof 3.5% and0.5% wasassigned on R2 inthe0–10%and30–50%centralityclassesandforall

ESE-selectedsamples.Forthe R3,anuncertaintyof0.5% wasassigned

inthe30–50%intervalwhileitwasfoundtobenegligibleforthe 0–10%class.Theuncertaintyassociatedwiththeresolutionfactor is smaller for the third harmonic than for the second harmonic, duetothemildercentralitydependenceofR3comparedwiththat

ofR2.

For the ESE-selected samples an additional source of system-aticuncertaintyontheresolutionoriginatesfromauto-correlations due to the usage of the TPC tracks both for q2 and R2

deter-mination. This potential bias is assessed by replacing the ratio



QQQV0C_n

/

MV0C

·

QQQTPC_n ∗

/

MTPC



/



QQQV0A_n

/

MV0A

·

QQQ_nTPC∗

/

MTPC



in Eq. (3) withtheone fromtheq2-integratedanalysis, followingthe same

approach used for the J

/ψ

azimuthal anisotropy measurement [83]. In this case, the systematic uncertainty was estimated to be 3

.

5% for the small-q2 and1% for the large-q2 samplesin the

0–10%centralityclass,and0

.

5% forbothq2-selectedclassesinthe

30–50%centralityclass,asreportedinTable1.Thelasttwosources ofsystematicuncertainty,relatedtotheresolution,areconsidered tobefullycorrelatedamongthedifferentpT intervals.

For the analysis of the pT-differential yield ratios in

ESE-selected and unbiased samples the reconstruction efficiency was verified to be independent of q2. Consequently, it cancels out in

theratioofthetwoESE-selectedclasses. 5. Results

5.1. Unbiasedflowharmonics

Fig.2showsthe average v2 (toppanels)and v3 (bottom

pan-els)coefficientsofpromptD0_{, D}+_,andD∗+ _{mesons measuredin}

theunbiased sample asa function of pT in the 0–10%(left

pan-els)and 30–50% (right panels) centralityclasses. The average vn

ofprompt D0, D+,and D∗+ mesons was computed by usingthe inversesquaredabsolutestatisticaluncertainties asweights,after having compared their compatibility [67]. The systematic uncer-tainties were propagated to the average by considering the con-tributions from the centrality dependence of the Rn resolution

and the correction for the beauty feed-down component in the D-meson yields as correlated among the D-meson species. The D-meson vn harmonicsare compared to thecorresponding

coef-ficients measured for charged pions and protons at midrapidity (

|

y

|

<

0

.

5) [39] aswellastoinclusiveJ

/ψ

mesonsatforward ra-pidity(2

.

5

<

y

<

4) [84].

The D-meson elliptic flow increases significantly from cen-tral to semi-central collisions, as expected from the increasing eccentricity of the interaction region. Conversely, the triangular flow is compatiblein the two centrality classes within the large uncertainties, following the milder centrality dependence of the third flow harmonic observed forlight-flavour particles [39]. For

pT

<

3–4 GeV

/

c (pT

<

4–5 GeV

/

c)themeasuredD-mesonv2 (v3)

islowerthanthatofpionsandprotons.Thisobservationis consis-tentwithinuncertaintieswiththehypothesisofamasshierarchy,

vn

(

D

)

<

vn

(

p

)

<

vn

(

π

)

, in thelow pT region (pT



3 GeV

/

c). In

semi-centraleventsthevncoefficientsofJ

/ψ

mesonsseemto

fol-low the mass hierarchy (vn

(

J

/ψ)

<

vn

(

D

)

). In central events the

datasuggestsasimilarbehaviour, howeverwithinthecurrent un-certaintiesnofirmconclusionscanbedrawn.Thisobservationcan be explained by the interplay between the anisotropic flow and theisotropicexpansionofthesystem(radialflow),whichimposes an equal velocity boost to all particles. For 4



pT



6–8 GeV

/

c,

the D-meson vn coefficients are similar to those of charged

pi-ons and lower than those of protons. This observation is con-sistent with a scaling of the vn coefficients with the numberof

constituentquarks,whichsupportsthehypothesisofparticle pro-duction via quark coalescence [85]. In the same pT interval, for

the30–50% centralityclass thelarger valuesof vn forDmesons

ALICE Collaboration Physics Letters B 813 (2021) 136054

Fig. 2. Averagev2(toppanels)andv3(bottompanels)coefficientsofpromptD0,D+,andD∗+ mesonsasafunctionofpTforPb–Pb collisionsat√sNN=5.02 TeV inthe

0–10%(leftpanels)and30–50%(rightpanels)centralityclasses.Thev2andv3ofπ±,p+ ¯p [39] andinclusiveJ/ψmesons [84] measuredatthesamecentre-of-massenergy andinthesamecentralityclassesareshownforcomparison.

up anddownquarks comparedto thatofcharm quarks [28] and (ii) the fraction of J

/ψ

mesons coming from beauty-hadron de-cays [86,87], which are expected to have lower v2 and v3 than

charmedmesons [26,88].Inthe0–10%centralityclass,thecurrent experimental uncertainties do not allow for firm conclusions on the expecteddifferencefor J

/ψ

andDmesons.The measured vn

coefficients forall thehadron speciesare compatible within un-certainties for pT



8 GeV

/

c.Similarvalues of vn coefficientsare

expected, because in thiskinematicrange the charm-quark mass issmallcomparedtothemomentum,andbecausethepath-length dependence of the in-medium parton energy loss is similar for high-pTcharmquarksandgluons.

In Fig. 3, the average D-meson vn coefficients are compared

to theoreticalcalculationsthatincludethe charm-quarktransport ina hydrodynamically expandingmedium.The theoretical uncer-tainties, where available, are displayed witha coloured band. In theTAMU [89],POWLANG HTL [34,56],PHSD [53],Catania [94,95], andBAMPSel[49] calculationstheinteractionsbetweenthecharm

quarksandthemediumconstituentsaremodelledwithcollisional processes, whilethe MC@sHQ+EPOS2 [26], LBT [57,90],LIDO [91,

92],BAMPSel+rad[55],DAB-MOD(M&T) [37,93],andLGR [96]

mod-els includealsoradiative processes.Thedifferenceinthe variants oftheBAMPSmodelindicatesthat inthismodelelasticcollisions are the dominantprocess that impartsa positive D-meson v2 in

the low and intermediate pT region. All the models except for

BAMPS include thehadronisation ofthe charm quark via coales-cence, in addition to the fragmentation mechanism. Initial-state event-by-event fluctuations are included in the POWLANG HTL, LIDO, PHSD, MC@sHQ+EPOS2, LBT, and DAB-MOD(M&T) models, whicharethereforetheonlyonesthatprovidepredictionsforthe triangular flow. Althoughthe models differinseveral aspects re-latedtotheinteractionsbothintheQGPandinthehadronicphase aswellastothemedium expansion,mostofthemprovideafair descriptionofthemeasuredvnharmonics.Thelargestdifferenceis

observedinthe2

<

pT

<

6 GeV

/

c intervalforthev2inthe30–50%

centrality class, where most of the models provide a prediction lowerthanthemeasuredpoints.ThisismoreevidentfortheLIDO model,whichshowsadeviationof5

.

4

σ

,andBAMPSel+rad,which

underestimatesthemeasured v2 byaboutafactortwowithmore

than10

σ

significance.In contrastto this,BAMPSel overestimates

themeasurement by about 3

σ

. The underestimation of thedata by the BAMPSel+rad model can be eventually due to the missing

implementationofthecharm-quarkcoalescencewithlightquarks fromthemedium,whichseemstobenecessaryinthedescription ofthe measured v2.In thesame pT range,theDAB-MOD model

overestimates the measured v2 in the 0–10% centrality class by

3

.

7

σ

.Thesediscrepanciesexpressed innumberofstandard devi-ationswere computedcombiningtheprobabilitytoobservea de-viationfromthenullhypothesis(i.e.themodelprediction)forall themeasuredpointsinthe2

<

pT

<

6 GeV

/

c interval,considering

boththeexperimental(statisticalandsystematic)andthe theoret-icaluncertainties, when available. The globalagreement between thedataandthe theoretical modelswas evaluated by computing the

χ

2

_/

_{ndf,asdonein [46].ThevaluesarereportedinTable2.All}

thecentralityclassesandvnharmonicswereconsideredwhenthe

modelpredictionswereavailable.Comparedtotheresultsin [46], foralmost all themodels the

χ

2

_/

_{ndf isfound to be higherthan}

unity,mostlikely becauseofthe improvedprecision ofthe mea-surement.Themodelsthatdescribethedatawith

χ

2

_/

_ndf

_<

_{2 are}

MC@sHQ+EPOS2, LBT, LGR, PHSD, POWLANG, Catania, and TAMU which is more in agreement with the data compared to [46], thanks to the improved description of the charm-quark coales-cenceinitslatestversion [89].Thesemodelsuseavalueof heavy-quark spatial diffusioncoefficient in therange 1

.

5

<

2

π

DsTc

<

7

atthecriticaltemperatureTc

=

155 MeV [97],whichisconsistent

withtheintervalobtainedin [46].Itishoweverimportantto con-siderthatnotallthetheoreticalmodelsprovidepredictionsforall thevnharmonicsinallthecentralityclassesreportedinthis

Fig. 3. Averagev2(toppanels)andv3(bottompanels)coefficientsofpromptD0,D+,andD∗+ mesonsasafunctionofpTforPb–Pb collisionsat√sNN=5.02 TeV inthe

0–10%(leftpanels)and30–50%(rightpanels)centralityclassescomparedwithmodelcalculations [26,34,37,49,53,55–57,89–95].

Table 2

Summaryofχ2_{/ndf valuesobtainedforthedifferentmodelpredictionscomparedwiththemeasured} D-mesonvnharmonics. Model pT(GeV/c) χ2/ndf v2 v3 global 0–10% 30–50% 0–10% 30–50% BAMPSel[49] [1–24] - 31.7/11 - - -BAMPSel+rad[55] [1–24] - 203.6/11 - - -Catania [94,95] [1–12] 3.1/7 14.0/8 15.1/7 8.1/4 40.3/26 DAB-MOD(M&T) [37,93] [1–8] 24.6/7 9.8/6 16.1/7 7.1/3 57.6/23 LBT [57,90] [1–36] 18.2/11 15.8/12 24.9/11 8.4/7 67.4/41 LIDO [91,92] [1–24] 10.7/10 62.0/11 17.8/10 12.5/6 102.9/37 LGR [96] [1–24] - 15.5/11 - - -MC@sHQ+EPOS2 [26] [1–36] - 15.7/12 - - -PHSD [53] [1–24] 13.2/10 19.6/11 7.9/10 8.6/6 48.9/37 POWLANG HTL [34,56] [1–12] 9.6/7 13.5/8 14.6/7 8.3/4 45.9/26 TAMU [89] [1–12] - 8.15/9 - -

-5.2. Event-shapeengineeredflowharmonicsandpT-differentialyields

The average v2 ofprompt D0,D+,andD∗+ mesonsmeasured

intheESE-selectedsamplesisshowninFig.4forthe0–10%(top row) and the 30–50% (bottom row) centrality classes. The mea-surementsinthesmall-q2 samplearereportedintheleftcolumn,

thoseinthelarge-q2 sample intherightcolumn,whilethe

mea-surements in the unbiased samples recomputed in the same pT

intervalsoftheESEanalysisareinthemiddlecolumn.Areduced

pT range (2

<

pT

<

16 GeV

/

c) andwider pT intervals compared

to the unbiased v2 measurement were adopted due to the

lim-ited size ofthe ESE-selectedsamples.The average v2 among the

three D-mesonspecieswas computedasdescribed inSec. 5.1.In Fig.5theratiobetweentheaverageD-meson v2 measuredinthe

ESE-selectedsampleswithrespecttothatintheunbiasedsample is depicted. The statistical uncertainties of the ratio were calcu-latedtakinginto considerationthedegree ofcorrelation between themeasurements intheESE-selectedandunbiasedsamples.The

systematicuncertaintiesarisingfromthecentralitydependenceof

Rn,thenon-flow contaminationsamongsub-events, andthe

cor-rectionforthebeautyfeed-downcontributionwere consideredas fullycorrelated.

TheD-mesonv2 wasfoundtobeonaverageabout50%higher

(lower)inthe20%oftheeventswithlargest(smallest)q2 inboth

the0–10%and30–50%centralityclasses.No significantcentrality dependencewas foundwithin the currentuncertainties.The cor-respondingvariation of the averageq2 in thesmall-q2 (large-q2)

sample withrespect tothe unbiased one was found tobe about 65% (75%) and 60% (65%) for the 0–10% and 30–50% centrality class, respectively. This confirms the correlation between the D-meson azimuthal anisotropy and the collective expansion of the bulkmatter alreadyobservedin [48]. Thismodificationofthe v2

coefficient was found to be independent of pT within

ALICE Collaboration Physics Letters B 813 (2021) 136054

Fig. 4. AverageofpromptD0_,D+_,andD∗+_{mesonv2asafunctionofpTinPb–Pb collisionsat}√_s

NN=5.02 TeV inthesmall-q2,large-q2(seetextfordetails),andunbiased samples,forthe0–10%(toppanels)and30–50%(bottompanels)centralityclasses,comparedtomodelcalculations [34,37,91,93–95].IntheLIDO,DAB-MOD,andCatania predictions,theESEselectionisperformedwithaq2estimator,whileinthePOWLANGmodeltheellipticeccentricityε2isused.

Fig. 5. RatiooftheaveragepromptD0_,D+_,andD∗+_{mesonv2coefficientsmeasuredinthesmall-q2(leftpanels)andlarge-q2(rightpanels)selectedsampleswithrespectto}

thatoftheunbiasedsampleasafunctionofpTinPb–Pb collisionsat√sNN=5.02 TeV forthe0–10%(toppanels)and30–50%(bottompanels)centralityclasses,compared

tomodelcalculations [34,37,91,93,95].

ofthemeasuredparticleandisrelatedtotheentireevent).A sim-ilartrendwasalsoobservedforlight-flavourparticles [66].

Figs.4and5alsocomparethemeasured v2 andv2 ratios

be-tweenESE-selectedandunbiasedsamplestothePOWLANG,LIDO, DAB-MOD, andCataniatheoretical predictions.ForthePOWLANG

Fig. 6. AverageoftheratioofpT-differentialD0,D+,andD∗+yieldsmeasuredintheESE-selectedsamplestothoseintheunbiasedsampleinPb–Pb collisionsat√sNN=

5.02 TeV forthe0–10%(toppanels)and30–50%(bottompanels)centralityclasses,comparedtothePOWLANG [34] andLIDO [91,92] predictions.

loss (Eloss [100]) were considered. In the LIDO, DAB-MOD, and

Catania modelsthe ESEselection isperformedwitha q2

estima-torcomputedstarting fromgeneratedquantities [91,93,95],while in the POWLANG model the elliptic eccentricity

ε

2 is directly

used [34].Thev2measuredinthesmall-q2sampleisdescribedby

alltheavailable modelswithintheuncertainties.Onthecontrary, in the 30–50% centrality class the LIDO, DAB-MOD, and Catania models underestimate the measurement in the large-q2 sample,

whichisinsteadwell describedby thePOWLANG HTLprediction. Inthe caseofPOWLANG lQCD,the theoreticalpredictionis com-patible with the measured v2 for pT

<

4 GeV

/

c and lower for

higher pT.The DAB-MODcalculationsgive abetter descriptionof

the experimental data withthe M&T approach for pT

<

5 GeV

/

c

andinthe Eloss caseforpT

>

5 GeV

/

c.When theratiosbetween

the v2 in theESE-selectedandthe unbiasedsamplesare

consid-ered, the models seem to better describe the measured values, owingtosimilardiscrepanciesbetweentheoreticalpredictionsand experimentaldataintheESE-selectedandunbiasedsampleswhich leadtosimilarratiovaluesinthedifferentmodels.Inthesmall-q2

samplesthemodelpredictionsaremoresimilartoeachotherand the discrepancies are less significant, also due to the larger ex-perimental uncertainties. Interestingly, different implementations of the same model with the studied transport parameterisations (i.e. POWLANG HTL vs. POWLANG lQCD, andDAB-MOD(M&T) vs. DAB-MOD(Eloss)) give similar predictions, suggestingthat the

ef-fect of the ESE selection is more related to the initial geometry and theunderlying hydrodynamic expansion ratherthan the dy-namicevolutionoftheheavyquarksinthemedium.

Tostudyapossibleinterplaybetweentheazimuthalanisotropy oftheeventandthecharm-quarkradialflow(atlow/intermediate

pT)andin-mediumenergyloss(athigh pT),theratioofthe

mea-suredper-eventyieldsofpromptD0_,D+_,andD∗+ _mesonsinthe

ESE-selectedandunbiasedsampleshasbeencalculatedasa func-tionof pT intherange2

<

pT

<

24 GeV

/

c.Theaverage D-meson

ratios,computedbyusingtheinverseofthesquaredrelative

statis-ticaluncertaintiesasweights,arecomparedtothePOWLANG and LIDOmodels inFig.6.ThePOWLANG modelpredicts ahardening (softening)ofthe pT distributions inthe large(small)-q2 class of

eventsdue to an interplaybetween the radial andelliptic flows, whilenosignificant modificationispredictedbythe LIDOmodel. Withinthe currentprecision,themeasured per-eventyieldratios andarefoundcompatiblewithunity,andhencetotheLIDOmodel predictions, andwith the POWLANG model in the case oflQCD, whilethemeasuredeffectseemstobe lowerthantheeffect pre-dictedwithHTLtransportcoefficients.

6. Conclusions

The elliptic and triangular flow of D0_{, D}+_{, and D}∗+ _mesons was measured withthe SP method at midrapidity (

|

y

|

<

0

.

8) as afunctionofpT incentral(0–10%)andsemi-central(30–50%)Pb–

Pbcollisionsat

√

sNN

=

5

.

02 TeV.

Compared to other particle species, the average D-meson vn

harmonics were found to be compatible with the hypothesis of a mass hierarchy for pT



3 GeV

/

c as observed for light-flavour

hadrons [39]. At intermediate pT, the D-meson vn is similar to

those of chargedpions, lower than those of protons, andhigher than those of J

/ψ

mesons, supporting the hypothesis of charm-quark hadronisation via coalescence. Moreover, the contribution tothehadronisationofcharmquarksfromcoalescencewithlight quarksfromthemediumseemstobenecessaryinthetheoretical modelstoquantitativelyreproducethemeasuredD-meson vn.For pT



8 GeV

/

c,theD-meson v2 andv3 arecompatiblewithin

un-certaintieswiththevaluesmeasuredfortheotherparticlespecies, indicatingasimilar path-lengthdependenceoftheenergylossof high-pT charm quarks and gluons. The comparison of the

mea-suredD-meson vn withtheoreticalcalculationssuggeststhat the

ALICE Collaboration Physics Letters B 813 (2021) 136054

Theellipticflowandthemodificationofthe pTdistributionsof

D0, D+, andD∗+ mesonswere alsoinvestigated withthe event-shape engineering technique. The D-meson v2 was found to be

larger (smaller)ineventswithlarger(smaller)q2,confirming the

correlation withaverage bulk elliptic flow. The ratios of the pT

-differential yields measured inthe ESE-selected samplesand the unbiased sample were found to be compatible with unity. The measurements in the ESE-selected samples are qualitatively de-scribedby theoreticalcalculationsandprovidenewconstraintsto modelsbasedoncharm-quarktransportinahydrodynamically ex-pandingmediumandcharm-quarkenergylossintheQGP. Declarationofcompetinginterest

Theauthorsdeclarethattheyhavenoknowncompeting finan-cialinterestsorpersonalrelationshipsthatcouldhaveappearedto influencetheworkreportedinthispaper.

Acknowledgements

The ALICE Collaboration would like to thank all its engineers andtechniciansfortheirinvaluablecontributionstothe construc-tion of the experiment and the CERN accelerator teams for the outstanding performance of the LHC complex. The ALICE Collab-oration gratefully acknowledges the resources and support pro-videdbyallGridcentresandtheWorldwideLHCComputingGrid (WLCG) collaboration. The ALICE Collaboration acknowledges the following fundingagenciesfortheir supportinbuildingand run-ningtheALICEdetector:A.I.AlikhanyanNationalScience Labora-tory(YerevanPhysicsInstitute)Foundation (ANSL),State Commit-teeofScienceandWorldFederationofScientists(WFS),Armenia; Austrian Academy of Sciences, Austrian Science Fund (FWF): [M 2467-N36] and Nationalstiftung für Forschung, Technologie und Entwicklung,Austria;MinistryofCommunicationsandHigh Tech-nologies, National Nuclear Research Center, Azerbaijan; Conselho Nacional de DesenvolvimentoCientífico e Tecnológico (CNPq), Fi-nanciadora de Estudose Projetos(Finep), Fundação de Amparoà Pesquisa do Estado de SãoPaulo (FAPESP) andUniversidade Fed-eraldoRioGrandedoSul(UFRGS),Brazil;MinistryofEducationof China (MOEC), MinistryofScience& Technology ofChina (MSTC) and NationalNatural Science Foundation of China (NSFC), China; Ministry of Science and Education and Croatian Science Founda-tion,Croatia;CentrodeAplicacionesTecnológicasyDesarrollo Nu-clear (CEADEN),Cubaenergía, Cuba;Ministry of Education, Youth and Sports of the Czech Republic, Czech Republic; The Danish Council for IndependentResearch | Natural Sciences, theVILLUM FONDEN andDanish NationalResearch Foundation (DNRF), Den-mark;Helsinki Institute ofPhysics(HIP), Finland;Commissariatà l’Énergie Atomique (CEA) and Institut National de Physique Nu-cléaire etde Physique desParticules(IN2P3)andCentre National de la Recherche Scientifique (CNRS), France; Bundesministerium für Bildung und Forschung (BMBF) and GSI Helmholtzzentrum fürSchwerionenforschungGmbH,Germany;GeneralSecretariatfor ResearchandTechnology,MinistryofEducation,Researchand Re-ligions,Greece;NationalResearchDevelopmentandInnovation Of-fice,Hungary; DepartmentofAtomicEnergy, GovernmentofIndia (DAE),DepartmentofScienceandTechnology,GovernmentofIndia (DST), University Grants Commission,Government ofIndia (UGC) andCouncilofScientific andIndustrialResearch(CSIR), India; In-donesian Institute of Science, Indonesia; Centro Fermi - Museo StoricodellaFisicaeCentroStudieRicercheEnricoFermiand Isti-tutoNazionalediFisicaNucleare(INFN),Italy;Institutefor Innova-tive ScienceandTechnology,NagasakiInstituteofAppliedScience (IIST),JapaneseMinistryofEducation,Culture,Sports,Scienceand Technology(MEXT)andJapanSocietyforthePromotionofScience (JSPS)KAKENHI, Japan;Consejo Nacionalde Ciencia(CONACYT)y

Tecnología, through Fondode Cooperación Internacional en Cien-cia y Tecnología (FONCICYT) and Dirección General de Asuntos delPersonalAcademico(DGAPA),Mexico;NederlandseOrganisatie voor Wetenschappelijk Onderzoek (NWO), Netherlands; The Re-search Council of Norway, Norway; Commission on Science and TechnologyforSustainableDevelopmentintheSouth(COMSATS), Pakistan;PontificiaUniversidadCatólicadelPerú,Peru;Ministryof Science andHigher Education,National Science Centre and WUT ID-UB,Poland;KoreaInstituteofScienceandTechnology Informa-tion and National Research Foundation of Korea (NRF), Republic of Korea;Ministry of Education and Scientific Research, Institute of Atomic Physics and Ministry of Research and Innovation and Institute of Atomic Physics, Romania; Joint Institute for Nuclear Research(JINR),MinistryofEducation andScienceoftheRussian Federation, National Research Centre Kurchatov Institute, Russian Science Foundation and Russian Foundation for Basic Research, Russia;Ministry ofEducation, Science,Research andSportofthe Slovak Republic, Slovakia; National ResearchFoundation ofSouth Africa,SouthAfrica;SwedishResearchCouncil(VR)andKnut& Al-iceWallenbergFoundation(KAW),Sweden;EuropeanOrganization forNuclearResearch,Switzerland;SuranareeUniversityof Technol-ogy(SUT), NationalScience andTechnology DevelopmentAgency (NSDTA) and Office of the Higher Education Commission under NRUprojectofThailand,Thailand;Turkish AtomicEnergyAgency (TAEK),Turkey;NationalAcademyofSciencesofUkraine,Ukraine; ScienceandTechnology FacilitiesCouncil (STFC),UnitedKingdom; NationalScienceFoundationoftheUnitedStatesofAmerica(NSF) andUnitedStatesDepartmentofEnergy, OfficeofNuclearPhysics (DOENP),UnitedStatesofAmerica.

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