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Physics Letters B
www.elsevier.com/locate/physletb
Azimuthally-differential pion femtoscopy relative to the third harmonic event plane 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 ra c t
Articlehistory:
Received5April2018
Receivedinrevisedform18June2018 Accepted19June2018
Availableonline22June2018 Editor: L.Rolandi
Azimuthally-differentialfemtoscopicmeasurements,beingsensitivetospatio-temporalcharacteristicsof thesourceaswellastothecollectivevelocityfieldsatfreezeout,provideveryimportantinformationon thenatureanddynamicsofthesystemevolution.WhiletheHBTradiioscillationsrelativetothesecond harmoniceventplanemeasuredrecentlyreflectmostlythespatialgeometryofthesource,modelstudies haveshownthattheHBTradiioscillationsrelativetothethirdharmoniceventplanearepredominantly defined by the velocity fields. In this Letter, we present the first results on azimuthally-differential pion femtoscopy relativeto the thirdharmonic event plane as afunctionofthe pionpair transverse momentumkTfordifferentcollisioncentralitiesinPb–Pbcollisionsat√s
NN=2.76 TeV.Wefindthatthe Rside andRoutradii,whichcharacterizethepionsourcesizeinthedirectionsperpendicularandparallel tothepiontransversemomentum,oscillateinphaserelativetothethirdharmoniceventplane,similar to the results from 3+1D hydrodynamical calculations.The observed radii oscillationsunambiguously signal acollectiveexpansionand anisotropyinthevelocityfields.Acomparisonofthe measuredradii oscillationswiththeBlast-Wavemodelcalculationsindicatethattheinitialstatetriangularityiswashed- outatfreezeout.
©2018EuropeanOrganizationforNuclearResearch.PublishedbyElsevierB.V.Thisisanopenaccess articleundertheCCBYlicense(http://creativecommons.org/licenses/by/4.0/).FundedbySCOAP3.
1. Introduction
Heavy-ion collisions at LHC energies create a hot and dense medium known as the quark–gluon plasma (QGP) [1]. The QGP fireball first expands, cools, and then freezes out into a collec- tionoffinal-statehadrons. Correlationsamongtheparticles carry information aboutthe space–time extent of the emitting source, and are imprinted on the final-state spectra dueto a quantum- mechanicalinterference effect [2]. Commonly known asintensity orHanbury–Brown–Twiss(HBT)interferometry,thecorrelation of twoidenticalparticlesatsmallrelativemomentum,isaneffective tooltostudythespace–time(“femtoscopic”)structureoftheemit- tingsourceinrelativisticheavy-ioncollisions [3].The initialstate of a heavy-ion collision is characterized by spatial anisotropies that lead to anisotropies in pressure gradients, andconsequently toazimuthalanisotropiesinfinalparticledistributions,commonly called anisotropic flow. Anisotropic flow is usually characterized by aFourier decompositionofthe particleazimuthal distribution andquantified by theflow coefficients vn andthe corresponding symmetry plane angles n [4]. Elliptic flow is quantified by the second flow harmoniccoefficient v2,whereas triangular flow [5]
is quantified by v3. Due to the position–momentum correlations
E-mailaddress:alice-publications@cern.ch.
in particle emission [6], the particles emitted at a particularan- gle relative to theflow plane carry informationaboutthe source asseenfromthatcorresponding direction;thesecorrelationsalso leadtotheHBTradiitobesensitivetothecollectivevelocityfields, fromwhichinformationaboutthedynamicsofthesystemevolu- tioncanbeextracted.
Azimuthally-differentialfemtoscopicmeasurementscanbeper- formed relative to the direction of different harmonics event planes [7,8]. The measurements of the HBT radii with respect to the first harmonic eventplane (directedflow) at the AGS [9]
revealed that the source was tilted relative to the beam direc- tion [10]. The HBT radii variations relative to the second har- monic event plane angle (2) provide information on the pion source elliptic eccentricity at freeze-out. The recent ALICE mea- surements [11] indicatethatduetothestrongin-planeexpansion the final-state source elliptic eccentricity is more than a factor 2–3 smaller compared to the initial-state. While the HBT radii modulations relative to 2 are defined mostly by the sourcege- ometry,theazimuthaldependenceoftheHBTradiirelativetothe third harmonic event plane (3) originate predominantly in the anisotropies ofthecollectivevelocityfields–foratriangular,but staticsourcetheradiidonotexhibit anyoscillations [12].Models studies [13,14] showthat theanisotropy inexpansion velocityas well asthesystemgeometricalshapecan bestronglyconstrained by azimuthally differential femtoscopic measurements relative to https://doi.org/10.1016/j.physletb.2018.06.042
0370-2693/©2018EuropeanOrganizationforNuclearResearch.PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense (http://creativecommons.org/licenses/by/4.0/).FundedbySCOAP3.
3.TheHBTradiioscillationsrelativetothethirdharmonicevent planehavebeenfirstobservedinAu–AucollisionsatRHICenergy bythePHENIXCollaboration [15]. Unfortunately,dueto largeun- certainties these measurements did not allow to obtain detailed informationontheoriginoftheobservedoscillations.
InthisLetter,thefirstazimuthally-differentialfemtoscopicmea- surement relative to the third harmonic event plane in Pb–Pb collisionsat√
sNN=2.76 TeV fromtheALICEexperimentarepre- sented. We compare our results to the toy-model calculations from [13] togetan insighton therole oftheanisotropies inthe velocityfieldsandthesystemshape.Inaddition,we compareour resultstoa 3+1Dhydrodynamicalcalculations [14] anda Blast- Wave Model [16] for a quantitative characterization of the final sourceshape.
2. Dataanalysis
Theanalysiswas performedover thedata sample recordedin 2011 during the second Pb–Pb running period at the LHC. Ap- proximately 2 million minimum bias events,29.2 million central trigger events,and 34.1 million semi-central trigger events were used.The minimum bias, semi-central, andcentral triggers used allrequireasignalinbothV0detectors [17].TheV0detector,also usedforthecentralitydetermination [18],isasmallangledetector ofscintillator arrayscovering pseudorapidityranges2.8<
η
<5.1 and−3.7<η
<−1.7 fora collision vertexoccurringatthe cen- teroftheALICEdetector.Theresultsofthisanalysisarereported forcollisioncentrality classesexpressed asrangesof thefraction oftheinelasticPb–Pbcrosssection:0–5%,5–10%,10–20%,20–30%, 30–40%,and40–50%.Events withtheprimaryeventvertexalong thebeamdirection|Vz|<8 cm wereused inthisanalysisto en- surea uniform pseudorapidity acceptance.A detaileddescription oftheALICEdetectorcanbefoundin [19,20].TheTimeProjection Chamber (TPC) has full azimuthal coverage and allows charged- particletrackreconstructioninthepseudorapidityrange|η
|<0.8, aswell asparticleidentificationvia thespecificionizationenergy lossdE/dxassociatedwitheachtrack.InadditiontotheTPC,the Time-Of-Flight(TOF)detectorwasusedforidentificationofparti- cleswithtransversemomentumpT>0.5 GeV/c.TheTPChas18sectorscoveringfullazimuthwith159padrows radiallyplacedineachsector.Trackswithatleast80spacepoints intheTPCwereusedinthisanalysis.Trackscompatiblewithade- cayin flight(kinktopology) wererejected. The trackquality was determinedbythe
χ
2 oftheKalmanfilterfittothereconstructed TPCclusters [21].Theχ
2 perdegree offreedom was requiredto belessthan4.Forprimarytrackselection,onlytrajectoriespassing within3.2 cm fromtheprimary vertex inthelongitudinal direc- tionand 2.4 cmin the transversedirection were used.Based on thespecific ionization energyloss intheTPC gascompared with the corresponding Bethe–Bloch curve, and the time of flight in TOF, a probability for each track to be a pion, kaon, proton, or electron was determined. Particles for which the pion probabil- itywas thelargestwere usedinthisanalysis.Thisresultedin an overallpurityabove95%,withsmallcontaminationfromelectrons in the region where the dE/dx for the two particle types over- lap.Pionswereselectedinthepseudorapidityrange|η
|<0.8 and 0.15<pT<1.5GeV/c.ThecorrelationfunctionC(q)wascalculatedas
C
(
q) =
A(
q)
B
(
q) ,
(1)whereq=p1−p2 is therelative momentumof twopions, A(q) isthedistributionofparticlepairsfromthesameevent,andB(q) isthe background distributionof uncorrelatedparticle pairs. The
background distribution is built by using the mixed-event tech- nique [22] in which pairs are made out of particles from three different events with similar centrality (less than 2% difference), event-plane angle(less than6◦ difference), andevent vertexpo- sition alongthe beamdirection(lessthan 4 cm difference). Both the A(q)andB(q)distributionsweremeasureddifferentiallywith respectto thethird harmonicevent-planeangleEP,3.Note,that measurements relativeto EP,3 will smearanycontributionfrom elliptic flow as the elliptic and triangular event planes are un- correlated [23]. The third harmonicevent-plane angle EP,3 was determinedusingTPCtracks.Toavoidauto-correlationeachevent wassplitintotwosubevents(−0.8<
η
<0 and0<η
<0.8).Pairs were chosen from one subevent and the third harmonic event- planeangleEP,3 wasestimatedusingtheparticlesfromtheother subevent, and vice-versa, with the event plane resolution deter- minedfromthecorrelationsbetweentheeventplanesdetermined indifferentsubevents [4].Requiringaminimumvalueinthetwo- trackseparationparametersϕ
∗= |ϕ
∗1−ϕ
2∗|andη
= |η
1−η
2| reducestwo-trackreconstruction effectssuchastracksplittingor trackmerging. The quantityϕ
∗ is definedin thisanalysisas the azimuthal angleofthetrackinthe laboratoryframeattheradial positionof1.6 m insidetheTPC. Splittingis theeffectwhenone trackisreconstructed astwo tracks,andmerging istheeffect of two tracks being reconstructed asone. Also, to reduce thesplit- tingeffect,pairsthatsharemorethan5%oftheTPCclusterswere removedfromtheanalysis.Itisobservedthatatlargerelativemo- mentumthecorrelationfunctionisaconstant,andthebackground pairdistributionis normalizedsuchthat thisconstantisequalto unity.Theanalysiswasperformedfordifferentcollisioncentralities inseveralrangesofkT,themagnitudeofthepion-pairtransverse momentumkT=(pT,1+pT,2)/2,andinbinsofϕ
=ϕ
pair−EP,3, whereϕ
pair is the pairazimuthal angle.The Bertsch–Pratt [3,24]out–side–long coordinate system was used with the long direc- tion pointing along the beamaxis, out along the transverse pair momentum, and side being perpendicular to the other two. The three-dimensionalcorrelationfunctionwasanalyzedintheLongi- tudinallyCo-MovingSystem(LCMS) [25],inwhichthetotallongi- tudinalmomentumofthepairiszero,p1,L= −p2,L.
To isolate the Bose–Einstein contribution in the correlation function, effects due to final-state Coulomb repulsion must be taken into account. For that, the Bowler–Sinyukov fitting proce- dure [26,27] wasused inwhich the Coulomb weight isonly ap- plied to the fraction of pairs (λ) that participate in the Bose–
Einstein correlation. In this approach, the correlation function is fittedby
C
(
q, ϕ ) =
N[(
1− λ) + λ
K(
q)(
1+
G(
q, ϕ ))],
(2)where N is the normalization factor. The function G(q,
ϕ
) de- scribes the Bose–Einstein correlations and K(q) is the Coulomb partofthetwo-pionwave functionintegratedoverasourcefunc- tion correspondingto G(q).Inthisanalysisthe Gaussian formof G(q,ϕ
)[28] wasusedG
(
q, ϕ ) =
exp−
q2outR2out( ϕ ) −
q2sideR2side( ϕ )
−
q2longR2long( ϕ ) −
2qoutqsideR2os( ϕ )
−
2qsideqlongR2sl( ϕ ) −
2qoutqlongR2ol( ϕ )
,
(3)wheretheparametersRout,Rside,andRlongaretraditionallycalled HBTradiiintheout,side,andlongdirections.Thecross-termsR2os, R2sl,andR2ol describethecorrelationintheout-side,side-long,and out-longdirections,respectively.
The systematic uncertainties on the extractedradii, discussed below,varyinkT andcentrality.Theyincludeuncertaintiesrelated
Fig. 1.TheazimuthaldependenceofR2out,R2side,andR2longasafunctionofϕ=ϕpair−3forcentralitypercentile20–30%andfourdifferentkTranges.Solidlinesrepresent thefittothefunctionalformsofEq. (4).Theshadedbandsshowthesystematicuncertainty.
to the tracking efficiency and track quality, momentum resolu- tion,differentvaluesforpaircuts(
ϕ
∗ andη
),andcorrelation functionfitranges [29].Similarlytotheazimuthallyinclusiveanal- ysis [29], different pair cuts were used, with the default values chosen based on a Monte Carlo study. The difference in the re- sultsfromusingdifferentpaircutsratherthanthedefaultpaircuts wereincludedinthesystematicuncertainties(1–4%).Fordifferent kTandcentralityranges,differentfittingrangesofcorrelationfunc- tion were usedas thewidth ofthe correlation function depends onkTandcentralityrange.Thedifferenceintheresultsfromusing differentfitrangesareduetothecontaminationofelectronsinthe particleidentificationandthenon-perfectGaussiansource(1–3%).Wealsostudiedthedifferenceintheresultsbyusingpositiveand negative pionpairs separately aswell asdata obtainedwithtwo opposite magnetic field polarities of the ALICE L3 magnet. They havebeenanalyzedseparatelyandasmalldifferenceintheresults (lessthan3%)hasbeenalsoaccountedforinthesystematicuncer- tainty.Thetotalsystematicuncertaintieswereobtainedbyadding inquadraturethecontributionsfromallvarioussourcesmentioned above.Thesystematicuncertaintyassociatedwiththeeventplane determination is negligible compared to other systematic uncer- tainties;theprocedureforthereactionplaneresolutioncorrection oftheresultsisdescribedinthenextsection.
3. Results
Fig.1presentsthedependenceof R2out, R2side,and R2long onthe pion emission angle relative to the third harmonic event plane forcentrality20–30%anddifferentkT ranges. Notethat R2out and R2side exhibit in-phase oscillations(for a quantitativeanalysis, see below).Withintheuncertaintiesofthemeasurement, R2long oscil- lations, if any, are insignificant. Oscillations of R2ol and R2sl radii (notshown)arefoundtobeconsistentwithzero,asexpecteddue
tothesourcesymmetryinlongitudinaldirection,andare notfur- ther investigated.The curves representthe fits to thedata using thefunctions [12]:
R2μ
( ϕ ) =
R2μ,0+
2R2μ,3cos(
3ϕ ) ( μ =
out,
side,
long),
R2os( ϕ ) =
R2os,0+
2R2os,3sin(
3ϕ ).
(4)Fitting the radii’s azimuthal dependence with the functional forms of Eq. (4) allows us to extract the average radii and the amplitudes ofoscillations.The
χ
2 per numberof degreeof free- dom is0.3–1.8 depending onkT andcentralityrange.The results for the average radii R2out,0, R2side,0, and R2os,0 were found to be consistent with those reported previously in [11] in azimuthally inclusiveanalysis.Theextractedamplitudesofoscillationshaveto be correctedforthefiniteeventplane resolution.Thereexistsev- eralmethodsforsuch acorrection [30],whichproduceconsistent results [31] well within uncertainties ofthisanalysis. The results shownbelow havebeenobtainedwith thesimplestmethod first usedbytheE895Collaboration [9],inwhichtheamplitudeofos- cillation isdivided by theeventplane resolution. Inthisanalysis the event plane resolution correction factor isabout 0.6–0.7,de- pendingoncentrality.Fig. 2 shows the oscillation parameters R2out,3, R2side,3, R2long,3, and R2os,3 for different centrality and kT ranges. All radii oscil- lations exhibit weak centrality dependence, likely reflecting the weak centrality dependence of the triangular flow itself. The kT dependence is different for different radii oscillations: while the magnitudes of R2out,3 and R2os,3 are smallest for the smallest kT range, it is opposite for R2side,3 (and,possibly for R2long,3), where the oscillationsbecome stronger.The parameter R2long,3 isconsis- tent with zerowithin the systematic uncertainties while R2os,3 is positive forall centralitiesandkT rangesexceptforthe lowestkT range0.2–0.3 GeV/c.Notethat R2out,3 and R2side,3 are negativefor
Fig. 2.The amplitudes of radii oscillationsR2out,3,R2side,3,R2long,3, andR2os,3versus centrality percentiles for fourkTranges. Square brackets indicate systematic uncertainties.
all centralities andkT ranges. In the toy model simulations [13]
such phases of radii oscillations were observed only in the so- called“flowanisotropydominatedcase”(acircularsourcewiththe radialexpansionvelocityincludingthethirdharmonicmodulation) andnot for“geometry dominated” case (triangular shape source withradialexpansionvelocityproportionaltoradialdistancefrom thecenter,withcornershavinglargestexpansionvelocity).
Fig. 3 shows the relative amplitudes of radius oscillations R2out,3/R2side,0, R2side,3/R2side,0,and R2os,3/R2side,0.Similarto thepre- vious analyses andtheoretical calculations [14] we report all the radii oscillations relative to the side radius the least affected by theemission timeduration. There existnoobvious centralityde- pendence. As the average radii decrease with increasing kT, the kT dependence of relative oscillation amplitudes appear much stronger for “out” and “out-side” radii, while “side” radius rela- tive amplitude exhibitsnokT dependencewiththe uncertainties.
The shaded bands in Fig. 3 indicate the results of 3+1D hydro- dynamical calculations [14]. These calculations assume constant shearviscositytoentropyratio
η
/s=0.08 andbulkviscositythat isnonzerointhehadronicphaseζ /s=0.04,andtheinitialdensity fromaGlauber MonteCarlomodel.The parametersofthemodel, were tuned to reproduce the measured chargedparticle spectra, the elliptic andtriangular flow. We find that the relative ampli- tudesR2side,3/R2side,0agreewiththeseresultsratherwell,whilethe relativeamplitudesR2out,3/R2side,0andR2os,2/R2side,0agreeonlyqual- itatively.According to the 3+1D hydrodynamical calculations, the negative signs of R2side,3 and R2out,3 parameters are an indication thattheinitialtriangularityhasbeenwashed-outorevenreversed atfreeze-outduetotriangularflow [14].Toinvestigate further on the final source shape, we compare our results to the Blast-Wave model calculations [16]. In that model,thespatialgeometryofthepionsourceatfreeze-outispa- rameterizedby
R
(φ) =
R0 1−
∞n=2
ancos
(
n(φ −
n))
,
(5)where n’s denote the orientations of the n-th order symmetry planes.Theamplitudesan andthephasesn aremodelparame- ters.Themagnitudeofthetransverseexpansionvelocityisparam- eterizedasvt=tanh
ρ
,wherethetransverserapidityρ
[13,16] isρ (˜
r, φ
b) = ρ
0˜
r1
+
∞n=2
2
ρ
ncos(
n(φ
b−
n))
.
(6)Here r˜=r/R(φ),and φb(φ) is the transverse boost directionas- sumed to be perpendicular to the surface of constant r.˜ The re- sults of this model presented below were obtained assuming a kinetic freeze-out temperature of 120 MeV, and maximum ex- pansionrapidity
ρ
0=0.8,tuned to describe single particlespec- tra.Fig. 4showstherelative amplitudesoftheradiusoscillations R2out,3/R2out,0,andR2side,3/R2side,0asafunctionofBlast-wavemodel third-order parameters, spatial anisotropy a3 and transverseflow anisotropyρ
3. Thin dashed lines represent the lines of constant relativeamplitudes,withnumbersnexttolinesindicatingtherel- ativeamplitudevalues.Thickdashed linesshowtheALICEresults forR2out,3/R2out,0 andR2side,3/R2side,0 withthethicknessofthelines indicating the uncertainties. The intersection of the two dashed lines correspondsto a3 andρ
3 parametersconsistent withALICE measurements.TheALICEdataandtheBlast-Wave modelcalcula- tions correspond topairs withkT=0.6 GeV/c andthe centrality range5–10%.Thecomparisonhavebeenalsoperformedforother centralities and the corresponding Blast-Wave model parameters have been deduced. Fig. 5 presents the final source spatial and transverse flow anisotropies for different centrality ranges from matchingthe ALICEdatawiththeBlast-Wavemodelcalculations.Thecontourscorrespondtoonesigmauncertaintyasderivedfrom
Fig. 3.AmplitudesoftherelativeradiioscillationsR2out,3/R2side,0,R2side,3/R2side,0,andR2os,2/R2side,0versuscentralityforfourkT ranges.Squarebracketsindicatesystematic uncertainties.Theshadedbandsarethe3+1Dhydrodynamicalcalculations [14] andthewidthofthebandsrepresenttheuncertaintiesinthemodelcalculations.
Fig. 4. The relative amplitudes of the radius oscillations R2out,3/R2out,0, and R2side,3/R2side,0 on the third-order anisotropies in space (a3) and trans- verse flow (ρ3) for the centrality range 5–10% and kT=0.6 GeV/c from the Blast-Wavemodel [16].Thethindashed linesshowthe linesofaconstantrela- tiveamplitude,inmagentafor R2out,3/R2out,0andindarkyellowfor R2side,3/R2side,0. ThethicklinesshowthecorrespondingALICEresults,withwidthofthelinesrep- resentingthe experimentaluncertainties. (Forinterpretationofthecolors inthe figure(s),thereaderisreferredtothewebversionofthisarticle.)
thefitofthemodeltothedata.Itisobservedthatthefinalsource anisotropyisclosetozero,significantlysmallerthantheinitialtri- angulareccentricitiesthataretypicallyoftheorderof0.2–0.3.The
Fig. 5.Blast-Wavemodel [16] sourceparameters,finalspatial(a3)andtransverse flow(ρ3)anisotropies,fordifferentcentralityranges,asobtainedfromthefittoAL- ICEradiioscillationparameters.Thecontoursrepresenttheonesigmauncertainty.
negativevaluesofthefinalsourceanisotropywouldbeinterpreted asthatthetriangularorientationattheinitial-stateisreversedat freezeout.
4. Summary
We have reported a measurement of two-pion azimuthally- differentialfemtoscopyrelativeto thethirdharmoniceventplane inPb–Pb collisions at√
sNN=2.76 TeV. Theobserved oscillations
oftheHBTradiiunambiguously indicateacollectiveexpansionof thesystemandanisotropyincollectivevelocityfieldsatfreeze-out.
Clearin-phaseoscillationsofRout and Rside,withboth R2out,3 and R2side,3parameters(asdefinedinEq. (4))beingnegative,havebeen observedforallcentralitiesandkT ranges.Accordingtomodelcal- culations [13] theobservedRoutandRsidein-phaseoscillationsare characteristicsofthesourcewithstrongtriangularflowandclose tozerospatialanisotropy.Thisconclusionisfurtherconfirmedbya detailedcomparisonofourresultswiththeBlast-Wavemodelcal- culations [16],fromwhichtheparametersofthesource,thespatial anisotropyandmodulationsintheradialexpansion velocity,have beenderived, withspatial triangularanisotropy beingmore than an orderof magnitudesmallerthan the typical initial anisotropy values.The oscillation amplitudesexhibit weak centrality depen- dence,andingeneraldecreasewithdecreasingkTexceptforR2side,3 whichonoppositeisthelargestinthesmallestkT bin.Theresults ofthe 3+1D hydrodynamic calculations [14] are in a good qual- itativeagreementwith ourmeasurements but, quantitatively,the modelpredictsa strongerdependenceof R2out,3 oscillations onkT thanobservedinthedata.
Acknowledgements
WethankJ. CimermanandB. Tomasikforprovidinguswiththe resultsoftheBlast-Modelcalculations [16].
The ALICECollaboration wouldlike to thank all its engineers andtechniciansfortheirinvaluablecontributionstotheconstruc- tionoftheexperimentandtheCERNacceleratorteamsfortheout- standingperformanceoftheLHCcomplex.TheALICECollaboration gratefully acknowledges the resources and support provided by allGrid centresandthe Worldwide LHCComputing Grid(WLCG) collaboration. The ALICE Collaboration acknowledges the follow- ing funding agencies for their support in building and running the ALICE detector: A.I. Alikhanyan National Science Laboratory (Yerevan Physics Institute) Foundation (ANSL), State Committee of Science and World Federation of Scientists (WFS), Armenia;
AustrianAcademy ofSciences andNationalstiftung fürForschung, Technologie und Entwicklung, Austria; Ministry of Communica- tions and High Technologies, National Nuclear Research Center, Azerbaijan; Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq), Universidade Federal do Rio Grande do Sul (UFRGS),FinanciadoradeEstudoseProjetos(Finep)andFundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP), Brazil;
MinistryofScience&Technology ofChina (MSTC),NationalNatu- ralScienceFoundation ofChina(NSFC) andMinistryofEducation ofChina (MOEC), China;MinistryofScience andEducation,Croa- tia;MinistryofEducation,YouthandSportsoftheCzechRepublic, Czech Republic; The Danish Council for Independent Research – NaturalSciences,theCarlsbergFoundationandDanishNationalRe- search Foundation (DNRF), Denmark;Helsinki Institute ofPhysics (HIP),Finland;Commissariatàl’ÉnergieAtomique (CEA)andInsti- tut Nationalde Physique Nucléaire etde Physique des Particules (IN2P3)andCentre National de laRecherche Scientifique (CNRS), France; Bundesministerium für Bildung, Wissenschaft, Forschung und Technologie (BMBF) and GSI Helmholtzzentrum für Schwe- rionenforschungGmbH,Germany;GeneralSecretariatforResearch and Technology, Ministry of Education, Research and Religions, Greece; National Research, Development and Innovation Office, Hungary; Department of Atomic Energy, Government of India (DAE),DepartmentofScienceandTechnology,GovernmentofIndia (DST),University Grants Commission, Governmentof India(UGC) andCouncil ofScientificandIndustrialResearch(CSIR), India;In- donesian Institute of Science, Indonesia; Centro Fermi – Museo StoricodellaFisicaeCentroStudieRicercheEnricoFermiandIsti- tutoNazionalediFisicaNucleare(INFN),Italy;InstituteforInnova-
tiveScience andTechnology,NagasakiInstituteofAppliedScience (IIST),Japan SocietyforthePromotionofScience (JSPS)KAKENHI and Japanese Ministry of Education, Culture, Sports, Science and Technology (MEXT), Japan; Consejo Nacional de Ciencia (CONA- CYT)yTecnología,throughFondodeCooperaciónInternacionalen CienciayTecnología(FONCICYT)andDirecciónGeneraldeAsuntos delPersonalAcademico(DGAPA),Mexico;NederlandseOrganisatie voor Wetenschappelijk Onderzoek (NWO), Netherlands; The Re- search Council of Norway, Norway; Commission on Science and Technology forSustainable Developmentinthe South(COMSATS), Pakistan;PontificiaUniversidadCatólicadelPerú,Peru;Ministryof ScienceandHigherEducationandNationalScienceCentre,Poland;
KoreaInstituteofScienceandTechnologyInformationandNational ResearchFoundationofKorea(NRF),RepublicofKorea;Ministryof EducationandScientific Research,InstituteofAtomic Physicsand RomanianNationalAgencyforScience,TechnologyandInnovation, Romania; Joint Institute for Nuclear Research (JINR), Ministry of EducationandScienceoftheRussianFederationandNationalRe- search Centre Kurchatov Institute, Russia; Ministry of Education, Science, ResearchandSportofthe Slovak Republic, Slovakia; Na- tionalResearchFoundationofSouthAfrica,SouthAfrica;Centrode AplicacionesTecnológicasyDesarrolloNuclear(CEADEN),Cubaen- ergía,CubaandCentrodeInvestigacionesEnergéticas,Medioambi- entalesyTecnológicas(CIEMAT),Spain;SwedishResearchCouncil (VR) andKnutandAlice Wallenberg Foundation (KAW), Sweden;
EuropeanOrganizationforNuclearResearch,Switzerland;National Science andTechnology Development Agency(NSDTA), Suranaree University of Technology (SUT) and Office of the Higher Educa- tionCommissionunderNRUprojectofThailand,Thailand;Turkish Atomic Energy Agency (TAEK), Turkey; National Academy of Sci- encesofUkraine,Ukraine;ScienceandTechnologyFacilitiesCoun- cil (STFC), United Kingdom; National Science Foundation of the UnitedStatesofAmerica(NSF)andU.S.DepartmentofEnergy,Of- ficeofNuclearPhysics(DOENP),UnitedStatesofAmerica.
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