First measurement of quarkonium polarization in nuclear collisions at the LHC

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First measurement of quarkonium polarization in

nuclear collisions at the LHC

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:

Contents lists available atScienceDirect

Physics

Letters

B

www.elsevier.com/locate/physletb

First

measurement

of

quarkonium

polarization

in

nuclear

collisions

at

the

LHC

.

ALICE

Collaboration



a

r

t

i

c

l

e

i

n

f

o

a

b

s

t

r

a

c

t

Articlehistory: Received9June2020

Receivedinrevisedform10February2021 Accepted12February2021

Availableonline22February2021 Editor:M.Doser

ThepolarizationofinclusiveJ/ψandϒ(1S)producedinPb–Pbcollisionsat√sNN=5.02 TeVattheLHC ismeasuredwiththeALICEdetector.Thestudyiscarriedoutbyreconstructingthequarkoniumthrough itsdecaytomuonpairsintherapidityregion2.5<y<4 andmeasuringthepolarandazimuthalangular distributions ofthe muons. Thepolarizationparameters λθ,λφ and λθ φ are measuredin thehelicity andCollins-Soperreferenceframes, inthetransversemomentuminterval2<pT<10 GeV/c andpT< 15 GeV/c fortheJ/ψand ϒ(1S),respectively.ThepolarizationparametersfortheJ/ψare foundtobe compatiblewithzero,withinamaximumofabouttwostandarddeviationsatlowpT,forbothreference framesandoverthewholepTrange.Thevaluesarecomparedwiththecorrespondingresultsobtained forppcollisionsat√s=7 and8TeVinasimilarkinematicregionbytheALICEandLHCbexperiments. Althoughwith much largeruncertainties, the polarizationparameters for ϒ(1S) productioninPb–Pb collisionsarealsoconsistentwithzero.

©2021TheAuthor(s).PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense (http://creativecommons.org/licenses/by/4.0/).FundedbySCOAP3_.

1. Introduction

Quarkonia,boundstatesofcharm(c)andanticharm(c)or bot-tom (b) and antibottom (b) quarks, represent an important tool to test our understanding of quantum chromodynamics (QCD), sincetheirproductionprocessinvolvesbothperturbativeand non-perturbative aspects. At high energy, the creation of the heavy quark-antiquark pair is a process that can be described using a perturbative QCD approach, dueto the large value of the charm andbottomquarkmasses(mc

∼

1

.

3 GeV/c2,mb

∼

4

.

2 GeV/c2 [1]). However, the subsequent formationof the bound state isa non-perturbativeprocessthatcanbedescribedonlybyempirical mod-els or effective field theory approaches. Among those, models based on Non-Relativistic QCD (NRQCD) [2] give the most suc-cessful description of the production cross section, as measured at high-energy hadron colliders (Tevatron, RHIC, LHC) [3–14]. In the NRQCD approach, the non-perturbative aspects are parame-terized via long-distance matrix elements (LDME), corresponding to the possible intermediate color, spin andangular momentum states ofthe evolving quark-antiquark pair. The valuesof LDMEs need tobe fittedon a subsetof theavailable measurements and can be then considered asuniversal quantities, inthe sense that they can be used in the calculation of production cross sections andotherobservablescorresponding,forexample,todifferent col-lisionsystemsandenergies.Othertheoryapproaches,astheColor

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

SingletModel [15],the ColorEvaporationModel [16] andthekT -factorization [17] are alsoused to describe thequarkonium pro-ductionprocess.

Among the various charmonium states, the J

/ψ

meson, with quantumnumbers JPC

=

1−−,was thefirsttobediscovered.Itis surelythemoststudied,alsoduetothesizeabledecaybranching ratiotodileptonpairs((5

.

961

±

0

.

033)%forthe

μ

+

μ

−channel [1]) thatrepresentsanexcellentexperimentalsignature.WhiletheJ/

ψ

production cross sections are well reproduced by NRQCD-based models,it wassoon realizedthat describing themeasured polar-izationofthisstaterepresentsamuchmoredifficultproblem [18]. The polarization, corresponding to the orientation of theparticle spin with respect to a chosen axis, can be accessed via a study ofthe polar(

θ )

andazimuthal (

φ

) productionangles, relative to thataxis,ofthetwo-bodydecayproductsinthequarkoniumrest frame.TheirangulardistributionW

(θ,

φ)

isparameterizedas

W

(θ, φ)

∝

1 3

+ λ

θ

×



1

+ λ

θcos2

θ

+ λ

φsin2

θ

cos 2

φ

+ λ

θ φsin 2

θ

cos

φ



,

(1) with the polarization parameters

λ

θ,

λ

φ and

λ

θ φ corresponding tovarious combinations ofthe elements ofthe spin density ma-trixof J/

ψ

production [19]. In particular, the two cases (

λ

θ

=

1,

λ

φ

=

0,

λ

θ φ

=

0)and(

λ

θ

= −

1,

λ

φ

=

0,

λ

θ φ

=

0)correspondtothe so-calledtransverseandlongitudinalpolarizations,respectively.At

https://doi.org/10.1016/j.physletb.2021.136146

leadingorder,thehigh-pT productionisdominatedbygluon frag-mentation andtherefore theJ/

ψ

wouldbe expectedto be trans-versely polarized [18].However, the resultsfromtheCDF experi-mentatTevatronshowedthattheJ/

ψ

exhibitsaverysmall polar-ization [20,21], anobservationwhich wasimpossibleto reconcile withtheNRQCDprediction.Asoftoday,ontheexperimentalside, accurate resultsoninclusiveandprompt(i.e.,removing contribu-tionsfromb-quarkdecays)J/

ψ

polarizationhavebecomeavailable atLHCenergies [22–25].Theyconfirmthat thisstateshowslittle or no polarization in a wide rapidity (up to y

=

4

.

5) and trans-versemomentumregion(from2to70GeV/c),withtheexception of the LHCbmeasurements at

√

s

=

7 TeV [24], where thevalue

λ

θ

= −

0

.

145

±

0

.

027, corresponding to a weak longitudinal po-larization, was obtained in the interval 2

<

pT

<

15 GeV/c and 2

<

y

<

4

.

5,inthehelicityframe(itsdefinitionwillbegivenlater inSec.3).Onthetheoryside,ahugeeffortwaspursuedinorderto movetoacompletenext-to-leadingorder(NLO)descriptionofthe J/

ψ

productionprocess [26,27], andtothe calculation ofthe po-larization variables [28,29]. Furtherimportantprogressincludes a quantitativeevaluationofthecontributionoffeed-downprocesses (J/

ψ

comingfromthedecayof

χ

c and

ψ(

2S

)

states)onthe polar-izationobservables [30].ItwasshownthatatNLOtherearerather largecancellationsbetweencontributionscorrespondingtothe dif-ferent possiblecombinations ofthespin andangularmomentum oftheintermediatecc states,reachingamoresatisfactory descrip-tionoftheabsenceofpolarizationobservedinthedata [31]. How-ever,thosedescriptionsusuallyrequiretheinclusionofbothcross sectionandpolarizationresultsinthefitoftheLDME,leadingtoa morelimitedpredictivepoweronthepolarizationobservablesand tolargevariationsinthevaluesoftheextractedLDMEvalues, de-pendingonthesetofdatausedfortheirdetermination.Finally,the description of the J/

ψ

production in the NRQCD framework was recently extendedto the low-pT region, andthepolarization pa-rameterswerestudiedinacolorglasscondensate(CGC)+NRQCD formalism,obtainingafairagreementwithLHCdataatforward ra-pidity [32].Measurementsofthepolarizationparameters arealso available forseveralbottomoniumstates,andinparticularforthe

ϒ(

1S

)

,

ϒ(

2S

)

and

ϒ(

3S

)

resonances,whichwereshowntoexhibit littleornopolarizationatLHCenergies [33–35].Approaches simi-lartothatadoptedforcharmonium,whichalsoneedtotake into account the rather complex feed-down decaystructure forthese states,leadtoafairagreementwiththeexperimentalresults [36]. In thisLetter, we movea step forwardby presentingthe first measurement of J/

ψ

and

ϒ(

1S

)

polarization in ultrarelativistic heavy-ion interactions performed by the ALICE Collaboration by studyingPb–Pbcollisionsat

√

sNN

=

5

.

02 TeV.Suchcollisions rep-resent animportantsourceofinformationfortheinvestigationof thephasediagram ofQCD [37],andinparticularforthestudy of the properties ofthe quark–gluon plasma (QGP), a state of mat-terwherequarksandgluonsarenotconfinedinsidehadrons [38]. Among the experimental observables studied in heavy-ion colli-sions the suppression of heavy quarkonium production is a fun-damentalsignal, sinceQGPformationpreventsthebindingofthe heavy-quarkpairduetothescreeningofthecolorcharge [39] and, moregenerally,hasstrongeffectsonthespectralfunctions [40].At LHC energies, another mechanism, corresponding to the (re)gen-eration of charmonium states in the QGP and/or when the sys-temhadronizes,becomesrelevant [41,42],inparticularatlow pT, dueto the largecharm-quark multiplicity (

>

100 pairsin a cen-tral Pb–Pb collision). The presence of a deconfined system may in principle affect also the polarization ofquarkonium states. In Ref. [43] the observation of a partial transverse polarization for the J/

ψ

was predicted incaseof QGPformation, dueto a modi-fication ofthenon-perturbativeeffectsinthehighenergy-density phase.Moregenerally,theobservedpromptJ/

ψ

areknowntobea mixtureofdirectproductionanddecayproductsfromhigher-mass

charmonium states (

ψ(

2S

)

,

χ

c). In nuclear collisions, since sup-pressioneffectsareexpectedtoaffectmorestronglythelessbound states,therelativecontributionofdirectandfeed-downproduction wouldchangewithrespecttothatinppcollisions,andtheoverall measured polarization may be different according to the poten-tially different polarization of the various states [44,45]. On the otherhand,thecontributionoftheregenerationmechanisminthe J/

ψ

formationprocessbyrecombinationofuncorrelatedcc pairsis likelytogiverisetounpolarizedproductionatlow pT.Finally,the possible presence ofpolarization is known to strongly affectthe acceptanceforJ/

ψ

detectioninthedileptondecay(upto20–30% inALICE [22]),andits measurementisan importantrequisitefor anunbiasedevaluationoftheabsoluteyieldsinnuclearcollisions. A first measurement of

ϒ(

1S

)

polarization in Pb–Pb collisions is alsopresentedin thisLetter, evenifthe correspondingcandidate sampleissmallerbyafactor

∼

30,leading tolargeruncertainties. Forsuch astate, considerationssimilar tothosediscussedforthe J/

ψ

should hold, exceptthat thecontributionof theregeneration mechanismshouldbenegligibleduetothemuchlower multiplic-ityofbottomquarkswithrespecttocharm.

The next sections ofthe Letter are organized asfollows. Sec-tion2contains ashortdescription oftheexperimental apparatus and some details on the data sample used in this analysis. The analysisprocedure andtheevaluationof systematicuncertainties are presented in Sec. 3, while the results on the J/

ψ

and

ϒ(

1S

)

polarization parameters

λ

θ,

λ

φ and

λ

θ φ are showninSec. 4.The conclusionsarepresentedinSec.5.

2. Experimentalsetupanddatasample

ThemeasurementdescribedinthisLetterisperformedwiththe ALICEdetector [46,47],whosemaincomponentsareacentral bar-relandaforwardmuonspectrometer.The lattercoversthe pseu-dorapidityregion

−

4

<

η

<

−

2

.

5 andisusedtodetectmuonpairs fromquarkoniumdecays [48].The muonspectrometer includesa hadronabsorbermadeofconcrete,carbonandsteelwitha thick-ness of 10 interaction lengths, followed by five tracking stations (cathode-pad chambers), with the central one embedded inside a dipole magnet witha 3 T

·

m field integral. Downstreamof the trackingsystem,aniron wallfiltersouttheremaining hadronsas wellaslow-momentummuonsoriginatingfrompionandkaon de-cays,andisfollowedbytwotriggerstations(resistiveplate cham-bers). Another forward detector, the V0 [49], composed of two scintillatorarrayslocatedatoppositesidesoftheinteractionpoint (IP) and covering the pseudorapidity intervals

−

3

.

7

<

η

<

−

1

.

7 and2

.

8

<

η

<

5

.

1,providestheminimumbias(MB)triggerwhich isgivenbyacoincidenceofsignalsfromthetwosides.Amongthe centralbarreldetectors,thetwo layersofthe SiliconPixel Detec-tor(SPD),with

|

η

|

<

2 and

|

η

|

<

1

.

4 coverage,andcorresponding totheinnerpartoftheALICEInnerTrackingSystem(ITS) [50],are used to determine the position of the interaction vertex. Finally, theZeroDegreeCalorimeters (ZDC) [51],locatedoneitherside of theIPat

±

112.5 malongthebeamaxis,detectspectator nucle-onsemittedatzerodegreeswithrespecttotheLHCbeamaxisand areusedtorejectelectromagneticPb–Pbinteractions.

The analysis is based on events where, in addition to the MB condition, two opposite-sign tracks are detected in the trig-gering system of the muon spectrometer (dimuon trigger). The dimuontriggerselectstrackseachhavingatransversemomentum above a thresholdnominally set at pμ_T

=

1 GeV/c, corresponding tothe value forwhichthe single-muontriggerefficiency reaches 50% [52]. The single-muon trigger efficiency reaches a plateau valueof98%at

∼

2

.

5 GeV/c.

am-Fig. 1. Examplesoffitstotheinvariant-massdistributionsinthehelicityreferenceframe.TheleftplotcorrespondstotheJ/ψmassregion,whileontherightafittothe ϒ(1S)massregionisshown.ThefitsareperformedusinganextendedCrystalBallfunctionfortheresonancesignals,whilethebackgroundisparameterizedwithavariable widthGaussian.

plitudedistribution [53,54],withmorecentraleventsleading toa largersignalintheV0.Inthisanalysis,eventscorrespondingtothe mostcentral90%oftheinelasticPb–Pbcrosssectionareselected, asfortheseeventstheMBtriggerisfullyefficientandtheresidual contaminationfromelectromagneticprocessesisnegligible.

The results of the analysis are obtained using the

√

sNN

=

5

.

02 TeV Pb–Pb data samplescollected by the ALICEexperiment during the years 2015and 2018, corresponding to an integrated luminosity Lint

∼

750 μb−1.

3. Dataanalysis

The J/

ψ

and

ϒ(

1S

)

candidates are formed by combining opposite-sign muons reconstructed using the tracking algorithm described in Ref. [48]. In order to reject tracks at the edge of thespectrometeracceptance,thecondition

−

4

<

η

μ

<

−

2

.

5 is re-quired. Inaddition, tracks musthave a radial transverse position at the end of the absorber in the range 17

.

6

<

Rabs

<

88

.

9 cm. Thisselectionisappliedtoremove trackspassingthroughthe in-ner and denser partof the absorber, which are strongly affected bymultiplescattering.Foreachmuoncandidate,amatchbetween tracksreconstructedinthetrackingsystemandtracksegmentsin themuontriggersystemisrequired.

TheJ/

ψ

polarizationparameters

λ

θ,

λ

φ and

λ

θ φ arestudiedas a function of transverse momentum in the intervals 2

<

pT

<

4, 4

<

pT

<

6 and 6

<

pT

<

10 GeV/c.For each pT interval, a two– dimensional (2D) grid of dimuon invariant-mass spectra is cre-ated, corresponding to intervals in cos

θ

and

φ

, where

θ

and

φ

are the polar andazimuthal emission angles, respectively, of the decay products in the J/

ψ

restframe, withrespect to the refer-ence axis. More in detail, the 2D grid covers the fiducial region

−

0

.

8

<

cos

θ <

0

.

8 (17intervals), 0

.

5

< φ <

π

−

0

.

5 rad(8 inter-vals, assuming asymmetric distributionaround

φ

=

π

), withthe choiceoftheboundariesaswellasthewidthoftheintervals dic-tatedbyacceptanceconsiderations.

Theanalysisisperformedchoosingtwodifferentreference sys-temsforthedeterminationoftheangularvariables.Inthe Collins-Soper(CS) framethez-axisisdefinedasthebisectoroftheangle betweenthedirectionofonebeamandtheoppositeofthe direc-tion of the other one inthe rest frame of the decaying particle, allowing therefore an evaluation of the polarization parameters with respectto the directionof motionof the collidinghadrons. Inthehelicity (HE)referenceframethe z-axis isgivenby the di-rectionofthedecayingparticleinthecenter-of-massframeofthe

collision,andthereforethepolarizationcanbeevaluated with re-specttothemomentumdirectionoftheJ/

ψ

itself.The

φ

=

0 plane istheonecontainingthetwobeamsintheJ/

ψ

restframe.

For each dimuon invariant-mass spectrum, the J/

ψ

raw yield isobtainedby means ofa binned maximum likelihoodfit inthe interval 2

.

1

<

mμμ

<

4

.

9 GeV/c2_{. The background continuum is} parameterized with a Gaussian distribution whose width varies linearlywiththemassor,alternatively,withafourthdegree poly-nomial functiontimesan exponential. TheJ

/ψ

signal ismodeled with a pseudo-Gaussian function or witha Crystal Ball function withasymmetrictailsonbothsidesofthepeak [55].

The J

/ψ

mass is kept free in the fits, while for each interval (i

,

j)in(cos

θ,

φ

)thewidthisfixedto

σ

Ji/ψ,j

=

σ

i,j,MC

J/ψ

· (

σ

J/ψ

/

σ

MC J/ψ

)

, i.e.,scalingtheresonancewidthextractedfromMonteCarlo(MC) simulations (

σ

_Ji_/ψ,j,MC) by the ratio between the width obtained by fitting the angle-integrated spectrum in data (

σ

J/ψ) and MC (

σ

MC

J/ψ) forthe pT interval underconsideration.The parametersof thenon-Gaussian tailsofthe resonanceare keptfixed tothe MC values.The

ψ(

2S

)

contribution,althoughcomparativelynegligible, is also taken into account in the fits, with its width and mass fixed in each fit to those of the J/

ψ

according to the relations

σ

ψ (2S)

=

σ

J/ψ

·

σ

ψ (MC2S)

/

σ

JMC/ψ andmψ (2S)

=

mJ/ψ

+

mψ (PDG2S)

−

mPDGJ/ψ,with theParticleDataGroup(PDG)massestakenfromRef. [1].InFig.1 (left)anexampleofafittotheinvariant-massspectrumintheJ/

ψ

massregionisshown.DuetothestabilityoftheextractedJ/

ψ

pa-rameters (mass, width),the fits were carriedout directlyon the sumofthe2015and2018invariantmassspectra.

The J

/ψ

raw yields asa function of theangular variables are thencorrected bythe productof theacceptanceanddetector ef-ficiency( A

×

ε

),which is evaluated asa functionof cos

θ

and

φ

ona 2D grid via MC simulations. The J

/ψ

are generated accord-ing to pT and y distributions directlytuned ondata [56] via an iterativeprocedure [57],andtheirdecaymuonsarepropagated in-side a realistic description of the ALICE setup, based on GEANT 3.21 [58]. The misalignment of the detection elements and the time-dependentstatusofeach electronic channelduring thedata takingperiodaretakenintoaccountaswell.IntheJ

/ψ

generation an isotropic distribution of decayproducts, corresponding to the assumptionofnopolarization,isadopted.Duetothechoiceof rel-ativelysmall(cos

θ

,

φ

)intervals,the A

×

ε

valuesforeachinterval are quite insensitiveto the specific angular distribution assumed inthegeneration.

cor-Fig. 2. FittotheJ/ψ2Dangulardistributionsinthehelicityreferenceframeprojectedalongcosθ(left)andφ(right)for2.5<y<4 and4<pT<6 GeV/c.Thedisplayed

uncertaintiesarestatistical.

rectedforacceptanceandefficiency,accordingtoEq. (1).Foreach combinationofsignalandbackgroundshapeusedinthefittothe dimuoninvariant-massspectra,aseparateevaluationofthe polar-izationparametersiscarriedoutandtheir averageistakenasthe best estimate. The statistical uncertaintyis given by the average ofthestatisticaluncertaintiesofthe2D fits,whiletherootmean square of the results provides the systematic uncertainty on the signal extraction,withtheabsolutevaluesrangingbetween0.002 and0.039.Theoverallproceduredescribedabovewaschecked be-forehand with a MC closure test. The 2D fits on the (cos

θ

,

φ

) distributions only allow a determinationof theabsolute value of

λ

θ φ,duetothepresenceofsin 2

θ

inthecorresponding termthat inducesanambiguityinitssign.Itischeckedthatthevaluesof

λ

θ and

λ

φ are stableagainstthechoice ofthesignof the

λ

θ φ term. In thefollowing the

λ

θ φ values corresponding to thechoice ofa positivesignarequoted.Fig.2illustrates anexampleofthefitto theangulardistributions.Forbettervisibility,boththedistribution andthefittedfunctionareprojectedalongonedimension.

Inaddition tothesystematicuncertaintyrelatedtothechoice of the mass shapes for signal and background, several other sources aretakeninto account.First,an alternative procedurefor extractingtheJ

/ψ

signaliscarriedout,bykeepingitswidthasa freeparameterintheinvariant-massfits.Thecorrespondingresults forthepolarizationparametersarethenobtainedandtheaverages ofthevaluescorrespondingtofixingthewidthornotaretakenas thecentralvaluesfor

λ

θ,

λ

φ and

λ

θ φ.Halfthedifferencebetween theresultsobtainedwithfreeorMC-anchoredwidthsisthen con-sidered as a further systematic uncertainty related to the signal extraction.Thisuncertaintyisfoundtobetheleadingcontribution tothetotalabsolutesystematicuncertaintyonthepolarization pa-rameters, and ranges between 0.001 and 0.063, the latter value correspondingtotheuncertaintyon

λ

HE_θ for2

<

pT

<

4 GeV/c.

Anothersourceofsystematicuncertaintyisrelatedtothe eval-uationofthetriggerefficiency.Themuontriggerresponsefunction asafunctionofthesinglemuontransversemomentum pμ_T canbe obtained via MC or with a procedure based on data [59]. Small deviationsare foundfor pμt

<

2 GeV/c which inducean effecton A

×

ε

forthe J

/ψ

.Therefore,the polarization parameters are re-calculated with A

×

ε

valuesweighted in such a waytoaccount for the deviations. The variation of the polarization parameters between thedifferent triggerefficiency estimatesis taken asthe relatedsystematicuncertainty, withvalues rangingfrom0.001 to 0.043,thehighestvaluesbeingfoundfor

λ

HE_θ in2

<

pT

<

4 GeV/c. The systematicuncertaintyrelatedtotheevaluationofthemuon trackingefficiencyisfoundtobenegligibleforthisanalysis,

allow-ingasignificantreductionofthetotalsystematicuncertaintywith respectto previous pp analyses [23].Indeed,although the differ-encebetweenefficienciescalculatedviaMCorfromdata [59] isof theorderof2%,adetailedinvestigationhasshownnodependence ontheangularvariablesandthereforenoeffectonthepolarization parameters.

Finally, the systematic uncertainty induced by the choice of the pT and y distributions used as an input for the calculation of A

×

ε

isevaluated testingalternative pT and y parameteriza-tions,whichareobtainedbyvaryingwithintheiruncertaintiesthe defaultdistributions directly tuned on Pb–Pb data.The polariza-tionparameters extractedwiththe modified values of A

×

ε

are comparedwiththoseobtainedwiththedefaultinput shapesand thecorresponding systematicuncertaintyextractedinthiswayis foundtorangebetween0.001and0.030,withthelargestvalue as-signedto

λ

HE_θ for2

<

pT

<

4 GeV/c.Theinfluenceofthechoiceof theangulardistributions oftheJ/

ψ

decayproductsforthe A

×

ε

calculationisalsoinvestigatedbymeansofan iterativeprocedure onthese input distributions. Theeffect isfound to be negligible, alsodueto thefact that the2D correction procedure onthe an-gularvariablesisbydefinitionrelativelyinsensitivetothespecific choiceofthecorrespondingdistributions.Asummaryofthevalues ofallthe absolutesystematicuncertainties, whichare considered asuncorrelatedasafunctionofpT,isreportedinTable1.The to-talsystematicuncertainties are obtained, foreach parameter and pTinterval,asthequadraticsumofthevalues.

Asimilarprocedureisfollowedfortheextractionofthe

ϒ(

1S

)

polarizationparameters. Duetothesmallercandidatesample, in-tegrated values over the kinematic interval 2

.

5

<

y

<

4, pT

<

15 GeV/c areobtained.Themaindifferencewithrespecttothe2D approachfollowed fortheJ/

ψ

is theuseof asimultaneous fitto the1D angulardistributions [23],afterintegrationover theother variables.Therequirementpμ_T

>

2 GeV/c,whichhelpsreducingthe combinatorialbackground, isincluded [60]. The

ϒ(

1S

)

signal ex-tractioninthevariouscos

θ

and

φ

intervalsisperformedbymeans ofinvariant-massfits(seetherightpanelofFig.1foranexample). ThefunctionschosenfortheresonancesarethesameasintheJ/

ψ

Table 1

SummaryoftheabsolutesystematicuncertaintiesontheevaluationoftheJ/ψ polarizationparameters.Alltheuncertaintiesareconsideredasuncorrelatedasafunction of pT.

Helicity Collins-Soper

Signal J/ψ Trigger Input Signal J/ψ Trigger Input

pT(GeV/c) extr. width eff. MC extr. width eff. MC

λθ 2<pT<4 0.030 0.063 0.043 0.030 0.026 0.049 0.015 0.009 4<pT<6 0.017 0.046 0.040 0.024 0.002 0.052 0.018 0.007 6<pT<10 0.039 0.005 0.018 0.017 0.022 0.001 0.011 0.006 λφ 2<pT<4 0.007 0.030 0.004 0.002 0.024 0.010 0.020 0.003 4<pT<6 0.003 0.035 0.003 0.003 0.002 0.010 0.020 0.003 6<pT<10 0.002 0.009 0.001 0.002 0.005 0.013 0.011 0.002 λθ φ 2<pT<4 0.021 0.029 0.024 0.001 0.013 0.010 0.017 0.015 4<pT<6 0.007 0.011 0.017 0.006 0.002 0.042 0.010 0.015 6<pT<10 0.020 0.019 0.007 0.008 0.007 0.042 0.003 0.013 Table 2

J/ψpolarizationparameters,measuredforPb–Pbcollisionsat√sNN=5.02 TeV,inthehelicityandCollins-Soper

referenceframesintherapidityinterval2.5<y<4.Thefirstuncertaintyisstatisticalandthesecondsystematic.

pT(GeV/c) Helicity Collins-Soper

λθ 2<pT<4 0.218±0.060±0.087 −0.157±0.049±0.058 4<pT<6 0.151±0.071±0.068 −0.057±0.059±0.055 6<pT<10 −0.070±0.068±0.047 −0.008±0.063±0.026 λφ 2<pT<4 −0.029±0.017±0.031 0.061±0.015±0.033 4<pT<6 −0.013±0.019±0.036 0.047±0.024±0.023 6<pT<10 0.047±0.021±0.010 0.024±0.032±0.018 λθ φ 2<pT<4 −0.124±0.028±0.043 −0.090±0.027±0.029 4<pT<6 −0.059±0.030±0.021 −0.040±0.034±0.046 6<pT<10 −0.025±0.031±0.030 0.018±0.035±0.044

or, alternatively,with asecond degree polynomial function times an exponential. The systematic uncertainty on the signal extrac-tion is calculated with the same procedure adopted for the J/

ψ

. An uncertaintyrelatedto thechoice ofthe signalwidth hasalso beenconsidered, takenasthehalf-difference betweentheresults obtained with the prescription described above andusing asan alternative prescription the pure MC values. The uncertainty on the trigger efficiency isnegligible, due to theadditional require-ment on the single-muontransverse momentum which selectsa pT-region wherethetrigger efficiencyisvery highandits evalu-ationvia dataandMCisconsistent.Finally,theprocedureforthe determination of the uncertainty related to the

ϒ(

1S

)

kinematic distributions used in theMC is the sameas forthe J/

ψ

. The to-talsystematicuncertaintiesforthe

ϒ(

1S

)

analysisarereportedin Table3,togetherwiththeresults.

4. Results

ThepolarizationparametersforJ

/ψ

inclusiveproductioninPb– Pbcollisionsat

√

sNN

=

5.02TeVinthehelicityandCollins-Soper reference framesare shown in Fig. 3 andthe corresponding nu-merical values are reportedin Table 2.In Fig.3,

λ

θ,

λ

φ and

λ

θ φ are alsocompared withthe LHCb [24] and ALICE[23] measure-mentsinppcollisionsat

√

s

=

7 and8TeV,respectively.

For all the pT intervals andin bothreference framesthe val-uesofthepolarizationparametersexhibitatmostslightdeviations from zero. In particular,

λ

HE_θ indicates a slight transverse polar-ization at low pT (

∼

2

.

1

σ

effect, calculated using the Gaussian approximation), while

λ

CS_θ showsaweaklongitudinalpolarization (

∼

2

.

1

σ

). When increasing pT, the central values of

λ

θ become close to zero. All values of

λ

φ and

λ

θ φ are, in absolute value, smaller than 0.1, exceptfor

λ

HE_{θ φ},which is

−

0

.

124 at low pT and deviatesfromzeroby

∼

2

.

4

σ

.

When comparingwiththepp results,nosignificantdifference is found with respectto ALICE resultsat

√

s

=

8 TeV, which are compatible with zero. A significant difference is found with re-specttothehigher-precisionLHCbresultsat

√

s

=

7 TeV,reaching

Table 3

ϒ(1S)polarizationparametersinthehelicityand Collins-Soperreference frames measuredinPb–Pbcollisionsat√sNN=5.02 TeVintherapidityinterval2.5<y<

4 andfortransversemomentumpT<15 GeV/c.Thefirstuncertaintyisstatistical

andthesecondsystematic.

Helicity Collins-Soper

λθ −0.090±0.395±0.101 0.418±0.526±0.178

λφ −0.094±0.072±0.020 −0.141±0.087±0.033

λθ φ −0.074±0.099±0.020 0.017±0.113±0.024

3

.

3

σ

in the interval 2

<

pT

<

4 GeV/c in the helicity reference frame, where pp data [24] indicate a small but significant de-greeof longitudinalpolarization, while the Pb–Pb resultsfavor a slightly transverse polarization. In Pb–Pb collisions at LHC ener-gies,a significantfractionofthedetected J/

ψ

originatesfromthe recombinationofcc pairs inthe QGPphase orwhen the system hadronizes.Moreover,thecontributionfromhigher-mass charmo-niumstatesdecayingtoJ/

ψ

couldvarybetweenppandPb-Pbdue todifferentsuppressioneffectsforeachstate innuclearcollisions. Therefore,theobservedhintforadifferentpolarization inpp and Pb–Pbmight be areflectionof thedifferentproduction and sup-pression mechanismsin the two systems,butmore precisedata, along with quantitative theory estimates, are needed for a def-inite conclusion. It should also be noted that the ALICE results refer to inclusive production, while LHCb has measured prompt J/

ψ

.However,asdiscussedinRef. [22],thesizeofthenon-prompt componentissmallinthecovered pT region(oftheorderof15% athighpT)anditspolarizationwas alsomeasuredtobesmallby CDF(

λ

HE_θ

∼ −

0

.

1 [21]),implyingthat theneteffectofthissource oninclusiveJ/

ψ

polarizationshouldbenegligible.

Fig. 3. InclusiveJ/ψpolarizationparametersasafunctionoftransversemomentumforPb–Pbcollisionsat√sNN=5.02TeV,comparedwithresultsobtainedinppcollisions

byALICEat√s=8 TeV[23] andbyLHCbforpromptJ/ψat√s=7 TeV[24] (theLHCbmarkerswereshiftedhorizontallyby+0.3 GeV/c forbettervisibility)intherapidity interval3<y<3.5.Theerrorbarsrepresentthetotaluncertaintiesfortheppresults,whileforPb–Pbstatisticalandsystematicuncertaintiesareplottedseparatelyasa verticalbarandashadedbox,respectively.Intheleftpartoftheplotthepolarizationparametersinthehelicityreferenceframearereported,intherightthoseforthe Collins-Soperframe.

5. Conclusions

The first measurement of the polarization parameters for J/

ψ

productioninnuclearcollisionsatLHCenergieswascarriedoutby theALICECollaborationinPb–Pbinteractionsat

√

sNN

=

5

.

02 TeV. The

λ

θ,

λ

φ and

λ

θ φ parameterswereevaluatedinthehelicityand Collins-Soperreferenceframesintherapidityinterval 2

.

5

<

y

<

4 andinthe transversemomentum interval 2

<

pT

<

10 GeV/c. All the parametervalues are closetozero, witha

∼

2

.

1

σ

indication forasmalltransversepolarizationinthehelicityframeatlow pT, and a corresponding indication for a smalllongitudinal polariza-tion inthe Collins-Soperframe(

∼

2

.

1

σ

effect).When comparing theseresultswithpp datatakenathigher energyattheLHC,an interesting feature is a significant difference in

λ

HE_θ with respect totheLHCbresultswhichshowedinsteadasmalllongitudinal po-larization inasimilar kinematicdomain.Thisfirstresultobtained forJ/

ψ

innuclearcollisionsanddescribedinthisLetterrepresents therefore a starting point forfuture studies connectingsuch fea-tures with the known differencesin the production mechanisms betweenppandnucleus–nucleuscollisions.Results werealso ob-tainedforthefirsttimeforthe

ϒ(

1S

)

polarization,integratedover pT andy,showing,withinthelargeuncertaintiesofthe measure-ment,valuescompatiblewiththeabsenceofpolarization.

Declarationofcompetinginterest

Theauthorsdeclarethattheyhavenoknowncompeting finan-cialinterestsorpersonalrelationshipsthatcouldhaveappearedto influencetheworkreportedinthispaper.

Acknowledgements

Fun-dação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) and Universidade Federal do Rio Grande do Sul (UFRGS), Brazil; Ministry of Education of China (MOEC), Ministry of Science & Technology of China (MSTC) and National Natural Science Foun-dation of China (NSFC), China; Ministry of Science and Educa-tion and Croatian Science Foundation, Croatia; Centro de Aplica-ciones Tecnológicas y Desarrollo Nuclear (CEADEN),Cubaenergía, Cuba;MinistryofEducation,YouthandSportsoftheCzech Repub-lic,Czech Republic;TheDanish Council forIndependent Research | Natural Sciences, the Villum Fonden and Danish National Re-search Foundation (DNRF), Denmark; HelsinkiInstitute of Physics (HIP),Finland;Commissariatàl’ÉnergieAtomique (CEA)and Insti-tut National de Physique Nucléaire et de Physique des Particules (IN2P3) andCentre Nationalde la Recherche Scientifique(CNRS), France; Bundesministerium für Bildung und Forschung (BMBF) andGSIHelmholtzzentrumfürSchwerionenforschungGmbH, Ger-many;GeneralSecretariatforResearchandTechnology,Ministryof Education,ResearchandReligions,Greece;NationalResearch, De-velopmentandInnovationOffice,Hungary;DepartmentofAtomic Energy, Government of India (DAE), Department of Science and Technology, Government of India (DST), University Grants Com-mission,GovernmentofIndia(UGC)andCouncil ofScientificand Industrial Research (CSIR), India; Indonesian Institute of Science, Indonesia;CentroFermi- MuseoStoricodellaFisicaeCentroStudi e Ricerche Enrico Fermi and Istituto Nazionale di Fisica Nucle-are (INFN), Italy; Institute forInnovative Science andTechnology, Nagasaki Institute of AppliedScience (IIST), Japanese Ministry of Education, Culture, Sports, Science and Technology (MEXT) and JapanSocietyforthePromotionofScience(JSPS)KAKENHI,Japan; Consejo Nacional de Ciencia (CONACYT) y Tecnología, through FondodeCooperaciónInternacionalenCienciayTecnología (FON-CICYT)andDirección Generalde AsuntosdelPersonalAcademico (DGAPA), Mexico; NederlandseOrganisatievoor Wetenschappelijk Onderzoek (NWO),Netherlands; TheResearch Councilof Norway, Norway; Commission on Science and Technology for Sustainable Development in the South (COMSATS), Pakistan; Pontificia Uni-versidad Católica del Perú, Peru; Ministry ofScience andHigher Education, National Science Centre and WUT ID-UB, Poland; Ko-rea Institute ofScience andTechnology Information andNational Research Foundation ofKorea (NRF), Republicof Korea; Ministry of Education and Scientific Research, Institute of Atomic Physics and Ministryof Research andInnovation and Institute of Atomic Physics,Romania;JointInstitute forNuclear Research(JINR), Min-istryofEducationandScience oftheRussianFederation, National Research Centre Kurchatov Institute, Russian Science Foundation andRussianFoundationforBasicResearch,Russia;Ministryof Ed-ucation, Science, Research andSport ofthe Slovak Republic, Slo-vakia;NationalResearchFoundation ofSouthAfrica,SouthAfrica; SwedishResearchCouncil(VR)andKnut&AliceWallenberg Foun-dation (KAW), Sweden; European Organization for Nuclear Re-search,Switzerland;SuranareeUniversityofTechnology(SUT), Na-tional Scienceand Technology DevelopmentAgency (NSDTA)and Officeof theHigher EducationCommission underNRU projectof Thailand,Thailand;TurkishAtomicEnergyAgency(TAEK),Turkey; National Academy of Sciences of Ukraine, Ukraine; Science and TechnologyFacilitiesCouncil(STFC),UnitedKingdom;National Sci-enceFoundation oftheUnitedStatesofAmerica(NSF)andUnited StatesDepartment ofEnergy, Officeof Nuclear Physics(DOE NP), UnitedStatesofAmerica.

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S. Acharya

141

,

D. Adamová

95

,

A. Adler

74

,

J. Adolfsson

81

,

M.M. Aggarwal

100

,

G. Aglieri Rinella

34

,

M. Agnello

30

,

N. Agrawal

10

,

54

,

Z. Ahammed

141

,

S. Ahmad

16

,

S.U. Ahn

76

,

Z. Akbar

51

,

A. Akindinov

92

,

M. Al-Turany

107

,

S.N. Alam

40

,

141

,

D.S.D. Albuquerque

122

,

D. Aleksandrov

88

,

B. Alessandro

59

,

H.M. Alfanda

6

,

R. Alfaro Molina

71

,

B. Ali

16

,

Y. Ali

14

,

A. Alici

10

,

26

,

54

,

N. Alizadehvandchali

125

,

A. Alkin

2

,

34

,

J. Alme

21

,

T. Alt

68

,

L. Altenkamper

21

,

I. Altsybeev

113

,

M.N. Anaam

6

,

C. Andrei

48

,

D. Andreou

34

,

A. Andronic

144

,

M. Angeletti

34

,

V. Anguelov

104

,

C. Anson

15

,

T. Antiˇci ´c

108

,

F. Antinori

57

,

P. Antonioli

54

,

N. Apadula

80

,

L. Aphecetche

115

,

H. Appelshäuser

68

,

S. Arcelli

26

,

R. Arnaldi

59

,

M. Arratia

80

,

I.C. Arsene

20

,

M. Arslandok

104

,

A. Augustinus

34

,

R. Averbeck

107

,

S. Aziz

78

,

M.D. Azmi

16

,

A. Badalà

56

,

Y.W. Baek

41

,

S. Bagnasco

59

,

X. Bai

107

,

R. Bailhache

68

,

R. Bala

101

,

A. Balbino

30

,

A. Baldisseri

137

,

M. Ball

43

,

S. Balouza

105

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D. Banerjee

3

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R. Barbera

27

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L. Barioglio

25

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G.G. Barnaföldi

145

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L.S. Barnby

94

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V. Barret

134

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P. Bartalini

6

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C. Bartels

127

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K. Barth

34

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E. Bartsch

68

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F. Baruffaldi

28

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N. Bastid

134

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S. Basu

143

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G. Batigne

115

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B. Batyunya

75

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D. Bauri

49

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J.L. Bazo Alba

112

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I.G. Bearden

89

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C. Beattie

146

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C. Bedda

63

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N.K. Behera

61

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I. Belikov

136

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A.D.C. Bell Hechavarria

144

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F. Bellini

34

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R. Bellwied

125

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V. Belyaev

93

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G. Bencedi

145

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S. Beole

25

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A. Bercuci

48

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Y. Berdnikov

98

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D. Berenyi

145

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R.A. Bertens

130

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D. Berzano

59

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M.G. Besoiu

67

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L. Betev

34

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A. Bhasin

101

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I.R. Bhat

101

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M.A. Bhat

3

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H. Bhatt

49

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B. Bhattacharjee

42

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A. Bianchi

25

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L. Bianchi

25

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N. Bianchi

52

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J. Bielˇcík

37

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J. Bielˇcíková

95

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A. Bilandzic

105

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G. Biro

145

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R. Biswas

3

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S. Biswas

3

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J.T. Blair

119

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D. Blau

88

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C. Blume

68

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G. Boca

139

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F. Bock

96

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A. Bogdanov

93

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S. Boi

23

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J. Bok

61

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L. Boldizsár

145

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A. Bolozdynya

93

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M. Bombara

38

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G. Bonomi

140

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H. Borel

137

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A. Borissov

93

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H. Bossi

146

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E. Botta

25

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L. Bratrud

68

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P. Braun-Munzinger

107

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M. Bregant

121

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M. Broz

37

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E. Bruna

59

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G.E. Bruno

33

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106

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M.D. Buckland

127

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D. Budnikov

109

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S.A. Bysiak

118

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D. Caffarri

90

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A. Caliva

107

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E. Calvo Villar

112

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J.M.M. Camacho

120

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R.S. Camacho

45

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P. Camerini

24

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F.D.M. Canedo

121

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A.A. Capon

114

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F. Carnesecchi

26

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R. Caron

137

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J. Castillo Castellanos

137

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A.J. Castro

130

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E.A.R. Casula

55

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F. Catalano

30

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C. Ceballos Sanchez

75

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P. Chakraborty

49

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S. Chandra

141

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W. Chang

6

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S. Chapeland

34

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M. Chartier

127

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S. Chattopadhyay

141

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S. Chattopadhyay

110

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A. Chauvin

23

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C. Cheshkov

135

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B. Cheynis

135

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V. Chibante Barroso

34

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D.D. Chinellato

122

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S. Cho

61

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P. Chochula

34

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T. Chowdhury

134

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P. Christakoglou

90

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C.H. Christensen

89

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P. Christiansen

81

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T. Chujo

133

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C. Cicalo

55

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L. Cifarelli

10

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26

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L.D. Cilladi

25

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F. Cindolo

54

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M.R. Ciupek

107

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G. Clai

54

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ii

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J. Cleymans

124

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F. Colamaria

53

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D. Colella

53

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A. Collu

80

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M. Colocci

26

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M. Concas

59

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iii

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G. Conesa Balbastre

79

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Z. Conesa del Valle

78

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G. Contin

24

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60

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J.G. Contreras

37

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T.M. Cormier

96

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Y. Corrales Morales

25

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P. Cortese

31

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M.R. Cosentino

123

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F. Costa

34

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S. Costanza

139

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P. Crochet

134

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E. Cuautle

69

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P. Cui

6

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L. Cunqueiro

96

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D. Dabrowski

142

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T. Dahms

105

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A. Dainese

57

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F.P.A. Damas

115

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137

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M.C. Danisch

104

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A. Danu

67

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D. Das

110

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I. Das

110

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P. Das

86

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P. Das

3

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S. Das

3

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A. Dash

86

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S. Dash

49

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S. De

86

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A. De Caro

29

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G. de Cataldo

53

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J. de Cuveland

39

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A. De Falco

23

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D. De Gruttola

10

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N. De Marco

59

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S. De Pasquale

29

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S. Deb

50

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H.F. Degenhardt

121

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K.R. Deja

142

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A. Deloff

85

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S. Delsanto

25

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131

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W. Deng

6

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P. Dhankher

49

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D. Di Bari

33

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A. Di Mauro

34

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R.A. Diaz

8

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T. Dietel

124

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P. Dillenseger

68

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Y. Ding

6

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R. Divià

34

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D.U. Dixit

19

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Ø. Djuvsland

21

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U. Dmitrieva

62

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A. Dobrin

67

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B. Dönigus

68

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O. Dordic

20

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A.K. Dubey

141

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A. Dubla

90

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107

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S. Dudi

100

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M. Dukhishyam

86

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P. Dupieux

134

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R.J. Ehlers

96

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V.N. Eikeland

21

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D. Elia

53

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B. Erazmus

115

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F. Erhardt

99

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A. Erokhin

113

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M.R. Ersdal

21

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B. Espagnon

78

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G. Eulisse

34

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D. Evans

111

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S. Evdokimov

91

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L. Fabbietti

105

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M. Faggin

28

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J. Faivre

79

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F. Fan

6

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A. Fantoni

52

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M. Fasel

96

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P. Fecchio

30

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A. Feliciello

59

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G. Feofilov

113

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A. Fernández Téllez

45

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A. Ferrero

137

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A. Ferretti

25

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A. Festanti

34

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104

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J. Figiel

118

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S. Filchagin

109

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D. Finogeev

62

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F.M. Fionda

21

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G. Fiorenza

53

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F. Flor

125

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A.N. Flores

119

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S. Foertsch

72

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P. Foka

107

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S. Fokin

88

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E. Fragiacomo

60

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U. Frankenfeld

107

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U. Fuchs

34

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C. Furget

79

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A. Furs

62

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M. Fusco Girard

29

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J.J. Gaardhøje

89

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M. Gagliardi

25

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A.M. Gago

112

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A. Gal

136

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C.D. Galvan

120

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P. Ganoti

84

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C. Garabatos

107

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J.R.A. Garcia

45

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E. Garcia-Solis

11

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K. Garg

115

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C. Gargiulo

34

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A. Garibli

87

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K. Garner

144

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P. Gasik

105

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107

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E.F. Gauger

119

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M.B. Gay Ducati

70

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M. Germain

115

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J. Ghosh

110

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P. Ghosh

141

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S.K. Ghosh

3

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M. Giacalone

26

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P. Gianotti

52

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P. Giubellino

59

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107

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P. Giubilato

28

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A.M.C. Glaenzer

137

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P. Glässel

104

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A. Gomez Ramirez

74

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V. Gonzalez

107

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143

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L.H. González-Trueba

71

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S. Gorbunov

39

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L. Görlich

118

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A. Goswami

49

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S. Gotovac

35

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V. Grabski

71

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L.K. Graczykowski

142

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K.L. Graham

111

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L. Greiner

80

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A. Grelli

63

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C. Grigoras

34

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V. Grigoriev

93

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A. Grigoryan

1

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S. Grigoryan

75

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O.S. Groettvik

21

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F. Grosa

30

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59

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J.F. Grosse-Oetringhaus

34

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R. Grosso

107

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R. Guernane

79

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M. Guittiere

115

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K. Gulbrandsen

89

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T. Gunji

132

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A. Gupta

101

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R. Gupta

101

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I.B. Guzman

45

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R. Haake

146

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M.K. Habib

107

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C. Hadjidakis

78

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H. Hamagaki

82

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G. Hamar

145

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M. Hamid

6

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R. Hannigan

119

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M.R. Haque

63

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86

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A. Harlenderova

107

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J.W. Harris

146

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A. Harton

11

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J.A. Hasenbichler

34

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H. Hassan

96

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Q.U. Hassan

14

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D. Hatzifotiadou

10

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54

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P. Hauer

43

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L.B. Havener

146

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S. Hayashi

132

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S.T. Heckel

105

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E. Hellbär

68

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H. Helstrup

36

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A. Herghelegiu

48

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T. Herman

37

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E.G. Hernandez

45

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G. Herrera Corral

9

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F. Herrmann

144

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K.F. Hetland

36

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H. Hillemanns

34

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C. Hills

127

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B. Hippolyte

136

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B. Hohlweger

105

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J. Honermann

144

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D. Horak

37

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A. Hornung

68

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S. Hornung

107

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R. Hosokawa

15

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133

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P. Hristov

34

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C. Huang

78

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C. Hughes

130

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P. Huhn

68

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T.J. Humanic

97

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H. Hushnud

110

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L.A. Husova

144

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N. Hussain

42

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S.A. Hussain

14

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D. Hutter

39

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J.P. Iddon

34

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127

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R. Ilkaev

109

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H. Ilyas

14

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M. Inaba

133

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G.M. Innocenti

34

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M. Ippolitov

88

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A. Isakov

95

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M.S. Islam

110

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M. Ivanov

107

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V. Ivanov

98

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V. Izucheev

91

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B. Jacak

80

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N. Jacazio

34

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54

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P.M. Jacobs

80

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S. Jadlovska

117

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J. Jadlovsky

117

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S. Jaelani

63

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C. Jahnke

121

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M.J. Jakubowska

142

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M.A. Janik

142

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T. Janson

74

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M. Jercic

99

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O. Jevons

111

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M. Jin

125

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F. Jonas

96

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144

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P.G. Jones

111

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J. Jung

68

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M. Jung

68

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A. Jusko

111

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P. Kalinak

64

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A. Kalweit

34

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V. Kaplin

93

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S. Kar

6

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A. Karasu Uysal

77

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D. Karatovic

99

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O. Karavichev

62

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T. Karavicheva

62

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P. Karczmarczyk

142

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E. Karpechev

62

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A. Kazantsev

88

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U. Kebschull

74

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R. Keidel

47

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M. Keil

34

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B. Ketzer

43

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Z. Khabanova

90

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A.M. Khan

6

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S. Khan

16

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A. Khanzadeev

98

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Y. Kharlov

91

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A. Khatun

16

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A. Khuntia

118

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B. Kileng

36

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B. Kim

61

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B. Kim

133

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D. Kim

147

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D.J. Kim

126

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E.J. Kim

73

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17

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J. Kim

147

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J.S. Kim

41

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J. Kim

104

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J. Kim

147

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J. Kim

73

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M. Kim

104

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S. Kim

18

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T. Kim

147

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147

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S. Kirsch

68

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I. Kisel

39

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S. Kiselev

92

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A. Kisiel

142

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J.L. Klay

5

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C. Klein

68

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J. Klein

34

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59

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S. Klein

80

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C. Klein-Bösing

144

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M. Kleiner

68

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A. Kluge

34

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M.L. Knichel

34

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125

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C. Kobdaj

116

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M.K. Köhler

104

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T. Kollegger

107

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75

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93

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91

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J. Konig

68

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S.A. Konigstorfer

105

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34

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G. Kornakov

142

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L. Koska

117

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O. Kovalenko

85

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V. Kovalenko

113

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M. Kowalski

118

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I. Králik

64

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A. Kravˇcáková

38

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L. Kreis

107

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M. Krivda

64

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111

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F. Krizek

95

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