Longitudinal and azimuthal evolution of two-particle transverse momentum correlations in Pb–Pb collisions at sNN=2.76TeV

Contents lists available atScienceDirect

Physics

Letters

B

www.elsevier.com/locate/physletb

Longitudinal

and

azimuthal

evolution

of

two-particle

transverse

momentum

correlations

in

Pb–Pb

collisions

at

√

s

_NN

=

2.76

TeV

.

ALICE

Collaboration



a

r

t

i

c

l

e

i

n

f

o

a

b

s

t

r

a

c

t

Articlehistory:

Received16November2019

Receivedinrevisedform21February2020 Accepted16March2020

Availableonline20March2020 Editor:M.Doser

Thispaperpresentsthefirstmeasurementsofthechargeindependent(CI)andchargedependent(CD) two-particletransversemomentumcorrelatorsGCI

2 andGCD2 inPb–Pbcollisionsat

√_s

NN=2.76TeV bythe

ALICEcollaboration.Thetwo-particletransversemomentumcorrelatorG2wasintroducedasameasure

ofthemomentumcurrenttransferbetweenneighboring systemcells.Thecorrelatorsaremeasuredas afunctionofpairseparation inpseudorapidity(

η

) andazimuth (

ϕ

)and asafunctionofcollision centrality. Fromperipheral to central collisions,the correlator GCI₂ exhibits alongitudinal broadening whileundergoingamonotonic azimuthalnarrowing.By contrast,GCD₂ exhibits anarrowing alongboth dimensions. These features are not reproduced by models such as HIJING and AMPT. However, the observed narrowing ofthecorrelatorsfrom peripheral tocentral collisions isexpectedto result from thestrongertransverseflowprofilesproducedinmorecentralcollisionsandthelongitudinalbroadening ispredictedtobesensitivetomomentumcurrentsand theshearviscosityperunitofentropydensity

η

/s ofthematterproducedinthecollisions.Theobservedbroadeningisfoundtobeconsistentwiththe hypothesizedlowerboundof

η

/s andisinqualitativeagreementwithvaluesobtainedfromanisotropic flowmeasurements.

©2020ConseilEuropéenpourlaRechercheNucléaire,.PublishedbyElsevierB.V.Thisisanopenaccess articleundertheCCBYlicense(http://creativecommons.org/licenses/by/4.0/).FundedbySCOAP3_.

1. Introduction

Measurementsofparticleproductionandtheircorrelations per-formedattheRelativisticHeavyIonCollider(RHIC)andtheLarge HadronCollider(LHC)provide compellingevidencethat the mat-terproducedinheavy-ioncollisionsischaracterizedby extremely hightemperaturesandenergy densitiesconsistent witha decon-fined, but strongly interacting Quark–Gluon Plasma (QGP) [1–4]. Collectiveflow, whichmanifests itself by theanisotropy of parti-cleproduction in the plane transverse to the beamdirection, is characterizedby theharmoniccoefficientsofa Fourierexpansion ofthe azimuthal distribution ofparticles relative to the reaction plane. Comparisons oftheseharmonic coefficientswith hydrody-namical model predictions indicate that the matter produced in thosecollisions hasa shear viscosityper unit ofentropydensity,

η

/

s, that nearly vanishes [2,5]. The shearviscosity quantifies the resistance that any medium presents to its anisotropic deforma-tion. It contributesto the transfer ofmomentum fromone fluid cell toits neighborsaswell asthe dampingof momentum fluc-tuations. The reach of

η

/

s effects is expected to grow with the lifetimeof the system. Recent measurements offlow coefficients andhydrodynamical predictions largely focus on the precise de-termination of

η

/

s [6–9]. However, quantitative descriptions of

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

heavy-ion collisions with hydrodynamical models generally rely on specific parametrizations of the initial conditions of colliding systems, i.e., their initial energyand entropydensity distribution in thetransverse plane, themagnitudeof initial fluctuations, the thermalizationtime,andseveralmodelparameters.Itisfoundthat theprecisionofmodelpredictionsishindered,inparticular,by un-certainties in the initial state conditions.Indeed, values ofshear viscositythatbestmatchtheobservedflowcoefficientsare depen-dent on the initial conditions, and unless the magnitude of the initial state fluctuationscan be preciselyassessed, theachievable precision on

η

/

s mightremainlimited [10,11].Systematicstudies ofcorrelationsbetweendifferentorderharmoniccoefficients [12], showntobesensitivetotheinitialconditionsandthetemperature dependenceof

η

/

s,canhelptoprovidefurtherconstraintstothose conditions and to the transport properties of the system. Novel approachesbasedonBayesianparameterestimation [13,14] bring progress on a simultaneous characterization of the initial condi-tions andtheQGP. Furthermore,itwas pointedout [15] that the strength of momentum current correlations may be sensitive to

η

/

s. Itwas shown, inparticular, thatthe longitudinalbroadening ofatransversemomentum(pT)correlator,formallydefinedbelow andhereafternamedG2,withincreasingsystemlifetimeisdirectly sensitiveto

η

/

s whileitdoesnothaveanyexplicitdependenceon theinitialstatefluctuationsinthetransverseplaneofthesystem.

A first measurement of the broadening of the two-particle transverse momentum correlator G2 was reported by the STAR

https://doi.org/10.1016/j.physletb.2020.135375

0370-2693/©2020ConseilEuropéenpourlaRechercheNucléaire,.PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense (http://creativecommons.org/licenses/by/4.0/).FundedbySCOAP3_.

collaboration [16]. Improvedtechniquesto correctfor instrumen-tal effects have since then been reported [17–19]. In this letter, these techniques are used to measure differential charge inde-pendent (CI) and charge dependent (CD) two-particle transverse momentum correlators, GCI₂ and GCD₂ , respectively, as a function of pair rapidity difference,



η

, and azimuthal angle difference,



ϕ

,for selected ranges of Pb–Pb collision centrality. The shapes ofthesecorrelatorsarestudiedwithatwo-componentmodeland thelongitudinalandazimuthalwidthsoftheirnear-sidepeaksare studiedasa function ofthePb–Pb collisioncentrality. The longi-tudinal broadeningof GCI

2 fromperipheral to central collisions is used to assess the magnitudeof

η

/

s of the matter produced in Pb–Pb collisions while the longitudinal and azimuthal widths of

GCD₂ areusedtoassesstheroleofcompetingeffects,including ra-dialflow,diffusion,andthebroadeningofjetsbyinteractionswith themedium. In that context, measurements of G2 are also com-paredwithpreviously reportedmeasurementsofthetwo-particle numbercorrelatorR2 andtwo-particletransversemomentum cor-relatorP2 [18].

2. TheG2correlator

ThedimensionlessvariantoftheG2correlator [15,20] reported inthisletterisdefinedaccordingto

G2

(

η

1

,

ϕ

1

,

η

2

,

ϕ

2

)

=

1



pT,1



pT,2





pT,1pT,2

ρ

2

(

p



1

,



p2

)

d pT,1d pT,2





ρ

1

(



p1

)

d pT,1





ρ

1

(



p2

)

d pT,2

− 

pT,1

(

η

1

,

ϕ

1

)



pT,2

(

η

2

,

ϕ

2

)

⎤

⎦

(1)

where



is the phase space region in which the measurement is performed;



p1 and



p2 are the three-momentum vectors of particles of a given pair; pT,1 and pT,2 their transverse mo-mentumcomponents,respectively;

ρ

1

(



pi

)

=

d3N

/

dpT,id

η

id

ϕ

i and

ρ

2

(



p1

,



p2

)

=

d6N

/

dpT,1d

η

1d

ϕ

1dpT,2d

η

2d

ϕ

2 representsingleand pairparticle densities, expressed asfunctionsof p



i, i

=

1

,

2, and

(



p1

,



p2

)

, respectively;



pT

(

η

i

,

ϕ

i

)

is the average transverse mo-mentum of particles observed at

(

η

i

,

ϕ

i

)

, with

η

i

,

ϕ

i, i

=

1

,

2, referring to single-track pseudorapidity and azimuthal angle, re-spectively; and



pT,i



=



ρ

1

(



pi

)

pT,id



pi is the inclusive average transversemomentum ofproduced particles, i

=

1

,

2,inthe con-sideredeventensemble.Experimentally,G2 iscalculatedas

G2

(

η

1

,

ϕ

1

,

η

2

,

ϕ

2

)

=

1



pT,1



pT,2





SpT

(

η

1

,

ϕ

1

,

η

2

,

ϕ

2

)



n1,1

(

η

1

,

ϕ

1

)



n1,2

(

η

2

,

ϕ

2

)



− 

pT,1

(

η

1

,

ϕ

1

)



pT,2

(

η

2

,

ϕ

2

)



(2) with SpT

(

η

1

,

ϕ

1

,

η

2

,

ϕ

2

)

=





n1,1 i n1,2



j=i pT,ipT,j

(3)

where n1,1 and n1,2 are the number of tracks on each event within bins centered at

η

1

,

ϕ

1 and

η

2

,

ϕ

2, and with transverse momentum pT,i, i

∈ [

1

,

n1,1

]

, and pT,j, j

=

i

∈ [

1

,

n1,2

]

, respec-tively. Angle brackets,

· · ·

, refer to event ensemble averages,



A



=

Nevents

1 A

/

Nevents.ThecorrelatorsGLS2 andGUS2 arefirst mea-suredforlike-sign(LS) andunlike-sign(US)pairs separately,and combined to obtain CI and CD correlators according to GCI₂

=

1 2



GUS₂

+

GLS₂



and GCD₂

=

₂1



GUS₂

−

GLS₂



, respectively [18]. Mea-surements of G2

(

η

1

,

ϕ

1

,

η

2

,

ϕ

2

)

are averaged across the longitu-dinal and azimuthal acceptances in which the measurement is

performedtoobtain G2

(

η

,



ϕ

)

,where



η

=

η

1

−

η

2 and



ϕ

=

ϕ

1

−

ϕ

2,withaproceduresimilartothatusedforR2 andP2 cor-relators [18].

3. Measurementtechniques

The resultspresentedinthisletterare basedon1

.

1

×

107 se-lected minimum bias (MB) Pb–Pb collisions at

√

sNN = 2.76 TeV collected during the 2010 LHC heavy-ion run by the ALICE ex-periment. Detailed descriptions of the ALICE detectors and their respective performances are given in Refs. [21,22]. The MB trig-ger was configured in order to have highefficiency forhadronic events,requiringatleasttwooutofthefollowingthreeconditions: i)twohitsinthesecond innerlayeroftheInner TrackingSystem (ITS),ii)asignalintheV0Adetector,iii)asignalintheV0C detec-tor.The amplitudesmeasured intheV0detectorsareadditionally used to estimate the collision centrality reported in nine classes corresponding to 0–5% (mostcentral), 5–10%, 10–20%,..., 70–80% (most peripheral)of the total interaction cross section [23]. The vertexpositionofeach collisionis determinedwithtracks recon-structed intheITSandtheTimeProjectionChamber (TPC)andis requiredtobeintherange

|

zvtx

|

≤

7 cmofthenominalinteraction point (IP).Pile-up events,identifiedaseventshavingmultiple re-constructedverticesintheITS,arerejected.Additionally,theextra activityobservedinslowresponsedetectors (e.g.,TPC)relative to that measuredinfastdetectors(e.g.,V0)foroutofbunchpile-up events isusedto discardtheseevents.Theremaining event pile-upcontaminationisestimatedtobenegligible.Longitudinally,the ITScovers

|

η

|

<

0

.

9,theTPC

|

η

|

<

0

.

9,V0A2

.

8

<

η

<

5

.

1 andV0C

−

3

.

7

<

η

<

−

1

.

7.Thesefourdetectorsfeaturefull azimuthal cov-erage.

The present measurement of the G2 correlators is based on charged particle tracks measured with the TPC detector in the transverse momentum range0

.

2

≤

pT

≤

2

.

0 GeV/c andthe pseu-dorapidity range

|

η

|

<

0

.

8. Inorder to ensure good track quality and to minimize secondary track contamination, the analysis is restricted to charged particle tracks involving a minimum of 50 reconstructed TPC space points out of a maximum of 159, and distances ofclosest approach (DCA) tothe reconstructedprimary vertexoflessthan3

.

2cm and2

.

4cm inthelongitudinaland ra-dial directions, respectively. An alternative criterion, used in the analysis of the systematic uncertainties, that relies on tracks re-constructedwiththecombinationoftheTPCandtheITSdetectors, henceforthcalled“globaltracks”,involvesaminimumof70 recon-structed TPC spacepoints, hitseitheron anyof two innerlayers oftheITS,orinthethirdinnerlayeroftheITS,andatighterDCA selection criterion inboth, longitudinal andradial directions, the latter one pT-dependent. Electrons (positrons),whose one of the largest sources are photon conversions into e+e− pairs, are sup-pressed discarding e+ ande− by removingtracks witha specific energylossdE

/

dx intheTPCcloserthan3

σ

dE/dx totheexpected medianforelectronsandatleast5

σ

dE/dx awayfromthe

π

,K and

p expectationvalues.

The single andpair efficiencies of the selected charged parti-clesare estimatedfromaMonteCarlo(MC)simulation usingthe HIJING event generator [24] with particle transport through the detectorperformedwithGEANT3 [25] tunedtoreproducethe de-tectorconditionsduringthe2010run.Correctionsforsingletrack losses due to non-uniform acceptance (NUA) are carried out us-ing aweighting technique [17] separatelyfordataandfor recon-structedMCdata.Weightsareextractedseparatelyforpositiveand negativetracks,foreachcollisioncentralityrange,asafunctionof

η

,

ϕ

, pT and the longitudinal position of the primary vertex of each event, zvtx. The pT-dependentsingle track efficiency correc-tionisextractedastheinverseoftheratioofthenumberofNUA correctedreconstructedHIJINGtrackstogeneratedtracks.Dataare

Fig. 1. Two-particletransversemomentumcorrelationsGCI

2 (top)andtheirlongitudinal(middle)andazimuthal(bottom)projectionsforthemostcentral(left),semi-central

(center)andperipheral(right)Pb–Pbcollisionsat √sNN=2.76TeV.Verticalbars(mostlysmallerthanthemarkersize)andshadedbluebandsrepresentstatisticaland

systematicuncertainties,respectively.Thesystematicuncertaintyonthelong-rangemeancorrelatorstrengthisquotedasδB inbothprojections.Under-correctedcorrelator valuesatη,ϕ=0 arenotshown.Seetextfordetails.

subsequentlycorrected withNUA andsingle trackefficiency cor-rections.Pairlossesduetotrackmergingorcrossingarecorrected inpartbasedonthetechniquedescribedin[18] andinpartbased ontheratioofthe averagenumberofreconstructedHIJING pairs relativeto the generatednumberof pairs.Corrections for pT de-pendentpairlossesarenotincludedinthereportedresultsgiven theyhavealarge(

>

20%)systematicuncertainty.Correlatorvalues at

|

η

|

<

0

.

05,

|

ϕ

|

<

0

.

04rad.,left under-correctedby thislast fact,arenotreportedinthiswork.However,thisdoesnotimpact theshapeandwidthoftheG2 correlator,whichareofinterestfor thedeterminationoftheviscousbroadening.Nofiltersareusedto suppresslike-sign(LS)particlecorrelationsresultingfromHanbury BrownandTwiss(HBT)effects.Forpions,whichdominatethe par-ticleproduction,HBTproduces apeakcenteredat



η

,



ϕ

=

0 in

GLS

2.Thewidthofthispeakdecreasesininverseproportiontothe sizeofthecollisionsystem.GiventhenumberofHBTpairsis rel-ativelysmallcomparedtothetotalnumberofpairsaccountedfor inGLS₂,theimpliedreductionofthelongitudinalbroadeningis rel-ativelymodestandthusnotconsideredinthisanalysis.

4. Statisticalandsystematicuncertainties

Statistical uncertainties on the strength of G2 are extracted using the sub-sample method with ten sub-samples. Systematic uncertaintiesare determined byrepeating theanalysisunder dif-ferent event and track selection conditions. Deviations from the nominal results are considered significant and assessed as sys-tematicuncertainties basedon a statisticaltest [26]. The impact ofpotential TPCeffectssensitive to themagnetic fieldpolarity is

assessedbysplittingthewholedatasampleintopositiveand nega-tivemagneticfieldconfigurations,whereasuncertaintiesassociated withthe collisioncentrality estimationare studied bycomparing nominal results, based on the V0 detector, with those obtained with an alternative centrality measure based on hit multiplicity on the two inner layers of the ITS. Effects of the kinematic ac-ceptanceinwhichthemeasurementisperformedareinvestigated byrepeatingtheanalysiswitheventsintherange

|

zvtx

|

<

3 cmof thenominalIP.Thepresenceofbiasescausedbysecondary parti-clesischeckedusingthe“globaltracks”selection criterion.Biases associated with pair losses are studied based on pair efficiency correctionsobtainedwithHIJING/GEANT3simulations.The largest systematic uncertainty amounts to a global shift in G2

(

η

,



ϕ

)

correlator strength which is independent of



η

and



ϕ

and is reported as

δ

B. This shift affects the magnitude of the projec-tions onto



η

and



ϕ

butnottheshapesofthenear-sidepeak,

|

ϕ

|

<

π

/

2,of G2 alongthesecoordinates.Systematic uncertain-tiesintheshapeofthenear-sidepeakofGCI₂ andGCD₂ aremainly due to the presence of secondary particles. Overall, systematic uncertainties on the shapes of the projections of GCI₂ and GCD₂

along the longitudinal (azimuthal) dimension amount to 4%(5%) and5%(10%),respectively,withdecreasingvaluestowards periph-eralevents.

5. Results

Fig.1presentsthecorrelatorsGCI₂

(

η

,



ϕ

)

measuredin0–5%, 30–40%,70–80%Pb–Pb collisions,andtheir respectiveprojections along the



η

and



ϕ

axes. The GCI₂ correlators feature sizable



ϕ

modulations,dominated inmid-centralcollisions by astrong ellipticflow

(

cos

(

2



ϕ

))

component.Onthenear-side,atopthe az-imuthal modulation, the GCI₂ correlatorsfeature a near-side peak whoseamplitudemonotonicallydecreasesfromperipheralto cen-tralcollisionswhileitslongitudinalwidthsystematicallybroadens. QualitativelysimilartrendswereobservedfortheR2andP2 corre-latorsreportedbyALICE [18] andtheGCI₂ correlator(therenamed

C )reportedbySTAR [16].Inmostcentralcollisions,theamplitude ofthe



ϕ

modulations associated withcollective flow decreases butthelongitudinalbroadeningremains.Additionally, adepletion centered at

(

η

,



ϕ

)

= (

0

,

0

)

consistent withprevious ALICE re-sults [27,28] canbeseen.

Inordertostudythecentralityevolutionofthenear-sidepeak of the GCI₂ and GCD₂ correlators independently of the underly-ingcollectiveazimuthalbehavior,theyareseparatelyparametrized withatwo-componentmodeldefinedas

F

(

η

,

ϕ

)

=

B

+

6



n=2 an

×

cos

(

n



ϕ

)

+

A

×

γ

η 2

ω

η

1 γη



e−  η ω_η  γη

×

γ

ϕ 2

ω

ϕ

1 γϕ



e−   ϕ ω_ϕ  γϕ , (4)

where B and an are intended to describe the long-range mean correlationstrengthandazimuthal anisotropy,whilethe bidimen-sional generalized Gaussian, defined by the parameters A,

ω

η ,

ω

ϕ ,

γ

η and

γ

ϕ ,isintendedtomodelthesignalofinterest.The

(

η

,



ϕ

)

= (

0

,

0

)

depletion present in the GCI₂ correlator is not properlymodeled by Eq. (4) andthe depletion area,

|

η

|

<

0

.

31 and

|

ϕ

|

<

0

.

26rad.,is excluded fromthe fit. Bidimensionalfits are carried out considering only statistical uncertainties. In the case ofthe GCI₂ correlator the

χ

2

_/

_{ndf values for semi-central to} peripheral collisions are found in the range 1–2; forcentral col-lisions they increase to 4. The area which contributes the most tothe increaseof the

χ

2

_/

_{ndf is theregion betweenthe} general-ized Gaussian andtheFourier expansion.Excluding thisarea the

χ

2

_/

_{ndf valuesobtainedin central collisionsare within the range} 1–2.3. Fits of GCD₂ give

χ

2

_/

_{ndf of the order of unity for} periph-eral to semi-central collisions and inthe range 2–3.5 for central collisions.Larger

χ

2

_/

_{ndf values observedincentral collisionsrise} becausethe nearside peak starts todepart fromthe generalized Gaussian description. The actual focusis on the evolution ofthe widths.The longitudinalandazimuthal widthsofthe correlators, denoted

σ

η and

σ

ϕ ,respectively,arethenextractedasthe

stan-darddeviationofthegeneralizedGaussian

σ

η(ϕ)

=









ω

η(ϕ)2

(

3

/

γ

η(ϕ)

)

(

1

/

γ

η(ϕ)

)

, (5)

andplottedasafunctionofcollisioncentralityinthetoppanelsof Fig.2forbothGCI₂ andGCD₂ correlators.Theglobalshiftofthe cor-relatorstrength,quoted asasystematicuncertaintyinthe projec-tionsofthecorrelators, doesnotaffecttheshapeofthenear-side peakofG2.Accordingly,thewidthsarenotaffectedeither. Corre-lationsbetweenthecontributorstothelongitudinalwidthandthe harmonicparameters forthe GCI₂ correlator are foundasfollows:

a2 anda4 areanti-correlatedwith

ω

η withvaluesintheranges

−

0.8to

−

0.4and

−

0.5–0,respectively,whilea3 iscorrelatedwith values 0–0.4. On the other hand, a2 and a4 are correlated with

Fig. 2. Toppanels:collisioncentralityevolutionofthelongitudinal (left)and az-imuthal(right) widthsofthe G2 CDandCIcorrelatorsmeasuredinPb–Pb

col-lisions at √sNN=2.76TeV. Centraland bottompanels:widthevolutionrelative

tothevalueinthemostperipheralcollisionsofthetwo-particle transverse mo-mentumcorrelationsGCI

2 (central)andGCD2 (bottom)alongthelongitudinal(left)

andazimuthal(right)dimensions.DataarecomparedwithHIJINGandAMPTmodel expectations.Indata,verticalbarsandshadedbandsrepresentstatisticaland sys-tematicuncertainties,respectively. Formodels,shadedbandsrepresentstatistical uncertainties.

γ

η with valueswithin 0.4–0.8 and 0–0.5, respectively, whilea3 is anti-correlated with values in the range

−

0.5–0. a2 correla-tions show no centralitydependence whilethe absolutevalue of

a3 anda4 correlationsdecreases fromcentral to peripheral colli-sions. In the caseof thecontributors to the azimuthal width, a2 anda4 arecorrelatedwith

ω

ϕ and with

γ

ϕ withvaluesinthe

ranges 0.5–0.8 and0.6–0.9,and0.6–0.9 and0.7–0.9, respectively, while a3 is anti-correlated withbothwith valueswithin

−

0.8to

−

0.5and

−

0.9to

−

0.7.Ontheazimuthaldimensiontheabsolute value of the harmoniccoefficientscorrelations decreases towards peripheralcollisions.Systematicuncertaintiesinthewidthsofthe near-sidepeak ofGCI

2 andGCD2 are mainlyduetothepresenceof secondary particles. Withthealternative trackselection criterion, systematicuncertaintiesonthelongitudinalandazimuthalwidths ofthenear-sidepeak areestimatedtobe2%and3%,respectively, for both GCI

2 and GCD2 , for most central events, with decreasing values towardsperipheral collisions. Uncertaintycontributions on the widths are not correlated withcentrality andaverages along centralityclassesareconsidered.Overall,maximumsystematic un-certaintiesof4%(2%)and3.5%(3%)areassignedtotheGCI₂ andGCD₂

widths,respectively,alongthelongitudinal(azimuthal)dimension. The impact ofthe size ofthe area excluded from the fit on the widthoftheGCI

2 correlatorisevaluatedenlargingtheareainboth dimensions. Only semi-central to central centrality classes have their corresponding longitudinal widths modified. The effect is a broadening from1.5%in the 30–40%class up to a broadeningof 20% in the 0–5% class incorporated as an additional asymmetric systematic uncertainty on the widths of GCI₂. On the azimuthal widthstheimpactisreducedtoa2%narrowing.

6. Discussion

Broadeningandnarrowingarehereafterintendedasthe behav-iorofthecorrelationfunction,measuredbyitswidths,whengoing from peripheral collisions, highvalues ofcentrality percentile, to centralcollisions,lowervaluesofcentralitypercentile.TheGCI₂ cor-relator broadens longitudinally but narrows in azimuth, whereas the GCD

2 correlator narrows both longitudinally and azimuthally. As shown in Fig. 3, these dependencies are qualitatively

consis-Fig. 3. Leftpanel:collisioncentralityevolutionofthelongitudinalwidthofnumbercorrelatorRCD

2 andtransversemomentumcorrelatorsP CD 2 andG

CD

2 .Centralpanel:idem

fortheazimuthalwidthofRCD2 ,P CD 2 andG

CD

2 .Rightpanel:collisioncentralityevolutionofthelongitudinalwidthofR CI 2,P

CI 2,andG

CI

2.DataforR2andP2arefrom[18].

Verticalbarsandshadedbandsrepresentstatisticalandsystematicuncertainties,respectively.

tent withthose of R2 and P2 correlatorsmeasured in the same kinematicrangebytheALICEcollaboration [18].NotethattheG2 correlatorissensitive totransversemomentum andnumber den-sityfluctuationssinceboth affectthemomentumcurrentdensity. Incontrast,R2 issensitivetonumberdensityfluctuationsandP2, sensitivetotransversemomentumfluctuations,isdesignedto min-imizethe contributionofthose numberdensityfluctuations [29]. Infact [29]

(

P2

+

1

) (

R2

+

1

)

= (

G2

+

1

)

(6)

so,theincreaseintransversemomentumcurrentscouldbedueto eithertheincreaseinmultiplicityortheincreaseoftransverse mo-mentum.TheGCD₂ andPCD₂ correlatorsfeatureapproximatelyequal widthswhile RCD

2 isapproximately30%widerthroughoutits cen-tralityevolution.ThecentralitydependenceofGCD₂ isqualitatively consistentwiththatofbalancefunction(BF)observations [30,31]. Phenomenologicalanalyses of theBFs suggest that their narrow-ingwithcentralityis largelydueto thepresenceofstrong radial flowanddelayedhadronizationinPb–Pb collisions [30].Itisthus reasonableto inferthat radialflow andlarger



pT



, inmore cen-tralcollisions, alsoproduce the observed narrowing of GCD₂ .This conjectureis supported by calculationsofthe collision centrality dependenceof GCD

2 azimuthal widthswiththe HIJING andAMPT models shown in the bottom right panel of Fig. 2. Radial flow mightalso explain the observed azimuthal narrowing of the GCI₂

correlatorwithcentrality,whichisreasonablywell reproducedby calculations with AMPT with string melting, but not by HIJING orAMPT calculationswithonlyhadronicrescatteringasshownin centralrightpanelofFig.2.

The broadening of the longitudinal width of the GCI₂ correla-toris ofparticular interest givenpredictions that it should grow inproportionto

η

/

s ofthematterproducedinthecollisions [15]. Asexpectedforasystemwithfiniteviscosity,itisfound thatGCI₂

broadenssignificantlywithincreasingcollisioncentrality,whileby contrast, GCD₂ exhibits a slight but distinct narrowing. This GCD₂

longitudinalnarrowing is expectedfroma boost ofparticle pairs by radial flow but is not properly accounted for by AMPT cal-culations shown in the bottom left panel of Fig. 2. Radial flow shouldalsoproduceanarrowing oftheGCI₂ correlator inthe lon-gitudinaldirection.Howevercompetingeffects,possiblyassociated withthefiniteshearviscosityofthesystem,areinsteadproducing a significant broadeningalthough reaching what seems a satura-tion level atsemi-central collisions. Note that HIJING andAMPT, withthe hadronic rescattering enabled, grosslyfail to reproduce the observed broadening and instead predict a slight narrowing (Fig.2 centralleft panel).AMPT withstring meltingandwithout thehadronicrescatteringphasequalitativelyreproducesthe longi-tudinalbroadeningofGCI₂,evenitssaturation,butgrosslymissthe narrowingof GCD

2 along that dimension andthus cannotbe con-sideredreliableinthiscontext.

Fig. 4. Two-particletransversemomentumcorrelationGCI

2 longitudinalwidth

evo-lutionwiththenumberofparticipantsinAu–Aucollisionsat√sNN=200GeV [16]

and inPb–Pb collisions at √sNN=2.76TeV, measured inthis work, usingthe

bi-dimensionalfitdescribedinthetext(2D) andthe methodusedbythe STAR experiment [16] (1D).Forcompleteness,STARRMSlowlimit [16] isalsoshown.

Particlesproduced byjet fragmentationarealsoknown to ex-hibit correlations and jet-medium interactions can broaden such correlations. Two-particle correlation measurements, of particles associated with high-pT jets, indeed show substantial broaden-ingoflow pTparticlecorrelationsrelativetocorrelationfunctions measuredinpp collisions [27,28,32].Thisbroadening,however,is observedinboththelongitudinalandazimuthaldirectionsinstark contrast with the behavior of the inclusive GCI

2 correlator mea-sured inthis work which exhibitsa significant narrowing in the azimuthaldirection.Additionally,thenumberofparticlesfromjets isrelativelysmallcomparedtothenumberfromthebulk. There-fore,althoughjetfragmentationmaycontributetothebroadening observedinthe longitudinaldirection,it isunlikelytoamount to asignificantcontributiongiventheobservednarrowinginthe



ϕ

directionandtherelativelylowimpactofcorrelationsfromjet par-ticles.

Fig.4 comparesresultsfromthisanalysiswiththose reported by the STAR collaboration [16]. For proper comparison, Fig. 4

presentsrootmeansquare(RMS)widthsof



η

projectionsofGCI₂

calculatedabovealongrangebaselineasintheSTARanalysis [16]. AlthoughSTARreportedresultsarebasedonthedimensional ver-sionofGCI₂,thesameexpressionasinEq. (1) butwithoutthe nor-malization



pT,1



pT,2



,thecorrelatorwidthsreportedinthisletter areidenticalforboth,thedimensionalanddimensionlessversions oftheG2 correlator.Thelongitudinalbroadeningmeasuredinthis analysis, using the 1D RMS method, amounts to 36% while that observedbySTARreaches74%showingalsoasaturationat semi-centralcollisions.Itwasverifiedthatthesmallerbroadeningseen inthisanalysisisnotaresultoftheslightlynarrowerlongitudinal acceptanceoftheALICEexperimentbytestingtheanalysismethod withMonteCarlomodelsreproducingtheapproximateshapeand strength of the measured correlation functions. The longitudinal

Fig. 5. Expectedlongitudinal widths for the mostcentral collisions ofthe two-particletransversemomentumcorrelationGCI2 fordifferentvaluesofη/s byusing

theexpressionsuggestedin [15].Datapointerrorbarsrepresenttotaluncertainties obtainedbyaddinginquadraturestatisticalandsystematicuncertainties.Inthe for-mulaσcisthelongitudinalwidthforthemostcentralcollisionsinferredbyusing

thisexpressionandrepresentedforeachoftheη/s valuesbythecolor discontin-uousbands(continuousforη/s=1/4π)atthehighestnumberofparticipants,σ0

isthelongitudinalwidthforthemostperipheralcollisions(onlytwoparticipants) whichisobtainedbyextrapolatingthefit,Tc isthecriticaltemperature,τ0isthe

formationtimeand τc,f thefreeze-outtime.Errorcapsinthesamecolorasthe

discontinuousbands,representuncertaintiesoftheinferredlongitudinalwidthsfor themostcentralcollisions(seetextfordetails).

broadeningofGCI₂ andits observedsaturation thusappears tobe potentiallydependentonthebeamenergy.

Interpreting the longitudinal broadeningof GCI

2 as originating exclusivelyfromviscouseffects,anestimateoftheshearviscosity perunitofentropydensity,

η

/

s,ofthematterproducedin heavy-ioncollisionscanbeextracted [16] usingtheexpression

σ

_c2

−

σ

₀2

=

4 Tc

η

s



1

τ

0

−

1

τ

c,f



(7)

derived in [15]. In Eq. (7)

σ

c is the longitudinal width for the mostcentralcollisions(ideally0%centrality),

σ

0 isthelongitudinal widthforthe mostperipheral collisions (ideally 100%centrality),

Tcisthecriticaltemperature,

τ

0istheformationtimeand

τ

c,fthe freeze-outtime.Thecorrelator widthforthemostperipheralPb– Pbcollisions at

√

sNN

=

2

.

76TeV is estimatedbased on a power lawextrapolationof themeasured values,shownin Fig.5,down to Npart

=

2. Canonical values are used for the critical tempera-ture, Tc

=

160 MeV [33],theformationtime

τ

0

=

1fm

/

c [33],and the freeze-out time,

τ

c,f

=

10

.

5 fm/c [34]. With these inputs in Eq. (7),GCI₂ longitudinalwidthsforthemostcentral collisionsare calculated forseveral values of

η

/

s

=

0

.

06, 1

/

4

π

, 0

.

14 and 0

.

22 and also shown in Fig. 5 as color discontinuous (continuous for

η

/

s

=

1

/

4

π

)bandsatthehighestnumberofparticipants. Consid-ering2%, 30%, and3% uncertainties for Tc (155

<

Tc

<

165TeV),

τ

0, and

τ

c,f (10

<

τ

c,f

<

11fm) respectively, the uncertainties of thefourobtainedGCI₂ longitudinalwidthsforthemostcentral col-lisions reach 9%, 10%, 12%, and 14%, respectively, also shown in Fig.5aserrorcapsinthesamecolorasthediscontinuous bands. TheGCI₂ correlatorwidthmeasuredincentralcollisionsthusfavors rather small values of

η

/

s, closeto the KSS limit of 1

/

4

π

[35]. The authors of Ref. [15] obtain the correlator width values, for Au–Au collisions at

√

sNN

=

200GeV,without an actual measure-ment of GCI

2 fromthe only available two-particle transverse mo-mentumcorrelatorwhichinitsturnwasinferredfromevent-wise mean transverse momentum fluctuations [36] and on its energy dependence [37]. Theyconstrain

η

/

s toa relativelywide interval 0.08–0.30. The precision of the STAR measurement is limited by therelativeuncertaintyoftheGCI

2 correlatorwidthsforAu–Au col-lisionsat

√

sNN

=

200GeV;

η

/

s

=

0.06–0.21 wasreportedin [16].

7. Conclusions

Measurementsof charge dependent (CD)andcharge indepen-dent(CI)transversemomentumcorrelatorsG2 inPb–Pbcollisions at

√

sNN

=

2

.

76 TeVwerepresentedaimingatthedeterminationof theshearviscosityperunit ofentropydensity,

η

/

s,ofthematter formed in such collisions. The near-side peak of the GCD

2 corre-lator is observed to significantly narrow with collision centrality bothinthelongitudinalandazimuthaldirections.Thisbehavioris foundtobesimilartothatofthechargebalancefunctionasa re-sult, mostlikely,ofanincrease oftheaverageradialflow velocity fromperipheraltocentralcollisions.Bycontrast,theGCI₂ correlator is foundto narrowonly inthe azimuthal directionwithcollision centralityandfeaturesasizablebroadeninginthelongitudinal di-rection.The observedbroadeningalong thelongitudinaldirection isexpectedbasedonfrictionforcesassociatedwiththefiniteshear viscosityofthesystem.Takingthemodelproposedin [15],an es-timateofthevalueof

η

/

s oforder1

/

4

π

,inqualitativeagreement with values obtained from other methods [14,38], is obtained. StringmeltingAMPT withoutthehadronicrescatteringphasehas beenfoundtoqualitativelyreproducethelongitudinalbroadening ofGCI₂ butgrosslymissesthenarrowingofGCD₂ alongthat dimen-sion. The observedsaturation in thelongitudinal broadeningand the sizable difference in broadening relative to that observed by STARmayresultfromtheinterplayofviscousforcesandkinematic narrowing associated toradial flow. In thelatter case,the differ-encecompared totheSTARresultsduetoa possibledependence on the beam energy could be better established with expanded experimentalmeasurements forenergiesinthebeamenergyscan (BES)atRHICorat5.02TeVattheLHC.

Declarationofcompetinginterest

Theauthorsdeclarethattheyhavenoknowncompeting finan-cialinterestsorpersonalrelationshipsthatcouldhaveappearedto influencetheworkreportedinthispaper.

Acknowledgements

Authors thank Dr. Sean Gavin and Dr. George Moschelli for fruitfuldiscussions.

The ALICECollaboration would like to thank all its engineers andtechniciansfortheirinvaluablecontributionstothe construc-tionoftheexperimentandtheCERNacceleratorteamsforthe out-standingperformanceoftheLHCcomplex.TheALICECollaboration gratefully acknowledges the resources and support provided by all Grid centresandthe WorldwideLHC ComputingGrid (WLCG) collaboration. The ALICE Collaboration acknowledges the follow-ingfundingagenciesfortheirsupportinbuildingandrunningthe ALICEdetector:A.I.AlikhanyanNationalScienceLaboratory (Yere-vanPhysics Institute)Foundation (ANSL),State Committeeof Sci-enceandWorld FederationofScientists(WFS), Armenia;Austrian AcademyofSciences,AustrianScienceFund(FWF):[M2467-N36] andNationalstiftung fürForschung, TechnologieundEntwicklung, Austria; Ministryof Communications andHigh Technologies, Na-tional Nuclear Research Center, Azerbaijan; Conselho Nacionalde DesenvolvimentoCientífico e Tecnológico(CNPq), Financiadorade Estudos e Projetos (Finep), Fundação 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 NationalNaturalScienceFoundation ofChina(NSFC),China; Min-istry of Science and Education and Croatian Science Foundation, Croatia; Centrode Aplicaciones TecnológicasyDesarrolloNuclear (CEADEN), Cubaenergía, Cuba; Ministry of Education, Youth and SportsoftheCzech Republic, CzechRepublic;TheDanish Council

forIndependentResearch|NaturalSciences,theVillumFonden and Danish National Research Foundation (DNRF), Denmark; Helsinki InstituteofPhysics(HIP),Finland;Commissariatà l’Energie Atom-ique(CEA), InstitutNationalde PhysiqueNucléaireetdePhysique desParticules(IN2P3)andCentreNationalde laRecherche Scien-tifique(CNRS)andRégiondesPaysdelaLoire,France; Bundesmin-isteriumfürBildungundForschung(BMBF)andGSI Helmholtzzen-trumfür Schwerionenforschung GmbH, Germany; General Secre-tariatforResearchandTechnology,MinistryofEducation,Research andReligions,Greece;National Research,Developmentand Inno-vationOffice,Hungary;DepartmentofAtomicEnergy,Government ofIndia (DAE),DepartmentofScienceandTechnology,Government ofIndia (DST),University Grants Commission,Government of In-dia(UGC)andCouncilofScientificandIndustrialResearch(CSIR), India; Indonesian Institute of Science, Indonesia; Centro Fermi -MuseoStoricodellaFisica e CentroStudie RicercheEnricoFermi and Instituto Nazionale di Fisica Nucleare (INFN), Italy; Institute for InnovativeScience and Technology, Nagasaki Institute of Ap-pliedScience(IIST),JapaneseMinistryofEducation,Culture,Sports, ScienceandTechnology (MEXT)andJapan Societyforthe Promo-tionofScience(JSPS)KAKENHI,Japan;ConsejoNacionaldeCiencia (CONACYT) yTecnología, through Fondode Cooperación Interna-cionalenCiencia yTecnología(FONCICYT)and DirecciónGeneral deAsuntosdelPersonalAcademico(DGAPA),Mexico;Nederlandse OrganisatievoorWetenschappelijkOnderzoek(NWO),Netherlands; TheResearchCouncilofNorway,Norway;CommissiononScience andTechnology forSustainableDevelopment inthe South (COM-SATS),Pakistan;PontificiaUniversidadCatólicadelPerú,Peru; Min-istryofScienceandHigherEducationandNationalScienceCentre, Poland;KoreaInstituteofScienceandTechnologyInformationand NationalResearch Foundation of Korea (NRF), Republic ofKorea; MinistryofEducation andScientific Research, Institute ofAtomic Physics and Ministry of Research and Innovation and Institute of Atomic Physics, Romania; Joint Institute for Nuclear Research (JINR), Ministry of Education andScience ofthe Russian Federa-tion,NationalResearchCentreKurchatovInstitute,RussianScience Foundation and Russian Foundation for Basic Research, Russia; Ministryof Education, Science, Research andSport of the Slovak Republic, Slovakia; National ResearchFoundation ofSouth Africa, South Africa; Swedish Research Council (VR) and Knut & Alice WallenbergFoundation(KAW),Sweden;EuropeanOrganizationfor NuclearResearch,Switzerland;SuranareeUniversityofTechnology (SUT),NationalScienceandTechnologyDevelopmentAgency (NS-DTA)andOffice ofthe Higher Education Commissionunder NRU project of Thailand, Thailand; Turkish Atomic Energy Authority (TAEK),Turkey;NationalAcademyofSciencesofUkraine,Ukraine; ScienceandTechnologyFacilitiesCouncil(STFC),UnitedKingdom; NationalScienceFoundationoftheUnitedStatesofAmerica(NSF) andUnitedStatesDepartmentofEnergy,OfficeofNuclearPhysics (DOENP),UnitedStatesofAmerica.

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J.T. Blair

119

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D. Blau

87

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C. Blume

68

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G. Boca

139

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F. Bock

33

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95

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A. Bogdanov

92

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S. Boi

23

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L. Boldizsár

145

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A. Bolozdynya

92

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M. Bombara

37

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G. Bonomi

140

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H. Borel

137

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A. Borissov

92

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144

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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

106

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M. Bregant

121

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M. Broz

36

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E.J. Brucken

43

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E. Bruna

58

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G.E. Bruno

105

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M.D. Buckland

127

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D. Budnikov

108

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H. Buesching

68

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S. Bufalino

30

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O. Bugnon

114

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P. Buhler

113

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P. Buncic

33

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Z. Buthelezi

72

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131

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J.B. Butt

14

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J.T. Buxton

96

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S.A. Bysiak

118

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D. Caffarri

89

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A. Caliva

106

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E. Calvo Villar

111

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R.S. Camacho

44

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P. Camerini

24

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A.A. Capon

113

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F. Carnesecchi

10

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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

54

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F. Catalano

30

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C. Ceballos Sanchez

52

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P. Chakraborty

48

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S. Chandra

141

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W. Chang

6

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S. Chapeland

33

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M. Chartier

127

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S. Chattopadhyay

141

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S. Chattopadhyay

109

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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

33

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D.D. Chinellato

122

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S. Cho

60

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P. Chochula

33

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T. Chowdhury

134

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P. Christakoglou

89

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C.H. Christensen

88

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P. Christiansen

80

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T. Chujo

133

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C. Cicalo

54

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L. Cifarelli

10

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26

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F. Cindolo

53

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J. Cleymans

124

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F. Colamaria

52

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D. Colella

52

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A. Collu

79

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M. Colocci

26

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M. Concas

58

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ii

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G. Conesa Balbastre

78

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Z. Conesa del Valle

61

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G. Contin

24

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127

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J.G. Contreras

36

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T.M. Cormier

95

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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

33

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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

95

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D. Dabrowski

142

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T. Dahms

104

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117

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A. Dainese

56

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F.P.A. Damas

114

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137

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M.C. Danisch

103

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A. Danu

67

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D. Das

109

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I. Das

109

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P. Das

85

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P. Das

3

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S. Das

3

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A. Dash

85

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S. Dash

48

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S. De

85

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A. De Caro

29

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G. de Cataldo

52

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J. de Cuveland

38

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A. De Falco

23

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D. De Gruttola

10

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N. De Marco

58

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S. De Pasquale

29

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S. Deb

49

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B. Debjani

3

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H.F. Degenhardt

121

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K.R. Deja

142

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A. Deloff

84

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S. Delsanto

25

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131

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D. Devetak

106

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P. Dhankher

48

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D. Di Bari

32

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A. Di Mauro

33

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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

33

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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

33

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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

106

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S. Dudi

99

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M. Dukhishyam

85

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P. Dupieux

134

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R.J. Ehlers

146

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V.N. Eikeland

21

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D. Elia

52

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H. Engel

74

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E. Epple

146

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B. Erazmus

114

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F. Erhardt

98

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A. Erokhin

112

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M.R. Ersdal

21

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B. Espagnon

61

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G. Eulisse

33

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D. Evans

110

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S. Evdokimov

90

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L. Fabbietti

104

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117

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M. Faggin

28

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J. Faivre

78

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F. Fan

6

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A. Fantoni

51

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M. Fasel

95

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P. Fecchio

30

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A. Feliciello

58

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G. Feofilov

112

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A. Fernández Téllez

44

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A. Ferrero

137

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A. Ferretti

25

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F. Flor

125

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S. Foertsch

72

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P. Foka

106

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S. Fokin

87

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E. Fragiacomo

59

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U. Frankenfeld

106

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U. Fuchs

33

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C. Furget

78

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A. Furs

62

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M. Fusco Girard

29

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J.J. Gaardhøje

88

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M. Gagliardi

25

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A.M. Gago

111

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A. Gal

136

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C.D. Galvan

120

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P. Ganoti

83

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C. Garabatos

106

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E. Garcia-Solis

11

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K. Garg

27

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C. Gargiulo

33

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A. Garibli

86

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K. Garner

144

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P. Gasik

104

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117

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E.F. Gauger

119

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M.B. Gay Ducati

70

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M. Germain

114

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J. Ghosh

109

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P. Ghosh

141

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S.K. Ghosh

3

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P. Gianotti

51

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P. Giubellino

58

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106

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P. Giubilato

28

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P. Glässel

103

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D.M. Goméz Coral

71

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A. Gomez Ramirez

74

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V. Gonzalez

106

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P. González-Zamora

44

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S. Gorbunov

38

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L. Görlich

118

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S. Gotovac

34

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V. Grabski

71

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L.K. Graczykowski

142

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K.L. Graham

110

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L. Greiner

79

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A. Grelli

63

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C. Grigoras

33

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V. Grigoriev

92

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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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J.F. Grosse-Oetringhaus

33

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R. Grosso

106

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R. Guernane

78

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M. Guittiere

114

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K. Gulbrandsen

88

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T. Gunji

132

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A. Gupta

100

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R. Gupta

100

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I.B. Guzman

44

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R. Haake

146

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M.K. Habib

106

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C. Hadjidakis

61

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H. Hamagaki

81

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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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85

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A. Harlenderova

106

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J.W. Harris

146

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A. Harton

11

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J.A. Hasenbichler

33

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H. Hassan

95

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D. Hatzifotiadou

10

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53

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P. Hauer

42

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S. Hayashi

132

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S.T. Heckel

68

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104

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E. Hellbär

68

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H. Helstrup

35

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A. Herghelegiu

47

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T. Herman

36

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E.G. Hernandez

44

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G. Herrera Corral

9

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F. Herrmann

144

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K.F. Hetland

35

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T.E. Hilden

43

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H. Hillemanns

33

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C. Hills

127

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B. Hippolyte

136

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B. Hohlweger

104

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D. Horak

36

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A. Hornung

68

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S. Hornung

106

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R. Hosokawa

15

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133

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P. Hristov

33

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C. Huang

61

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C. Hughes

130

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P. Huhn

68

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T.J. Humanic

96

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H. Hushnud

109

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L.A. Husova

144

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N. Hussain

41

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14

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D. Hutter

38

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J.P. Iddon

33

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127

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R. Ilkaev

108

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M. Inaba

133

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G.M. Innocenti

33

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M. Ippolitov

87

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A. Isakov

94

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M.S. Islam

109

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M. Ivanov

106

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V. Ivanov

97

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V. Izucheev

90

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B. Jacak

79

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N. Jacazio

53

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P.M. Jacobs

79

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S. Jadlovska

116

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J. Jadlovsky

116

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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

98

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O. Jevons

110

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M. Jin

125

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F. Jonas

95

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144

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P.G. Jones

110

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J. Jung

68

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M. Jung

68

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A. Jusko

110

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P. Kalinak

64

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A. Kalweit

33

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V. Kaplin

92

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S. Kar

6

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A. Karasu Uysal

77

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O. Karavichev

62

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T. Karavicheva

62

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P. Karczmarczyk

33

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E. Karpechev

62

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A. Kazantsev

87

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U. Kebschull

74

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R. Keidel

46

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M. Keil

33

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B. Ketzer

42

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Z. Khabanova

89

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A.M. Khan

6

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S. Khan

16

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S.A. Khan

141

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A. Khanzadeev

97

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Y. Kharlov

90

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A. Khatun

16

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A. Khuntia

118

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B. Kileng

35

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B. Kim

60

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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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H. Kim

17

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147

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J. Kim

147

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J.S. Kim

40

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J. Kim

103

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J. Kim

147

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J. Kim

73

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M. Kim

103

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S. Kim

18

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T. Kim

147

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T. Kim

147

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S. Kirsch

38

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68

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I. Kisel

38

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S. Kiselev

91

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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

58

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S. Klein

79

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C. Klein-Bösing

144

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M. Kleiner

68

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33

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M.L. Knichel

33

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A.G. Knospe

125

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C. Kobdaj

115

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M.K. Köhler

103

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T. Kollegger

106

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75

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N. Kondratyeva

92

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90

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J. Konig

68

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33

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L. Koska

116

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O. Kovalenko

84

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V. Kovalenko

112

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M. Kowalski

118

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I. Králik

64

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A. Kravˇcáková

37

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L. Kreis

106

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M. Krivda

64

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110

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F. Krizek

94

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K. Krizkova Gajdosova

36

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M. Krüger

68

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E. Kryshen

97

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M. Krzewicki

38

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96

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V. Kuˇcera

60

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C. Kuhn

136

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P.G. Kuijer

89

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L. Kumar

99

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S. Kumar

48

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85

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84

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62

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62

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108

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94

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J. Kvapil

110

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60

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60

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147

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38

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27

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P. Ladron de Guevara

71

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79

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R. Langoy

129

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33

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20

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51

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33

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R. Lavicka

36

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T. Lazareva

112

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R. Lea

24

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L. Leardini

103

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J. Lee

133

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147

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89

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113

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J. Lehrbach

38

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93

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120

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19

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145

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12

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6

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129

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110

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17

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38

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127

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106

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96

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19

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96

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143

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21

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92

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C. Loizides

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P. Loncar

34

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X. Lopez

134

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E. López Torres

8

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J.R. Luhder

144

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M. Lunardon

28

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59

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39

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62

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33

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20

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42

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136

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R.D. Majka

146

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M. Malaev

97

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Q.W. Malik

20

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L. Malinina

75

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iii

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D. Mal’Kevich

91

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P. Malzacher

106

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G. Mandaglio

55

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V. Manko

87

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F. Manso

134

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V. Manzari

52

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6

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M. Marchisone

135

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66

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24

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J. Margutti

63

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A. Marín

106

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C. Markert

119

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M. Marquard

68

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103

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P. Martinengo

33

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125

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44

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M. Martinez Pedreira

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M. Masera

25

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54

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114

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52

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138

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104

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117

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80

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121

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A. Matyja

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118

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M. Mazzilli

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M.A. Mazzoni

57

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68

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22

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Y. Melikyan

62

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92

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A. Menchaca-Rocha

71

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C. Mengke

6

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29

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113

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M. Meres

13

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S. Mhlanga

124

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Y. Miake

133

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L. Micheletti

25

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104

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75

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91

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A. Mischke

63

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i

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69

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106

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A. Modak

3

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N. Mohammadi

33

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63

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85

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M. Mohisin Khan

16

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iv

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44

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62

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79

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R.H. Munzer

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