Longitudinal asymmetry and its effect on pseudorapidity distributions in Pb–Pb collisions at sNN=2.76 TeV

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Physics

Letters

B

www.elsevier.com/locate/physletb

Longitudinal

asymmetry

and

its

effect

on

pseudorapidity

distributions

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

Article history:

Received30October2017

Receivedinrevisedform9March2018 Accepted15March2018

Availableonline22March2018 Editor:L.Rolandi

FirstresultsonthelongitudinalasymmetryanditseffectonthepseudorapiditydistributionsinPb–Pb collisions at√sNN =2.76 TeVattheLargeHadronColliderareobtainedwiththe ALICEdetector.The longitudinal asymmetry arises becauseofanunequal number ofparticipatingnucleons fromthe two collidingnuclei,andisestimatedforeacheventbymeasuringtheenergyintheforward neutron-Zero-Degree-Calorimeters(ZNs).Theeffectofthelongitudinalasymmetryismeasuredonthepseudorapidity distributionsofchargedparticlesintheregions|

η

|<0.9,2.8<

η

<5.1 and−3.7<

η

<−1.7 bytaking theratioofthepseudorapiditydistributionsfromeventscorrespondingtodifferentregionsofasymmetry. Thecoefficientsofapolynomialfittotheratiocharacterisetheeffectoftheasymmetry.AMonteCarlo simulationusingaGlaubermodelforthecollidingnucleiistunedtoreproducethespectrumintheZNs andprovidesarelationbetweenthemeasurablelongitudinalasymmetryandtheshiftintherapidity( y0) oftheparticipantzoneformedbytheunequalnumberofparticipatingnucleons.Thedependenceofthe coefficientofthelinearterminthepolynomialexpansion,c1,onthemeanvalueofy0isinvestigated.

©2018TheAuthor(s).PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense (http://creativecommons.org/licenses/by/4.0/).FundedbySCOAP3_.

1. Introduction

Ina heavy-ion collision,the numberof nucleons participating fromeach ofthe two collidingnuclei isfinite, andwillfluctuate event-by-event. The kinematic centre of mass of the participant zone,definedastheoverlapregionofthecollidingnuclei,in gen-eralhasafinitemomentuminthenucleon–nucleoncentreofmass frame because of the unequal number of nucleons participating fromthetwonuclei.Thismomentumcausesalongitudinal asym-metry in the collision and corresponds to a shift of rapidity of the participantzone withrespect to the nucleon–nucleon centre ofmass (CM) rapidity,termed therapidity-shift y0. The value of

y0isindicativeofthemagnitudeofthelongitudinalasymmetryof

thecollision [1,2].Assumingthenumberofnucleonsparticipating fromeachofthetwonucleiis A and B,thelongitudinal asymme-tryinparticipantsisdefinedas

α

part

=

_AA−₊B_B andtherapidity-shift

canbeapproximatedasy0

∼

=

12ln

A

B atLHCenergies [2].

The shift in the CM frame of the participant zone, which evolvesintoastateofdensenuclearmatter,needstobeexplored in heavy-ion collision models. Comparison of model predictions with the observed



-polarisation, possibly due to vorticity from the initial state angular momentum surviving the evolution, re-quiresaprecisedetermination ofinitial conditionsandhencethe

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

shiftintheCMframe [3–5].Such ashiftmayalsoaffect observa-tions on correlationsamongst particles,which eventually provide informationaboutthestate ofthematterthroughmodel compar-isons.Further,theresultantdecreaseintheCMenergymayaffect various observables includingthe particle multiplicity.The trans-verse spectraareknowntobe affectedby theinitialgeometryof the events, as estimated through techniques of event shape en-gineering, indicating an interplay between radial and transverse flow [6].Themeasurementoflongitudinalasymmetrywillprovide anewparametertowardseventshapeengineering,affectingmany otherobservables.

The simplest of all possible investigations into the effect of longitudinal asymmetry is a search for modification ofthe kine-maticdistributionoftheparticles.Thepseudorapiditydistribution (dN

/

d

η

)ofsoftparticles,averagedoveralargenumberofevents, is symmetric in collisions of identical nuclei. These distributions were observed to be asymmetric in collisions of unequal nuclei such as d–Au [7] and p–Pb [8–10] and have been explained in termsoftherapidity-shiftoftheparticipantzone [11].Ina heavy-ioncollision,theeffectoftherapidity-shiftoftheparticipantzone shouldbediscernibleinthedistributionofproducedparticles.This smalleffectcan beestimatedby takingtheratioof pseudorapid-ity distributions inevents corresponding todifferent longitudinal asymmetries [2].

It was suggested that the rapidity distribution of an event, scaled by the average rapidity distribution, can be expanded in termsofChebyshevpolynomials, wherethecoefficientsof

expan-https://doi.org/10.1016/j.physletb.2018.03.051

0370-2693/©2018TheAuthor(s).PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense(http://creativecommons.org/licenses/by/4.0/).Fundedby SCOAP3_.

sionaremeasuresofthestrengthoflongitudinalfluctuationsand canbedeterminedbymeasuringthetwoparticlecorrelation func-tion [12]. Usingthe samemethodology,the event-by-event pseu-dorapidity distributions are also expanded in terms of Legendre polynomials [13].TheATLASCollaborationexpandedthe pseudora-piditydistributionsintermsofLegendrepolynomialsandobtained thecoefficientsbystudyingpseudorapiditycorrelations [14].

Inthepresentwork,theeventsare classifiedaccordingtothe asymmetrydeterminedfromthemeasurementofenergiesof neu-tron spectators on both sides of the collision [2]. The effect of asymmetryisinvestigatedbytakingtheratioofthemeasuredraw dN

/

d

η

distributionsforeventsfromdifferentregionsofthe distri-butionofmeasuredasymmetry.Amajoradvantageofstudyingthis ratioisthecancellationof(i)systematicuncertainties and(ii)the effectsofshortrange correlations. Thefirst measurements ofthe effectofasymmetry ontherawdN

/

d

η

distributionsarereported here.

Thepaperisorganisedasfollows:Sect.2providesan introduc-tion to the experimental setup andthe details of the data sam-ple.Section3discusses thecharacterisation ofthechangeinraw dN

/

d

η

distributions for events classified in different asymmetry regions.Section 4 describesthe simulationsemployed to provide arelationbetweenthemeasuredasymmetryandtherapidity-shift

y0 of the participant zone. The relation between the parameter

characterisingthechangeinrawdN

/

d

η

distributionsisshownfor differentcentralities inSect.5,along withits relationto the esti-matedvaluesof y0.

2. Experimentaldetailsanddatasample

TheanalysisusesdatafromPb–Pb collisioneventsat

√

sNN

=

2.76TeV, recordedintheALICEexperimentin2010,witha min-imumbias trigger [15,16]. The data used inthe presentanalysis isrecordedintheneutronZeroDegreeCalorimeters (ZNs),theV0 detectors,theTimeProjectionChamber(TPC)andtheInner Track-ingSystem(ITS).Both ZNsandV0detectorsare oneithersideof theinteractionvertex,thoseinthedirectionofpositive pseudora-pidityaxisarereferredasV0AandZNAandthoseintheopposite directionarereferredasV0CandZNC.Adetaileddescriptionofthe ALICEdetectorsandtheirperformancecanbefoundelsewhere [17,

18].

Theeventasymmetryis estimatedusing theenergymeasured inthetwoZNssituated114metresawayfromthenominal inter-actionpoint(IP)oneitherside.TheZNsdetectonlyspectator neu-tronsthatarenotboundinnuclearfragments,sincethelatterare bentawaybythemagneticfieldoftheLHCseparationdipole.The ZNdetectionprobability forneutrons is 97.0%

±

0.2%(stat)

±

3% (syst) [19]. The relative energyresolution of the1n peak at 1.38 TeVis21%fortheZNAand20% fortheZNC [19].Theproduction ofnuclearfragmentsincreaseswithcollisionimpactparameter de-grading the resolution on the number of participating nucleons. TheenergyintheZNsisagoodmeasureofthenumberof specta-torneutronsonlyforthemorecentralcollisions [18].Theanalysis islimited tothe top 35% mostcentral sample andemploys data from

∼

2

.

7 millionevents.

The raw dN

/

d

η

distributions in the region

|

η

|

<

0

.

9 are ob-tainedbyreconstructingthechargedparticletracksusingtheTPC and ITS. The requirements on the reconstructed tracks obtained using the measurements in these detectors are the same as in other earlieranalyses [15]. The measured amplitudes inthe V0A

(

+

2

.

8

<

η

<

+

5

.

1

)

andV0C (

−

3

.

7

<

η

<

−

1

.

7) are used to es-timate the raw dN

/

d

η

distributions of charged particles in the forwardregions. Both V0AandV0Care scintillatorcounters,each withfour segments in pseudorapidity andeight segments in az-imuth.Therawdistributions measuredare termedasdN

/

d

η

dis-tributionsthroughoutthemanuscript.Inordertoensureauniform detectorperformance,thepresentanalysisuseseventswithz

po-sition (along the beam direction) of the interaction vertex, Vz,

within

±

5 cm of the IP in ALICE. The centrality of Pb–Pb col-lisionswas estimatedby twoindependentmethods.Oneestimate wasbasedonthechargedparticlemultiplicityreconstructedinthe TPCandtheother wasbasedon theamplitudesintheV0 detec-tors[20].

3. Analysisandsystematicuncertainties

Inthepresentanalysis,changesintherawpseudorapidity dis-tribution ofchargedparticles areinvestigated fordifferentvalues ofmeasuredasymmetryoftheevent.Themethodofmeasurement oftheasymmetryandtheparameterscharacterisingthechangein dN

/

d

η

distributionsarediscussedinthissection.

3.1. Analysis

Anyeventasymmetryduetounequalnumberofnucleonsfrom the two participatingnucleimaymanifest itself inthe longitudi-naldistributions,i.e.dN

/

d y (or dN

/

d

η

)oftheproducedparticles because of a shift in the effectiveCM. Assuming that the rapid-itydistributions can bedescribed by a symmetricfunction about a mean y0 ( y0

=

0

.

0 for symmetricevents), the ratioofthe

dis-tributions forasymmetric and symmetric eventsmay be written as

(

dN

/

d y

)

asym

(

dN

/

d y

)

sym

=

f

(

y

−

y0

)

f

(

y

)

∝

∞



n=0 cn

(

y0

)

yn (1)

Foranyfunctionalformoftherapiditydistribution,thisratiomay beexpandedinaTaylorseries.Thecoefficientscn ofthedifferent

termsin theexpansiondepend onthe shapeandtheparameters oftherapiditydistribution [2].IntheALICEexperiment,the pseu-dorapiditiesoftheemittedparticleswere measured.Theeffectof arapidity-shift y0 onthepseudorapiditydistributionis discussed

inSect.4.2.

Theunequalnumberofparticipatingnucleonswillyielda non-zero y0 ofthe participant zone andwill causean asymmetry in

thenumberofspectators.Thisasymmetrycanprovideinformation aboutthemeanvaluesof y0 usingtheresponsematrixdiscussed

inSect.4.Theasymmetryofeacheventisestimatedbymeasuring theenergyintheZNsonbothsidesoftheinteractionvertex:EZNA

onthesidereferredtoastheA-side(

η

>

0)andEZNC ontheside

referred to astheC-side (

η

<

0).A smalldifference inthe mean andtherelativeenergyresolutionofthe1n peakat1.38TeVwas observed in theperformance ofthe two ZNs [19]. Foreach cen-tralityinterval,theenergydistributionineachZNisdividedbyits mean,andthe widthofthe EZNC

/



EZNC



distributionis scaledto

thewidthofthecorrespondingdistributionusingEZNA.The

asym-metryinZNisdefinedas

α

ZN

=

ε

ZNA

−

ε

ZNC

ε

ZNA

+

ε

ZNC

(2) where

ε

ZNC(A)isadimensionlessquantityforeachevent,obtained

afterscalingthedistributionsofEZNC(A)asdescribedabove.

For the 15–20% centrality interval, Fig. 1 showsthe distribu-tionofthe asymmetry

α

ZN.Toinvestigatethesignificanceofthis

distribution,the contributionof theresolutionof ZNsto the res-olution of the asymmetry parameter

α

ZN is evaluated. For each

centralityinterval,valuesofEZNC andEZNAaresimulatedforeach

Fig. 1. ThedistributionoftheasymmetryparameterαZNforthe15–20%centrality

interval.Thedistributionisdemarcatedintothreeregionsusing|αcut

ZN|.AGaussian

fittothedistributionyieldsawidthof0.13.

corresponding tothe average numberofneutrons andthe corre-sponding energy resolution. The average number of neutrons is estimatedby dividing the experimental distribution of energyin ZNby1.38TeV.Thesevaluesareusedtoobtain

α

ZNforeachevent

andits distribution.The widthofthe distributioncorresponds to theintrinsicresolutionofthemeasuredparameter

α

ZN andvaries

from0.023 to0.050 fromthemostperipheral (30–35%)selection to themostcentral (0–5%) selection.The observed widthof 0.13 ofthedistributionof

α

ZN reportedinFig.1isconsiderablylarger

than the resolution of

α

ZN (0.027 for the centralityinterval

cor-responding to the data in the figure) and the increase in width maybeattributedtotheevent-by-eventfluctuationsinthe num-ber of neutrons detected in each ZN. To investigatethe effectof

α

ZN on the dN

/

d

η

distributions, the events are demarcated into

three regions of asymmetry by choosing a cut value

α

cut ZN. These

regions correspond to (i)

α

ZN

<

−

α

_ZNcut (Region 1), (ii)

α

ZN

≥

α

_ZNcut

(Region 2)and(iii)

−

α

cut

ZN

≤

α

ZN

<

α

ZNcut (Region3). Regions1and

2 are referred to as the asymmetric regions and Region3 is re-ferredtoasthesymmetricregion.

Theeffectofthemeasuredasymmetry

α

ZNonthe

pseudorapid-itydistributionsisinvestigatedbystudyingtheratioofdN

/

d

η

dis-tributionineventsfromtheasymmetricregion tothosefromthe symmetricregion.There aresmalldifferencesinthedistributions ofcentrality andvertexposition inevents ofdifferentregions of asymmetry.Itisnecessarytoensurethatanycorrelationbetween theratioofdN

/

d

η

andtheasymmetryisnotduetoasystematic effectofashiftintheinteractionvertex.Toeliminateanypossible systematicbiasonthemeasureddistributions,thedN

/

d

η

distribu-tionsare correctedbyweightfactorsobtainedbynormalisingthe numberofeventsinasymmetricandsymmetricregionsineach1% centralityintervalandeach1cmrangeofvertexpositions.

For the 15–20% centrality interval, the distributions of these factorsinthetwocasescorrespondingtotheasymmetryregions 1 and 2 havea mean of 1.0and an rms of 0.05 and0.06 respec-tively.Theweightfactorsdonotshowanysystematicdependence onthepositionofthevertex.Thisisexpectedconsideringthelarge distancebetweentheZNsascomparedtovariationsinthevertex position.Thefactorsshowasystematicdependenceon1% central-itybinswithineach centralityinterval.The1% centralitybinwith thegreaternumberofparticipantstendstohavemoreasymmetric events,presumablytocompensateforthedecreaseintheeffective CMenergyduetothemotionoftheparticipantzone;theweight

factoris1.08forthemostcentral15–16%centralitybinandis0.94 forthe19–20%centralitybin.

The ratio of dN

/

d

η

for events corresponding to different re-gions of asymmetry,asshowninFig. 1,is determined.For

|

η

|

<

1

.

0, the ratio is obtained using dN

/

d

η

for tracks. For

|

η

|

>

1

.

0, the ratioshowninFig.2(a) and(b)isobtainedfromamplitudes measured inV0Aandthe oneshownin Fig.2(c)and(d)isfrom amplitudesmeasuredinV0C.ThesquaresinFig.2(a)and(c) rep-resent the ratio ofdN

/

d

η

inthe asymmetry Region1 to that in Region3(R13),andthestarsrepresentthecorresponding ratioin Region2toRegion3(R23).Thefilledcircles inFig.2(b)and(d) are obtained by (i) reflecting thedata points labelled R23 across

η

=

0 and (ii) taking the averages of R13 and reflected-R23 for

|

η

|

<

1

.

0.Athirdorderpolynomial isfittedto thepointsandthe values of the coefficients cn along with the

χ

2 are shown. The

polynomialfittotheratioofdN

/

d

η

distributionhasadominantly linearterm.Asmallresidualdetectoreffectisobservedwhen de-termining c1 using data measured in V0A andwhen using data

measured in V0C. In all subsequent discussion, the values of c1

quoted are the mean ofvalues obtainedfrom themeasurements inV0AandV0C.

Considering thatthe eventsamplescorresponding to different regions ofasymmetry areidenticalinall aspectsother thantheir valuesofmeasured

α

ZN,theobservationofnon-zerovaluesofc1

can be attributedto the asymmetry.For a fixed centrality inter-val, c1 depends on the choice of

α

ZNcut. The analysis is repeated

for differentvalues of

α

cut

ZN andthe dependenceof c1 on

α

ZNcut is

shown in Fig. 3, for different centralities. For each centrality in-terval thecoefficient c1 has alineardependenceon

α

ZNcut andthe

slope increaseswithdecreasingcentrality;c1 increasesforevents

corresponding to larger values of average event asymmetry. The rangeofvaluesof

α

cut

ZN wasguidedbytheresolutionandthewidth

of the distribution of

α

ZN, as mentioned in reference to Fig. 1.

Increasing thevalue of

α

cut

ZN increasesthe mean



α

ZN



forevents

from theasymmetric class (Region 1or Region2), andincreases theRMSof

α

ZNforeventsfromthesymmetricclass(Region3).

3.2. Systematicuncertainties

The current method of analysisuses the ratio of two dN

/

d

η

distributions from events divided on the basis of measurements inZNs,within acentralityinterval.Alleffects duetolimited effi-ciency,acceptanceorcontamination wouldcancelwhileobtaining the value oftheratio.The contributionsto thesystematic uncer-taintiesonc1 areestimatedduetothefollowingsources:

1. Centralityselection: the ratioofdN

/

d

η

is obtainedfromthe measurements of tracks in the ITS+TPC at midrapidity and charge particlesignalamplitudesintheV0atforward rapidi-ties. For theformer, theeventcentrality isdetermined using themeasurementsintheV0andforthelatterusingthetrack multiplicityintheTPC.Theanalysisisrepeatedby interchang-ingthecentralitycriteriaandtheresultantchangeinthe val-uesofc1 fordifferentcentralityintervalsisintherange0.1%

to3.6%.

2. V0AandV0C:thesystematicuncertaintyonthemeanvalueof

c1 isestimatedbyassumingauniformprobabilitydistribution

forthecorrectvalue ofc1 to lie betweenthe twovalues

ob-tainedusingthecharged-particle signalamplitudesmeasured intheV0AandtheV0C.The uncertaintyisintherange2.1% to4.6%anddoesnotdependonthecentralityvalue.

3. Vertexposition:theanalysisis repeatedforthe zpositionof theinteraction vertex

|

Vz

|

≤

3

.

0 cm.Forthemostcentral

Fig. 2. TheratioofdN/dηdistributionforeventsfromthedifferentregionsofαZN distributionofFig.1.ThedN/dηdistributionsareobtainedasdescribedinSect.2.

(a) Thesquare(star)symbolscorrespondingtoR13(R23)areobtainedbytakingtheratioofdN/dηofeventsfromRegion1(Region2)toRegion3.(b)Thedatapointsare obtainedafterreflectionacrossη=0 asdescribedinthetext.Thedatafor|η|>1.0 inpanels(a)and(b)arefrommeasurementsinV0Aandinpanels(c)and(d)arefrom measurementsinV0C.

Fig. 3. Thecoefficient

c1

characterisingthechangeindN/dηdistributionfor asym-metricregionsisshownfordifferentvaluesofαcut

ZN (αZNcutdemarcatesthe

asymmet-ricandsymmetricevents)foreachcentralityinterval.

centralityinterval,theresultschangeby3.3%andforallother centralityintervals,thechangesarelessthan1.3%.

4. Weightfactorsfornormalisation:theanalysisisalsorepeated withouttheweightfactorsmentionedinSect.3.1forthe cen-tralityandthevertexnormalisationinthenumberofevents. Thechangeintheresultsis4.9%inthemostcentralclassand lessthan1%forallothercentralityintervals.

Thetotalsystematicuncertaintyisobtainedbyaddingthefour uncertainties in quadrature. The resultant uncertainty is in the range2.3%to5.8%andisshownbythebandinFig.8.

4. Simulations

Thesimulationusedforobtaining arelationbetween rapidity-shift y0 andthe measurableasymmetry

α

ZN is described in this

section.Thissimulationhasthreecomponents:(i)aGlauberMonte Carlo to generate number of participants and spectator protons andneutrons, (ii) a function parametrised to fit the average loss ofspectator neutrons dueto spectatorfragmentation(the loss of spectatorneutrons ineacheventissmeared aroundthisaverage) and (iii)the response of the ZNto single neutrons. The simula-tion encompassing the above is referred to in the presentwork asTunedGlauberMonteCarlo(TGMC),andreproducestheenergy distributions in the ZNs. The effect of y0 on the pseudorapidity

distributionshasbeenestimatedusingadditionalsimulationsfora GaussiandN

/

d y andarealsodescribedinthissection.

4.1. Asymmetryandrapidity-shift

TheGlauberMonteCarlomodel [21] usedinthepresentwork assumesa nucleon–nucleoninteractioncrosssection of64mb at

√

sNN

=

2.76TeV. The model yields the numberof participating

nucleonsintheoverlapzonefromeachofthecollidingnuclei.The rangeofimpactparametersforeach5%centralityintervalistaken fromourPb–Pbcentralitypaper [20].Foreach centralityinterval, 0.4millioneventsaregenerated.

Foreachgenerated event,thenumberofparticipatingprotons andneutronsisobtained,enablingadeterminationofthe rapidity-shift y0 andthevarious longitudinalasymmetries.IfAandBare

thenumberofspectators(spectatorneutrons)inthetwocolliding nuclei,theasymmetryisreferredtoas

α

spec(

α

spec−neut).Fig.4(a)

showsthe correspondencebetween y0 and

α

part.Figs. 4 (b)and

(c) show the relation between y0 and

α

spec and

α

spec−neut

re-spectively [2].Thesefiguresshowthattherapidity-shifty0 canbe

estimatedbymeasuring

α

specor

α

spec−neutinanyexperimentthat

Fig. 4. Rapidity-shift

y0

asafunctionofasymmetryin(a)numberofparticipants, (b)numberofspectators, (c)numberofspectatorneutronsand(d)energyinZNobtained usingTGMCasdescribedinthetext.Theresultsinallfourpanelsareshownforthe15–20%centralityinterval.

Fig. 5. (a)DistributionofenergyinZNCineach5%centralityintervalforeventssimulatedusingTGMCandfortheexperimentaldata.Thepeakofthedistributionshiftsto smallervaluesof

EZNC

withincreasingcentrality.(b) DistributionoftheasymmetryparameterαZNinthesimulatedeventsandinexperimentaldatafordifferentcentralities.

Thewidthofthedistributionincreaseswithincreasingcentrality.Forclarity,only5distributionsareshown.Thedistributionscorrespondingto20–25% and25–30%lie betweenthoseof15–20%and30–35%.

onthenumberofparticipantsworsenstheprecisionin determin-ing y0.Fig.4(d)showstherelationbetweeny0and

α

ZNobtained

inTGMC,asdescribedinthenextparagraph.

The Glauber MonteCarloistuned to describe the experimen-tal distributions of ZN energy. For each 1% centrality interval, the mean number of spectator neutrons (Ns) is obtained in the

GlauberMonteCarlo.FoldingtheZNresponseyieldsthesimulated valuesofmeanenergyasafunctionofcentrality.The experimen-tallymeasuredmeanenergyintheZNisalsodeterminedforeach 1%centralityinterval.Theratioofthemeasuredvalueofmean en-ergy to the simulated value of mean energy gives the fractional loss(f )ofneutronsduetospectatorfragmentsthatveerawaydue tothemagneticfield. Thevalueoff forthe0–5%centrality inter-valis0.19. Forallother centralities itvariesfrom0.40 for5–10% to0.55for30–35%centralityinterval.Afluctuationproportionalto thenumberofremaining neutrons(Ns

× (

1

−

f

)

)is incorporated

toreproducetheexperimentaldistributionoftheenergydeposited intheZNshowninFig.5(a).ThepeakandtheRMSoftheenergy distributions matchwell.The fractional difference intheposition of the peak varies between3.7% for the 0–5% centrality interval and0.1% for the30–35% centrality interval. The fractional differ-enceinRMSforthemostcentralclassis8.6%andisintherange 1.0–2.0%forall other centralityintervals. Thedistributions ofthe asymmetryparameterfortheTGMCeventsandthemeasureddata foreachcentralityintervalareshowninFig.5(b).TheTGMC

con-tains information of y0 and

α

ZN for each event. A scatter plot

between y0 and

α

ZNisshowninFig.4(d)forthe15–20%

central-ityinterval.Thisconstitutestheresponsematrix.Foranymeasured value of

α

ZN,the distribution of y0 can be obtained. Any

differ-ence in the experimental and TGMC distributions of

α

ZN can be

accountedforby scalingthe y0 distributionbythe ratioof

num-berofeventsindatatothenumberinTGMCas

f

(

y0

,

α

ZNData

)

=

f

(

y0

,

α

ZNTGMC

)

NData_events

NTGMC_events

,

(3)

withData(TGMC)inthesuperscriptofnumberofevents,Nevents,

denoting the experimental data (TGMC events). For each of the three regions of asymmetry shown in Fig. 1, corresponding to a chosenvalueof

α

cut

ZN

=

0

.

1,thedistributionofrapidity-shift y0

ob-tained using the response matrix is shown in Fig. 6. It isworth mentioningthatthewidthofthedistributionofy0foreventsfrom

Region 3,corresponding to

−

α

cut

ZN

≤

α

ZN

<

α

cutZN, is comparableto

thewidthsofthecorresponding distributionsfromRegions1and 2.Theeffectofdifferenceinthevalueofthemeansofthey0

dis-tributionsisinvestigatedinthepresentwork.

4.2. Effectofrapidity-shiftonpseudorapiditydistributions

The effect ofa shift inthe rapidity distribution by y0 on the

measurablepseudorapiditydistribution(dN

/

d

η

)isinvestigated us-ingsimulations.Foreachevent,therapidityofchargedparticlesis

Fig. 6. Thedistributionofrapidity-shifts forthe eventsfromthe threedifferent regionsofmeasuredasymmetryshowninFig.1.Determinationof

y0

usesthe dif-ferenceinnumberofnucleons.Forsmallvaluesofthisdifference,thechangesin valuesnear

y0

=0 arediscrete,andaresmearedintoacontinuousdistributionas

y0increases.

generatedfromaGaussiandistributionofachosenwidth

σy

[22]. ThepseudorapidityisobtainedbyusingtheBlast-Wavemodelfit to the data for the transverse momentum distributions and the experimentally measured relativeyields ofpions, kaonsand pro-tons [23].Tosimulatetheeffectofdifferentwidthsoftheparent rapidity distribution fordifferent centralities, different

σ

y widths

arechosentoreproducethemeasured FWHM(FullWidthatHalf Maximum) of the pseudorapidity distribution [24]. Forthe most central(0–5%)class,a value3.86isusedforthewidthofthe ra-pidity distribution,anda value 4.00 isused forthe widthofthe leastcentralclassemployedinthisanalysis(30–35%).

Thedistributionof rapidity-shift y0,similar tothe oneshown

in Fig. 6, is obtained for each centrality interval and each

α

cut ZN

usingTGMC.Fig.7(a)showsthe



y0



asafunctionof

α

cut_ZN for

dif-ferentcentralities.Oneobservesalinearrelationbetweenthetwo quantities, showing that an asymmetry in the ZN measurement, arisingfromtheunequal numberofparticipatingnucleons, is re-latedtothe meanrapidity-shift



y0



.The rapidity distributionof

theparticlesproducedineacheventisgeneratedassuminga Gaus-sianformcentred abouta y0,which isgeneratedrandomly from

the y0 distribution.Events witharapidity distributionshifted by

y0

=

0 yieldanasymmetricpseudorapiditydistribution.Athird

or-derpolynomialfunctionin

η

isfittedtotheratioofthesimulated dN

/

d

η

fortheasymmetricregiontothesimulateddN

/

d

η

forthe symmetricregion. Thevaluesofthe coefficientsintheexpansion dependupontherapidity-shift y0andtheparameters

characteris-ingthedistribution [2].

The simulations described above were repeated for different valuesof

α

cut

ZN to obtainthepseudorapiditydistributions for

sym-metric and asymmetric regions. Fitting third order polynomial functions to the ratios of the simulated pseudorapidity distribu-tions determines the dependenceof c1 on

α

ZNcut.Fig. 7 (b)shows

that c1 hasalineardependenceon

α

cutZN foreachcentrality

inter-val. The difference in the slopes for different centralities is due to differencesinthedistributions of y0 andtodifferencesin the

widthsoftherapiditydistributions.

Itisimportanttonotethattheparameterc1,characterisingthe

asymmetry inthe pseudorapidity distribution,showsa linear de-pendence on the parameter

α

cut

ZN in the event sample generated

usingTGMCandsimulationsforaGaussiandN

/

d y,akintothe de-pendenceoftheestimatedvalueofrapidity-shift y0 forthesame

sampleofevents.

5. Results

The longitudinalasymmetry ina heavy-ioncollision has been estimatedfromthedifference intheenergyofthespectator neu-tronson both sidesofthe collisionvertex. The effectof the lon-gitudinal asymmetry is observed in the ratioof dN

/

d

η

distribu-tions corresponding to differentasymmetries. The linear term in a polynomial fitto thedistribution ofthe ratiois dominant, and ischaracterisedbyitscoefficientc1.Thecentralitydependenceof

the coefficient c1 for

α

ZNcut

=

0

.

1 is shown in Fig. 8. It is worth

emphasising thatthevaluesofc1 andhenceits centrality

depen-dence are affected by (i) the distribution of rapidity-shift y0 for

each centralityinterval, (ii) the chosen value of

α

cut

ZN, as seen in

Fig.7and(iii) the shapeorthewidthofthe parentrapidity dis-tributionforeachcentrality.Fig.8alsoshowstheresultsobtained usingsimulationsasdescribed inSec. 4.2for

α

cut

ZN

=

0

.

1.The

sys-tematicuncertaintyonthesimulatedeventsampleisestimatedby (i) varying the resolution ofZNs from 20% to 30%, (ii) assuming all charged particles are pions and(iii) varying thewidth of the parentrapiditydistributionwithintherangecorresponding tothe uncertainties onFWHMquoted inRef. [24]. Thesimulatedevents showagoodagreementwiththeexperimentaldataproviding

cre-Fig. 7. (a)Theestimatedmeanvalueofrapidity-shifty0fortheasymmetricregioncharacterisedbydifferentvaluesofαcut

ZN foreachcentralityinterval.(b)Thecoefficient c1characterisingthechangeinthepseudorapiditydistributionsfordifferentvaluesofαcut

ZN,foreachcentralityinterval.TheseresultsareobtainedusingTGMCandsimulated

Fig. 8. Themeanvaluesofthecoefficient

c1

areshownasfilledcirclesfordifferentcentralities.ThesecorrespondtotheratioofdN/dηdistributionsofpopulationsofevents demarcatedbyαcut

ZN =0.1.Thesquaresshowthecorrespondingvaluesfromsimulations,andcorrespondtoαcutZN=0.1 inFig.7,fordifferentcentralities.Thesystematic

uncertaintiesareshownasbands.

Fig. 9. Foreachsetofeventscharacterisedbyαcut

ZN,themeasuredvaluesof

coef-ficient

c1

asafunctionofestimatedvaluesofmeanrapidity-shiftobtainedusing TGMCasdescribedinthetext.Theresultsareshownfordifferentcentralities.The uncertaintiesfory0shownarestatisticalandwithinitssymbolsize.Thelinesare linearfitspassingthroughtheorigin.

dencetotheassumptions ofthesimulation,inparticularthatthe asymmetryinthedistributionsarisesfromtheshiftofrapidity of theparticipantzone.

There are two quantities fromindependent measurements for eachselection ofasymmetricevents.Theseare (i) c1,the

param-eter characterising the effect of asymmetry in the dN

/

d

η

distri-butions andshowninFig.3and(ii) themeanrapidity-shift



y0



obtainedfromthemeasured asymmetry,filteredthrough the cor-responding responsematrix (Fig. 4 (d)), andshown inFig. 7 (a). Therelationbetweenc1 and



y0



isshowninFig.9.The

parame-terc1 showsalineardependenceon



y0



foreachcentrality.The

differenceintheslopesindicatesthesensitivityofthelongitudinal asymmetry tothedetails oftherapidity distribution.Fora Gaus-sianrapiditydistributionthecorrespondingparameterc1wouldbe

relatedtotherapidity-shiftasc1

=

_σy0

y2

[2],implyingthattheslope isinverselyproportionaltothesquareofthewidthofthe distribu-tion.Theobservationofan increaseintheslopewithanincrease in the centrality in the present data indicates a decrease in the widthofthepseudorapiditydistributionwithincreasingcentrality. Such a decrease in the width of the pseudorapidity distribution withincreasingcentralityhasbeenobservedindependentlyby

fit-tingthe pseudorapiditydistributions ina broadrangeof pseudo-rapidity [24].

6. Conclusions

The present analysis demonstratesthe existence ofa longitu-dinalasymmetry inthe collisionofidenticalnucleidueto fluctu-ationsin thenumberofparticipants fromeachcollidingnucleus. This asymmetry has beenmeasured in the ZNs inthe ALICE ex-periment (Fig. 1), andaffects thepseudorapidity distributions, as demonstratedbytakingtheratioofdistributionofeventsfromthe asymmetric region tothe corresponding onefromthe symmetric region(Fig.2).Theeffectcanbecharacterisedbythecoefficientof thelinearterminthepolynomialexpansionoftheratio.The coef-ficientsshowalineardependenceon

α

cut

ZN,aparametertoclassify

the events into symmetric and asymmetric regions (Fig. 3). Dif-ferent values of

α

cut

ZN correspond to different valuesof the mean

rapidityshift



y0



(Fig.7(a)).Theparameterdescribingthechange

inthepseudorapiditydistributions(c1)hasasimpleexplanationin

the rapidity-shift



y0



of theparticipantzone (Fig.9). The

analy-sisconfirms thatthelongitudinaldistributions areaffectedbythe rapidity-shiftoftheparticipantzonewithrespecttothenucleon– nucleonCMframe.Theresultsprovidesupporttotherelevanceof numberofnucleons affectingtheproductionofchargedparticles, evenatsuchhighenergies.

The longitudinal asymmetry is a good variable to classify the eventsandprovidesinformationontheinitialstateofeach event. Asystematicstudyoftheeffectsoflongitudinalasymmetryon dif-ferentobservables, e.g.theoddharmonicsofanisotropicflow, the forward-backwardcorrelations, thesourcesizes, inheavy-ion col-lisions may reveal other characteristics ofthe initial state andof particleproductionphenomena.

Acknowledgements

The ALICECollaboration would like to thank all its engineers andtechniciansfortheirinvaluablecontributionstothe construc-tion of the experiment and the CERN accelerator teams for the outstanding performance of the LHC complex. The ALICE Collab-oration gratefully acknowledges the resources and support pro-videdbyallGridcentresandtheWorldwideLHCComputingGrid (WLCG) collaboration. The ALICE Collaboration acknowledges the following fundingagenciesfortheir supportin buildingand run-ningthe ALICEdetector:A.I. AlikhanyanNationalScience Labora-tory(YerevanPhysicsInstitute)Foundation (ANSL),State Commit-teeofScienceandWorldFederationofScientists(WFS),Armenia;

AustrianAcademy ofSciences andNationalstiftung fürForschung, Technologie und Entwicklung, Austria; Ministry of Communica-tions and High Technologies, National Nuclear Research Center, Azerbaijan; Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq), Universidade Federal do Rio Grande do Sul (UFRGS), Financiadora de Estudos e Projetos (Finep) and Fun-dação de Amparo à Pesquisa do Estado de São Paulo (FAPESP), Brazil; Ministry of Science & Technology of China (MSTC), Na-tional Natural Science Foundation of China (NSFC) and Ministry of Education of China (MOEC), China; Ministry of Science, Edu-cation andSport and Croatian Science Foundation, Croatia; Min-istryofEducation,YouthandSportsoftheCzechRepublic, Czech Republic; The Danish Council for Independent Research | Natu-ral Sciences, the Carlsberg Foundation and Danish National Re-search Foundation (DNRF), Denmark;Helsinki Institute ofPhysics (HIP),Finland;Commissariatàl’EnergieAtomique(CEA)and Insti-tut Nationalde Physique Nucléaire etde Physique des Particules (IN2P3)andCentre National de laRecherche Scientifique (CNRS), France; Bundesministerium für Bildung, Wissenschaft, Forschung und Technologie (BMBF) and GSI Helmholtzzentrum für Schw-erionenforschung GmbH, Germany; General Secretariat for Re-search andTechnology,Ministry ofEducation, Researchand Reli-gions,Greece;NationalResearch,DevelopmentandInnovation Of-fice,Hungary;DepartmentofAtomicEnergy,GovernmentofIndia (DAE),DepartmentofScienceandTechnology,GovernmentofIndia (DST),University Grants Commission, Governmentof India(UGC) andCouncil ofScientificandIndustrialResearch(CSIR), India; In-donesian Institute of Science, Indonesia; Centro Fermi – Museo StoricodellaFisicaeCentroStudieRicercheEnricoFermiand Isti-tutoNazionalediFisicaNucleare(INFN),Italy;Institutefor Innova-tiveScienceandTechnology,NagasakiInstituteofAppliedScience (IIST),Japan Societyforthe PromotionofScience(JSPS)KAKENHI andJapanese Ministry of Education, Culture, Sports, Science and Technology (MEXT), Japan; Consejo Nacional de Ciencia (CONA-CYT)yTecnología,throughFondodeCooperaciónInternacionalen CienciayTecnología (FONCICYT)andDirección Generalde Asun-tosdelPersonalAcademico(DGAPA),Mexico;Nederlandse Organ-isatievoorWetenschappelijk Onderzoek(NWO),Netherlands; The ResearchCouncil ofNorway, Norway;CommissiononScienceand TechnologyforSustainableDevelopmentintheSouth(COMSATS), Pakistan;PontificiaUniversidadCatólicadelPerú,Peru;Ministryof ScienceandHigherEducationandNationalScienceCentre,Poland; KoreaInstituteofScienceandTechnologyInformationandNational ResearchFoundationofKorea(NRF),RepublicofKorea;Ministryof EducationandScientificResearch,Institute ofAtomicPhysicsand Romanian National Agency for Science, Technology and Innova-tion,Romania;JointInstituteforNuclear Research(JINR),Ministry ofEducation andScience of the Russian FederationandNational Research Centre Kurchatov Institute, Russia; Ministry of Educa-tion,Science,ResearchandSportoftheSlovakRepublic, Slovakia; NationalResearch Foundation of SouthAfrica, South Africa; Cen-tro de Aplicaciones Tecnológicas y Desarrollo Nuclear (CEADEN), Cubaenergía,Cuba,Ministeriode CienciaeInnovacion andCentro de Investigaciones Energéticas, Medioambientales y Tecnológicas (CIEMAT),Spain; Swedish Research Council (VR) and Knut& Al-iceWallenbergFoundation(KAW),Sweden;EuropeanOrganization forNuclear Research, Switzerland; NationalScience and Technol-ogyDevelopment Agency (NSDTA), Suranaree University of Tech-nology(SUT)andOfficeoftheHigherEducationCommissionunder NRUprojectofThailand,Thailand;TurkishAtomic EnergyAgency (TAEK),Turkey;NationalAcademyofSciencesofUkraine,Ukraine; ScienceandTechnologyFacilitiesCouncil(STFC),UnitedKingdom; NationalScienceFoundationoftheUnitedStatesofAmerica(NSF)

andUnitedStatesDepartmentofEnergy,OfficeofNuclearPhysics (DOENP),UnitedStatesofAmerica.

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ALICECollaboration

S. Acharya

137

,

J. Adam

96

,

D. Adamová

93

,

J. Adolfsson

32

,

M.M. Aggarwal

98

,

G. Aglieri Rinella

33

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M. Agnello

29

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N. Agrawal

46

,

Z. Ahammed

137

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N. Ahmad

15

,

S.U. Ahn

78

,

S. Aiola

141

,

A. Akindinov

63

,

M. Al-Turany

106

,

S.N. Alam

137

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J.L.B. Alba

111

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D.S.D. Albuquerque

122

,

D. Aleksandrov

89

,

B. Alessandro

57

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R. Alfaro Molina

73

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A. Alici

11

,

25

,

52

,

A. Alkin

3

,

J. Alme

20

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T. Alt

69

,

L. Altenkamper

20

,

I. Altsybeev

136

,

C. Alves Garcia Prado

121

,

C. Andrei

86

,

D. Andreou

33

,

H.A. Andrews

110

,

A. Andronic

106

,

V. Anguelov

103

,

C. Anson

96

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T. Antiˇci ´c

107

,

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55

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52

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124

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114

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69

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25

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57

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104

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34

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19

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103

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114

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33

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131

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7

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T. Dietel

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Ø. Djuvsland

20

,

A. Dobrin

33

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D. Domenicis Gimenez

121

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B. Dönigus

69

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O. Dordic

19

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L.V.R. Doremalen

62

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A.K. Dubey

137

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A. Dubla

106

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L. Ducroux

132

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A.K. Duggal

98

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M. Dukhishyam

87

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P. Dupieux

131

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R.J. Ehlers

141

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D. Elia

51

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E. Endress

111

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H. Engel

68

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E. Epple

141

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B. Erazmus

114

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F. Erhardt

97

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B. Espagnon

60

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S. Esumi

130

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G. Eulisse

33

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J. Eum

17

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D. Evans

110

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S. Evdokimov

112

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L. Fabbietti

104

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34

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J. Faivre

80

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A. Fantoni

49

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M. Fasel

94

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81

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L. Feldkamp

70

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A. Feliciello

57

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G. Feofilov

136

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A. Fernández Téllez

2

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A. Ferretti

24

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A. Festanti

27

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33

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V.J.G. Feuillard

74

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131

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J. Figiel

118

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M.A.S. Figueredo

121

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S. Filchagin

108

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D. Finogeev

61

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F.M. Fionda

20

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22

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M. Floris

33

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S. Foertsch

75

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P. Foka

106

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S. Fokin

89

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E. Fragiacomo

58

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A. Francescon

33

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A. Francisco

114

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U. Frankenfeld

106

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G.G. Fronze

24

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U. Fuchs

33

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C. Furget

80

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A. Furs

61

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M. Fusco Girard

28

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J.J. Gaardhøje

90

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M. Gagliardi

24

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A.M. Gago

111

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K. Gajdosova

90

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M. Gallio

24

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C.D. Galvan

120

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P. Ganoti

84

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C. Garabatos

106

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E. Garcia-Solis

12

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K. Garg

26

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C. Gargiulo

33

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P. Gasik

104

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34

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E.F. Gauger

119

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M.B. Gay Ducati

72

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M. Germain

114

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J. Ghosh

109

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P. Ghosh

137

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S.K. Ghosh

4

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P. Gianotti

49

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P. Giubellino

106

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33

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57

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P. Giubilato

27

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E. Gladysz-Dziadus

118

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P. Glässel

103

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D.M. Goméz Coral

73

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A. Gomez Ramirez

68

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A.S. Gonzalez

33

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P. González-Zamora

2

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S. Gorbunov

40

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L. Görlich

118

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S. Gotovac

117

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V. Grabski

73

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L.K. Graczykowski

138

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K.L. Graham

110

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L. Greiner

81

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A. Grelli

62

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C. Grigoras

33

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V. Grigoriev

82

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A. Grigoryan

1

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S. Grigoryan

76

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J.M. Gronefeld

106

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F. Grosa

29

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J.F. Grosse-Oetringhaus

33

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R. Grosso

106

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L. Gruber

113

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F. Guber

61

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R. Guernane

80

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B. Guerzoni

25

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K. Gulbrandsen

90

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T. Gunji

129

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A. Gupta

100

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R. Gupta

100

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I.B. Guzman

2

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R. Haake

33

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C. Hadjidakis

60

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H. Hamagaki

83

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G. Hamar

140

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J.C. Hamon

133

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M.R. Haque

62

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J.W. Harris

141

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A. Harton

12

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H. Hassan

80

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D. Hatzifotiadou

11

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52

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S. Hayashi

129

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S.T. Heckel

69

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E. Hellbär

69

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H. Helstrup

35

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A. Herghelegiu

86

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E.G. Hernandez

2

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G. Herrera Corral

10

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F. Herrmann

70

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B.A. Hess

102

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K.F. Hetland

35

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H. Hillemanns

33

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C. Hills

126

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B. Hippolyte

133

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J. Hladky

65

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B. Hohlweger

104

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D. Horak

37

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S. Hornung

106

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R. Hosokawa

80

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130

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P. Hristov

33

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C. Hughes

127

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T.J. Humanic

16

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N. Hussain

42

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T. Hussain

15

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D. Hutter

40

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D.S. Hwang

18

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S.A. Iga Buitron

71

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R. Ilkaev

108

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M. Inaba

130

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M. Ippolitov

82

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89

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M. Irfan

15

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M.S. Islam

109

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M. Ivanov

106

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V. Ivanov

95

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V. Izucheev

112

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B. Jacak

81

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N. Jacazio

25

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P.M. Jacobs

81

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M.B. Jadhav

46

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J. Jadlovsky

116

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S. Jaelani

62

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C. Jahnke

34

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M.J. Jakubowska

138

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M.A. Janik

138

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P.H.S.Y. Jayarathna

124

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C. Jena

87

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S. Jena

124

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M. Jercic

97

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R.T. Jimenez Bustamante

106

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P.G. Jones

110

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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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J.H. Kang

142

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V. Kaplin

82

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S. Kar

137

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A. Karasu Uysal

79

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O. Karavichev

61

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T. Karavicheva

61

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L. Karayan

106

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103

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P. Karczmarczyk

33

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E. Karpechev

61

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U. Kebschull

68

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R. Keidel

143

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D.L.D. Keijdener

62

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M. Keil

33

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B. Ketzer

43

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Z. Khabanova

91

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P. Khan

109

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S.A. Khan

137

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A. Khanzadeev

95

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Y. Kharlov

112

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A. Khatun

15

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A. Khuntia

47

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M.M. Kielbowicz

118

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B. Kileng

35

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B. Kim

130

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D. Kim

142

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D.J. Kim

125

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H. Kim

142

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J.S. Kim

41

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J. Kim

103

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M. Kim

59

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M. Kim

142

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S. Kim

18

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T. Kim

142

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S. Kirsch

40

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I. Kisel

40

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S. Kiselev

63

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A. Kisiel

138

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G. Kiss

140

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J.L. Klay

6

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C. Klein

69

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J. Klein

33

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C. Klein-Bösing

70

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S. Klewin

103

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A. Kluge

33

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M.L. Knichel

103

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33

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A.G. Knospe

124

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C. Kobdaj

115

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M. Kofarago

140

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M.K. Köhler

103

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T. Kollegger

106

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V. Kondratiev

136

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N. Kondratyeva

82

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E. Kondratyuk

112

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A. Konevskikh

61

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M. Konyushikhin

139

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M. Kopcik

116

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M. Kour

100

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C. Kouzinopoulos

33

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O. Kovalenko

85

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V. Kovalenko

136

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M. Kowalski

118

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G. Koyithatta Meethaleveedu

46

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I. Králik

64

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A. Kravˇcáková

38

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L. Kreis

106

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M. Krivda

110

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64

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F. Krizek

93

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E. Kryshen

95

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M. Krzewicki

40

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A.M. Kubera

16

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V. Kuˇcera

93

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C. Kuhn

133

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P.G. Kuijer

91

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A. Kumar

100

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J. Kumar

46

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L. Kumar

98

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S. Kumar

46

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S. Kundu

87

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P. Kurashvili

85

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A. Kurepin

61

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61

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A. Kuryakin

108

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S. Kushpil

93

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M.J. Kweon

59

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Y. Kwon

142

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S.L. La Pointe

40

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P. La Rocca

26

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C. Lagana Fernandes

121

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Y.S. Lai

81

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I. Lakomov

33

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R. Langoy

39

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K. Lapidus

141

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C. Lara

68

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A. Lardeux

74

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19

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A. Lattuca

24

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E. Laudi

33

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R. Lavicka

37

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R. Lea

23

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L. Leardini

103

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S. Lee

142

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F. Lehas

91

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S. Lehner

113

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J. Lehrbach

40

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R.C. Lemmon

92

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V. Lenti

51

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E. Leogrande

62

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I. León Monzón

120

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P. Lévai

140

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X. Li

13

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J. Lien

39

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R. Lietava

110

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B. Lim

17

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S. Lindal

19

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V. Lindenstruth

40

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S.W. Lindsay

126

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C. Lippmann

106

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M.A. Lisa

16

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V. Litichevskyi

44

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W.J. Llope

139

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62

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20

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V. Loginov

82

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C. Loizides

81

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P. Loncar

117

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X. Lopez

131

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E. López Torres

9

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A. Lowe

140

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P. Luettig

69

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J.R. Luhder

70

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M. Lunardon

27

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G. Luparello

58

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23

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M. Lupi

33

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T.H. Lutz

141

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A. Maevskaya

61

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M. Mager

33

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S. Mahajan

100

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S.M. Mahmood

19

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A. Maire

133

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R.D. Majka

141

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M. Malaev

95

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L. Malinina

76

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iv

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D. Mal’Kevich

63

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P. Malzacher

106

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A. Mamonov

108

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V. Manko

89

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F. Manso

131

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V. Manzari

51

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Y. Mao

7

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M. Marchisone

75

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128

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J. Mareš

65

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G.V. Margagliotti

23

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A. Margotti

52

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J. Margutti

62

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A. Marín

106

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C. Markert

119

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M. Marquard

69

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N.A. Martin

106

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P. Martinengo

33

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J.A.L. Martinez

68

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M.I. Martínez

2

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G. Martínez García

114

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M. Martinez Pedreira

33

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S. Masciocchi

106

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M. Masera

24

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A. Masoni

53

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E. Masson

114

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A. Mastroserio

51

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A.M. Mathis

104

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34

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P.F.T. Matuoka

121

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A. Matyja

127

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C. Mayer

118

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J. Mazer

127

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M. Mazzilli

31

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M.A. Mazzoni

56

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F. Meddi

21

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Y. Melikyan

82

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A. Menchaca-Rocha

73

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E. Meninno

28

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J. Mercado Pérez

103

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M. Meres

36

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S. Mhlanga

99

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Y. Miake

130

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44

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104

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K. Mikhaylov

63

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76

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J. Milosevic

19

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62

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47

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106

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J. Mitra

137

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C.M. Mitu

67

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N. Mohammadi

62

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B. Mohanty

87

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M. Mohisin Khan

15

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v

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D.A. Moreira De Godoy

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2

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S. Moretto

27

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114

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33

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49

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117

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70

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137

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M. Mukherjee

4

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141

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M.G. Munhoz

121

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43

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69

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129

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75

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L. Musa

33

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J. Musinsky

64

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124

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J.W. Myrcha

138

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4

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46

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R. Nair

85

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46

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52

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11

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51

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A. Narayan

46

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14

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H. Natal da Luz

121

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127

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2

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87

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46

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137

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108

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63

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33

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71

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124

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M. Nicassio

106

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67

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138

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90

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89

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89

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V. Nikulin

95

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11

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52

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2

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126

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89

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20

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17

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103

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i

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141

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33

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103

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45

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140

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138

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121

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141

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116

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71

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32

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118

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83

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103

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90

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135

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28

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71

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P. Palni

7

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J. Pan

139

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46

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74

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V. Papikyan

1

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