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

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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 ra c t

Articlehistory:

Received16November2019

Receivedinrevisedform21February2020 Accepted16March2020

Availableonline20March2020 Editor:M.Doser

Thispaperpresentsthefirstmeasurementsofthechargeindependent(CI)andchargedependent(CD) two-particletransversemomentumcorrelatorsG^CI₂ andG^CD₂ 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 G^CI₂ exhibits alongitudinal broadening whileundergoingamonotonic azimuthalnarrowing.By contrast,G^CD₂ 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/softhematterproducedinthecollisions.Theobservedbroadeningisfoundtobeconsistentwiththe hypothesizedlowerboundofη/sandisinqualitativeagreementwithvaluesobtainedfromanisotropic flowmeasurements.

©^{2020ConseilEuropéenpourlaRecherche}Nucléaire,.PublishedbyElsevierB.V.Thisisanopenaccess articleundertheCCBYlicense(http://creativecommons.org/licenses/by/4.0/).FundedbySCOAP³.

1. Introduction

Measurementsofparticleproductionandtheircorrelationsper- formedattheRelativisticHeavyIonCollider(RHIC)andtheLarge HadronCollider(LHC)provide compellingevidencethat themat- 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 coefficientswithhydrody- 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,byun- certainties in the initial state conditions.Indeed, values ofshear viscositythatbestmatchtheobservedflowcoefficientsaredepen- dent on the initial conditions, and unless the magnitude of the initial state fluctuationscan be preciselyassessed, theachievable precision on

η

/smightremainlimited [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(p_T)correlator,formallydefinedbelow andhereafternamedG2,withincreasingsystemlifetimeisdirectly sensitiveto

η

/swhileitdoesnothaveanyexplicitdependenceon 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/©^{2020ConseilEuropéenpourlaRecherche}Nucléaire,.PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense (http://creativecommons.org/licenses/by/4.0/).FundedbySCOAP³.

collaboration [16]. Improvedtechniquesto correctforinstrumen- 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, G^CI₂ and G^CD₂ , 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 G^CI₂ 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 G^CD₂ areusedtoassesstheroleofcompetingeffects,includingra- dialflow,diffusion,andthebroadeningofjetsbyinteractionswith themedium. In that context, measurements of G₂ are also com- paredwithpreviously reportedmeasurementsofthetwo-particle numbercorrelatorR2 andtwo-particletransversemomentumcor- relatorP₂ [18].

2. TheG2correlator

ThedimensionlessvariantoftheG₂correlator [15,20] reported inthisletterisdefinedaccordingto

G2

( η

1

, ϕ

1

, η

2

, ϕ

2

)

=

¹

^pT,1

^pT,2

p_T,1p_T,2

ρ

2

(

p

₁

,

p₂

)

dp_T,1dp_T,2

ρ

1

(

p1

)

dpT,1

ρ

1

(

p2

)

dpT,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 pi, 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,idpi 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

S_pT

( 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

S_pT

( η

₁

, ϕ

₁

, η

₂

, ϕ

₂

) =

_n1,1

i n1,2

j=ⁱ

p_T,ip_T,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 p}T,j, j=ⁱ∈ [¹,n1,2]^{, respec-} tively. Angle brackets, · · ·^{, refer to event ensemble averages, A}=Nevents

1 A/Nevents.ThecorrelatorsG^LS₂ andG^US₂ arefirstmea- suredforlike-sign(LS) andunlike-sign(US)pairs separately,and combined to obtain CI and CD correlators according to G^CI₂ =

1 2

G^US₂ +^GLS2

and G^CD₂ = ¹₂

G^US₂ −^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)asignalintheV0Cdetec- 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 determinedwithtracksrecon- structed intheITSandtheTimeProjectionChamber (TPC)andis requiredtobeintherange|^zvtx|≤^{7 cmofthenominal}interaction point (IP).Pile-up events,identifiedaseventshavingmultiplere- constructedverticesintheITS,arerejected.Additionally,theextra activityobservedinslowresponsedetectors (e.g.,TPC)relative to that measuredinfastdetectors(e.g.,V0)foroutofbunchpile-up events isusedto discardtheseevents.Theremaining eventpile- upcontaminationisestimatedtobenegligible.Longitudinally,the ITScovers|

η

|<0.9,theTPC|

η

|<0.9,V0A2.8<

η

<5.1 andV0C

−³.7<

η

<−¹.7.Thesefourdetectorsfeaturefull azimuthalcov- 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 inthelongitudinalandra- dial directions, respectively. An alternative criterion, used in the analysis of the systematic uncertainties, that relies on tracks re- constructedwiththecombinationoftheTPCandtheITSdetectors, henceforthcalled“globaltracks”,involvesaminimumof70recon- 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/dxintheTPCcloserthan3

σ

dE/dx totheexpected medianforelectronsandatleast5

σ

dE/dx awayfromthe

π

,K and pexpectationvalues.

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] tunedtoreproducethede- tectorconditionsduringthe2010run.Correctionsforsingletrack losses due to non-uniform acceptance (NUA) are carried out us- ing aweighting technique [17] separatelyfordataandforrecon- structedMCdata.Weightsareextractedseparatelyforpositiveand negativetracks,foreachcollisioncentralityrange,asafunctionof

η

,

ϕ

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

Fig. 1.Two-particletransversemomentumcorrelationsG^CI₂ (top)andtheirlongitudinal(middle)andazimuthal(bottom)projectionsforthemostcentral(left),semi-central (center)andperipheral(right)Pb–Pbcollisionsat √

sNN=².76TeV.Verticalbars(mostlysmallerthanthemarkersize)andshadedbluebandsrepresentstatisticaland systematicuncertainties,respectively.Thesystematicuncertaintyonthelong-rangemeancorrelatorstrengthisquotedasδBinbothprojections.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 p_T 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,whichdominatethepar- ticleproduction,HBTproduces apeakcenteredat

η

,

ϕ

₌0 in G^LS₂.Thewidthofthispeakdecreasesininverseproportiontothe sizeofthecollisionsystem.GiventhenumberofHBTpairsisrel- ativelysmallcomparedtothetotalnumberofpairsaccountedfor inG^LS₂,theimpliedreductionofthelongitudinalbroadeningisrel- 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

assessedbysplittingthewholedatasampleintopositiveandnega- 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.Thepresenceofbiasescausedbysecondaryparti- 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 δB. This shift affects the magnitude of the projec- tions onto

η

and

ϕ

butnottheshapesofthenear-sidepeak,

|

ϕ

_|<

π

/2,of G2 alongthesecoordinates.Systematicuncertain- tiesintheshapeofthenear-sidepeakofG^CI₂ andG^CD₂ aremainly due to the presence of secondary particles. Overall, systematic uncertainties on the shapes of the projections of G^CI₂ and G^CD₂ along the longitudinal (azimuthal) dimension amount to 4%(5%) and5%(10%),respectively,withdecreasingvaluestowardsperiph- eralevents.

5. Results

Fig.1presentsthecorrelatorsG^CI₂(

η

,

ϕ

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

η

and

ϕ

axes. The G^CI₂ correlators feature sizable

ϕ

modulations,dominated inmid-centralcollisions by astrong ellipticflow(cos(2

ϕ

))component.Onthenear-side,atoptheaz- imuthal modulation, the G^CI₂ correlatorsfeature a near-side peak whoseamplitudemonotonicallydecreasesfromperipheraltocen- tralcollisionswhileitslongitudinalwidthsystematicallybroadens.

QualitativelysimilartrendswereobservedfortheR2andP2corre- latorsreportedbyALICE [18] andtheG^CI₂ 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 ALICEre- sults [27,28] canbeseen.

Inordertostudythecentralityevolutionofthenear-sidepeak of the G^CI₂ and G^CD₂ correlators independently of the underly- ingcollectiveazimuthalbehavior,theyareseparatelyparametrized withatwo-componentmodeldefinedas

F

( η , ϕ ) =

^B

+

6 n=2

a_n

×

^cos

(

n

ϕ )

+

^A

× γ

η 2

ω

_η

1 γη

e⁻ ω^ηη

^γη

× γ

ϕ 2

ω

ϕ

1 γϕ

e^{− ωϕ}ϕ

^γϕ

, (4)

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

ω

η,

ω

ϕ,

γ

ηand

γ

ϕ,isintendedtomodelthesignalofinterest.The (

η

,

ϕ

)=(0,0) depletion present in the G^CI₂ 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 G^CI₂ 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 betweenthegeneral- ized Gaussian andtheFourier expansion.Excluding thisarea the

χ

²/ndf valuesobtainedin central collisionsare within the range 1–2.3. Fits of G^CD₂ give

χ

²/ndf of the order of unity forperiph- 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

ηand

σ

ϕ,respectively,arethenextractedasthestan- darddeviationofthegeneralizedGaussian

σ

η(ϕ)

=

ω

²_η(ϕ)

(

3

/ γ

_η(ϕ)

)

(

1

/ γ

η(ϕ)

)

^{, (5)}

andplottedasafunctionofcollisioncentralityinthetoppanelsof Fig.2forbothG^CI₂ andG^CD₂ correlators.Theglobalshiftofthecor- relatorstrength,quoted asasystematicuncertaintyintheprojec- tionsofthecorrelators, doesnotaffecttheshapeofthenear-side peakofG₂.Accordingly,thewidthsarenotaffectedeither.Corre- lationsbetweenthecontributorstothelongitudinalwidthandthe harmonicparameters forthe G^CI₂ 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)andaz- imuthal(right) widthsofthe G2 CDandCIcorrelatorsmeasuredinPb–Pbcol- lisions at √_s

NN=².76TeV. Centraland bottompanels:widthevolutionrelative tothevalueinthemostperipheralcollisionsofthetwo-particle transversemo- mentumcorrelationsG^CI₂ (central)andG^CD₂ (bottom)alongthelongitudinal(left) andazimuthal(right)dimensions.DataarecomparedwithHIJINGandAMPTmodel expectations.Indata,verticalbarsandshadedbandsrepresentstatisticalandsys- 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. a}2 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 andwith

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 ofG^CI₂ andG^CD₂ are mainlyduetothepresenceof secondary particles. Withthealternative trackselection criterion, systematicuncertaintiesonthelongitudinalandazimuthalwidths ofthenear-sidepeak areestimatedtobe2%and3%,respectively, for both G^CI₂ and G^CD₂ , for most central events, with decreasing values towardsperipheral collisions. Uncertaintycontributions on the widths are not correlated withcentrality andaverages along centralityclassesareconsidered.Overall,maximumsystematicun- certaintiesof4%(2%)and3.5%(3%)areassignedtotheG^CI₂ andG^CD₂ widths,respectively,alongthelongitudinal(azimuthal)dimension.

The impact ofthe size ofthe area excluded from the fit on the widthoftheG^CI₂ 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 G^CI₂. On the azimuthal widthstheimpactisreducedtoa2%narrowing.

6. Discussion

Broadeningandnarrowingarehereafterintendedasthebehav- iorofthecorrelationfunction,measuredbyitswidths,whengoing from peripheral collisions, highvalues ofcentrality percentile, to centralcollisions,lowervaluesofcentralitypercentile.TheG^CI₂ cor- relator broadens longitudinally but narrows in azimuth, whereas the G^CD₂ correlator narrows both longitudinally and azimuthally.

As shown in Fig. 3, these dependencies are qualitatively consis-

Fig. 3.Leftpanel:collisioncentralityevolutionofthelongitudinalwidthofnumbercorrelatorR^CD₂ andtransversemomentumcorrelatorsP₂^CDandG^CD₂ .Centralpanel:idem fortheazimuthalwidthofR^CD₂ ,P^CD₂ andG^CD₂ .Rightpanel:collisioncentralityevolutionofthelongitudinalwidthofR^CI₂,P^CI₂,andG^CI₂.DataforR2andP2arefrom[18].

Verticalbarsandshadedbandsrepresentstatisticalandsystematicuncertainties,respectively.

tent withthose of R2 and P2 correlatorsmeasured in the same kinematicrangebytheALICEcollaboration [18].NotethattheG2 correlatorissensitive totransversemomentum andnumberden- sityfluctuationssinceboth affectthemomentumcurrentdensity.

Incontrast,R2 issensitivetonumberdensityfluctuationsandP2, sensitivetotransversemomentumfluctuations,isdesignedtomin- imizethe contributionofthose numberdensityfluctuations [29].

Infact [29]

(

P₂

+

¹

) (

R₂

+

¹

) = (

G₂

+

¹

)

(6) so,theincreaseintransversemomentumcurrentscouldbedueto eithertheincreaseinmultiplicityortheincreaseoftransversemo- mentum.TheG^CD₂ andP^CD₂ correlatorsfeatureapproximatelyequal widthswhile R^CD₂ isapproximately30%widerthroughoutitscen- tralityevolution.ThecentralitydependenceofG^CD₂ 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^{, inmorecen-} tralcollisions, alsoproduce the observed narrowing of G^CD₂ .This conjectureis supported by calculationsofthe collision centrality dependenceof G^CD₂ azimuthal widthswiththe HIJING andAMPT models shown in the bottom right panel of Fig. 2. Radial flow mightalso explain the observed azimuthal narrowing of the G^CI₂ 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 G^CI₂ correla- toris ofparticular interest givenpredictions that it should grow inproportionto

η

/softhematterproducedinthecollisions [15].

Asexpectedforasystemwithfiniteviscosity,itisfound thatG^CI₂ broadenssignificantlywithincreasingcollisioncentrality,whileby contrast, G^CD₂ exhibits a slight but distinct narrowing. This G^CD₂ 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 oftheG^CI₂ correlator inthelon- 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 thehadronicrescatteringphasequalitativelyreproducesthelongi- tudinalbroadeningofG^CI₂,evenitssaturation,butgrosslymissthe narrowingof G^CD₂ along that dimension andthus cannotbe con- sideredreliableinthiscontext.

Fig. 4.Two-particletransversemomentumcorrelationG^CI₂ longitudinalwidthevo- 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 toex- hibit correlations and jet-medium interactions can broaden such correlations. Two-particle correlation measurements, of particles associated with high-p_T jets, indeed show substantial broaden- ingoflow pTparticlecorrelationsrelativetocorrelationfunctions measuredinpp collisions [27,28,32].Thisbroadening,however,is observedinboththelongitudinalandazimuthaldirectionsinstark contrast with the behavior of the inclusive G^CI₂ 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

directionandtherelativelylowimpactofcorrelationsfromjetpar- ticles.

Fig.4 comparesresultsfromthisanalysiswiththose reported by the STAR collaboration [16]. For proper comparison, Fig. 4 presentsrootmeansquare(RMS)widthsof

η

projectionsofG^CI₂ calculatedabovealongrangebaselineasintheSTARanalysis [16].

AlthoughSTARreportedresultsarebasedonthedimensionalver- sionofG^CI₂,thesameexpressionasinEq. (1) butwithoutthenor- malization^pT,1^pT,2^{,thecorrelatorwidthsreportedinthisletter} areidenticalforboth,thedimensionalanddimensionlessversions oftheG2 correlator.Thelongitudinalbroadeningmeasuredinthis analysis, using the 1D RMS method, amounts to 36% while that observedbySTARreaches74%showingalsoasaturationatsemi- centralcollisions.Itwasverifiedthatthesmallerbroadeningseen inthisanalysisisnotaresultoftheslightlynarrowerlongitudinal acceptanceoftheALICEexperimentbytestingtheanalysismethod withMonteCarlomodelsreproducingtheapproximateshapeand strength of the measured correlation functions. The longitudinal

Fig. 5. Expectedlongitudinal widths for the mostcentral collisions ofthe two- particletransversemomentumcorrelationG^CI₂ fordifferentvaluesofη/sbyusing theexpressionsuggestedin [15].Datapointerrorbarsrepresenttotaluncertainties obtainedbyaddinginquadraturestatisticalandsystematicuncertainties.Inthefor- mulaσcisthelongitudinalwidthforthemostcentralcollisionsinferredbyusing thisexpressionandrepresentedforeachoftheη/svaluesbythecolordiscontin- uousbands(continuousforη/s=1/4π)atthehighestnumberofparticipants,σ0 isthelongitudinalwidthforthemostperipheralcollisions(onlytwoparticipants) whichisobtainedbyextrapolatingthefit,Tc isthecriticaltemperature,τ0isthe formationtimeand τc,f thefreeze-outtime.Errorcapsinthesamecolorasthe discontinuousbands,representuncertaintiesoftheinferredlongitudinalwidthsfor themostcentralcollisions(seetextfordetails).

broadeningofG^CI₂ andits observedsaturation thusappears tobe potentiallydependentonthebeamenergy.

Interpreting the longitudinal broadeningof G^CI₂ as originating exclusivelyfromviscouseffects,anestimateoftheshearviscosity perunitofentropydensity,

η

/s,ofthematterproducedinheavy- ioncollisionscanbeextracted [16] usingtheexpression

σ

_c²

− σ

₀²

=

⁴ T_c

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), T_cisthecriticaltemperature,

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, T_c=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),G^CI₂ 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 thefourobtainedG^CI₂ longitudinalwidthsforthemostcentralcol- lisions reach 9%, 10%, 12%, and 14%, respectively, also shown in Fig.5aserrorcapsinthesamecolorasthediscontinuous bands.

TheG^CI₂ 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√

s_NN=^{200GeV,without an actualmeasure-} ment of G^CI₂ 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 therelativeuncertaintyoftheG^CI₂ correlatorwidthsforAu–Aucol- 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 G^CD₂ corre- lator is observed to significantly narrow with collision centrality bothinthelongitudinalandazimuthaldirections.Thisbehavioris foundtobesimilartothatofthechargebalancefunctionasare- sult, mostlikely,ofanincrease oftheaverageradialflow velocity fromperipheraltocentralcollisions.Bycontrast,theG^CI₂ correlator is foundto narrowonly inthe azimuthal directionwithcollision centralityandfeaturesasizablebroadeninginthelongitudinaldi- rection.The observedbroadeningalong thelongitudinaldirection isexpectedbasedonfrictionforcesassociatedwiththefiniteshear viscosityofthesystem.Takingthemodelproposedin [15],anes- timateofthevalueof

η

/soforder1/4

π

,inqualitativeagreement with values obtained from other methods [14,38], is obtained.

StringmeltingAMPT withoutthehadronicrescatteringphasehas beenfoundtoqualitativelyreproducethelongitudinalbroadening ofG^CI₂ butgrosslymissesthenarrowingofG^CD₂ alongthatdimen- 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

Theauthorsdeclarethattheyhavenoknowncompetingfinan- cialinterestsorpersonalrelationshipsthatcouldhaveappearedto influencetheworkreportedinthispaper.

Acknowledgements

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

The ALICECollaboration would like to thank all its engineers andtechniciansfortheirinvaluablecontributionstotheconstruc- tionoftheexperimentandtheCERNacceleratorteamsfortheout- 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 CommitteeofSci- 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