Search for collectivity with azimuthal J/ψ-hadron correlations in high multiplicity p–Pb collisions at √sNN = 5.02 and 8.16 TeV

a r t i c l e i n f o a b s t ra c t

Articlehistory:

Received27September2017

Receivedinrevisedform14February2018 Accepted14February2018

Availableonline2March2018 Editor:M.Doser

WepresentameasurementofazimuthalcorrelationsbetweeninclusiveJ/ψandchargedhadronsinp–Pb collisionsrecordedwiththeALICEdetectorattheCERNLHC. TheJ/ψ arereconstructedatforward(p- going, 2.03<y<3.53) and backward(Pb-going,−⁴.46<y<−².96) rapidity viatheirμ⁺μ⁻ decay channel,whilethechargedhadronsarereconstructedatmid-rapidity(|η_|<1.8).Thecorrelationsareex- pressedintermsofassociatedcharged-hadronyieldsperJ/ψtrigger.A rapiditygapofatleast1.5unitsis requiredbetweenthetriggerJ/ψandtheassociatedchargedhadrons.Possiblecorrelationsduetocollec- tiveeffectsareassessedbysubtractingtheassociatedper-triggeryieldsinthelow-multiplicitycollisions fromthoseinthehigh-multiplicitycollisions.Afterthesubtraction,weobserveastrongindicationofre- mainingsymmetricstructuresatϕ_≈0 andϕ_≈π,similartothosepreviouslyfoundintwo-particle correlationsatmiddleand forwardrapidity.Thecorrespondingsecond-orderFouriercoefficient(v2)in thetransverse momentumintervalbetween3and 6 GeV/cisfound tobepositivewithasignificance ofabout5σ.TheobtainedresultsaresimilartotheJ/ψ v2coefficientsmeasuredinPb–Pbcollisionsat

√_s

NN=⁵.02 TeV,suggestingacommonmechanismattheoriginoftheJ/ψ v2.

©^{2018TheAuthor.PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense} (http://creativecommons.org/licenses/by/4.0/).FundedbySCOAP³.

1. Introduction

The measurement of angular correlations between particles produced in hadron andnucleus collisions is a powerful tool to studytheparticleproductionmechanisms.Usuallythetwo-particle correlation function is expressed in terms of differences in the azimuthal angle (

ϕ

) and pseudorapidity (

η

) of the emitted particles.Inminimum-biasproton–proton(pp)collisions,thedom- inant structuresin the correlation function are a near-side peak at(

ϕ

,

η

)≈(0,0) and an away-side ridge located at

ϕ

≈

π

andelongated in

η

[1]. The near-side peak originates from jet fragmentation,resonancedecaysandfemtoscopiccorrelations.The away-sideridge resultsfromfragmentationofrecoiljets. Incolli- sionsofheavy ions,the two-particlecorrelation functionexhibits additionallong-rangestructureselongatedin

η

[2].Thesestruc- tures are usually interpreted as signatures of collective particle flowproduced during thehydrodynamic evolution ofthefireball.

Theyare analyzedin termsof theFouriercoefficients ofthe rel- ativeangledistributions.Assumingfactorization,thesecoefficients arethenrelatedtotheFouriercoefficients(vn)oftheparticleaz- imuthal distribution relative to the common symmetry plane of thecollidingnuclei’soverlaparea.

E-mailaddress:alice-publications@cern.ch.

The discovery of a near-side ridge inhigh-multiplicity pp [3]

andp–Pb [4] collisions hasincreased theinterest intwo-particle angular correlations in smallcollision systems.These discoveries werefollowedbytheobservationthatthenear-sideridgeinp–Pb collisions is accompanied by an away-side one [5,6]. Long-range structureshavealsobeen reportedintwo-particle correlationsin d–Aucollisions atRHIC [7,8]. Furtherstudiesusing multi-particle correlations have proven that the observed long-range correla- tions are of a collective origin [9–11]. Moreover, the transverse- momentumandparticle-massdependenciesofthevncoefficients inp–Pbcollisionshavebeenfoundtobesimilartothosemeasured inA–Acollisions,suggestingacommonhydrodynamicoriginofthe observedcorrelations[12,13].Alternativeinterpretations,including Color-GlassCondensate basedmodels[14] andfinal-stateparton–

partonscattering[15],havealsobeenproposed.Long-rangecorre- lationsofforwardandbackwardmuonswithmid-rapidityhadrons have also been found in p–Pb collisions ata center-of-mass en- ergypernucleonpair√

sNN=⁵.02 TeV[16].Theresultsshowthat thesecorrelations persistacross wide rapidity ranges andextend intothehighmuontransverse-momentuminterval,whichisdom- inatedbydecaysofheavyflavors.

Inppcollisions,theJ/ψ resonanceisformedmainlyfrompairs ofc and¯c quarksproducedinhardscatteringreactionsduringthe initialstageofthecollision.Thetheoreticalmodelsdescribingthe https://doi.org/10.1016/j.physletb.2018.02.039

0370-2693/©^{2018TheAuthor.PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense}(http://creativecommons.org/licenses/by/4.0/).Fundedby SCOAP³.

J/ψ productioncombinecalculationsoftheproductionofc^{c pairs}¯ within a perturbative Quantum Chromodynamics approach with thesubsequent non-perturbativeformationofthe c¯c boundstate [17]. Inp–Pbcollisions, theproductionis affectedby themodifi- cationof partondistribution functionsinside thenucleus [18] as wellaspossibleenergylossandinelasticscatteringinsidenuclear matter [19,20]. In A–A collisions, there are two additional com- peting phenomena that influencethe J/ψ production.First isthe suppressed production dueto the dissociation of the cc pairs¯ in thequark–gluonplasma [21].Second istheJ/ψ enhancementvia recombination of charm quarks thermalized in the medium [22, 23].Therecombinationisexpectedtobecomeprevalentincentral collisionsattheLHCenergies.

Recently,theALICECollaborationhaspublishedaprecisemea- surement of the second-order Fourier coefficient, v2, of the az- imuthal distribution ofthe J/ψ production inPb–Pb collisions at

√sNN=⁵.02 TeV [24]. The results show significant v2 incentral andsemi-centralcollisions.ThemeasuredJ/ψ v2atlowandinter- mediate transverse momentum can be qualitatively described by a transport model in which the J/ψ azimuthal anisotropy is in- heritedfrom that ofrecombined charm quarks[25,26]. However, athighertransversemomentumthedatastill indicatessignificant v₂ while the transport model predicts significantly smaller val- uescomingmostlyfrompath-lengthdependentsuppressioninthe almond-shapedinteractionregionofthecollidingnucleiandfrom non-prompt J/ψ produced from b-hadron decays assuming ther- malizedb quarks.Giventheseresults inPb–Pb collisions, itis of interesttostudytheJ/ψ-hadronazimuthalcorrelationsalsointhe smallerp–Pb system. The recombinationofcharm quarks,if any, should havemuch smallerimpact,due tothe smallernumber of initially producedcharm quarks withrespectto Pb–Pb collisions.

The small system size should not lead to a sizeable path-length dependentsuppression.Nevertheless,thestudyoftheJ/ψ-hadron azimuthal correlations could allow to determine whenever J/ψ production is affected by the medium possibly created in these collisions[27–29].

In this Letter, we present results for long-range correlations between forward (p-going, 2.03<y<3.53) and backward (Pb- going,−⁴.46<y<−².96)inclusiveJ/ψ andmid-rapiditycharged hadrons in p–Pb collisions at √

sNN=⁵.02 and 8.16 TeV. Inclu- siveJ/ψ referstobothpromptJ/ψ (directanddecaysfromhigher mass charmonium states) and non-prompt J/ψ (feed down from b-hadrondecays).

2. Experimentalsetupanddatasamples

Adetaileddescriptionofthe ALICEapparatuscanbe foundin Ref. [30].Below,webrieflydescribethedetectorsystemsessential forthepresentanalysis.

Inthefollowing,

η

and y_labwilldenotethepseudorapidityand rapidity in the ALICE laboratory system. The muons are recon- structedinthemuonspectrometercoveringtherangeof−⁴<

η

<

−².5.Thespectrometercontainsafrontabsorberlocatedbetween 0.9and5 mfrom thenominalinteraction point. Theabsorber is followed by five tracking stations, each made of two planes of CathodePadChambers.Thethirdstationisplacedinsideadipole magnetwith3Tmfieldintegral.Thetrackingstationsarefollowed byanironwallwithathicknessof7.2interactionlengthsandtwo triggerstations,eachoneconsistingoftwoplanesofResistivePlate Chambers.

Thepositionoftheinteractionpointisobtainedusingtheclus- tersreconstructedin theSiliconPixelDetector(SPD) [31,32].The SPDislocatedinthecentralbarreloftheALICEapparatusandop- eratedinsidealargesolenoidal magnetprovidingauniform0.5 T magneticfield parallel tothebeamline. The SPDconsistsoftwo

cylindricallayerswhichcover|

η

|<2.0 and |

η

|<1.4 withrespect to the nominal interaction-point, for the inner and outer layer, respectively. The associated charged hadrons at mid-rapidity are reconstructedviatheso-called SPDtracklets,shorttracksegments formedfromtheclustersinthetwolayersoftheSPDandthepri- maryvertex[32].

The V0 detector [33] consists of two rings of 32 scintillator counterseach,covering2.8<

η

<5.1 (V0-A)and−³.7<

η

<−¹.7 (V0-C),respectively.Itisusedfortriggeringandevent-multiplicity estimation.

The data samples presented here were collected during the 2013and2016p–PbLHC runs.The collisionenergy was√

sNN= 5.02 and 8.16 TeV forthe 2013 and 2016 data samples,respec- tively. Part of the 5.02 TeV data were collected during the 2016 p–Pbrun.Datawithbothbeamconfigurations,namelyPb–nucleus momentum(denotedasPb–pcollisions)orprotonmomentum(de- notedasp–Pbcollisions)orientedtowardsthemuonspectrometer, have been analyzed.The asymmetric beamenergies, imposed by the two-in-one LHC magnet design, resulted in collisions whose nucleon–nucleoncenter-of-massreferencesystemisshiftedinra- pidity by 0.465 inthe directionoftheproton beamwithrespect to theALICElaboratorysystem. The datawere takenwitha trig- gerthatrequiredcoincidence ofminimum-bias(MB)anddimuon triggers.TheMBtriggerwasprovidedbytheV0detectorrequest- ing a signal in both V0-A andV0-C rings. Its efficiency isfound to beabout98%[34].Thedimuon triggerrequiredatleastapair ofopposite-signtracksegmentsinthe muontriggersystem, each withatransversemomentum(pT) abovethethresholdoftheon- linetriggeralgorithm. Thisthresholdwassetto provide50%effi- ciencyformuontrackswithpT=⁰.5 GeV/c.

The collected data samples of p–Pb and Pb–p collisions at 5.02 TeV (8.16 TeV) correspond to integrated luminosities of 8.1 and5.8 (8.7and 12.9) nb⁻¹,respectively. The maximuminterac- tion pile-upprobabilityrangedup to3% and8% during2013and 2016datataking,respectively.

3. Event,trackanddimuonselection

Thebeam-inducedbackgroundisrejectedbyrequiringthatthe timing signals from both rings of the V0 detector are compati- blewithparticlescomingfromcollisionevents.Eventscontaining multiple collisions (pile-up) are rejected by requiring one single interaction vertexreconstructedinthe SPDandby exploitingthe correlation betweenthe number of clustersin the two layers of theSPDandthenumberofthereconstructedSPDtracklets.

The longitudinal position ofthe reconstructed primary vertex (zvtx) is required to be within ±^{10 cm from the nominal inter-} action point. The reconstructed SPDtracklets are selectedby ap- plying a z_vtx-dependent pseudorapidity cut. The cut is adjusted to exclude the contribution from the edges of the SPD where the detector acceptance is low. For example, we select tracklets within −¹.8<

η

<0.5, −¹.3<

η

<1.3 and −⁰.5<

η

<1.8 for events withzvtx=^{10,0 and}−^{10 cm,} respectively.The contribu- tion from fake and secondary tracklets is reduced by applying a

| |<5 mrad cut onthe difference betweentheazimuthal an- gles ofthe clustersin thetwo layers of theSPD withrespect to the primary vertex. With this cut, the mean pT of the selected chargedhadronsisfoundtobeapproximately0.75 GeV/c [16].

Thetracksreconstructedinthemuonspectrometerarerequired toemergeataradialtransversepositionbetween17.6and89.5 cm fromtheendofthefrontabsorber inordertoavoidregionswith higher material budget. The tracks reconstructed in the tracking chambers are identified as muons by requiring their matching withcorrespondingtracksegmentsinthetriggerchambers.Back- ground tracks are removed with a selection on the product of

Fig. 1.TheMμμ distributioninthe3<p^μμ_T <6 GeV/cintervalfittedwithacombinationofaCB2functionforthesignalandaVWGfunctionforthebackground,for high-multiplicity(leftpanel)andlow-multiplicity(rightpanel)p–Pbcollisionsat√

sNN=⁸.16 TeV.

the total track momentum and the distance of closest approach to the primary vertexin the transverse plane [35]. The selected dimuons are defined as pairs of opposite-sign muon tracks hav- ing−⁴<yμμ

lab <−².5,transversemomentum pμμ

T between0and 12GeV/c andinvariantmass Mμμ between1and5 GeV/c².Only eventswithatleastonedimuonsatisfyingtheseselection criteria areconsidered.

Thedatasamplesaresplitintomultiplicityclassesbasedonthe totalchargedepositedinthetworings(V0-AandV0-C)oftheV0 detector(V0M)[34].Thehigh-multiplicity(low-multiplicity)event classisdefinedas0–20%(40–100%)oftheMBtriggereventsam- ple.

4. Analysis

TheMμμ distributionineachevent-multiplicityclassandpμμ T binisfit withthecombinationof an extendedCrystal Ball(CB2) functionfortheJ/ψ signal andaVariable-WidthGaussian (VWG) functionfor thebackground [36]. Thetail parameters ofthe CB2 function were fixed to the values used in [37,38]. The J/ψ peak position and width were obtained from the fit in the 0–100%

eventclassandfixedtothesevaluesintheotherevent-multiplicity classes.Examplesof the Mμμ fitin the0–20% andthe 40–100%

event classes in the 3< pμμ

T <6 GeV/c interval are shown in Fig.1.

TheangularcorrelationsbetweenJ/ψ andchargedhadronsare obtained from the associated-particle (SPD tracklets) yields per dimuontrigger.Theyieldsaredefinedas

Yⁱ

(

zvtx

,

M_μμ

,

p^μμ_T

, ϕ , η )

=

¹

N_trigⁱ

(

z_vtx

,

M_μμ

,

p^μμ_T

)

d²Nⁱ_assoc

(

zvtx

,

M_μμ

,

p^μμ_T

)

d

ϕ

d

η

=

¹

N_trigⁱ

(

zvtx

,

M_μμ

,

p^μμ_T

)

S Eⁱ

(

zvtx

,

M_μμ

,

p^μμ_T

, ϕ , η )

M Eⁱ

(

zvtx

,

M_μμ

,

p^μμ_T

, ϕ , η ) ,

(1) whereNⁱ_trig(zvtx,Mμμ,pμμ

T )isthenumberofdimuons,Nⁱ_assoc(zvtx, Mμμ,pμμ

T )isthenumberofassociatedSPDtrackletscorrectedfor acceptanceandcombinatorialeffects(asshowninthesecondline oftheequationanddescribedbelow),

ϕ

and

η

=^yμμ_lab−

η

tracklet are theazimuthal angleand (pseudo)rapiditydifference between the trigger dimuon and the associated SPD tracklet. The yields arecalculatedseparatelyineach event-multiplicityclass (index i)

and 1 cm-widez_vtx interval.Thedistribution

S Eⁱ

(

z_vtx

,

M_μμ

,

p^μμ_T

, ϕ , η ) =

^d2Nisame

(

z_vtx

,

M_μμ

,

p^μμ_T

)

d

ϕ

d

η

isthe yieldofassociated SPDtrackletsfromthesameevent. The distribution

M Eⁱ

(

z_vtx

,

M_μμ

,

p^μμ_T

, ϕ , η )

= α

ⁱ

(

z_vtx

,

M_μμ

,

p^μμ_T

)

^d

2Nⁱ_mixed

(

z_vtx

,

M_μμ

,

p^μμ_T

)

d

ϕ

d

η

is constructed using the event-mixing technique, i.e. combining dimuons from one event with SPD tracklets from other events selected in the same event-multiplicityclass and zvtx interval. It servesbothtocorrectfordetectoracceptanceandefficiencyandto takeintoaccountthecombinatorialbackground.Thenormalization factor

α

ⁱ(zvtx,Mμμ,pμμ

T ) is defined as 1/(d²N_mixedⁱ (zvtx,Mμμ, pμμ

T )/d

ϕ

d

η

)in the

η

regioncorresponding to themaximal acceptance[16].

Withineachevent-multiplicityclassandbinofMμμ,pμμ T ,

ϕ

and

η

,theyieldsYⁱaveragedoverz_vtxareobtainedbyfittingthe distribution YⁱNtrig(zvtx)ⁱM Eⁱ(zvtx) to the distribution S Eⁱ(zvtx). A Poissonlikelihoodfitisusedinordertoproperlydealwiththe casesoflownumberoftracklets.Then,theaverageyieldsarepro- jected on the

ϕ

axis in the rangeof 1.5<|

η

|<5 using the methoddescribedin[16].

In order to extract the yields per J/ψ trigger, the yields per dimuontriggerineach event-multiplicityclass, pμμ

T and

ϕ

bins arefitasafunctionofMμμusingthefollowingsuperposition Yⁱ

(

M_μμ

) =

^S

S

+

BY_Jⁱ_/ψ

+

^B

S

+

BYⁱ_B

(

M_μμ

),

(2) where S and B are the number of J/ψ and the background dimuons in each bin of Mμμ obtained from the invariant mass fit (using a CB2 function for the J/ψ signal anda VWG function forthe background)described above, YJ/ψ is theassociatedyield corresponding to theJ/ψ triggerand YB(Mμμ)is asecond-order polynomial function aimed to describe the associated yields cor- responding to the background. The fit range is chosen between 1.5and4.5 GeV/c².Examplesoffitsinhigh-multiplicityandlow- multiplicityeventclassesareshowninFig.2.

Fig.3showstheobtainedassociatedtrackletyieldsperJ/ψtrig- ger for p–Pb and Pb–p collisions at √

s_NN=⁵.02 and 8.16 TeV.

Fig. 2.Exampleofassociatedtrackletyieldsperdimuontriggerinthe3<p^μμ_T <6 GeV/cintervalforhigh-multiplicity(leftpanel)andlow-multiplicity(rightpanel)p–Pb collisionsat√

sNN=8.16 TeV.TheresultofthefitwiththefunctionfromEq. (2) isrepresentedwiththebluesolidline.Thedashedredlinecorrespondstotheassociated trackletyieldsperbackgrounddimuon.(Forinterpretationofthecolorsinthefigure(s),thereaderisreferredtothewebversionofthisarticle.)

As expected, in low-multiplicity collisions we observe a signifi- cant correlation structure on the away side (Fig. 3, top panels), presumably originating from the fragmentation of recoil jets. In high-multiplicity collisions (Fig. 3, middlepanels), a possible en- hancementon both near(

ϕ

≈^{0) andaway (}

ϕ

≈

π

) side can be spotted on top of the away-side structure. Inorder to isolate possiblecorrelationsduetocollectiveeffectsbetweentheJ/ψ and theassociatedtracklets,weapplythesamesubtractionmethodas inpreviousmeasurements[5,6,12,16],namelysubtractingtheYJ/ψ yieldsinlow-multiplicitycollisionsfromthoseinhigh-multiplicity collisions (Fig. 3, bottom panels). The subtraction method relies ontheassumptions thatthejetcorrelationsontheaway sidere- mainunmodified asafunction oftheeventmultiplicity andthat there are no significant correlations due to collective effects in low-multiplicitycollisions(seediscussioninSection6).

In order to quantify the remaining correlation structures, the subtractedyieldsY_J^sub_/ψ(

ϕ

)arefitwith

a₀

+

^2a1cos

ϕ ₊

2a₂cos 2

ϕ .

(3)

Thesecond-orderFouriercoefficient V2{^J/ψ−^tracklet,sub}^ofthe azimuthalcorrelationbetweentheJ/ψ andtheassociatedcharged hadronsisfinally calculatedasa₂/b^high₀ . Thedenominator b^high₀ = a0+^blow0 corresponds to the combinatorial baseline of the high- multiplicity collisions, wherethe parameter b^low₀ isthe combina- torial baseline of the low-multiplicity collisions obtained at the minimumoftheper-triggeryields,namelyin

ϕ

<

π

/6.Thepa- rameterb^low₀ isthenormalizationfactorusedinFig.3.Theparam- etera₁,whichdescribesthe strengthof theremaining away-side correlationstructure,isfoundtobecompatiblewithzeroinprac- ticallyall p^J_T^/ψ intervals, inbothp–PbandPb–pcollisionsatboth 5.02and8.16 TeV.

As an alternative extraction method, the calculation of b^low₀ , thesubtractionoflow-multiplicityfromhigh-multiplicitycollision yieldsandthefittoEq. (3) isdoneineachbinofMμμ separately.

Then the V2{^J/ψ−^tracklet,sub} ^{coefficientisextractedby fitting} V₂{

μμ

−^tracklet,sub}(^Mμμ) witha superposition similar tothe onedefinedinEq. (2)

V2

{ μμ −

tracklet

,

sub

}(

M_μμ

)

=

^S

S

+

^BV2

{

^J

/ψ −

^tracklet

,

sub

} +

^B

S

+

^BV2B

{ μμ −

^tracklet

,

sub

}(

^Mμμ

),

(4)

where the V₂^B{

μμ

− ^tracklet,sub}(Mμμ) is the second-order Fouriercoefficientoftheazimuthalcorrelation betweentheback- ground dimuons and associated tracklets. The background co- efficient V₂^B{

μμ

−^tracklet,sub}(^Mμμ) is parameterized with a second-order polynomial function. This parameterization is cho- sen since it reproduces the dimuon v2(Mμμ) constructed from the measured muon v2 coefficient [16] assuming that thedomi- nant partof thebackground iscombinatorial.An exampleof the V2{

μμ

−^tracklet,sub}(Mμμ)fitisshowninFig.4.

Following theprocedure used inRefs. [5,12,16], the V2{^J/ψ− tracklet,sub} ^{coefficient is factorized into a product of J/}ψ and charged-hadronv2 coefficients.Thus,theJ/ψ second-orderFourier azimuthalcoefficient v^J₂^/ψ{²,sub}^isobtainedas

v^J₂^/ψ

{

²

,

sub

} =

^V2

{

^J

/ψ −

^tracklet

,

sub

}/

^vtracklet₂

{

²

,

sub

},

⁽⁵⁾

wherethe v^tracklet₂ {²,sub}^{isthetracklet}second-order Fourieraz- imuthal coefficient obtained by performing the analysis consid- ering SPD tracklets as both trigger and associated particles. The obtained values of v^tracklet₂ {²,sub} ^{are between 0.067 and 0.069} depending on the beam configuration and collision energy, with 1–2%relativestatisticaluncertaintyand5–6.5%relativesystematic uncertainty.

5. Systematicuncertainties

The combined statistical and systematic uncertainties of the measured v^tracklet₂ {²,sub} ^{coefficient for each beam} configuration andcollisionenergyaretakenasglobalsystematicuncertaintiesof thecorrespondingv^J₂^/ψ{²,sub}coefficients.

Alltheothersystematicuncertaintiesofthe v^J₂^/ψ{²,sub}^coeffi- cientsareobtainedforeachdatasampleandpTintervalseparately.

Thefollowingsourcesareconsidered.

A possibleinaccurate correction for theSPDacceptance isas- sessed by varying the z_vtx range between±^{8 and}±^{12 cm. Sys-} tematicuncertaintiesareassignedonlyinthecasesofasignificant changeoftheresults.Thesignificanceisdefinedaccordingtothe proceduredescribedinRef. [39].

Thesystematiceffectrelatedtotheuncertaintyoftheshapeof thedimuonbackgroundyields YB(Mμμ)isestimatedbyperform- ing thefitwithEq. (2) usingalinearfunction forthebackground termandvaryingthefitrange.Thesystematiceffectcomingfrom the uncertainty ofthe signal-to-backgroundratio S/B is checked

Fig. 3.AssociatedtrackletyieldsperJ/ψ triggerin3<p^J_T^/ψ<6 GeV/c inp–PbandPb–pcollisionsat√_s

NN=⁵.02 TeV(leftpanels)and8.16 TeV(rightpanels).Thetop andthemiddlepanelscorrespondtothelow-multiplicityandthehigh-multiplicityeventclasses,respectively.Thebottompanelsshowtheyieldsafterthesubtractionof thelow-multiplicitycollisionyieldsfromthehigh-multiplicitycollisionones.Thesolidlinerepresentthefittothedataasdescribedinthetext.Thedashed,dot-dashed anddottedlinescorrespondtotheindividualtermsofthefitfunctiondefinedinEq. (3).Alltheyieldsarenormalizedtothevalueinϕ<π/6 inthelow-multiplicity (40–100%)eventclass.Onlythestatisticaluncertaintiesareshown.(Forinterpretationofthecolorsinthefigure(s),thereaderisreferredtothewebversionofthisarticle.)

by employing various invariant mass fit functions, both for the backgroundandfortheJ/ψ signal.Themaximal differenceofthe resultsobtainedwiththeabovecheckswithrespecttothedefault approachistakenasthecorrespondingsystematicuncertainty.

The uncertainty arising fromthe employed analysis approach isobtainedasthedifferencebetweenthetwoextractionmethods describedinSection4.

AsdescribedinSection 4,bydefaultthemixed-eventdistribu- tion M E(

ϕ

,

η

)isnormalizedtounityinthe

η

region corre- spondingto themaximal acceptance. Asan alternativeapproach, normalizingtheintegral ofM E(

ϕ

,

η

)tounity isused.No sig-

nificant effect on the obtained results is observed and thus no systematicuncertaintyisassigned.

The usedevent-mixingtechnique can introducesystematicbi- ases. The event multiplicity distribution of the selected dimuons (1<Mμμ<5 GeV/c²) differs fromthat of the J/ψ signal. Since the charged-hadronspectra andthe charged-hadron densityasa functionof

η

changewitheventmultiplicity[34],thenon-uniform (bothintheazimuthalandlongitudinaldirections)SPDacceptance can introduceabias.The corresponding systematicuncertaintyis evaluated by doing the event mixing in finer event-multiplicity bins.

Table 1

Summaryofabsolutesystematicuncertaintiesofthev^J₂^/ψ{²,sub}coefficients.Theuncertaintiesvarywithintheindicatedrangesdependingonp^J_T^/ψ.Thevaluesnotpreceded byasignrepresentdouble-sideduncertainties.

Source of systematics √

sNN=5.02 TeV √

sNN=8.16 TeV

p–Pb Pb–p p–Pb Pb–p

Acceptance correction 0 to 0.019 0 to 0.057 0 to 0.011 0 to 0.007

Background shape 0.007 to 0.013 0.015 to 0.056 0.011 to 0.013 0.003 to 0.012

Extraction method 0.003 to 0.015 0.010 to 0.040 0.002 to 0.011 0.008 to 0.018

Event mixing 0.003 to 0.015 0.004 to 0.025 0.002 to 0.008 0.004 to 0.012

Residualaway-side jetcorrelation

– −^{0.030 to 0} −^{0.018 to 0 –}

Total +^{0.009 to}+^0.024 +^{0.024 to}+^0.084 +^{0.013 to}+^0.019 +^{0.015 to}+^0.021

−^{0.009 to}−^0.024 −^{0.024 to}−^0.090 −^{0.015 to}−^0.026 −^{0.015 to}−^0.021

Fig. 4. Example ofthe fit from Eq. (4) in the 3<p^μμ_T <6 GeV/c intervalfor p–Pbcollisionsat√

sNN=8.16 TeV.ThedashedlinecorrespondstotheV₂^B{μμ− tracklet,sub}(Mμμ).

Thenon-uniformacceptanceofthemuonspectrometercoupled to sizeable correlations between the dimuons and SPD tracklets can bias azimuthally the sample of SPD tracklets used for event mixing.Inordertocheckforpossibleeffectsonourmeasurement, theevent mixingis performedinintervals ofazimuthal angleof theselecteddimuons.Weobserveno significantsystematiceffect astheobtainedresultsshownegligibledeviationswithrespectto theresultsusingthedefaultevent-mixingtechnique.

The effectof a possibleresidual near-side peak is checkedby varying the rapidity gapbetween the trigger dimuons and asso- ciated charged-hadrons from 1.0to 2.0units. We observe no in- dicationofincreasing v₂ withreducedgapandthusconsiderthe defaultgapof1.5unitssufficienttoeliminateanysignificantresid- ualnear-sidepeakcontribution.

As shown in Section 4, the recoil-jet away-side correlation structureinthehigh-multiplicityeventclassisgreatlydiminished after the subtraction of the low-multiplicity event class. By de- fault,any remaining away-side structureis supposed to be taken intoaccount bythe cos

ϕ

termin Eq. (3).In ordertocheck for residual effects we proceed in the following way. First, the cor- relation function in the low-multiplicityevent class is fitwith a Gaussianfunctioncenteredat

ϕ

₌

π

.Then,thecorrelationfunc- tion in the high-multiplicity event class is fit with the function from Eq. (3), where the cos

ϕ

term is replaced by a Gaussian function with a width fixed to the value obtained from the fit inthelow-multiplicitycollisions.No clearsignature ofsystematic changeoftheresultsisseen,exceptsomehintsofapossibleeffect inthe highest p^J_T^/ψ interval. Conservatively,we assign systematic uncertainty as the difference with respect to the default analy-

sis approach. Since the typical values of the Gaussian width are around 1 rad, one-sided (negative) systematic uncertainty is as- signed.

In Table 1 we presenta summary ofthe assigned systematic uncertainties ofthe v^J₂^/ψ{²,sub}coefficients. No sizeable correla- tionsbetweenthep^J_T^/ψ intervalsareobservedandthereforeinthe followingtheuncertaintiesareconsidereduncorrelated.

OurmeasurementisforinclusiveJ/ψ.ThefractionofJ/ψ from decaysofb-hadronsreachesuptoabout15%atp^J_T^/ψ≈^{6 GeV/c in} p–Pb collisions at√

s_NN=⁵.02 [40] and 8.16 TeV [41]. Therefore the feed-down contribution is unlikely to influence significantly ourresults.Inprinciple,apossiblestrongmultiplicitydependence of the feed-down fraction can potentially affect the subtraction approach. However, no evidenceforsuch a strong dependenceis observedinppcollisions[42].

As additionalcross-checks the analysis is done using alterna- tive event-multiplicity estimators, varying the tracklet | | ^cut, applyingacutontheasymmetry oftransversemomentumofthe twomuontracks,removingthepile-upcutsandexcludingtheSPD regionswithnon-uniformacceptanceinpseudorapidity.Thecorre- sponding resultsare foundto be compatiblewiththoseobtained with the defaultanalysis approach andtherefore no further sys- tematicuncertaintiesareassigned.

6. Results

In Fig. 5 we report the measured v^J₂^/ψ{2,sub} coefficients as a function of p^J_T^/ψ for p–Pb andPb–p collisions at √

sNN=⁵.02 and8.16 TeV.Upto p^J_T^/ψ of3 GeV/c,nosignificantdeviationfrom zeroisobservedforeitherp–PborPb–pcollisionsatthetwocolli- sionenergies.Onthecontrary,inthep^J_T^/ψ intervalbetween3and 6 GeV/c, the v^J₂^/ψ{²,sub} ^{is found to be positive although with} largeuncertainties.AsalsoshowninFig.5,thev^J₂^/ψ coefficientsin 2.5<y<4 in centralPb–Pb collisions at√

s_NN=⁵.02 TeV reach maximalvaluesinthesamep^J_T^/ψ interval[24].

Twomethods are employed inorder toobtain theprobability thatthe v^J₂^/ψ{²,sub}^iszerointhe3<p^J_T^/ψ<6 GeV/c interval.In thefirstmethod,thev^J₂^/ψ{²,sub}^{valuesinthetwo pJ}_T^{/ψ intervals} (3<p^J_T^/ψ<4 GeV/c and4<p^J_T^/ψ<6 GeV/c) are combined into aweightedaverageforeach rapidityandcollisionenergy.Theob- tainedprobabilitiesare0.13%and0.13%(7.8%and0.23%)forp–Pb and Pb–pcollisions, respectively, at√

sNN=⁸.16 TeV (5.02 TeV).

Combining all eight v^J₂^/ψ{²,sub} ^{values yields a total probabil-} ity of1.7×^10−7.This corresponds to a 5.1

σ

significanceof the measured positive v^J₂^/ψ{²,sub} ^{coefficient. The second method is} Fisher’s combinedprobability test[43].Withthismethodoneob- tainsprobabilities of0.14%and0.23% (10.3%and0.41%) forp–Pb and Pb–p collisions at √

s_NN=⁸.16 TeV (5.02 TeV), respectively.

Fig. 5.v^J₂^/ψ{²,sub}^inbinsofpJT^/ψ forp–Pb,2.03<y<3.53 (leftpanels), andPb–p,−⁴.46<y<−².96 (rightpanels), collisionsat √_s

NN=⁵.02 TeV(toppanels)and 8.16 TeV(bottompanels).Theresultsarecomparedtothev^J₂^/ψ{^EP}^{coefficientsmeasuredincentralPb–Pbcollisionsat}√

sNN=⁵.02 TeVinforwardrapidity(2.5<y<4) usingeventplane(EP)basedmethods[24].Thestatisticalanduncorrelatedsystematicuncertaintiesarerepresentedbylinesandboxes,respectively.Thequotedglobal systematicuncertaintiescorrespondtothecombinedstatisticalandsystematicuncertaintiesofthemeasuredv^tracklet₂ {2,sub}coefficient.

The total probability is 1.4×^{10−6 which} corresponds to a 4.7

σ

significance.Inthecalculationoftheaboveprobabilities,bothsta- tistical and systematic uncertainties of the measured values are takenintoaccount.Theglobalsystematicuncertaintyisnottaken intoaccountasitisirrelevantinthecaseofthezerohypothesis.

Theanalysismethod presentedin thisLetterrelies onthe as- sumptionthattherearenosignificantcorrelationsduetocollective effectsinthelow-multiplicityeventclass.Incaseofapresenceof suchcorrelations,themeasuredV₂{^J/ψ−^tracklet,sub}^isequalto V2

{

J

/ψ −

tracklet

,

high

} −

^blow0

b^high₀ V2

{

J

/ψ −

tracklet

,

low

},

(6) whereV2{^J/ψ−^tracklet,high}^andV2{^J/ψ−^tracklet,low}^arethe second-orderFouriercoefficientsof theazimuthal correlation be- tween the J/ψ and the associated charged hadrons in the high- multiplicity and the low-multiplicity collisions, respectively, and b^low₀ /b^high₀ ≈^{1/3 is the ratio of the} combinatorial baseline in the low-multiplicityandhigh-multiplicitycollisions (see Fig.3). Asis demonstratedinRef. [44],theassumptionofnosignificantcollec- tivecorrelationsinthelow-multiplicitycollisionsiscertainlyques- tionablefor light-flavor hadrons.Our dataindicates the same,as weobserveastatisticallysignificantincreaseofthemeasuredval- uesofv^tracklet₂ {²,sub}^whensubtractingalowerevent-multiplicity, e.g.60–100%,class.Ultimately,thevalueofthev^tracklet₂ coefficient isfoundtobe about17%higherincasenosubtractionisapplied.

Therefore, replacing the subtracted v^tracklet₂ {²,sub} ^{coefficient in} Eq. (5) bythenon-subtractedcoefficientwouldmeanthatthev^J₂^/ψ coefficients are up to 17% lower with respect to the measured v^J₂^/ψ{²,sub} coefficients. However, assuming that the v^J₂^/ψ coeffi- cientsfollowthesametrendasafunctionofeventmultiplicityas the v^tracklet₂ coefficient, they wouldbe up to 17% higherwithre- specttothe measured v^J₂^/ψ{²,sub}coefficients. Subtracting lower

event-multiplicity classesinthe measurementofthe v^J₂^/ψ{²,sub} coefficientdoesnotimprovetheprecisionofourmeasurement,be- causeofthe limitedamountofJ/ψ signal in thelow-multiplicity collisions.

Thenuclearmodification factorofJ/ψ inp–PbandPb–pcolli- sions[37,38] aswellasthecharged-particle v₂ coefficient[45–47]

inppcollisionsshow nosignificant√

sNN dependence.Asseenin Fig.5,the measured v^J₂^/ψ{²,sub} ^{coefficientsat}√

sNN=⁵.02 and 8.16 TeValsoappeartobeconsistentwitheachother.Thelargest absolute difference between the results at the two collision en- ergies is observed in Pb–p collisions in the 3<p^J_T^/ψ<6 GeV/c interval. The significance of this difference is rather low (below 1.5

σ

), because ofthe large uncertainties of the measurement at

√sNN=⁵.02 TeV. Hence, the data for the two collision energies arecombinedasaweightedaveragetakingintoaccountbothsta- tistical and systematic uncertainties. In Fig. 6, we present these combinedresultsforp–PbandPb–pcollisionstogetherwithmea- surementsandmodelcalculationsforPb–Pb collisionsat√

sNN= 5.02 TeV[25].

In Pb–Pb collisions, the positive v^J₂^/ψ coefficients at p^J_T^/ψ be- low3–4 GeV/carebelievedtooriginatefromtherecombinationof charmquarksthermalizedinthemedium andaredescribedfairly well by the transport model[25] (seeFig. 6). In p–Pbcollisions, theamountof producedcharmquarksis smallandthereforethe contribution from recombination should be negligible. Our mea- suredvalues at p^J_T^/ψ<3 GeV/c are compatiblewithzero,in line withthisexpectation.Thereisonepublication[28] whichsuggests that even in p–Pbcollisions a sizeable contributionfrom recom- bination could occur due to canonical enhancement effects. The uncertaintiesofourresultsdonotallowtoconfirmortoruleout thisscenario.

InPb–Pbcollisions,themeasured v^J₂^/ψ coefficientsexceedsub- stantiallythetheoreticalpredictionsatp^J_T^/ψ>4 GeV/c,wherethe

Fig. 6.Combined v^J₂^/ψ{²,sub} ^{coefficientsinp–Pb andPb–pcollisionscompared} tothe results incentral and semi-central Pb–Pb collisions at √

sNN=⁵.02 TeV [24] and the transport model calculations for semi-central Pb–Pb collisions at

√sNN=5.02 TeV[25].Thesolidlinecorrespondstothecontributionfrompath- lengthdependentsuppressioninsidethe medium.Thebandshowsthe resulting v^J₂^/ψ includingalsotherecombinationofthermalizedcharmquarksandthefeed- downfromb-hadrondecaysassumingthermalizationofbquarks.

main contributionto v^J₂^/ψ is expectedto come frompath-length dependent suppression inside the medium [25] (see Fig. 6). In p–Pbcollisions,themedium, ifany,hasamuchsmallersize [48]

and hence very little, if any, path-length dependent effects are expected. In principle, the feed-down from decays of b-hadrons cangive a positive v^J₂^/ψ athightransversemomentum incaseof a positive b quark v2. However, the latter would have to reach unreasonably high values given the magnitude of the measured v^J₂^/ψ{²,sub} ^{andthesmallfeed-downfraction.Despitethesecon-} siderations, the measured positive v^J₂^/ψ coefficients would imply thattheJ/ψ participatesinthecollectivebehaviorofthep–Pbcol- lisionsystem.

7. Summary

We presented a measurement of the angular correlations between forward and backward J/ψ and mid-rapidity charged hadronsinp–PbandPb–pcollisionsat√

sNN=⁵.02 and8.16 TeV.

The data indicate persisting long-range correlation structures at

ϕ

≈^{0 and}

ϕ

≈

π

, reminiscentofthe doubleridge previously found in charged-particle correlations at mid- and forward ra- pidity. The corresponding v^J₂^/ψ{²,sub} ^{coefficients in 3}<p^J_T^/ψ<

6 GeV/c are found to be positive with a total significance of 4.7

σ

to 5.1

σ

. The obtained values, albeit with large uncertain- ties, are comparablewith those measured in Pb–Pb collisions at

√sNN =⁵.02 TeV in forward rapidity. Although the underlying mechanism is not understood, the comparable magnitudeof the v^J₂^/ψ coefficientsathightransversemomentuminp–PbandPb–Pb collisions indicates that thismechanism could be similarin both collisionsystems.

Acknowledgements

The ALICE Collaboration would like to thank all its engineers andtechnicians fortheir invaluablecontributionstotheconstruc- tionoftheexperimentandtheCERNacceleratorteamsfortheout- standingperformanceoftheLHCcomplex.TheALICECollaboration

gratefully acknowledges the resources and support provided by all Grid centresandthe WorldwideLHC ComputingGrid (WLCG) collaboration. The ALICE Collaboration acknowledges the follow- ing funding agencies for their support in building and running the ALICE detector: A.I. Alikhanyan National Science Laboratory (Yerevan Physics Institute) Foundation (ANSL), State Committee of Science and World Federation of Scientists (WFS), Armenia;

Austrian Academyof SciencesandNationalstiftung 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 andSports andCroatian ScienceFoundation, Croatia; Min- istryofEducation,Youth andSportsofthe CzechRepublic, 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)andInsti- tut National de Physique Nucléaire et de Physique des Particules (IN2P3) andCentre Nationalde la Recherche Scientifique (CNRS), France; Bundesministerium für Bildung, Wissenschaft, Forschung und Technologie (BMBF) and GSI Helmholtzzentrum für Schwe- rionenforschungGmbH,Germany;GeneralSecretariatforResearch and Technology, Ministry of Education, Research and Religions, Greece; National Research, Development and Innovation Office, Hungary; Department of Atomic Energy, Government of India (DAE),DepartmentofScienceandTechnology,GovernmentofIndia (DST), University Grants Commission,Government ofIndia (UGC) andCouncil ofScientificandIndustrialResearch(CSIR), India;In- donesian Institute of Science, Indonesia; Centro Fermi – Museo StoricodellaFisicaeCentroStudieRicercheEnricoFermiandIsti- tutoNazionalediFisicaNucleare(INFN),Italy;InstituteforInnova- tive ScienceandTechnology,NagasakiInstituteofAppliedScience (IIST),Japan SocietyforthePromotion ofScience(JSPS)KAKENHI and Japanese Ministry of Education, Culture, Sports, Science and Technology(MEXT),Japan;ConsejoNacionaldeCiencia(CONACYT) yTecnología,throughFondodeCooperaciónInternacionalenCien- cia y Tecnología (FONCICYT) and Dirección General de Asuntos delPersonalAcademico(DGAPA),Mexico;NederlandseOrganisatie voor Wetenschappelijk Onderzoek (NWO), Netherlands; The Re- search Council of Norway, Norway; Commission on Science and Technology forSustainableDevelopmentintheSouth(COMSATS), Pakistan;PontificiaUniversidadCatólicadelPerú,Peru;Ministryof ScienceandHigherEducationandNationalScienceCentre,Poland;

KoreaInstituteofScienceandTechnologyInformationandNational ResearchFoundationofKorea(NRF),RepublicofKorea;Ministryof Education andScientific Research,Institute ofAtomicPhysicsand Romanian National Agency for Science, Technology and Innova- tion,Romania;JointInstituteforNuclearResearch(JINR),Ministry of Education andScience of theRussian Federation andNational Research Centre Kurchatov Institute, Russia; Ministry of Educa- tion,Science,ResearchandSportoftheSlovakRepublic,Slovakia;

National ResearchFoundation ofSouth Africa, South Africa; Cen- tro de Aplicaciones Tecnológicas y Desarrollo Nuclear (CEADEN), Cubaenergía, Cuba,Ministeriode Cienciae Innovacion andCentro de Investigaciones Energéticas, Medioambientales y Tecnológicas (CIEMAT),Spain;SwedishResearchCouncil(VR) andKnut&Alice WallenbergFoundation(KAW),Sweden;EuropeanOrganizationfor Nuclear Research, Switzerland; National Science and Technology Development Agency (NSDTA), Suranaree University of Technol-