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Physics Letters B
www.elsevier.com/locate/physletb
Multiplicity dependence of jet-like two-particle correlation structures in p–Pb collisions at √
s NN = 5 . 02 TeV
.ALICE Collaboration
a r t i c l e i n f o a b s t ra c t
Articlehistory:
Received23June2014
Receivedinrevisedform8October2014 Accepted15November2014
Availableonline20November2014 Editor:L.Rolandi
Two-particle angular correlations between unidentified charged trigger and associated particles are measured by the ALICE detector in p–Pb collisions at a nucleon–nucleon centre-of-mass energy of 5.02 TeV. The transverse-momentum range 0.7< pT,assoc<pT,trig <5.0 GeV/c is examined, to include correlations induced by jets originating from low momentum-transfer scatterings (minijets).
The correlations expressedas associated yield pertrigger particleare obtained inthe pseudorapidity range |η|<0.9. The near-side long-range pseudorapidity correlations observed in high-multiplicity p–Pb collisions aresubtractedfromboth near-sideshort-rangeand away-sidecorrelations inorderto remove the non-jet-like components.The yields in the jet-like peaksare foundto be invariant with event multiplicitywiththeexceptionofeventswithlowmultiplicity.Thisinvarianceisconsistentwith the particlesbeingproduced via the incoherentfragmentation of multiple parton–parton scatterings, while the yield related tothe previously observedridge structures is not jet-related.The number of uncorrelatedsourcesofparticleproductionisfoundtoincreaselinearlywithmultiplicity,suggestingno saturationofthenumber ofmulti-partoninteractionseven inthehighestmultiplicityp–Pb collisions.
Further, the number scales only in the intermediate multiplicity regionwith the number of binary nucleon–nucleoncollisionsestimatedwithaGlauberMonte-Carlosimulation.
©2014TheAuthors.PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense (http://creativecommons.org/licenses/by/3.0/).FundedbySCOAP3.
1. Introduction
Data fromp–Pb collisions atthe LHChave resultedin several surprising measurements with observations which are typically found in collisions of heavy ions and are understood to be due to a collective expansion of the hot and dense medium (hydro- dynamicflow).Inparticular,so-calledridgestructureswhichspan over a large range in pseudorapidity (
η
) have been observed in two-particlecorrelations[1–3].Theirmodulationinazimuthisde- scribedbyFouriercoefficientsandisdominatedbythoseofsecond (v2) andthird (v3) order[2–4].Theyarealsofoundinthecorre- lationsoffourparticles [4,5]whichare lesssensitive tonon-flow effectslike resonancedecays andjets. Evidence forthe existence ofacommonflow velocityfieldhasbeenfurthercorroboratedby particle-identification measurements ofthe same observables[6].Theyrevealedthatthev2ofpions,kaonsandprotonsasafunction ofpT showsacharacteristicmassorderingaswellasacrossingof pion andproton v2 atabout 2.5 GeV/c which is reminiscent of measurements in Pb–Pb collisions [7]. These findings hintat po- tentially novel mechanisms in collisions of small systems which are far from being understood theoretically. Several authors de-
E-mailaddress:alice-publications@cern.ch.
scribetheresultsinthecontextofhydrodynamics[8–12],butalso explanations in the framework of saturation models successfully describesomeofthemeasurements[13,14].
While measurements of these correlations are suggestive of similarities between Pb–Pb and p–Pb collisions, measurements sensitive to energy loss in a hot and dense medium reveal no or minor modifications with respect to pp collisions. The inclu- sivehadronnuclearmodificationfactorRpA ofminimum-biasp–Pb eventsshowsnosignificantdeviationsfromunityupto20 GeV/c [15].Measurementsofthedijettransverse momentumimbalance show comparable results to simulated pp collisions at the same center-of-massenergy,independentoftheforwardtransverseen- ergy[16].
Towards a more complete picture of the physical phenom- ena involved in p–Pb collisions, it is interesting to study QCD interactions in the pT range where these ridge-like structures have been observed. Parton scatterings with large transverse- momentumtransfer(Q2ΛQCD,typicallycalledhardinteractions) leadtophenomenasuchashigh-pTjets.QCD-inspired modelsex- trapolate these interactions to the low-pT region where several such interactions can occur per nucleon–nucleon collision (mul- tiple partoninteractions –MPIs)andcanhencecontribute signif- icantly to particleproduction [17,18].The objective ofthe analy- sis presented in this paper is to investigate if jet-like structures http://dx.doi.org/10.1016/j.physletb.2014.11.028
0370-2693/©2014TheAuthors.PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense(http://creativecommons.org/licenses/by/3.0/).Fundedby SCOAP3.
inthis low-pT region show modifications asa function ofevent multiplicityin additionto theappearance oftheridge-like struc- tures. The analysis employs two-particle azimuthal correlations within |
η
|<0.9 fromlow to intermediatetransverse momentum (0.7<pT<5 GeV/c) inp–Pb collisions. After subtractionof the long-rangepseudorapidity ridge-like structures, the yields of the jet-like near- and away-side peaks are studied as a function of multiplicity.Asalreadyshowninppcollisions,thisanalysisproce- dureallowstheextractionoftheso-callednumberofuncorrelated seeds,whichinPYTHIAisproportionaltothenumberofMPIs[19].Thusthepresentedresultsallowtodrawconclusionsonthecon- tributionofhard processestoparticleproductionasafunctionof eventmultiplicity.
Thepaperis structured asfollows:Section 2 presentsthe ex- perimental setup followed by the event and track selections in Section3andtheanalysisdetailsinSection4.Theresultsarepre- sentedinSection5followedbyasummary.
2. Experimentalsetup
Inthepresentanalysis,p–Pb collisiondataatacentre-of-mass energyof√
sNN=5.02 TeV collectedbytheALICEdetectorin2013 are used. The energies of the beams were 4 TeV for the proton beamand1.58 TeV per nucleonforthelead beam. Thenucleon–
nucleon centre-of-mass system moveswith respect to the ALICE laboratorysystemwitharapidityof−0.465,i.e.inthedirectionof theprotonbeam.Inthefollowing,
η
denotesthepseudorapidityin thelaboratorysystem.A detailed description of the ALICE detector can be found in Ref.[20].Thesubdetectorsusedinthepresentanalysisforcharged particletrackingaretheInner TrackingSystem (ITS)andtheTime ProjectionChamber (TPC),bothoperatinginasolenoidalmagnetic fieldof0.5 Tandcoveringacommonacceptanceof|
η
|<0.9.The ITSconsistsofsixlayersofsilicondetectors:twolayersofSilicon PixelsDetectors (SPD),twolayersofSiliconDriftDetectorsandtwo layersofSiliconStripDetectors,fromtheinnermosttotheouter- mostones.TheTPCprovidestrackingandparticleidentificationby measuring the curvature of the tracks in the magnetic field and thespecificenergylossdE/dx.TheVZEROdetector,whichconsists oftwoarraysof32scintillator tileseach, coversthe fullazimuth within 2.8<η
<5.1 (VZERO-A) and−3.7<η
<−1.7 (VZERO-C) andisusedfortriggering,eventselectionandeventcharacteriza- tion. The trigger requires a signal of logical coincidence in both VZERO-AandVZERO-C. The VZERO-A,located inthe flight direc- tionofthePbions,isused todefine eventclassescorresponding to differentparticle-multiplicity ranges. In addition, two neutron Zero Degree Calorimeters (ZDCs), located at 112.5 m (ZNA) and−112.5 m (ZNC)fromtheinteractionpoint,areusedfortheevent selection.TheZNAhasanacceptanceof96%forneutronsoriginat- ing fromthe Pbnucleusandthe deposited energyis usedas an alternativeapproachtodefinetheevent-multiplicityclasses.
3. Eventandtrackselection
The employed event selection [21] accepts 99.2% of all non- single-diffractivecollisions. Beam-inducedbackgroundisremoved by a selection on the signal amplitude and arrival times in the two VZERO detectors.The primary vertexposition is determined fromthetracks reconstructedinthe ITSandTPCasdescribed in Ref.[22].Thevertexreconstruction algorithmisfullyefficientfor eventswithatleastonereconstructedprimarychargedparticlein thecommonTPCand ITSacceptance.Events withthecoordinate ofthereconstructedvertexalongthebeamaxiszvtx within10 cm from the nominal interaction point are selected. About 8·107
eventspasstheseeventselectioncriteriaandareusedfortheanal- ysis.
The analysis uses charged-particle tracks reconstructed in the ITSand TPCwith0.2<pT<5 GeV/c within a fiducialregion of
|
η
|<η
max withη
max=0.9. The track selection is the same as in Ref. [2] and is based on selections on the number of space points, thequality of thetrackfit andthenumber ofhitsinthe ITS, aswell astheDistance ofClosestApproach (DCA)to there- constructed collision vertex. The track selection is varied in the analysisforthestudyofsystematicuncertainties[2].The efficiency and purity of the track reconstruction andthe track selection for primary charged particles (defined as the prompt particlesproduced inthe collision,including decayprod- ucts, except those from weak decays of strange particles) are estimated froma Monte-Carlo simulationusing the DPMJET ver- sion 3.05 event generator [23] with particle transport through the detector using GEANT3 [24] version 3.21. The efficiency and acceptance for track reconstruction is 68–80% for the pT range 0.2–1 GeV/c,and80%for pT>1 GeV/c withthe aforementioned track selections. The reconstruction performance is independent ofthep–Pb eventmultiplicity.Theremaining contaminationfrom secondaryparticlesduetointeractionsinthedetectormaterialand weakdecaysdecreasesfromabout5%to1% inthe pT rangefrom 0.5 to 5 GeV/c. The contribution fromfake tracks, false associa- tionsofdetectorsignals,isnegligible.Correctionsfortheseeffects arediscussedinSection4.Alternatively,efficienciesareestimated using HIJING version 1.36 [25] with negligible differences in the results.
In order to study the multiplicity dependence of the two- particle correlations, the events are divided into classes defined accordingtothechargedepositionintheVZERO-Adetector(called V0Awhen referring to it asa multiplicity estimator). The events are classified in 5% percentile ranges of the multiplicity distri- bution, denoted as“0–5%” to “95–100%” from thehighest to the lowestmultiplicity.
TheVZERO-AdetectorislocatedinthedirectionofthePbbeam andthussensitive tothe fragmentationofthePbnucleus, andis used as default multiplicity estimator. Two other estimators are employed to studythebehaviour of thetwo-particle correlations asafunctionofthe
η
-gapbetweenthe detectorusedtomeasure the multiplicity andthe trackingdetectors. Theseare CL1, where the signal is taken from the outer layer of the SPD (|η
|<1.4), andZNA,whichusestheZNAdetector(|η
|>8.8).Duetothelim- ited efficiencyofthe ZNA,resultsare only presentedforthe95%highest-multiplicity events. These estimators select events with differentrangesofmultiplicityatmidrapidity.WhiletheV0Aesti- matorselectseventclasseswithonaverageabout5to69charged particles within |
η
|<0.9 and pT larger than 0.2 GeV/c, the CL1 has a slightly larger range (about 2 to 78) and the ZNA has a smallerrange(about10to46).The observablesinthisanalysisarecalculated foreventswith atleastoneparticlewithpT>0.2 GeV/cwithin|
η
|<0.9.Monte- Carlosimulationsshow thatthisselection reducesthenumberof eventscomparedtoallinelasticeventsbyabout2%.Theseevents are concentrated at low multiplicity in the 80–100% multiplicity classes.4. Analysis
The two-particle correlationsbetweenpairs oftrigger andas- sociated charged particles are expressed as the associated yield per trigger particle ina giveninterval of transverse momentum, foreachmultiplicityclass.Theassociatedper-triggeryieldismea- suredasafunctionoftheazimuthaldifference
ϕ
(definedwithin−
π
/2 and 3π
/2) and of the pseudorapidity differenceη
. Thecondition pT,assoc<pT,trig betweentransverse momentaoftrigger andassociatedparticlesisrequired.
Theassociatedyieldpertriggerparticleisdefinedas
1 Ntrig
d2Nassoc
d
η
dϕ =
S( η , ϕ ) ·
C( η , ϕ ),
(1) where Ntrig is the total number of trigger particles in the event class and pT interval. The signal distribution S(η
,ϕ
) = 1/Ntrigd2Nsame/dη
dϕ
is the associated yield per trigger par- ticleforparticlepairsfromthe sameevent.The correction factor C isdefinedas:C
( η , ϕ ) =
B( η )
B
( η , ϕ ) ,
(2)where B describes the pair acceptance and pair efficiency of the detector while B is the pair acceptance of a perfect but pseudorapidity-limiteddetector,i.e.atriangular shapedefinedby B(
η
)=1− |η
|/(2·η
max).Inthisway,theresultingassociated yields per trigger particle count only the particles entering the detectoracceptance, asit isrequired forthe definition ofuncor- relatedseeds,seebelowandthedetaileddiscussioninRef.[19].B(
η
,ϕ
)=α
d2Nmixed/dη
dϕ
is constructed by correlat- ingthetriggerparticlesinoneeventwiththeassociatedparticles from different events in the same multiplicity class and within thesame2 cm-widezvtx interval(eacheventismixedwithabout 5–20events).Itisnormalizedwithafactorα
whichischosensuch thatB(η
,ϕ
)isunityatϕ
=η
≈0 forpairswherebothpar- ticlestravelinapproximatelythesamedirection.Theyielddefined byEq.(1)is constructedforeach zvtx interval toaccount fordif- ferencesinpair acceptanceandinpairefficiency. Afterefficiency correction(describedbelow)thefinalper-triggeryieldisobtained by calculatingtheaverage ofthe zvtx intervalsweighted by Ntrig. A selection on the openingangle of the particlepairs is applied in order to avoid a bias due to the reduced efficiency for pairs withsmallopeningangles.Pairsarerequiredtohaveaseparation of|ϕ
min∗ |>0.02 rad or |η
|>0.02,whereϕ
∗min isthe mini- malazimuthaldistanceatthesameradiusbetweenthetwotracks withintheactivedetectorvolumeafteraccountingforthebending inthemagneticfield.Furthermore,correlationsinduced bysecondary particles from neutral-particle decays are suppressed by cutting on the invari- ant mass (minv) of the particle pair. In this way pairs are re- moved which are likely to stem from a
γ
-conversion (minv<0.04 GeV/c2), aK0s decay(|minv−m(K0)|<0.02 GeV/c2) ora Λ decay(|minv−m(Λ)|<0.02 GeV/c2).Thecorrespondingmassesof thedecayparticles(electron,pion,orpion/proton)areassumedin theminvcalculation.
Each trigger and each associated particle is weighted with a correction factor that accounts for reconstruction efficiency and contamination by secondary particles. These corrections are ap- plied as a function of
η
, pT and zvtx. The correction procedure is validated by applying it to simulated events and comparing theper-triggerpairyieldswiththeinputMonte-Carlosimulations.The remaining difference after all corrections (Monte-Carlo non- closure)isfoundtobenegligible.
4.1. Long-rangecorrelationssubtraction
In addition to the jet-like peaks, ridge structures have been observedin p–Pb collisions[2,3]. Theselong-rangestructuresare mostlyindependent of
η
outsidethejet-like peakandassumed to be independent below the peak and their modulation in az- imuthis described by a Fourierexpansion up to thethird order.Tostudythepropertiesofthe jet-likepeaks,thesestructuresare subtracted.
On the near side (−
π
/2<ϕ
<π
/2), the jet-like peak is centeredaround (η
=0,ϕ
=0),whiletheridgestructuresex- tend to largeη
.Thus thenear side is divided intoshort-range (|η
|<1.2)andlong-range(1.2<|η
|<1.8)correlationsregions which arecorrectlynormalizedandsubtracted fromone another.Fig. 1showsthe
ϕ
-distributionsoftheper-triggeryieldinthese tworegionsinthehighest(0–5%)andlowest(95–100%)multiplic- ityclasses.On the away side (
π
/2<ϕ
<3π
/2) the jet contribution is alsoelongatedinη
.Thejetandridgecontributioncantherefore not be disentangled. As the ridge structuresare mostly symmet- ricaroundϕ
=π
/2 (thesecondFouriercoefficientisfourtimes larger than the third coefficient [2,3]), the near-side long-range correlations aremirrored aroundϕ
=π
/2 andsubtracted from the away side (measured in |η
|<1.8). Also shown in Fig. 1 are theϕ
-distributions ofthe symmetrized long-range correla- tions andthe correlations after subtraction. Obviously, this sym- metrization procedure doesnot accountcorrectly foroddFourier coefficients. Toassesstheeffectofthethirdcoefficient ontheex- tracted observables, an additional 2v23cos 3ϕ
functional formis subtracted before the symmetrization. The v3 is estimated as a function ofmultiplicity withthesubtraction proceduredescribed inRef.[2].Theinfluenceofthev3contributionisillustratedinthe bottomleftpanelofFig. 1.Theeffectofthesymmetrizationofthe thirdFouriercomponentontheaway-sideyieldamountsupto4%andisamajorcontributiontothesystematicuncertainties.
4.2. Observables
The event-averaged near-side, Nassoc,near side, and away-side, Nassoc,away side, per-trigger yields are sensitive to the fragmen- tation properties of low-pT partons. They are calculated as the integral of the
ϕ
projection of the long-range subtracted per- triggeryield(bincounting)respectivelyinthenear-sideandaway- sidepeaks,abovethecombinatorialbackground.Bydefinitionafter subtractingthelong-rangecorrelations(1.2<|η
|<1.8)fromthe short-range one (|η
|<1.2),the baselineshould bezero.Never- theless, owingtominordifferencesbetweenthedetectorefficien- ciesandthoseestimatedwiththeMonte-Carlosimulations anda slightdependenceofthesingle-particledistributiononη
,asmall residual baselineispresent(about0.003, hardlyvisibleinFig. 1), whichistakenintoaccount.Fig. 1showsthat theaway-sidepeak isslightlywiderthan thenear-sidepeak. Therefore,the near-side yield is evaluated in the region |ϕ
|<1.48 and the away-side yieldin|ϕ
|>1.48.Forthesystematicuncertaintyestimation,the value1.48 hasbeenvariedby±0.09.Alternatively, the yields arealso calculated witha fitmethod, using two Gaussians on the near side and one Gaussian on the away side superimposed on a constant baseline [19]. The differ- ences between the results obtained with the two methods are includedinthesystematicuncertainties.
Theaveragenumberoftriggerparticlesdependsonthenumber of parton scatterings per event as well as on the fragmentation propertiesofthepartons.Therefore,theratiobetweenthenumber oftriggerparticlesandtheper-triggeryieldsiscomputedwiththe goal to reduce thedependence on fragmentationproperties.This ratio,calledaverage numberofuncorrelatedseeds, isdefinedfor symmetric pTbinsas:
Nuncorrelated seeds=
NtrigNcorrelated triggers
=
Ntrig1
+
Nassoc,near side+
Nassoc,away side,
(3) where the correlated triggers are calculated as the sum of the trigger particle and theparticles associatedto that trigger parti-Fig. 1.Per-triggeryieldasafunctionofϕwith0.7<pT,assoc<pT,trig<5 GeV/cinthe0–5%eventclass(left)and95–100%eventclass(right).Thedistributionsshowthe correlationsbeforesubtraction(bluecircles),thelong-rangecorrelations(blacktriangles)scaledaccordingtotheηregioninwhichtheyareintegrated,thesymmetrized near-sidelong-rangecorrelations(greensquares)andthecorrelationsafterlong-rangecorrelations(LRC)subtraction(reddiamonds).Theverticalarrowsindicatetheinte- grationregionswhilethecurveinthebottomleftpanelshowsthemagnitudeofthethirdFouriercomponentontheawayside.Statisticaluncertaintiesareshownbutare smallerthanthesymbolsize.(Forinterpretationofthereferencestocolorinthisfigure,thereaderisreferredtothewebversionofthisarticle.)
cle. In PYTHIA, forpp collisions [19], the uncorrelatedseeds are found to be linearlycorrelated to the number of MPIs in a cer- tain pT range,independentofthe
η
rangeexplored.Theselection pT>0.7 GeV/c hasbeen foundoptimalsince itisclose toΛQCD andhighenoughtoreducecontributionsofhadronsatlow pT,e.g.fromresonancesandstringdecays.
4.3.Systematicuncertainties
Table 1summarizesthesystematicuncertainties relatedtothe near-side and away-side long-range-subtracted yields extraction andto theuncorrelatedseedscalculation. Thelargestuncertainty (5%)fortheyieldsisduetotheintegrationmethodestimatedfrom thedifferencebetweenbincountingandthefit.Thev3-component estimation gives rise to an uncertainty only on the away side which is multiplicity-dependent. It is indicated by the range in thetable wherethe largestvalue of 4%is obtainedforthe high- estmultiplicity.Other non-negligibleuncertainties are duetothe trackselection (2%),thepile-upcontamination (1%),estimatedby excludingthetracks fromdifferentcollidingbunch crossings, and theuncertaintyonthetrackingefficiency(3%)[15].
The total uncertainty for the yields is 6–8%, which translates into 3% uncertainty for the uncorrelated seeds where, owing to thedefinition,some uncertainties cancel.The total uncertaintyis mostlycorrelated betweenpointsandbetweenthedifferentesti- mators.
5. Results
The near-side and away-side per-trigger yields are shown in Fig. 2 as a function of V0A multiplicity class for three different
Table 1
Summaryofthesystematicuncertainties.Theuncertaintiesareindependentofmul- tiplicity,apartfromtheeffectofthethirdFouriercomponentv3.
Source Near-side
yield
Away-side yield
Uncorrelated seeds
Bin counting vs. fit 5% 5% 1%
Baseline estimation negl. 1% negl.
v3component 0% 0–4% 0–1%
Track selection 2% 2% negl.
Tracking efficiency 3% 3% 3%
Pile-up 1% 1% negl.
MC closure negl. negl. negl.
Event generator negl. negl. negl.
Total 6% 6–8% 3%
pT ranges.Fortherange0.7 GeV/c<pT,assoc<pT,trig<5.0 GeV/c (redtriangles),thenear-side(away-side)per-triggeryieldincreases fromabout0.14(0.08)inthelowestmultiplicityclassuptoabout 0.25(0.12)at60%,anditremainsnearlyconstantfrom60%tothe highestmultiplicityclass.
Thetriggerparticlescanoriginatebothfromsoftandhardpro- cesses, while theassociated particles mostly belong to the mini- jetswhichoriginatefromhard processes.Therefore,inthe region where the associated yields per trigger particle show a plateau, thehard processesandthenumberofsoftparticles mustexhibit thesameevolutionwithmultiplicity.Thiscan bemoreeasilyun- derstood with an example eventcontaining Nminijets with Nassoc associatedparticleseach anda backgroundof Nsoft particleswith noazimuthalcorrelation.Inthisscenario,theassociatedyieldper trigger-particleis:
Fig. 2.Near-side(leftpanel)andaway-side(rightpanel)per-triggeryieldsafterlong-rangecorrelationssubtractionasafunctionofV0Amultiplicityclassforseveral pT cutsfortrigger andassociatedparticles:0.7–5.0 GeV/c(redtriangles), 0.7–5.0 GeV/cfor pT,assoc and2–5 GeV/c for pT,trig (bluecircles)aswellas2–5 GeV/c(black circles).Statistical(lines)andsystematicuncertainties(boxes)areshown,eventhoughthestatisticalonesaremostlysmallerthanthesymbolsize.(Forinterpretationofthe referencestocolorinthisfigure,thereaderisreferredtothewebversionofthisarticle.)
Fig. 3.Near-side(leftpanel)andaway-side(rightpanel)per-triggeryieldsafterlong-rangecorrelationssubtractionasafunctionofthemidrapiditychargedparticlemulti- plicityfortheV0A(redcircles),CL1(bluesquares)andZNA(blacktriangles)multiplicityestimators.Statistical(lines)andsystematicuncertainties(boxes)areshown,even thoughthestatisticalonesaresmallerthanthesymbolsize.(Forinterpretationofthereferencestocolorinthisfigure,thereaderisreferredtothewebversionofthis article.)
associated yield
trigger particle
=
Nminijets·
Nassoc(
Nassoc−
1)/
2 Nminijets·
Nassoc+
Nsoft.
(4)When the overall multiplicity, i.e.the denominator, changes, the fractionisconstantifNminijets(hardprocesses)andNsoft(softpro- cesses) increase by the same factor. The given example can be easilyextendedtoseveraleventsandtoadifferentnumberofas- sociatedparticlesperminijet.
Increasingthe pT thresholdofthetriggerparticlesto 2 GeV/c (bluecirclesinFig. 2),resultsinlargeryieldsbutwithqualitatively the samemultiplicity dependence. The plateauregion extends in this case up to the 80% multiplicity class. Increasing also the threshold forthe associated particles to 2 GeV/c (black squares)
reduces theyields whilethe plateauremains overa wide multi- plicityrange.
Tocompareresultsobtainedwithdifferentmultiplicityestima- tors, for each multiplicity class the average number of charged particles atmidrapidity (|
η
|<0.9)with pT>0.2 GeV/c hasbeen computed. Fig. 3showstheper-triggeryieldsinthenear-sideand in the away-side peaks asa function ofthe midrapidity charged particlemultiplicity forthestandardestimatorV0Aaswell asfor CL1andZNA.Asdiscussedabove,themultiplicityrangecoveredby these estimators dependson the separation in pseudorapidity of theestimatorandthetrackingdetector.Thenear-side(away-side) yields forV0A and ZNA show the same behaviour in the region between 10 and45 charged particles in which their multiplicityFig. 4.Near-side(leftpanel)andaway-side(rightpanel)per-triggeryieldsasafunctionofV0Amultiplicityclasswith(redcircles)andwithout(blacksquares)subtractionof thelong-rangecorrelations.Statistical(lines)andsystematicuncertainties(boxes)areshown,eventhoughthestatisticalonesaremostlysmallerthanthesymbolsize.(For interpretationofthereferencestocolorinthisfigure,thereaderisreferredtothewebversionofthisarticle.)
rangeoverlaps:amild increasefromabout0.2(0.1)toabout0.25 (0.13).Below10chargedparticles,theyieldsforV0Adecreasesig- nificantlytoabout0.14onthenearsideand0.08ontheawayside.
Theyields forCL1exhibit asteeper slopethan thetwo otheres- timators.Thisbehaviourisexpectedfromtheevent-selectionbias imposedbytheoverlapping
η
-regionofeventselectionandtrack- ing:onthe nearside(away side)thevalue increasesfromabout 0.04to0.27(fromabout0.02to0.15).TheCL1trendsarequalita- tivelyconsistentwiththeresultsinpp collisions[19].Theoverall behaviourforeachestimatorissimilarwhenusinghigher pT cuts forassociatedandtriggerparticles.Akey stepof theanalysis procedureis the subtractionofthe long-rangecorrelations. Toassessthe effectof thissubtraction, a comparisonbetween theyields withand withoutthe ridge con- tribution has been performed. The determination of the yields in thesetwo cases is,however, slightly different, since the non- subtracteddistributiondoesnothaveazerobaselinebyconstruc- tion. In this case, the baseline is determined in the long-range correlationsregion(1.2<|
η
|<1.8)betweenthenear-sideridge andtheaway-sidepeakat1.05<|ϕ
|<1.22.Theeffectofthe subtractionof thelong-rangecorrelationson themeasured yieldsforthe V0Aestimatorispresented inFig. 4, where the near-side and away-side per-trigger yields with (red circles) and without (black squares) long-range correlations sub- tractionare shown.The yieldsagree witheachother inthemul- tiplicityclassesfrom50%to100%,consistentwiththeobservation that no significant long-rangestructure exists inlow-multiplicity classes.Forhigher-multiplicityclasses,adifferenceisobserved:the near-sideyieldincreasesuptoabout0.34withoutthesubtraction compared to about 0.25with subtraction. On the away side the value is about0.23 compared to 0.13. Thus, in the highestmul- tiplicity class, the subtraction procedure removes 30–40% of the measuredyields.Thesameobservationismadefortheothermul- tiplicityestimators.
Theconclusion drawnearlier, thatthe hard processesandthe number of soft particles show the same evolution with multi- plicity,isonlyvalidwhenthelong-rangecorrelationsstructureis subtracted.Thisobservationisconsistentwithapicturewherethe minijet-associatedyieldsinp–Pb collisionsoriginatefromtheinco-
Fig. 5.Toppanel:numberofuncorrelated seedsas afunctionofthe midrapid- itychargedparticlemultiplicity.ShownareresultsfortwopTcuts:0.7 GeV/c<
pT,assoc<pT,trig<5.0 GeV/c (red circles) and 2.0 GeV/c<pT,assoc<pT,trig<
5.0 GeV/c(blacksquares).Eachofthemisfitwithalinearfunctioninthe0–50%
multiplicityclasses;opensymbolsarenotincludedinthefit.Statistical(lines)and systematicuncertainties(boxes)areshown, eventhoughthe statisticalones are smallerthanthesymbolsize.Bottompanel:ratiobetweenthenumberofuncorre- latedseedsandthelinearfitfunctions.Blackpointsaredisplacedslightlyforbetter visibility.(Forinterpretationofthereferencestocolorinthisfigure,thereaderis referredtothewebversionofthisarticle.)
herentfragmentationofmultipleparton–partonscatterings,while thelong-rangecorrelationsappearunrelatedtominijetproduction.
Whiletheyieldsgiveinformationabouttheparticlesproduced in a single parton–parton scattering, the uncorrelated seeds cal- culation(Eq. (3)) provides thenumberof independentsources of particleproduction.Theuncorrelatedseedsareproportionaltothe numberofMPIsinPYTHIA.
Fig. 6.Ratiobetweenuncorrelatedseedsand Ncoll estimatedwithintheGlauber modelasafunctionofV0Amultiplicityclass.Statistical(lines)andsystematicun- certainties(boxes)areshown,eventhoughthestatisticalonesaresmallerthanthe symbolsize.Toaidthecomparison,thehigherpTrangehasbeenscaledbyafactor 8.3toagreewiththelowerpTrangeinthe50–55%multiplicityclass.
Fig. 5 presents the uncorrelated seeds as a function of the midrapidity charged-particle multiplicity for two pT cuts. In the range2 GeV/c<pT,assoc<pT,trig<5 GeV/c,thenumberofuncor- relatedseeds increaseswithmultiplicityfromabout0toabout3.
Theuncorrelatedseeds exhibit alinearincrease withmidrapidity chargedparticlemultiplicity Nch inparticularathighmultiplicity.
Toquantifythisbehaviour, alinearfit isperformedinthe0–50%
multiplicityclassandtheratiotothedataispresentedinthebot- tompanel.
The linear description ofthe data is validfor Nch>20 while deviationsatlowermultiplicity areobserved.Deviations fromlin- earityare not surprisingasotherobservables, e.g. themean pT [26] andthe RpA [27],show a changein dynamicsasa function ofmultiplicity.Inthis pT range,theuncorrelatedseedsare rather similartothenumberofparticlesaboveacertain pTthresholdas the denominator of Eq. (3)is close to unity. On the contrary, in the range0.7 GeV/c<pT,assoc<pT,trig<5.0 GeV/c thedenomi- natorisfarfromunity.Inthisregion,thenumberofuncorrelated seeds increases with multiplicity from about 2 to about20. The lineardescriptionextendsoveraslightlywiderrangebutadepar- tureisalsoobservedatlowmultiplicity.
It is interesting to relate the number of uncorrelated seeds to the number of nucleon–nucleon collisions, which in heavy- ion collisions is described successfully by Glauber models [28]
(Ncoll,Glauber).However,inp–Pb collisions,ongoingstudies[27](to be published in [29]) indicate that modifications to the Glauber Monte-Carlosimulationsareneededforacorrectestimationofthe numberofhardprocesses.
Fig. 6 presents the ratio between uncorrelated seeds and Ncoll,Glauber (calculated with a Glauber Monte-Carlo simulation) asa functionofV0A multiplicity classfortwo pT cuts. Ascaling oftheuncorrelatedseeds withNcoll,Glauber within3% isobserved between25% and55% multiplicity classes.At higher multiplicity, for the 0.7 GeV/c<pT,assoc<pT,trig<5.0 GeV/c (2.0 GeV/c<
pT,assoc<pT,trig<5.0 GeV/c) range, theratio betweenthe num- berofuncorrelatedseeds andthenumberofcollisions estimated within the Glauber Monte-Carlo simulations deviates up to 25%
(60%)fromits average.At low multiplicity thedeviationis about 30%(25%).Thisshowsthatcontrarytotheexpectationforasemi- hard process, the number of uncorrelated seeds is not strictly proportional to the number of binary collisions. For further de-
tails, we refer the reader to the publication Ref. [29], which is in preparation. Some of these deviations could be dueto a bias inducedbythecentralityestimator.Monte-Carlosimulationsindi- cate that by using multiplicity to define eventclasses, a bias on themeannumberofhard collisionspereventisintroduced:high (low)multiplicitybiastowardseventswithhigher(lower)number of semi-hard processes. Inaddition, low-multiplicity p–Pb events result from collisions witha larger than average proton–nucleus impact parameter, which, for peripheral collisions, corresponds also to a larger than average proton–nucleon impact parameter [30].Therefore,in low-multiplicitycollisions thenumber ofMPIs isexpectedtodecrease,whichisconsistentwiththemeasurement.
6. Summary
Two-particleangularcorrelationsofchargedparticleshavebeen measured in p–Pb collisions at √
sNN=5.02 TeV and expressed asassociatedyieldspertriggerparticle.Long-rangepseudorapidity correlationshavebeensubtractedfromtheper-triggeryieldsinor- dertostudythejet-likecorrelationpeaks.Near-sideandaway-side jet-likeyieldsarefoundtobeapproximatelyconstantoveralarge rangeinmultiplicity,withtheexceptionofeventswithlowmulti- plicity.Thisindicates thatathighmultiplicity hardprocessesand numberofsoftparticleshavethesameevolutionwithmultiplicity.
These findings are consistent witha picture where independent parton–parton scatteringswithsubsequentincoherentfragmenta- tion produce the measured minijet associated yields, while the ridge yields, whichvary withmultiplicity,are the resultofother sources.Thisimposessignificantconstraintsonmodelswhichaim atdescribing p–Pb collisions.Theymustreproduce such an inco- herent superposition while also describing observations like the ridge structures andthe increase of mean pT withevent multi- plicity.
The number of uncorrelated seeds increases almost linearly withmultiplicity,exceptatverylowmultiplicity.Thus,withinthe measuredrange,thereisnoevidenceofasaturationinthenumber of multiple parton interactions. Furthermore, it is observed that the number of uncorrelated seeds scales only in the intermedi- atemultiplicityregionwiththenumberofbinarynucleon–nucleon collisions estimated withGlauber Monte-Carlo simulations, while at high and low multiplicities some biases could possibly cause thescalebreaking.
Acknowledgements
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- ing funding agencies for their support in building and running the ALICEdetector:State CommitteeofScience,WorldFederation of Scientists (WFS) and Swiss Fonds Kidagan, Armenia, Conselho Nacional de Desenvolvimento Científico e Tecnológico(CNPq), Fi- nanciadora de Estudose Projetos(FINEP),Fundaçãode Amparoà Pesquisa do Estado de São Paulo (FAPESP); National Natural Sci- enceFoundation of China (NSFC),the ChineseMinistry ofEduca- tion(CMOE)andtheMinistryofScienceandTechnology ofChina (MSTC); Ministryof Education and Youth of the Czech Republic;
Danish Natural Science Research Council, the Carlsberg Founda- tion andtheDanish NationalResearchFoundation;The European ResearchCouncilundertheEuropeanCommunity’sSeventhFrame- work Programme; Helsinki Institute of Physics and the Academy
of Finland; French CNRS-IN2P3, the ‘Region Pays de Loire’, ‘Re- gion Alsace’, ‘Region Auvergne’ and CEA, France; German BMBF and the Helmholtz Association; General Secretariat for Research andTechnology,MinistryofDevelopment,Greece;HungarianOTKA andNationalOfficeforResearchandTechnology (NKTH); Depart- mentof Atomic Energy andDepartment ofScience andTechnol- ogyof the Government of India; Istituto Nazionale di Fisica Nu- cleare (INFN) and Centro Fermi – Museo Storico della Fisica e CentroStudi e Ricerche “Enrico Fermi”,Italy; MEXTGrant-in-Aid forSpeciallyPromotedResearch,Japan;JointInstitute forNuclear Research, Dubna; National Research Foundation of Korea (NRF);
CONACYT,DGAPA,México,ALFA-ECandtheEPLANETProgram(Eu- ropean Particle Physics Latin American Network) Stichting voor FundamenteelOnderzoekderMaterie(FOM)andtheNederlandse OrganisatievoorWetenschappelijkOnderzoek(NWO),Netherlands;
ResearchCouncil ofNorway(NFR); PolishMinistryofScience and HigherEducation;NationalScienceCentre,Poland;MinistryofNa- tionalEducation/Institute for Atomic Physics andCNCS-UEFISCDI, Romania;MinistryofEducationandScienceofRussianFederation, Russian Academy of Sciences, Russian Federal Agency of Atomic Energy, Russian Federal Agency for Science andInnovations and The Russian Foundation for Basic Research; Ministry of Educa- tion of Slovakia; Department of Science and Technology, South Africa; CIEMAT, EELA, Ministerio de Economía y Competitividad (MINECO) of Spain, Xunta de Galicia (Consellería de Educación), CEADEN, Cubaenergía, Cuba, and IAEA (International Atomic En- ergy Agency); Swedish Research Council (VR) and Knut & Alice WallenbergFoundation(KAW);UkraineMinistryofEducationand Science;UnitedKingdomScienceandTechnologyFacilitiesCouncil (STFC);TheUnitedStatesDepartmentofEnergy,theUnitedStates NationalScience Foundation, the State ofTexas, andthe State of Ohio.
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ALICECollaboration
