s
N N
=
5 TeV proton-lead
collisions
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Collaboration
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Articlehistory:
Received10December2015 Receivedinrevisedform27September 2016
Accepted30September2016 Availableonline6October2016 Editor: W.-D.Schlatter
Two-particle angular correlations are studied in proton-lead collisions at a nucleon–nucleon centre-of-mass energy of √sN N=5 TeV, collected with the LHCb detector at the LHC. The analysis is based on data recorded in two beam configurations, in which either the direction of the proton or that of the lead ion is analysed. The correlations are measured in the laboratory system as a function of relative pseudorapidity,
η
, and relative azimuthal angle, φ, for events in different classes of event activityand for different bins of particle transverse momentum. In high-activity events a long-range correlation on the near side, φ≈0, is observed in the pseudorapidity range 2.0 <
η
<4.9. This measurement of long-range correlations on the near side in proton-lead collisions extends previous observations into the forward region up toη
=4.9. The correlation increases with growing event activity and is found to be more pronounced in the direction of the lead beam. However, the correlation in the direction of the lead and proton beams are found to be compatible when comparing events with similar absolute activity in the direction analysed.©2016 The Author. Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). Funded by SCOAP3.
1. Introduction
Studies of two-particle angular correlations are an important experimentalmethodtoinvestigatethedynamicsofmulti-particle production in QCD and to probe collective effects arising in the dense environment of a high-energy collision. The highest parti-cledensitiesandmultiplicitiesreachedinproton–proton(pp)and proton-lead collisions (pPb) at the LHC are of a similar size to those in non-central nucleus–nucleus (AA) collisions. This moti-vates lookingfor signatureswhich were sofar mainly studiedin AAcollisions.
Two-particle correlations are conveniently described by two-dimensional (
η
,
φ
)-correlation functions. For pairs of prompt chargedparticles their separations inpseudorapidity,η
, andin theazimuthal angle,φ
, aremeasured in thelaboratory system. Structuresinthecorrelationfunctionareclassifiedintoshort-range (|
η
|
2) and long-range (|
η
|
2) effects. On the near-side (|φ|
≈
0) a short-range “jet peak” atη
≈
0 is the dominant structure, caused by the fact that in the fragmentation process thefinal-stateparticlesarecollimatedaroundtheinitialparton.To balancethemomentum,thepeakisaccompaniedbyalong-range structureontheawayside(|φ|
≈
π
)causedbyparticlesthatare oppositeinazimuthalangle.Due to the different momentum fractions carried by the col-lidingpartons and the resulting individual boosts, the away-side structureisnotrestrictedin
η
,butelongatedoveralargerange. Incomplexheavy-ioncollisions,theseshort- andlong-rangestruc-turesare modified asa resultofthestronglyinteractingmedium that isformeddepending onthe centralityofthecollision. Long-rangecorrelationsonthenear- andaway-sideareobserved,which are typically explained as being the result of a hydrodynamical flowofthedeconfinedmedium[1].Measurementsinveryrare pp
collisionsthathaveanextremelyhighparticlemultiplicityrevealed asimilarunexpectedlong-rangecorrelationonthenearside[2–4]. Thisstructure, oftenreferred toasthenear-side “ridge”, hasalso beenconfirmedinhigh-multiplicity pPb collisions[5–9],whereit wasfoundtobemuchmorepronouncedthanin pp collisions.
Thetheoreticalinterpretationofthemechanismresponsiblefor the ridge in pp and pPb is still underdiscussion. Various mod-els have been proposed such as gluon saturation in the frame-work of a colour-glass condensate [10–13] or the hydrodynamic evolutionofahighdensitypartonicmedium [14],multiparton in-teractions[15–17],jet-mediuminteractions [18,19],andcollective effects[20–24]inducedbytheformationandexpansionofa high-densitysystempossiblyproducedinthesecollisions.Analysesthat have seen the near-side ridge at the LHC have been performed in the central rapidity region, probing ranges up to
|
η
|
=
2.
5. In a recent analysis [9] larger pseudorapidities were also accessed in measurements of muon–hadron correlations betweenthe for-ward (2.
5<
|
η
|
<
4.
0) andthe central (|
η
|
<
1.
0) region.For the presentmeasurement theforwardacceptance oftheLHCb detec-tor,uniqueamongtheLHCexperiments,isusedtostudytheridge phenomenonin pPb collisions.Proton-lead collisionsareanalysed inthe rangeof2.
0<
η
<
4.
9 andin thedirectionsofthe protonhttp://dx.doi.org/10.1016/j.physletb.2016.09.064
0370-2693/©2016TheAuthor.PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense(http://creativecommons.org/licenses/by/4.0/).Fundedby SCOAP3.
andtheleadbeamsseparately.Confirmationofthe ridge correla-tionatlargepseudorapiditiesandcomparisonofitsmagnitudefor thetwobeamdirectionsprovidenewinputtothetheoretical un-derstandingoftheunderlyingmechanisms.
2. Experimentalsetup
The analysis isbased on data collected with the LHCb detec-tor during the proton-lead data-taking period in 2013. The LHC provided pPb collisions ata nucleon–nucleon centre-of-mass en-ergyof
√
sN N=
5 TeV,correspondingtoa protonbeamenergyof4 TeV and a lead beam energy of 1.58 TeV per nucleon. Due to thisasymmetric beamconfiguration,thereis a relativeboost be-tweentherapidityintheLHCblaboratoryframe,ylab,andy inthe
nucleon–nucleoncentre-of-massframe,correspondingtoashiftof 0
.
47 units.TheLHCb detector[25,26]is asingle-arm forward spectrome-tercoveringthepseudorapidity range2
<
η
<
5 inthelaboratory frame. Depending on the direction of the proton and the lead beam, two different configurations are distinguished. In the for-ward configurationtheprotonbeampointstopositiverapidity,into the LHCb spectrometer, and the recorded collisions are referred to as p+
Pb.The opposite backward configuration, in whichthe leadbeampointstopositiverapidity,isreferredtoasPb+
p.The measurement is performed in the LHCb laboratory frame, prob-ing rapidities y in the nucleon–nucleon centre-of-mass frame of 1.
5<
y<
4.
4 in the p+
Pb configuration and−
5.
4<
y<
−
2.
5 in the Pb+
p configuration. The data used forthis analysis cor-respondto an integrated luminosity of 0.
46 nb−1 inthe p+
Pb configurationand0.
30 nb−1 forthePb+
p configuration.The LHCb detector, designed for the study of particles con-taining b or c quarks, includes a high-precision tracking system consisting of a silicon-strip vertex detector (VELO) surrounding the interaction region, a large-area silicon-strip detector located upstream of a dipole magnet with a bending power of about 4 Tm,andthreestations ofsilicon-stripdetectorsandstraw drift tubes placed downstream of the magnet. The polarity of the dipole magnet was reversed once for each configuration to av-erage over small asymmetries in the detection of charged parti-cles.The trackingsystemprovides ameasurement ofmomentum of charged particles with a relative uncertainty that varies from 0.5% at low momentum to 1.0% at 200 GeV
/
c. Different types ofchargedhadronsaredistinguished usinginformationfromtwo ring-imagingCherenkovdetectors.Photons,electronsandhadrons are identified by a calorimetersystem consisting of scintillating-padandpreshowerdetectors,anelectromagneticcalorimeteranda hadroniccalorimeter.Muonsareidentifiedbya systemcomposed ofalternating layersofiron andmultiwireproportionalchambers. Theonlineeventselectionisperformedbyatrigger,whichconsists of a hardware stage, based on information from the calorimeter andmuon systems,followedbyasoftwarestage, whichappliesa fulleventreconstruction. Duringdatatakingof pPb collisions,an activity trigger in the hardware stage acceptednon-empty beam bunch crossings, and the softwarestage acceptedevents with at leastonereconstructedtrackintheVELO.3. Dataselectionandcorrections
MonteCarlosimulationsare usedto evaluatethe efficiencyof thefollowingselectionsandtoestimatetheremaining contamina-tionintheselectedtracksample.Proton-lead collisionsin p
+
Pb and Pb+
p configurations are simulated using the Hijing gen-erator [27] inversion 1.383bs.2. As a cross-check, proton–proton collisions at a centre-of-mass energy of 8 TeV aresimulated us-ing Pythia [28] in a special LHCb configuration [29] and withahighaverageinteractionrate(largepile-up)toreproducethelarger particle multiplicity in proton-lead collisions. Particle decays are simulatedby EvtGen[30].Theinteractionofthe generated parti-cleswiththedetector,anditsresponse,areimplementedusingthe Geant4toolkit[31]asdescribedinRef.[32].
Themeasurementsarebasedonproton-leadcollisionsthatare dominated by single interactions; fewer than 2% of the bunch crossingshavemorethanoneinteraction.Eacheventisrequiredto haveexactlyone reconstructedprimary vertexcontainingatleast five tracks. Beam-related background interactions are suppressed byrequiringthepositionofthereconstructedprimaryvertextobe within
±
3 standarddeviationsaroundthemeaninteractionpoint, separately foreach coordinate.The meanvalue andthe widthof this luminous region are determined separately from a Gaussian fit to the distribution of reconstructed primary vertices of each datasample. Dependingonthepolarityofthemagneticfieldand theresultingbeamoptics,thesizeofthestandarddeviationalong the beam axisis approximately 40 mm or 60 mm,while in the transverse direction it is around 30 μm. While pPb interactionsare mostlikely producedinthisregion,beam-relatedbackground extends furtheralongthe beamline.Beam gaseventsor interac-tions withdetectormaterial can produce a very highnumber of particles; however, insuch cases the total energydeposit in the calorimeter is much smaller than that of typical pPb collisions.
Events with too small a ratio of the number of clusters in the electromagnetic calorimeterto that inthe VELO are rejected; in-dividuallowerboundsaredefinedforcollisions inthe p
+
Pb and Pb+
p configurationusingsimulation.The angular correlationsare determined for charged particles that are directly produced in the pPb interaction. The measure-mentisbasedontrackstraversingthefulltrackingsystem,which restricts charged particles in pseudorapidity to 2
.
0<
η
<
4.
9. In addition, particles are required to have a transverse momentumpT
>
0.
15 GeV/
c andatotalmomentump>
2 GeV/
c.Reconstruc-tion artefacts, such as fake tracks,are suppressed using a multi-variate classifier.The remaining average fractionoffake tracks is oftheorderof7% and12% inthe p
+
Pb andPb+
p samples, re-spectively. The probability ofreconstructing fake tracks increases with thenumber of hitsin thetracking detectors.Thus, the dif-ference between the data samples is due to the higher average particleandhitmultiplicitythat ispresentinthedirectionofthe leadremnant.ToselectprimarytracksoriginatingdirectlyfromthepPb collisionthe impactparameter ofeach trackwithrespect to the reconstructed primary vertexmust not exceed 1.2 mm, after whichthefractionofremainingtracksfromsecondaryparticlesis estimatedtobelessthan3
.
5%.Theinefficiencyinfindingchargedparticlesarisesfromtwo ef-fects: limited detector acceptance in the range of 2
.
0<
η
<
4.
9, andlimitations ofthe trackreconstruction. Forparticles fulfilling thekinematicrequirements,theacceptancedescribesthefraction that reach the end of the downstream tracking stations and is about 70% on average. In contrast, the track reconstruction ef-ficiency varies from 96% for low-multiplicity events to 60% for eventswiththehighestmeasuredmultiplicity.Afterapplyingtheselectionrequirements,theremaining proba-bilitiesofselectingfaketracks,
P
fake,andsecondaryparticles,P
sec,aswellastheefficienciesrelatedtothedetectoracceptance,
acc,
and the track reconstruction,
tr, are estimated in simulation as
a function of the angularvariables
η
andφ
, the transverse mo-mentum pT, and the hit-multiplicity in the VELO,N
VELOhit . Eachreconstructedtrackisassignedaweight,
ω
,thataccountsforthese effects:Fig. 1. Hit-multiplicitydistributionintheVELOforselectedeventsoftheminimum-biassamplesinthe(left)p+Pb and(right)Pb+p configurations.Theactivityclasses aredefinedasfractionsofthefulldistribution,asindicatedbycolours(shades).The0–3%classisasub-sampleofthe0–10%class.(Forinterpretationofthereferencesto colourinthisfigurelegend,thereaderisreferredtothewebversionofthisarticle.)
Table 1
Relativeevent-activityclassesdefined bytheVELO-hit multiplicity,NVELOhit ,ofan
event.TheclassesaredefinedasfractionsoftheNhit
VELOdistributionfor
minimum-biasrecordedeventsinthep+Pb orPb+p configuration.The0–3%classisa sub-sampleofthe0–10%class.Forillustrationpurposestheaveragenumber,
NchMC,of
promptchargedparticleswithp>2 GeV/c,pT>0.15 GeV/c and2.0<η<4.9 is
listedforeventssimulatedwiththeHijingeventgenerator.Statisticaluncertainties arenegligible.
Relative activity class p+Pb Pb+p
RangeNhit
VELO NchMC RangeNVELOhit NchMC
50–100% very low 0–1200 18.9 0–1350 29.2
30–50% low 1200–1700 30.0 1350–2000 47.4
10–30% medium 1700–2400 42.8 2000–3000 70.9
0–10% high 2400–max 63.6 3000–max 106.7
0–3% very high 3000–max 73.7 3800–max 126.4
4. Activityclassesanddatasamples
Two-particle correlations show a strong dependence on the number of particles produced within a collision. The hit multi-plicityin the VELO is proportional to this global eventproperty. Withitscoverageinpseudorapidityrangingfrom1
.
9<
η
<
4.
9 in theforwarddirectionand−
2.
5<
η
<
−
2.
0 inthebackward direc-tion,theVELOcanprobethetotalnumberofchargedparticlesper eventmorecomprehensivelythanothersub-detectorsofLHCb.Theanalysispresentedinthispaperisbasedonasubsetofthe totaldata setrecorded during the2013 pPb runningperiod.The
p
+
Pb and Pb+
p minimum bias sampleseach consist of about 1.
1×
108 eventswhichare randomlyselectedfromtheabout10 timeslargerfull sample.Thehigh-multiplicitysamplescontainall recordedeventswithatleast2200 hits intheVELO andamount toabout1.
1×
108eventsinPb+
p and1.
3×
108 eventsinPb+
pcollisions.
Five event-activity classes are defined as fractions of the hit-multiplicity distributions of the minimum-bias samples, as indi-catedinFig. 1.SincecollisionsrecordedinthePb
+
p configurationreach larger hit-multiplicities compared to those in the p
+
Pb configuration,the relative classesare definedseparately for each configuration.The 50–100%class contains approximatelythe 50% ofeventswiththelowesteventactivities,followedbythe30–50% and10–30% classesrepresentingmedium-activityevents,andthe 0–10%and0–3% classesofhigh-activity events.Theranges defin-ingtheactivityclassesarelistedinTable 1.Foreachclass,average numbersofchargedparticles, NchMC,are quotedforillustration,basedonthe Hijing eventgenerator.
Thelong-rangecorrelationsinthedirectionofthefragmenting proton(p
+
Pb configuration)andthe directionof the fragment-ingleadion(Pb+
p configuration)arecomparedforclassesofthe same absoluteactivity in the pseudorapidity range of 2.
0<
η
<
Table 2
Commonabsoluteactivitybinsfor the p
+
Pb andPb+p samples.Theactivity of p+
Pb eventsis scaledtomatchthesame activityrangesofPb+p events,asexplainedinthetext.Forillustrationpurposestheaveragenumber,
NchMC,of
promptchargedparticleswith p>2 GeV/c,pT>0.15 GeV/c and2.0<η<4.9 is
listedforeventssimulatedwiththeHijingeventgenerator.Theuncertaintiesare duetothescalingfactorof0.77±0.08.Statisticaluncertaintiesarenegligible.
Commonabsolute activitybin Nhit VELO-range inPb+p scale p+Pb Pb+p NchMC NchMC Bin I 2200–2400 62.8±6.6 64.4 Bin II 2400–2600 68.4±7.1 67.0 Bin III 2600–2800 73.7±7.6 76.4 Bin IV 2800–3000 79.2±7.9 82.4 Bin V 3000–3500 86.7±8.2 92.9
4
.
9.Here aproperassignmentofequivalent activityclassesneeds to take into account the fact that the VELO acceptance is larger thanthepseudorapidityintervalofinterest.Assumingalinear re-lationbetweenthetotalnumberofVELOhitsandthenumberof tracks inthe range 2.
0<
η
<
4.
9, one findsthat N VELO hitsin thePb+
p configurationcorrespondtoN/(
0.
77±
0.
08)
VELOhits inthe p+
Pb case.The uncertaintyinthescalingfactoraccounts for deviations fromperfect linearity in the data that are not re-producedinthesimulation,andispropagatedintothesystematic uncertaintiesoftheresults.Fivecommonabsoluteactivityclasses, labelledI–V,aredefinedinthehigh-activityregionandarelistedin Table 2 with the corresponding average numbers of charged
particles fromsimulation.Thequoted uncertainties inthe p
+
Pb samplearerelatedtothesystematicuncertaintyofthescaling fac-tor.Theanalysisisrepeatedusinganalternativeevent-activity clas-sification,basedonthemultiplicityofselectedtracksintherange 2
.
0<
η
<
4.
9.Inanalogytothenominalapproachusingthe VELO-hitmultiplicity,thesamefractionsofthefulldistributionareused to define relative activity classes for both beam configurations. Similarly, five common activity bins for the p+
Pb and Pb+
psamples are defined in the intermediate to high-activity classes. The results are found to be independent of thedefinition of the activityclasses.
5. Analysismethod
Two-particle correlations are measured separately for events in each activity class. The track sample containing the selected candidates of primary charged particles is divided into three pT
intervals: 0
.
15–1.
0 GeV/
c,1.
0–2.
0 GeV/
c and 2.
0–3.
0 GeV/
c.For each event, all candidates within a given pT interval areidenti-fiedastrigger particles.Byselectingatriggerparticleallremaining candidateswithin thesameintervalcomposethegroup of
associ-Fig. 2. Two-particlecorrelationfunctionsforeventsrecordedinthep+Pb configuration,showingthe(left)lowand(right)highevent-activityclasses.Theanalysedpairsof promptchargedparticlesareselectedinapTrangeof1–2 GeV/c.Thenear-sidepeakaroundη= φ =0 istruncatedinthehistograms.
ated particles.Particle pairs are formed by combiningevery trig-ger particle with each associated particle. Due to the symmetry aroundtheorigin,differencesinazimuthalangle
φ
aretakenin the range[
0,
π
]
and asabsolute values inη
. For visualisation purposesplotsaresymmetrized.Thetwo-particlecorrelation func-tion is composed ofa signal part S(
η
,
φ)
, a background partB
(
η
,
φ)
,anda normalizationfactor B(
0,
0)
.The totalfunction isdefinedastheassociatedyieldpertriggerparticle,givenby1 Ntrig d2Npair d
η
dφ
=
S(
η
, φ)
B(
η
, φ)
×
B(
0,
0),
(2)where Npair is thenumber ofparticle pairsfound in a (
η
,
φ
)bin.ThenumberoftriggerparticleswithinagivenpTintervaland
activityclassisdenotedbyNtrig.ThesignaldistributionS
(
η
,
φ)
describestheassociatedyieldpertriggerparticleforparticlepairs,
Nsame,formedfromthesameevent,andisdefinedas
S
(
η
, φ)
=
1 Ntrigd2Nsame
d
η
dφ
.
(3)FollowingtheapproachinRef.[6],thesumovertheeventsis per-formed separately forNtrig andford2Nsame
/
dη
dφ
beforetheratioiscalculated.The backgrounddistribution B
(
η
,
φ)
is de-finedforparticlepairsofmixedevents,B
(
η
, φ)
=
d 2Nmix
d
η
dφ
,
(4)anddescribes the yield of uncorrelatedparticles. The Nmix pairs
areconstructedbycombiningalltriggerparticlesofaneventwith theassociatedparticlesoffivedifferentrandomeventsinthesame activity class, whose vertex positions in the beam direction are within 2 cm ofthe original event.As a result, effects duetothe detectoroccupancy, acceptanceandmaterialare accountedforby dividingthesignalby thebackgrounddistribution,wherethe lat-ter is normalised to unity around the origin. The factor B
(
0,
0)
describesthe associated yield forparticles of a pairtravelling in approximatelythe samedirectionandthus havingthemaximum pairacceptance.All trigger and associated particles in the signal and back-ground distributions are weighted with the correction factors
ω
described inSection3.Furthermore,alternative correctionfactors determinedfromthelargepile-uppp simulationusingPythiaare appliedto evaluatesystematicuncertainties. Theresulting associ-atedcorrelation yields agree within 3% withthenominal results. To estimate the influence of the track selection, the correction factors are also determined with a maximum impact parameter relaxedtotwicethenominalvalue,andthevalueofthe multivari-ate classifier used to suppressfake tracks is varied by
±
5%. Theresulting different correction factors are applied to the measure-ments whichare thencomparedtothenominalcorrectedresults. The differencedueto thedifferentpromptselection isnegligible, whilethealternativefaketracksuppressionresultsinamaximum variationof3%.Typical variationsaremuchsmaller.Theeffecton thefinalresults,obtainedaftersubtractingaglobaloffset,is negli-gible.
6. Results
Two-particle correlation functions for events recorded in the
p
+
Pb configurationarepresentedinFig. 2.Thecorrelationfor par-ticleswith1<
pT<
2 GeV/
c isshownforeventsofthe50–100%and0–3%class,representinglowandvery-higheventactivities, re-spectively.Both histogramsaredominatedbythejetpeak around
η
≈ φ ≈
0 which is due to correlations of particles originat-ing fromthesamejet-like objectsandthusbeingboostedclosely together.Forbettervisualisation ofadditionalstructures,inall 2D-histogramsthejetpeakistruncated.Thesecondprominentfeature isvisibleontheaway-side(φ
≈
π
)overalongrangeinη
and combinesjetand(potential)ridgecontributions.Theeventsample with very high eventactivity (Fig. 2, right) shows an additional, lesspronounced,long-rangestructurecentredatφ
=
0,whichis not presentin the corresponding low-activity sample. The struc-ture,oftenreferredtoasthenear-sideridge,iselongatedoverthe fullmeasuredη
rangeof2.
9 units.Thisobservationoftheridge forparticles producedin proton-leadcollisions atforward rapidi-ties,2.
0<
η
<
4.
9,extendspreviousmeasurementsattheLHC.Two-particlecorrelationsforeventsrecordedinthePb
+
pcon-figuration are shown in Fig. 3, for particle pairs with 1
<
pT<
2 GeV
/
c. The 50–100% and 0–3% activity classes in the Pb+
psample exhibitthesamecorrelationstructuresasthe correspond-ing classesinthe p
+
Pb sample.Whiletheshapeandmagnitude of the jet peak and the away-side ridge appear to be of similar sizesinbothbeamconfigurations,thenear-sideridgeismore pro-nouncedforparticlesinthedirectionoftheleadbeam.Forthe3% ofeventswiththehighesteventactivity,thenear-sideridgeinthe Pb+
p sample ismuch moreprominent thanthat in the p+
Pb sample.Similar behaviour is found whenanalysing particlepairs with larger transverse momenta in the interval 2
<
pT<
3 GeV/
c. InFig. 4the correlationfunctionsinthis pT rangearepresentedfor
the 3%highest-activity eventsrecordedinthe p
+
Pb andPb+
pconfigurations. The near-side ridge is present in both samples; howeverin the p
+
Pb sampleit isonly marginally visiblewhile in the Pb+
p samplea stronglypronounced ridge is found. The short-range jetpeak inthishigher pT intervalis morecollimatedFig. 3. Two-particlecorrelationfunctionsforeventsrecordedinthePb+p configuration,showingthe(left)lowand(right)highevent-activityclasses.Theanalysedpairsof promptchargedparticlesareselectedinapTrangeof1–2 GeV/c.Thenear-sidepeakaround(η= φ =0)istruncatedinthehistograms.
Fig. 4. Two-particlecorrelationfunctionsforeventsrecordedinthep+Pb (left)andPb+p (right)configurations,showingthe0–3%event-activityclass.Theanalysedpairs ofpromptchargedparticlesareselectedinapTrangeof2–3 GeV/c.Thenear-sidepeakaround(η= φ =0)istruncatedineachhistogram.
totalmomentumoftheparticles.Asaresult,thenear-sideridgeis visibletowards
|
η
|
valuesslightlybelow2.
0 withoutbeing cov-eredbythejetpeak.Inorder to studythe evolution ofthe long-rangecorrelations onthenearandaway sidesin moredetail,one-dimensional pro-jectionsofthecorrelationfunctionon
φ
arecalculated,Y
(φ)
≡
1 Ntrig dNpair dφ
=
1η
b−
η
a ηb ηa 1 Ntrig d2Npair dη
dφ
dη
.
(5) The short-range correlations, e.g. of the jet peak, are excluded by averaging the two-dimensional yield over the interval fromη
a=
2.
0 toη
b=
2.
9.Sincerandomparticlecombinationspro-ducea flat pedestalin theyield, thecorrelation structuresof in-terest are extracted by using the zero-yield-at-minimum (ZYAM) method[33,34].Byfittingasecond-orderpolynomialtoY
(φ)
in therange0.
1< φ <
2.
0,theoffsetisestimatedastheminimum of the polynomial. This value, further denoted as CZYAM, issub-tractedfrom Y
(φ)
toshiftitsminimumtobe atzeroyield.The uncertaintieson CZYAM duetothelimitedsamplesizeandthefitrangearebelow0
.
002 forallindividualmeasurements.Thesubtractedone-dimensional yieldsforthe p
+
Pb (full cir-cles)and Pb+
p (opencircles) data samplesare shownin Fig. 5 forall activity classesand pT intervals. The correlation increaseswitheventactivity,butdecreases towardshigher pT wherefewer
particlesare found.Since moreparticles are emittedinto the ac-ceptance of the detectorin the Pb
+
p comparedto the p+
Pb configuration,alargeroffsetisobserved,asindicatedbytheZYAMconstants.AlldistributionsinFig. 5showamaximumat
φ
=
π
, marking the centre of the away-side ridge, which balances the momentumofthenear-side(the jetpeakisexcluded inthis rep-resentation). Thelower activityclasses,50–100% and30–50%, do nothaveacorrespondingmaximumatφ
=
0.The30–50%event class of thePb+
p sampleshows a first changein shape ofthe distributionatφ
=
0.Thepicturechangeswhenprobingthe in-termediate activityclass10–30%.Inall pT intervalsofthe Pb+
psampletheemergenceofthenear-sideridgewithasecond maxi-mumat
φ
=
0 isclearlyvisible.Inthe p+
Pb sampletheevent activityisstillnothighenoughtoformaclearnear-sidestructure. Inthehigh-activityclasses,0–10%and0–3%,thenear-sideridgeis strongly pronounced in the Pb+
p sample inall pT intervals. Inthe p
+
Pb samplethenear-sidestructureislessdistinct;however the1<
pT<
2 GeV/
c intervalshowsaclearnear-sideridge.Aqualitativelysimilarbehaviourisseenintheforward-central correlationsstudied by theALICEexperiment[9],witha forward muon trigger and central associated particles. Here also a clear ridge effect is observed, which grows with increasing event ac-tivity,andindicationsare seenthat itis morepronounced inthe hemisphereofthePbnucleus.
Comparison of the ZYAM-subtracted yields shows that the away-side ridge is always more prominent than the near-side ridge.Theridgeontheaway-sideisonlyweaklydependenton pT,
while the near-side ridge appears most pronounced in the bin 1
<
pT<
2 GeV/
c.Comparing p+
Pb and Pb+
p,one finds thatespeciallyforhigheventactivitiesthenear-sideridgeismore pro-nouncedinthePbhemisphere.
Study of the one-dimensional yields within a pT interval for
ap-Fig. 5. One-dimensionalcorrelationyieldasafunctionofφobtainedfromthe ZYAM-methodbyaveragingover 2.0< η<2.9.The subtractedyieldsare pre-sented for √sN N=5 TeV proton-leadcollisions recorded in p
+
Pb (full greencircles)andPb+p (openbluecircles)configurations.TheZYAMconstantisgiven ineachpanel.Eventclassesarecomparedforlowtovery-highactivitiesfromtop tobottom,anddifferentintervalsofincreasingpTfromlefttoright.Onlystatistical
uncertaintiesareshown.Errorbarsareoftensmallerthanthemarkers.(For inter-pretationofthereferencestocolourinthisfigurelegend,thereaderisreferredto thewebversionofthisarticle.)
proximately unchanged, while the near side starts to form the additionalridgewhenacertaineventactivityisreached.This turn-on,however,appearstobeatdifferentactivitiesinthep
+
Pb and Pb+
p configurations.Thesame qualitativeobservationsin thevariousanalysisbins, including the emergence of the near-side ridge, are found when using the track-based approach for the definition of the activity classesasasystematiccheck.Thetotalcorrelationyieldvariesby onlya few percent,andthe maximumvariation doesnot exceed 10% inthelow-pT range.Theemergenceofthenear-sideridge in
theZYAM-subtractedyieldisunaffectedbythechangeoftheevent activitydefinition.
Further systematic effects related to the event selection are evaluatedbyincludingeventswithmultiplereconstructedprimary vertices.Thechangeofthefinal correlation yieldisnegligible.As another cross-check, data recorded in magnet up and down po-laritiesareanalysedseparately.Theresultsareingoodagreement witheachother.
Toinvestigatetheactivitydependenceofthelong-range corre-lationsinthe p
+
Pb andPb+
p samplesinmoredetail,common bins in absolute activity for both samples are studied. For thispurpose, events of both samples are probed in which a similar number of charged particles are emitted into the forward direc-tion.Eventsofbothsamplesaregroupedintofivenarrowactivity bins, asdefinedinTable 2.Fig. 6 comparesthe ZYAM-subtracted two-particle correlation yields in therange 1
<
pT<
2 GeV/
c,inwhich the near-side ridge is most pronounced. The uncertainty bands representthe systematic uncertaintyon the scaling factor, which translates the activity of the p
+
Pb configurationto that ofthe Pb+
p configuration.For p+
Pb andPb+
p events ofthe sameactivityin theforwardregion,theobservedlong-range cor-relations become compatible within the uncertainties, except for binIinwhichtheaway-side yieldin p+
Pb isstillslightlymore pronounced. Thenear-sidecorrelation inthebeam(p) andtarget (Pb) fragmentationhemispheresshowsaconsistent increasewith increasingeventactivity.7. Summaryandconclusions
Two-particleangularcorrelationsbetweenpromptcharged par-ticlesproducedinpPb collisionsat
√
sN N=
5 TeV havebeenmea-sured for the first time in the forward region, using the LHCb detector. The angular correlations are studied in the laboratory frameinthepseudorapidityrange2
.
0<
η
<
4.
9 overthefullrange of azimuthal angles, probing particle pairs in different commonpT intervals. With the asymmetric detector layout, the analysis
is performedseparately for the p
+
Pb and Pb+
p beam config-urations, which probe rapidities in the nucleon–nucleon centre-of-mass frame of 1.
5<
y<
4.
4 and−
5.
4<
y<
−
2.
5, respec-tively. The strength ofthe near-side ridge observed in the back-ward(Pb+
p configuration)regionappearstobeofsimilarsizeto that found in theforward(p+
Pb configuration)region. The rel-ative shift of aboutone unit in nucleon–nucleon centre-of-mass rapidity betweenthe twoconfigurations produces nosizeable ef-fect on the near-side ridge within the accuracy of the measure-ment.Foreventswithhigheventactivityalong-rangecorrelation on the near side (the ridge) is observed in both configurations. While thecorrelationstructureontheaway sideshrinkswith in-creasing pT,thenear-side ridgeis mostpronouncedin therange1
<
pT<
2 GeV/
c. The observation of the ridge in the forwardregion extends previous LHC measurements, which show similar qualitative features. Furthermore, the correlation dependence on the eventactivity is investigated for relative and absolute activ-ityranges.Thecorrelation structuresonthenearsideandonthe away side both grow stronger withincreasing eventactivity. For identicalabsoluteactivityrangesinthep
+
Pb andPb+
pconfig-urations theobservedlong-rangecorrelationsarecompatiblewith eachother.
Acknowledgements
We express our gratitude to our colleagues in the CERN ac-celerator departments for the excellent performance of the LHC. We thank the technical andadministrative staff at the LHCb in-stitutes. We acknowledge support from CERN and from the na-tional agencies: CAPES, CNPq, FAPERJ and FINEP (Brazil); NSFC (China); CNRS/IN2P3 (France); BMBF, DFG and MPG (Germany); INFN (Italy); FOMandNWO(TheNetherlands);MNiSW andNCN (Poland);MEN/IFA(Romania); MinESandFANO(Russia);MINECO (Spain);SNSFandSER(Switzerland);NASU(Ukraine);STFC(United Kingdom); NSF (USA). We acknowledge the computingresources that are provided by CERN, IN2P3 (France), KIT and DESY (Ger-many), INFN (Italy), SURF (The Netherlands), PIC (Spain), GridPP (United Kingdom), RRCKI (Russia), CSCS (Switzerland), IFIN-HH (Romania), CBPF (Brazil), PL-GRID (Poland) and OSC (USA). We areindebtedtothecommunitiesbehindthemultipleopensource
thep+Pb samplearescaledtoagreewiththehit-multiplicitiesofthePb+p sample.Theuncertaintybandrepresentsthesystematiclimitationofthescalingprocedure.The errorbarsrepresentthestatisticaluncertainty.(Forinterpretationofthereferencestocolourinthisfigurelegend,thereaderisreferredtothewebversionofthisarticle.)
softwarepackagesonwhich wedepend.Weare alsothankfulfor the computing resources and the access to software R&D tools provided by Yandex LLC (Russia). Individual groups or members havereceived supportfromAvHFoundation(Germany),EPLANET, MarieSkłodowska-Curie Actions andERC (EuropeanUnion), Con-seil Général de Haute-Savoie, Labex ENIGMASS and OCEVU, Ré-gionAuvergne(France),RFBR(Russia),GVA,XuntaGalandGENCAT (Spain),TheRoyalSocietyandRoyalCommissionfortheExhibition of1851(UnitedKingdom).
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LHCbCollaboration
