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Articlehistory:
Received24October2016
Receivedinrevisedform12April2017 Accepted24May2017
Availableonline29May2017 Editor:L.Rolandi
Electronsfromheavy-flavourhadrondecays(charmandbeauty)weremeasuredwiththeALICEdetector in Pb–Pb collisions at acentre-of-mass of energy √sNN=2.76 TeV. The transverse momentum(pT)
differentialproductionyieldsatmid-rapiditywereusedtocalculatethenuclearmodificationfactorRAA
intheinterval3<pT<18 GeV/c.The RAA showsastrong suppressioncomparedtobinaryscalingof
ppcollisionsatthesameenergy(uptoafactorof4)inthe10%mostcentralPb–Pb collisions.Thereis acentralitytrendofsuppression,andaweaker suppression(downtoafactorof2)insemi-peripheral (50–80%)collisionsisobserved.ThesuppressionofelectronsinthisbroadpTintervalindicatesthatboth
charmandbeautyquarksloseenergywhentheytraversethehotmediumformedinPb–Pbcollisionsat LHC.
©2017TheAuthor.PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense (http://creativecommons.org/licenses/by/4.0/).FundedbySCOAP3.
1. Introduction
High-energyheavy-ioncollisions providea uniqueopportunity tostudy theproperties ofthe hot anddense strongly-interacting systemcomposed ofdeconfined quarks andgluons – the quark-gluonplasma(QGP).TheformationofaQGPispredictedbylattice QCDcalculations[1–4].Acrossovertransitionfromhadronic mat-teratzerobaryochemical potentialisexpectedtotakeplaceonce thesystemtemperaturereachesvaluesaboveT
≈
155MeVand/or theenergy densityaboveε
≈
0.5 GeV/fm3 [5,6].To characterise thephysical propertiesof thisshort-lived QGP(lifetime of about 10 fm/c[7])experimentalstudiesuseauto-generatedprobes,such as high-energy partons created early in the collision, thermally emittedphotons, andparticle correlationssensitiveto the collec-tiveexpansionandthedynamicsofthesystem.Inparticular,the interactionofhigh-pT partonswiththe QGP, leadingto modifications oftheinternal jet structure (jet quench-ing),wasfirstproposedin[8]andisstudiedasasensitiveprobeof themediumproperties[9].Jetquenchingwasfirstobserved exper-imentallyviathestrongsuppressionofhightransversemomentum particleproductioninheavy-ioncollisionsattheRelativisticHeavy IonCollider(RHIC) [10–13].Similar observationshave sincebeen reportedby the Large HadronCollider (LHC) experiments at col-lision energies larger by one order of magnitude with hadrons
[14–16]andextendedtofullyreconstructedjets[17–19].
Heavyflavours(charmandbeauty)aresensitivetoolsfor stud-ies of the in-medium parton energy loss, providing qualitatively
E-mailaddress:alice-publications@cern.ch.
different sensitivity to the medium properties as compared to gluonorlight-quarkinducedjets[20,21].Theproductionofheavy quarksiswellunderstoodintermsoftheperturbativeQCD(pQCD) formalism. Good agreement between the theoretical calculations and measurements of various heavy-flavour particle production cross sections in hadronic collisions is established over a wide rangeofcentre-of-mass energies fromRHIC [22–24],through the Tevatron[25–27]totheLHC[28–32].
Interactions between partons and the medium can occur via both inelastic (radiative parton energy loss) [33–35] and elastic (collisionalenergyloss)[36–39]processesthatdependonthe par-tontype andthepropertiesofthemedium. Theinteractionswith the medium modify the radiation pattern of the shower by in-ducing longitudinal drag (and associated longitudinal diffusion), transversediffusion,andenhancedsplittingofthepropagating par-tons.Onaverage,foragivenpartonenergy,gluonsareexpectedto losemoreenergythanquarksduetothedifferenceintheCasimir colour factor[40] controllingthe strength of thecoupling to the coloured medium. Moreover, the energy loss is predicted to de-pend onthe mass ofthe quark [41–45]. Inparticular, forquarks withenergies comparableto their massthe radiativeenergy loss isexpectedto besmaller thanformorehighly-energetic partons. Consequentlytherelativeroleofelasticprocessesforheavyquarks is enhanced andthe heavy quarks of moderate energies are ex-pected to be moresensitive, ascompared to light quarks, to the longitudinal drag and diffusion coefficients[39] that are propor-tional to the inverse of the mass of the parton. Moreover, as a result of multiple elastic collisions and possible in-medium res-onant interactions within the hot matter, low-momentum heavy quarkscouldreachthermalisationinthemedium[46].
http://dx.doi.org/10.1016/j.physletb.2017.05.060
0370-2693/©2017TheAuthor.PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense(http://creativecommons.org/licenses/by/4.0/).Fundedby SCOAP3.
The predicted hierarchy of energy loss
E
g> E
light-q>
E
charm> E
beauty [41] motivated experimental studies of the suppression patterns of heavy-flavour hadrons and their decay products.Uptonowthein-mediumenergylossofheavy flavours at the LHC has been studied via open charm measurements of prompt D mesons [47,48], heavy-flavour decay muon measure-ments at forward rapidity [31], non-prompt J/ψ
, and measure-ments ofb-jet production[49].At RHIC the nuclearmodification of heavy-flavour production has been studied via its semilep-tonic decays [50,51] and via measurements of D mesons [52]. The measurement that we report covers the electron (electron andpositron) pT interval 3–18 GeV/c,probing athigh pT the in-medium interaction of b quarks with momentum of a few tens of GeV/c.The modifications of particle yields are quantified using the nuclear modificationfactor RAA. It isconstructed by dividingthe
pT-differentialyieldinnucleus–nucleus(AA)collisions,dNAA
/
dpT, by thecrosssection inpp collisions, dσpp/
dpT, scaledby the av-erage of the nuclear overlap function TAA for the considered centralityclass[53]RAA
=
dNAA
/
dpT TAAdσ
pp/
dpT.
(1)Byconstruction, RAA isunitywhennonucleareffectsarepresent.
RAA values consistent withunity havebeen measured forcolour neutralparticles (direct photons, W and Z bosons) inPb–Pb col-lisions at
√
sNN=
2.
76 TeV [54–58] as well as for charged par-ticlesand heavy-flavourproductionin p–Pb collisionsat√
sNN=
5.
02 TeV[59–61].This paper reports on the suppression (RAA
<
1) of electrons fromsemi-leptonicdecaysofcharmandbeautyhadronsmeasured at high-transverse momentum (pT>
3 GeV/c)
at mid-rapidity (|
y|
<
0.
6) inPb–Pb collisions at√
sNN=
2.
76 TeV using the AL-ICEdetector.Thesuppressionismeasuredasafunctionofcollision centralityandpT intheinterval3<
pT<
18 GeV/c.Thenexttwo sectionsofthepaperdefinetheexperimentalsetupandthe analy-sisdetailstogetherwiththediscussionofsystematicuncertainties on the measured electron spectra. The electron yields measured in bins of centrality defined as fractions of the total hadronic cross-section of Pb–Pb collisions are then presented. Finally the pT-differentialRAAinthe0–10%,10–20%,20–30%,30–40%,40–50% and50–80%centralityclassesarepresentedandcomparedtothe measurementof muonsfromheavy-flavour hadrondecaysat for-wardrapidities[31]aswellastocalculationsofin-mediumenergy lossofheavyquarks.2. Apparatus,datasampleandanalysis
2.1. Detectorsetup
The measurements were carriedout using theALICE detector at the LHC [62] with Pb-ion beams at a centre-of-mass energy of
√
sNN=
2.
76 TeV. A complete description of the experimen-tal setup and theperformance ofdetectors can be found in[63, 64]. Particle track reconstruction and particle identification were performedbased on informationfromthe Inner Tracking System (ITS), the Time Projection Chamber (TPC), and the Electromag-neticCalorimeter(EMCal),locatedinsideasolenoidmagnet,which generates a 0.
5 T field parallel to the beamdirection. The event centrality determination was based on the signals from the V0 detector, which is a set of scintillator arrays. Moreover, the V0 detectortogether withtheneutronZero-DegreeCalorimeters(ZN) wasusedfortriggeringandbeambackgroundrejection.TheITSiscomposedofsixcylindricallayers:twoSiliconPixel Detectors(SPD),twoSiliconDriftDetectors(SDD),andtwoSilicon
StripDetectors(SSD).TheSPDbarrelconsistsofstavesdistributed intwolayersaroundthebeampipeatradiusof3.9cmand7.6 cm, covering a length of 28.2 cm in the z direction. The outermost layeroftheITS(SSD)islocated43cmfromthebeamaxis.
The TPC witha radial extent of 85–247 cm, enables charged particletrackingbeyondtheITSandparticleidentificationviathe measurementoftheparticlespecific ionisationenergylosswithin theNe–CO2 gasmixture.TheTPCprovidesupto159independent spacepointsperparticletrack.
ChargedparticletracksarereconstructedintheTPCfrom pT
≈
0.
15 GeV/c,|
η
|
<
0.
9 andfullazimuth.UsingtheITSandTPCspace points the particlemomentum is determinedfromthe combined trackfitwitharesolutionofabout1%at1 GeV/c and
about3%at 10 GeV/c
[64].The front face of the EMCal is positioned at about 450 cm fromthebeamaxisintheradial directionandthedetectoris ap-proximately 110 cmdeep.The detectorisalayeredPb-scintillator samplingcalorimetercovering107degreesinazimuthanda pseu-dorapidityregion
|
η
|
<
0.
7.Thecalorimeterdesignincorporateson average a moderateactive volume densitythat results ina com-pactdetectorofabout20radiationlengths.The V0 detectorconsists of two arrays of 32 scintillator tiles placedatdistances z
=
3.
4 m(V0-A)andz= −
0.
9 m(V0-C)from the nominalinteraction point. V0-A and V0-C cover the full az-imuth, andpseudorapidity intervalsof 2.
8<
η
<
5.
1 and−
3.
7<
η
<
−
1.
7, respectively. The detector was used for triggering and eventcentralitydetermination.TheZNaretwoidenticalsetsofforwardhadroniccalorimeters whicharelocatedonbothsidesrelativetotheinteractionpointat z
≈
114 m.2.2. Eventsampleandtrigger
The data sample used forthis analysiswas collected in 2011 anditconsistsof14
·
106 mostcentralcollisions(0–10%)and13·
106 semi-central collisions (10–50%) recorded witha minimum-bias trigger, and 3.
2·
106 collisions (0–90%) triggered with the EMCal. The minimum-bias trigger was a coincidence of signals from the V0-A and V0-C detectors. The timing resolution of the V0systemisbetterthan1nsanditprovidesanefficient discrim-ination ofthe beam–beamcollisions fromthe backgroundevents produced upstream of the experiment. Additional suppression of thebackgroundwasprovidedbytiminginformationfromtheZDC. The minimum-bias triggerincluded two trigger classesfor most-centralandsemi-centralcollisions, whichwere selectedonlineby applyingthresholdsontheV0signalamplitudes.TheEMCalprovidestwohierarchically-configuredtriggerlevels (Level-0andLevel-1).Forthisanalysisthedatawererecordedwith the L1 trigger in coincidence withthe V0 minimum-bias trigger. ThetriggerlogicoftheLevel-1triggeremployedaslidingwindow algorithm of 4
×
4 towers with a sliding step of 2 towers along either of the surface axes. An event was rejected unlessthe en-ergy summed within atleast one set of the 16 adjacent towers was greater than a threshold.Additionally, the trigger logic was configured to adjust the online threshold accordingto the event centralityestimatedfromtheanaloguesumoftheV0detector sig-nals. Thethresholdwas adjustedsuch thatthe rejectionratewas approximately constant asa function ofthe eventcentrality. The thresholdsvariedfrom7 GeVin10%mostcentraleventsto2 GeV inthemostperipheralevents.Theofflineselectionretainedonlyeventswherethecoordinate of thereconstructed vertexalong the beamdirectionwas within
±
10 cm around the nominal interaction point. The eventvertex reconstructionisfullyefficientfortheeventcentralitiesconsidered inthisanalysis.Fig. 1. Triggerturn-oncurves:theratioofinclusiveelectronsinEMCaltriggeredeventstominimum-biaseventsasafunctionofassociatedtrackpTincentralitybinsbetween
0%and50%.ThelowerrightpanelshowsasimilarratioobtainedwithEMCalclustersforcentrality50–80%.ThepTfromwhichthespectrafromtheminimum-biastrigger
totheEMCaltriggerareusedareindicatedwithblackdashedlines.Thescalingfactorswhichwereobtainedbyfits(redlines)aresummarised inTable 1.(Forinterpretation ofthereferencestocolourinthisfigure,thereaderisreferredtothewebversionofthisarticle.)
Collisions were classified into different centrality classes in termsofpercentilesofthehadronicPb–Pb crosssectionusingthe signalamplitudesintheV0detector.Theeventcentralitywas re-latedtothenuclearoverlapfunctionTAAviaaGlaubermodel[65]. Detailsonthecentralitydeterminationcanbefoundin[53].
Toobtaintheinclusiveelectronspectrautilising minimumbias and EMCal triggers, in each centrality class, the per-event yield ofelectrons from the EMCal triggered sample was scaled to the minimum-bias yield by normalisation factors determined with a data-drivenmethod.Fig. 1showstheratioofpT-differentialyields oftheelectroncandidatetracksfromtheEMCaltriggered sample totheminimum-biastriggersampleasafunctionofthetrack pT. Theelectroncandidateswereselectedbasedontheionisation en-ergy loss in the TPC gas and the ratio of the EMCal cluster en-ergyandthemomentum oftheparticle track(detailsofelectron identificationare givenin the next section). Because of the lim-itedelectronyieldinthesemi-peripheraleventclass(50–80%)the correction for the trigger enhancement in that interval was ob-tained asthe ratio of the energy distributions of EMCal clusters forthetwotriggertypes(showninpanel (f)ofFig. 1).The inclu-sive pT spectrumofelectronsisformed bytheelectronspectrum fromminimum-biaseventsbelowthetriggerplateau(indicatedby dashedlinesinFig. 1)andthespectrum measuredwithonlythe EMCal trigger inthe plateauregion. The difference in the shape ofthecurvesinFig. 1for pT belowtheplateauisaconsequence oftheparticlemixturecontributingtotheEMCalclustersand re-sponseof theEMCal to chargedhadrons. The scaling factors and the transition from the minimum-bias sample to the triggered sample were determined by fits with a constant to the high-pT plateauregions.Thescalingfactorsforallcentralityclassesaswell as the pT at which the switch from the minimum-bias to the EMCaltriggerspectraoccursaresummarised inTable 1.The uncer-taintyonthefactors(also reportedinTable 1)wasobtainedfrom theindividual fitsandthereforeit isdriven bythe statistical un-certaintyofthemeasuredspectra.Thescalingfactorswithin cen-tralities0–50% were extractedusing theelectron tracks, whereas for centralities larger than 50% the spectrum of EMCal clusters is used. The relative difference in the scaling factors depending on whether electrons or clusters were selected was studied and shownto bebelow8.5%.Thisdifferencewas includedinthe
sys-Table 1
SummaryforcentralitydependenceoftheEMCaltriggerscalingfactor.Middle col-umn:trigger scaling factors(togetherwith their absolutestatisticaluncertainty) extractedfromtheratioofelectrons(orEMCalcluster) pTspectrainEMCal
trig-geredandminimum-biasevents.Rightcolumn:particle pTatwhichthespectrum
measuredinminimum-biaseventsandEMCaltriggeredeventsareswitchedtoform theinclusiveelectronpTspectrum.Seetextfordetails.
Centrality Scaling factor PlateauabovepT
(GeV/c) 0–10% 38±2.2 9 10–20% 32±3.5 9 20–30% 35±2.9 8 30–40% 34±2.5 6 40–50% 41±5.2 6 50–80% 89±3.5 6
tematicuncertaintyof themeasurement forall centralityclasses.
Table 1correspondstoFig. 1. 2.3. Electronreconstruction
Forthereconstructionofelectronsinthisanalysistrackswitha minimum of 100out of 159possible TPC space points were re-tained. In addition, tracks were selected using their distance of closestapproach(DCA)totheprimaryvertex.Acceptedtrackswere within
|
DCAxy|
<
2.
4 cm in the transverse plane and|
DCAz|
<
3.
2 cm along the beam axis. Furthermore, the tracks were se-lected within a fiducial pseudorapidity acceptance of|
η
|
<
0.
6. Each track was required to contain at least one point measured in theSPDandat leastthree hitsout ofthe maximumof sixin theITS.Moreover,theelectroncandidateswereselectedby apply-ingacutonthespecificionisationenergyloss(dE/
dx)withinthe TPC. ThemeasureddE/
dx wasrequiredtobe between−
1 to3σ, whereσ
isdE/
dx resolution, fromthe expectedmean of dE/
dx forelectrons.Thisselectionishereafterindicatedas−
1<
nTPCσ
<
3. ThetracksextrapolatedtothesensitivevolumeoftheEMCalwere matchedwithaclusterifthecluster-trackresidualinazimuthand pseudorapidity was within awindow of|
ϕ
|
<
0.
05 and|
η
|
<
0.
05.Suchmatching criteriacorresponds to aneffectiveradius of about6 timeslarger thanthe effectiveMoliere radius forEMCal, thusitisfullyefficientforelectrontrackswithpT>
2 GeV/c.
Fig. 2. Left: TheratioofE/p asafunctionofnTPC
σ in10%mostcentralPb–Pbevents(pT>3 GeV/c),wherep isthechargedparticlemomentum,E isthematchedEMCal
clusterenergy,andσTPCistheresolutionontheenergylossintheTPCgasexpectedforelectrons.Right: E/p forelectronsintwotransversemomentumranges.Theblue
opensymbolsshowsthehadroncontamination–anE/p distributionforparticles3.5σ awayfromthemeanofthetrueelectronTPC-dE/dx distributionnormalised to theelectronE/p atsmallvaluesoftheratio(awayfromtheelectronsignal).(Forinterpretationofthereferencestocolourinthisfigure,thereaderisreferredtotheweb versionofthisarticle.)
Additionalhadronrejectionusedthecombinationoftheenergy depositedwithinEMCalandacut ontheelectromagneticshower shape[64,66].Sincetheshowerfromanelectronisfullycontained andaccuratelymeasuredbytheEMCal,theratiooftheenergy(E) measuredbytheEMCalandthemomentum(p)forelectrontracks isapproximatelyunity(E
/p
≈
1).The E/p distribution
is qualita-tivelydifferentinthecaseofhadrons.TheE/p asafunctionofthe nTPCσ forchargedparticles matchedwithan EMCal cluster in10% mostcentral eventsis shown in Fig. 2.From the primary tracks matchedtoanEMCalclustertheelectroncandidateswereselected usinga momentumindependent cutof 0.
9<
E/p<
1.
3. Further-more,theshapesofthemeasured showersinthecalorimetercan be characterised by the two eigenvalues (λ
0 andλ
1) of the co-variancematrixbuiltfromthetowercoordinatesweightedbythe logarithms ofthetower energies.Theseeigenvalues maybeused todifferentiatebetweenincidentparticlespecies[64].Aselection ofλ
21<
0.
3,correspondingtotheshorter-axisoftheshowershape projectedonto theEMCal surface,was applied,because the char-acteristicelectromagneticshowerofanelectronispeakedatλ
21 of about0.25independentoftheclusterenergy.Theremaining hadron backgroundinthe electronsample was estimatedwithadata-drivenapproachandstatisticallysubtracted from the sample. The shape of the residual hadron background
in E/p at the position of the electron peak was reconstructed
using the E/p distribution for hadron-dominated tracks selected withnTPCσ
<
−
3.
5.The E/p distributionof the hadronswas then normalised tomatchthe distributionoftheelectroncandidatein 0.
4<
E/p
<
0.
7 (away fromthe trueelectron peak). An exampleofthe E/p distributionstogether withtheestimatedhadron
con-taminationfortwotransversemomentumintervalsisshowninthe rightpanelofFig. 2.Thehadroncontamination islessthan5% at pT
<
10 GeV/c inallcentralityclasses.AthighpT,itislargerthan 10%withamaximumofabout15%atpT=
18 GeV/c.Theefficienciesrelatedtothecutsontheionisationenergyloss inthe TPCwere estimatedwithdata-driven techniques[64].The EMCalefficiencies were calculatedusing MonteCarlosimulations of proton-proton (PYTHIA [67]) and heavy-ion collisions (HIJING
[68]) with complete detectorresponse modelled byGEANT [69]. Theproductofdetectoracceptanceandreconstructionefficiencies forinclusiveelectronsforthe10%mostcentralcollisionsisshown intheleftpanelofFig. 3.Theefficiencieswereestimatedforeach
centralityclass separately.Avariation ofabout2.5–3% wasfound betweenthemostcentral(0–10%)andperipheral(50–80%)events. 2.4. Backgroundelectronsubtraction
Themainsourcesofelectronscontributingtotheinclusive elec-tron sample in this analysis are: a) heavy-flavour hadron decay electrons;b)electronsfromleptonicdecaysofquarkonia(J
/ψ
andϒ
mesons); c) electrons from W and Z/γ
∗ decays; d) the so-calledphotonic electrons,originatingfromphotonconversionsand Dalitz decays ofneutralmesons (mainlyπ
0 andη
);ande) neu-tralkaondecays;however,thecontributionfromthenon-photonic electrons created in vector meson and Ke3 decays is negligible (<
0.
1%) [30] in the momentum range considered in this analy-sis.Thecontributionofthephotonicelectronstotheinclusive elec-tron sample was measured by the invariant mass method. The invariant massdistributionwas determinedbypairingevery elec-tron trackfrom the inclusivesample with an oppositely-charged trackselectedwith
−
3<
nσTPC<
3toincreasethechancefor find-ingthepairs.Pairssatisfyingelectronidentificationselectionsand pairs satisfyingacut on theinvariant massofminv<
0.
1 GeV/c
2 wereselectedforfurtheranalysis.Theseselectedunlike-signpairs, however,containnot onlytruephotonicelectronsbutalsoa con-tribution from random pairs. This combinatorial background to photonicelectrons was estimatedusingtheinvariant mass distri-butionofthelike-signelectrons(NeL S),anditwassubtractedfromthatofunlike-signpairs(NeU L S)toobtainthenumberofraw
pho-tonicelectrons:Nraw
eγ
=
NeU L S−
NeL S.The efficiency for the identification of the photonicelectrons by the invariant mass method (εeγ) was estimated from Monte Carlosimulationswithfulldetectorresponseandwasfoundtobe centralityindependent.Theefficiency,shownintherightpanelof
Fig. 3,isabout30%atpe
T
=
4 GeV/c and
risingto55%at18 GeV/c.
The number of photonic electrons present within the inclu-sive electron sample was calculated as the raw photonic elec-tron yield corrected for the reconstruction efficiency such that: Neγ=
Nraweγ/
εe
γ.Thefractionofphotonicelectrons withinthe in-clusiveelectronsample inthe10%mostcentralcollisionsisabout 30% at pT=
3 GeV/c,
dropsto25% at12 GeV/c and
remains ap-proximatelyconstantathigherpT consideredinthisanalysis.Fig. 3. Left: ProductofdetectoracceptanceandreconstructionefficiencyforinclusiveelectronsasafunctionoftheelectronpT.Thestatisticaluncertaintyissmallerthanthe
sizeofthepoints.Right: Photonicelectronreconstructionefficiencyviainvariantmass(εeγ)asafunctionofpToftheelectron.
The contribution to the inclusive electrons from J
/ψ
decays was estimated using a phenomenological interpolation at√
s=
2.76 TeVofthe pT-differentialcrosssectionsmeasuredinpp colli-sionsatvariouscentre-of-massenergies[70] andscalingwiththe nuclearmodificationfactorRJAA/ψ (pT)measuredattheLHC[71,72]. In 3<
pT<
4 GeV/c, the contribution is 5.5% in the most cen-tralcollisions anddecreasesathigh-pT.The contributionfromϒ
statesestimatedfromthe crosssectionmeasured inpp collisions[73]wasfoundtobenegligible.
The contributionof electrons from W-boson andZ/γ∗ decays wasestimatedusingthecrosssectionobtainedfromthePOWHEG eventgenerator[74]forpp collisionsandscaledwith
TAA assum-ingRAA=
1.ThecontributionispTdependentandforW-bosonsit increasesfrom1%at10 GeV/c to
about6%at17 GeV/c whereas
thecontribution from Z/
γ
∗ isbelow 1% for pT<
10 GeV/c and
increasesto2.4%at17 GeV/c.
Theheavy-flavourdecayelectronyieldwasreconstructed from theinclusiveelectronyieldby firstsubtractingthephotonic elec-tron yield, then correcting the result of the subtraction for the efficiency,andfinally,bysubtractingthefeed-downelectronsfrom J
/ψ
andW,Z/γ∗decays.3. Systematicuncertainties
The sources of systematic uncertainty on the reconstructed heavy-flavour decay electron pT spectrum can be grouped into threecategories:
– eventselection(theeventnormalisation,includingthescaling oftheEMCaltriggereventsandtheeventcentralityselection); – electronsignal extraction (uncertaintiesoriginatingfrom
cor-rectionsrelatedtotrackingandparticleidentification); – non-heavy-flavourbackgrounddetermination.
Anoverviewofthesystematicuncertaintiesispresentedin Ta-ble 2.Forsourcesthat dependoncentrality(allbut “tracking/ma-terial” fromTable 2)theuncertaintieswereevaluatedseparatelyin eacheventclass.Inevery casea weakcentralitydependencewas found(deviations oflessthan 3%).Inthe figuresofSection 4the systematicuncertainties are represented as shaded boxes around thedatapoints.
Eventnormalisation. Acomparisonoftheeventnormalisation obtainedwiththe EMCalclustersandthenormalisationobtained fromtheinclusiveelectronsshowedamaximumdeviationof8.5%. This deviation, independent of centrality and pT, is included as theuncertaintyontheyieldobtainedwiththetriggereddata.The
Table 2
Summaryofsystematicuncertaintiesontheheavy-flavourelectronyieldsgrouped accordingtotheirsources.Whereapplicabletheuncertaintywasestimatedfortwo pTvalues,3and10GeV/c (forthelatternumbersareshowninparentheses).For
detailsontheextractionoftheuncertaintiesseetext.
Source pTdependence (GeV/c) Uncertainty (%)
EMCal trigger correction only high-pT 8.5
Centrality estimation n/a <0.1–3 Tracking/material weak within 3–14 5
E/p 3 (10) 3 (3) nTPC σ 3 (10) 3 (7) Photonic background 3 (10) 5 (5) J/ψelectron background 3 (10) 1 (<1) W electron background 3 (10) 0 (<1) Z/γ∗electron backgrounds 3 (10) <1 (<2)
contributiontothesystematicuncertaintyduetothe1.1% relative uncertainty onthe fractionofhadronic crosssection used inthe Glauberfittodeterminethecentralityislessthan0.1% inthe cen-tral eventclass (0–10%) and3% in the semi-peripheral centrality class(50–80%)[47,75].
Electronidentification. The systematic uncertainties on the corrections for track reconstruction, track selection and electron identificationwereassessedviamultiplevariationsoftheanalysis selections.Foreachsetofcutstheanalysiswasrepeatedand com-pared tothe results obtainedwith the defaultset ofcuts. These variationsincludedchangesintrackqualitycuts,suchasthe min-imumnumberofthe spacepointsin theTPCandassociatedhits intheITS.Theuncertaintieswereestimatedasafunctionoftrack pT andfor each centrality class separately.In addition, the elec-tron identificationcuts inthe TPC (nTPCσ ) andEMCal(E
/p range)
werevariedaroundtheirnominalvalues.Theuncertainty originat-ingfromtheknowledgeofthematerialbudgetwas estimatedvia completedetectorsimulationswiththeradiationlengthvariedby±
7%[76].Subtractionofphotonicbackground. The uncertainty on the subtracted background electrons from photon conversions and Dalitz decayswas obtained by varyingthe invariant masscut on theelectronpairswithin0
.
07<
minv<
0.
15 GeV/c2andthe mini-mum pTofthetrackspairedwithelectroncandidatesbetween0.3 and0.6GeV/c.
SubtractionofelectronsfromJ
/ψ
. Theuncertaintyonthe sub-tractedbackgroundelectronsfromJ/ψ
decayswasestimatedfrom the experimental uncertainties on measured production yields in heavy-ioncollisions[71,77].ElectronsfromW andZ
/
γ
∗. TheyieldofelectronsfromW de-cayswasvariedby±
15%onthebasisofthecomparisonoftheW productioncrosssectionasgivenbythePOWHEGeventgeneratorFig. 4. Differentialyieldsofelectronsfromsemi-leptonicdecays ofheavy-flavour hadronsinclassesofcentralityofPb–Pb collisionsat√sNN=2.76 TeV.
andthe existing measurements in pp collisions at the LHC [78]. ThecontributionfromZ/
γ
∗ di-electrondecaysanditsuncertainty wasestimatedusingthePOWHEGeventgeneratorandconsidered together with the uncertainties on the process production cross section measured inpp collisions [79]. Giventhesmall contribu-tionof theelectrons from Z/
γ
∗ decays tothe electronspectrum ofthisanalysisthederiveduncertaintywasfoundbelow1%atthe highestmomentumconsidered.4. Results
The pT-differentialinvariantyieldsofheavy-flavourdecay elec-tronscorrectedforacceptanceandefficiencyinthe0–10%,10–20%, 30–40%,40–50%and50–80%centralityclassesinPb–Pb collisions at
√
sNN=
2.76TeVareshowninFig. 4.OnlytheEMCaltriggered data are shown for the 50–80% centrality class due to a lack of statisticsintheminimumbiasdatasample.The production cross section of heavy-flavourdecay electrons inpp collisionsat
√
s=
2.
76 TeV,neededtocomputethenuclear modificationfactorRAA(Eq.(1)),wasobtainedfrommeasurementsandFONLLpQCDcalculations[80,81].ForpT
<
12 GeV/c the
mea-surementat√
s=
2.
76 TeV wasused[30].ForpT>
12 GeV/c there
isnomeasurementatthisenergy.Thus,anextrapolatedcross sec-tionwasconstructedfromthemeasurementat√
s=
7 TeV bythe ATLAS Collaboration[82,83] andthe ratioofcrosssectionsatthe twocollisionenergiesobtainedfromFONLL[84].Theuncertainties ofthe pp referencesareabout20% for pT<
12 GeV/c and
about 15%for pT>
12 GeV/c,
includingtheuncertaintyfromthescaling with√
s,whichwas estimatedbyconsistently varyingtheFONLL calculationparametersatthetwoenergies[84].Fig. 5showstheresultingRAA ofheavy-flavourdecayelectrons for all centralityclasses. The uncertainty on the average nuclear overlap function
TAAfor each centrality selection was takenas determined in [53]. It varies from 4% in the 10% most central events to 7% in the 50–80% centrality class, and it is shown as a box at RAA=
1 in the figure.In all cases,taking intoaccount the pT trend of the RAA and the statistical uncertainties of the measurement athigh-pT, theelectron productionyields are sup-pressedrelativetoanincoherentsuperpositionofpp collisions.In the 10% most central events the RAA reaches values below 0.4, while for the more peripheral events the suppression is weaker. This centrality dependenceof the suppression patternis qualita-tivelyconsistentwithin-mediumenergylossofheavyquarksdue to a decrease of medium’sinitial energy densityandthe system sizefromcentraltoperipheralcollisions.Inproton–leadcollisions, whereformationofa hot,denseand long lived QGPis not expected, the suppression is not observed. The nuclearmodificationfactor RpPb measuredforelectronsfrom heavy-flavour hadron decays is consistent with unity [61]. This control measurement inp–Pb collisions confirms that the strong suppression in Pb–Pb collisions is a result of final state effects. The left panel of Fig. 6shows the comparisonbetween RpPb for minimum-bias p–Pb collisions at
√
sNN=
5.
02 TeV and RAA for the10%mostcentralPb–Pb collisions.Theresultreportedherefor electrons at mid-rapidity is consistent withthe measurement of the suppressionpatternformuonsfromthesemi-leptonicdecays of heavy-flavour hadrons at forward rapidity [31], in both, most centralandsemi-peripheralcollisions(seeFig. 6).Theleptonmea-Fig. 5. RPbPbofelectronsfromheavy-flavourhadrondecaysincentralitybinsofPb–Pb collisionsat√sNN=2.76 TeV.ThesolidbandatRPbPb=1 bracketstheuncertainty
Fig. 6. Left: RPbPbofelectronsandmuons[31]fromheavy-flavourhadrondecaysin10%mostcentralPb–Pb collisionsshowntogetherwithRpPbofelectronsfromminimum biasproton–leadcollisionsat√sNN=5.02 TeV[61].Right: RPbPbofelectronsinsemi-peripheralPb–Pb collisions(50–80%selectionforelectronsand40–80%formuons.
Fig. 7. RPbPbofelectronsfromheavy-flavourhadrondecaysmeasuredin10%most
centralPb–Pb collisionsat√sNN=2.76 TeV comparedtovarioustheoretical
calcu-lations[86–98].
surementsshow remarkablesimilarityin thesuppression pattern that,within the uncertainties, doesnot exhibit a rapidity depen-dence.
The pT spectrum of electrons is sensitive to both charm and beauty quark energy loss. From the decay kinematics and the pT-differential cross sections of parent hadrons with charm and beauty,it followsthat electrons of pT below5 GeV/c are mostly sensitive to charm energy loss. On the other hand, in pp col-lisions a large fraction (more than 60%) of the electrons with pT
>
10 GeV/c originate
fromb-quarks[82,66,30,85,81].The elec-tronyieldathigh-pT isthereforeexpectedtocontainasignificant contributionfromBmesonswithpTupto30 GeV/c.
Consequently, thestrongsuppressionofelectronsforpT>
10 GeV/c is
consistent within-mediumenergylossofb-quarks.5. Comparisonwithmodels
The RAA ofelectrons fromheavy-flavourhadron decaysinthe mostcentral Pb–Pb collisions is compared to theoretical models thatinclude heavyquark interactions withthe medium inFig. 7. Mostofthesemodelswere previouslycompared tothe RAA ofD mesons in most central Pb–Pb collisions [75,48] as well as the positive ellipticflow ofthe Dmesons andelectrons from heavy-flavour hadron decays in semi-central Pb–Pb collisions [99,100].
We note that thesemodelsdiffer inthetheoretical realisation of the medium properties, and of its dynamics, and also in imple-mentationsofthehadronisationandofhadron–hadroninteractions inthelatestagesoftheheavy-ioncollision.Alsotheheavy-quark cross-section usedasinput tothe calculationmaydifferbetween themodels(PYTHIA,FONLLandPOWHEG).
Djordjevic. The calculation by Djordjevic et al. [86] at pT
>
5 GeV/c isconsistentwiththemeasurementwithinthe uncertain-tiesincludingtheslowincreaseoftheRAAasafunctionofelectronpT. The model takes into account both radiative and collisional contributions toparton energyloss.Specifically, theradiative en-ergy loss calculationsare an extension of theDGLV [101] model towardsafinitesizedynamicalmedium,finitemagneticmass,and runningcoupling.Themodeldoesequallywellinreproducingthe magnitudeandpT dependenceoftheDmesonsRAA[48].
Vitev. ThecalculationsbyVitev etal.[90]alsocapturethe mag-nitude of the suppression and reproduce the pT dependence of theelectronsseeninthedata.Thein-mediummodificationofthe heavy quark distribution anddecayprobabilities are evaluated in aco-movingplasma.Thepredictionsforheavy-flavourdecay elec-tronsuppressionareobtainedwithanimprovedperturbativeQCD descriptionofheavyflavourdynamicsinathermalmediumwhere theformation anddissociationofheavy-flavourmesonsare com-bined withparton-level charmandbeautyquarkradiative energy loss.Themodelincludingthedissociationofheavy-flavourhadrons capturesalsothesuppressionofDmesons.
WHDG. The band corresponding tothe WHDG model calcula-tions [87–89]isconsistent withthemeasurementwithin the un-certainties; however, it systematically underpredicts the suppres-sionbelow12GeV
/c.
Interestingly,thesamecalculationcompared to the Dmesons RAA reproduced the datavery well. The model includes elastic aswell as inelastic energy loss of heavy-quarks, andthepath length (geometric)fluctuationswithin astatic ther-malcoloured mediumwithitsdensityastheonlyfreeparameter determined via a statistical comparison of the model with the chargedparticleproductioninheavy-ioncollisions.TAMU. The RAA obtained within the TAMU model of heavy
quark transport within a strongly coupled thermal medium in-cluding theelastic scatterings withthe medium (resonance scat-teringandcoalescence processes)[91]underpredicts the suppres-sion at low-pT while it captures the magnitude of the data for
pT
>
12 GeV/c.
We note that TAMU also underpredicts the D mesonsRAAanditssuccessfortheelectronsathigh-pTmaybe re-latedtotheb-quarkenergylossforwhichthefractionfromelastic processesisincreasedascomparedtocharmquarks.Ontheotherhand,TAMUreproduces the measured v2 of Dmesonsand elec-tronsfromheavy-flavourhadrondecaysaccurately[99,100].
BAMPS. The BAMPS [96–98] calculation, which is a partonic transport modelusingtheBoltzmann equation,is shownfortwo scenarios. The BAMPScoll. calculation considering only the colli-sional energyloss in an expandingquark-gluon plasma overesti-matesthemagnitudeofthesuppressionwithintheregioncovered by the measurement. The calculation obtained within the same framework where both the elastic and radiative processes were considered(BAMPScoll.+rad.)describesthedataratherwell.A sim-ilarconclusioncanbedrawnfromthecomparisontotheD-meson RAA. On the other hand,the BAMPScoll. reproduces qualitatively the v2 ofDmesonsandelectrons fromheavy-flavourhadron de-cays,buttheBAMPScoll.+rad. underestimatestheDmesonv2[99,
100].
MC@sHQ+EPOS2. The results of the Monte Carlo model
in-cludinga hydrodynamic calculation of themedium coupled with collisional and radiative parton energy loss MC@sHQ+EPOS2 [93]
areconsistentwiththemeasurementwithintheuncertainties.The modelbestdescribesthe dataat pT
>
12 GeV/c. Thismodel also worksbetterfortheDmesons RAAatpT>
10 GeV/c ascompared tolower momentum(meson pT below10 GeV/c). Theauthors of themodelemphasise thatthescatteringinthehadronicphaseis notpresentintheircalculationandcanhavesubstantialeffecton the low-pT suppressionand ellipticflow calculationsthat under-predictsthemeasurement[99,100].Cao, Qin, Bass. The calculation by Cao,Qin,andBass [92] re-produces the measured RAA at high-pT (above 12 GeV
/c)
while itunderpredicts thesuppression forlow-pT.The modelevaluates thedynamicsofenergylossandflowofheavy quarkswithinthe frameworkofaLangevinequationcoupledtoa(2+
1)-dimensional viscoushydrodynamicmodelthatsimulatesthespace–time evolu-tionof theproduced hot anddense QCD matter. Thiscalculation reproduced thesuppression ofDmesonsvery accurately,bothin strengthandthe pT-dependence.POWLANG. Theresultoftheheavy-quarktransportcalculation usingtherelativisticLangevinequationwithcollisionalenergyloss, POWLANG[94,95],isshownfortwochoicesofheavy-flavour trans-port coefficientswithin thequark-gluon plasma.In thePOWLANG HTL [94] the coefficients are evaluated by matching the weak-couplingcalculationswithhard-thermal-loop(HTL) resultforsoft collisionswithaperturbativeQCDcalculationforhardscatterings. ThisHTLvariantpredicts a fallingtrend with pT of theelectrons that isincompatible withthe dataand overpredictsthe suppres-sionathighmomentum.Conversely,thecalculation thatincludes the transport coefficients obtained fromthe Lattice QCD simula-tions[95]predictstherising RAA.However,itreportslargervalues thanthemeasuredonesanditisincompatiblewiththemeasured magnitude of the suppression. The width of the theory curves envelopes thespread inthe resultsof thecalculation that is ob-tained when considering two different decoupling temperatures Tdec (155 MeV and 170 MeV) from the hydrodynamic evolution ofthefireball.Therelatively smallwidthofthebandssuggestsa weaksensitivityofthesuppressiontotheTdec.Similartothe elec-tron case,POWLANG HTL capturesthe suppressionforDmesons below 5 GeV
/c predicting
much lower RAA at high-pT than ob-servedinthedata.Interestingly,asinthecaseoftheTAMUmodel, thePOWLANGHTLcalculationsprovideafairdescriptionoftheD mesonsv2 measuredattheLHC.Giventhelevelofagreementofthetheoreticalmodelswiththe dataonv2 and RAAofpromptDmesons[75,48,99]andelectrons fromheavy-flavourdecays,thefollowinggeneralconclusionsarise: – models incorporating the complete dynamical and thermal
evolutionofthemediumarefavouredbythedata;
– the measurementindicates the needforboth, collisionaland radiative,energylossofheavy quarkstobeconsideredto ex-plain themagnitude andthe pT dependence ofthe suppres-sion.
6. Summary
The pT-differential yields of electrons fromsemi-leptonic de-cays of charm and beauty hadrons were measured at 3
<
pT<
18 GeV/c inseveralcentralityclassesofPb–Pb collisionsat√
sNN=
2.
76 TeV atmid-rapidity. Thenuclear modificationfactor RAA for the 10% mostcentral eventsshowsa strong suppression of elec-trons fromheavy-flavour hadron decays. Consistent withthe ex-pectationofadecreaseofthemedium’sinitialenergydensityand a decreasingsystemsizefromcentraltoperipheralcollisions, the suppression issignificantly weakerin moreperipheralevents.No significant suppressionisobservedinp–Pbcollisions,indicating a strong in-medium energyloss of both charm andbeauty quarks in Pb–Pb collisions. Inparticular, the strongsuppression at high-momentum indicates that b-quarks lose a substantial fraction of their energy. The suppression of electrons is quantitatively con-sistent with measurements of RAA of muonsfrom semi-leptonic heavy-flavourdecaysin2.
5<
y<
4,disfavouringa strong depen-denceofenergylossonrapidity intherange|
y|
<
4.Theoretical calculations that include collisional and radiative in-medium en-ergylossforbothcharmandbeautyquarksreproducethe experi-mentalfindings.Inparticular,modelsincorporatingthedynamical evolutionofthemediumarepreferredbythedata.Acknowledgements
The ALICECollaboration would like to thank all its engineers andtechniciansfortheirinvaluablecontributionstothe construc-tion of the experiment and the CERN accelerator teams for the outstanding performance of the LHC complex. The ALICE Collab-oration gratefully acknowledges the resources and support pro-videdbyallGridcentresandtheWorldwideLHCComputingGrid (WLCG) collaboration. The ALICE Collaboration acknowledges the following fundingagenciesfortheir supportin buildingand run-ning the ALICE detector: A.I. Alikhanyan National Science Labo-ratory (Yerevan Physics Institute) Foundation (ANSL), State Com-mittee of Science and World Federation of Scientists (WFS), Ar-menia; Austrian Academy of Sciences and Nationalstiftung für Forschung, Technologie und Entwicklung, Austria; Conselho Na-cionalde DesenvolvimentoCientíficoe Tecnológico(CNPq), Finan-ciadora de Estudose Projetos(Finep) andFundaçãode Amparoà PesquisadoEstadodeSãoPaulo(FAPESP),Brazil;Ministryof Edu-cationofChina (MOEofChina),MinistryofScience&Technology of China (MOST of China) and National Natural Science Founda-tion of China (NSFC), China; Ministry of Science, Education and Sports andCroatian ScienceFoundation,Croatia; Centrode Inves-tigacionesEnergéticas,MedioambientalesyTecnológicas(CIEMAT), Cuba;MinistryofEducation,YouthandSportsoftheCzech Repub-lic,Czech Republic;Danish NationalResearchFoundation (DNRF), TheCarlsbergFoundationandTheDanishCouncilforIndependent Research–Natural Sciences,Denmark; Helsinki Institute ofPhysics (HIP),Finland;Commissariatàl’EnergieAtomique(CEA)and Insti-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)andGSI Helmholtzzentrum für Schweri-onenforschung GmbH, Germany; Ministry of Education, Research andReligiousAffairs,Greece;NationalResearch,Developmentand Innovation Office, Hungary; Department of Atomic Energy, Gov-ernment of India (DAE), India; Indonesian Institute of Science,
Education and National Science Centre, Poland; Ministry of Ed-ucation and Scientific Research, Institute of Atomic Physics and RomanianNationalAgencyforScience,TechnologyandInnovation, Romania; Joint Institute for Nuclear Research (JINR), Ministry of EducationandScienceoftheRussianFederationandNational Re-search Centre Kurchatov Institute, Russia; Ministry of Education, Science,Researchand SportoftheSlovak Republic, Slovakia; Na-tional Research Foundation of South Africa, South Africa; Korea Institute ofScienceandTechnology Information andNational Re-search Foundation ofKorea (NRF),South Korea;Centro de Inves-tigacionesEnergéticas,MedioambientalesyTecnológicas(CIEMAT) andMinisteriode Cienciae Innovacion, Spain;Knut&Alice Wal-lenberg Foundation (KAW) and Swedish Research Council (VR), Sweden;EuropeanOrganizationforNuclearResearch,Switzerland; National Science and Technology Development Agency (NSDTA), OfficeoftheHigher Education CommissionunderNRU projectof ThailandandSuranareeUniversity ofTechnology (SUT), Thailand; TurkishAtomic Energy Agency (TAEK),Turkey; NationalAcademy ofSciences ofUkraine,Ukraine; ScienceandTechnology Facilities Council (STFC), United Kingdom; National Science Foundation of theUnitedStatesofAmerica(NSF)andUnitedStatesDepartment ofEnergy,OfficeofNuclearPhysics(DOENP),UnitedStates. References
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