Measurement of the production of high-pT electrons from heavy-flavour hadron decays in Pb-Pb collisions at √sNN=2.76 TeV

.ALICE Collaboration

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

Articlehistory:

Received24October2016

Receivedinrevisedform12April2017 Accepted24May2017

Availableonline29May2017 Editor:L.Rolandi

Electronsfromheavy-flavourhadrondecays(charmandbeauty)weremeasuredwiththeALICEdetector in Pb–Pb collisions at acentre-of-mass of energy √_s

NN=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].Acrossovertransitionfromhadronicmat- teratzerobaryochemical potentialisexpectedtotakeplaceonce thesystemtemperaturereachesvaluesaboveT ≈^155MeVand/or theenergy densityabove

ε

≈ 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 (jetquench- ing),wasfirstproposedin[8]andisstudiedasasensitiveprobeof themediumproperties[9].Jetquenchingwasfirstobservedexper- imentallyviathestrongsuppressionofhightransversemomentum particleproductioninheavy-ioncollisionsattheRelativisticHeavy IonCollider(RHIC) [10–13].Similar observationshave sincebeen reportedby the Large HadronCollider (LHC) experiments atcol- lision energies larger by one order of magnitude with hadrons [14–16]andextendedtofullyreconstructedjets[17–19].

Heavyflavours(charmandbeauty)aresensitivetoolsforstud- ies of the in-medium parton energy loss, providing qualitatively

E-mailaddress:[email protected].

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]processesthatdependonthepar- tontype andthepropertiesofthemedium. Theinteractionswith the medium modify the radiation pattern of the shower by in- ducing longitudinal drag (and associated longitudinal diffusion), transversediffusion,andenhancedsplittingofthepropagatingpar- 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 Eg > E_light-q >

Echarm> Ebeauty [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) p_T interval 3–18 GeV/c,probing athigh p_T 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 p_T-differentialyieldinnucleus–nucleus(AA)collisions,dN_AA/dp_T, by thecrosssection inpp collisions, d

σ

pp/dpT, scaledby theav- erage of the nuclear overlap function ^TAA ^{for the considered} centralityclass[53]

R_AA

=

^dNAA

/

dp_T

^TAA

^d

σ

pp

/

dp_T

.

(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 sectionsofthepaperdefinetheexperimentalsetupandtheanaly- 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 hadrondecaysatfor- 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 p_T≈ 0.15 GeV/c,|

η

|<0.9 andfullazimuth.UsingtheITSandTPCspace points the particlemomentum is determinedfromthe combined trackfitwitharesolutionofabout1%at1 GeV/candabout3%at 10 GeV/c[64].

The front face of the EMCal is positioned at about 450 cm fromthebeamaxisintheradial directionandthedetectorisap- proximately 110 cmdeep.The detectorisalayeredPb-scintillator samplingcalorimetercovering107degreesinazimuthandapseu- 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 V0systemisbetterthan1nsanditprovidesanefficientdiscrim- ination ofthe beam–beamcollisions fromthe backgroundevents produced upstream of the experiment. Additional suppression of thebackgroundwasprovidedbytiminginformationfromtheZDC.

The minimum-bias triggerincluded two trigger classesformost- 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 centralityestimatedfromtheanaloguesumoftheV0detectorsig- 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.Theeventcentralitywasre- 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. 1showstheratioofp_T-differentialyields oftheelectroncandidatetracksfromtheEMCaltriggered sample totheminimum-biastriggersampleasafunctionofthetrackpT. Theelectroncandidateswereselectedbasedontheionisationen- 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).Theinclu- sive p_T spectrumofelectronsisformed bytheelectronspectrum fromminimum-biaseventsbelowthetriggerplateau(indicatedby dashedlinesinFig. 1)andthespectrum measuredwithonlythe EMCal trigger inthe plateauregion. The difference in the shape ofthecurvesinFig. 1for pT belowtheplateauisaconsequence oftheparticlemixturecontributingtotheEMCalclustersandre- 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-p_T plateauregions.Thescalingfactorsforallcentralityclassesaswell as the pT at which the switch from the minimum-bias to the EMCaltriggerspectraoccursaresummarised inTable 1.Theuncer- taintyonthefactors(also reportedinTable 1)wasobtainedfrom theindividual fitsandthereforeit isdriven bythe statisticalun- 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 includedinthesys-

Table 1

SummaryforcentralitydependenceoftheEMCaltriggerscalingfactor.Middlecol- umn:trigger scaling factors(togetherwith their absolutestatisticaluncertainty) extractedfromtheratioofelectrons(orEMCalcluster) pTspectrainEMCaltrig- 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,theelectroncandidateswereselectedbyapply- ingacutonthespecificionisationenergyloss(dE/dx)withinthe TPC. ThemeasureddE/dxwas requiredtobe between−^{1 to3}

σ

, where

σ

isdE/dx resolution, fromthe expectedmean of dE/dx forelectrons.Thisselectionishereafterindicatedas−¹<n^TPCσ <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, thusitisfullyefficientforelectrontrackswithp_T>2 GeV/c.

Fig. 2.Left:TheratioofE/pasafunctionofn^TPC_σ in10%mostcentralPb–Pbevents(pT>3 GeV/c),wherepisthechargedparticlemomentum,EisthematchedEMCal clusterenergy,andσ^TPCistheresolutionontheenergylossintheTPCgasexpectedforelectrons.Right:E/pforelectronsintwotransversemomentumranges.Theblue opensymbolsshowsthehadroncontamination–anE/pdistributionforparticles3.5σ awayfromthemeanofthetrueelectronTPC-dE/dxdistributionnormalised to theelectronE/patsmallvaluesoftheratio(awayfromtheelectronsignal).(Forinterpretationofthereferencestocolourinthisfigure,thereaderisreferredtotheweb versionofthisarticle.)

Additionalhadronrejectionusedthecombinationoftheenergy depositedwithinEMCalandacut ontheelectromagneticshower shape[64,66].Sincetheshowerfromanelectronisfullycontained andaccuratelymeasuredbytheEMCal,theratiooftheenergy(E) measuredbytheEMCalandthemomentum(p)forelectrontracks isapproximatelyunity(E/p≈^{1).The E}/pdistribution isqualita- tivelydifferentinthecaseofhadrons.TheE/pasafunctionofthe n^TPCσ 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 (λ0 and λ1) of the co- variancematrixbuiltfromthetowercoordinatesweightedbythe logarithms ofthetower energies.Theseeigenvalues maybeused todifferentiatebetweenincidentparticlespecies[64].Aselection ofλ²₁<0.3,correspondingtotheshorter-axisoftheshowershape projectedonto theEMCal surface,was applied,because thechar- acteristicelectromagneticshowerofanelectronispeakedatλ²₁ 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 withn^TPCσ <−³.5.The E/p distributionof the hadronswas then normalised tomatchthe distributionoftheelectroncandidatein 0.4<E/p<0.7 (away fromthe trueelectron peak). An example ofthe E/p distributionstogether withtheestimatedhadron con- taminationfortwotransversemomentumintervalsisshowninthe rightpanelofFig. 2.Thehadroncontamination islessthan5% at p_T<10 GeV/c inallcentralityclasses.Athighp_T,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

Themainsourcesofelectronscontributingtotheinclusiveelec- tron sample in this analysis are: a) heavy-flavour hadron decay electrons;b)electronsfromleptonicdecaysofquarkonia(J/ψand ϒ mesons); c) electrons from W and Z/

γ

^∗ decays; d) the so- calledphotonicelectrons,originatingfromphotonconversionsand Dalitz decays ofneutralmesons (mainly

π

⁰ and

η

);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 thisanaly- sis.

Thecontributionofthephotonicelectronstotheinclusiveelec- tron sample was measured by the invariant mass method. The invariant massdistributionwas determinedbypairingeveryelec- tron trackfrom the inclusivesample with an oppositely-charged trackselectedwith−³<n^TPCσ <3toincreasethechanceforfind- ingthepairs.Pairssatisfyingelectronidentificationselectionsand pairs satisfyingacut on theinvariant massofm_inv<0.1 GeV/c² wereselectedforfurtheranalysis.Theseselectedunlike-signpairs, however,containnot onlytruephotonicelectronsbutalsoacon- tribution from random pairs. This combinatorial background to photonicelectrons was estimatedusingtheinvariant massdistri- butionofthelike-signelectrons(N_eL S),anditwassubtractedfrom thatofunlike-signpairs(N_eU L S)toobtainthenumberofrawpho- tonicelectrons:N^raw_eγ =^Ne^{U L S}−^Ne^{L S}.

The efficiency for the identification of the photonicelectrons by the invariant mass method (

ε

e^γ) was estimated from Monte Carlosimulationswithfulldetectorresponseandwasfoundtobe centralityindependent.Theefficiency,shownintherightpanelof Fig. 3,isabout30%atp^e_T=^{4 GeV}/candrisingto55%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:

Ne^γ =^Nraw_eγ /

ε

e^γ.Thefractionofphotonicelectrons withinthein- clusiveelectronsample inthe10%mostcentralcollisionsisabout 30% at pT=^{3 GeV}/c,dropsto25% at12 GeV/c andremains ap- proximatelyconstantathigherp_T consideredinthisanalysis.

Fig. 3.Left:ProductofdetectoracceptanceandreconstructionefficiencyforinclusiveelectronsasafunctionoftheelectronpT.Thestatisticaluncertaintyissmallerthanthe sizeofthepoints.Right:Photonicelectronreconstructionefficiencyviainvariantmass(εe^γ)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 nuclearmodificationfactorR^J_AA^/ψ (pT)measuredattheLHC[71,72].

In 3<p_T<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 toabout6%at17 GeV/c whereas thecontribution from Z/

γ

^∗ isbelow 1% for p_T<10 GeV/c and increasesto2.4%at17 GeV/c.

Theheavy-flavourdecayelectronyieldwasreconstructed from theinclusiveelectronyieldby firstsubtractingthephotonicelec- 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 (uncertaintiesoriginatingfromcor- rectionsrelatedtotrackingandparticleidentification);

– non-heavy-flavourbackgrounddetermination.

AnoverviewofthesystematicuncertaintiesispresentedinTa- 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)

n^TPC_σ 3 (10) 3 (7)

Photonic background 3 (10) 5 (5)

J/ψelectron background 3 (10) 1 (<1)

Welectron background 3 (10) 0 (<1)

Z/γ^∗electron backgrounds 3 (10) <1 (<2)

contributiontothesystematicuncertaintyduetothe1.1% relative uncertainty onthe fractionofhadronic crosssection used inthe Glauberfittodeterminethecentralityislessthan0.1% inthecen- 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.Foreachsetofcutstheanalysiswasrepeatedandcom- pared tothe results obtainedwith the defaultset ofcuts. These variationsincludedchangesintrackqualitycuts,suchasthemin- imumnumberofthe spacepointsin theTPCandassociatedhits intheITS.Theuncertaintieswereestimatedasafunctionoftrack p_T andfor each centrality class separately.In addition, the elec- tron identificationcuts inthe TPC (n^TPCσ ) andEMCal(E/p range) werevariedaroundtheirnominalvalues.Theuncertaintyoriginat- 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<m_inv<0.15 GeV/c²andthemini- mum pTofthetrackspairedwithelectroncandidatesbetween0.3 and0.6GeV/c.

SubtractionofelectronsfromJ/ψ.Theuncertaintyonthesub- tractedbackgroundelectronsfromJ/ψ decayswasestimatedfrom the experimental uncertainties on measured production yields in heavy-ioncollisions[71,77].

ElectronsfromWandZ/

γ

^∗.TheyieldofelectronsfromW de- cayswasvariedby±^{15%onthebasisofthecomparisonoftheW} productioncrosssectionasgivenbythePOWHEGeventgenerator

Fig. 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-flavourdecayelec- 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 modificationfactorR_AA(Eq.(1)),wasobtainedfrommeasurements

andFONLLpQCDcalculations[80,81].ForpT<12 GeV/cthemea- surementat√

s=².76 TeV wasused[30].ForpT>12 GeV/cthere isnomeasurementatthisenergy.Thus,anextrapolatedcrosssec- tionwasconstructedfromthemeasurementat√

s=^{7 TeV bythe} ATLAS Collaboration[82,83] andthe ratioofcrosssectionsatthe twocollisionenergiesobtainedfromFONLL[84].Theuncertainties ofthe pp referencesareabout20% for p_T<12 GeV/c andabout 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 ^TAA^{for 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 R_AA = ^{1 in the figure.In all cases,taking intoaccount} the pT trend of the RAA and the statistical uncertainties of the measurement athigh-p_T, theelectron productionyields aresup- 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 R_pPb 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 R_pPb 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√_s

NN=².76 TeV.ThesolidbandatRPbPb=^{1 bracketsthe}uncertainty ontheaveragenuclearoverlapfunction(^TAA^).

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√_s

NN=².76 TeV comparedtovarioustheoreticalcalcu- 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 p_T-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].Theelec- tronyieldathigh-pT isthereforeexpectedtocontainasignificant contributionfromBmesonswithpTupto30 GeV/c.Consequently, thestrongsuppressionofelectronsforp_T>10 GeV/cisconsistent 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 fromheavy- 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 isconsistentwiththemeasurementwithintheuncertain- tiesincludingtheslowincreaseoftheR_AAasafunctionofelectron pT. 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.ThecalculationsbyVitevetal.[90]alsocapturethemag- nitude of the suppression and reproduce the pT dependence of theelectronsseeninthedata.Thein-mediummodificationofthe heavy quark distribution anddecayprobabilities are evaluated in aco-movingplasma.Thepredictionsforheavy-flavourdecayelec- tronsuppressionareobtainedwithanimprovedperturbativeQCD descriptionofheavyflavourdynamicsinathermalmediumwhere theformation anddissociationofheavy-flavourmesonsare com- bined withparton-level charmandbeautyquarkradiative energy loss.Themodelincludingthedissociationofheavy-flavourhadrons capturesalsothesuppressionofDmesons.

WHDG. The band corresponding tothe WHDG modelcalcula- tions [87–89]isconsistent withthemeasurementwithin theun- certainties; however, it systematically underpredicts thesuppres- 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 astaticther- 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 thesuppres- 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-pTmaybere- latedtotheb-quarkenergylossforwhichthefractionfromelastic processesisincreasedascomparedtocharmquarks.Ontheother

hand,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.Asim- 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 p_T>12 GeV/c.Thismodel also worksbetterfortheDmesons RAAatpT>10 GeV/cascompared 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-p_T.The modelevaluates thedynamicsofenergylossandflowofheavy quarkswithinthe frameworkofaLangevinequationcoupledtoa(2+1)-dimensional viscoushydrodynamicmodelthatsimulatesthespace–timeevolu- tionof theproduced hot anddense QCD matter. Thiscalculation reproduced thesuppression ofDmesonsvery accurately,bothin strengthandthe pT-dependence.

POWLANG.The resultoftheheavy-quarktransportcalculation usingtherelativisticLangevinequationwithcollisionalenergyloss, POWLANG[94,95],isshownfortwochoicesofheavy-flavourtrans- 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 overpredictsthesuppres- 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 T_dec (155 MeV and 170 MeV) from the hydrodynamic evolution ofthefireball.Therelatively smallwidthofthebandssuggestsa weaksensitivityofthesuppressiontotheTdec.Similartotheelec- 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 quarkstobeconsideredtoex- 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/cinseveralcentralityclassesofPb–Pb collisionsat√ s_NN= 2.76 TeV atmid-rapidity. Thenuclear modificationfactor RAA for the 10% mostcentral eventsshowsa strong suppression ofelec- 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 athigh- 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 strongdepen- denceofenergylossonrapidity intherange|^y|< 4.Theoretical calculations that include collisional and radiative in-medium en- ergylossforbothcharmandbeautyquarksreproducetheexperi- mentalfindings.Inparticular,modelsincorporatingthedynamical evolutionofthemediumarepreferredbythedata.

Acknowledgements

The ALICECollaboration would like to thank all its engineers andtechniciansfortheirinvaluablecontributionstotheconstruc- 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 buildingandrun- 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;MinistryofEdu- 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; CentrodeInves- tigacionesEnergéticas,MedioambientalesyTecnológicas(CIEMAT), Cuba;MinistryofEducation,YouthandSportsoftheCzechRepub- lic,Czech Republic;Danish NationalResearchFoundation (DNRF), TheCarlsbergFoundationandTheDanishCouncilforIndependent Research–Natural Sciences,Denmark; Helsinki Institute ofPhysics (HIP),Finland;Commissariatàl’EnergieAtomique(CEA)andInsti- tut National de Physique Nucléaire et de Physique des Particules (IN2P3) andCentre Nationalde la Recherche Scientifique (CNRS), France; Bundesministerium für Bildung, Wissenschaft, Forschung und Technologie(BMBF)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,