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Physics Letters B

www.elsevier.com/locate/physletb

Measurement of electrons from heavy-flavour hadron decays in p–Pb collisions at √

s _NN = ⁵ . 02 TeV

.ALICE Collaboration

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

Articlehistory:

Received12October2015

Receivedinrevisedform12November2015 Accepted21December2015

Availableonline31December2015 Editor:L.Rolandi

Theproductionofelectronsfromheavy-flavourhadrondecayswasmeasuredasafunctionoftransverse momentum(pT)inminimum-biasp–Pb collisions at√_s

NN=⁵.02 TeV using theALICEdetectoratthe LHC. The measurementcoversthe pTinterval 0.5<pT<12 GeV/cand the rapidityrange −¹.065<

ycms<0.135 in the centre-of-mass reference frame. The contribution of electrons from background sources was subtractedusing an invariant mass approach. The nuclear modification factor RpPb was calculatedbycomparingthepT-differentialinvariantcrosssectioninp–Pbcollisionstoappreferenceat thesamecentre-of-massenergy,whichwasobtainedbyinterpolatingmeasurements at√

s=².76 TeV and √_s

=^{7 TeV. The RpPb is consistentwithunity within}uncertainties ofabout 25%,whichbecome largerforpTbelow1 GeV/c.Themeasurementshowsthatheavy-flavourproductionisconsistentwith binary scaling,sothat asuppression inthe high-pT yieldin Pb–Pbcollisions hasto beattributed to effectsinducedbythehotmediumproducedinthefinalstate.Thedatainp–Pbcollisionsaredescribed byrecentmodelcalculationsthatincludecoldnuclearmattereffects.

©^{2015CERNforthebenefitoftheALICE}Collaboration.PublishedbyElsevierB.V.Thisisanopen accessarticleundertheCCBYlicense(http://creativecommons.org/licenses/by/4.0/).FundedbySCOAP³.

1. Introduction

TheQuark-GluonPlasma(QGP)[1,2],acolour-deconfined state of strongly-interacting matter, is predicted to exist at hightem- peratureaccordingtolatticeQuantumChromodynamics(QCD)cal- culations[3].Theseconditionscan bereachedinultra-relativistic heavy-ion collisions [4–10]. Charm and beauty (heavy-flavour) quarks are mostly produced in initial hard scattering processes on a very short time scale, shorter than the formation time of theQGPmedium[11],andthus experiencethefulltemporaland spatial evolutionof thecollision. Whileinteracting withtheQGP medium, heavy quarks lose energy via elastic andradiative pro- cesses [12–14]. Heavy-flavour hadrons are therefore well-suited probestostudythepropertiesoftheQGP.Theeffectofenergyloss onheavy-flavourproduction canbe characterised viathe nuclear modificationfactor(R_AA)ofheavy-flavourhadrons.The R_AAisde- fined as the ratio of the heavy-flavour hadron yield in nucleus–

nucleus (A–A)collisions to that in proton–proton (pp) collisions scaled by the average number of binary nucleon–nucleon colli- sions.The RAA isstudieddifferentiallyasafunctionoftransverse momentum(p_T), rapidity(y)andcollisioncentrality.Itwas mea- sured at the Relativistic Heavy Ion Collider (RHIC) [15–18] and at the Large Hadron Collider (LHC) [19–22]. At RHIC, in central

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

Au–Au collisionsat√

s_NN=200 GeV the R_AA of charmed mesons and of electrons from heavy-flavour hadron decays shows that their productionisstronglysuppressedby afactorofabout5for pT>3 GeV/c at mid-rapidity. For the mostcentral Pb–Pb colli- sions at √

sNN=².76 TeV at the LHC, a suppression by a factor of5–6isobservedforcharmedmesonsfor pT>5 GeV/c atmid- rapidity[22].

The interpretation of the measurements in A–A collisions re- quires the study of heavy-flavour production in p–A collisions, whichprovidesaccesstocoldnuclearmatter(CNM)effects.These effects are not related to the formation of a colour-deconfined medium, but are present in case of colliding nuclei (or proton–

nucleus). An important CNM effect inthe initial state is parton- density shadowing or saturation, which can be described using modified parton distribution functions (PDF) in the nucleus [23]

or using the Color Glass Condensate (CGC) effective theory [24].

FurtherCNMeffects includeenergyloss[25] intheinitial andfi- nalstatesandaCronin-likeenhancement[26]asaconsequenceof multiplescatterings[25,27].

The influence of the CNM effects can be studied by measur- ing the nuclearmodification factor RpA. Like the RAA,the RpA is defined such that it is unity if there are no nuclear effects. For minimum-biasp–Acollisions,itcanbeexpressedas[28]

RpA

=

¹ A

d

σ

pA

/

dpT

d

σ

pp

/

dpT

,

(1)

http://dx.doi.org/10.1016/j.physletb.2015.12.067

0370-2693/©^{2015CERNforthebenefitoftheALICE}Collaboration.PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense (http://creativecommons.org/licenses/by/4.0/).FundedbySCOAP³.

whered

σ

pA/dpT andd

σ

pp/dpT arethe pT-differential production crosssectionsofagivenparticlespeciesinp–Aandppcollisions, respectively,and Aisthenumberofnucleonsinthenucleus.

Cold nuclear matter effects were recently investigated at the RHIC and the LHC [29–44]. At RHIC, the nuclear modification factor of electrons from heavy-flavour hadron decays in central d–Au collisions (0–20%) at √

s_NN=^{200 GeV is larger than unity} atmid-rapidity in thetransverse momentum interval 1.5<pT<

5 GeV/c [42]. The corresponding measurement for muons from heavy-flavour hadron decays in central d–Au collisions shows a suppressionatforwardrapidityandanenhancementatbackward rapidity [43]. Theoretical modelsthat includethe modificationof thePDF inthe nucleuscanneitherexplain the enhancementnor thelargedifferencebetweenforwardandbackwardrapidity.Possi- bleexplanationsincludetheCronin-likeenhancement[26] dueto radial flow ofheavy mesons[45].At the LHC,the pT-differential nuclear modification factor R_pPb of D mesons measured in p–Pb collisions at √

sNN=⁵.02 TeV [44] is consistent with unity for pT>1 GeV/c andisdescribedbytheoretical calculationsthat in- clude gluon saturation effects. Both atRHIC andat theLHC, the p/d–Ameasurementsindicatethatinitial-stateeffectsalonecannot explainthestrongsuppressionseenathigh-pTinnucleus–nucleus collisions.

In this Letter, the pT-differential invariant cross section and the nuclear modification factor RpPb of electrons from heavy- flavourhadron decaysmeasuredinminimum-biasp–Pbcollisions at√

sNN=⁵.02 TeV withALICEattheLHCarepresented.Themea- surementcoverstherapidityrange−¹.065<ycms<0.135 inthe centre-of-masssystem(cms)forelectronswithtransversemomen- tum0.5<pT<12 GeV/c.Thisrapidity coverage resultsfromthe samerigidityofthepandPbbeamsattheLHC,leadingtoarapid- ityshiftof |^yNN|=⁰.465 between the nucleon–nucleoncms and thelaboratoryreferenceframe,inthedirectionofthepbeam.At low pT,themeasurementprobestheproductionofcharm-hadron decays[46],providingsensitivitytothegluonPDFintheregimeof Bjorken-xoftheorderof10⁻⁴[47],whereasubstantialshadowing effectisexpected[48].

ToobtainthenuclearmodificationfactorRpPbofelectronsfrom heavy-flavour hadron decays, the p_T-differential invariant cross section in p–Pb collisions at √

sNN=⁵.02 TeV was compared to a pp reference multiplied by 208, the Pb mass number. The pp reference was obtained by interpolating the p_T-differential cross sectionmeasurementsat√

s=².76 TeV and7 TeV.

The Letter is organised as follows. The experimental appara- tus, data sample and event selection are described in Section 2.

The electron reconstruction strategy and the pp reference spec- trumareexplainedinSections3and4,respectively.Themeasured pT-differentialinvariantcrosssection,thenuclearmodificationfac- tor R_pPb ofelectronsfromheavy-flavourhadrondecaysandcom- parisonofR_pPbtomodelcalculationsarereportedinSection5.

2. Experimentalapparatus,datasampleandeventselection

A detailed description of the ALICE apparatus can be found in [49,50]. Electrons are reconstructed at mid-rapidity using the centralbarreldetectors(describedbelow)locatedinsideasolenoid magnet, which generates a magnetic field B=⁰.5 T along the beamdirection.

TheInnerTrackingSystem(ITS),theclosestdetectortothein- teraction point, includes sixcylindricallayers of silicondetectors withthreedifferenttechnologies(pixel,driftandstrip)atradiibe- tween 3.9 cm and 43 cmwith a pseudorapidity coverage inthe laboratoryreferenceframeinthefullazimuthbetween|

η

_lab|<2.0 atsmallradiiand|

η

lab|<0.9atlargeradii[49,51].Thetwoinner- mostlayers formthe Silicon Pixel Detector (SPD), which plays a

keyroleinprimaryandsecondaryvertexreconstruction.Atanin- cidentangleperpendiculartothedetectorsurfaces,thetotalmate- rialbudgetoftheITScorrespondsonaverageto7.7%ofaradiation length [51].The maintracking device inthecentral barrelis the TimeProjectionChamber(TPC) [52],whichsurroundstheITSand covers a pseudorapidity rangeof|

η

lab|< 0.9 inthefull azimuth.

Thetrackreconstructionproceedsinwardfromtheouterradiusof the TPCto theinnermostlayer ofthe ITS[50]. The TPCprovides particle identificationviathe measurementofthespecific energy lossdE/dx.TheTime-Of-Flightarray(TOF),basedonMulti-gapRe- sistivePlateChambers,coversthefullazimuthand|

η

lab|< 0.9at a radial distanceof 3.7 mfrom the interaction point [53]. Using the particle time-of-flight measurement, electrons can be distin- guishedfromhadronsfor pT≤².5 GeV/c.Thecollisiontime,used forthecalculationofthetime-of-flighttotheTOFdetector,ismea- suredby anarray ofCherenkovcounters,theT0detector,located at +^{350 cm and} −^{70 cm from the} interaction point along the beamdirection[54].TheElectromagneticCalorimeter(EMCal),sit- uatedbehindtheTOF,isasamplingcalorimeterbasedonShashlik technology[55].Itsgeometricalacceptanceis107^◦inazimuthand

|

η

lab|< 0.7. Inthis analysis, theazimuthal angleand

η

coverage were limitedto100^◦ and0.6, respectively,toensure uniformde- tectorperformance.

The minimum-bias (MB) p–Pb datasample used inthis anal- ysis was collected in 2013. The trigger condition required a co- incidence of signalsbetween thetwo V0scintillator hodoscopes, placed on either side ofthe interaction point at2.8<

η

lab<5.1 and−³.7<

η

lab<−¹.7,synchronisedwiththepassageofbunches frombothbeams[54].The backgroundduetointeractions ofone ofthetwobeamsandresidualparticlesinthebeamvacuumtube was rejectedintheofflineeventselectionbycorrelating thetime informationofthe V0detectorswiththatfromthe twoZeroDe- greeCalorimeters(ZDC) [50],thatarelocated112.5 mawayfrom the interaction point along the beam pipe, symmetrically on ei- therside.Theprimaryvertexwasreconstructedwithtracksinthe ITSandtheTPC[50].Eventswithaprimaryvertexlocatedfarther than ±^{10 cm from thecentreofthe}interaction regionalong the beamdirectionwererejected.About10%oftheeventsdonotfulfil thisselectioncriterion.Asampleof100millioneventspassedthe offline eventselection, corresponding toan integrated luminosity Lint=⁴⁷.8±¹.6 μb⁻¹,giventhecrosssection

σ

_MB^V0₌2.09±⁰.07 b fortheminimum-biasV0triggercondition [56].Theefficiencyfor thetriggerconditionandofflineeventselectionislargerthan99%

fornon-single-diffractive(NSD)p–Pbcollisions [57].

3. Analysis

A combination of electron identification (eID) strategies with different detectors offers the largest pT reach for the measure- mentofelectronsfromheavy-flavourhadrondecays.Inparticular, it ensures that thesystematic uncertainties andthe hadron con- taminationaresmalloverthewholetransversemomentumrange.

Throughoutthepaper,theterm‘electron’isusedforelectronsand positrons. The capabilityofthe TPCtoidentifyelectrons via spe- cific energy loss dE/dx in thedetector was usedover the whole momentum range 0.5<p_T<12 GeV/c. However, itis subjectto ambiguous identification of hadrons (pions, kaons, protons and deuterons)below2.5 GeV/candabove6 GeV/cintransversemo- mentum. At low transverse momentum (0.5< p_T<2.5 GeV/c), these ambiguities were resolved by measuring the time-of-flight oftheparticlefromtheinteractionregiontotheTOFdetectorand combiningitwiththemomentummeasurement,todeterminethe particlemass.Inthehighmomentumregion(6<pT<12 GeV/c), theEMCalwasusedtoreducethehadroncontamination.Electrons are separatedfromhadronsbycalculatingtheratiooftheenergy

Fig. 1.(a):MeasureddE/dxintheTPCasfunctionofmomentump expressedasadeviationfromtheexpectedenergylossofelectrons, normalisedbytheenergy-loss resolution(σTPC) aftereIDwithTOF.Thesolidlinesindicatethen^TPC_σ selectioncriteriafortheTPCandTOFeIDstrategy.(b):E/pdistributionofelectrons(−¹<n^TPC_σ <3) andhadrons(n^TPC_σ <−3.5)inthetransversemomentuminterval6<pT<8 GeV/c.TheE/pdistributionofhadronswasnormalisedtothatofelectronsinthelowerE/p range(0.4–0.6),wherehadronsdominate.Thesolidlinesindicatetheappliedelectronselectioncriteria.(Forinterpretationofthereferencestocolorinthisfigurelegend, thereaderisreferredtothewebversionofthisarticle.)

deposited(E) intheEMCaltothemomentum(p).Sinceelectrons depositall oftheir energyin theEMCal,the ratio E/pis around unity forelectrons, while the ratio for charged hadronsis much smalleronaverage.

Theselection criteriaforcharged-particle tracksare similar to those applied in previous analyses measuring the production of electrons from heavy-flavour hadron decays in pp collisions [58, 59].In orderto haveoptimaleIDperformance with theTPC, the analysis was restricted to the pseudorapidity range |

η

lab|<0.6 inthe laboratoryframe forelectrons withtransverse momentum 0.5<pT<12 GeV/c.Up to a pT of6 GeV/c,a signal in thein- nermost layer of the SPD was required in order to reduce the background from photon conversions. In addition, this selection was further constrained by requiring hits in both SPD layers, to reducethenumberofincorrectmatchesbetweencandidatetracks andhits reconstructed in the first layer of the SPD. At high p_T, wheretheEMCal was used,trackswithhitsin eitheroftheSPD layerswereselectedinordertominimisetheeffectofdeadareas ofthefirst SPDlayer withinthe acceptanceregion ofthe EMCal, asinpreviousanalyses[58,59].

TheelectronidentificationwithTPCandTOFwasbasedonthe numberofstandard deviations(n^TPCσ orn^TOFσ ) forthe specific en- ergy loss and time-of-flight measurements, respectively. The nσ variable is computedas a difference betweenthe measured sig- nal and the expected one for electrons divided by the energy loss (

σ

TPC) or time-of-flight (

σ

TOF) resolution. The expected sig- nal and resolution originate from parametrisations of the detec- tor signal, which are described in detail in [50]. In the trans- verse momentum interval 0.5<pT<2.5 GeV/c, particles were identified as electrons if they satisfied −⁰.5<n^TPCσ <3, which yields an identification efficiency of 69%. In the transverse mo- mentuminterval 2.5<p_T<6 GeV/c,a tighterselection criterion of 0<n^TPCσ <3 was applied (with an eID efficiency of 50%) to reduce the hadron contamination at higher transverse momen- tum.Toresolvetheaforementionedambiguitiesatlowtransverse momentum (pT≤².5 GeV/c), only tracks with |^nTOFσ |<3 were accepted. Fig. 1(a) shows the measured dE/dx in the TPC with respecttotheexpecteddE/dxforelectronsnormalisedtotheex- pectedresolution

σ

TPCaftertheeIDwithTOF.Thesolidlinesindi- catetheselectioncriteriausedforthetransversemomentuminter-

val0.5<pT<2.5 GeV/c,indicatingthatthehadroncontamination withintheresultingelectroncandidatesampleissmall.Inthehigh momentumregion(6<pT<12 GeV/c),electronswereselectedif theysatisfied−¹<n^TPCσ <3 and0.8<E/p<1.2 (seeFig. 1(b)).

The hadron contamination in the electron candidate sample was determined by parametrising the TPC signal in momentum slicesforpT≤^{6 GeV}/casdoneinpreviousanalyses[58,59].In the transverse momentum interval 6<pT<12 GeV/c, the E/p dis- tribution forhadronsidentified via the specific energyloss mea- suredinthe TPC(n^TPCσ <−³.5) wasnormalised inthelower E/p range(0.4–0.6)tothecorrespondingE/pdistributionforidentified electrons (−¹<n^TPCσ <3) (see Fig. 1(b)).The number ofhadrons with an E/p ratio between 0.8 and 1.2was thus determined in momentum slices. The hadron contamination ranged from2% at 5<p_T<6 GeV/c to 15% at10<p_T<12 GeV/c andwas corre- spondingly subtracted. For pT<5 GeV/c, the contamination was foundtobenegligible.

Theresultingelectroncandidatesample,alsoreferredtoasthe

‘inclusiveelectronsample’inthefollowing,stillcontainselectrons fromsourcesotherthanheavy-flavourhadrondecays.Themajority of theremaining backgroundoriginates fromphoton conversions inthedetectormaterial(

γ

→^{e+e−) andDalitzdecaysofneutral} mesons,e.g.

π

⁰_→

γ

e⁺e⁻ and

η

→

γ

e⁺e⁻.Theseelectronsare hereafterdenotedas‘photonicelectrons’.

Inpreviousanalysesofelectronsfromheavy-flavourhadronde- caysinppcollisionsbytheALICECollaboration,thecontributionof electronsfrombackgroundsourceswasestimatedviaadata-tuned Monte Carlo cocktail and subtracted from the inclusive electron sample [58,59].Thepioninput tothecocktail wasbasedon pion measurementswithALICE[60,61],whileheaviermesonswereim- plemented via m_T scaling[62],andphotonsfromhard scattering processes(direct

γ

,

γ

^∗)wereobtainedfromnext-to-leadingorder (NLO)calculations[63].Theresultingsystematicuncertaintyofthe sumofall backgroundsourceswas large, inparticularatlow p_T, wherethesignal-to-background ratioissmall[58,59].Inorder to reduce this uncertainty, in this analysis an invariant mass tech- nique[16] was usedto estimatethe numberofelectrons coming frombackgroundsources.

Photonicelectronsareproducedine⁺e⁻pairsandcanthusbe identified using an invariant mass technique (photonic method).

Fig. 2.Invariant massdistributionsofunlike-sign andlike-signelectronpairsfor theinclusiveelectronpTinterval0.5<pT<0.6 GeV/c.Thedifferencebetweenthe distributionsyieldsthephotoniccontribution.

Allinclusiveelectrons were paired withother tracks inthe same eventpassingloosertrackselectionandelectronidentificationcri- teria(e.g.−³<n^TPCσ <3).Looserselectioncriteriawereappliedto increase the efficiencyto findthe photonic partner. Fig. 2shows theinvariant massdistributions ofunlike-sign andlike-signelec- tron pairs for the inclusive electron in the interval 0.5<pT<

0.6 GeV/c. The like-sign distribution estimates the uncorrelated pairs.Subtractingthesefromtheunlike-signpairsyieldsthenum- ber of electrons with a photonic partner N_phot^raw (see Fig. 2). An invariant mass smaller than 0.14 GeV/c² was required. Accord- ing to simulations, the peak around zero in the photonic elec- tronpairdistribution isdueto photonconversions; theexponen- tialtail to higher valuesoriginates fromDalitz decays of neutral mesons.

The efficiency

ε

phot to find photonic electron pairs was esti- matedusingMonteCarlosimulations.Asampleofp–Pbcollisions was generated with HIJING v1.36 [64]. Toincrease the statistical precision at high p_T, one cc or bb pair decaying semileptoni- cally usingthe generatorPYTHIAv6.4.21 [65] withthePerugia-0 tune[66] was added ineach event.The generatedparticles were propagated throughtheapparatususingGEANT3 [67]anda real- isticdetectorresponse wasappliedto reproducetheperformance of the detector systemduring data taking period.The simulated transversemomentumdistributionsofthe

π

⁰ and

η

mesonswere weighted to match the measured shapes, where the

π

⁰ input was basedon themeasured charged-pion spectra [68,69]assum- ing Nπ⁰=¹/2(Nπ⁺+^Nπ⁻) andthe

η

input was derived via mT scaling.Theefficiency

ε

phot isdefinedasthefractionofelectrons fromphotonicoriginforwhichthepartnercouldbefoundwithin the defined acceptance of the analysis, i.e. the geometrical ac- ceptanceof theALICEapparatustogether with thesuperimposed track selection and electron identification criteria. The efficiency

ε

phot increasessharplywithpT from35%to80%between0.5and 3 GeV/c and remains at 80% up to 12 GeV/c. The raw photonic electron distribution N^raw_phot was then corrected by the efficiency

ε

phot as N_phot(pT)=^Nraw_phot(pT)/

ε

phot(pT) andsubtracted fromthe inclusiveelectronyieldtoobtaintheyieldofelectronsfromheavy- flavour hadron decays. The signal-to-background ratio (ratio of non-photonic to photonicyield) ranges from0.2 at 0.5 GeV/c to 4at10 GeV/c.

The remaining electrons are then those from semileptonic heavy-flavourhadrondecays(N_hfe^raw),besidesasmallresidualback- ground contribution originating from semileptonic kaon decays

anddielectron decaysofJ/ψ mesons. Thelatteris theonly non- negligible contribution from quarkonia.These contributions were subtractedfromthecorrectedinvariantcrosssection,asdescribed lateroninthissection.

ThepT-differentialinvariantcrosssection

σ

hfeofelectronsfrom heavy-flavourhadrondecays,1/2(e⁺+^e−),wascalculatedas

1 2

π

pT

d²

σ

_hfe

dpTdy

=

¹ 2

1

ϕ

p^centre_T 1 y p_T

c_unfoldN^raw_hfe

(

^geo

×

^reco

×

^eID

)

σ

_MB^V0

N_MB

,

(2) where p^centre_T arethecentresofthe pTbinswithwidths pT,and

ϕ

and ydenotethegeometricalacceptanceinazimuthandra- piditytowhichtheanalysiswasrestricted,respectively.N_MBisthe numberofeventsthatpasstheselectioncriteriadescribedinSec- tion 2 and

σ

_MB^V0 is the p–Pb cross section for the minimum-bias V0 trigger condition. The rawspectrum ofelectrons from heavy- flavour hadron decays(N^raw_hfe) wascorrected fortheacceptanceof the detectors in the selected geometrical region of the analysis (

^geo),thetrackreconstructionandselectionefficiency(

^reco),and the eID efficiency(

^eID). These correctionswere computedusing theaforementionedMonteCarlosimulations.Onlytheefficiencyof theTPCelectronidentificationselectioncriterionforp_T<6 GeV/c was determined usinga data-driven approach based on then^TPCσ distribution [59]. Themeasurement oftheelectron pT isaffected by the finite momentum resolution and by electron energy loss duetobremsstrahlunginthedetectormaterial[49],whichisnot corrected for in the trackreconstruction algorithm. These effects distort theshape of the pT distribution,which fallssteeply with increasingmomentum.Todeterminethiscorrection(cunfold),anit- erativeunfoldingprocedurebasedonBayes’theoremwas applied [70,71].

The aforementioned residual background contributions, elec- tronsfromsemileptonickaondecaysanddielectrondecaysofJ/ψ mesons,were estimatedasan invariant crosssectionwithMonte Carlosimulationsandfoundtobelessthan3%perpTbinandsub- tractedfromthecorrectedinvariant crosssection ofnon-photonic electrons.Morespecifically,thecontributionfromJ/ψmesonswas implemented by using a parametrisation for pp collisions based on the interpolation of J/ψ measurements from RHIC at √

s= 200 GeV,Tevatron at√

s=¹.96 TeV,andthe LHCat√

s=^{7 TeV} accordingto [72].Decays ofJ/ψ mesonswithin |^ylab|< 1.0were considered. Theparametrisationandits associatedsystematicun- certainty werescaled frompptop–Pbcollisions assumingbinary collision scaling.Potentialdeviationsfrombinary collision scaling wereconsideredbyassigning a50%systematicuncertaintyonthe normalisation. The parametrisationwithits uncertainties usedas inputfortheMonteCarlosimulationsisconsistentwiththemea- suredJ/ψ crosssectioninp–Pbcollisions[38].

The systematic uncertainties were estimated as a function of pT by repeating theanalysis withdifferentselection criteria. The systematicuncertaintieswereevaluatedforthespectrumobtained afterthesubtractionofthephotonicyieldN_photfromtheinclusive spectrum andbefore removing the remaining backgroundcontri- butions originatingfromsemileptonickaondecaysanddielectron decays of J/ψ mesons. The sources of systematic uncertaintyfor theinclusiveanalysisandthedeterminationoftheelectronback- groundarelistedinTable 1.

The systematic uncertainties for tracking and eID are pT de- pendentduetotheusageofthevariousdetectorsinthedifferent momentumintervals.Thelatteralsoincludestheuncertaintiesdue tothedeterminationofthehadroncontamination.The3%system- aticuncertaintyforthematchingbetweenITSandTPCwastaken from [73], where the matching efficiency of charged particles in

Table 1

Systematicuncertaintiesforthedifferentmomentumintervals.

Variable 0.5<pT<2.5 GeV/c 2.5<pT<6 GeV/c 6<pT<12 GeV/c

Tracking 4.3% 2.2% 3%

Matching 4.2% 3% 3.2%

eID 3.6% 3.6% 3.2% (6–8 GeV/c)

5.1% (8–10 GeV/c) 15.1% (10–12 GeV/c) Photonic

method

6.9% (0.5–1 GeV/c) 2.4% 4.5%

3.7% (1–2.5 GeV/c)

Unfolding 1% 1% <1%

Total 9.9% (0.5–1 GeV/c) 5.8% 7.1% (6–8 GeV/c) 8.0% (1–2.5 GeV/c) 8.1% (8–10 GeV/c)

16.4% (10–12 GeV/c)

data was compared to Monte Carlosimulations. The uncertainty ofthe TOF-TPC matching efficiencywas estimatedby comparing thematching efficiency indata andMonte Carlosimulations us- ingelectrons fromphoton conversions, whichwere identified via topological cuts. The uncertainty amounts to 3%. The TPC-EMCal matching uncertainty was assigned to be 1%, as determined by varyingthesizeofthematchingwindowin

η

andazimuth

ϕ

for charged-particle tracksthat were extrapolatedto thecalorimeter.

Theresultingmatchinguncertaintieswerecombinedinquadrature forthevarious pTintervalsshowninTable 1.

The listed uncertainties for the photonic method include the uncertainties on eID and tracking. In addition, the Monte Carlo sample was divided into two halves. The first was treated as realdataand thesecond was used tocorrect theresulting spec- trum.Deviationsfromtheexpected pTspectrumofelectronsfrom heavy-flavour hadron decays resulted in a 2% systematic uncer- tainty for pT≤^{6 GeV}/c and 4% above. The uncertainty on the re-weighting of the

π

⁰- and

η

-meson pT distributions inMonte Carlosimulationswasestimatedbychangingtheweightsby±^10%.

The variation yielded a 2% uncertainty for pT≤².5 GeV/c on thep_T-differentialinvariantcrosssectionofelectronsfromheavy- flavour hadron decays.This source ofuncertainty isnegligible at higherpT.Theinvariantmasstechniquegivesasystematicuncer- taintysmallerbyafactorof≥^{4 andofabout1.4forp}T≤^{1 GeV}/c and3<pT<12 GeV/c,respectively, comparedto theone ofthe cocktailsubtractionmethod[59].Thereduction inuncertainty,in particularatlow pT,proves the advantageof usingthe invariant mass technique for the estimation of electrons from background sources.

Theuncertaintyofthe pTunfoldingprocedurewasdetermined by employing an alternativeunfolding method (matrix inversion) and,asdescribedin[59],bycorrectingthedatawithtwodifferent MonteCarlosamplescorrespondingtodifferentp_Tdistributions.In additiontotheaforementionedsignal-enhancedMonteCarlosam- ple,aminimum-biassample wasused.Thecomparisonofthere- sultingpT spectrarevealedanuncertaintyof1%forpT≤^{6 GeV}/c, andsmaller than1% above6 GeV/c.The systematicuncertainties ofthe heavy-flavour electron yield dueto the subtractionof the remaining backgroundoriginatingfromsemileptonic kaondecays anddielectrondecaysfromJ/ψmesonsaresmallerthan0.5%.This wasestimatedbychangingtheparticleyieldsby±^{50% and}±^100%

fortheJ/ψmesonandthesemileptonickaondecays,respectively.

The individual sources of systematic uncertainties are uncor- related. Therefore,they were added in quadratureto give a total systematicuncertainty rangingfrom 5.8% to 16.4% depending on the pT bin. The normalisation uncertainty on the luminosity is of 3.7%[56].

Fig. 3showstheinterval2.5<p_T<8 GeV/cofthep_T-differen- tialinvariant crosssection ofelectrons fromheavy-flavourhadron decaysinminimum-biasp–Pbcollisionsat√

s_NN=⁵.02 TeV,com-

Fig. 3.The pT-differentialinvariant crosssectionofelectronsfromheavy-flavour hadron decaysinminimum-biasp–Pbcollisions at√

sNN=5.02 TeV,comparing theresultsoftheeIDstrategiesinthetwotransitionregionsat2.5and6 GeV/c.

ThecentrevaluesareslightlyshiftedalongthepT-axisinthetransitionregionsfor bettervisibility.Theresultsagreewithin1%.DetailsontheeIDstrategiescanbe foundinthetext.

paringtheresultsofthevariouseIDstrategiesinthetwotransition regions at 2.5 GeV/c and 6 GeV/c. A consistency within 1% is found.

4. ppreference

In order to calculate the nuclear modification factor R_pPb, a reference cross section forpp collisions at the samecentre-of- mass energyis needed. Since pp dataat √

s=⁵.02 TeV are cur- rently not available, the reference was obtained by interpolating the p_T-differential cross sections of electrons from heavy-flavour hadrondecaysmeasuredinpp collisionsat√

s=².76 TeV andat

√s=^{7 TeV [58,59].Theanalysisdescribed in thispaperrequires} a referenceinthe interval0.5<p_T<12 GeV/c.While the√

s= 2.76 TeV analysiswascarriedoutinthisp_Trange,the√

s=^{7 TeV} measurement is limited to the p_T interval 0.5<p_T<8 GeV/c.

Thus, to extendthe p_T interval up to 12 GeV/c a measurement by theATLAS Collaborationin the p_T interval 7<p_T<12 GeV/c was used [74]. The published ATLAS measurement, d

σ

/dp_T, was dividedby1/(2

π

p^centre_T y),wherep^centre_T denotesthecentralval- ues of the p_T bins, and y the rapidity range covered by the measurement.Intheoverlapinterval7<p_T<8 GeV/c theALICE andATLASmeasurements,whichagreewithinuncertainties,were combined as a weighted average. The inverse quadratic sum of statistical and systematic uncertainties of the two spectra were used as weights. Perturbative QCD (pQCD) calculations at fixed order withnext-to-leading-log (FONLL) resummation[75–77] de- scribe all aforementioned pp results [58,59] within experimental and theoretical uncertainties. The pp references are measured in asymmetric rapiditywindow(|^ycms|<0.8 at √

s=².76 TeV and

|^ycms|<0.5 at√

s=^{7 TeV).Theeffectduetothedifferentasym-} metricrapiditywindowinthisanalysiswasestimatedwithFONLL andismuchsmallerthanthesystematicuncertaintiesofthedata, thereforeiswasneglected.

Anassumption aboutthe √

s dependenceoftheheavy-flavour productioncross sectionsisrequired fortheinterpolation. Calcu- lationsbasedonpQCDareconsistentwithapower-lawscalingof theheavy-flavourproductioncrosssectionwith√

s[78]. Therefore,

Fig. 4.The pT-differentialinvariantcross sectionofelectronsfromheavy-flavour hadrondecaysinminimum-biasp–Pbcollisionsat√

sNN=5.02 TeV.Thepprefer- enceobtainedviatheinterpolationmethodisshown,notscaledbyA,forcompar- ison.Thestatisticaluncertaintiesareindicatedforbothspectrabyerrorbars,the systematicuncertaintiesareshownasboxes.

thisscalingwasusedtocalculatetheinterpolateddatapoints.The statisticaluncertainties ofthespectraat√

s=².76 TeV and √ s= 7 TeV were added in quadrature with weights according to the

√sinterpolation.Theweightedcorrelatedsystematicuncertainties (tracking,matchingandeID)ofthespectraat√

s=².76 TeV and

√s=^{7 TeV wereaddedlinearly,whiletheweighted} uncorrelated uncertainties(ITS layerconditions,unfolding andcocktail system- atics) were added in quadrature. The weights were determined accordingtothe√

sinterpolation.Theuncorrelatedandcorrelated uncertaintieswerethenaddedinquadrature.

Thesystematicuncertaintyofthebin-by-bininterpolationpro- cedurewasaddedinquadraturetothepreviousones.Itwas esti- matedbyusingalinearorexponentialdependenceon√

sinstead ofapowerlaw.Theratiosoftheresulting p_T spectratothebase- linepp reference were usedto estimate asystematic uncertainty of⁺₋₁₀⁵%.

The resulting pp reference cross section is well described by FONLLcalculations.Thesystematicuncertaintiesofthenormalisa- tionsrelatedtothedeterminationoftheminimum-biasnucleon–

nucleon cross sections of the input spectra were likewise inter- polated, yielding a normalisation uncertainty of 2.3% for the pp referencespectrum,assumingthattheyareuncorrelated.

5. Results

The p_T-differential invariant cross section of electrons from heavy-flavour hadron decays in the rapidity range −¹.065<

y_cms<0.135 for p–Pbcollisions at √

s_NN=⁵.02 TeV isshown in Fig. 4andcomparedwiththeppreferencecrosssection. Thever- tical bars represent the statistical uncertainties, while the boxes indicate the systematic uncertainties. The systematic uncertain- ties of the p–Pb cross section are smaller than those of the pp cross section, in particularat low transverse momentum, mainly as a consequence of the estimation of the electron background via the invariant mass technique. For the pp analysis, the back- ground was subtracted via the cocktail method. At low pT, the electrons mainly originate from charm-hadron decays, while for p_T≥^{4 GeV}/c beauty-hadron decays are the dominant source in ppcollisions[46].

Fig. 5.NuclearmodificationfactorRpPbofelectronsfromheavy-flavourhadronde- caysasafunctionoftransversemomentumforminimum-biasp–Pbcollisionsat

√_s

NN=⁵.02 TeV,comparedwiththeoreticalmodels[25,27,45,48,75],asdescribed inthetext.Theverticalbarsrepresentthestatisticaluncertainties,andtheboxes indicatethesystematicuncertainties.Thesystematicuncertaintyfromthenormali- sation,commontoallpoints,isshownasafilledboxathighpT.

The nuclear modificationfactor R_pPb ofelectrons from heavy- flavour hadron decays asa function of transverse momentum is showninFig. 5.Thestatisticalandsystematicuncertaintiesofthe spectra in p–Pb andpp were propagated as independent uncer- tainties. The normalisation uncertainties ofthe pp referenceand thep–Pbspectrumwereaddedinquadratureandareshownasa filledboxathightransversemomentuminFig. 5.

The R_pPbisconsistentwithunitywithinuncertaintiesoverthe whole pT rangeofthe measurement.Theproductionofelectrons from heavy-flavourhadron decays isthus consistent withbinary collisionscaling ofthereferencespectrumforpp collisionsatthe samecentre-of-massenergy.Thesuppressionoftheyieldofheavy- flavour production in Pb–Pb collisions at high-pT is therefore a finalstateeffectinducedbytheproducedhotmedium.

Given the large systematic uncertainties, our measurement is also compatiblewithan enhancement in the transversemomen- tum interval 1<p_T<6 GeV/c asseen at mid-rapidity in d–Au collisionsat√

sNN=^{200 GeV[42].Suchan}enhancementmightbe causedbyradialflowassuggestedbystudiesonthemeanpT asa functionoftheidentifiedparticlemultiplicity[68].

The data are described within the uncertainties by pQCD cal- culations including initial-state effects (FONLL [75] + ^EPS09NLO [48] nuclear shadowingparametrisation).The resultssuggestthat initial-state effects are small at high transverse momentum in Pb–Pb collisions.CalculationsbySharmaet al.whichincludeCNM energy loss, nuclear shadowing andcoherent multiple scattering atthepartoniclevelalsodescribethedata[27].Calculationsbased on incoherent multiple scatterings by Kang et al. predict an en- hancement atlow p_T [25]. The formation of a hydrodynamically expanding medium and consequently flow of charm and beauty quarks are expectedto result in an enhancement in the nuclear modification factor RpPb [45]. To quantify the possible effect on R_pPb,a blastwavecalculationwithparameters extractedfromfits to the pT spectraoflight-flavourhadrons[68] measured inp–Pb collisions was employed. The model calculation agrees with the data. However, the present uncertainties of the measurement do not allowusto discriminateamongthe aforementionedtheoreti- calapproaches.

6. Summaryandconclusions

The pT-differential invariant cross section for electrons from heavy-flavourhadron decaysin minimum-bias p–Pb collisions at

√sNN=⁵.02 TeV was measured in the rapidity range −¹.065<

ycms<0.135 and the transverse momentum interval 0.5<pT<

12 GeV/c using the combination of three electron identification methods.Theapplicationofthe invariantmass techniqueto sub- tractelectronsnotoriginatingfromopenheavy-flavourhadronde- cays largely reducedthe systematicuncertainties withrespect to the cocktail subtraction method, in particular at low transverse momentum.The pp reference forthe nuclearmodification factor R_pPb was obtained by interpolating the measured p_T-differential cross sections of electrons from heavy-flavour hadron decays at

√s=².76 TeV and√

s=^{7 TeV.The R}pPb isconsistent withunity withinuncertaintiesofabout25%,whichbecomelargerforpT be- low1 GeV/c.Thepresentedcalculationsdescribethe datawithin uncertainties.Theresultssuggestthatheavy-flavourproductionin minimum-bias p–Pbcollisions scales withthe number of binary collisions,although within uncertainties thedata are alsoconsis- tentwithanenhancementabovethisscaling.Theconsistencywith unity of the RpPb at high pT indicates that the suppression of heavy-flavourproductioninPb–Pb collisions isofdifferentorigin thancoldnuclearmattereffects.

Acknowledgements

The ALICECollaboration wouldlike to thank all its engineers andtechniciansfortheirinvaluablecontributionstotheconstruc- tionoftheexperimentandtheCERNacceleratorteamsfortheout- standingperformanceoftheLHCcomplex.TheALICECollaboration gratefully acknowledges the resources and support provided by allGrid centresandthe Worldwide LHCComputing Grid(WLCG) Collaboration. The ALICE Collaboration acknowledges the follow- ing funding agencies for their support in building and running theALICEdetector:State CommitteeofScience,World Federation ofScientists (WFS) andSwiss Fonds Kidagan, Armenia; Conselho Nacionalde Desenvolvimento Científico e Tecnológico(CNPq), Fi- nanciadorade Estudose Projetos(FINEP),Fundação de Amparoà Pesquisa do Estado de São Paulo (FAPESP); NationalNatural Sci- enceFoundation ofChina (NSFC),the Chinese MinistryofEduca- tion(CMOE)andtheMinistryofScienceandTechnology ofChina (MSTC); Ministry ofEducation and Youth of the Czech Republic;

Danish Natural Science Research Council, the Carlsberg Founda- tionandtheDanish NationalResearchFoundation;The European ResearchCouncilundertheEuropeanCommunity’sSeventhFrame- work Programme; Helsinki Institute of Physics and the Academy of Finland; French CNRS-IN2P3, the ‘Region Pays de Loire’, ‘Re- gion Alsace’, ‘Region Auvergne’ and CEA, France; German Bun- desministerium fur Bildung, Wissenschaft, Forschung und Tech- nologie(BMBF)andtheHelmholtzAssociation;GeneralSecretariat for Research and Technology, Ministry of Development, Greece;

HungarianOrszagos Tudomanyos KutatasiAlappgrammok (OTKA) andNationalOfficeforResearchandTechnology (NKTH); Depart- mentofAtomicEnergyandDepartmentofScienceandTechnology of the Government of India; Istituto Nazionale di Fisica Nucle- are (INFN) andCentroFermi –Museo Storico dellaFisica e Cen- troStudi e Ricerche “Enrico Fermi”,Italy; MEXT Grant-in-Aid for SpeciallyPromotedResearch,Japan;JointInstituteforNuclear Re- search,Dubna;NationalResearchFoundationofKorea(NRF);Con- sejoNacionaldeCiencayTecnologia(CONACYT),DirecciónGeneral de Asuntos del Personal Academico (DGAPA), México, Amerique Latine Formation academique – European Commission (ALFA-EC) andtheEPLANETProgram (EuropeanParticlePhysicsLatin Ameri- canNetwork);StichtingvoorFundamenteelOnderzoekderMaterie

(FOM)andtheNederlandseOrganisatievoorWetenschappelijkOn- derzoek (NWO), Netherlands; Research Council ofNorway (NFR);

NationalScienceCentre,Poland;MinistryofNationalEducation/In- stitute for Atomic Physics and National Council of Scientific Re- search in Higher Education (CNCSI-UEFISCDI), Romania; Ministry ofEducationandScience ofRussianFederation, RussianAcademy ofSciences,RussianFederalAgencyofAtomicEnergy,RussianFed- eral Agency for Science and Innovations and The Russian Foun- dation for BasicResearch; Ministry ofEducation of Slovakia; De- partment of Science and Technology, Republic of South Africa, South Africa; Centro de Investigaciones Energeticas, Medioambi- entales yTecnologicas (CIEMAT),E-Infrastructureshared between EuropeandLatin America(EELA),MinisteriodeEconomíayCom- petitividad (MINECO) of Spain, Xunta de Galicia (Consellería de Educación), Centro de Aplicaciones TecnológicasyDesarrollo Nu- clear(CEADEN),Cubaenergía,Cuba,andIAEA(InternationalAtomic EnergyAgency);SwedishResearchCouncil (VR)andKnut& Alice WallenbergFoundation (KAW);UkraineMinistryofEducationand Science;UnitedKingdomScienceandTechnologyFacilitiesCouncil (STFC);TheUnitedStatesDepartmentofEnergy,theUnitedStates NationalScience Foundation, the State of Texas, andthe State of Ohio; Ministry of Science, Education and Sports of Croatia and Unity throughKnowledge Fund, Croatia; Council ofScientific and IndustrialResearch(CSIR),NewDelhi,India;PontificiaUniversidad CatólicadelPerú.

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