Dielectron and heavy-quark production in inelastic and high-multiplicity proton–proton collisions at √s=13 TeV

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Dielectron and heavy-quark production in inelastic and high-multiplicity proton–proton collisions at √

s = ^{13 TeV}

.ALICE Collaboration

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

Articlehistory:

Received23May2018

Receivedinrevisedform8October2018 Accepted6November2018

Availableonline9November2018 Editor: M.Doser

Themeasurementofdielectronproductionispresentedasafunctionofinvariantmassandtransverse momentum(pT)atmidrapidity(|^ye|<0.8)inproton–proton(pp)collisionsatacentre-of-massenergy of√

s=^{13 TeV.The} contributionsfromlight-hadrondecaysare calculatedfromtheirmeasured cross sections in pp collisions at √

s=^{7 TeV or13 TeV. The remaining continuum stems from correlated} semileptonicdecays ofheavy-flavour hadrons.Fitting the data withtemplates fromtwo differentMC eventgenerators,PYTHIAandPOWHEG,thecharmandbeautycrosssectionsatmidrapidityareextracted for the first timeat thiscollision energy:dσc^c¯/dy|y=⁰=⁹⁷⁴±¹³⁸(stat.)±¹⁴⁰(syst.)±²¹⁴(BR) μb anddσ_b¯b/dy|^y=⁰=⁷⁹±¹⁴(stat.)±¹¹(syst.)±⁵(BR)μb usingPYTHIAsimulationsanddσc^c¯/dy|^y=⁰= 1417±¹⁸⁴(stat.)±²⁰⁴(syst.)±³¹²(BR) μb anddσ_b¯b/dy|^y=⁰=⁴⁸±¹⁴(stat.)±⁷(syst.)±³(BR) μb for POWHEG. These values, whose uncertainties are fully correlated between the two generators, are consistent with extrapolations fromlower energies. The different results obtained withPOWHEG and PYTHIA implydifferent kinematic correlations ofthe heavy-quark pairs inthese two generators.

Furthermore, comparisons of dielectron spectra in inelastic events and in events collected with a trigger on high charged-particle multiplicities are presented in various pT intervals. The differences are consistentwith thealreadymeasuredscaling oflight-hadronand open-charmproductionathigh charged-particle multiplicity as a function of pT. Upper limits for the contribution of virtual direct photonsareextractedat90%confidencelevelandfoundtobeinagreementwithpQCDcalculations.

©^{2018TheAuthor.PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense} (http://creativecommons.org/licenses/by/4.0/).FundedbySCOAP³.

1. Introduction

Heavy-flavour quarks (charm and beauty) are copiously pro- duced by inelastic partonic scatterings in high-energy proton–

proton (pp) collisions at the CERN Large Hadron Collider (LHC).

Theirlarge masses(mQ) make it possible to calculate their pro- ductioncrosssectionswithperturbative quantum chromodynam- ics (pQCD) [1–3]. Hence, experimental measurements of heavy- quarkproductionprovideanexcellent testofpQCDinthisenergy regime.Flavourconservationallowsheavy quarksto beonlypro- duced in pairs. Charm hadrons and their decay products reflect theinitialangularcorrelationoftheheavy-quarkpairs,whereasin thecaseofdecaysofbeautyhadronsthecorrelation isweakened dueto their large masses. The contribution from the simultane- oussemileptonicdecaysofthecorrespondingheavy-flavourhadron pairsdominatesthedileptonyieldintheintermediatemassregion (IMR)1<m<3 GeV/c².Hence,dielectronmeasurementscanbe usedtostudycharmandbeautyproduction.

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

The ALICE Collaboration has reported charm and beauty pro- duction cross section measurements at midrapidity (|^y|<0.5) in pp collisions at centre-of-mass energies of √

s=².76 and 7 TeV [4–10]. The charm measurement at √

s=^{7 TeV is com-} plementedby ATLASdataextendingtohighertransversemomen- tum(pT) and|^y|<2.1 [11].Furthermore, theCMS Collaboration has provided a variety of charm and bottom measurements at midrapidityat√

s=².76,5and7 TeV [12–20].Atforwardrapid- ity(2<y<5), theLHCb Collaborationhas measuredcharm and beauty productioncross sectionsin pp collisions at √

s=^{5,7, 8} and 13 TeV [21–24]. These results are generally in good agree- ment with pQCD calculations at next-to-leading order (NLO) in the strong coupling constant (

α

s) with all-order resummation of the logarithms of pT/mQ (FONLL) [1–3]. Though the measured charm production cross sections consistently lie on the upper edge of the systematic uncertainties of the theory calculations.

Recently, the ALICE Collaboration has measured the charm and beautyproductioncrosssectionsinpp collisionsat√

s=^{7 TeV us-} ing electron–positron pairs(dielectrons) fromcorrelatedsemilep- tonicdecaysofheavy-flavourhadrons [25].Suchanapproachwas firstperformedby thePHENIXCollaborationinpp andd–Au col- lisions at √

s_NN=^{200 GeV at the} Relativistic Heavy Ion Collider https://doi.org/10.1016/j.physletb.2018.11.009

0370-2693/©^{2018TheAuthor.PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense}(http://creativecommons.org/licenses/by/4.0/).Fundedby SCOAP³.

(RHIC) [26–28].Thesemeasurementshavetheadvantagethatthey probethefull pT rangeofheavy-quarkpairsandcontaincomple- mentaryinformationabouttheinitialcorrelationofcharmquarks, i.e.theunderlyingproductionmechanism,whichisnotaccessible inconventionalsingleheavy-flavourmeasurements.

The measurement of direct photons, i.e. those produced in hardscatteringsbetweenincomingpartonsinhadroniccollisions, provides another important test of pQCD. Furthermore, at pT<

3 GeV/c, where the applicability of perturbation theory may be questionable,experimentaldataofdirect-photonproductioninpp collisions serve as a crucial reference to establish the presence ofthermal radiation fromthe hot and dense medium createdin heavy-ioncollisions [29–32]. The measurementof real(massless) directphotonsatlow pT ischallenging becauseofthelargeback- groundofhadron decay photons. Thisbackgroundcan be largely reducedby measuring thecontribution of virtual direct photons, i.e. direct e⁺e⁻ pairs, to the dielectron invariant-mass spectrum abovethe

π

⁰ mass [29,30].

Proton–proton collisions in which a large number of charged particles are producedhave recentlyattractedthe interest ofthe heavy-ion community [33,34]. These events exhibit features that are similar to those observed in heavy-ion collisions, e.g. collec- tive effects, such as long-range angular correlations [35–40] or enhanced strangeness production [41]. Charged-hadron pT spec- tra in pp collisions at √

s=13 TeV show a hardening with in- creasingmultiplicity,an effectthat arisesnaturally fromjets [42].

Also, heavy-quark production is found to scale faster than lin- early with the charged-particle multiplicity in pp collisions at

√s=7 TeV [43,44]. This motivates the study of dielectron pro- ductioninhigh-multiplicity pp collisions.In thelow massregion (mee<1 GeV/c²), dielectron measurements provide further in- sight into possible modifications of the light vector and pseudo- scalar meson production via their resonance and/or Dalitz de- cays, whereas in the IMR they allow for complementary studies oftheheavy-flavourproduction.AtLHCenergies,thecontribution fromopen charmalready dominatesthedielectron continuum at mee≈⁰.5 GeV/c².Moreover,ifathermalisedsystemwerecreated insuchhigh-multiplicitypp collisions,asignalofthermal(virtual) photonsshouldbepresent.

Inthisletter,firstresultsofcharmandbeautyproductioncross sections at midrapidity in inelastic (INEL) and high-multiplicity (HM)pp collisions at√

s=^{13 TeV are reported.Thepaperis or-} ganisedasfollows:theALICEapparatusandthedatasamplesused intheanalysisaredescribedinSection 2,thedataanalysisisdis- cussed in Section 3, Section 4 introduces the cocktail of known hadronicsources, andthe results are presentedand discussedin Section5.

2. TheALICEdetectoranddatasamples

A detailed description of the ALICE apparatus andits perfor- mancecanbefoundin [45–48].Thedetectorsusedinthisanalysis arebrieflydescribedbelow.

TrajectoriesofchargedparticlesarereconstructedintheALICE central barrelwiththeInner TrackingSystem(ITS) andthe Time Projection Chamber (TPC) that reside within a solenoid, which provides a homogeneous magneticfield of0.5 T along the beam direction. The ITS consists of sixcylindrical layers of silicon de- tectors,withradialdistancesfromthebeamaxisbetween3.9 cm and43 cm. The two innermost layers are equipped with Silicon PixelDetectors(SPD),thetwointermediatelayersarecomposedof SiliconDriftDetectors, andthetwo outermostlayersare madeof SiliconStripDetectors.TheTPC,maintrackingdeviceintheALICE central barrel, isa 5 m longcylindricalgaseous detectorextend- ing from 85 cmto 247 cm in radial direction. It provides up to

159spacialpointspertrackforcharged-particlereconstructionand particle identification(PID)throughthemeasurement ofthespe- cificionisationenergylossdE/dxinthegasvolume.

The PID is complementedby theTime-Of-Flight (TOF) system located at a radial distance of 3.7 m from the nominal interac- tionpoint.It measuresthearrivaltime ofparticles relativetothe eventcollisiontime providedby theTOFdetectoritselforby the T0detectors,twoarraysofCherenkovcounterslocatedatforward rapidities [49].

CollisioneventsaretriggeredbytheV0detectorthatcomprises two plasticscintillatorarraysplacedon bothsidesoftheinterac- tionpointatpseudorapidities2.8<

η

<5.1 and−³.7<

η

<−¹.7.

TheV0isalsousedtorejectbackgroundeventslikebeam-gasin- teractions, collisionswithde-bunchedprotonsorwithmechanical structuresofthebeamline.

ThedatasamplesusedinthisletterwererecordedwithALICE in2016duringtheLHCpp runat√

s=^{13 TeV.Fortheminimum-} bias eventtrigger that is used to define thedata sample for the analysis of inelastic pp collisions, coincident signals in both V0 scintillatorsarerequiredtobesynchronouswiththebeamcrossing time definedby theLHCclock. Eventswithhighcharged-particle multiplicities are triggered on by additionally requiring the total signal amplitudemeasured intheV0detectortoexceedacertain threshold. At the analysis level, the 0.036 percentile of inelastic events withthe highest V0 multiplicity (V0M) isselected to de- fine the high-multiplicity event class. This value is low enough to avoid inefficiencies due to trigger threshold variations during data taking. Track segmentsreconstructed inthe SPDare extrap- olated back to the beam line to define the interaction vertex.

Events with multiple verticesidentified with the SPDare tagged as pile-up and removed from the analysis [48]. The vertex in- formation may be improved based on the information provided by tracks reconstructed in the ITSand TPC. To assure a uniform detector coverage within |

η

_|<0.8, the vertexposition along the beamdirectionisrestrictedto±^{10 cmaroundthenominalinter-} action point.A totalof 455×¹⁰⁶ minimum-bias(MB) pp events and79.2×¹⁰⁶ high-multiplicitypp eventsareconsideredforfur- ther analysis, which corresponds to an integrated luminosity of L_int^MB=⁷.87±⁰.40 nb⁻¹ and L_int^HM=².79±⁰.15 pb⁻¹, respec- tively.The luminosity determinationisbased onthe visiblecross sectionfortheV0-basedminimum-biastrigger,measuredinavan derMeerscancarriedoutin2015 [50].Aconservativeuncertainty of5%isassignedtothismeasurement,toaccountforpossiblevari- ationsofthecrosssectionbetweenthetwodata-takingperiods.

3. Dataanalysis

Electron¹ candidates are selected fromcharged-particle tracks reconstructedintheITSandTPCinthekinematicrange|

η

e|<0.8 and p_T,e>0.2 GeV/c. Basic track quality criteria are applied, e.g. a sufficient number of space points measured in the TPC and ITS as well as a good track fit. The contribution from sec- ondary tracks is reduced by requiring a maximum distance of closest approach (DCA) to the primary vertex in the transverse plane (DCAxy<1.0 cm)andinthelongitudinaldirection(DCAz<

3.0 cm).Tofurthersuppressthecontributionfromphotonconver- sions inthedetectormaterial,electroncandidates arerequiredto have a hitin the firstSPDlayer andno ITSclustersshared with otherreconstructedtracks.

The electronidentification isbasedon thecomplementary in- formationprovidedbytheTPCandTOF.ThedetectorPIDresponse,

1 Theterm‘electron’isusedforbothelectronsandpositronsifnotstatedother- wise.

Fig. 1.Opposite-signspectrumN+−,thecombinatorialbackgroundBandthesignalSinminimum-bias(left)andhigh-multiplicity(right)events.Onlystatisticaluncertainties areshown.

Table 1

Sourcesofsystematicuncertainties.

Source Minimum bias High multiplicity

Trackreconstruction 13% 13%

Electronidentification 2% 2%

Conversionrejection (mee<0.14 GeV/c²)

2% 2%

Acceptancecorrection factor(R)

2% 2%

Vertexdistributionbias – 6%

Multiplicitydependence oftrackingandPID

– 6%

Total 14% 15%

n(

σ

_i^DET),isexpressedintermsofthedeviationbetweenthemea- suredandexpectedvalue ofthespecificionisationenergylossin theTPCortime-of-flightintheTOFforagivenparticlehypothesis iandmomentum,normalisedbythedetectorresolution(

σ

^DET).In theTPC, electronsareselectedintherangen

σ

_e^TPC<3 andpi- onsarerejectedbyrequiringn

σ

_π^TPC>4.Furthermore,kaonsand protonsarerejectedwith_n

σ

_K^TPC>4 and_n

σ

_p^TPC>4,unless thecandidateispositivelyidentifiedasanelectronintheTOF,i.e.

fulfillingn

σ

_e^TOF<3.Forparticlesthatareoutsiden

σ

_K^TPC<4 andn

σ

_p^TPC<4 theTOFinformationisonlyusedtoselectelec- troncandidateswith _n

σ

_e^TOF<3 ifthetrackhasan associated hitintheTOFdetector.

Sinceexperimentally theoriginofeach electronorpositronis unknown,allelectroncandidatesarepairedconsidering combina- tionswithopposite(N₊₋)butalsosame-signcharge(N_±±).Most oftheelectronpairs arisefromthecombinationoftwo electrons originatingfromdifferentmotherparticles.Thesepairsgiveriseto thecombinatorialbackgroundB thatisestimatedviathegeomet- ric mean of same-sign pairs √

N₊₊N₋₋ within the same event.

Opposite- andsame-sign pairsincludecorrelatedbackground,e.g.

originating from

π

⁰ decays with two e⁺e⁻ pairs in the final state (

π

⁰_→

γ

^(∗)

γ

^(∗)_→e⁺e⁻e⁺e⁻), which includes decay chan- nelswithrealphotonsandtheirsubsequentconversionindetector material.Such processes lead to opposite andsame-sign pairsat equalrate.Thebackgroundestimateneedstobecorrectedforthe differentdetectoracceptanceofoppositeandsame-signpairs.This correctionfactoris determinedby dividingtheyields ofuncorre- latedopposite(M₊₋)andsame-signpairs(M_±±)inmixedevents:

R=^M+−/(2√

M₊₊M₋₋). The dielectron signal is then obtained as S=^N+−−^B=^N+−−^2R√

N₊₊N₋₋. The signal S is shown togetherwiththeopposite-signspectrumN₊₋andthecombinato- rialbackgroundBinFig.1forminimum-biasandhigh-multiplicity

events.In themass interval 0.2<mee<3 GeV/c², thesignal-to- backgroundratiovariesinMBeventsbetween0.3and0.04witha minimumaroundmee≈⁰.5 GeV/c²andisroughlyconstantat0.2 intheIMR [51].In HMevents,theminimumreaches0.01 andis about0.08intheIMR.

Electron–positron pairs from photon conversion in the de- tector material, contributing to the low mass spectrum below 0.14 GeV/c²,are removed by using their distinct orientation rel- ativetothemagneticfield [25].

The data are corrected for the reconstruction efficiencies us- ing detailed Monte Carlo (MC) simulations. For this, pp events are generated with the Monash 2013 tune of Pythia 8 [52] for light-hadrondecays andthe Perugia 2011tune of Pythia 6.4for heavy-flavour decays [53] and the resulting particles are prop- agated through a detector simulation using Geant 3 [54]. The choiceofthedifferentPythiaversionsismotivatedbythefactthat the Perugia 2011 tune describes reasonably well the transverse momentum spectra of heavy-flavour hadrons while the Monash 2013 tune reproduces many of the relevant light-hadron multi- plicities [55,56].Thesignalreconstructionefficiencieswerestudied asa function of mee and pairtransverse momentum pT,ee sepa- ratelyforthedifferente⁺e⁻ sources:resonanceandDalitzdecays of relevant mesons as well as correlated semileptonic decays of charm and beauty hadrons. The total signal reconstruction effi- ciency is obtainedby weighting the efficiencyof each dielectron sourceby itsexpectedcontributionandisfoundtobe about20%

in0.7<m_ee<1.2 GeV/c²andapproaches30%atlowerandhigher masses.

Different aspects of the analysis are considered as possible sources ofsystematicuncertainties, whichare summarisedinTa- ble1.Thesystematicuncertaintiesduetothetrackreconstruction areestimatedbycomparingtheefficiencyoftheITS–TPCmatching, therequirementofahitinthefirstSPDlayer,andtherequirement ofnosharedITSclustersinMCsimulationsanddata.Theresidual disagreementsbetweendataandMCaddtoa6.5%uncertaintyon thesingle tracklevel,which leads toa 13%uncertainty forpairs.

TheMC simulations werealsocheckedtoreproduce alldetails of the PIDselection withina systematicuncertaintyof 2%for e⁺e⁻ pairs.The purityofthe electronsample is estimatedtobe >93%

over therelevant pT range,witha pT-integratedhadroncontam- ination of about4%. The resulting hadron contamination on the dielectronsignalisfoundtobenegligible.Formee<0.14 GeV/c², a 2%uncertainty onthe conversionrejectionwas estimatedfrom the yield change when tightening the selection to reject photon conversions.A2%uncertaintyonthesignalyieldduetothecorrec- tionfactorRisobtainedbyrepeatingtheeventmixingindifferent eventclasses,definedbythepositionofthereconstructedprimary

vertex andby the charged-particle multiplicity. The efficiency of theminimum-biastriggertoselectinelasticeventswithan e⁺e⁻ pairintheALICEacceptance(|

η

e|<0.8 and pT,e>0.2 GeV/c) is estimatedtobe(99±¹)% fromtheMonash2013tuneofPythia8.

Thisand the luminosity uncertaintyof 5% [50] are globaluncer- tainties, which are not included in the point-to-point uncertain- ties. No significant variation of systematic uncertainties on mass orpT,eeisobservedintheanalysis,andthesametotaluncertainty of14%isassignedaspoint-to-pointcorrelateduncertaintiesonthe differentialdielectroncrosssectionininelasticpp collisions.

The analysis of the high-multiplicity data has additional sys- tematicuncertainties.First,nodedicatedhigh-multiplicityMCsim- ulation was performed. In such events the vertex distribution is biasedmore than inMB eventsby the asymmetric pseudorapid- itycoverage ofthe two V0detectors. Thechange ofthe detector acceptancewithvertexposition could lead toa difference inthe numberofreconstructedelectronsofupto3%,whichresultsinan uncertainty of6% for e⁺e⁻ pairs. Second, a possible multiplicity dependenceofthereconstructionandPIDefficiencyiscoveredby anuncertaintyof6% [57].Addedinquadrature,thisamountstoa totaluncertaintyof15%.

4. Cocktailofknownhadronicsources

The dielectron spectrum measured in pp collisions at √ s= 13 TeV iscomparedwiththeexpectationsfromallknownhadron sources, i.e. the hadronic cocktail, contributing to the dielectron spectrum in the ALICE central barrel acceptance (|

η

e|<0.8 and p_T,e>0.2 GeV/c). A fast MC simulation is used to estimate the contributionfrom

π

⁰,

η

,

η

,

ρ

,

ω

andφdecaysinpp collisions,as detailedin [25].

Followingtheapproachoutlinedin [58],thepionpT-spectrum at √

s=^{13 TeV is} approximated by scaling the p_T-spectrum of charged hadrons [42] by the pion-to-hadron ratio measured at

√s=7 TeV [59,60]. The difference with respect to the same procedure based on the pion-to-hadron ratio measured at √

s= 2.76 TeV [59,61] issmaller than1% atlow pT andreaches5% at high pT.The chargedhadron pT-spectraat√

s=^{13 TeV arenor-} malised toINEL>0 events, i.e.inelasticcollisions that produce at leastonechargedparticlein|

η

|<1,ratherthanINELevents.This iscorrectedtakingthe21%differenceinthepTintegrateddNch/d

η

valuesforthesetwoeventclasses [42].Aconservativeuncertainty of10%isassignedonthisextrapolation.

Afit of theobtained charged-pion pT-spectrum witha modi- fiedHagedornfunctionisthentakenasproxyfortheneutral-pion p_T-distribution. The simulated cross section per unit rapidity of the

π

⁰ is d

σ

/dy|y=⁰=¹⁵⁵.2 mb. For the

η

meson a fit ofthe measured

η

/

π

⁰ ratioinpp collisions at√

s=^{7 TeV isused [62].}

TheMonash2013tuneofPythia8describesthe

ρ

/

π

⁰ and

ω

/

π

⁰

ratiosmeasured in pp collisionsat √

s=².76 and7 TeV, respec- tively [55,56]. Therefore,MC simulations obtained withthistune at √

s=^{13 TeV are used to obtain the}

ρ

/

π

⁰ and

ω

/

π

⁰ ratios.

Based on the

η

/

π

⁰,

ρ

/

π

⁰ and

ω

/

π

⁰ data,the ratios athigh pT are 0.5±⁰.1, 1.0±⁰.2 and 0.85±⁰.17, respectively.The

η

and φ mesons are generated assuming m_T scaling, replacing p_T with m²−^m2_π+(pT/c)² [63]. For themT scaling, particle yields are normalisedathighpT relative tothe

π

⁰ yield:0.40±⁰.08 for

η

(from Pythia6 calculations) and0.13±⁰.04 for φ [64]. The de- tector response,includingmomentumandangularresolutions, as wellasBremsstrahlungeffectsobtainedfromfullMCsimulations, isappliedtothedecayelectrons asafunctionofpT,e,

η

eandthe azimuth

ϕ

e.Thisresultsinamassresolutionofapproximately1%.

Thefollowingsources ofsystematicuncertaintieswere evaluated:

the input parameterisations of the measured spectra as a func- tion of p_T (

π

^±,

η

/

π

⁰ and

ω

/

π

⁰), the branching fractions of all

includeddecaymodes,themT scalingparametersandtheresolu- tionsmearing.Forthehigh-multiplicitycocktail,theinputhadron p_T-distributions are adjusted according to the measured modifi- cations of the charged-hadron pT spectra [42]. The uncertainties of the cocktail from light-hadron decaysare about±^{15%, reach-} ing up to+^{50% intheregion dominatedby the}

η

mesondueto uncertainties in theextrapolation tolow pT. The multiplicity de- pendencehasanuncertaintythatvariesbetweenabout12%atlow p_T and40%athighp_T.

The Perugia 2011 tune of Pythia 6.4, which includes NLO parton showering processes, is used to estimate the contri- butions of correlated semileptonic decays of open charm and beauty hadrons [53,65]. As an alternative, the NLO event gener- ator Powheg isalso considered [66–69]. The resultingsame-sign spectrum is subtracted fromthe opposite-sign distribution as in the data analysis. Detector effects are implemented as for the light-hadron cocktail. The spectra are normalised to cross sec- tions atmidrapiditythatarebasedonFONLL [1–3] extrapolations of the ALICE measurements at 7 TeV [8–10]. Following the de- scription in [70], this leads to cross sections per unit rapidity of d

σ

cc/dy|y=0=¹²⁹⁶⁺₋¹⁷²₁₆₂ ^{μb and d}

σ

_bb/dy|y=0=⁶⁸⁺₋¹⁵₁₆ ^{μb at}

√s=^{13 TeV.Thequoted}uncertainties takeintoaccountboththe measured uncertaintyand the FONLL extrapolationuncertainties.

Thelatter(dominatedbyscaleuncertaintiesbutalsoincludingPDF andmass uncertainties)are considered to be fullycorrelated be- tweenthetwoenergies [71].Forthehigh-multiplicitycocktail,the opencharmcontributionisweightedasafunctionofpTaccording tothemeasuredenhancementofD mesonswith p_T>1 GeV/c at

√s=7 TeV [43].Thesameweightsareappliedtotheopenbeauty contribution as no significant difference between the production ofD mesonsandJ/ψ frombeauty-hadrondecaysisobserved [43].

For electrons originating from charm or beauty hadrons with pT<1 GeV/c,thesameweightasfor1<pT<2 GeV/cisassumed intheabsenceofa measurement.Thisleads toanuncertaintyon themultiplicity dependenceofabout40%atlow pT decreasingto 20%athighpT.

The J/ψ contribution is simulated with Pythia 6.4 and nor- malised to the cross section at √

s=^{13 TeV,} extrapolated with FONLL [9] fromthemeasurementat√

s=^{7 TeV bytheALICECol-} laboration [72].Inthehigh-multiplicitycocktail, theJ/ψ isscaled according to a dedicated, pT-integrated measurement [44]. The ψ(2S)contributionisnormalisedtotheJ/ψ basedonacrosssec- tionratioof

σ

_{ψ (}2S)→^e+e−/

σ

J/ψ→^e+e−=(1.59±⁰.17)% [73].

5. Results

The dielectron cross sections are reported within the ALICE central barrel acceptance |

η

e|<0.8 and pT,e>0.2 GeV/c, i.e.

withoutcorrection tofullphase space.The result,integratedover p_T,ee<6 GeV/c, isshown asa functionof m_ee in theleft panel of Fig. 2. The data are compared withthe expectation from the hadronic decaycocktail, using Pythia forthe heavy-flavourcom- ponents,andfoundtobeinagreementwithinuncertainties.Good agreementbetweendataandcocktail calculationsisalsofoundas a functionof pT,ee,whichisshownforthreemeeintervalsinthe rightpanelofFig.2.

Figs. 3 and 4 show the ratios of the dielectron spectra in high-multiplicity over inelastic events as a function of mee for different p_T,ee intervals. To account for the trivial scaling with charged-particle multiplicity, the ratio is scaled by the factor dNch/d

η

(HM)/^dNch/d

η

(INEL) = ⁶.27 ± ⁰.22, where dNch/ d

η

(HM)=³³.29±⁰.39 and ^dNch/d

η

(INEL)=⁵.31±⁰.18 are thecharged-particlemultiplicitiesin|

η

_ch|<0.5 measuredinhigh- multiplicityandinelasticpp collisions,respectively [42].Inthisra- tio,themultiplicity-independentuncertaintiescancelandthetotal

Fig. 2.Thedielectroncrosssectionininelasticpp collisionsat√

s=^{13 TeV asafunctionofinvariantmass(left)andofpairtransversemomentumindifferentmassintervals} (right).Theglobalscaleuncertaintyonthepp luminosity(5%)isnotshown.Thestatisticalandsystematicuncertaintiesofthedataareshownasverticalbarsandboxes.

Theexpectationfromthehadronicdecaycocktailisshownasaband,andthebottomleftplotshowstheratiodatatococktailtogetherwiththecocktailuncertainty.

Fig. 3.RatioofdielectronspectrainHMandINELeventsscaledbythecharged- particle multiplicity.The statistical andsystematic uncertaintiesofthe data are shownasverticalbarsandboxes.Theexpectationfromthehadronicdecaycock- tailcalculationisshownasagreyband.

systematicuncertaintyreducesto 9%. The ratioisin goodagree- mentwiththehadronicdecaycocktailcalculationsoverthewhole measuredmeeandpT,eerange.Thisisthefirstmeasurementsen- sitive to the production of

π

⁰,

η

,

ω

and φ in high-multiplicity pp collisions.The result confirms the hypothesis that these light mesons have the same multiplicity dependence as a function ofm_T,whichwasusedintheconstructionofthehigh-multiplicity hadron cocktail. From the agreement between data and cocktail inthe high-pT range(3<pT,ee<6 GeV/c), which isdominated by open beauty,it can be also concluded for the first time that the open beauty production has a multiplicity dependence sim- ilar to that of open charm. This puts additional constraints on mechanisms used to describe heavy-flavour production in high- multiplicity pp collisions, such as multiple parton interactions, percolationorhydrodynamicmodels.

In the intermediate mass region (1.03<mee<2.86 GeV/c²), whichisdominatedbyopenheavy-flavourdecays,thedataarefit- ted simultaneously in m_ee and p_T,ee (for p_T,ee<6 GeV/c) with PythiaandPowhegtemplates ofopen charmandbeautyproduc- tion,keepingthelight-flavourandJ/ψ contributions fixed,which introducesnegligibleuncertaintiesontheheavy-flavourcrosssec- tion.ThePythiaandPowhegleast-squarefitsofdielectronspectra ininelasticeventsprojectedover p_T,eeandm_ee areshowninthe

left and right panels of Fig. 5, respectively. The resulting cross sections are summarised in Table 2. The first uncertainty is the statistical uncertainty resulting from the fits and the second is the systematic uncertainty, which is determined by moving the data points coherently upward and downward by their system- aticuncertaintiesandrepeatingthefits.Thebranchingfractionof charm-hadrondecaystoelectronsistakenas(9.6±⁰.4)% [74].An additional uncertaintyof 9.3% is added in quadratureto account fordifferencesinthe c/D⁰ ratiomeasured byALICEinpp colli- sions at√

s=^{7 TeV,whichis 0}.543±⁰.061(stat.)±⁰.160(syst.) for pT>1 GeV/c [75], and the LEP average of 0.113±⁰.013± 0.006 [76].Thistranslatesintoa22%uncertaintyatthepairlevel.

Thebranching fractionofbeautyhadronsdecayingintoelectrons, includingviaintermediatecharmhadrons,is(21.53±⁰.63)% [74], whichleadstoa6%uncertaintyonthedielectron-basedcrosssec- tionmeasurement.Likethestatisticalandsystematicuncertainties, thesebranchingfractionuncertaintiesarefullycorrelatedbetween thePythiaandPowhegbasedresults.

Theresultsareconsistentwithextrapolationsfromlowerener- giesbasedonpQCDcalculationsdiscussedintheprevioussection.

There is a strong anti-correlation between the fitted charm and beautycrosssections.Thesizeabledifferenceinthecrosssections betweenthetwo MCeventgenerators arecomparabletowhat is observedat√

s=7 TeV [25].Thedifferentcrosssectionsobtained fromfits withPythiaandPowhegsimulations are causedby ac- ceptancedifferencesofe⁺e⁻ pairsfromheavy-flavourhadronde- cays inthesetwoeventgeneratorsbecauseofdifferentkinematic correlationsoftheheavyquarkpairs,inparticularinrapidity.The fractionofe⁺e⁻ pairsthatfall intotheALICEacceptanceandthe intermediate mass region originating from cc pairs at midrapid- ityis14% inPythiaand10%inPowheg.Thispointstoimportant differences in the heavy quark production mechanisms between thetwogenerators.Itshouldbestressedthatsingleheavy-flavour measurementsappearinsensitivetothesedifferencesasthecross sectionsobtainedfromsuchmeasurements agreebetweenPythia andPowhegbased extrapolations [7,11,22]. Therefore,dielectrons provide complementary information on heavy-flavour production that,ifproperlymodelled,shouldleadtoconsistentcrosssections withPythiaandPowheg.

Table 2 also summarises the corresponding cross sections for thehigh-multiplicitydata.IncaseofPythia,themeasured charm crosssectiontranslatesintoanenhancementof1.86±⁰.40(stat.)± 0.40(syst.) relative to the charged-particle multiplicity increase.

Thisisconsistentwiththemodelledmultiplicitydependenceused

Fig. 4.RatioofdielectronspectrainHMandINELeventsscaledbythecharged-particlemultiplicityindifferentpT,eeintervals.Thestatisticalandsystematicuncertaintiesof thedataareshownasverticalbarsandboxes.Theexpectationfromthehadronicdecaycocktailcalculationisshownasagreyband.

Fig. 5.Projectionoftheheavy-flavourdielectronfit(greyline)ininelasticpp collisionsat√

s=13 TeV ontothedielectronmass(left)andpT,ee(right)usingthePythiaand Powhegeventgenerators.Thelinesshowthecharm(red)andbeauty(magenta)contributionsafterthefit.Theglobalscaleuncertaintyonthepp luminosity(5%)isnot shown.Thestatisticalandsystematicuncertaintiesofthedataareshownasverticalbarsandboxes.ThefitswithPythiaandPowhegresultinaχ²/ndf of57.8/66 and 52.6/66,respectively.

asinputforthecocktailinFigs.3and4.Forthebeautycrosssec- tiontheobservedenhancementis1.63±⁰.50(stat.)±⁰.35(syst.). This is consistent withthe multiplicity dependence observed for open charm,buta scalingwithcharged-particle multiplicity can- notbeexcluded.

Thefractionofrealdirectphotonstoinclusivephotonscanbe extractedfromthedielectronspectrum atsmallinvariant masses assuming the equivalence between this fraction and the ratio of virtual direct photons to inclusive photons. The data are fit- ted minimising the

χ

², in bins of p_T,ee, with the sum of the light-flavour cocktail (f_LF(m_ee)), open heavy-flavour contribution

(fHF(mee)) and a virtual direct photon component (f_direct(mee)), whose shape is described by the Kroll–Wada equation [77,78]

in the quasi-real virtual photon regime (p_T,ee m_ee). The nor- malisation of the open heavy-flavour component is fixed to the measured opencharmandbeautycrosssectionspresentedabove, using the Pythia simulations for the nominal fit. As systematic uncertaintyestimate, thePowhegsimulationisused instead.The light-flavourcocktail andvirtual directphotontemplates are nor- malised independently to the data in mee<0.04 GeV/c², i.e. in a mass window in which both Dalitz decays and direct pho- tons have the same 1/m_ee dependence. The direct-photon frac-

Pythia Powheg

dσcc/dy|y=0 974±138(stat.)±140(syst.)μb 1417±184(stat.)±204(syst.)μb dσ_bb/dy|^y=⁰ 79±¹⁴(stat.)±¹¹(syst.)μb 48±¹⁴(stat.)±⁷(syst.)μb dσcc/dy|^HMy=0 4.14±⁰.67(stat.)±⁰.66(syst.)μb 5.95±⁰.91(stat.)±⁰.95(syst.)μb

dσ_bb/dy|^HMy=0 0.29±0.07(stat.)±0.05(syst.)μb 0.17±0.07(stat.)±0.03(syst.)μb

Table 3

Upperlimitsat 90% C.L.on thedirect-photonfractions incomparisonwith the expectationininelasticpp collisionsbasedonaNLOpQCDcalculationforafac- torisationandrenormalisationscalechoiceofμ=pT[80].

Data sample 1<pT,ee<2 2<pT,ee<3 3<pT,ee<6

GeV/c GeV/c GeV/c

Minimum bias 0.057 0.072 0.023

High multiplicity 0.060 0.083 0.055

pQCD 0.003 0.007 0.013

tion r is then extracted by fitting the data in the mass interval 0.14<m_ee<0.32 GeV/c²,i.e.abovethe

π

⁰ masstosuppressthe mostdominanthadronbackground,withthefollowingexpression:

d

σ

/dmee=^{r f}dir(mee)+(1−^r)fLF(mee)+ ^fHF(mee).

Nosignificantdirectphotoncontributionisobservedinneither theinelasticnorthehigh-multiplicityevents [51].Upperlimitsat 90%confidencelevel(C.L.)areextractedwiththeFeldman–Cousins method [79] andsummarisedinTable3togetherwithpredictions fromperturbative QCD calculations for inelastic events [80]. The current uncertainties prevent any conclusions on the scaling of direct-photonproductionwithcharged-particlemultiplicity.

6. Summaryandconclusion

We have presented the first measurement of dielectron pro- ductionat midrapidity (|^ye|<0.8) in proton–protoncollisions at

√s=^{13 TeV.The dielectroncontinuumcan bewell described by} theexpectedcontributionsfromdecaysoflight- andheavy-flavour hadrons. The charm and beauty cross sections are extracted for the first time atmidrapidity at √

s=^{13 TeV and are consistent} withextrapolations fromlower energies based on pQCD calcula- tions.ThedifferencesobservedbetweenPowhegandPythiaimply differentkinematiccorrelationsofthe heavy-quarkpairsinthese twoeventgenerators.Thereforedielectronsare uniquelysensitive to the heavy quark production mechanisms. The comparison of thedielectronspectraininelasticevents andin eventswithhigh charged-particlemultiplicitiesdoesnotrevealmodificationsofthe spectrum beyondthe already established onesof light and open charmhadrons.Theupperlimitsonthedirect-photonfractionsare consistentwithpredictionsfromperturbativequantumchromody- namicscalculations.

Acknowledgements

TheALICECollaborationwouldliketothankWernerVogelsang forprovidingtheNLOpQCDcalculationsfordirectphotonproduc- tion.

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 the ALICE detector: A. I. Alikhanyan National Science Laboratory (YerevanPhysicsInstitute)Foundation (ANSL),State Committeeof Science andWorld Federation ofScientists (WFS), Armenia; Aus- trian Academy of Sciences and Nationalstiftung für Forschung, Technologie und Entwicklung, Austria; Ministry of Communica- tions and High Technologies, National Nuclear Research Center, Azerbaijan; Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq), Universidade Federal do Rio Grande do Sul (UFRGS),Financiadorade EstudoseProjetos(Finep)andFundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP), Brazil;

MinistryofScience &TechnologyofChina(MSTC),NationalNatu- ral ScienceFoundationofChina (NSFC)andMinistryofEducation ofChina (MOEC),China;MinistryofScienceandEducation,Croa- tia;MinistryofEducation,YouthandSportsoftheCzechRepublic, CzechRepublic;TheDanishCouncilforIndependentResearchNat- ural Sciences, the CarlsbergFoundation and Danish National Re- search Foundation (DNRF), Denmark; HelsinkiInstitute of Physics (HIP),Finland;Commissariatàl’ÉnergieAtomique (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) and GSI Helmholtzzentrum für Schwer- ionenforschungGmbH, Germany;GeneralSecretariat forResearch and Technology, Ministry of Education, Research and Religions, Greece; National Research, Development and Innovation Office, Hungary; Department of Atomic Energy, Government of India (DAE),DepartmentofScienceandTechnology,GovernmentofIndia (DST), University Grants Commission,Government ofIndia (UGC) andCouncilofScientific andIndustrialResearch(CSIR),India; In- donesian Institute of Sciences, Indonesia; Centro Fermi - Museo StoricodellaFisicaeCentroStudieRicercheEnricoFermiandIsti- tutoNazionalediFisicaNucleare(INFN),Italy;InstituteforInnova- tiveScience andTechnology,NagasakiInstituteofAppliedScience (IIST),Japan SocietyforthePromotionofScience (JSPS)KAKENHI and Japanese Ministry of Education, Culture, Sports, Science and Technology (MEXT), Japan; Consejo Nacional de Ciencia (CONA- CYT)yTecnología,throughFondodeCooperaciónInternacionalen CienciayTecnología(FONCICYT)andDirecciónGeneraldeAsuntos delPersonalAcademico(DGAPA),Mexico;NederlandseOrganisatie voor Wetenschappelijk Onderzoek (NWO), Netherlands; The Re- search Council of Norway, Norway; Commission on Science and Technology forSustainable Developmentinthe South(COMSATS), Pakistan;PontificiaUniversidadCatólicadelPerú,Peru;Ministryof ScienceandHigherEducationandNationalScienceCentre,Poland;

KoreaInstituteofScienceandTechnologyInformationandNational ResearchFoundationofKorea(NRF),RepublicofKorea;Ministryof EducationandScientific Research,InstituteofAtomic Physicsand RomanianNationalAgencyforScience,TechnologyandInnovation, Romania; Joint Institute for Nuclear Research (JINR), Ministry of EducationandScienceoftheRussianFederationandNationalRe- search Centre Kurchatov Institute, Russia; Ministry of Education,