Beauty production in pp collisions at √s=2.76 TeV measured via semi-electronic decays

Contents lists available atScienceDirect

Physics Letters B

www.elsevier.com/locate/physletb

Beauty production in pp collisions at √

s = ² . 76 TeV measured via semi-electronic decays

.ALICE Collaboration

^∗

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

Articlehistory:

Received29May2014

Receivedinrevisedform14August2014 Accepted10September2014

Availableonline17September2014 Editor:L.Rolandi

Keywords:

LHC

ALICEexperiment ppcollisions Singleelectrons Heavy-flavourproduction Beautyproduction

The ALICE CollaborationattheLHC reportsmeasurementoftheinclusiveproduction crosssectionof electronsfromsemi-leptonicdecaysofbeautyhadronswithrapidity|^y|<0.8 andtransversemomentum 1<pT<10 GeV/c,in pp collisions at√

s=².76 TeV. Electronsnot originating from semi-electronic decay of beauty hadrons are suppressed using the impact parameter of the corresponding tracks.

The production cross section of beauty decayelectrons is compared to the result obtainedwith an alternative method which usesthe distributionof the azimuthal angle between heavy-flavour decay electrons and charged hadrons.Perturbative QCD predictions agree with the measured cross section within the experimental and theoretical uncertainties. The integrated visible cross section, σb→^e= 3.47±⁰.40(stat)⁺₋¹₁^._.¹²₃₃(sys)±⁰.07(norm)μb, was extrapolated to full phase space using Fixed Order plus Next-to-LeadingLog (FONLL) calculations to obtainthe totalbb production¯ cross section, σ_bb¯=

130±¹⁵.1(stat)⁺₋⁴²₄₉^._.¹₈(sys)⁺₋³₃^._.⁴₁(extr)±².5(norm)±⁴.4(BR)μb.

©^{2014TheAuthors.PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense} (http://creativecommons.org/licenses/by/3.0/).FundedbySCOAP³.

1. Introduction

PerturbativeQuantumChromodynamics(pQCD) calculationsof theproductionofheavy(charmandbeauty)quarkscanbecarried outwithwell-controlledaccuracy,duetothehard(high Q²)scale imposedbythelargemassofheavyquarks[1–3].Inaddition,the largemassimpliesthatheavyquarkproductioninhighenergycol- lisionsofheavyionsoccursearlycomparedtotheformationtime ofthestronglyinteractingpartonicmattergeneratedinsuchcolli- sions[4–7].Therefore,thestudyofheavyquark productioninpp collisionsisofinterestfortworeasons:themeasurementoftheir productioncrosssectionprovidesessentialtestsofpQCD,andsuch measurements yield the necessary reference for the correspond- ingmeasurementsperformedinheavy-ioncollisions.Propertiesof thestronglyinteracting,partonicmediumgeneratedinhighenergy heavy-ioncollisionsarestudiedusingvariousheavy-quarkobserv- ables[8–11].

The ALICE Collaboration has reported heavy-flavour measure- mentsin pp collisions at√

s=².76 TeV for Dmesonproduction viahadronicdecaysatmid-rapidity[12],heavy-flavourhadronpro- duction via semi-leptonic decays to electrons (mid-rapidity) and muons (forward rapidity) [13,14], and J/ψ production using the di-muon (forward rapidity) and di-electron (mid-rapidity) decay channels[15].AllmeasurementsareingoodagreementwithpQCD calculations for inclusive qq¯ production, and with QCD-inspired

*

[email protected].

modelsforJ/ψproduction.Sincebothcharmandbeautyhadrons decaysemi-leptonically,themeasureddistributionofheavy-flavour decaymuonsandelectronshavecontributionsfromboth.

The objective of the analyses presented here is to obtain the total beauty production cross section by measuring the pT-differentialinclusiveproductioncrosssectionofelectronsfrom semi-electronic decays of beauty hadrons. The measurement is performed in the mid-rapidity region (|^y|<0.8) with the ALICE detectorfor1<p_T<10 GeV/c,inppcollisionsat√

s=².76 TeV.

Thetotalbb production¯ crosssectionisdeterminedbytheextrap- olation of the measured pT-differential production cross section to full pT and y ranges. The measured relative beauty contri- bution to the heavy-flavour decay electrons and the inclusive production cross section of electrons from semi-electronic de- cays of beauty hadrons are compared to the predictions from three differentpQCD calculations (FONLL[1],GM-VFNS [16],and k_T-factorization [3]). The primary analysispresented here uses a trackimpactparameterdiscriminant,whichtakesadvantageofthe relativelylonglifetimeofbeautyhadrons(c

τ

_∼500 μm)compared to charm hadrons. A second method discriminates beauty from charm production using the distribution of the azimuthal angle betweenheavy-flavourdecayelectronsandchargedhadrons,

ϕ

. For beauty hadron decays the width of the near-side peak,

ϕ

around zero, is indeedlarger than that of charm hadron decays, duetothedecaykinematics oftheheaviermassbeautyhadrons.

The differenceisexploitedto measurethe relativebeautycontri- bution totheheavy-flavourdecayelectron population,whichcan http://dx.doi.org/10.1016/j.physletb.2014.09.026

0370-2693/©^{2014TheAuthors.PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense}(http://creativecommons.org/licenses/by/3.0/).Fundedby SCOAP³.

beusedalongwiththemeasuredheavy-flavourelectronspectrum tocompute theproductioncrosssection ofelectronsfrombeauty hadrondecays.

2. Eventandtrackselection

The dataset usedfor theseanalyses was recordedduring the 2011LHC runwithppcollisionsat√

s=².76 TeV.TheMinimum Bias(MB)collisionsweretriggeredusingtheV0scintillatordetec- tors,locatedintheforward(2.8<

η

<5.1)andbackward(−³.7<

η

<−¹.7) regions, andthe SiliconPixelDetector (SPD), which is the innermost part of the Inner Tracking System (ITS). The SPD consistsoftwocylindricallayersofhybridsiliconpixelassemblies, coveringapseudo-rapidityinterval|

η

|<2.0 and|

η

|<1.4 forthe innerandouter layer,respectively.BoththeV0andSPDdetectors coverthefullazimuth.TheMBtriggerrequiredatleastonehitin eitheroftheV0scintillatordetectorsorintheSPD,incoincidence withthepresenceofanLHCbunchcrossing.Additionaldetailscan be found in [12]. The MB trigger crosssection was measured to be 55.4±¹.0 mb usinga vander Meer scan [17]. A fraction of MB eventswere triggered independently of theread-out state of the Silicon Drift Detector (SDD), which equips the two interme- diate layers of the ITS. The Electromagnetic Calorimeter (EMCal) isa samplingcalorimeter basedon Shashliktechnology, covering apseudo-rapidityinterval|

η

_|<0.7 andcovering100^◦ inazimuth [18].TheEMCalSingleShower(SSh)triggersystemgeneratesafast energysum(800ns) atTriggerLevel 0foroverlapping groupsof 4×^{4 (}

η

_×

ϕ

)adjacentEMCaltowers,followedbycomparisontoa thresholdenergy[19].ThedatasetrecordedwiththeEMCaltrig- gerrequiredthat theMB triggercondition was fulfilled,andthat atleastone SShsumexceededa nominalthresholdenergyof3.0 GeV.Theresultsreportedarebasedon51.5millionMBevents(in- tegratedluminosity of0.9nb⁻¹)and0.64millionEMCaltriggered events(integrated luminosity of 14.9nb⁻¹). The impact parame- teranalysiswasperformedsolelyontheMBsample.Themethod basedon thedistributionof theazimuthal anglebetweenheavy- flavourdecayelectrons andchargedhadrons(i.e.electron–hadron correlation)wasdone usingboththeMB andEMCaltriggersam- ples.Intheofflineanalysis,eventswhichsatisfiedthetriggercon- ditionswere requiredtohaveacollision vertexwithatleasttwo trackspointingto itandthe vertexpositionalong thebeam line tobewithin±^{10cmofthenominalcentre oftheALICEdetector.}

Charged particle tracks were reconstructed offline using the TimeProjectionChamber(TPC)[20]andtheITS[21].Tohaveaho- mogeneouslyreconstructedsampleoftracks,theSDDpointswere alwaysexcludedfromthetrackreconstructionusedfortheseanal- yses.EMCal clusterswere generatedoffline via analgorithm that combinessignalsfromadjacentEMCaltowers.Theclustersizewas constrainedbytherequirementthateachclustercontainsonlyone local energymaximum. In the caseof the EMCal-based analysis, chargedtrackswerepropagatedtotheEMCalandmatchedtoclus- tersin the EMCal detector.The matching requiredthe difference betweentheclusterpositionandtrackextrapolationattheEMCal surfacetobesmallerthan0.025unitsin

η

and0.05radiansin

ϕ

.

Electrons were identified using the TPC, Timeof Flight (TOF), and EMCal detectors [13]. Background hadrons, in particular chargedpions,wererejectedusingthespecificenergyloss,dE/dx, ofchargedparticlesmeasuredintheTPC. Trackswere requiredto have a dE/dx value between one standard deviation below and threestandard deviations abovethe expectedvalue forelectrons.

In the low momentum region (below 2.0 GeV/c for the impact parameteranalysisandbelow2.5 GeV/c forthe correlationanal- ysis) electron candidates were required to be consistent within threestandarddeviationswiththeelectrontime offlighthypoth- esis.TOF-baseddiscriminationisnotefficientathighertransverse

Fig. 1.(Colour online.)(a)Transverseimpactparameter(d0)distributionsofelec- tronsfrombeautyandcharmhadrondecays,lighthadrondecays,andphotoncon- versions obtainedwith PYTHIA6simulationsintheelectron pTrange1<pT<

6 GeV/c,alongwiththemeasureddistributionofconversionelectrons.Thedistri- butionsarenormalizedtothesameintegratedyield.(b)Ratiosofthemeasuredand simulatedd0distributionsofconversionelectronsintheranges1<pT<6 GeV/c.

momentum andtheTOF was notrequired.The EMCal-basedcor- relation analysisrequired E/pto be within awindow of0.8and 1.2timesthe nominalvalue of E/p forelectrons, where E isthe energydepositedintheEMCalandpisthetrackmomentummea- suredinthetrackingsystem.Trackswere requiredtohavehitsin the SPD in order to suppress the contribution of electrons that originatedfromphotonconversionsintheinnertrackingdetector materialandtoimprovetheresolutiononthetrackimpactparam- eter.

3. Analysis

3.1. Impactparametertechnique

The measured electron sample contains contributions from beautyandcharmhadron decays,alongwithbackgroundsources.

The backgroundis primarily composed of electrons fromphoton conversions inthe beam-pipe andITS material,

π

⁰ and

η

Dalitz decays,anddi-electrondecaysoflightneutralvectormesons.The relative contribution ofelectrons from beautyhadron decays can be enhanced by selecting onthe displacement of electron tracks fromtheprimaryvertexoftheppcollision,asdescribedindetail in[22].

Therelativelylonglifetimeofbeautyhadronswasexploitedby selecting on the transverse impact parameter (d0), which is the projectionofthechargedtrackdistanceofclosestapproachtothe primary vertexvectoronto thetransverseplane,perpendicular to thebeamline. Thesignofd₀ isgivenaccordingtothetrackposi- tionrelativetotheprimaryvertexafterthetrackhasbeenspatially extendedinthedirectionperpendiculartoits pT vector.Thereso- lutionofd0 isbetterthan85 μmforpT>1 GeV/c.Fig. 1(a)shows the impactparameter distributionforall significant contributions to themeasured electron sample inthe range1<pT<6GeV/c.

The distributions were obtainedusing aMonte Carlo(MC) simu- lation withGEANT3 [23], wherethe pp collisions were produced using the PYTHIA 6 event generator (Perugia-0 tune) [24]. Each

Fig. 2.(Colour online.)Rawspectrumofelectronsfromtheimpactparameteranal- ysis(opencircles) comparedtobackgroundsources(fromcharmhadrondecays, photonconversions,Dalitzdecays,andhadroncontamination)asafunctionofpT. Thebackgroundsourcesoriginatingfromlightflavourhadronswereobtainedusing aMCsimulationandreweightedaccordingtotheπ⁰pTspectrummeasuredwith ALICE[25].Thecharmhadrondecaybackgroundwasestimatedusingthecharm hadronspectrameasuredwithALICE[26].Therawyieldafterbackgroundsources aresubtractedisalsoshown(filledcircles).Theerrorbarsrepresentthestatistical uncertainties.

sourcehasadistinct d0 distribution.The d0 distributionofelec- trons from Dalitz decays is relatively narrow compared to that frombeauty hadron decays, since Dalitz electrons are effectively generatedatthecollisionvertex.Thecharmhadrondecayandcon- versionelectrond0distributionsarebroaderthanthatoftheDalitz decaydistributionsincetheyemergefromsecondaryvertices,but arenotasbroadasthosefrombeautydecays.Forcomparison,the d0 distributionofconversionelectronsfromdataisalsoshownin thefigure.Thispuresampleofelectronsfromphotonconversions inthe detector material was identified using a V0-finderand an optimizedsetoftopologicalselectionrequirements.Fig. 1(b)shows the ratioof the impact parameter distribution from data to that fromsimulationintherange1<pT<6 GeV/c.The ratioisclose tounity,showinggoodagreementofthesimulationandmeasure- mentofphotonconversionelectroncandidates.

A selection on the transverse impact parameter d₀ was ap- plied in order to maximize the signal to background (S/B) ratio ofelectrons frombeauty hadron decays.The requirementon the minimumimpact parameter is pT dependent, since the widthof the d0 distribution dependson pT. The S/B ratio varieswith pT duetodifferentimpactparameterselectionefficiencyforthevar- ioussources. Therefore, separate pT-dependent parameterizations of the d0 selection requirement were obtained for the analyses whichutilizeTPC-TOFandTPC-onlyforelectronselection.Electron candidatesaccepted forthe TPC-TOF analysissatisfied the condi- tion |d0|>64+480·exp(−0.56pT) (with d0 in μm and pT in GeV/c),while|^d0|>54+⁷⁸⁰·^exp(−⁰.56p_T)wasrequiredforthe TPC-onlyanalysis.

The raw p_T distribution of electrons, after the application of trackselectioncriteria,isshowninFig. 2,alongwiththe pT dis- tributionsofelectronsfromthevariousbackgroundsources(charm hadrondecays,photon conversions, Dalitz/di-electrondecays,and hadron contamination). The background distributions were ob- tainedfroma MC simulation,withGEANT3. The pT distributions ofthebackgroundsourceswerenormalizedtothetotalnumberof eventswhich passed the event selection requirements,and were correctedforthe efficiencytoreconstructa primarycollisionver- tex. Among all background contributions, Dalitz decay electrons and photon conversions are dominant at low p_T, where more than 80% of the background can be attributed to

π

⁰ Dalitz de-

cays andconversions ofphotonsfrom

π

⁰ decays.At high pT the contribution from charm hadron decays is significant. The con- tribution from heavy quarkonia decays also becomes significant at high p_T, although this contribution is strongly suppressed in the analysis since the selection on d₀ strongly suppresses tracks fromsuchdecays.ThePYTHIAsimulationdoesnotpreciselyrepro- duce the pT-differential spectra ofbackground sources measured indata.Therefore, thesources ofbackgroundelectrons simulated with PYTHIAwere reweighted according to the

π

⁰ p_T spectrum measuredwithALICE[25]andwerethenpropagatedintheALICE apparatususingGEANT3. The spectraofother light mesonswere estimatedvia mT-scalingof the

π

⁰ spectrum.The electron back- ground from charm hadron decays was estimated based on the charmhadronspectrameasuredwithALICE.TheDmesonproduc- tioncrosssectionswereobtainedbyapplyinga√

s scalingtothe crosssectionsmeasuredat√

s=^{7 TeV[26].Thescalingfactorwas} definedastheratioofthecrosssectionsfromtheFONLLcalcula- tionsat2.76and7TeV.Thetheoreticaluncertaintyonthescaling factorwas evaluated by varyingquark mass andtheperturbative scalesasdescribedin[27].TheDmesonproductioncrosssections were measured withALICE, withlimited precision and pT cover- age,in pp collisions at √

s=².76 TeV [12]. Thesemeasurements were found to be in agreement withthe scaled 7 TeV measure- mentswithin statisticaluncertainties. AcontributionfromΛc de- cays was included using the measured ratio

σ

(Λc)/

σ

(D⁰+^D+) fromZEUS [28].The backgroundelectrons survivingtheselection criteria, including thecondition ond₀, were subtracted from the measured electron distribution. Hadron contamination was esti- mated using a simultaneous fit of theelectron and the different hadron componentsofthe TPCdE/dx distributioninmomentum slices.Thecontaminationwasnegligiblebelow4 GeV/cbutissig- nificantathighermomenta.At8 GeV/citwasfoundtobeapprox- imately 7%. The contamination was statistically subtracted from the measured electron distribution. The resulting pT distribution isshownasfilledcirclesinFig. 2.

The electron yield from beauty hadron decays was corrected forgeometricalacceptance,trackreconstructionefficiency,electron identificationefficiency,andefficiencyofthed0 cut.Theinvariant crosssection ofinclusiveelectronproductionfrombeautyhadron decays inthe range |^y|<0.8 was then calculated usingthe cor- rectedelectron p_T spectrum,thenumberofMBppcollisions and theMBcrosssection.Thedetailsaredescribedin[22].

Toevaluatesystematicuncertainties,theanalysiswasrepeated withmodifiedtrackselectionandParticleIDentification(PID)cri- teria.Thecontributionstothesystematicuncertaintyarelistedin Table 1.The systematicuncertainties duetothetrackingefficien- ciesandPIDefficienciesare⁺₋¹⁵₁₈(±¹⁵)% forpT<2 GeV/c(2<pT<

6 GeV/c).Thesereach≈⁺₋²⁰₄₀^{% at8 GeV}/cduetotheuncertaintyof thehadroncontaminationsubtraction,whichis≈⁺₋⁸₃₀^{% at8 GeV}/c.

Additionalcontributionstothetotalsystematicuncertaintyinclude thed0selection,evaluatedbyrepeatingthefullanalysiswithmod- ifiedselection criteria, andthe subtractionof light flavor hadron decay background and charm hadron decay background, which wereobtainedbypropagatingthestatisticalandsystematicuncer- taintiesof thelightflavor andcharmhadron measurements used as analysis input. The light hadron decay background systematic uncertainty includes the uncertainty of the mT-scaling, which is conservatively takento be 30%.All systematicuncertainties were addedinquadraturetoobtainthetotalsystematicuncertainty.

3.2. Azimuthalelectron–hadroncorrelationtechnique

This analysisis based on theshape of the distribution ofthe differenceinazimuth(

ϕ

)betweenelectronsandhadrons,andin

Table 1

Contributionstothesystematicuncertaintyofthemeasurementofelectronsfrombeautyhadrondecayswiththeimpactparameter method,fortheranges1<pT<2 GeV/c(centre column)and2<pT<8 GeV/c(rightcolumn).Thetotalsystematicuncertaintyis calculatedasthequadraturesumofallcontributions.

Uncertainty source Systematicuncertainty(%)

1<pT<2 GeV/c

2<pT<8 GeV/c

Track matching ±² ±²

ITS number of hits ±¹⁰ ±¹⁰

Number of TPC clusters for tracking +^1,−¹⁰ ±¹

Number of TPC clusters for PID ±³ ±³

TOF PID ±3 n.a.

TPC PID ±10 ±10

Trackηand charge dependence ±2 ±2

Minimumd0requirement +^15,−²⁵ ±¹⁵

Light hadron decay background ≈¹⁵ <3

Charm hadron decay background +^40,−⁶⁰ <10

Fig. 3.(Colour online.)Theazimuthalcorrelationbetweenheavy-flavourdecayelec- tronsandchargedhadrons,scaledbythenumberofelectronsisshownfor(a) the MBeventsin the p^e_T range1.5 to 2.5 GeV/c and (b)the EMCal eventsinthe p^e_T range4.5to6.0 GeV/c.ThediamondsrepresenttheMCdistributionforelec- tronsfromcharmhadrondecays,squaresaretheMCdistributionforelectronsfrom beautyhadrondecays.ThelineistheMCfit(Eq.(2))tothedatapoints(circles).

particularofthe peak at

ϕ

around zero(near-side).Due tothe differentdecaykinematicsofcharmandbeautyhadrons,thewidth ofthe near-sidepeak is largerfor beautythanforcharm hadron decays.ThismethodhasbeenpreviouslyusedbytheSTARexper- iment[29].Asimilar methodbasedonthe invariantmassoflike chargesignelectron–kaonpairs[30]was usedbythePHENIXex- perimenttoextractarelativebeautycontributiontothemeasured heavy-flavourelectronproductioncrosssection.

The analysis was performed using the MB and EMCal trigger datasets.Electronswereselectedintherange1<pT<10 GeV/c.

FortheMBanalysistheselectedelectronsreachedout toatrans- versemomentumof6 GeV/c,whiletheanalysisusingEMCaltrig- geredeventsselectselectronsintherange2.5<p_T<10 GeV/c.

The electron sample (Ne_incl) contains electrons from heavy- flavourhadrondecaysandtheaforementionedbackgroundsources, listedinSection3.1.Di-electronpairsfromphotonconversionsand

π

⁰ Dalitzdecaysdominateatlow pT andwereidentifiedbypair- ingelectrons withoppositelychargedpartnertracksandcalculat- ingtheinvariantmass(M_e+e⁻)ofeache⁺e⁻ pair.Thedistribution

forthebackgroundelectronsispeakedatlowM_e+e⁻,whilenocor- relationsignalispresentinthelowM_e+e⁻ regionfortheelectrons from heavy-flavour decays. These unlike charge-sign (ULS) pairs contain true conversion andDalitz decay electrons, along with a smallfractionofheavy-flavourelectronsthatwerewronglypaired withabackgroundelectron.Thelattercanbeidentifiedby calcu- latingtheinvariantmassoflikecharge-sign(LS)pairs.UsingaMC simulation with GEANT3, where pp collisions are generated us- ing PYTHIA6(Perugia-0tune)andbycomparing theULSandLS invariant mass distribution theselection criteriaon Me⁺e⁻, iden- tical for the LS and ULS pairs, were determined. Electrons with M_e+e⁻<50(100)MeV/c² forthe EMCal(MB) analysis were iden- tifiedasbackground.Thebackgroundfindingefficiency(

) ranges from∼^{20%atlow p}Tto∼^{66%for p}Tabove4 GeV/c.

Thenumberofheavy-flavourhadrondecayelectronscanbeex- pressedas

N_eHF

=

^Ne_incl

−

¹

⁽

^NeULS

⁻

^NeLS

^),

⁽¹⁾

where N_eULS (N_eLS) are the numberof electrons which formed a ULS(LS)pairwitha M_e+e⁻ satisfyingthepreviouslymentionedse- lection criteria. Each electron contribution from Eq.(1) is taken, along with the charged hadrons in the event and the heavy- flavour decay electron–hadron azimuthal correlation distribution,

1

Ne(_d^dN_ϕ)e_HF−^h,wasconstructed.

Todeterminethefractionofelectrons frombeautyhadronde- cays themeasured azimuthal e–h correlation distributionwas fit withthefunction

1 N_eHF

dN

d

ϕ

e_HF−h

=

^C

+

^rb

1 Ne_b

dN

d

ϕ

e_b−^h

+ (

1

−

^rb

)

¹ Ne_c

dN

d

ϕ

ec−^h

,

(2)

where rb, a free parameterof the fit,is the fractionofelectrons frombeautytothetotalnumberofelectronsfromallheavy-flavour decays,

ϕ

isthe azimuthal anglebetweenthe electron andthe charged hadron. The distributions of the azimuthal correlations (_d^dN_ϕ)e_b(c)−^hforelectronsfrombeauty(charm)hadrondecayswere takenfromthepreviouslymentionedMCsimulation,andthecon- stant C accounts for the uncorrelated background. Fig. 3 shows themeasuredazimuthalcorrelation,scaledbythenumberofelec- trons, along with the MC fit templates and the full fit for both (a) the MB and (b) the EMCal trigger analyses, in the pT range of 1.5–2.5 GeV/c and 4.5–6 GeV/c,respectively. For each pT bin themeasureddistributionwasfitonthenear-side,overtherange

|

ϕ

_|<1.5 rad.Fromthefit,therelativebeautyfraction(r_b)isex- tracted asa function of pT. The values of rb obtained from the MB andEMCaltriggeredsamples werefound toagreewithin the

Table 2

Contributionstothesystematicuncertaintyofthefractionofelectronsfrombeautytothetotalnumberofelectronsfromheavy-flavourdecaysmea- suredusingthee–hazimuthalcorrelationtechnique,fortheMBtrigger(centre column)andEMCaltrigger(rightcolumn)analyses.Thetotalsystematic uncertaintyiscalculatedasthequadraturesumofallcontributions.

Uncertainty source Systematic uncertainty (%) MB EMCal

Number of TPC clusters for tracking ±8 5

TPC PID ±^{5 (}+⁵,−^{20) forp}T< (>)3.5 GeV/c ±^{5 (}±^{10) forp}T< (>)3.5 GeV/c

TOF PID ±^{5 n.a.}

EMCal PID n.a. ±^{10 (}±^{5) forp}T< (>)3.5 GeV/c

e⁺e⁻invariant mass negligible ±^{10 (}±^{5) forpT}< (>)3.5 GeV/c

Associated electron PID ±1 ±1 (±5) forpT< (>)4.5 GeV/c

Associated hadron momentum ±8 ±10 (±5) forpT< (>)3.5 GeV/c

Fit range negligible negligible (±5) forpT< (>6)GeV/c

Light hadron decay background ±¹ ±^{25 (}±^{5) forp}T< (>)3.5 GeV/c

systematicand statisticaluncertainties in the overlapping pT in- tervals.Hence, inthe common pT range,thefinal results forthe relativebeautycontribution toheavy-flavourdecay electrons was obtainedastheweightedaverage oftheresultsfromtheMBand EMCalsamples.

The main sources of systematic uncertainty include the elec- tron identification selection criteria and the background finding efficiency.Aspreviously explained,thebackgroundelectronswere identifiedusinginvariant massM_e+e⁻.Theselectedmassrequire- ment,asasourceofsystematicuncertaintywasfound tobeneg- ligible for the MB analysis and reached a maximum of 10% for p_T<3.5 GeV forthe EMCalanalysis. Theefficiencyofthe invari- antmassmethodwascalculatedusingaMCsample.FortheEMCal analysisaMCsimulationenhanced with

π

⁰ and

η

mesons,flatin p_T,wasusedinordertoincreasestatisticsofbackgroundelectrons athigh pT,astheMB MC sample didnot provideenough statis- tics.The bias fromthe enhancement is corrected by reweighting to obtainthe correct pT-distribution ofthe

π

⁰ (see Section 3.1).

Overall,the systematicuncertainties rangefrom9 to21% forthe MBanalysisandfrom12to33%inthecaseoftheEMCalanalysis, dependingonthetransversemomentum.Thefinalsystematicun- certaintieswereobtainedbycombiningthesetwomeasurements, yielding 17% for the lower momentum region (pT<3.5 GeV/c) and⁺₋¹⁶₂₅% forthehighermomentumregion(3.5<pT<10 GeV/c).

AllsystematicuncertaintiesarelistedinTable 2.

FortheMB analysisthehadron contamination to theelectron samplewasestimatedusingasimultaneousfitoftheelectronand the different hadron components of the TPC dE/dx distribution inmomentum ranges,while forthe EMCalanalysisthe contami- nation was estimatedusing a fit to the E/p distribution in mo- mentumslices.The contamination wasfound tobe negligiblefor p_T<4(6)GeV/c fortheMB(EMCal)analysis.Forthehighestp_Tof the MB analysis the contamination was 5% andreached 20% for thehighest pT oftheEMCalanalysis. No subtractionofthiscon- taminationwas performed. Insteaditistakenintoaccountinthe PIDsystematicuncertainties.Inaddition,amixedeventtechnique wasused tocross-check thatdetectoracceptance effectsarewell reproducedintheMCsample.Forthemixedevent

ϕ

correlation distribution,electronsfromEMCaltriggereventsandhadronsfrom theMBsamplewereselected.HadronswereselectedonlyfromMB eventstoremovethebiasfromEMCaltriggersampleinthecorre- lationdistributionfrommixedevent. Themixedeventcorrelation distributionwasfoundtobeflatovertheentire

ϕ

range,imply- ing that detector effects do not bias the correlation distribution.

Hence amixedeventcorrection was not applied to theresulting

ϕ

distribution.

4. Results

The relative beauty contribution to heavy-flavour decay elec- trons obtained from the impact parameter analysis, along with

Fig. 4.(Colour online.)(a)Relativebeautycontributiontotheheavy-flavourelectron yield;measuredfromtheazimuthalcorrelationsbetweenheavy-flavourdecayelec- tronsandchargedhadrons(blackcircles)comparedtothatfromthemethodbased onthetrackimpactparameter(redsquares).Thegreendashed,reddotted,andblue dot-dashedlinesrepresenttheFONLL[1],kT-factorization[3],andGM-VFNS[16]

predictions,respectively.(b)ThepT-differentialinclusiveproductioncrosssectionof electronsfrombeautyhadrondecaysobtainedusingtheimpactparametermethod (redsquares)andthee–hcorrelation(blackcircles)method.Forbothpanels,the errorbars(boxes)representthestatistical(systematic)uncertainties.Thenotation b(→c)→e isusedtoindicatethattherelativebeautycontributionincludesthose electronswhichoriginatedirectlyfrombeautyhadrondecaysandthosewhichorig- inatefromcharmhadrondecays,wherethecharmhadronisthedecayproductof abeautyhadron.

that extracted from the azimuthal correlation method, is shown asa function of p_T in Fig. 4(a). Forthe impact parameteranaly- sisthebeautycontributiontotheheavy-flavourelectronspectrum was measured,whilethecharmcontributionwas calculatedfrom thecharmhadronspectrameasuredbyALICEasdescribedinSec- tion 3.1. Within the statistical and systematic uncertainties the resulting fractions are in agreement with each other and show that the beauty contribution to the total heavy-flavourspectrum iscomparabletothecontributionfromcharmforp_T>4 GeV/c.

The measurements are compared to the central, upper, and lower predictionsofthreesetsofpQCD calculations[1,16,3],rep- resented by the various lines. The central values of the fraction ofelectronsfrombeautyhadrondecayswerecalculatedusingthe

Fig. 5.(Colour online.)(a)pT-differentialinclusiveproductioncrosssectionofelec- tronsfrom beautyhadron decays.The greendashed,reddotted, and bluedot- dashedlinesrepresenttheFONLL[1],kT-factorization[3],andGM-VFNS[16]un- certaintyrange,respectively.(b)–(d)Ratiosofthedataandthecentralpredictionof pQCDcalculationsforelectronsfrombeautyhadrondecays.Forallpanels,theerror bars(boxes)representthestatistical(systematic)uncertainties.

centralvaluesofthebeautyandcharmtoelectroncrosssections.

The upper (lower) predictions were obtained by calculating the beauty fraction using the upper (lower) uncertainty limit of the beautytoelectroncrosssectionandthelower(upper)limitofthe charmtoelectroncrosssection.Theupperandlowerlinesdemon- strate the uncertainty range of the calculations, which originate fromthe variationoftheperturbativescales andtheheavy quark massesasdescribedin[1–3].Eachpredictiondescribestherelative beautycontributionfractionoverthewhole p_T range.

The pT-differential production cross section of electrons from beautyhadrondecaysmeasuredusingtheimpactparameteranal- ysisisshowninFig. 4(b)anditiscomparedto thespectrumob- tainedusingthebeautyfractionfromthee–hcorrelation analysis andthemeasuredheavy-flavourdecayelectroncrosssectionfrom [13].Thisalternativeapproachagreeswiththeresultobtainedus- ing the impact parameter technique. As the resulting spectrum obtained using the impact parameter based analysis (|^y|<0.8) yieldedfiner p_T intervalsandsmalleruncertaintiesthisresultfor pT<8 GeV/c isusedwiththehigherpT sliceofthee–hcorrela- tionanalysis(|^y|<0.7)toobtainthetotalbeautyproductioncross section.

Themeasured pT-differentialcross section,obtainedusingthe impact parameter analysis for pT<8 GeV/c and including the highest p_T point from the correlation analysis, in the p_T range 1–10 GeV/c isshowninFig. 5(a)alongwithacomparisontothe upper andlower uncertaintylimits of the aforementioned pQCD calculations. Fig. 5(b)–(d)showstheratioof thedatato thecen- traltheoreticalpredictions.Thedataandpredictionsareconsistent within theexperimental andtheoretical uncertainties. Duetothe uncertainty of the measured luminosity all measured cross sec- tionshaveanadditionalnormalizationuncertaintyof1.9%[17].

The visible cross section of electrons from beauty hadron decays at mid-rapidity (|^y|<0.8) was obtained by integrating

Fig. 6.(Colour online.)Inclusivebeautyproductioncrosssectionperrapidityunit measuredatmid-rapidityasafunctionofcentre ofmassenergyinppcollisions (PHENIX[30]andALICE[22]results)andpp collisions¯ (UA1[31]andCDF[32]re- sults)alongwiththe comparisontoFONLLcalculations.Errorbarsrepresentthe statisticalandsystematicuncertaintiesaddedinquadrature.TheFONLLcalculation wasperformedforthefiveexperimentalrapidityrangesandcentre ofmassener- giesshowninthefigure,andthesepointsaredrawnasacurve.

the pT-differential cross section in the measured pT range (1<

pT <10 GeV/c), obtaining

σ

b→^e=³.47±⁰.40(stat)⁺₋¹₁^._.¹²₃₃(sys)± 0.07(norm)μb.Thevisiblecross sectionisthen scaledby thera- tio ofthetotal crosssection ofelectrons originatingfrombeauty hadron decays from FONLL in the full pT range to the FONLL cross section integrated in the measured pT range. The central value ofthe extrapolation factorwas computed using theFONLL prediction withthecentral valuesof thequark massand pertur- bativescale.Theuncertaintieswereobtainedbyvaryingthequark mass andperturbative scale and recalculatingthe ratio,which is given separately in the results as extrapolation uncertainty. For theextrapolationthebeautyhadrontoelectronbranchingratioof BRH_b→^e+^BRHb→Hc→e=⁰.205±⁰.007[33]isused.

The beautyproduction cross section at mid-rapidity, per unit rapidity, ^dσ_b¯b

dy = ²³.28 ± ².70(stat)⁺₋⁸₈^._.⁹²₇₀(sys)⁺₋⁰₀^._.⁴⁹₆₅(extr) ± 0.44(norm)μb,isshowninFig. 6asafunction ofcentre ofmass energy for experimental measurements [30,32,31], including the result obtainedby ALICEat7 TeV [22].The total beautyproduc- tioncrosssectionwasobtainedbyextrapolatingtothefullyrange and is found to be

σ

_{bb¯ =}130±¹⁵.1(stat)⁺₋⁴²₄₉^._.¹₈(sys)⁺₋³₃^._.⁴₁(extr)± 2.5(norm)±⁴.4(BR)μb. The corresponding prediction of FONLL is

σ

_bb¯=⁹⁵.5⁺₋¹³⁹_66.5 μb.

5. Summary

The inclusive invariant production cross section of electrons from semi-leptonicdecaysof beautyhadronsis reportedatmid- rapidity (|^y|<0.8) inthe transverse momentumrange 1<pT<

10 GeV/c,inppcollisionsat√

s=².76 TeV.Theprimarymeasure- mentutilizedaselectionoftracksbasedontheirimpactparameter to identifydisplacedelectrons frombeautyhadron decays.Anal- ternative method, which utilized the measured electron–hadron azimuthalcorrelations,wasfoundtobeinagreementwiththere- sultsfromtheimpactparametermethod.Theresultsarecompared to pQCD calculations and agreement between data and theory