Direct photon production in Pb-Pb collisions at \(\sqrt{s_{NN}}\)=2.76 TeV

Contents lists available atScienceDirect

Physics Letters B

www.elsevier.com/locate/physletb

Direct photon production in Pb–Pb collisions at √

s _NN = ² . 76 TeV

.ALICE Collaboration

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

Articlehistory:

Received5October2015

Receivedinrevisedform17December2015 Accepted14January2016

Availableonline19January2016 Editor:L.Rolandi

Direct photon productionatmid-rapidity inPb–Pb collisions at√_s

NN=².76 TeV was studiedin the transverse momentumrange0.9<pT<14 GeV/c.Photonsweredetectedwiththe highlysegmented electromagnetic calorimeter PHOS and viaconversions inthe ALICE detector materialwith the e⁺e⁻ pairreconstructedinthecentral trackingsystem. Theresultsofthetwomethodswerecombinedand directphotonspectraweremeasuredforthe0–20%,20–40%,and40–80%centralityclasses.Forallthree classes,agreementwasfoundwithperturbativeQCDcalculationsforpT^{5 GeV}/c.Directphotonspectra downtopT≈^{1 GeV}/ccouldbeextractedforthe20–40%and0–20%centralityclasses.Thesignificance ofthedirectphotonsignalfor0.9<pT<2.1 GeV/c is2.6σ forthe0–20%class.Thespectruminthis pT rangeand centralityclasscanbe describedbyan exponentialwithan inverseslopeparameter of (297±^12stat±^41syst)MeV.State-of-the-artmodelsforphotonproductioninheavy-ioncollisions agree withthedatawithinuncertainties.

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1. Introduction

Thetheoryofthestronginteraction,QuantumChromoDynam- ics(QCD), predictsa transitionfromordinary nuclearmatter toa statewherequarksandgluonsare nolongerconfinedtohadrons [1,2].Thecreationandstudyofthisdeconfinedpartonicstate,the Quark–Gluon Plasma (QGP), is the major objective in the exper- imental program ofheavy-ion collisions atthe Relativistic Heavy Ion Collider (RHIC) [3–6] and the Large Hadron Collider (LHC) [7–15].

Directphotons,definedasphotonsnotoriginatingfromhadron decays, are a valuable tool to study details of the evolution of the medium created in heavy-ion collisions. Unlike hadrons, di- rect photons are produced at all stages of the collision and es- cape from the hot nuclear matter basically unaffected [16], de- liveringdirect information on theconditions at thetime ofpro- duction: prompt direct photons produced in hard scatterings of incoming partons provide information on parton distributions in nuclei;deconfinedquark–gluonmatteraswellashadronicmatter created in the course of the collision emit thermal direct pho- tons, carrying informationabout the temperature, collective flow and space–time evolution of the medium [17]. Different trans- versemomentum(pT)regions aredominatedbyphotonsemitted atdifferentstagesofthecollision.Promptdirectphotonsfollowa powerlawspectrumanddominateathightransversemomentum (p_T^{5 GeV}/c).Atlowertransversemomenta(p_T^{4 GeV}/c)one

E-mailaddress:[email protected].

expectscontributionsfromthethermalizedpartonicandhadronic phases with an approximately exponential spectrum [18,19]. In addition,other directphotonproductionmechanisms,likethein- teractionofhard scatteredpartonswiththemedium(“jet-photon conversion”)[20,21],maybeimportantforpT^{10 GeV}/c.

The direct photonspectrum at low pT,therefore, contains in- formationon theinitialtemperatureandspace–timeevolution of the thermalizedmedium created inheavy-ion collisions. The ob- served thermaldirect photonspectrum isa sumofcontributions from all stages of the collision after thermalization, where the earliest, hotteststageandlater, cooler stagescanmake compara- ble contributions [22]. High photon emission rates at the largest temperaturesintheearly stage arecompensatedbyan expanded space–time volume andblue-shiftdueto radial flow in thelater stage.Thiscomplicatestheinterpretationofinverseslopeparame- tersofdirectphotonspectra,butacorrelation betweentheslope andtheinitialtemperaturestillexists[23].

Thefirstmeasurementofadirectphotonspectruminrelativis- ticA–Acollisions was presentedby theWA98 Collaboration[24].

The direct photon yield was measured at the CERN SPS in cen- tralPb–Pbcollisions at√

sNN=¹⁷.3 GeV intherange1.5<pT<

4 GeV/c.The signal can be interpreted eitheras thermalphoton radiation froma quark–gluonplasma andhadronicgas orasthe effectofmultiplesoftscatteringsoftheincomingpartonswithout theformationofaQGP[19].ThePHENIXexperimentmeasuredthe directphotonspectruminAu–Aucollisionsat√

s_NN=^{200 GeV in} the range 1^pT^{20 GeV}/c [25,26]. It was found that at high pT (5^pT^{21 GeV}/c) thedirect photonspectrum measured in Au–Aucollisions agreeswiththeonemeasuredinpp collisionsat http://dx.doi.org/10.1016/j.physletb.2016.01.020

0370-2693/©^{2016CERNforthebenefitoftheALICE}Collaboration.PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense (http://creativecommons.org/licenses/by/4.0/).FundedbySCOAP³.

thesameenergyafterscalingwiththenumberofbinarynucleon–

nucleoncollisions(Ncoll).Scalingofhigh-pT directphotonproduc- tion with Ncoll in Pb–Pb collisions atLHC energywas confirmed by the ATLAS [27] and CMS [28] experiments in the measure- mentofisolatedphotons, i.e., photonswithlittlehadronicenergy in a cone around them,in the ranges 22<pT<280 GeV/c and 20<p_T<80 GeV/c, respectively. The absence ofsuppression of high pT isolated photonsin A–A collisions withrespect to N_coll scaled pp collisions, in contrast to the observed suppression of hadrons, isconsistentwiththe latterbeingduetoenergyloss of hardscatteredquarksandgluonsinthemedium.

Directphotonproductionatlow pT (^{3 GeV}/c) inAu–Aucol- lisionsat√

s_NN=200 GeV wasstudiedbythePHENIXexperiment inthemeasurement ofvirtual photons(e⁺e⁻ pairsfrominternal conversions)[29]andwithrealphotons[30].Aclearexcessofdi- rectphotonsabove theexpectationfromscaled pp collisionswas observed.The excess was parameterized by an exponential func- tionwithinverseslopeparameters Teff=²²¹±^19stat±^19systMeV (virtual photon method[29]) and Teff=²³⁹±^25stat±^{7syst MeV} (real photon method [30]) forthe 0–20% most central collisions.

The measured spectrum can be described by models assuming thermal photon emission from hydrodynamically expanding hot matterwithinitial temperaturesin therange300–600 MeV [31].

Themeasurementofadirect-photonazimuthalanisotropy(elliptic flow),whichwas foundtobesimilarinmagnitudetothepionel- lipticflowatlow p_T inAu–Au collisionsat√

s_NN=^{200 GeV[32],} providesafurtherimportantconstraintformodels.Thesimultane- ous description ofthe spectraandelliptic flow ofdirect photons currentlyposesachallengeforhydrodynamicmodels[33].

In thisletter, the first measurement of direct photon produc- tionfor pT^{14 GeV}/c inPb–Pb collisionsat√

sNN=².76 TeV is presented.

2. Detectorsetup

Photons were measured using two independent methods: by the Photon Conversion Method (PCM) and with the electromag- neticcalorimeterPHOS.Intheconversionmethod,theelectronand positrontracksfromaphotonconversionweremeasuredwiththe Inner Tracking System(ITS) and/or the TimeProjection Chamber (TPC).

The ITS [34] consists of two layers of Silicon Pixel Detectors (SPD) positioned ata radial distance of 3.9 cmand 7.6 cm, two layersofSiliconDriftDetectors(SDD)at15.0 cmand23.9 cm,and twolayersofSiliconStripDetectors(SSD)at38.0 cmand43.0 cm.

Thetwo innermostlayers coverapseudorapidity rangeof|

η

|<2 and|

η

_|<1.4,respectively.TheTPC[35]isalarge(85 m³)cylindri- caldriftdetectorfilledwitha Ne–CO2–N2 (90–10–5)gasmixture.

Itcoversthepseudorapidityrange|

η

|<0.9 overthefullazimuthal angle with a maximum tracklength of 159 reconstructed space points. With the magnetic field of B=⁰.5 T, e⁺ and e⁻ tracks can bereconstructed down to p_T≈^{50 MeV}/c, depending onthe positionof the conversionpoint. The TPC provides particleiden- tificationvia themeasurementofthespecificenergyloss(dE/dx) witharesolutionof5.2%inppcollisionsand6.5%incentralPb–Pb collisions [36].The ITSandtheTPCwere alignedwithrespectto eachother totheleveloflessthan 100 μmusingcosmic-ray and pp collision data [37]. Particle identification is furthermore pro- videdby theTime-of-Flight(TOF)detector[38] locatedataradial distanceof 370<r<399 cm. Thisdetector consistsof Multigap ResistivePlateChambers(MRPC) andprovidestiming information withanintrinsicresolutionof50 ps.

PHOS[39]is anelectromagnetic calorimeterwhich consistsof three modules installed ata distance of 4.6 mfrom theinterac- tionpoint.Itsubtends260^◦<

ϕ

<320^◦inazimuthand|

η

|<0.13

inpseudorapidity. Eachmoduleconsistsof3584detectorcells ar- ranged in a matrix of 64×^{56 lead tungstate crystals each of} size 2.2ײ.2×^{18 cm3. The signal from each cell is measured} by an avalanche photodiode (APD) associated with a low-noise charge-sensitive preamplifier. To increase the light yield, reduce electronicnoise,andimproveenergyresolution,thecrystals,APDs, andpreamplifiersare cooled toa temperatureof−^{25◦C.The re-} sultingenergyresolutionis

σ

E/E=(1.3%/E)⊕(3.3%/√

E)⊕¹.12%, where E isinGeV.ThePHOSchannelswerecalibratedinppcolli- sionsbyaligningthe

π

⁰peakpositioninthetwo-photoninvariant massdistribution.

Two scintillator hodoscopes (V0-A and V0-C) [40] subtending 2.8<

η

<5.1 and−³.7<

η

<−¹.7,respectively,wereusedinthe minimumbiastriggerinthePb–Pbrun.Thesumoftheamplitudes ofV0-AandV0-Cserved asa measureofcentralityinthePb–Pb collisions.

3. Dataanalysis

This analysis is based on data recorded by the ALICE exper- iment in the first LHC heavy-ion run in the fall of 2010. The detector readout was triggered by the minimum bias interaction trigger based on trigger signals from the V0-A, V0-C, and SPD detectors.TheefficiencyfortriggeringonaPb–Pbhadronicinterac- tionrangedbetween98.4%and99.7%,dependingontheminimum bias trigger configuration. The events were divided into central- ity classes accordingto the V0-A andV0-C summed amplitudes.

Onlyeventsinthecentralityrange0–80%wereusedinthisanaly- sis.Toensureauniformtrackacceptanceinpseudorapidity

η

,only events with a primary vertex within ±^{10 cm from the nominal} interactionpoint alongthebeamline(z-direction)wereused.Af- terofflineeventselection,13.6×^{106 eventswereavailableforthe} PCManalysisand17.7×^{106 eventsforthePHOSanalysis.}

The directphoton yieldisextractedona statisticalbasisfrom the inclusive photon spectrum by comparing the measured pho- tonspectrumtothespectrumofphotonsfromhadrondecays.The yieldof

π

⁰s,whichcontributeabout80–85%ofthedecayphotons (cf. Fig. 1),was measured simultaneouslywiththe inclusivepho- ton yield. Besidesphotons from

π

⁰ decays,the second andthird mostimportantcontributionstothedecayphotonspectrumcome from

η

and

ω

decays.

An excessofdirectphotonsabove thedecayphoton spectrum canbequantifiedbythe pT dependentdoubleratio

R_γ

≡ γ

incl

π

param⁰

γ

_decay

π

param⁰

= γ

incl

γ

_decay

^,

⁽¹⁾

where

γ

incl is themeasured inclusive photon spectrum,

π

_param⁰ a parameterizationofthemeasured

π

⁰spectrum,and

γ

decaythecal- culated decayphotonspectrum.ThePCMandPHOS

π

⁰ measure- ments are described in [41]. The double ratiohas the advantage that some of thelargest systematic uncertainties cancel partially orcompletely.Using thedoubleratio,thedirectphoton yieldcan becalculatedfromtheinclusivephotonyieldas

γ

_direct

₌ γ

_incl

₋ γ

_decay

₌ (

1

−

¹

R_γ

) · γ

_incl

.

(2) ThePCMandPHOSanalyseswereperformedindependently.Com- bined directphotonspectra weredetermined basedoncombined double ratios andcombined inclusivephoton spectra.In contrast totakingtheaverageofthePCMandPHOSdirect-photonspectra, thisapproach allowed usto usetheinformation frombothmea- surements also when one measurement of Rγ fluctuated below unity.

In the PCM analysis, photons are reconstructed via a sec- ondaryvertexfindingalgorithmwhichprovidesdisplacedvertices withtwoopposite-chargedaughters.Thepositivelyandnegatively chargeddaughtertracksarerequiredtocontainreconstructedclus- tersin the TPC. Only trackswith a transverse momentum above 50 MeV/c and a ratioof the numberof reconstructed TPCclus- tersoverthenumberoffindableTPCclusters(accountingfortrack length,spatiallocationandmomentum)largerthan0.6werecon- sidered.Toidentifye⁺ande⁻,thespecificenergylossintheTPC [36] was required to be within a band of[−³

σ

,5

σ

] ^{around the} average electron dE/dx, and be more than 3

σ

above the aver- agepion dE/dx (where the second condition is only applied for trackswith p_T>0.4 GeV/c). Trackswith an associated signal in theTOFdetectorwereonlyacceptedaselectroncandidatesifthey wereconsistentwiththeelectronhypothesiswithina ±⁵

σ

band.

Thevertexfindingalgorithm usesthe Kalmanfiltertechniquefor thedecay/conversionpointandfourmomentumdeterminationof theneutral parent particle (V⁰) [42]. V⁰s result from

γ

conver- sionsbutalsofromstrangeparticledecays(K_s⁰, or ¯).Further selection was performed on the level of the reconstructed V⁰. V⁰s with a decay point with radius r<5 cm were rejected to remove

π

⁰ and

η

Dalitz decays.The transversemomentum com- ponentq_T=^pesinθV0,e [43]oftheelectronmomentum, p_e,with respecttothe V⁰ momentum was restrictedtoqT<0.05 GeV/c.

Basedontheinvariantmassofthee⁺e⁻ pairandthepointingof theV⁰totheprimaryvertex,thevertexfindercalculatesa

χ

²(

γ

) value whichreflects the level ofconsistency withthe hypothesis that the V⁰ comes from a photon originating fromthe primary vertex.Aselectionbasedonthis

χ

²(

γ

)valuewasusedtofurther reducecontamination inthephotonsample. Randomassociations ofelectronsandpositronswerefurtherreducedby makinguseof thesmallopeningangleofthee⁺e⁻pairfromphotonconversions attheconversionpoint.

Therawphotonspectrum,constructedfromthesecondaryver- tex candidates passing the selection described above, was cor- rected for the reconstruction efficiency, the acceptance and the contamination.ThedetectorresponsewassimulatedforPb–Pbcol- lisionsusing HIJING[44] together withtheGEANT 3.21 transport code[45].The resultingefficiencycorrectionis dominatedbythe conversionprobabilityofphotonsintheALICEmaterial.Theinte- gratedmaterialbudgetofthebeampipe,theITSandtheTPCfor r<1.8 m correspondsto(11.4±⁰.5)% ofaradiationlengthX₀,re- sultinginaphoton conversionprobability thatsaturates atabout 8.5% for pT^{2 GeV}/c [36,42]. The photon finding efficiencyfor converted photonsis of the order of 50–65% over the measured p_T range for all centralities. The purity of the photon candidate sample for pT<3 GeV/c extracted from simulation is 98–99%

inperipheral and91–97% in the mostcentral collisions. Further- more,secondaryphotoncandidates, mainlyphotonsfromthede- cay K⁰_s →²

π

⁰_→4

γ

,not removed bythe

χ

²(

γ

)selection, were subtractedstatisticallybasedonthemeasured K_s⁰spectrum[46].A correctionoflessthan2% forphotonsfrompile-upcollisions was appliedforthe 40–80%class for pT<2 GeV/c.At higher pT and formorecentralclassesthiscorrectionisnegligible.

InthePHOSanalysis,clusters(eachcelloftheclustermusthave atleastone commonedgewithanothercell ofthe cluster)were usedasphotoncandidates.Toestimatethephotonenergy,theen- ergiesofcellswithcenterswithinaradiusRcore=³.5 cm fromthe clustercenterofgravityweresummed.Comparedtothefullclus- terenergy,thiscoreenergy(Ecore)islesssensitivetooverlapswith low-energyclustersin ahighmultiplicity environment.The non- linearity in theconversion of the reconstructed tothe true pho- tonenergyintroduced bythisapproachisreproduced byGEANT3 MonteCarlosimulations.Thecontributionofhadronicclusterswas reducedbyrequiring E_cluster>0.3 GeV, N_cells>2 andby accept-

ingonlyclustersaboveaminimumlateralclusterdispersion[41].

The latter selection rejects hadrons punching though the crystal and producing a large signal in the photodiode of a single cell.

With a minimum time betweenbunch crossings of525 ns, pos- siblepile-upcontributionsfromotherbunchcrossingsisremoved by a loose cut on the cluster arrival time |^t|<150 ns. For sys- tematicuncertaintystudies,photonswerealsoreconstructedwith a pT-dependent dispersion cut and witha charged particle veto (CPV)cut onthedistancebetweenthePHOSclusterpositionand thepositionofextrapolatedchargedtracksonthePHOSsurfaceto suppressclustersfromchargedparticles[41].Both dispersionand CPVcutswere tuned usingpp collision datatoprovide aphoton efficiencyatthelevelof96–99%.

Theproductofacceptanceandefficiency(A·

ε

) wasestimated by embeddingsimulatedphoton clustersintorealeventsandap- plying the standard reconstruction. PHOS properties (energy and position resolutions, residual de-calibration, absolute calibration, non-linear energyresponse) were tuned in the simulation to re- produce the pT dependence of the

π

⁰ peak position and width [41].In peripheralevents,A·

ε

forthedefaultselection(nodisper- sioncut,noCPVcut)hasavalueofabout0.022at pT=^{1 GeV}/c.

For higher pT, A·

ε

decreases and saturates at about 0.018 for p_T^{5 GeV}/c.The decreaseof A·

ε

with p_T resultsfromtheuse of Ecore.In central collisions, A·

ε

increases by up to about10%

duetoclusteroverlaps.ApplyingthedispersionandCPVcuts, the efficiencyisreducedby5–10%inperipheralcollisionsandthecen- tralitydependencebecomesnegligible.

The contamination of the photon spectrum measured with PHOSoriginates mainly from

π

^± and ^p,¯ ⁿ¯ annihilation inPHOS, with other contributions being much smaller. Application of the dispersion and CPV cuts reduces the overall contamination at pT≈¹.5 GeV/c from about 15% to 2–3% and down to 1–2% at p_T∼^{3–4 GeV}/c.The subtraction ofcontamination is basedon a data driven approach: the probability to pass the CPV and dis- persion cuts and the calorimeter response to hadrons are esti- matedusingidentified

π

^±,^p¯ ^{tracks;thephotoncandidatespectra,} measuredwithdifferentcuts(default,dispersion,CPV,both)were decomposed into

γ

,

π

^±, p¯ and n¯ contributions, assuming equal contaminationfrom ^p¯ ^andn.¯ ^Thecontamination calculatedinthis wayagreeswiththatestimatedfroma HIJINGsimulation.Finally, the photon contribution from K_s⁰→²

π

⁰_→4

γ

decays was sub- tracted basedon the measured K_s⁰ spectrum [46] asin the PCM analysis.

To calculatethe

γ

decay/

π

⁰ ratio,a Monte Carloapproach was used to simulateparticle decays into photons both for the PCM andthePHOSanalysis.Thelargestcontributionscomefrom

π

⁰,

η

, and

ω

decays.Contributionsofother hadronswerealso included butwerefoundtobenegligible.Toallowforacancellationofsome uncertaintiescommontothephotonand

π

⁰yieldinEq.(1),each analysis (PCM, PHOS) used the

π

⁰ spectrum measured with the respectivemethod.

The

η

mesoncontributionisestimatedbyusingtwoapproaches whichassume:(i)transversemass(mT)scalingofthe

π

⁰ andthe

η

spectrum whichis consistent withmeasurements at RHIC [31, 47] or(ii) thatthe p_T spectrumof the

η

hasthe sameshape as theK⁰_s spectrum[46]asbothparticlesshouldbeaffectedbyradial flowinthesamewayduetotheir similarmasses.The maximum deviationbetweenthesetwocasesoccursatpT≈².5 GeV/cwhere (i) corresponds to a

η

/

π

⁰ ratioof about0.4whereas (ii) givesa ratio ofabout0.5. The absoluteyield of

η

mesons in both cases was fixed at pT>5 GeV/c to reproducethe measured

η

/

π

⁰ ra- tioat√

s_NN=^{200 GeV:0}.46±⁰.05[48].Thestatisticalprecision ofthe

η

signalin the2010and2011datasets istoolow tofur- therconstrainthesetwoassumptions withameasurement ofthe

η

spectrum.Theaverageofthesetwocasesisusedforthedecay

Fig. 1.(Coloronline.) Relativecontributionsofdifferenthadronstothetotaldecay photonspectrumasafunctionofthedecayphotontransversemomentum(PCM case).

Table 1

SummaryofthesystematicuncertaintiesofthePCManalysisinpercentage.Uncer- taintiesarecharacterizedaccordingtothreecategories:point-by-pointuncorrelated (A),correlatedinpTwithmagnitudeoftherelativeuncertaintyvaryingpoint-by- point(B),andconstantfractionaluncertainty(C).Itemsinthetablewithcategories (A, B)summarizesourcesofuncertaintieswhichareeitheroftype AorB.

Centrality 0–20% 20–40% 40–80%

pT(GeV/c) 1.2 5.0 1.2 5.0 1.2 5.0

γinclyield

Track quality (A) 0.6 0.6 0.2 0.2 0.2 0.7

Electron PID (A, B) 1.5 6.9 0.9 4.8 0.7 4.0

Photon selection (A, B) 4.0 1.8 2.4 2.1 1.5 1.3

Material (C) 4.5 4.5 4.5 4.5 4.5 4.5

γ_incl/π⁰

Track quality (A) 0.7 1.7 0.8 0.4 0.6 1.3

Electron PID (A, B) 1.2 4.8 0.9 3.8 0.9 4.0

Photon selection (A, B) 3.2 3.2 3.0 1.5 2.5 2.4

π⁰yield (A) 1.6 2.9 1.7 2.7 0.5 3.0

Material (C) 4.5 4.5 4.5 4.5 4.5 4.5

γdecay/π⁰

π⁰spectrum (B) 0.5 1.2 0.8 1.8 0.5 3.2

ηyield (C) 1.4 1.4 1.4 1.4 1.4 1.4

ηshape (B) 1.6 0.5 1.2 0.2 1.0 0.2

TotalRγ 6.2 8.1 5.7 7.0 5.7 8.3

Totalγincl 6.2 8.5 5.2 6.9 4.8 6.2

photoncalculation,whilehalfthedifferenceistakenasacontribu- tiontothesystematicuncertaintyofthe

η

mesoncontributionin additiontothe normalizationuncertaintyquoted above.The con- tributionof

ω

mesondecayphotonsisbelow∼^{3% andm}Tscaling ofthemeasured

π

⁰ spectrumwith(dNω/dm_T)/(dNπ⁰/dm_T)=⁰.9 isused[49].Therelativecontributionsofthedifferenthadronsto thetotaldecayphotonspectrumareshowninFig. 1.

Themainsourcesofsystematicuncertaintiesinthedetermina- tionoftheinclusivephotonspectrumandRγ forthePCManalysis are listedin Table 1.The two largestuncertainties are relatedto the material budget of the ALICE detectorand the Monte Carlo- basedefficiencycorrectionstotheinclusivephotonand

π

⁰ spec-

Table 2

SummaryofsystematicuncertaintiesofthePHOSanalysisinpercentage.Uncertain- tiesarecharacterizedaccordingtothreecategories:point-by-pointuncorrelated(A), correlatedinpTwithmagnitudeoftherelativeuncertaintyvaryingpoint-by-point (B),andconstantfractionaluncertainty(C).Uncertaintiesmarkedwith*cancelin thedoubleratioRγ.

Centrality 0–20% 20–40% 40–80%

pT(GeV/c) 2 10 2 10 2 10

γinclyield

Efficiency (B) 3.0 3.0 0.7 0.7 2.5 2.5

Contamination (B) 2.0 2.0 1.3 1.3 2.9 0.5

Conversion (C) 1.7 1.7 1.7 1.7 1.7 1.7

Acceptance (C) 1.0 1.0 1.0 1.0 1.0 1.0

∗Global E scale (B) 9.6 9.0 6.1 5.9 5.8 6.3

∗Non-linearity (B) 2.2 0.1 2.1 0.1 2.0 0.1

π⁰yield

Yield extraction (A) 2.7 4.0 3.1 5.2 1.8 2.9

Efficiency (B) 1.8 1.8 2.7 2.2 2.5 2.5

Acceptance (C) 1.0 1.0 1.0 1.0 1.0 1.0

Pileup (C) 1.0 1.0 1.0 1.0 1.0 1.0

Feed-down (B) 2.0 2.0 2.0 2.0 2.0 2.0

γdecay/π⁰

π⁰spectrum (B) 1.3 4.3 1.8 1.8 1.8 1.8

ηcontribution (B) 2.2 1.7 2.2 1.6 2.1 1.6

TotalRγ 6.8 7.9 5.9 6.5 6.1 6.0

Totalγincl 12.4 12.7 9.7 10.0 9.8 9.6

tra.Thematerialbudgetuncertaintywasestimatedinppcollisions by comparing the measured number of converted photons (nor- malizedtothemeasuredchargedparticlemultiplicity)withGEANT simulationresultsinwhichparticleyieldsfromPYTHIAandPHO- JETwereusedasinput.Uncertaintiesrelatedtotrackselectionand electronidentificationwereestimatedbyvariationofthecuts.For instance,weobserveasmallvariationinresultsdependingonthe minimumthresholdforelectrontracks.Thisismostlikelyrelated to differenttracking performance forreal data andinthe Monte Carlo simulation forlow-pT particles (pT ^{50 MeV}/c). The un- certainty relatedto thechoiceofthisthresholdwas estimatedby increasingtheminimum pTfrom50 MeV/cupto100 MeV/c.Un- certainties relatedtofalsely reconstructedelectron–positron pairs from Dalitz decaysasconversion pairs were obtainedby varying theminimumradialdistanceR_minofreconstructedelectrontracks fromthestandardvalue ofR_min=^{5 cm upto R}min=^{10 cm.The} estimation ofthesystematicuncertaintyof theelectron selection includes a contribution estimated by the variation of the dE/dx cuts.

InthedoubleratioRγ,manyuncertaintiespartiallycancel.The uncertaintieson Rγ werethereforeobtainedbyevaluatingtheef- fect of cut variations directlyon Rγ. Uncertaintiesrelatedto the decay photon spectrum are similar for PCM and PHOSanalyses:

they includetheuncertaintyduetothe

π

⁰ spectrumparameteri- zation, difference ofshapesof

π

⁰ spectrameasured by PCMand PHOS,anduncertaintiesduetotheshapeandabsolutenormaliza- tionofthe

η

spectrum.Uncertaintiesduetocontributionsofother hadronsarenegligible.

The main systematic uncertainties of the PHOS analysis are summarizedinTable 2.Fortheinclusivephotonspectrum,theun- certainty of theefficiency calculationis estimatedcomparing the PIDcutefficiencyinMonteCarloandrealdata.Thecontamination uncertainty is estimated comparing the photon purity calculated withadatadrivenapproachandwithMonteCarloHIJINGsimula- tions.Theconversionprobabilityisestimatedcomparing

π

⁰yields inppcollisionswithandwithoutmagneticfield.Theglobalenergy andnon-linearityuncertainties,whichmostlycancelinRγ,arees- timatedcomparingcalibrationsbasedonthe

π

⁰ peakpositionand on the electron E/p peak position.The centrality dependenceof the energy scale uncertainty results from the larger background

Fig. 2.(Coloronline.) ComparisonofinclusivephotonspectrameasuredwithPCM andPHOSinthe0–20%,20–40%,and40–80%centralityclasses.Theindividualspec- traweredividedbythecorresponding combinedPCMand PHOSspectrum.The shownerrorsonly reflecttheuncertaintiesoftheindividual measurements.The boxesaroundunityindicatenormalizationuncertainties(type C).

underthe

π

⁰ peak in central eventsand therefore larger uncer- taintiesinthepeakposition.

Amoredetaileddescriptionofthesingle photonselection and especiallyoftheadditional

π

⁰ uncertaintiesforboththePCMand PHOSanalysescanbefoundinRef.[41].

ThecomparisonoftheindividualPHOSandPCMinclusivepho- ton spectra, normalized to the averaged spectrum, is shown in Fig. 2. Statistical and point-to-point uncorrelated systematic un- certainties (type A) are combined and presented as error bars, point-to-point correlated systematic uncertainties (type B) are shownasboxes,andcommonnormalizationsystematicuncertain- ties(type C)are shownasbandsaround unity. The uncertainties aredominatedbyp_T-correlatedcontributions.TheindividualPHOS andPCMdoubleratiosareshowninFig. 3.Thepartialcancellation oftheenergyscale uncertainties(PHOS) andthematerial budget uncertainties(PCM)istakenintoaccountintheshownuncertain- ties.

The levelof agreement betweenthe PHOSand PCM inclusive photon spectra and double ratios Rγ was quantified taking into account the correlation of theuncertainties in pT andcentrality.

To this end, pseudo data points for the ratio of the PHOS and PCM inclusive photon spectra and double ratios were generated simultaneouslyfor all three centralityclasses underthe assump- tion of the null hypothesis that the ratio is unity for all points, i.e.,that bothmeasurements resultfromthesame originaldistri- bution.The types BandC systematicuncertainties give rise to a shiftedbaseline, aroundwhich thepseudodatapoints are drawn froma Gaussian witha standard deviation given by the statisti- calandtype Auncertainties. Atest statistict was definedasthe sumofthesquareddifferencesofthepseudodatapointswithre- specttothe nullhypothesisin unitsofthetype A andstatistical

Fig. 3.(Color online.) Comparisonofdouble ratiosRγ measuredwith PCMand PHOSforthe0–20%,20–40%,and40–80%centralityclasses.Errorbarsreflectthe statisticalandtypeAsystematicuncertainty,theboxesrepresentthetype Band Csystematicuncertainties.Thecancellationofuncertainties(energyscale,material budget)inthedoubleratioRγ istakenintoaccountintheshownsystematicun- certainties.

uncertainties. A p-value was calculatedasthe fractionofpseudo experimentswithvaluesoft largerthanobservedintherealdata [50].The corresponding significancein units ofthe standard de- viation of a one-dimensional normal distribution was calculated based on a two-tailed test. The PHOS and PCM inclusive pho- ton spectra were found to agree within 1.2 standard deviations, thePHOSandPCMdoubleratiosagreewithin0.4standarddevia- tions.

4. Results

TheinclusivephotonspectraanddoubleratiosofthePCMand PHOS analyses are combined astwo independent measurements to obtain the error-weighted average. The uncertainties common tobothmeasurements(triggerefficiency,centralitydetermination, etc.) are negligible in comparison to the uncorrelated, analysis- specific uncertainties. For each centrality selection the average doubleratioRγ isusedtogetherwiththeaveragedinclusivepho- tonspectrumtoobtainthefinaldirectphotonspectrum,according to Eq.(2). Forthe 0–20% centralityclass and p_T=^{2 GeV}/c, this resultsintypes A,B,andCsystematicuncertainties of

σ

A=².5%,

σ

B=².3%, and

σ

C=³.0% for the combined double ratio and of

σ

A=^20%,

σ

B =^18%,

σ

C=^{24% for the combined direct photon} spectrum.

The combinedPCM and PHOSdoubleratios Rγ measured for threecentralityclassesareshowninFig. 4.Adirectphotonexcess is observed for all centrality classes for p_T^{4 GeV}/c, and also for1^pT^{4 GeV}/c inthemostcentralclass.Themeasurements arecomparedwiththeexpectedRγ forthepromptphotoncontri- butionascalculatedwithnext-to-leading-order(NLO)perturbative

Fig. 4.(Color online.) CombinedPCMand PHOS doubleratio Rγ inthe 0–20%, 20–40%, and 40–80% centrality classes compared with pQCD calculations for nucleon–nucleoncollisionsscaledbythenumberofbinarycollisionsforthecorre- spondingPb–Pbcentralityclass.ThedarkbluecurveisacalculationfromRefs.[51, 52]whichusestheGRVphotonfragmentationfunction[53].TheJETPHOXcalcu- lations[54]wereperformedwithtwodifferentpartondistributionfunctions,CT10 [55]andEPS09[56],andtheBFGIIfragmentationfunction[57].

QCD calculations.The prompt photon expectationsinFig. 4 were determined as1+^Ncoll

γ

pQCD/

γ

_decay wherethenumber ofbinary nucleon–nucleoncollisions(N_coll=¹²¹⁰.8±¹³².5,438.4±^42,and 77.2±^{18 forthe 0–20%,20–40%,and40–80% class,}respectively) wascalculatedwithaMonteCarloGlaubercode[58]usinganin- elastic nucleon–nucleon cross section of

σ

_NN^inel₌64±^{5 mb. The} decayphoton spectra

γ

decay werecalculatedastheproductofthe (

γ

decay/

π

⁰)|MC ratio from the decay photon calculation and the combinedPHOSandPCM

π

⁰ spectra.Three differentdirectpho- toncalculationsareshown,twobasedonJETPHOX(withdifferent partondistributionfunctions)[54],andonefromRefs.[51,52].The band around the latterreflects the factorization, renormalization, and fragmentation scale uncertainty whereas the bands around theJETPHOXcalculationsalso includetheuncertaintyofthe par- tondistributionfunctions.Inallthreecentralityclasses,theexcess agrees withthecalculated prompt directphoton contributions at high pT^{5 GeV}/c. The contribution of prompt direct photons cannotbecalculatedstraightforwardlyforpT^{2 GeV}/c;theircon- tribution relative to the decay photons, however, is expected to be small. The excess of about 10–15% for the 0–20% centrality classintherange0.9^pT².1 GeV/c indicatesthepresence of anothersource of directphotons incentral collisions. The signif- icance of the excess at each data point in this pT range in the 0–20%centralityclass isabout2

σ

.Consideringall datapoints in 0.9^pT².1 GeV/c,thesignificanceofthedirectphotonexcess isabout2.6

σ

whichisonlyslightlylargerthanthesignificanceof the individual points dueto the correlation ofsystematic uncer- taintiesin p_T.

Fig. 5.(Coloronline.) DirectphotonspectrainPb–Pbcollisionsat√

sNN=2.76 TeV for the0–20% (scaledbya factor100),the 20–40% (scaledbya factor10)and 40–80%centralityclassescomparedtoNLOpQCDpredictionsforthedirectphoton yieldinppcollisionsatthesameenergy,scaledbythenumberofbinarynucleon collisionsforeachcentralityclass.

TheresultingdirectphotonspectraareshowninFig. 5.Arrows represent 90% upperconfidence limits. The sameNLO pQCD cal- culationsthat wereused inFig. 4aredirectlycomparedwiththe measureddirect-photonspectra.Inaddition,thepQCD calculation usedinthePb–PbdirectphotonpredictionbyPaquetetal.[59]is shownasa dashed lineinFig. 5. Thiscalculationwas performed downtopT≈1 GeV/cbyusinglargescales

μ

(>2pγ

T)andrescal- ingtheresultsothatitagreeswithacalculationdonewithsmaller scales athigher p_T.Thesystematicuncertaintyofthiscalculation isestimatedtobe about25%for p_T^{5 GeV}/c,growingtoabout 60% at p_T≈^{1 GeV}/c. All calculations were scaled with the cor- respondingnumberofnucleon–nucleoncollisionsinthecentrality class.SimilartoRγ,anagreementwiththesetheoreticalestimates of pQCD photon production in peripheral, mid-central, and cen- tral collisions for p_T^{5 GeV}/c is found. Anagreement between N_coll-scaled pQCD calculation anddata for isolated direct photon yields was also found at higher p_T (>20 GeV/c) by ATLAS [27]

andCMS[28].

In mid-central and more clearly in central collisions an ex- cess of direct photons at low p_T^{4 GeV}/c with respect to the pQCD photon predictions is observed, which might be re- lated to the production of thermal photons. In models in which thermal photonproduction inthe earlyphase dominates,the in- verse slope parameter reflects an effective temperature averaged over the different temperatures during the space–time evolution of themedium. Inorder toextract theslope parameter, a p_T re- gion isselectedwhere thecontributionofprompt directphotons is small. The pQCD contribution from the calculation by Paquet et al. [59], shown as a dashed line in Fig. 5, is subtracted and the remaining excess yield is fit with an exponential function

∝^exp(−^pT/T_eff).The extracted inverseslope parameter is T_eff=

Fig. 6.(Coloronline.) ComparisonofmodelcalculationsfromRefs.[59–62]withthe directphotonspectrainPb–Pbcollisionsat√

sNN=².76 TeV forthe0–20%(scaled byafactor100),the20–40%(scaledbyafactor10)and40–80%centralityclasses.

AllmodelsincludeacontributionfrompQCDphotons.Forthe0–20%and20–40%

classesthefitwithanexponentialfunctionisshowninaddition.

(297±^12stat±^41syst)MeV inthe range 0.9<pT<2.1 GeV/c for the 0–20% class and Teff= (410±^84stat±^140syst)MeV in the range 1.1<p_T<2.1 GeV/c for the 20–40% class. Alternatively, to estimate the sensitivity to the pQCD photon contribution, the slopewasextractedwithoutthesubtractionofpQCDphotons.This yields inverse slopes of T^{no subtr}_eff =(304±^11stat±^40syst)MeV for the0–20%classandT_eff^{no subtr}=(407±^61stat±^96syst)MeV forthe 20–40%class.The dominantcontributiontothesystematicuncer- taintyoftheinverseslopesisduetothetype Buncertainties.

Asignificantcontributionofblueshifted photonsfromthe late stagesofthecollisionevolutionwithhighradialflowvelocitieshas tobe takenintoaccount[22,63].Thismakestherelationbetween themedium temperatureandtheinverseslopeparameterlessdi- rectandacomparisontofulldirectphoton calculationsincluding thephotonsemittedduringtheQGPandhadrongasphaseisnec- essaryto extract the initial temperature. A comparisonto state- of-the-artdirectphoton calculationsisshowninFig. 6.All shown modelsassume the formationof aQGP. The hydrodynamic mod- els,which fold thespace–time evolutionwithphoton production rates, use QGP rates from Ref. [64] andequations of state from latticeQCD. Allmodels includethecontributionfrompQCD pho- tons,however,differentparameterizationsareused.Themodelof van Heesetal.[60] isbased onideal hydrodynamicswithinitial flow(priortothermalization)[65].Thephotonproductionratesin thehadronicphasearebasedonamassiveYang–Millsdescription ofgas of

π

, K,

ρ

, K^∗,anda1 mesons,along withadditionalpro- ductionchannels(including anti-/baryons)evaluated withthein- medium

ρ

spectral function [19]. Bremsstrahlungfrom

π

–

π

and K–K¯ isalsoincluded[66],inthecalculationshownheretogether with

π

–

ρ

–

ω

channelsrecentlydescribedinRef. [67].The space–

timeevolutionstartsat

τ

0=⁰.2 fm/cwithtemperaturesT0=^682, 641,461 MeVforthe0–20%,20–40%,and40–80%classes,respec-

tively, atthe center of the fireball.The calculation by Chatterjee et al. [61,68] is based on an event-by-event (2+1D) longitudi- nally boost invariant ideal hydrodynamic model with fluctuating initialconditions.An earlierpredictionwithsmooth initialcondi- tions waspresentedinRef.[69].Hadrongasratesaretakenfrom themassiveYang–MillsapproachofRef.[19].Bremsstrahlungfrom hadron scatteringis notincluded.The hydrodynamicevolution in themodelofChatterjeeetal.starts at

τ

0=⁰.14 fm/cwithan av- erage temperatureat the centerof the fireball of T0≈^{740 MeV} forthe0–20% classand T0≈680 MeV forthe 20–40%class.The calculationbyPaquetetal.[59]usesevent-by-event(2+^1D)lon- gitudinally boost invariant viscous hydrodynamics [70] with IP- Glasma initial conditions [71]. Viscous corrections were applied to the photon production rates [59,72,73]. The same hadron gas rates as described above for the calculation by van Hees et al.

are used. The hydrodynamic evolution starts at

τ

0 =⁰.4 fm/c with an initial temperature (averaged over all volume elements with T >145 MeV) of T0=385 MeV for the 0–20% class and T0=350 MeV for the 20–40% class. The PHSDmodel prediction byLinnyketal.[62]isbasedonanoff-shelltransportapproachin which thefull evolution of thecollision is described microscopi- cally.Bremsstrahlungfromthescatteringofhadronsisasignificant photon source in this model. The comparison of the measured direct-photonspectratothecalculationsinFig. 6indicatesthatthe systematicuncertainties donot allowusto discriminatebetween themodels.

5. Conclusions

The p_T differential invariant yield ofdirect photons has been measuredforthefirsttimeinPb–Pbcollisionsat√

s_NN=².76 TeV for transversemomenta 0.9<p_T<14 GeV/c andfor threecen- tralityclasses:0–20%,20–40%,and40–80%.Twoindependentand consistentmeasurements (PCM,PHOS)havebeenaveragedtoob- tain the final results.In all centralityclasses,the spectra athigh transverse momentum pT^{5 GeV}/c followtheexpectationfrom pQCD calculations of the direct photon yield in pp collisions at the same energy, scaled by the number of binary nucleon col- lisions. Within the sensitivity of the current measurement, no evidence for medium influence on direct photon production at high pT is observed. Inthe low pT region, pT^{2 GeV}/c,no di- rect photon signal can be extracted in peripheral collisions, but in mid-centralandcentral collisions an excess above theprompt photon contributions is observed. An inverse slope parameter of T_eff=(297±^12stat±^41syst)MeV isobtained forthe0–20% most central collisions from an exponential function fit to the direct photon spectrum, after subtraction of the pQCD contribution, in therange0.9<pT<2.1 GeV/c.Modelswhichassumetheforma- tionofaQGPwerefoundtoagreewiththemeasurementswithin uncertainties.

Acknowledgements

We would like to thank RupaChatterjee, Olena Linnyk, Jean- François Paquet, Ralf Rapp, and Werner Vogelsang for providing calculationsshowninthispaperandforusefuldiscussions.

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