Direct Photon Production In Pb-pb Collisions At Root S(nn)=2.76 Tev

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SISTEMA DE BIBLIOTECAS DA UNICAMP

REPOSITÓRIO DA PRODUÇÃO CIENTIFICA E INTELECTUAL DA UNICAMP

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https://www.sciencedirect.com/science/article/pii/S0370269316000320

DOI: 10.1016/j.physletb.2016.01.020

Direitos autorais / Publisher's copyright statement:

©2016 by Elsevier. All rights reserved.

DIRETORIA DE TRATAMENTO DA INFORMAÇÃO

Cidade Universitária Zeferino Vaz Barão Geraldo

CEP 13083-970 – Campinas SP

Fone: (19) 3521-6493

http://www.repositorio.unicamp.br

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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

r

a

c

t

Article history: Received5October2015

Receivedinrevisedform17December2015 Accepted14January2016

Availableonline19January2016 Editor:L.Rolandi

Direct photon productionatmid-rapidity inPb–Pb collisions at√sNN=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,agreementwasfoundwithperturbativeQCDcalculationsforpT5 GeV/c.Directphotonspectra

downtopT≈1 GeV/c couldbeextractedforthe20–40%and0–20%centralityclasses.Thesigniﬁcance

ofthedirectphotonsignalfor0.9<pT<2.1 GeV/c is 2.6

σ

forthe0–20%class.Thespectruminthis

pT rangeand centralityclasscanbe describedbyan exponentialwithan inverseslopeparameter of (297_±12stat_±₄₁syst₎_MeV._{State-of-the-art}_models_for_photon_production_in_heavy-ion_collisions _agree

withthedatawithinuncertainties.

1. Introduction

Thetheoryofthestronginteraction,Quantum ChromoDynam-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 of pro-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 (pT

5 GeV

/

c).Atlowertransversemomenta(pT

4 GeV

/

c)one

_{E-mail address:}_{alice-publications@cern.ch}_.

expectscontributionsfromthethermalizedpartonicandhadronic phases with an approximately exponential spectrum [18,19]. In addition,other directphotonproductionmechanisms,likethe in-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.Thiscomplicatestheinterpretationofinverseslope parame-tersofdirectphotonspectra,butacorrelation betweentheslope andtheinitialtemperaturestillexists[23].

Theﬁrstmeasurementofadirectphotonspectrumin relativis-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

√

sNN

=

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

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thesameenergyafterscalingwiththenumberofbinarynucleon– nucleoncollisions(Ncoll).Scalingofhigh-pT directphoton produc-tion with Ncoll in Pb–Pb collisions atLHC energywas conﬁrmed by the ATLAS [27] and CMS [28] experiments in the measure-mentofisolated photons,i.e., photonswithlittlehadronicenergy in a cone around them,in the ranges 22

<

pT

<

280 GeV

/

c and 20

<

pT

<

80 GeV

/

c, respectively. The absence ofsuppression of high pT isolated photonsin A–A collisions withrespect to Ncoll scaled pp collisions, in contrast to the observed suppression of hadrons, isconsistentwiththe latterbeingduetoenergyloss of hardscatteredquarksandgluonsinthemedium.

Directphotonproductionatlow pT (

3 GeV

/

c) inAu–Au col-lisionsat

√

sNN

=

200 GeV wasstudiedbythePHENIXexperiment inthemeasurement ofvirtual photons(e+e− pairsfrominternal conversions)[29]andwithrealphotons[30].Aclearexcessof di-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 foundtobesimilarinmagnitudetothepion el-lipticﬂowatlow pT inAu–Au collisionsat

√

sNN

=

200 GeV[32], providesafurtherimportantconstraintformodels.The simultane-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 pT

≈

50 MeV

/

c, depending onthe positionof the conversionpoint. The TPC provides particle iden-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 the interac-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

.

2

×

2

.

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

σE

/

E

= (

1

.

3%

/

E

)

⊕ (

3

.

3%

/

√

E

)

⊕

1

.

12%, where E isinGeV.ThePHOSchannelswerecalibratedinpp colli-sionsbyaligningthe

π

0_peak_position_in_the_two-photon_invariant 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–Pbhadronic interac-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%wereusedinthis analy-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

0_s,_which_contribute_about_80–85%_of_the_decay_photons (cf. Fig. 1),was measured simultaneouslywiththe inclusive pho-ton yield. Besidesphotons from

π

0 _decays,_the _second _and_third mostimportantcontributionstothedecayphotonspectrumcome from

η

and

ω

decays.

An excessofdirectphotonsabove thedecayphoton spectrum canbequantiﬁedbythe pT dependentdoubleratio

Rγ

≡

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

0_spectrum,_and

_γ

decaythe cal-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 Rγ

)

· γ

incl

.

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

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In the PCM analysis, photons are reconstructed via a sec-ondaryvertexfindingalgorithmwhichprovidesdisplacedvertices withtwoopposite-chargedaughters.Thepositivelyandnegatively chargeddaughtertracksarerequiredtocontainreconstructed clus-tersin the TPC. Only trackswith a transverse momentum above 50 MeV/c and a ratioof the numberof reconstructed TPC clus-tersoverthenumberoffindableTPCclusters(accountingfortrack length,spatiallocationandmomentum)largerthan0.6were con-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 (wherethe second condition is only applied for trackswith pT

>

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(Ks0,

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 _transverse_momentum com-ponentqT

=

pesin

θ

V 0,e [43]oftheelectronmomentum, pe,with respecttothe V0 _momentum _was _restricted_to_q

T

<

0

.

05 GeV

/

c. Basedontheinvariantmassofthee+e− pairandthepointingof theV0_to_the_primary_vertex,_the_vertex_ﬁnder_calculates_a

_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

₎

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

Therawphotonspectrum,constructedfromthesecondary ver-tex candidates passing the selection described above, was cor-rected for the reconstruction eﬃciency, the acceptance and the contamination.ThedetectorresponsewassimulatedforPb–Pb col-lisionsusing HIJING[44] together withtheGEANT 3.21 transport code[45].The resultingeﬃciencycorrectionis dominatedbythe conversionprobabilityofphotonsintheALICEmaterial.The inte-gratedmaterialbudgetofthebeampipe,theITSandtheTPCfor

r

<

1

.

8 m correspondsto

(

11

.

4

±

0

.

5

)

% ofaradiationlength X0, 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

pT 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, mainlyphotonsfromthe de-cay K0_s

→

2

π

0

_→

₄

_γ

_,_not _removed _by_the

_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,the en-ergiesofcellswithcenterswithinaradiusRcore

=

3

.

5 cm fromthe clustercenterofgravityweresummed.Comparedtothefull clus-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 Ecluster

>

0

.

3 GeV, Ncells

>

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 clustersintorealeventsand ap-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(no disper-sioncut,noCPVcut)hasavalueofabout0.022at pT

=

1 GeV

/

c. For higher pT, A

· ε

decreases and saturates at about 0.018 for pT

5 GeV

/

c.The decreaseof A

· ε

with pT resultsfromtheuse of Ecore.In central collisions, A

· ε

increases by up to about10% duetoclusteroverlaps.ApplyingthedispersionandCPVcuts, the eﬃciencyisreducedby5–10%inperipheralcollisionsandthe cen-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 pT

∼

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 and

¯

n.

¯

Thecontamination calculatedinthis wayagreeswiththatestimatedfroma HIJINGsimulation.Finally, the photon contribution from K_s0

→

2

π

0

_→

₄

_γ

_decays _was sub-tracted basedon the measured K0

s 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

0_yield_in_Eq.₍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 pT spectrumof the

η

hasthe sameshape as theK0

s spectrum[46]asbothparticlesshouldbeaffectedbyradial ﬂowinthesamewayduetotheir similarmasses.The maximum deviationbetweenthesetwocasesoccursatpT

≈

2

.

5 GeV

/

c where (i) corresponds to a

η

/

π

0 _ratio_of _about_0.4_whereas _(ii) _gives_a 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

√

sNN

=

200 GeV:0

.

46

±

0

.

05[48].Thestatisticalprecision ofthe

η

signalin the2010and2011datasets istoolow to fur-therconstrainthesetwoassumptions withameasurement ofthe

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

Table 1

SummaryofthesystematicuncertaintiesofthePCManalysisinpercentage. Uncer-taintiesarecharacterizedaccordingtothreecategories:point-by-pointuncorrelated (A),correlatedinpTwithmagnitudeoftherelativeuncertaintyvarying point-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

γincl/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 π0_{yield (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 π0_{spectrum (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 Total Rγ 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,whilehalfthedifferenceistakenasa contribu-tiontothesystematicuncertaintyofthe

η

mesoncontributionin additiontothe normalizationuncertaintyquoted above.The con-tributionof

ω

mesondecayphotonsisbelow

∼

3% andmTscaling ofthemeasured

π

0 _spectrum_with

₍

_dNω

_/

_dm

T

)/(

dNπ0

/

dmT

)

=

0

.

9 isused[49].Therelativecontributionsofthedifferenthadronsto thetotaldecayphotonspectrumareshowninFig. 1.

Themainsourcesofsystematicuncertaintiesinthe determina-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), correlatedin

p

Twithmagnitudeoftherelativeuncertaintyvaryingpoint-by-point (B),andconstantfractionaluncertainty(C).Uncertaintiesmarkedwith*cancelin thedoubleratio

R

γ.

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 π0_yield

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 π0_{spectrum (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 Total Rγ 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 simulationresultsinwhichparticleyieldsfromPYTHIAand PHO-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

/

c upto100 MeV

/

c. Un-certainties relatedtofalsely reconstructedelectron–positron pairs from Dalitz decaysasconversion pairs were obtainedby varying theminimumradialdistanceRminofreconstructedelectrontracks fromthestandardvalue ofRmin

=

5 cm upto Rmin

=

10 cm.The estimation ofthesystematicuncertaintyof theelectron selection includes a contribution estimated by the variation of the dE/dx cuts.

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

π

0 _spectrum parameteri-zation, difference ofshapesof

π

0 _spectra_measured _by _PCM_and PHOS,anduncertaintiesduetotheshapeandabsolute normaliza-tionofthe

η

spectrum.Uncertaintiesduetocontributionsofother hadronsarenegligible.

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

π

0_yields inppcollisionswithandwithoutmagneticﬁeld.Theglobalenergy andnon-linearityuncertainties,whichmostlycancelinRγ ,are es-timatedcomparingcalibrationsbasedonthe

π

0 _peak_position_and on the electron E

/

p peak position.The centrality dependenceof the energy scale uncertainty results from the larger background

(6)

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

underthe

π

0 _peak _in _central _events_and _therefore _larger uncer-taintiesinthepeakposition.

Amoredetaileddescriptionofthesingle photonselection and especiallyoftheadditional

π

0 _{uncertainties}_for_both_the_PCM_and PHOSanalysescanbefoundinRef.[41].

ThecomparisonoftheindividualPHOSandPCMinclusive pho-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,andcommonnormalizationsystematic uncertain-ties(type C)are shownasbandsaround unity. The uncertainties aredominatedbypT-correlatedcontributions.TheindividualPHOS andPCMdoubleratiosareshowninFig. 3.Thepartialcancellation oftheenergyscale uncertainties(PHOS) andthematerial budget uncertainties(PCM)istakenintoaccountintheshown uncertain-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 original distri-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 wasdeﬁnedasthe sumofthesquareddifferencesofthepseudodatapointswith re-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)inthedoubleratio

R

γ istakenintoaccountintheshownsystematic

un-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, thePHOSandPCMdoubleratiosagreewithin0.4standard devia-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 isusedtogetherwiththeaveragedinclusive pho-tonspectrumtoobtainthefinaldirectphotonspectrum,according to Eq.(2). Forthe 0–20% centralityclass and pT

=

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 pT

4 GeV

/

c, and also for1

pT

4 GeV

/

c inthemostcentralclass.Themeasurements arecomparedwiththeexpectedRγ forthepromptphoton contri-butionascalculatedwithnext-to-leading-order(NLO)perturbative

(7)

Fig. 4. (Color online.) CombinedPCMand PHOS doubleratio Rγ inthe 0–20%,

20–40%, and 40–80% centrality classes compared with pQCD calculations for nucleon–nucleoncollisionsscaledbythenumberofbinarycollisionsforthe corre-spondingPb–Pbcentralityclass.ThedarkbluecurveisacalculationfromRefs.[51, 52]whichusestheGRVphotonfragmentationfunction[53].TheJETPHOX calcu-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(Ncoll

=

1210

.

8

±

132

.

5,438

.

4

±

42,and 77

.

2

±

18 forthe 0–20%,20–40%,and40–80% class,respectively) wascalculatedwithaMonteCarloGlaubercode[58]usingan in-elastic nucleon–nucleon cross section of

σ

inel

NN

=

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 _different_direct pho-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;their con-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

pT

2

.

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

pT

2

.

1 GeV

/

c,thesigniﬁcanceofthedirectphotonexcess isabout2

.

6

σ

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

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

/

c byusinglargescales

μ

(>

2pγT

)

and rescal-ingtheresultsothatitagreeswithacalculationdonewithsmaller scales athigher pT.Thesystematicuncertaintyofthiscalculation isestimatedtobe about25%for pT

5 GeV

/

c,growingtoabout 60% at pT

≈

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 pT

5 GeV

/

c is found. Anagreement between Ncoll-scaled pQCD calculation anddata for isolated direct photon yields was also found at higher pT (

>

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 pT

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 pT 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

/

Teff

)

.The extracted inverseslope parameter is Teff

=

(8)

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 in}_the _range ₀

_.

₉

_<

_p

T

<

2

.

1 GeV

/

c for the 0–20% class and Teff

= (

410

±

84stat

±

140syst

)

MeV in the range 1

.

1

<

pT

<

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 Tno subtr

eff

= (

304

±

11stat

±

40syst

)

MeV for the0–20%classandT_effno subtr

= (

407

±

61stat

±

96syst

)

MeV forthe 20–40%class.The dominantcontributiontothesystematic uncer-taintyoftheinverseslopesisduetothetype Buncertainties.

Asignificantcontributionofblueshifted photonsfromthe late stagesofthecollisionevolutionwithhighradialflowvelocitieshas tobe takenintoaccount[22,63].Thismakestherelationbetween themedium temperatureandtheinverseslopeparameterless di-rectandacomparisontofulldirectphoton calculationsincluding thephotonsemittedduringtheQGPandhadrongasphaseis nec-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 withadditional pro-ductionchannels(including anti-/baryons)evaluated withthe in-medium

ρ

spectral function [19]. Bremsstrahlungfrom

π

–

π

and

K –K is

¯

alsoincluded[66],inthecalculationshownheretogether with

π

–

ρ

–

ω

channelsrecentlydescribedinRef. [67].The space– timeevolutionstartsat

τ

0

=

0

.

2 fm

/

c withtemperaturesT0

=

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 initial condi-tions waspresentedinRef.[69].Hadrongasratesaretakenfrom themassiveYang–MillsapproachofRef.[19].Bremsstrahlungfrom hadron scatteringis notincluded.The hydrodynamicevolution in themodelofChatterjeeetal.starts at

τ

0

=

0

.

14 fm

/

c withan 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 pT differential invariant yield ofdirect photons has been measuredfortheﬁrsttimeinPb–Pbcollisionsat

√

sNN

=

2

.

76 TeV for transversemomenta 0

.

9

<

pT

<

14 GeV

/

c and for three cen-tralityclasses:0–20%,20–40%,and40–80%.Twoindependentand consistentmeasurements (PCM,PHOS)havebeenaveragedto ob-tain the ﬁnal results.In all centralityclasses,the spectra athigh transverse momentum pT

5 GeV

/

c follow theexpectationfrom 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

Teff

= (

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.Modelswhichassumethe forma-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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