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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
Articlehistory: 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.ThespectruminthispT rangeand centralityclasscanbe describedbyan exponentialwithan inverseslopeparameter of
(297±12stat±41syst)MeV.State-of-the-artmodelsforphotonproductioninheavy-ioncollisions agree
withthedatawithinuncertainties.
©2016CERNforthebenefitoftheALICECollaboration.PublishedbyElsevierB.V.Thisisanopen accessarticleundertheCCBYlicense(http://creativecommons.org/licenses/by/4.0/).FundedbySCOAP3.
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(pT4 GeV/
c)oneE-mailaddress: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 inthe range 1
pT20 GeV/
c [25,26]. It was found that at highpT (5
pT21 GeV/
c) thedirect photonspectrum measured inAu–Aucollisions agreeswiththeonemeasuredinpp collisionsat
http://dx.doi.org/10.1016/j.physletb.2016.01.020
0370-2693/©2016CERNforthebenefitoftheALICECollaboration.PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense (http://creativecommons.org/licenses/by/4.0/).FundedbySCOAP3.
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 and20
<
pT<
80 GeV/
c, respectively. The absence ofsuppression ofhigh 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–Aucol-lisionsat
√
sNN=
200 GeV wasstudiedbythePHENIXexperimentinthemeasurement 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 ispresented.
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 onthepositionof 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.
13inpseudorapidity. 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-sultingenergyresolutionisσ
E/
E= (
1.
3%/
E)
⊕ (
3.
3%/
√
E
)
⊕
1.
12%, where E isinGeV.ThePHOSchannelswerecalibratedinpp colli-sionsbyaligningtheπ
0peakpositioninthetwo-photoninvariantmassdistribution.
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
0s,whichcontributeabout80–85%ofthedecayphotons(cf. Fig. 1),was measured simultaneouslywiththe inclusive pho-ton yield. Besidesphotons from
π
0 decays,the second andthirdmostimportantcontributionstothedecayphotonspectrumcome from
η
andω
decays.An excessofdirectphotonsabove thedecayphoton spectrum canbequantifiedbythe pT dependentdoubleratio
Rγ
≡
γincl
π
param0γ
decayπ
param0=
γincl
γ
decay,
(1)where
γ
incl is themeasured inclusive photon spectrum,π
param0 aparameterizationofthemeasured
π
0spectrum,andγ
decaythe
cal-culated decayphotonspectrum.ThePCMandPHOS
π
0measure-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.
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
[−
3σ
,
5σ
]
around the average electron dE/
dx, and be more than 3σ
above the aver-agepion dE/
dx (wherethe second condition is only applied for trackswith pT>
0.
4 GeV/
c). Trackswith an associated signal intheTOFdetectorwereonlyacceptedaselectroncandidatesifthey wereconsistentwiththeelectronhypothesiswithina
±
5σ
band. Thevertexfindingalgorithm usesthe Kalmanfiltertechniquefor thedecay/conversionpointandfourmomentumdeterminationof theneutral parent particle (V0) [42]. V0s result fromγ
conver-sionsbutalsofromstrangeparticledecays(Ks0,or
¯
).Furtherselection was performed on the level of the reconstructed V0.
V0s with a decay point with radius r
<
5 cm were rejected to removeπ
0 andη
Dalitz decays.The transversemomentumcom-ponentqT
=
pesinθV 0
,e [43]oftheelectronmomentum, pe,withrespecttothe V0 momentum was restrictedtoq
T
<
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
)
valuewasusedtofurtherreducecontamination 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 efficiencyforconverted 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 K0s
→
2π
0→
4γ
,not removed bytheχ
2(
γ
)
selection, weresubtractedstatisticallybasedonthemeasured Ks0spectrum[46].A correctionoflessthan2% forphotonsfrompile-upcollisions was appliedforthe 40–80%class for pT
<
2 GeV/
c.At higher pT andformorecentralclassesthiscorrectionisnegligible.
InthePHOSanalysis,clusters(eachcelloftheclustermusthave atleastone commonedgewithanothercell ofthe cluster)were usedasphotoncandidates.Toestimatethephotonenergy,the en-ergiesofcellswithcenterswithinaradiusRcore
=
3.
5 cm fromtheclustercenterofgravityweresummed.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 andbyaccept-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 theπ
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 forpT
5 GeV/
c.The decreaseof A·
ε
with pT resultsfromtheuseof 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 atpT
≈
1.
5 GeV/
c from about 15% to 2–3% and down to 1–2% atpT
∼
3–4 GeV/
c.The subtraction ofcontamination is basedon adata 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 intoγ
,π
±, p and¯
n contributions,¯
assuming equal contaminationfrom p and¯
n.¯
Thecontamination calculatedinthis wayagreeswiththatestimatedfroma HIJINGsimulation.Finally, the photon contribution from Ks0→
2π
0→
4γ
decays wassub-tracted basedon the measured K0
s spectrum [46] asin the PCM
analysis.
To calculatethe
γ
decay/
π
0 ratio,a Monte Carloapproach wasused to simulateparticle decays into photons both for the PCM andthePHOSanalysis.Thelargestcontributionscomefrom
π
0,η
,and
ω
decays.Contributionsofother hadronswerealso included butwerefoundtobenegligible.Toallowforacancellationofsome uncertaintiescommontothephotonandπ
0yieldinEq.(1),eachanalysis (PCM, PHOS) used the
π
0 spectrum measured with therespectivemethod.
The
η
mesoncontributionisestimatedbyusingtwoapproaches whichassume:(i)transversemass(mT)scalingoftheπ
0 andtheη
spectrum whichis consistent withmeasurements at RHIC [31, 47] or(ii) thatthe pT spectrumof theη
hasthe sameshape astheK0
s spectrum[46]asbothparticlesshouldbeaffectedbyradial
flowinthesamewayduetotheir similarmasses.The maximum deviationbetweenthesetwocasesoccursatpT
≈
2.
5 GeV/
c where(i) corresponds to a
η
/
π
0 ratioof about0.4whereas (ii) givesaratio ofabout0.5. The absoluteyield of
η
mesons in both cases was fixed at pT>
5 GeV/
c to reproducethe measuredη
/
π
0ra-tioat
√
sNN=
200 GeV:0.
46±
0.
05[48].Thestatisticalprecisionofthe
η
signalin the2010and2011datasets istoolow to fur-therconstrainthesetwoassumptions withameasurement oftheFig. 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
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 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-tributionofω
mesondecayphotonsisbelow∼
3% andmTscalingofthemeasured
π
0 spectrumwith(
dNω/
dmT
)/(
dNπ0/
dmT)
=
0.
9isused[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
0spec-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 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). Theun-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.Theestimation 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 spectrumparameteri-zation, difference ofshapesof
π
0 spectrameasured by PCMandPHOS,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
0yieldsinppcollisionswithandwithoutmagneticfield.Theglobalenergy andnon-linearityuncertainties,whichmostlycancelinRγ ,are es-timatedcomparingcalibrationsbasedonthe
π
0 peakpositionandon the electron E
/
p peak position.The centrality dependenceof the energy scale uncertainty results from the larger backgroundFig. 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 eventsand therefore largeruncer-taintiesinthepeakposition.
Amoredetaileddescriptionofthesingle photonselection and especiallyoftheadditional
π
0 uncertaintiesforboththePCMandPHOSanalysescanbefoundinRef.[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)inthedoubleratioRγ 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, thisresultsintypes A,B,andCsystematicuncertainties of
σ
A=
2.
5%,σ
B=
2.
3%, andσ
C=
3.
0% for the combined double ratio and ofσ
A=
20%,σ
B=
18%,σ
C=
24% for the combined direct photonspectrum.
The combinedPCM and PHOSdoubleratios Rγ measured for threecentralityclassesareshowninFig. 4.Adirectphotonexcess is observed for all centrality classes for pT
4 GeV/
c, and alsofor1
pT4 GeV/
c inthemostcentralclass.ThemeasurementsarecomparedwiththeexpectedRγ forthepromptphoton contri-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–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
+
Ncollγ
pQCD/
γ
decay wherethenumber ofbinarynucleon–nucleoncollisions(Ncoll
=
1210.
8±
132.
5,438.
4±
42,and77
.
2±
18 forthe 0–20%,20–40%,and40–80% class,respectively) wascalculatedwithaMonteCarloGlaubercode[58]usingan in-elastic nucleon–nucleon cross section ofσ
inelNN
=
64±
5 mb. Thedecayphoton spectra
γ
decay werecalculatedastheproductofthe(
γ
decay/
π
0)
|
MC ratio from the decay photon calculation and thecombinedPHOSandPCM
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 photonscannotbecalculatedstraightforwardlyforpT
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
.
9pT2.
1 GeV/
c indicatesthepresence ofanothersource 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.
9pT2.
1 GeV/
c,thesignificanceofthedirectphotonexcessisabout2
.
6σ
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 byusinglargescalesμ
(>
2pγT)
andrescal-ingtheresultsothatitagreeswithacalculationdonewithsmaller scales athigher pT.Thesystematicuncertaintyofthiscalculation
isestimatedtobe about25%for pT
5 GeV/
c,growingtoabout60% at pT
≈
1 GeV/
c. All calculations were scaled with thecor-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 betweenNcoll-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 tothe 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=
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 forthe 0–20% class and Teff
= (
410±
84stat±
140syst)
MeV in therange 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 forthe0–20%classandTeffno 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 withadditionalpro-ductionchannels(including anti-/baryons)evaluated withthe in-medium
ρ
spectral function [19]. Bremsstrahlungfromπ
–π
andK –K is
¯
alsoincluded[66],inthecalculationshownheretogether withπ
–ρ
–ω
channelsrecentlydescribedinRef. [67].The space– timeevolutionstartsatτ
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 atτ
0=
0.
14 fm/
c withanav-erage temperatureat the centerof the fireball of T0
≈
740 MeVforthe0–20% classand T0
≈
680 MeV forthe 20–40%class.ThecalculationbyPaquetetal.[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 atτ
0=
0.
4 fm/
cwith an initial temperature (averaged over all volume elements with T
>
145 MeV) of T0=
385 MeV for the 0–20% class andT0
=
350 MeV for the 20–40% class. The PHSDmodel predictionbyLinnyketal.[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 TeVfor transversemomenta 0
.
9<
pT<
14 GeV/
c and for threecen-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 theexpectationfrompQCD 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,nodi-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% mostcentral 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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ALICECollaboration