Direct photon elliptic flow in Pb–Pb collisions at sNN=2.76 TeV

(1)

Contents lists available atScienceDirect

Physics

Letters

B

www.elsevier.com/locate/physletb

Direct

photon

elliptic

ﬂow

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: Received23May2018

Receivedinrevisedform16October2018 Accepted19November2018

Availableonline23November2018 Editor:L.Rolandi

Theellipticﬂowofinclusiveanddirectphotonswasmeasuredatmid-rapidityintwocentralityclasses 0–20% and 20–40% in Pb–Pb collisions at √sNN=2.76 TeV by ALICE. Photons were detected with

the highly segmentedelectromagneticcalorimeter PHOS and viaconversions inthe detectormaterial with the e+e− pairs reconstructed in the central tracking system. The results of the two methods were combinedand the direct-photon elliptic ﬂowwas extracted inthetransverse momentumrange 0.9<pT<6.2 GeV/c.Acomparison toRHICdata showsasimilarmagnitudeofthemeasured

direct-photon ellipticﬂow.Hydrodynamic andtransportmodelcalculationsare systematicallylowerthanthe data,butarefoundtobecompatible.

1. Introduction

Thetheoryofthestronginteraction,Quantum ChromoDynam-ics (QCD), predicts a transition from ordinary hadronic matter to a new state where quarks and gluons are no longer con-ﬁned to hadrons [1,2]. Lattice calculations predict a chiral and deconﬁnement crossover transitions over the temperature range 145–163 MeV[1,2], which is accessiblein collisions of ultrarela-tivisticheavyions.Thecreationandstudyofthepropertiesofthis hotstronglyinteractingmatter–Quark–GluonPlasma(QGP)–are themainobjectivesoftheALICEexperiment.

Thehotstronglyinteractingmatter,createdinnucleus–nucleus collisions,expands,coolsandfinallytransformstoordinary hadro-nicmatter. Toexperimentally studythe quark matter properties, severalobservableswereproposed.Here,weconcentrateon study-ing the development of collectiveflow using directphotons.Direct photonsarethephotonsnotoriginatingfromhadronicdecaysbut produced in electromagnetic interactions. Unlike hadrons, direct photonsare produced atall stagesofthe collision. Incoming nu-cleipassingthrougheachotherproducedirectphotonsin scatter-ingsoftheir partonicconstituents.Inaddition, (thermal)photons are emitted in the deconfined quark–gluon plasma and hadronic matter, characterized bythe thermaldistributions ofpartons and hadrons,respectively.Sincethemeanfreepathofaphotoninhot matterismuchlargerthanthetypicalsizesofthecreatedfireball [3],directphotonsescapethecollisionzoneunaffected,delivering direct informationon the conditions at the productiontime and onthedevelopmentofcollectiveflow.

_E-mail_address:_alice_{-publications}_@cern_.ch_.

The observations ofa strong azimuthal asymmetry of particle production over a wide rapidity range in nucleus–nucleus colli-sions was oneofthekey resultsobtainedatRHIC[4–7] and LHC [8–12] energies. It was interpreted as a consequence of collec-tive expansion – collectiveflow –of thematter having aninitial spatial asymmetry, which is more prominent in collisions with non-zeroimpactparameter.Toquantifythecollectiveflow,the az-imuthal distributions of final state particles are expanded in the series1

+

2

vncos

[

n

(

ϕ

−

R P

)

]

[13],dependingonthedifference

betweentheparticleazimuthalangle

ϕ

andthereactionplane ori-entation

R P,deﬁnedbytheimpactparameterandbeamaxis.At

mid-rapiditythesecondharmonicv2(ellipticﬂow)reﬂectsthe

ex-pansionofthealmond-likeshapeofthehotmattercreatedbythe mutual penetration of the collidingnuclei. Higher harmonics v3,

v4,etc.aresensitivetoﬂuctuationsoftheinitialshapeofthe

cre-ated hot matter and are typically much smaller than v2, except

forcentralcollisions,where v2 decreases duetoamore

symmet-ric geometry. Collectiveflow is sensitive to the equation of state ofhotmatterandtheamountofshearviscosity.Theinitialspatial asymmetryoftheexpandingfireballdiminisheswithtime,forany equation of state. Forstrongly interactingmatter thisasymmetry translatesintoanazimuthalanisotropyinmomentumspace,while forfreestreamingweaklyinteractingmatterthereisnofinal par-ticleazimuthalanisotropy.

Hadrons providethepossibilitytotestwithhighprecision the flowpatternofthelateststageofthecollision,whenthehot mat-ter decouples intofinal particles. Complementary tothem, direct photonsprovide thepossibilityto investigatethedevelopment of flow during the evolution of hot matter. First calculations pre-dicted that the photon emission rate from the hot quark–gluon orhadronmatterincreaseswithtemperatureas

∝

T2exp

(

−

Eγ

/

T

)

[14], whereEγ isthephotonenergyandT isthetemperatureof

https://doi.org/10.1016/j.physletb.2018.11.039

(2)

ALICE Collaboration / Direct photon elliptic ﬂow in Pb–Pb 309

thematter. Then, thelow transverse momentum (pT

4 GeV

/

c)

partis controlledby thecoolerlateststage,andthehigh pT part

(pT

5 GeV

/

c)ofthe spectrumbythehot initialstate. However,

detailedcalculationswhich include the full hydrodynamic evolu-tion(seee.g. [15])show thatcontributions ofallstagesare com-parable for all pT regions asa higher temperature of the initial

stageiscompensatedbyalargerspace–timevolumeandstronger radial flow of the later stages. Since the observed direct-photon flowistheconvolutionofallstagesofthecollision,includingthe contributionfromtheinitial stagewhen theflowpatternhasnot yet developed, the calculations predict much smaller azimuthal anisotropyforthermalphotonsthanforhadrons[16,17].

Thefirstmeasurementofadirect-photonspectrumin relativis-ticnucleus–nucleuscollisionswaspresentedbytheWA98 collabo-ration [18], and later also by the PHENIX Collaboration [19–22], and by the ALICE Collaboration [23]. The first measurement of elliptic flow of direct photons in Au–Au collisions at

√

sNN

=

200 GeV was performedby the PHENIX Collaboration [24]. Sur-prisingly, it was found to be close to the flow of hadrons [25]. RecentPHENIXresults, presentingmoreprecise measurementsof ellipticandtriangularflow extendedto lower pT [26],confirmed

thisearlyresult.Thediscrepancybetweenexperimentalresultsand theorypredictionstriggeredasetoftheoreticalstudies,whichcan besplitintotwo classes.Themain ideainthefirstclassof mod-els[27–44] istoincreasetheemissionofdirectphotonsfromthe laterstagesofthecollisionand/orsuppressemissionoftheinitial stage. In the second class of models [45–47], a new azimuthally asymmetricsourceofdirect photonsisconsideredlike jet-matter interactionsorsynchrotronradiationinthefieldofcollidingnuclei. Thesetheoreticalefforts considerablyreduce thediscrepancy,but consistentreproductionofboththedirect-photonspectraandflow isstill missing.The measurementofdirect-photon flowathigher collision energy is important asan independent confirmation of the results at lower energy, and could also allow to disentangle betweendifferentcontributions.

Inthispaper,we presentthefirstmeasurement ofthe direct-photonflowinPb–PbcollisionsattheLHCandcompareour find-ingstoRHICresultsandtopredictionsofhydrodynamicaswellas transportmodels.

2. Detectorsetup

Thedirectphotonflowisbasedonthemeasurementofthe el-lipticflowofinclusivephotonsandtheestimationofthe contribu-tionofdecayphotonsusingtheavailablehadronflowresults. Pho-tonsarereconstructed viatwo independentmethods: thePhoton ConversionMethod(PCM)andwiththeelectromagnetic calorime-terPHOS.

Intheconversionmethod,theelectronandpositrontracksfrom photonconversionsare measuredwiththeInnerTrackingSystem (ITS)and/ortheTimeProjectionChamber(TPC).TheITS[48] con-sists of two layers of Silicon Pixel Detectors (SPD) positioned at radial distancesof 3.9 cmand7.6 cm, two layers ofSiliconDrift Detectors(SDD)at15.0 cmand23.9 cm,andtwolayersofSilicon StripDetectors(SSD)at38.0 cm and43.0 cm.Thetwoinnermost layers cover a pseudorapidity range of

|

η

|

<

2 and

|

η

|

<

1

.

4, re-spectively.TheTPC[49] isalarge(85 m3)cylindricaldriftdetector ﬁlledwithaNe–CO2–N2 (85.7/9.5/4.8%)gasmixture.Itcoversthe

pseudorapidityrange

|

η

|

<

0

.

9 overthefull azimuthalanglewith amaximumtracklengthof159reconstructed spacepoints.With thesolenoidal magnetic ﬁeld of B

=

0

.

5 T, electron andpositron trackscanbereconstructeddownto pT

≈

50 MeV

/

c.TheTPC

pro-vides particle identiﬁcation via the measurement of the speciﬁc energyloss(dE/dx) witha resolutionof5.2%inppcollisions and 6.5% in central Pb–Pb collisions [50]. The ITS and the TPC were

alignedwithrespecttoeachothertotheleveloflessthan100 μm usingcosmic-rayandpp collisiondata[51].Particle identiﬁcation isalsoprovided bythe Time-of-Flight(TOF) detector[52] located ataradialdistanceof370

<

r

<

399 cm.Thisdetectorconsistsof MultigapResistivePlateChambers(MRPC)andprovidestiming in-formationwithanintrinsicresolutionof50 ps.

PHOS[53] isan electromagneticcalorimeterwhichconsistsof three modules installed at a radial distance of 4.6 m from the interaction point. It subtends 260◦

<

ϕ

<

320◦ in azimuth and

|

η

|

<

0

.

12 in pseudorapidity. Each module consists of 3584 de-tector cells arranged ina matrix of 64

×

56 lead tungstate crys-tals each of size 2

.

2

×

2

.

2

×

18 cm3. The signal from each cell ismeasured by an avalanchephotodiode (APD)associatedwitha low-noisecharge-sensitivepreampliﬁer.Toincreasethelightyield, reduce electronic noise,andimproveenergy resolution,theAPDs andpreampliﬁersare cooledto atemperatureof

−

25◦C.The re-sultingenergyresolutionis

σ

E

/

E

= (

1

.

8%

/

E

)

⊕ (

3

.

3%

/

√

E

)

⊕

1

.

1%, where E is inunits ofGeV. The energydeposition ineach PHOS celliscalibratedinpp collisionsbyaligningthe

π

0 _peak_position

inthetwo-photoninvariantmassdistribution.

FortheminimumbiastriggerinthePb–Pb runandeventplane orientation calculation,two scintillatorarray detectors (V0–Aand V0–C) [54] are used, which subtend 2

.

8

<

η

<

5

.

1 and

−

3

.

7

<

η

<

−

1

.

7,respectively. EachoftheV0 arraysconsistsof32 chan-nels and is segmented in four rings in the radial direction, and each ringis dividedintoeight sectorsintheazimuthal direction. ThesumofthesignalamplitudesoftheV0–AandV0–Cdetectors servesasameasureofcentralityinthePb–Pb collisions.

3. Dataanalysis

ThisanalysisisbasedondatarecordedbytheALICEexperiment 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 signals from the V0–A, V0–C, and SPD detectors. The eﬃciencyfortriggeringonaPb–Pb hadronicinteractionranged be-tween98.4%and99.7%.Theeventsaredividedintothecentraland semi-centralcentralityclasses0–20%and20–40%,respectively, ac-cordingtotheV0–AandV0–Csummedamplitudes[55].Toensure auniformtrackacceptanceinpseudorapidity

η

,onlyeventswitha primaryvertexwithin

±

10 cm fromthenominalinteractionpoint along thebeamline(z-direction)areused.Afteroﬄineevent se-lection, 13

.

6

×

106 _events_are _available _for_the _PCM _analysis_and

18

.

8

×

106 eventsforthePHOSanalysis.

The direct-photonellipticflow isextractedon astatistical ba-sisbysubtractingtheellipticflowofphotonsfromhadron decays from the inclusive photon elliptic flow. We assume that in each bin ofthe photon transverse momentum the measured inclusive photonflowcanbedecomposedas

vγ₂,inc

=

Nγ,dir Nγ,inc

vγ₂,dir

+

Nγ,dec Nγ,inc

vγ₂,dec

,

(1)

whereNγ,inc

=

Nγ,dir

+

Nγ,decistheinclusivephotonyieldwhich

can be decomposed into the contributions of direct (Nγ,dir) and

decay(Nγ,dec) photons. The vγ ,inc

2 , v

γ,dir

2 and v

γ,dec

2 are the

cor-respondingphotonﬂows.Itisconvenienttoexpressdirect-photon ﬂowintermsoftheratioRγ

=

Nγ,inc

/

Nγ,dec,theinclusivephoton

ﬂow vγ₂,inc,andthedecayphotonﬂowvγ₂,dec:

vγ₂,dir

=

v γ,inc 2 Rγ

−

v γ,dec 2 Rγ

−

1

.

(2)

The ratioRγ was measuredinthesamedataset in[23],whereas

(3)

which is also known as cocktail simulation. The PCM and PHOS measurements of inclusive photon ﬂow are performed indepen-dently.Theyarethencombinedandusedwiththecombinedratio

Rγ aswellasthecalculateddecayphotonﬂow.

Thephoton ellipticﬂow v2 iscalculatedwiththeScalar

Prod-uct(SP)method,whichisa two-particlecorrelationmethod[56], usingapseudorapiditygapof

|

η

|

>

0

.

9 betweenthephotonand thereferenceﬂow particles.The appliedgapreduces correlations not relatedtotheeventplane

n,such asthe onesdueto

reso-nancedecaysandjets,knownasnon-flow effects.TheSPmethod usesthe Q -vector,computedfromasetofreferenceflowparticles (RFP)definedas:

Qn

=

i∈RFP wieinϕi

,

(3)

where

ϕ

i istheazimuthal angleofthe i-thRFP,n is theorderof

theharmonicandwi isa weightappliedforevery RFP.TheRFPs

aretakenfromtheV0–AandV0–Cdetectors.Sincethesedetectors donotprovidetrackinginformation,wesumovertheV0–A/V0–C cells,whiletheamplitudesofthesignalfromeachcell,whichare proportionaltothenumberofparticlesthat causea hit,areused asaweight wi.Thenon-uniformityofthedetectorazimuthal

effi-ciencyistakenintoaccountbyapplyingtheinverseofthe event-averagedsignalasaweightforeachoftheV0 segments,together witha recenteringprocedure [50,57].More specifically, the ellip-ticflow v2 iscalculatedusingtheunitflowvectoru

2

=

ei2ϕ built

fromreconstructedphotons

v2

=

u2

·

QA∗ 2 MA

u2

·

QC∗ 2 MC

QA 2 MA

·

QC∗ 2 MC

,

(4)

wherethetwopairs ofbracketsinthenumeratorindicatean av-erage over all photonsand over all events; MA and MC are the

estimates of multiplicity from the V0–A andV0–C detectors, re-spectively;and Q

A∗

2 , Q

C∗

2 are thecomplexconjugatesoftheﬂow

vectorcalculatedinsub-eventAandC,respectively.

In the PCM analysis, photons converting into e+e− pairs are reconstructedwithanalgorithmwhichsearchesfordisplaced ver-tices with two oppositely charged daughter tracks. Only good quality TPCtrackswitha transversemomentum above50 MeV/c and a pseudorapidity of

|

η

|

<

0

.

9 are considered. The vertex ﬁnding algorithm uses the Kalman ﬁlter technique for the de-cay/conversion point and four-momentum determination of the neutral parent particle (V0₎ _[₅₈_]. _Further _selection _is _performed

on the level of the reconstructed V0. Only V0s with a con-version points at radii between 5

<

R

<

180 cm are accepted such that the

π

0 _and

_η

_-meson _Dalitz _decays _are _rejected _and

to ensure a good coverage by the tracking detectors of the con-version daughters. To identify an e+e− pair, the speciﬁc energy loss (dE/dx)intheTPC[50] ofbothdaughtersisused.The trans-verse momentum componentqT ofthe electron momentum, pe,

withrespecttotheV0 _{momentum-vector}_is_restricted_to_be_q T

<

0

.

05

1

− (

α

/

0

.

95

)

2 GeV/c,where

α

isthe energy asymmetry of the conversion daughters. Random associations of electrons and positronsarefurtherreducedbyselectingV0swithcos

(θ )

>

0

.

85, where

θ

is the pointing angle, which is the angle between the momentum-vector ofthee+e− pairandthevector that connects theprimaryvertexandtheconversionpoint.Basedonthe invari-ant mass of the e+e− pair andthe pointing angle of the V0 to theprimary vertex,thevertexﬁndercalculatesa

χ

2 _value_which

reﬂects the levelof consistency withthe hypothesis that the V0

Table 1

Summaryoftherelativesystematicuncertainties(in%)oftheinclusivephoton el-lipticﬂowinthePCMandPHOSanalysis,andofthedecayphotonsimulation.All contributionsareexpectedtobecorrelatedinpTwiththemagnitudeoftherelative

uncertaintyvaryingpoint-by-point.

Centrality 0–20% 20–40% pT(GeV/c) 2.0 5.0 2.0 5.0 PCM Photon selection 2.4 4.2 2.1 4.0 Energy resolution 1.0 1.0 1.0 1.0 Eﬃciency 3 3 1.9 1.9 Total 4.0 5.3 3.0 4.5 PHOS

Eﬃciency & contamination 3.0 3.0 0.7 0.7

Event plane ﬂatness 2.0 2.0 1.4 1.4

Total 3.5 3.5 1.6 1.6

Decay photon calculation

Parameterization of vπ

2 1.3 3.6 0.8 2.2

η/π0_{normalization} _1.7 _3.2 _1.7 _2.4

Total 2.2 4.8 1.9 3.3

comesfromaphotonoriginatingfromtheprimaryvertex.A selec-tion basedonthis

χ

2 _value _is_used_to_further_reduce

contamina-tion in thephoton sample. The main sources ofbackgroundthat remain after these selection criteria are V0s reconstructed from

π

±e∓,

π

±

π

∓,

π

±K∓ ande±K∓pairs,whichisimportanttotake intoaccountasshownin[59].Theellipticﬂowofthisbackground issubtractedusingaside-bandmethodapproach.Inthismethod, the dE/dx informationof bothconversion daughters iscombined into a1-dimensionalquantity.Thesignal isa peakeddistribution andtheside-bandsaredominatedbybackgroundsources. The v2

oftheside-bandsismeasuredandsubtractedfromthemainsignal region using the purityof the photon sample, which isobtained byﬁttingMonteCarlotemplatestothedata.Thecorrectiontothe measured inclusive photon ﬂow is ofthe order of5% for central and2.5%forsemi-centralcollisions,respectively.

Thesystematicuncertaintiesoftheinclusivephotonﬂow mea-sured with PCM are summarized in Table 1. The uncertainties related to the photon selection (

|

η

|

, R, min pT, qT,

χ

2

/

ndf and

cos

(θ )

)areobtainedbyvaryingtheselectioncriteria,andthe sys-tematic uncertainties relatedto the contamination of thephoton sample are quantiﬁedby theuncertaintyonthe backgroundﬂow subtraction. Theenergyresolutionuncertainties,whicharedueto detector resolution effects and bremsstrahlung of electrons, are estimated by comparing vγ₂,inc distributions as a function of the reconstructedandtruepTusingMCsimulations.Theuncertainties

related to the variation of reconstruction eﬃciency in- and out-of-plane are calculated from studying the photon reconstruction eﬃciencyasafunctionofthetrackmultiplicity.Formostofthese sources onlyasmalldependenceon pT andcollisioncentralityis

observed.

InthePHOSanalysis,thesamephotonselectioncriteriaare ap-plied as in the direct-photon spectra analysis [23]. Cells with a common edge with another cell that are both above the energy thresholdof25MeVarecombinedintoclusterswhichareusedas photoncandidates.Toestimatethephoton energy,theenergiesof allcells oronlythosewithcenterswithinaradius Rcore

=

3

.

5 cm

from thecluster center ofgravity are summed. Comparedto the fullclusterenergy,thecoreenergyislesssensitivetooverlapswith low-energyclustersinahighmultiplicityenvironment,andiswell reproducedby GEANT3MonteCarlosimulations[23]. The full en-ergyisusedforthesystematicuncertaintyestimate.The contribu-tionofhadronicclustersisreducedbyrequiringEcluster

>

0

.

3 GeV,

(4)

lat-ALICE Collaboration / Direct photon elliptic ﬂow in Pb–Pb 311

Fig. 1. Comparisonofthemeasuredinclusivephotonﬂow(vγ ,₂inc)totheindividualPCMandPHOSmeasurements(vγ ,₂ind)inthe0–20%(left)and20–40%(right)centrality classes.Theindividualresultsaredividedbythecombined vγ ,₂inc.Theverticalbarsoneachdatapointindicatethestatisticaluncertaintiesandtheboxesindicatethe systematicuncertainties.

eralclusterdispersion[60].Thelatterselectionrejectsrareevents when hadronspunch through the crystal andhadronically inter-act with APD, producing a large signal in one cell of a cluster, not proportional to the energy deposition. In addition to these cuts, we also apply a pT-dependent dispersion cut and perform

achargedparticleveto(CPV).TheCPVremovesclustersbasedon theminimal distancebetweenthe PHOScluster positionandthe positionofextrapolatedchargedtracks onthe PHOSsurface,and isusedtosuppresshadroncontribution[60]. Bothdispersionand CPVcutsaretuned usingpp collisiondatatoprovide thephoton reconstructionandidentiﬁcationeﬃciencyatthelevelof96–99%. MeasurementswithdifferentcombinationsofdispersionandCPV cutsare used forthe estimate of systematicuncertainties. Possi-blepileupcontributionfromother bunchcrossingsisremoved by aloosecutontheclusterarrival time

|

t

|

<

150 ns,whichissmall comparedtoaminimumtimebetweenbunchcrossingsof525 ns. To estimate the reconstruction and identiﬁcation eﬃciencies and correction for energy smearing with their possible depen-denceontheanglewithrespecttotheeventplane,weembedded simulated photon clusters into real data events and applied the standard reconstruction procedure. PHOS properties (energy and position resolutions, residual de-calibration, absolute calibration, non-linear energy response) are tuned in the simulation to re-produce the pT-dependence of the

π

0 peak position and width

[60].Thecorrectionfortheeventplanedependenceofthe recon-structionand identification efficiencies, which comes as additive totheobservedphotonflow,islessthan10−3 _both_in_central_and

mid-central collisions and is comparableto the statistical uncer-tainties of the embedding procedure. The correction due to the energy smearing, is estimated to be 4% and 1% for central and semi-centralcollisions,respectively.Thecontaminationofthe pho-tonsample measured withPHOSoriginatesmainly from

π

± and

¯

p,n annihilation,

¯

withothercontributionsbeingmuchsmaller.The applicationofthedispersionandCPVcutsreducestheoverall con-taminationatpT

≈

1

.

5 GeV/c fromabout15%to2–3%anddownto

1–2%atpT

∼

3–4 GeV

/

c.Toestimateandsubtractthehadron

con-tribution,thePHOSresponsematricesareconstructedfor

π

±,K,p andp using

¯

realdataorMonteCarlosimulationsandconvoluted withthemeasuredspectra,ﬂowandrelativeyieldsofhadrons.

Systematicuncertaintiesoftheinclusivephotonflowmeasured with PHOS are summarized in Table 1. They can be split into two groups: contributions related to the contamination and de-pendence ofreconstruction,identificationandsmearingefficiency ontheanglewithrespecttotheeventplane,anduncertainties re-latedtotheflatnessoftheeventplanecalculation,theeventplane resolution andthe contributionofnon-flow effects.Uncertainties ofthe firstgroup are estimatedby comparingthefully corrected photonflow measuredwithdifferentsetsofidentificationcriteria andwithfull andcoreenergy.Uncertaintiesof thesecond group areestimatedbycomparinginclusivephotonflowsmeasured sep-arately withthe V0–A andV0–C detectors. Note that because of thelimitedazimuthalacceptance,PHOSismuchmoresensitiveto thenon-flatnessoftheeventplanedistributioncomparedtoPCM. Inthecombinationoftheinclusivephotonv2resultsfromPCM

andPHOS,both measurements aretreatedasindependent. Possi-ble correlations dueto the use of the same V0Aand V0C event plane vectors are found to be negligible. To take into account correlationsofthe individual measurementsin binsoftransverse momentum, we describethe measured inclusivephoton ﬂows as vectorsv

γ₂,inc,PCM,v

₂γ,inc,PHOS,wherethevectorcomponents corre-spondto themeasured pT bins, andthecorrelations ofthetotal

uncertainties are described by covariance matrices Vv2,PCM and

Vv2,PHOS,respectively. The elements of thecovariance matrixare calculatedassuminguncorrelatedstatisticaluncertaintiesandfully correlated

(

ρ

=

1

)

systematicuncertainties; Vi j

=

Vstat,i j

+

Vsyst,i j,

where Vsyst,i j

=

ρσ

syst,iσsyst,j,for pT bini and j.Then, the

com-binedinclusivephotonﬂowisthevector

vγ₂,inc

= (

V_v−1 2,PCM

+

V −1 v2,PHOS

)

−1

× (

V−_v1 2,PCM

v γ,inc,PCM 2

+

V− 1 v2,PHOS

v γ,inc,PHOS 2

).

(5)

The inclusivephoton v2 measured withPCMandPHOSare

com-paredinFig.1,whichshowsthe ratiooftheindividualvalues to the combinedﬂow. The PCMand PHOSmeasurements arefound to be consistent witheach other with p-values of0.93 and0.43 forthecentralityclasses0–20%and20–40%,respectively.

The decay photon ﬂow is estimated using a cocktail simula-tion.Decaysthatcontribute morethan1% ofthetotaldecay

(5)

pho-Fig. 2. Ellipticﬂowofdecayphotonsfromπ0_,_η_,_ω_,_and_the_total_cocktail_simulation_as_a_function_of_transverse_momentum_in_the_0–20%_(left)_and_20–40%_(right)_centrality

classes.Thebandrepresentsthetotaluncertaintyofthetotalcocktailsimulation.

ton yield are taken intoaccount:

π

0

_→

₂

_γ

_,

_η

_→

₂

_γ

_,

_ω

_→

_{γ π}

0_,

K0

s

→

2

π

0

→

4

γ

.Other contributions arenegligible comparedto

thesystematicuncertaintiesofthecocktail.Indecaysof

η

and

ω

mesons only photonsproduced directly in decays are accounted, while those coming from daughter

π

0 _decays _are _already

ac-countedin

π

0 _{contribution.}_The_K0

s decaydoesnotcontribute

sig-nificantlytothephotonsamplemeasuredwiththePCMapproach. Therefore, we correct the PHOS measurement for this contribu-tionbeforecombiningthePHOSandPCMmeasurements.Herewe usethesameapproach asin thedirect-photonspectrum analysis [23],butthistime thesimulationoftheellipticflowisadded.To estimate the ellipticflow of neutralpions, a parametrization has been made of the charged pion flow measured under the same conditions,i.e., chargedpions measured intheTPCandreference particlesintheV0–AandV0–Cdetectors[61,62] areused.To es-timatethecontributionof

η

and

ω

mesons,themeasured elliptic ﬂowofchargedandneutralkaons[61] isscaled,assumingscaling with the transverse kinetic energy K ET

=

mT

−

m. The

compar-ison of different contributions and overall decay photon ﬂow is shownin Fig. 2. The v2 contributions were added withweights,

proportionaltotherelativedecayphotonyieldofamesonintotal decayyield[23].Thewidthofthecoloredbandrepresentsthe sys-tematicuncertainties ofthedecayphotonellipticﬂow vγ₂,dec.The decay photon ﬂow is mainly determined by the

π

0 _ﬂow, _while

other contributions make relatively small corrections: the

η

and

ω

contributions slightlyreduce the decay photon elliptic ﬂow at

pT

<

2 GeV/c andincrease itcompared tothe

π

0 contributionat

higher pT.The systematicuncertainties ofthedecayphoton ﬂow

are summarized in Table 1. The largest uncertainties come from theparametrizationofthechargedpionellipticﬂowandfromthe relativeyield

η

/

π

0_.

4. Results

The vγ₂,inc measured in two centrality classes are shown in Fig.3.Theellipticﬂowcoeﬃcientsofinclusivephotonsanddecay photonsareverysimilar overthefullrange0

.

9

<

pT

<

6

.

2 GeV/c.

Asthefractionofdirectphotonovertheinclusivephotonyieldis relativelysmall,

∼

10%inourpT range[23],thecollectiveﬂowof

inclusivephotonsisdominatedbythedecayphotonﬂow.In mod-els based on relativistic hydrodynamics the medium is assumed

to be in or close to local thermal equilibrium. An equation of stateisusedtorelatethermodynamicquantitiesliketemperature, energy density, and pressure. Photon production is modeled by foldingthe space–timeevolutionofa collisionwith temperature-dependent photon production rates in the QGP and the hadron gas.Anotherapproachistaken, e.g.,inthePHSDtransportmodel in which the QGP degrees of freedom are modeled as massive strongly-interactingquasi-particles[63].Forbothclassesofmodels the development of a strong early elliptic flow, necessary to re-producetheobserveddirect-photonflow,givesrisetoalargepion elliptic flow atfreeze-out andthereforeto a large inclusive pho-tonellipticflow.Itisthereforeanimportanttesttocheckwhether amodelcandescribeboththeinclusiveandthedirect-photon el-liptic flow. The prediction of the hydrodynamic model described in[64] fortheinclusivephoton v2 intherange1

<

pT

<

3 GeV/c

isabout40%abovethedata,thoughthemagnitudeoftheelliptic ﬂow of unidentiﬁedhadrons is reproduced within 10–20% accu-racy inthis pT range [65].The PHSDmodel [63] alsopredictsan

∼

40%higherinclusivephotonflow,eventhoughitreproducesthe unidentifiedhadronflowwell.

Thedirect-photonv2iscalculatedfromthecombinedPCMand

PHOSphoton excess Rγ [23], thecombinedinclusive v2,andthe

calculated decay photon v2. In the propagation of uncertainties,

therelativelysmallsigniﬁcanceofthephotonexcessofabout1–3 standard deviations(dependingonthecentralityclass andpT

in-terval) requiresspecialattention. This isillustrated fora selected

pT interval in the left panel ofFig. 4 which showsthe obtained

vγ₂,dir andits uncertaintyasa function ofthe photonexcess Rγ .

TheGaussianfunctioninthispanelrepresentsthemeasuredvalue ofRγ inthispT interval(dashedline)andits1

σ

totaluncertainty

(darkblueshadedarea).ForRγ

1

.

05 onelosesthesensitivityto

vγ₂,dir astheuncertainties, indicated bythe redshaded band, in-creasedrastically.WiththecurrentuncertaintiesonRγ wecannot ruleoutcompletelythat Rγ

1

.

05.

Weaddressthelimitedsigniﬁcanceofthedirect-photonexcess by employing aBayesian approach. The parameters Rγ,t, vγ₂,inc,t,

vγ₂,dec,t denotingthetruevaluescarry theindex“t”andthe mea-suredquantities Rγ,m,vγ

,dec,m

2 , v

γ,dec,m

2 theindex“m”.Notethat

(6)

Fig. 3. Ellipticﬂowofinclusivephotonsanddecayphotons,comparedtohydrodynamic[31] andtransportPHSD[30] modelpredictionsinthe0–20%(left)and20–40% (right)centralityclasses.Theverticalbarsoneachdatapointindicatethestatisticaluncertaintiesandtheboxesindicatethesizesofthetotaluncertainties.

Fig. 4. Left:Centralvalue(solidredline)anduncertaintyofthedirect-photonv2foraselectedpTinterval.Theupperandloweredgesoftheredshadedareacorrespondto

thetotaluncertaintyofvγ ,2dirasobtainedfromlinearGaussianpropagationoftheuncertaintiesσ(v

γ ,inc 2 )andσ(v

γ ,dec

2 ).TheGaussian(witharbitrarynormalization)reﬂects

themeasuredvalueofRγ inthispTinterval(bluedashedline)andits±1σ uncertainty(dark-blueshadedinterval).Right:Posteriordistributionofthetruevalueofvγ ,2dir

forthesameintervalintheBayesianapproach.Notethatthedistributionhasanon-Gaussianshape,implyingthatthe±2σintervaltypicallycorrespondstoaprobabilityof lessthan95.45%aswouldbethecaseforaGaussian.

themeasuredvalue Rγ,m canﬂuctuatebelowunity.Theposterior

distributionofthetrueparameterscanbewrittenas

P

(

ϑ

|

m

)

∝

P

(

m

|ϑ)

π

(

ϑ ),

π

(

ϑ )

≡

π

(

Rγ,t

)

= (

Rγ,t,1

−

1

, ...,

Rγ,t,n

−

1

),

(6) whereinm

= (

Rγ,m

,

v

γ2,inc,m

,

v γ,dec,m 2

)

,

ϑ = (

Rγ,t

,

vγ2,inc,t

,

v γ,dec,t 2

)

.

Hereweusethenotation introducedinEq. (5):vectorsrepresent sets of measurements in different pT bins andn is the number

ofthesebins.The function

π

(

Rγ,t

)

encodes theprior knowledge

aboutRγ .ThemultivariateHeaviside

functioncorrespondstoa constant(improper) priorfor Rγ,t

≥

1.Theprobability toobserve

acertainsetofmeasured valuesgiventhetruevaluesismodeled withmultivariate GaussiansG

(

x

;

μ

,

V

)

(where

μ

is thevectorof meanvaluesandV isthecovariancematrix):

P

(

m

|ϑ) =

x=Rγ,vγ₂,inc,vγ₂,dec

G

(

xm

;

xt

,

Vx). (7)

Bysamplingthe posteriordistribution P

(

ϑ

|

m

)

,we obtaintriplets

(

Rγ

,

vγ₂,inc

,

vγ₂,dec

)

foreach pT binfromwhichwecalculatevγ2,dir

accordingto Eq. (2).An example ofthe resultingdistribution for

vγ₂,dir isshown inFig. 4(right panel).The mediansof the vγ₂,dir

distributions are taken as central values. The lower and upper edges oftheerrorbars correspondtovalues ofvdir₂ atwhich the integralofthev2 distributionis15.87%and84.13%ofthetotal

in-tegral. In case of a Gaussian distribution thiscorresponds to 1

σ

uncertainties.

Theresultsforthedirect-photonellipticﬂowforthetwo cen-tralityclasses, 0–20% and20–40%,are shown inFig. 5. The total uncertainties, reﬂecting the Bayesian posterior distributions, are shown as boxes, and the error bars represent statistical

(7)

uncer-Fig. 5. EllipticﬂowofdirectphotonscomparedwithPHENIXresults[26] forthe0–20%(left)and20–40%(right)centralityclasses.Theverticalbarsoneachdatapoint indicatethestatisticaluncertaintiesandtheboxesthetotaluncertainty.

Fig. 6. Ellipticﬂowofdirectphotonscomparedtomodelcalculationsinthe0–20%(left)and20–40%(right)centralityclasses.Theverticalbarsoneachdatapointindicate thestatisticaluncertaintiesandtheboxesthetotaluncertainty.

tainties. The correlation of v2,dir points for different pT bins as

quantiﬁedbythecorrelationmatrixisstrongatlow pT

2 GeV

/

c

(correlation coeﬃcients typically in the range 0.6–0.75) whereas the uncertainties at high pT are dominated by statistical

uncer-tainties.We compareour resultsto measurements madeatRHIC energiesbythePHENIXcollaboration[26].Theinclusivephotonv2

wasmeasuredbyPHENIXthroughthereconstructionofe+e−pairs from photon conversions and withan electromagnetic calorime-ter.Thedirect-photonellipticﬂowinAu–AucollisionsatRHICand inPb–Pbcollisions attheLHCare foundtobe compatiblewithin uncertainties.A simpleexplanationofthelargeandsimilar direct-photonellipticﬂowforpT

2 GeV

/

c atRHICandtheLHCisthat

thebulkofthethermaldirectphotonsisproducedlateat temper-aturesclosetothetransitiontemperatureTc.Thisisinterestingas

naïvelyone wouldexpectthe T2 _temperature_dependence_of_the

photonemissionratetomaketheearly hotQGPphaseafter ther-malizationalsothebrightestphase.

Fig.6comparesthemeasureddirect-photonellipticﬂowvγ₂,dir

totheestimateddecayphotonellipticflowvγ₂,dec,markedas cock-tail,andtothepredictionsofseveraltheoreticalmodels.Similarly tomeasurementsatRHICenergies[24],wefindthatthedirectand decayphoton ellipticflow are similar. Wecompare our measure-mentstostate-of-the-arthydrodynamicmodelcalculations[31,66] and thePHSDtransport model [63]. The measured direct-photon elliptic flow is systematically higherthan theoretical predictions, butisstillcompatible.

Inordertoquantifythedeviationofthedirect-photon v2

mea-surementfroma certainhypothesiswithafrequentist p-valueor, equivalently,thecorrespondingnumberofstandarddeviations,we use aBayesian-inspired method[67].In thisapproach,the likeli-hoodL

(

vγ₂,inc,m

|

v₂γ,dir,t

)

servesasateststatisticandisobtainedby

(8)

integratingover the nuisance parameters

vγ₂,dec,t and Rγ

,t using

theirBayesianposteriordistributionsasweights.Wefocusonthe interval 0

.

9

<

pT

<

2

.

1 GeV

/

c inwhich the contributionof

ther-malphotonsis expectedtobe important.The signiﬁcance ofthe deviationfrom the hypothesis vγ₂,dir,t

=

0 for individual pT bins

isintherange1.8–2.1

σ

forthe0–20%classand0.9–1.5

σ

forthe 20–40%class.Wealsogoastepfurtherandestimatethecombined signiﬁcanceofthedeviationfromthehypothesisvγ₂,dir

≡

0 forthis

pT interval. Thistestsinaddition howwell the shapeof vγ₂,inc,m

asa functionof pT agrees withv₂γ,dec,m

/

Rγ ,i.e., withthe

expec-tationforvγ₂,dir

≡

0.Weestimatethecovariancematrixdescribing thecorrelation by characterizing the differentsources of system-aticuncertaintiesof Rγ ,theinclusive,andthedecayphotonﬂow aseitherfullyuncorrelatedor fullycorrelated in pT. Varyingthe

assumptions about the correlation of the data points we obtain signiﬁcancesof typically lessthan 1

σ

forboth centrality classes. Whiletheappliedmethodisessentialforameaningfulcomparison ofthevγ₂,dirdatawithdifferentmodelpredictions,themethodsto estimatethecovariancematrixcanbeimprovedinfutureanalyses.

5. Conclusions

Insummary,wereporttheﬁrstmeasurementofellipticﬂowof inclusiveanddirect photonsasa function of transverse momen-tumintherange0

.

9

<

pT

<

6

.

2 GeV/c forcentralandsemi-central

Pb–Pbcollisionsat

√

sNN

=

2

.

76 TeV.Theellipticﬂowofinclusive

photonswas measured withthescalarproductmethod, indepen-dentlyintheelectromagneticcalorimeterPHOSandwiththe pho-tonconversionmethodwherethereferenceparticlesinbothcases were measured by the V0–A and V0–C detectors. The combined inclusivephotonvγ₂,inc,togetherwiththecalculateddecayphoton

vγ₂,dec andthepreviously measured Rγ areusedto calculatethe elliptic ﬂow of direct photons. The measured direct-photon ﬂow

vγ₂,dir appearstobe closeto thedecayphoton flowforboth cen-tralityclasses,similar to observations atlower collision energies. Moreover,themeasured vγ₂,dir issimilar tothemeasurements by the PHENIX collaboration at RHIC. The considered hydrodynamic andtransportmodelspredictalargerinclusivephotonellipticflow (byapproximately 40%) anda smaller direct-photon elliptic flow than observed. With current uncertainties, however, these mod-els are consistent with the presented direct-photon elliptic flow data. Future measurements using a larger statistics dataset will greatlyincreasetheprecisionofthismeasurementandallowusto extendthe measurementtohigher pT,since thestatistical

uncer-taintyisdominatingthe totaluncertaintyfor pT

>

2

.

0 GeV/c and

pT

>

3

.

0 GeV/c forthePHOSandPCMinclusivephotonﬂow

mea-surement, respectively. Inaddition, a larger statisticsdataset will alsohelptoconstrainthesystematicuncertaintiesontheinclusive anddecayphotonﬂow,aswellasthemeasurementofRγ overthe wholepTrange.Afurtherreductionofthesystematicuncertainties

is expected from improved detector knowledge. For instance, in caseofPCMthelargestsystematicuncertaintyinthemeasurement of Rγ is related to modeling the material inwhich the photons convert.Calibrating regions ofthe detectorwithlesswell known materialbudget basedonregions withvery well knownmaterial mightsigniﬁcantlyreducetheoverallmaterialbudgetuncertainty. TheRγ measurementcanbeimprovedfurtherbymeasuring neu-tralpion and etameson spectra in a combinedPCM-calorimeter approachinwhichonedecayphotonismeasuredthrough conver-sionandtheotherwithacalorimeter.

Acknowledgements

We wouldlike to thank ElenaBratkovskaya andJean-François Paquetforprovidingcalculationsshowninthispaperandfor use-fuldiscussions.

The ALICE Collaboration would like to thank all its engineers andtechniciansfortheir invaluablecontributions tothe construc-tionoftheexperimentandtheCERNacceleratorteamsforthe out-standingperformanceoftheLHCcomplex.TheALICECollaboration gratefully acknowledges the resources and support provided by all Gridcentres andtheWorldwide LHC ComputingGrid (WLCG) collaboration. The ALICE Collaboration acknowledges the follow-ing funding agencies for their support in building and running the ALICE detector: A. I. Alikhanyan National Science Laboratory (YerevanPhysicsInstitute)Foundation (ANSL),State Committeeof Science andWorld Federation ofScientists (WFS), Armenia; Aus-trian Academy of Sciences and Österreichische Nationalstiftung für Forschung, Technologie undEntwicklung, Austria; Ministry of CommunicationsandHighTechnologies,NationalNuclearResearch Center, Azerbaijan;Conselho NacionaldeDesenvolvimento Cientí-ficoe Tecnológico(CNPq),UniversidadeFederal doRioGrandedo Sul (UFRGS),Financiadorade Estudose Projetos(Finep)and Fun-dação de Amparo à Pesquisa do Estado de São Paulo (FAPESP), Brazil; Ministry of Science & Technology of China (MSTC), Na-tionalNaturalScienceFoundationofChina(NSFC)andMinistryof EducationofChina(MOEC),China;MinistryofScienceand Educa-tion,Croatia;MinistryofEducation,YouthandSportsoftheCzech Republic,CzechRepublic;TheDanishCouncilforIndependent Re-search – Natural Sciences, the Carlsberg Foundation and Danish NationalResearchFoundation (DNRF),Denmark;HelsinkiInstitute ofPhysics(HIP),Finland;Commissariatàl’EnergieAtomique(CEA) andInstitutNationaldePhysiqueNucléaireetdePhysiquedes Par-ticules (IN2P3) and Centre National de la Recherche Scientifique (CNRS), France; Bundesministerium für Bildung, Wissenschaft, Forschung und Technologie (BMBF) and GSI Helmholtzzentrum fürSchwerionenforschungGmbH,Germany;GeneralSecretariatfor ResearchandTechnology,MinistryofEducation,Researchand Re-ligions, Greece; National Research, Development and Innovation Office, Hungary; Department of Atomic Energy, Government of India (DAE), Department of Science andTechnology, Government of India(DST), University Grants Commission, Governmentof In-dia (UGC)andCouncil of Scientific andIndustrialResearch, India (CSIR), India; Indonesian Institute of Sciences, Indonesia; Centro Fermi –Museo Storicodella Fisica e CentroStudi e Ricerche En-ricoFermiandInstitutoNazionale diFisica Nucleare (INFN),Italy; Institute forInnovativeScienceandTechnology,NagasakiInstitute of AppliedScience (IIST),Japan Societyforthe Promotion of Sci-ence(JSPS)KAKENHIandJapanese MinistryofEducation,Culture, Sports, Science and Technology (MEXT), Japan; Consejo Nacional deCiencia(CONACYT)yTecnología,throughFondodeCooperación Internacional en Ciencia y Tecnología (FONCICYT) and Dirección General de Asuntos del Personal Academico (DGAPA), Mexico; NederlandseOrganisatievoorWetenschappelijkOnderzoek(NWO), Netherlands; The ResearchCouncil ofNorway, Norway; Commis-sion on Science and Technology for Sustainable Development in theSouth(COMSATS),Pakistan;PontificiaUniversidadCatólicadel Perú,Peru;MinistryofScienceandHigherEducationandNational Science Centre, Poland; Korea Institute of Science and Technol-ogyInformationandNationalResearchFoundationofKorea(NRF), Republic ofKorea; Ministry ofEducation and Scientific Research, Institute of Atomic Physics and Romanian National Agency for Science, Technology and Innovation, Romania; Joint Institute for Nuclear Research(JINR),MinistryofEducation andScience ofthe Russian FederationandNationalResearchCentre Kurchatov Insti-tute, Russia; Ministry of Education, Science, Research and Sport

(9)

of the Slovak Republic, Slovakia; National Research Foundation of South Africa, South Africa; Centro de Aplicaciones Tecnológi-casyDesarrolloNuclear (CEADEN),Cubaenergía, CubaandCentro de Investigaciones Energéticas, Medioambientales y Tecnológicas (CIEMAT),Spain;SwedishResearchCouncil(VR)andKnut&Alice WallenbergFoundation(KAW),Sweden;EuropeanOrganizationfor Nuclear Research, Switzerland; National Science and Technology Development Agency (NSDTA), Suranaree University of Technol-ogy(SUT) andOﬃce ofthe Higher Education Commission under NRUprojectofThailand,Thailand;Turkish AtomicEnergyAgency (TAEK),Turkey;NationalAcademyofSciencesofUkraine,Ukraine; ScienceandTechnology FacilitiesCouncil(STFC),UnitedKingdom; NationalScienceFoundationoftheUnitedStatesofAmerica(NSF) andUnitedStatesDepartmentofEnergy,OﬃceofNuclearPhysics (DOENP),UnitedStatesofAmerica.

References

[1]S.Borsanyi,Z.Fodor,etal.,FullresultfortheQCDequationofstatewith2+1 ﬂavors,Phys.Lett.B370 (1)(2014)99–104,arXiv:1309.5258 [hep-lat]. [2]A.Bazavov,etal.,ThechiralanddeconﬁnementaspectsoftheQCDtransition,

Phys.Rev.D85(2012)054503,arXiv:1111.1710 [hep-lat].

[3]M.H.Thoma,Dampingrateofahardphotoninarelativisticplasma,Phys.Rev. D51(1995)862–865,arXiv:hep-ph/9405309 [hep-ph].

[4]BRAHMSCollaboration,I.Arsene,et al.,Quarkgluonplasmaandcolorglass condensateatRHIC?TheperspectivefromtheBRAHMSexperiment,Nucl.Phys. A757(2005)1–27,arXiv:nucl-ex/0410020 [nucl-ex].

[5]B.B.Back,etal.,ThePHOBOSperspectiveondiscoveriesatRHIC,Nucl.Phys.A 757(2005)28–101,arXiv:nucl-ex/0410022 [nucl-ex].

[6]PHENIX Collaboration, K. Adcox,et al., Formation ofdensepartonicmatter inrelativisticnucleus–nucleuscollisionsatRHIC:experimentalevaluationby the PHENIXcollaboration,Nucl.Phys.A 757(2005)184–283,arXiv:nucl-ex/ 0410003 [nucl-ex].

[7]STARCollaboration,J.Adams,etal.,Experimentalandtheoreticalchallengesin thesearchforthequarkgluonplasma:theSTARcollaboration’scritical assess-mentoftheevidencefromRHICcollisions,Nucl.Phys.A757(2005)102–183, arXiv:nucl-ex/0501009 [nucl-ex].

[8]ALICECollaboration,K.Aamodt,etal.,EllipticﬂowofchargedparticlesinPb– Pbcollisionsat2.76TeV,Phys.Rev.Lett.105(2010)252302,arXiv:1011.3914 [nucl-ex].

[9]ALICECollaboration,K.Aamodt,etal.,Harmonicdecompositionoftwo-particle angularcorrelationsinPb–Pbcollisionsat√sN N=2.76 TeV,Phys.Lett.B708

(2012)249–264,arXiv:1109.2501 [nucl-ex].

[10]ALICECollaboration,K.Aamodt,etal.,Higherharmonicanisotropicﬂow mea-surementsofchargedparticlesinPb–Pbcollisionsat√sNN=2.76 TeV,Phys.

Rev.Lett.107(2011)032301,arXiv:1105.3865 [nucl-ex].

[11]ATLAS Collaboration,G.Aad,et al.,Measurementofthepseudorapidityand transversemomentumdependenceoftheellipticﬂowofchargedparticlesin lead–leadcollisionsat√sN N=2.76 TeVwiththeATLASdetector,Phys.Lett.B

707(2012)330–348,arXiv:1108.6018 [hep-ex].

[12]CMSCollaboration,S.Chatrchyan,etal.,Centralitydependenceofdihadron cor-relations andazimuthalanisotropyharmonicsinPbPbcollisionsat√sN N=

2.76 TeV,Eur.Phys.J.C72(2012)2012,arXiv:1201.3158 [nucl-ex].

[13]S.Voloshin,Y.Zhang,Flowstudy inrelativisticnuclearcollisionsbyFourier expansionofazimuthalparticledistributions,Z.Phys.C70 (1)(1996)665–672, arXiv:hep-ph/9407282 [hep-ph].

[14]J.I. Kapusta, P. Lichard, D. Seibert, High-energy photons from quark–gluon plasmaversushothadronicgas,Phys.Rev.D44(1991)2774–2788,Erratum: Phys.Rev.D47(1993)4171.

[15]C.Shen,U.W.Heinz,J.-F.Paquet,C.Gale,Thermalphotonsasaquark–gluon plasmathermometerreexamined, Phys.Rev.C89 (4) (2014)044910,arXiv: 1308.2440 [nucl-th].

[16]R.Chatterjee,H. Holopainen,I.Helenius,T.Renk,K.J.Eskola,Ellipticﬂowof thermalphotonsfromevent-by-eventhydrodynamic model,Phys.Rev.C88 (2013)034901,arXiv:1305.6443 [hep-ph].

[17]C.Shen,U.W.Heinz,J.-F.Paquet,I.Kozlov,C.Gale,Anisotropicﬂowof ther-malphotonsasaquark–gluonplasmaviscometer,Phys.Rev.C91 (2)(2015) 024908,arXiv:1308.2111 [nucl-th].

[18]WA98Collaboration,M.Aggarwal,etal.,Observationofdirectphotonsin cen-tral158AGeV208Pb+208Pbcollisions,Phys.Rev.Lett.85(2000)3595–3599, arXiv:nucl-ex/0006008 [nucl-ex].

[19]PHENIXCollaboration,S.Adler,etal.,Centralitydependenceofdirectphoton production in√sNN=200 GeVAu+Aucollisions, Phys.Rev.Lett.94(2005)

232301,arXiv:nucl-ex/0503003 [nucl-ex].

[20]PHENIXCollaboration,A.Adare,etal.,Enhancedproductionofdirectphotons inAu+Aucollisionsat√sNN=200 GeVandimplicationsfortheinitial

temper-ature,Phys.Rev.Lett.104(2010)132301,arXiv:0804.4168 [nucl-ex]. [21]PHENIXCollaboration,S.Afanasiev,etal.,Measurementofdirectphotonsin

Au+Aucollisionsat√sNN=200 GeV,Phys.Rev.Lett.109(2012)152302,arXiv:

1205.5759 [nucl-ex].

[22]PHENIX Collaboration, A. Adare, et al., Centrality dependence of low-momentumdirect-photonproductioninAu+Aucollisionsat√sNN=200 GeV,

Phys.Rev.Lett.C91 (6)(2015)064904,arXiv:1405.3940 [nucl-ex].

[23]ALICECollaboration,J.Adam,etal.,DirectphotonproductioninPb–Pb colli-sionsat√sNN=2.76 TeV,Phys.Lett.B754(2016)235–248,arXiv:1509.07324

[nucl-ex].

[24]PHENIXCollaboration,A.Adare,etal.,Observationofdirect-photoncollective ﬂowin√sN N=200 GeVAu+Aucollisions,Phys.Rev.Lett.109(2012)122302,

arXiv:1105.4126 [nucl-ex].

[25]PHENIXCollaboration,A.Adare,etal.,Measurementsofhigher-orderﬂow har-monicsinAu+Aucollisionsat √sN N=200 GeV,Phys.Rev.Lett.107(2011)

252301,arXiv:1105.3928 [nucl-ex].

[26]PHENIXCollaboration,A.Adare,etal.,Azimuthallyanisotropicemissionof low-momentumdirect photonsinAu+Aucollisionsat √sN N=200 GeV, arXiv:

1509.07758 [nucl-ex].

[27]R.Chatterjee,E.S.Frodermann,U.W.Heinz,D.K.Srivastava,Ellipticﬂowof ther-malphotonsinrelativisticnuclearcollisions,Phys.Rev.Lett.96(2006)202302, arXiv:nucl-th/0511079 [nucl-th].

[28]R.Chatterjee,D.K.Srivastava,Ellipticﬂowofthermalphotonsandformation timeofquarkgluonplasmaat RHIC,Phys.Rev.C79(2009)021901, arXiv: 0809.0548 [nucl-th].

[29]H.vanHees,C.Gale,R.Rapp,Thermalphotonsandcollectiveﬂowatthe Rel-ativisticHeavy-IonCollider,Phys. Rev.C84(2011)054906,arXiv:1108.2131 [hep-ph].

[30]O.Linnyk,W.Cassing,E.L.Bratkovskaya,Centralitydependenceofthedirect photonyieldandellipticﬂowinheavy-ioncollisionsat√sN N=200 GeV,Phys.

Rev.C89 (3)(2014)034908,arXiv:1311.0279 [nucl-th].

[31]C.Gale,Y. Hidaka, S. Jeon, S.Lin,J.-F. Paquet,R.D. Pisarski,D. Satow,V.V. Skokov,G.Vujanovic,Productionandellipticﬂowofdileptonsandphotonsin amatrixmodelofthequark–gluonplasma,Phys.Rev.Lett.114(2015)072301, arXiv:1409.4778 [hep-ph].

[32]B.Muller,S.-Y.Wu,D.-L.Yang,Ellipticﬂowfromthermalphotonswith mag-neticﬁeldinholography,Phys.Rev.D89 (2)(2014)026013,arXiv:1308.6568 [hep-th].

[33]H.vanHees,M.He,R.Rapp,Pseudo-criticalenhancementofthermalphotons inrelativisticheavy-ioncollisions?,Nucl.Phys.A933(2015)256–271,arXiv: 1404.2846 [nucl-th].

[34]A.Monnai,Thermalphoton v2 withslowquarkchemicalequilibration,Phys.

Rev.C90 (2)(2014)021901,arXiv:1403.4225 [nucl-th].

[35]M.Dion,J.-F.Paquet,B.Schenke,C.Young,S.Jeon,C.Gale,Viscousphotonsin relativisticheavyioncollisions,Phys.Rev.C84(2011)064901,arXiv:1109.4405 [hep-ph].

[36]F.-M.Liu,S.-X.Liu,Quark–gluonplasmaformationtimeand directphotons fromheavyioncollisions,Phys.Rev.C89 (3)(2014)034906,arXiv:1212.6587 [nucl-th].

[37]G.Vujanovic,J.-F.Paquet,G.S.Denicol,M.Luzum,B.Schenke,S.Jeon,C.Gale, Probingtheearly-timedynamicsofrelativisticheavy-ioncollisionswith elec-tromagnetic radiation, Nucl. Phys. A 932(2014) 230–234, arXiv:1404.3714 [hep-ph].

[38]L. McLerran, B. Schenke, The glasma, photons and the implications of anisotropy,Nucl.Phys.A929(2014)71–82,arXiv:1403.7462 [hep-ph]. [39]L. McLerran, B. Schenke, A tale of tails: photon rates and ﬂow in

ultra-relativistic heavy ion collisions, Nucl. Phys. A 946(2016) 158–170, arXiv: 1504.07223 [nucl-th].

[40]F. Gelis, H. Niemi, P.V. Ruuskanen, S.S. Rasanen, Photon production from nonequilibriumQGPinheavyioncollisions,J.Phys.G30(2004)S1031–S1036, arXiv:nucl-th/0403040 [nucl-th].

[41]Y.Hidaka,S.Lin,R.D.Pisarski,D.Satow,Dileptonandphotonproductionin thepresenceofanontrivialPolyakovloop,J.HighEnergyPhys.10(2015)005, arXiv:1504.01770 [hep-ph].

[42]O.Linnyk,E.L.Bratkovskaya,W.Cassing,EffectiveQCDandtransport descrip-tionofdileptonandphotonproductioninheavy-ioncollisionsandelementary processes,Prog.Part.Nucl.Phys.87(2016)50–115,arXiv:1512.08126 [nucl-th]. [43]V.Vovchenko,I.A.Karpenko, M.I.Gorenstein,L.M.Satarov,I.N. Mishustin,B. Kämpfer, H.Stoecker, Electromagneticprobesofa pure-glueinitialstatein nucleus–nucleuscollisionsatenergiesavailableattheCERNLargeHadron Col-lider,Phys.Rev.C94 (2)(2016)024906,arXiv:1604.06346 [nucl-th]. [44]T. Koide,T. Kodama, Anisotropy oflow energy direct photons in

relativis-ticheavyion collisions, J.Phys. G43 (9) (2016)095103, arXiv:1605.05127 [nucl-th].

[45]S.Turbide,C.Gale,R.J.Fries,Azimuthalasymmetryofdirectphotonsinhigh energy nuclearcollisions, Phys. Rev.Lett. 96 (2006) 032303, arXiv:hep-ph/ 0508201 [hep-ph].

(10)

[46]K. Tuchin, Electromagnetic radiationbyquark–gluon plasmaina magnetic ﬁeld,Phys.Rev.C87 (2)(2013)024912,arXiv:1206.0485 [hep-ph].

[47]G.Basar,D.Kharzeev,D.Kharzeev,V.Skokov,Conformalanomalyasasource ofsoftphotonsinheavyioncollisions, Phys.Rev.Lett.109(2012)202303, arXiv:1206.1334 [hep-ph].

[48]ALICECollaboration,K.Aamodt,etal.,TheALICEexperimentattheCERNLHC, J.Instrum.3(2008)S08002.

[49]J.Alme,etal.,TheALICETPC,alarge3-dimensionaltrackingdevicewithfast readoutforultra-highmultiplicityevents,Nucl.Instrum.MethodsPhys.Res., Sect.A622(2010)316–367,arXiv:1001.1950 [physics.ins-det].

[50]ALICECollaboration,B.B.Abelev,etal.,PerformanceoftheALICEExperimentat theCERNLHC,Int.J.Mod.Phys.A29(2014)1430044,arXiv:1402.4476 [nucl -ex].

[51]ALICECollaboration,K.Aamodt,etal.,AlignmentoftheALICEInnerTracking Systemwithcosmic-raytracks,J.Instrum.5(2010)P03003,arXiv:1001.0502 [physics.ins-det].

[52]A.Akindinov,etal.,TheALICETime-Of-Flightsystem:construction,assembly andqualitytests,NuovoCimentoB124(2009)235–253.

[53] ALICECollaboration,G.Dellacasa,etal.,ALICEtechnicaldesignreportofthe photonspectrometer(PHOS),CERN-LHCC-99-04.

[54] ALICECollaboration,P.Cortese,etal.,ALICEtechnicaldesignreportonforward detectors:FMD,T0andV0,CERN-LHCC-2004-025.

[55]ALICECollaboration,B.Abelev,et al.,CentralitydeterminationofPb–Pb col-lisionsat √sN N=2.76 TeV withALICE,Phys. Rev.C88 (4)(2013)044909,

arXiv:1301.4361 [nucl-ex].

[56]STARCollaboration,C. Adler,et al.,Ellipticﬂow fromtwoand fourparticle correlationsinAu+Aucollisionsats(NN)∗∗(1/2) =130-GeV,Phys.Rev.C66 (2002)034904,arXiv:nucl-ex/0206001 [nucl-ex].

[57]ALICECollaboration,E.Abbas,etal.,PerformanceoftheALICEVZEROsystem, J.Instrum.8(2013)P10016,arXiv:1306.3130 [nucl-ex].

[58]ALICECollaboration,B.Abelev,etal.,Neutralpionandηmesonproductionin proton–protoncollisionsat√s=0.9 TeVand√s=7 TeV,Phys.Lett.B717 (2012)162–172,arXiv:1205.5724 [hep-ex].

[59]F.Bock, C.Loizides,T.Peitzmann,M.Sas, Impactofresidualcontamination oninclusiveanddirectphotonﬂow,J.Phys.G44 (1)(2017)025106,arXiv: 1606.06077 [nucl-ex].

[60]ALICECollaboration,B.B.Abelev,etal.,Neutralpionproductionatmidrapidity inppandPb–Pbcollisionsat√sNN=2.76 TeV,Eur.Phys.J.C74 (10)(2014)

3108,arXiv:1405.3794 [nucl-ex].

[61]ALICE Collaboration,B.B.Abelev,et al.,Ellipticﬂow ofidentiﬁed hadronsin Pb–Pbcollisionsat√sNN=2.76 TeV,J.HighEnergyPhys.06(2015)190,arXiv:

1405.4632 [nucl-ex].

[62]ALICECollaboration,B.Abelev,etal.,Anisotropicﬂowofchargedhadrons, pi-onsand(anti-)protonsmeasuredathightransversemomentuminPb–Pb col-lisionsat√sN N=2.76 TeV,Phys.Lett.B719(2013)18–28,arXiv:1205.5761

[nucl-ex].

[63]O.Linnyk,V.Konchakovski,T.Steinert,W.Cassing,E.L.Bratkovskaya,Hadronic andpartonicsourcesofdirectphotonsinrelativisticheavy-ioncollisions,Phys. Rev.C92 (5)(2015)054914,arXiv:1504.05699 [nucl-th].

[64]J.-F.Paquet,C.Shen,G.S.Denicol,M.Luzum,B.Schenke,S.Jeon,C.Gale,The productionofphotonsinrelativisticheavy-ioncollisions,Phys.Rev.C93(2016) 044906,arXiv:1509.06738 [hep-ph].

[65]S. Ryu,J.-F.Paquet,C.Shen,G.Denicol,B.Schenke,S. Jeon,C.Gale,Effects ofbulk viscosity and hadronicrescatteringinheavy ioncollisions at ener-giesavailableattheBNLRelativisticHeavyIonColliderandattheCERNLarge HadronCollider,Phys.Rev.C97 (3)(2018)034910,arXiv:1704.04216 [nucl-th]. [66]R.Chatterjee,P.Dasgupta,D.K.Srivastava,Anisotropicﬂowofthermalphotons atenergiesavailableattheBNLRelativisticHeavyIonColliderandattheCERN LargeHadronCollider,Phys. Rev.C96 (1)(2017)014911, arXiv:1702.02378 [nucl-th].

[67]R.D.Cousins,V.L.Highland,Incorporatingsystematicuncertaintiesintoan up-perlimit,Nucl.Instrum.MethodsPhys.Res.,Sect.A320(1992)331–335.