Measurement of the production cross section of three isolated photons in pp collisions at root s=8 TeV using the ATLAS detector

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Physics

Letters

B

www.elsevier.com/locate/physletb

Measurement

of

the

production

cross

section

of

three

isolated

photons

in

pp collisions

at

√

s

=

8 TeV

using

the

ATLAS

detector

.TheATLASCollaboration

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

Articlehistory:

Received21December2017

Receivedinrevisedform19March2018 Accepted20March2018

Availableonline23March2018 Editor:W.-D.Schlatter

Ameasurementoftheproductionofthreeisolatedphotons inproton–proton collisionsata

centre-of-mass energy√s=8 TeVis reported. Theresults are basedonan integratedluminosity of 20.2 fb−1

collectedwiththeATLASdetectorattheLHC.Thedifferentialcrosssectionsaremeasuredasfunctionsof

thetransverseenergyofeachphoton,thedifferenceinazimuthalangleandinpseudorapiditybetween

pairsofphotons,theinvariantmassofpairsofphotons,andtheinvariantmassofthetriphotonsystem.

Ameasurementoftheinclusivefiducialcrosssectionisalsoreported.Next-to-leading-orderperturbative

QCD predictionsare comparedto the cross-sectionmeasurements. The predictionsunderestimate the

measurement ofthe inclusivefiducial crosssectionand the differentialmeasurements atlow photon

transverse energiesand invariantmasses. Theyprovideadequatedescriptionsofthe measurementsat

highvaluesofthephotontransverseenergies,invariantmassofpairsofphotons,andinvariantmassof

thetriphotonsystem.

©2018TheAuthor.PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense

(http://creativecommons.org/licenses/by/4.0/).FundedbySCOAP3_.

1. Introduction

Theproductionofthreepromptphotonsinproton–proton(pp) collisions, pp →γ γ γ + X , providesatestinggroundfor perturba-tivequantumchromodynamics(pQCD).Thisprocess israreinthe StandardModel(SM)since theleading-order(LO) contributionto triphotonproductionisoforder α3

EM.Themeasurementof tripho-tonproductioncanbeperformedinabroaderrangeofkinematic regionsthanin2→2reactionssuchasinclusive-photon [1–4] and diphoton [5–7] production.Thisprovidesacomplementarytestof pQCDinprocesseswithphotonsinthefinalstate.

Precise measurements of triphoton production can be used to improve the description of this process in Monte Carlo (MC) models. In addition, SM triphoton production provides one of themainirreduciblebackgroundsforsomebeyond-the-SM(BSM) searches.Potential BSM processesinclude the associated produc-tion of a photon and an exotic neutral particle decaying into a photonpair (qq→X0_{γ), where X}0 _{can bea Kaluza–Klein} gravi-ton (GKK) [8–10] or a pseudoscalar(a) [11]. Moreover, triphoton production is also the main background to the predicted decay of the Z boson into three photons. The current upper limit at 95% confidence level on the branching fraction for Z →3γ is 2.2×10−6[12].

Three photons can be produced via two main mechanisms: direct and fragmentation production. In the case of the direct

 _{E-mailaddress:atlas.publications@cern.ch.}

production process, three photons are produced in the hard in-teraction via the annihilation of an initial-state quark–antiquark pair (qq→γ γ γ). In the fragmentation process, at least one of the photons arises from the fragmentationof a high-transverse-momentum (high-pT) parton(qg→γ γq[γ]). Direct photonsare typically isolated,while thoseoriginatingfromthe fragmentation processareusuallyaccompaniedbynearbypartons. Measurements of final-statephotons includean isolation requirementto reduce background contributions from neutral-hadron decays into pho-tons. As a consequence,signal processes with one or more frag-mentationphotonsarealsosuppressed.

This Letter presents measurements of three-photon produc-tion. The analysis is performed using 20.2±0.4 fb−1 of ATLAS data at a centre-of-mass energy of √s=8 TeV [13]. The mea-surements study the topology and kinematics of the individual photons, pairs of photons, and the three-photon system. Differ-ential cross sectionsare measured asfunctionsof thetransverse energy1 of the leading photon (Eγ1

T ), the second-highest-ET pho-ton (Eγ2

T ) and the third-highest-ET photon (EγT3); the difference

1 _{ATLASusesaright-handedcoordinatesystemwithitsoriginatthenominal}

in-teractionpoint(IP)inthecentreofthedetectorandthez-axisalongthebeampipe. Thex-axispointsfromtheIPtothecentreoftheLHCring,andthey-axispoints upwards.Cylindricalcoordinates(r,φ)areusedinthetransverseplane,φbeingthe azimuthalanglearoundthez-axismeasuredinradians.Thepseudorapidityis de-finedintermsofthepolarangleθas η= −ln tan(θ/2). Thetransverseenergyis definedasET=E sinθ,whereE istheenergy.

https://doi.org/10.1016/j.physletb.2018.03.057

0370-2693/©2018TheAuthor.PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense(http://creativecommons.org/licenses/by/4.0/).Fundedby SCOAP3_.

in azimuthal angle and inpseudorapidity betweenpairs of pho-tons(φγ1γ2_,φγ1γ3_{, φ}γ2γ3_, |_ηγ1γ2|_,|_ηγ1γ3|_, |_ηγ2γ3|_);the invariantmass ofpairsofphotons(mγ1γ2_,mγ1γ3 _{and mγ}2γ3_);and the invariant mass of the triphoton system (mγ γ γ ). A measure-mentof theinclusivefiducial crosssection isalso reported. Pho-tonsarerequiredtobeisolatedbasedontheamountoftransverse energy, excluding the photon contribution, inside a cone of size R ≡(η−ηγ₎2_{+ (φ − φ}γ₎2_{=0.4 centredaroundeach photon} direction(definedbythephotonpseudorapidity ηγ and azimuthal angle φγ ). Finally, the measurements are compared to next-to-leading-order(NLO)QCDcalculations.

2. ATLASdetector

The ATLAS detector [14] is a multi-purpose detector with a forward–backwardsymmetric cylindricalgeometry. The most rel-evantsystemsforthepresentmeasurementaretheinnerdetector, immersed ina 2 T magnetic field produced by a thin supercon-ductingsolenoid,andthecalorimeters. Atsmallradii,theinner de-tectorismadeupoffine-granularitypixelandmicrostripdetectors. Thesesilicon-baseddetectorscoverthepseudorapidityrange|η|< 2.5. A gas-filled straw-tube transition radiation tracker comple-mentsthesilicontrackeratlargerradiiintherange|η|<2.0 and alsoprovideselectronidentificationcapabilitiesbasedontransition radiation. The electromagnetic calorimeter is a lead/liquid-argon samplingcalorimeterwithaccordiongeometry.Thecalorimeteris divided into a barrel section covering |η|<1.475 and two end-capsectionscovering1.375<|η|<3.2.For|η|<2.5 itisdivided intothreelayersindepth,whicharefinelysegmentedin ηandφ. A thin presampler layer, covering |η|<1.8, is used to correct forfluctuationsinupstreamenergylosses.Thehadronic calorime-ter in the region |η|<1.7 uses steel absorbers with scintillator tilesastheactivemedium.Liquid-argon withcopperabsorbersis usedinthehadronicend-capcalorimeters,whichcovertheregion 1.5<|η|<3.2.Events are selectedusing a first-leveltrigger im-plementedincustom electronics,whichreducestheeventrateto a value of 75 kHz using a subset of detector information. Soft-ware algorithms with access to the full detectorinformation are thenused inthehigh-level triggerto yielda recordedeventrate ofabout400 Hz [15].

3. MonteCarlosimulationsandtheoreticalpredictions 3.1. Monte Carlo simulations

The MC samples were generated to study the characteristics ofthesignal andbackgroundevents.TheMC program MadGraph 5.1.4.4[16] interfacedwith Pythia8.186 [17] wasusedtosimulate signalevents.Thepartonicsubprocesswassimulatedby MadGraph toincludetheleading-ordermatrixelement(qq→γ γ γ),whereas P_{ythia was added to include the initial- and final-state parton} showers and the fragmentation of partons into hadrons. The LO CTEQ6L1partondistributionfunctions(PDFs) [18] areusedto pa-rameterise theparton momentum distributions inthe proton. To study the effect of the contribution of photon fragmentation, a PythiaMCsample supplementedbyQEDfinal-stateradiationwas generated with LO CTEQ6L1 PDFs. This sample includes the LO diphoton, photon+jet and dijet processes with initial-state and final-stateradiationmodelledbythepartonshower(PS).

The MC program Sherpa 1.4.1 [19] was used to estimate the background arising from electrons misreconstructed as photons. Three processes were simulated with at least one high-pT elec-tronandphotoninthefinalstate: e+e−γ, e+e−γ γ,and e±νeγ γ. The matrixelements were calculatedwithup to threefinal-state partonsatLOinpQCD andused theCT10PDFsatNLO [20].The

matrixelements were mergedwiththe Sherpaparton-shower al-gorithm [21] followingtheME+PS@LOprescription [22].

The generated signal and background event samples were passed through the Geant4-based [23] ATLAS detector and trig-ger simulation programs [24]. The signal and background sam-ples include a simulation of the underlying event (UE) where Pythiaevent-generatorparametersweresetaccordingtothe“AU2” tune [25].Thegenerationofthesimulatedeventsamplesincludes the effectofmultiple pp interactions per bunchcrossing, aswell asthe effectof thedetectorresponse to interactions frombunch crossingsbefore orafter theone containing the hard interaction. These MC eventswere weighted to reproduce the distributionof theaveragenumberofinteractionsperbunchcrossingobservedin thedata.ThegeneratedMCeventsarereconstructedandanalysed withthesameprogramchainasthedata.

3.2. Next-to-leading-order pQCD predictions

The NLO pQCD predictions presented in this Letter are com-puted using the programs MCFM [26,27] and MadGraph5_ aMC@NLO 2.3.3 [28]. The strong coupling constant is calculated at two loopswith αS(mZ)=0.118 and the electromagnetic cou-pling constant isset to αEM=1/137.In addition,the numberof massless quark flavoursisset tofiveandthe CT10 parameterisa-tionsoftheprotonPDFsatNLOareused.

The MCFMprogramincludesNLO pQCDcalculationsofthe di-rect contribution,whereas the productionofa photon viaparton fragmentationisestimatedfromtheLOQCDmatrixelement multi-pliedbytheBFG IIparton-to-photonfragmentationfunctions [29]. Therenormalisationscale μR,factorisationscale μF and fragmen-tation scale μf are chosen to be μR=μF=μf=mγ γ γ . In ad-dition, the MCFM calculations are performed using an isolation criterion whichrequiresthetotaltransverseenergyfromthe par-tonsinside a coneof size R =0.4 aroundthe photondirection to satisfy Eiso_T <10 GeV. The MCFM NLO pQCD predictions re-fer tothepartonlevel whilethemeasurements areperformedat the particlelevel.Since the Eiso

T requirementatthe particlelevel is applied after the subtraction of the UE transverse energy, it is expected that parton-to-hadron corrections to the NLO pQCD predictions are small. This is confirmed by computing the ratio of the particle-level cross section for a MadGraph sample inter-faced with Pythia with UE effects to thecomputed crosssection withouthadronisation andUEeffects.Theratioisconsistentwith unityoverthemeasuredrangeofthevariablesunderstudy. There-fore,nocorrectionisappliedtotheMCFMNLOpQCDcalculations. Deviations fromunity of O(1%) on the parton-to-hadron correc-tion factorsare foundwhen thehadronisation andUEeffects are includedusing Herwig++ 7.0.1 [30].Predictionsbasedonother pro-tonPDFsets,namelyMSTW2008 [31] andNNPDF2.1 [32],arealso computed. Differences of +5% and +6% in thecalculation of the inclusivefiducialcrosssectionarefoundusingtheMSTW2008and NNPDF2.1 PDF sets, respectively, whereas the dependence of the shapeofthedifferentialcrosssectionsonthePDFsetsisfoundto besmall.

MadGraph5_aMC@NLOcalculationsincludetheNLOpQCD con-tribution of directprocesses andapply a smoothly varying isola-tion cone to the photons [33]. This isolation requirement regu-larises the photoncollinear divergenceswhich appearin the cal-culation of the matrix element and removes the contribution of photonsresultingfromthefragmentationofaparton:E_Tiso(R)<

Eγ_T(1−cosR)/(1−cos R0),where R0=0.4 andEisoT (R)isthe sum of the transverse energies of the particles around the pho-ton up to R. The MadGraph5_aMC@NLOcalculations are inter-faced with Pythia 8.212 [34] in the NLO+PS prescription to in-cludethe initial- andfinal-statepartonshowersandthe

hadroni-sation [35]. Therenormalisationandfactorisationscalesarechosen tobeequaltothetransversemassoftheclusteredjetsfromthe fi-nalstate partonsandphotonsdefinedinthematrixelement.This choicefollowstherecommendationsinRef. [28] when interfacing the MadGraph5_aMC@NLOcalculationsto Pythia. Afterthe gener-ation,theisolation value ofthephotonis computedby summing thetransverseenergyofallfinal-stateparticles (excludingmuons andneutrinos) insideaconeofsize R =0.4 around thephoton candidate.Events with Eiso

T >10 GeV foranyof the photonsare excluded.

4. Eventselection

The data considered in this analysis were taken in stable beam conditions and satisfy detector and data-quality require-ments.Eventsarerecordedusingadiphotontriggerwitha trans-verseenergythreshold of20GeV. The triggerefficiencyforpairs ofisolated photonswith Eγ_T >22 GeV and |ηγ_{|<2.37 ishigher} than 99%. Events are required to have a reconstructed primary vertex with at least two associated tracks with pT>500 MeV and |η|<2.5, consistent with originating from the same three-dimensionalspotwithintheluminousregionofthecolliding pro-tonbeams.Ifmultipleprimary verticesarereconstructed,theone withthehighestsumofthe p2_Toftheassociatedtracksisselected astheprimaryvertex.

Photonandelectroncandidatesarereconstructedfromclusters ofenergydepositedintheelectromagneticcalorimeter.Candidates withoutamatchingtrackorreconstructedconversionvertexinthe inner detector are classified as unconverted photons [36]. Those with a matching reconstructed conversion vertex or a match-ing track consistent with originating from a photon conversion areclassifiedasconverted photons.Photons reconstructed within

|ηγ_{|<2.37 are retained. Those in the transitionregion between} the barrel and end-caps (1.37<|ηγ_{|<1.56) or regions of the} calorimeteraffected by read-out or high-voltage failures are not consideredintheeventreconstruction.

Photon candidates passing loose identification requirements, based on the energy leaking into the hadronic calorimeter and the lateral shower shape in the second layer of the electromag-netic calorimeter, are retained [1,2]. The photon cluster energies arecorrectedusinganinsitucalibrationbasedonthe Z→e+e− reconstructedmasspeak [37]. Oncethesecorrectionsareapplied, thethreereconstructedphotonswiththehighesttransverse ener-giesEγ1

T ,E γ2

T and E γ3

T ineacheventareretained.Eventswith E γ1

T , Eγ2

T and E γ3

T greaterthan27 GeV,22 GeVand15 GeV,respectively, and with a R distance in the η–φ plane above 0.45 between pairsof photons, are selected.Additionally, the invariant massof thetriphoton systemmγ γ γ is requiredto beabove 50 GeV.This requirementcorrespondstotheminimumvalueof mγ γ γ predicted atparticlelevelbythesignalMCsampledescribedinSection3.

Twofurthercriteriaareusedtodefinethesignalregionandthe background-enriched regions used to estimate the jet-to-photon misidentificationbackground. A tight photon-identification selec-tion [36] is applied to reject hadronic jet background, by im-posingrequirementson ninediscriminating variables (referredto as“shower shapes”) computed fromthe energy leaking into the hadroniccalorimeterandthe lateralandlongitudinal shower de-velopment in the electromagnetic calorimeter. The efficiency of this selection for one photon is ≈67% (>90%) for Eγ_T ≈15 GeV (>100GeV). Forthe MC simulations, theshower-shape variables areshiftedtocorrectforsmalldifferencesintheaveragevalues be-tweendataandthesimulation.Inaddition, Eγ_T- and ηγ -dependent factorsare applied to correctfor theresidual mismatchbetween the photon identification efficiencies in the simulation and the data. The isolation of the photon Eiso

T is based on the amount

of transverse energy inside a cone of size R =0.4 in the η–φ plane around the photon candidates, excluding an area of size η× φ =0.125×0.175 centredon the photon energycluster. The isolation transverseenergy iscomputedfromthe topological clusters ofcalorimeter cells [38]. The measured Eiso_T is corrected for the leakage of the photon’s energy into the isolation cone and the estimatedcontributions from the UE and pile-up. These lattertwo correctionsare computedsimultaneously onan event-by-event basis andthe combined correction is typically between 1.5and2.0GeV [3].The Eiso

T valueforisolatedphotonsisrequired to be lower than Eiso

T =0.025·E γ

T +2.7 [GeV]. The efficiency of theisolationrequirementistypicallyabove80%andincreasesasa function of Eγ_T. The numberof dataeventsselected inthesignal regionis1085. Forbackgroundstudies,twoalternative categories ofphotonsaredefined. First,non-tightphoton candidatesare de-fined as those passing the loose selection but not satisfyingthe tight identification criteria for at least one of the shower-shape variables computedfrom theenergy deposits incells of the first layer of the EM calorimeter. Second, non-isolated photon candi-datesaredefinedtohave Eiso

T > 0.025·E γ

T +4.7 [GeV]. 5. Backgroundestimationandsignalextraction

Thebackgroundcontributionstothesignalcomefromhigh-pT jets andelectrons that are misidentified asisolated photons (re-ferredtoasjetandelectronbackgrounds).Theestimationofthese backgroundsisexplainedinthefollowing.

5.1. e–γ misidentification

The number of background events due to e–γ misidentifica-tion isestimatedusingthe MCsamples listedin Section3.1.The Sherpa MC events were weighted to correct the e–γ misidenti-fication rates to match those found in data (referred to as e–γ

scalefactorsinthefollowing).Theseweightswereestimatedfrom Z→e+e−eventswhereatleasteithertheelectronorthepositron was reconstructed asaphoton. The expectednumberofelectron background events in the signal region is 71 ± 2 (stat), which correspondsto(6.5±0.2)%oftheselectedevents.Asystematic un-certainty iscomputedby propagating the uncertaintyinthe e–γ

scalefactorstotheestimationoftheyield(seeSection7). ThenormalisationoftheMCsamplesistestedbyfittingthe sig-nal, e–γ andjet–γ misidentificationcontributionstothedataasa functionof mγ γ γ in theregion 50<mγ γ γ<125 GeV.Since86% ofelectronbackgroundeventscomefromprocesseswherea pho-tonisemittedbyanelectronorpositronoriginatingfromthe de-cayofa Z boson (pp→Z→e+e−γ),apeakaround mγ γ γ ≈mZ isexpected.Toenhancetherelativecontributionofelectronsthat are misidentified asphotons, only eventswith at leastone con-vertedphoton areconsidered.SignalandelectronbackgroundMC events are used to describe the shape ofthe mγ γ γ distribution, whereasdataeventswithatleastonenon-tightidentifiedphoton areusedtodescribethejetbackgroundcontribution.Thefitgives an electron backgroundyield that is consistent with the MC es-timation, since it predicts a correction factor equal to 1.0± 0.4 (stat).Moreover,theresultofthefitisfoundtobeindependentof thedefinitionofnon-tightidentifiedphotonsandachangeof<2% isfoundwhentheisolationrequirementisloosenedby1GeV. 5.2. Jet–γ misidentification

Alargebackgroundfromjet–γ misidentificationremainsinthe selected sample, even after imposing the tight identification and isolation requirements on the photons. The jet background origi-nates frommulti-jet ( j j j), photon + jets (γj j), and diphoton +

jets (γ γj) processes in which at least one jet is misidentified asa photon. The two-dimensional-sideband method exploitedin Refs. [2,3,5,39–41] tomeasure theinclusivephoton anddiphoton differential cross sections is used to perform an in situ statisti-cal subtraction of the background. The method uses the photon isolation energyandphoton identificationcriteriatodiscriminate prompt photons from jets. It relies on the fact that the correla-tionsbetweentheisolationandidentificationvariablesinjet back-groundeventsaresmall,andthatthesignalcontamination inthe non-tightornon-isolatedcontrolregionislow.

Thetwo-dimensional-sidebandmethodcountsallcombinations of photonsmeeting or failingto meet the tight identification or isolation criteria.Four categoriesaredefinedforeach photon, re-sulting in 64 categories of events where 63 of these categories correspondto j j j, γj j, and γ γj background-enriched regions. The inputsofthemethod arethe numberofeventsineach category, the correlation between the isolation andidentification variables injetbackgroundevents(Rbg_{),thesignalleakagefractionsin} non-tightandnon-isolated regions,andtheexpectednumberof elec-tronbackgroundeventsineachcategory. Thecorrelationbetween theisolation andidentification variablesis takentobe negligible (Rbg_{=1.0)basedonstudiesinsimulatedbackgroundsamplesand} ondataina background-dominatedregion [3].The signalleakage fractionsandelectron-backgroundeventsare estimatedusingthe MCsamplesdescribedinSection3.1.

Themethodallowstheextractionofthenumberoftrue three-photonsignalevents(Nγ γ γ ),thenumberofeventswhereatleast one,twoandthreecandidatesaretruejetsandthetightand isola-tionefficienciesforfakephotoncandidatesfromjets(“fakerates”). Thenumberofeventsineachcategory isexpressedasafunction ofthe followingparameters: signal,electron- and jet-background yields,signal leakagefractions,fakerates,andRbg_.Then,the sys-tem of 64 independent equations is grouped into 21 dependent linearequations whichare solved iteratively usinga χ2 minimi-sation procedure. The size of each bin of the observables under studyischosentohaveasufficientlylargenumberofeventsto ap-plythismethodbin-by-bin.Thestatisticaluncertaintyofthesignal andjet background-enrichedregions ispropagatedtothe estima-tionofthethree-photonsignalyieldviapseudo-experiments.

The signal purity, defined as Nγ γ γ/NSR, where NSR is the number of selected events in the signal region, is found to be (55±5)% (stat), witha value of≈45%(≈60%)atlow (high) Eγ_T. The fractions of γ γj, γj j and j j j events are (33±2)% (stat), (5±2)% (stat)and(0.2±0.2)% (stat)respectively. Systematic un-certainties are assigned to the modelling of the non-tight and non-isolated signalleakage fractionsandto thevalue of Rbg _(see Section7).

6. Unfoldingtoparticlelevel

Theproductioncrosssectionforthreeisolatedphotonsis mea-sured as functions of Eγ1 T , E γ2 T , E γ3 T , φγ1γ2, φγ1γ3, φγ2γ3, |ηγ1γ2|_,|_ηγ1γ3|_, |_ηγ2γ3|_{, mγ}1γ2_,mγ1γ3_{, mγ}2γ3 _{and mγ γ γ . The} fiducialphase-spaceregionislistedinTable1.Thepredictions of theMC generators atparticlelevelare definedusingthose parti-cles witha lifetime τ longer than 30 ps;these particles are re-ferredtoas“stable”.Theparticlesassociatedwiththeoverlaid pp collisions are not considered. The particle-levelisolation require-ment on thephotons is builtby summing the transverse energy ofall stableparticles, exceptformuons andneutrinos,in acone of size R =0.4 around the photon direction. The contribution fromtheUEissubtractedusingthesameprocedureasappliedto thedataatthereconstruction level [3]. Thedatadistributions af-terbackgroundsubtractionareunfoldedtotheparticlelevelusing

Table 1

Fiducialphase-spaceregiondefinedatparticlelevel. Requirements on Phase-space region

EγT E γ1 T >27 GeV, E γ2 T >22 GeV, E γ3 T >15 GeV mγ γ γ _mγ γ γ_{>50 GeV} Rγ γ _Rγ γ_>0.45 |ηγ_{| |η}γ_{| <2.37 (excluding 1.37<|η}γ_{| <1.56)}

Isolation EisoT <10 GeV

bin-by-bincorrectionfactorsdeterminedusingthesignalMC sam-ple. Thecorrection factors take intoaccount theefficiency ofthe eventandphotonselectioncriteriaandthesmallmigrationeffects. Ofthesignaleventsreconstructedinagivenbin,thefractionthat are generatedinthesamebinistypically foundtobe >93%. The datadistributionsareunfoldedtotheparticlelevelviatheformula

dσ

d A(i)=

Nsig_(i)C(i)

A(i)L ,

where foragiven bini, (dσ/d A) isthedifferential crosssection asafunction ofobservable A, Nsig isthenumberof background-subtracted data events, C is the correction factor, L is the in-tegrated luminosity and A is the width of the bin. The cor-rection factors are computed using the MC sample of events as C(i)=NMC

part(i)/NMCreco(i), where NMCpart(i) is the number of events which satisfythekinematicconstraintsofthe phase-spaceregion at theparticle level, and NMC_reco(i) is thenumber ofevents which fulfilall theselectioncriteriaatthereconstructionlevel.The cor-rection factors vary between 1.5 and 3.3 asfunctions of photon transverse energy,invariantmassofpairs ofphotons, andthe in-variant mass of the triphoton system, whereas they have a con-stantvaluecloseto2.5asfunctionsofthedifferenceinazimuthal angleandinpseudorapiditybetweenpairsofphotons.

7. Experimentalandtheoreticaluncertainties 7.1. Experimental uncertainties

The sources of experimental systematic uncertainty that af-fect the measurements are the photon energy scale and resolu-tion, photon identification, jet and electron background subtrac-tion,modellingofthephoton isolation,the photonfragmentation contribution,theunfoldingprocedureandtheluminosity.

•Photonenergyscaleandresolution. The uncertainty due to the photon energy scale is estimated by varying the photon energiesintheMCsimulation [37].Thisuncertaintymostly af-fectsthe C(i)correctionfactor.Theeffectofthisvariationon the estimationof thecross section istypically <2%.In addi-tion,theuncertaintyinthe energyresolutionisestimatedby smearing photon energies inthe MC simulationasdescribed in Ref. [37]. The resulting uncertaintyin the cross section is typically<0.1%.

•Photonidentificationefficiency. The uncertainty inthe pho-tonidentificationefficiencyisestimatedfromtheeffectof dif-ferences betweenshower-shapevariabledistributions in data andsimulation [36].Thisuncertaintyaffectstheestimationof the non-tightsignal leakage fractionsandthe C(i) correction factor and is fully correlated between photons. The correla-tionbetweentightandnon-tightidentificationvariablesisalso considered in thepropagation ofthe uncertainty.The result-ing uncertainty in the cross section is ≈10% (≈4%) at low (high) E_Tγ.

•Photonidentificationandisolationcorrelationinthe back-ground. Thephotonisolationandidentificationvariablesused

to define the two-dimensional backgroundsidebands are as-sumedtobeindependentinjetbackgroundevents(Rbg=1.0). Any correlation between these variables affects the estima-tion of signal purityand leads to systematicuncertainties in thebackground-subtractionprocedure.Thevalueof Rbg _is es-timated using background MC samples and is found to be consistent with unity within ±10% [3,41]. This value of Rbg isverifiedusingbackground-enrichedregionsindata.The as-sumption of Rbg_{=1.0 is found to hold within ±10% in the} kinematicregionofthemeasurementspresentedhere.The re-sulting uncertaintyin thecross section is ≈8% (≈4%) atlow (high) Eγ_T.

•Photonisolationmodelling. Differencesbetweendataand sig-nal MC events in the modelling of the isolation distribution can lead to systematicuncertainties inthe estimation ofthe non-isolated signal leakage fractions and the C(i) correction factor. Two subsamples are selected from data by applying either the tight or non-tight identification criteria to each photon; the subsample selected withnon-tight identification criteria isexpectedto be enriched inbackgroundcandidates. The Eiso

T value for thenon-tight candidates is scaled so that the integral for Eiso

T >10 GeV, where the contribution from the signal is expected to be negligible, matches that of the tight candidates.Therescaled backgrounddistribution is sub-tractedfromthatofthetightphotoncandidatestoextractthe isolation profile of signal-like candidates. These distributions areusedtoderiveSmirnovtransformations [36].TheSmirnov transformation shifts the photon isolation values event-by-event in MC simulation to match the isolation distribution foundindata.ThisSmirnov-transformedMCsampleisusedto estimate newdifferential crosssections.Differences fromthe nominalresultsaretakenassystematicuncertainties.The re-sulting uncertaintyin thecross section is ≈7% (≈4%) atlow (high) Eγ_T.

•Photonfragmentationcontribution. Theadmixture ofdirect and fragmentationphotons affects theestimation of the sig-nal leakage fractions which are used in the jet background subtraction procedure and the C(i) correction factor. A pho-ton originating from the fragmentation of a parton can be modelledintheMCsimulationbyallowingtheradiationofa photon byaparton.Asample offragmentationphotonsis se-lected byapplyingtheeventselectiontoadiphotonMC sam-ple(seeSection3.1).Thisselectsthree-photoneventswhereat leastoneofthefinal-statephotonsresultsfromfragmentation. The diphoton MC sample predicts that formore than98% of theeventsthesub-sub-leadingphotonoriginatesfromparton bremsstrahlung. Differences in the isolation distributions be-tween directandfragmentationphotonsareexpected. There-fore, a template fit to the sub-sub-leading photon isolation distributionisperformedtodeterminetheoptimaladmixture ofthenominalanddiphotonMCsamples.Thedirectand frag-mentation isolation templates are given by the nominal and diphotonMCsamplesrespectively,whereasthejetbackground template is takenfroma datacontrol region wherethe sub-sub-leadingphotoncandidatesatisfiesthenon-tightselection. The fitestimates thatabout40% ofthesub-sub-leading pho-tonsoriginate fromfragmentation, asmodelledbythe dipho-ton MCsample. Thisvalueisused tomergethenominaland diphotonMCsamples.ThenewMCsampleisusedtoestimate the signal leakage fractions and the C(i) correction factors. The deviationof thedifferential crosssection fromthe value obtained usingthe Smirnov-transformedMC sample istaken asthesystematicuncertainty.Thisavoidsdoublecountingthe effect ofthephoton isolation modelling. Theresulting uncer-taintyinthecrosssectionis≈4%.

Table 2

Breakdownoftherelativesystematicuncertaintiesinthemeasurementofthe in-clusivefiducialcrosssection.

Source Relativesystematic

uncertainty Photon identification efficiency 7.9% Identification and isolation correlation in the background 7.7% Photon isolation modelling 5.8% Photon fragmentation contribution 3.9% Photon energy scale and resolution 1.6%

Unfolding 0.6%

e–γmisidentification 0.1% Measurement of the integrated luminosity 1.9%

Total 13%

• e–γ misidentification. The uncertainty inthe electron back-groundcontaminationisestimatedbypropagating the uncer-taintyinthe e–γ scalefactors(seeSection5.1),whichaffects theprediction ofthe e–γ misidentificationrates,to the esti-mationofthecrosssection.Theresultinguncertaintyis≈0.1%.

• Unfoldingprocedure. Theeffectofunfoldingisinvestigatedby usingsmoothfunctionstore-weightthesignalMCsimulation to matchthedata distributionsafter backgroundsubtraction. The dataare unfolded using thisreweighted MC sample and theresultingcrosssectionsarecomparedtothenominal mea-surements. The differential cross sectionsare found to differ by<1%.

• Othersources. Theeffectofdifferentamountsofpile-upis es-timatedbycomparingtheratioofdatatoMCsimulatedsignal forhighandlow pile-upsamples.No dependenceof this ra-tio on pile-up conditions is found. In addition, the effect of thetriggerefficiencyontheestimationofthecrosssection is foundtobe<0.3%.Theuncertaintyintheintegrated luminos-ityis1.9% [13].

The total systematic uncertainty is computed by adding in quadrature the uncertainties from the sources listed above and is found to be ≈ 13%. It decreases as a function of Eγ_T from

≈15%to≈10%.Forregionswith Eγ1

T 50 GeV, E γ2

T 50 GeVand Eγ3

T 30 GeV, theuncertaintyofthemeasurements isdominated bythestatisticaluncertaintyofthedata.Table2showsthe break-down ofthe systematic uncertainties inthe measurement ofthe inclusive fiducial cross section. The statistical uncertainty in the measuredinclusivefiducialcrosssectionis≈9%.

7.2. Theoretical uncertainties

The followingsources ofuncertaintyinthetheoretical predic-tionsareconsideredforthe MCFMand MadGraph5_aMC@NLO cal-culations.

• The uncertainty in the NLO QCD calculations due to terms beyondNLO isestimated by repeating the calculationsusing valuesof μR, μF and μf scaledby factors 0.5and2. For the MadGraph5_aMC@NLOcalculations,onlythe μ_Rand μ_Fscales arevaried.Inaddition,thescales areeithervaried simultane-ously,individuallyorbyfixingoneandvaryingtheothertwo. The final uncertainty istaken asthe largest deviationofthe possiblevariationswithrespecttothenominalvalue.

• TheuncertaintyintheNLOQCDcalculationsdueto uncertain-tiesinthe protonPDFsisestimatedbyrepeatingthe calcula-tions usingthe52additionalsetsfromtheCT10error analy-sis [20].

• TheuncertaintyintheNLOQCDcalculationsduetothevalue of αS(mZ)=0.118 is estimated byrepeating the calculations

Fig. 1. Measured differentialcrosssectionsfortheproductionofthreeisolatedphotons(dots)asfunctionsof(a) Eγ1

T ,(b) E γ2

T and(c) E γ3

T .TheNLOQCDcalculationsfrom

MCFMand MadGraph5_aMC@NLOarealsoshown.Thethicknessofeachtheoreticalpredictioncorrespondstothetheoreticaluncertainty.Thebottompartofeachfigure showstheratiosofpredictedandmeasureddifferentialcrosssections.Theredinner (blackouter)errorbarsrepresentthesystematicuncertainties(thestatisticaland systematicuncertaintiesaddedinquadrature).Formostofthedatapoints,theinnererrorbarsaresmallerthanthemarkersizeandthusnotvisible.(Forinterpretationof thecoloursinthefigure(s),thereaderisreferredtothewebversionofthisarticle.)

usingtwo additionalsets ofprotonPDFs [20] employing dif-ferentvaluesof αS(mZ),namely αS(mZ)=0.116 and0.120. Thedominanttheoreticaluncertaintyinthepredictedcross sec-tion arises fromthe missing terms beyondNLO andamounts to 10–12%.Theuncertaintyarising fromthePDFvariations amounts to 2–3%and theuncertainty arising fromthe value of αS(mZ) is below2%.Thetotaltheoreticaluncertaintyisobtainedbyaddingin quadraturethe individual uncertaintieslisted above andamounts to10–13%.

8. Results

The measured inclusive fiducial cross section forthe produc-tionof threeisolated photonsinthe phase-spaceregiongivenin Table1is

σmeas=72.6±6.5(stat.)±9.2(syst.)fb,

where“stat.”and“syst.” denotethestatisticalandsystematic un-certainties.ThefiducialcrosssectionspredictedatNLOby MCFM andMadGraph5_aMC@NLOare

σNLO=31.5+₋3_2..2₅fb (MCFM),

σNLO+PS=46.6+₋35..76fb (MadGraph5_aMC@NLO).

The NLO QCD calculationsunderestimate the measured inclu-sive fiducial cross section by factors of 2.3 and 1.6 for MCFM and MadGraph5_aMC@NLO, respectively. The additionof the par-ton showertothe MadGraph5_aMC@NLOpredictionimprovesthe agreementwiththemeasuredvalue.TheNLOelectroweak correc-tions are small andcannot account forthe observed differences between NLO QCD and the measurements [42]. Similar discrep-ancies between the NLO calculations and the measurements are found forthepredictionoftheinclusivefiducialcross sectionfor

γ γ, Wγ γ and Zγ γ production [5,43,44].TheNNLOcalculations, which are availablefor thecomputation of γ γ butnot for γ γ γ production, significantly improve thedescription of the diphoton fiducialcrosssection [6,45].

Fig. 1 shows the three-isolated-photonsdifferential cross sec-tions as functions of Eγ1

T , E γ2

T and E γ3

T . The measurements are compared to NLO QCD predictionsfrom MCFM and MadGraph5_ aMC@NLO. The NLO QCD calculationsfailto describe theregions of low Eγ1

T , E γ2

T and E γ3

Fig. 2. Measured differentialcrosssectionsfortheproductionofthreeisolatedphotons(dots)asfunctionsof(a) mγ1γ2_{,(b) m}γ1γ3_{,(c) m}γ2γ3 _{and(d) m}γ γ γ_.TheNLOQCD

calculationsfrom MCFMand MadGraph5_aMC@NLOarealsoshown.Thethicknessofeachtheoreticalpredictioncorrespondstothetheoreticaluncertainty.Thebottom partofeachfigureshowstheratiosofpredictedandmeasureddifferentialcrosssections.Theredinner(blackouter)errorbarsrepresentthesystematicuncertainties(the statisticalandsystematicuncertaintiesaddedinquadrature).Formostofthedatapoints,theinnererrorbarsaresmallerthanthemarkersizeandthusnotvisible. between data and the predictions. The description of the

mea-surements by the theory is improved at high Eγ_T. In particular, MadGraph5_aMC@NLO calculations describe the measured cross sectionsfor Eγ2

T  50GeVand E γ3

T  30 GeVwithin the statisti-calandsystematicuncertainties,whereasMCFMdescribesthedata onlyatthehighestvaluesof Eγ1

T , E γ2

T and E γ3

T .

AcomparisonoftheNLO calculationstothemeasurements as functions of mγ1γ2_{, mγ}1γ3_{, mγ}2γ3 _{and mγ γ γ is shown in Fig. 2.} The MCFMcalculations underestimatethe measurements by 50% in the low invariant mass regions, whereas the differences are 30–40%for mγ1γ2_{150 GeV, mγ}1γ3_{75 GeV, mγ}2γ3_{75 GeVand} mγ γ γ150 GeV.The MadGraph5_aMC@NLOcalculationsalso un-derestimatethedataby30–50%inthelowinvariantmassregions. However, they tend to give a better description of the measure-ments for mγ1γ2 _{150 GeV, mγ}1γ3 _{75 GeV, mγ}2γ3_{75 GeV} andmγ γ γ  150 GeV. For such regions, MadGraph5_aMC@NLO predictionsare25–30%higherthanthe MCFMestimates.

Fig.3 shows the three-isolated-photons differential cross sec-tions asfunctionsofφγ1γ2_{, φ}γ1γ3_,φγ2γ3_, |_ηγ1γ2|_,|_ηγ1γ3| and|ηγ2γ3|_{.The theoretical calculationsunderestimatethe} nor-malisationofthemeasurements.Thisisduetothefactthatthese distributionsare mainly populatedby low-Eγ_T photons. Both NLO

QCD calculations give an adequate description of the shape of the differential cross sections as functions of |ηγ1γ2|_, |_ηγ1γ3| and|ηγ2γ3|_{. Aquantitative comparisonof theNLO QCD} predic-tions to the measurements as functions of φγ1γ2_{, φ}γ1γ3 _and φγ2γ3 _{is performedwitha χ}2 _{fitto the cross-section} normali-sationincludingbothstatisticalandsystematicuncertainties. This teststhedescriptionoftheshapeofthedifferentialcrosssections. The total systematic uncertainty is considered to be fully corre-latedacross bins andis includedin the χ2 _{definitionusing} nui-sance parameters. Afterthe χ2 _{minimisation,scale factors equal} to ≈ 1.6 (MadGraph5_aMC@NLO) and ≈ 2.3 (MCFM) are found foreach angulardistribution independently. Both theoretical pre-dictionsgiveanadequatedescriptionoftheshapeof dσ/dφγ2γ3 (χ2_{/ndof=6/5 and 7/5for MadGraph5_aMC@NLOand MCFM,} re-spectively,wherendofisthenumberofdegreeoffreedom).In ad-dition, MadGraph5_aMC@NLOcalculationsdescribeadequatelythe shape of dσ/dφγ1γ2 _{and dσ/dφ}γ1γ3 _(χ2_/ndof=_{6/5 and 7/5,} respectively) but not MCFM (χ2_{/ndof=13/5 and 14/5,} respec-tively). This showsthe importance of the addition of the parton shower to improve the description of the shape of dσ/dφγ1γ2 and dσ/dφγ1γ3_.

Fig. 3. Measured differentialcrosssectionsfortheproductionofthreeisolatedphotons(dots)asfunctionsof(a)φγ1γ2_,(b)φγ1γ3_,(c)φγ2γ3_,(d)|_ηγ1γ2|_,(e)|_ηγ1γ3|_and

(f)|ηγ2γ3|_{.TheNLOQCDcalculationsfrom MCFMand MadGraph5_aMC@NLOarealsoshown.Thethicknessofeachtheoreticalpredictioncorrespondstothetheoretical}

uncertainty.Thebottompartofeachfigureshowstheratiosofpredictedand measureddifferentialcrosssections.Theredinner(blackouter)errorbarsrepresentthe systematicuncertainties(thestatisticalandsystematicuncertaintiesaddedinquadrature).Forsomeofthedatapoints,theinnererrorbarsaresmallerthanthemarkersize andthusnotvisible.

9. Summary

Ameasurementoftheproductioncrosssectionofthreeisolated photonsin pp collisions at √s=8 TeV withthe ATLAS detector atthe LHC is presented using a data set with an integrated lu-minosity of 20.2 fb−1. Differential cross sections asfunctions of Eγ1 T , E γ2 T , E γ3 T , mγ1γ2, mγ1γ3, mγ2γ3, mγ γ γ , φγ1γ2,φγ1γ3,φγ2γ3,

|ηγ1γ2|_, |_ηγ1γ3|_{, and}|_ηγ2γ3| _{are measured for photons with} Eγ1 T >27 GeV, E γ2 T >22 GeV, E γ3 T >15 GeV, mγ γ γ >50 GeV, and|ηγ|<2.37,excludingtheregion1.37<|ηγ|<1.56.The dis-tancebetweenpairsofphotonsinthe η–φplaneisrequiredtobe R >0.45.Theselectionofisolatedphotonsisensuredby requir-ingthatthe transverseenergyina coneofsizeR =0.4 around thephotonissmallerthan10 GeV.

Theinclusivefiducial crosssection ismeasured to be σmeas= 72.6±6.5(stat.)±9.2(syst.)fb.TheNLOQCDcalculations under-estimatethe measured inclusivefiducialcrosssection by afactor 2.3for MCFM and1.6 for MadGraph5_aMC@NLO.Both NLO QCD predictionsunderestimatethemeasurementsinthelowtransverse energy and invariant mass regions. The MadGraph5_aMC@NLO predictions give an adequate description of the measured cross-sectiondistributions for Eγ2

T 50 GeVand E γ3

T 30 GeV andfor mγ1γ2_{150 GeV, mγ}1γ3_{75 GeV, mγ}2γ3_{75 GeV and mγ γ γ}  150 GeV. Both NLO calculations give an adequate description of theshapeofthemeasuredcrosssection asfunctionsof|ηγ1γ2|_,

|ηγ1γ3| _and |_ηγ2γ3|_{, whereas they underestimate the} normal-isationofthemeasurements. Inaddition,both theoretical predic-tionsinadequatelydescribethenormalisationofthemeasurements as functions of φγ1γ2_{, φ}γ1γ3 _{and φ}γ2γ3_{. MCFM predictions} giveanadequatedescriptionoftheshapeof dσ/dφγ2γ3 _andfail to describe the shape of dσ/dφγ1γ2 _{and dσ/dφ}γ1γ3_{, whereas} M_{adGraph5_aMC@NLOpredictionsgiveanadequatedescriptionof} theshapeofthemeasured crosssectionsasfunctionsofallthree angularvariables. The measurements provide a test of pQCD for the description of the dynamics oftriphoton production and in-dicate the need for improved modelling of this process in MC models.

Acknowledgements

We thankCERN for thevery successful operation ofthe LHC, aswell asthe support stafffromour institutions without whom ATLAScouldnotbeoperatedefficiently.

WeacknowledgethesupportofANPCyT,Argentina;YerPhI, Ar-menia; ARC, Australia; BMWFW and FWF, Austria; ANAS, Azer-baijan;SSTC, Belarus; CNPq and FAPESP, Brazil; NSERC, NRC and CFI,Canada; CERN; CONICYT,Chile; CAS, MOSTandNSFC, China; COLCIENCIAS, Colombia; MSMT CR, MPO CR and VSC CR, Czech Republic;DNRFandDNSRC,Denmark;IN2P3-CNRS,CEA-DRF/IRFU, France; SRNSFG, Georgia; BMBF, HGF, andMPG, Germany; GSRT, Greece;RGC,HongKongSAR,China;ISF,I-COREandBenoziyo Cen-ter, Israel; INFN, Italy; MEXT and JSPS, Japan; CNRST, Morocco; NWO, Netherlands; RCN,Norway; MNiSW andNCN, Poland;FCT, Portugal; MNE/IFA, Romania; MES of Russiaand NRC KI, Russian Federation;JINR;MESTD,Serbia; MSSR,Slovakia; ARRSandMIZŠ, Slovenia;DST/NRF,SouthAfrica;MINECO,Spain;SRCand Wallen-berg Foundation, Sweden; SERI, SNSF and Cantons of Bern and Geneva, Switzerland; MOST, Taiwan; TAEK, Turkey; STFC, United Kingdom;DOEandNSF, UnitedStatesofAmerica. Inaddition, in-dividualgroupsandmembershavereceivedsupportfromBCKDF, theCanadaCouncil,Canarie,CRC,ComputeCanada,FQRNT,andthe OntarioInnovationTrust, Canada;EPLANET, ERC,ERDF,FP7, Hori-zon 2020 andMarie Skłodowska-Curie Actions, European Union; Investissements d’Avenir Labex and Idex, ANR, Région Auvergne andFondationPartagerleSavoir,France;DFGandAvHFoundation,

Germany;Herakleitos,ThalesandAristeiaprogrammesco-financed byEU-ESF andtheGreekNSRF;BSF,GIFandMinerva, Israel;BRF, Norway; CERCA Programme Generalitat de Catalunya, Generalitat Valenciana,Spain;theRoyalSocietyandLeverhulmeTrust,United Kingdom.

The crucial computingsupport from all WLCG partnersis ac-knowledged gratefully,in particularfromCERN, theATLAS Tier-1 facilities at TRIUMF (Canada), NDGF (Denmark, Norway, Swe-den),CC-IN2P3(France),KIT/GridKA(Germany),INFN-CNAF(Italy), NL-T1(Netherlands),PIC(Spain),ASGC(Taiwan),RAL(UK)andBNL (USA),theTier-2facilitiesworldwideandlargenon-WLCGresource providers.Majorcontributorsofcomputingresourcesare listedin Ref. [46].

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TheATLASCollaboration

M. Aaboud137d,G. Aad88,B. Abbott115,O. Abdinov12,∗,B. Abeloos119,S.H. Abidi161,O.S. AbouZeid139, N.L. Abraham151,H. Abramowicz155, H. Abreu154, Y. Abulaiti148a,148b,B.S. Acharya167a,167b,a,

S. Adachi157,L. Adamczyk41a, J. Adelman110,M. Adersberger102,T. Adye133, A.A. Affolder139, Y. Afik154, C. Agheorghiesei28c, J.A. Aguilar-Saavedra128a,128f,S.P. Ahlen24,F. Ahmadov68,b, G. Aielli135a,135b,

S. Akatsuka71, T.P.A. Åkesson84, E. Akilli52, A.V. Akimov98,G.L. Alberghi22a,22b,J. Albert172, P. Albicocco50, M.J. Alconada Verzini74,S. Alderweireldt108, M. Aleksa32, I.N. Aleksandrov68,

C. Alexa28b,G. Alexander155, T. Alexopoulos10,M. Alhroob115, B. Ali130,M. Aliev76a,76b, G. Alimonti94a, J. Alison33,S.P. Alkire38,C. Allaire119, B.M.M. Allbrooke151,B.W. Allen118, P.P. Allport19,

A. Aloisio106a,106b,A. Alonso39, F. Alonso74,C. Alpigiani140,A.A. Alshehri56,M.I. Alstaty88, B. Alvarez Gonzalez32,D. Álvarez Piqueras170,M.G. Alviggi106a,106b,B.T. Amadio16,

Y. Amaral Coutinho26a,C. Amelung25,D. Amidei92, S.P. Amor Dos Santos128a,128c, S. Amoroso32, C. Anastopoulos141, L.S. Ancu52,N. Andari19,T. Andeen11, C.F. Anders60b, J.K. Anders18,

K.J. Anderson33,A. Andreazza94a,94b, V. Andrei60a, S. Angelidakis37,I. Angelozzi109,A. Angerami38, A.V. Anisenkov111,c,A. Annovi126a,C. Antel60a,M. Antonelli50, A. Antonov100,∗,D.J. Antrim166,

F. Anulli134a, M. Aoki69, L. Aperio Bella32, G. Arabidze93,Y. Arai69,J.P. Araque128a, V. Araujo Ferraz26a, A.T.H. Arce48,R.E. Ardell80, F.A. Arduh74,J-F. Arguin97, S. Argyropoulos66, A.J. Armbruster32,

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P.J. Bakker109, D. Bakshi Gupta82,E.M. Baldin111,c, P. Balek175,F. Balli138, W.K. Balunas124, E. Banas42, A. Bandyopadhyay23,Sw. Banerjee176,e,A.A.E. Bannoura177, L. Barak155,E.L. Barberio91,

D. Barberis53a,53b, M. Barbero88,T. Barillari103,M-S Barisits65, J.T. Barkeloo118,T. Barklow145,

N. Barlow30,S.L. Barnes36b, B.M. Barnett133,R.M. Barnett16,Z. Barnovska-Blenessy36c,A. Baroncelli136a, G. Barone25, A.J. Barr122,L. Barranco Navarro170,F. Barreiro85, J. Barreiro Guimarães da Costa35a,

R. Bartoldus145, A.E. Barton75,P. Bartos146a, A. Basalaev125, A. Bassalat119,f, R.L. Bates56, S.J. Batista161, J.R. Batley30,M. Battaglia139,M. Bauce134a,134b,F. Bauer138,K.T. Bauer166,H.S. Bawa145,g,

J.B. Beacham113, M.D. Beattie75,T. Beau83,P.H. Beauchemin165,P. Bechtle23,H.P. Beck18,h,H.C. Beck58, K. Becker122,M. Becker86,C. Becot112, A.J. Beddall20e, A. Beddall20b,V.A. Bednyakov68,

M. Bedognetti109,C.P. Bee150, T.A. Beermann32,M. Begalli26a, M. Begel27, J.K. Behr45,A.S. Bell81, G. Bella155, L. Bellagamba22a, A. Bellerive31,M. Bellomo154, K. Belotskiy100,N.L. Belyaev100, O. Benary155,∗, D. Benchekroun137a,M. Bender102,N. Benekos10, Y. Benhammou155,

E. Benhar Noccioli179,J. Benitez66,D.P. Benjamin48, M. Benoit52,J.R. Bensinger25, S. Bentvelsen109, L. Beresford122,M. Beretta50,D. Berge45,E. Bergeaas Kuutmann168, N. Berger5,L.J. Bergsten25,

J. Beringer16,S. Berlendis57, N.R. Bernard89,G. Bernardi83, C. Bernius145,F.U. Bernlochner23,T. Berry80, P. Berta86,C. Bertella35a, G. Bertoli148a,148b,I.A. Bertram75, C. Bertsche45, G.J. Besjes39,

O. Bessidskaia Bylund148a,148b,M. Bessner45,N. Besson138, A. Bethani87,S. Bethke103,A. Betti23, A.J. Bevan79,J. Beyer103, R.M. Bianchi127,O. Biebel102,D. Biedermann17,R. Bielski87, K. Bierwagen86, N.V. Biesuz126a,126b, M. Biglietti136a,T.R.V. Billoud97,M. Bindi58, A. Bingul20b, C. Bini134a,134b,

S. Biondi22a,22b,T. Bisanz58, C. Bittrich47,D.M. Bjergaard48,J.E. Black145,K.M. Black24,R.E. Blair6, T. Blazek146a, I. Bloch45, C. Blocker25, A. Blue56,U. Blumenschein79, Dr. Blunier34a, G.J. Bobbink109, V.S. Bobrovnikov111,c,S.S. Bocchetta84,A. Bocci48,C. Bock102,D. Boerner177, D. Bogavac102,

A.G. Bogdanchikov111, C. Bohm148a,V. Boisvert80, P. Bokan168,i, T. Bold41a,A.S. Boldyrev101,

A.E. Bolz60b, M. Bomben83, M. Bona79,J.S. Bonilla118,M. Boonekamp138,A. Borisov132, G. Borissov75, J. Bortfeldt32, D. Bortoletto122, V. Bortolotto62a,D. Boscherini22a, M. Bosman13,J.D. Bossio Sola29, J. Boudreau127, E.V. Bouhova-Thacker75,D. Boumediene37, C. Bourdarios119,S.K. Boutle56,A. Boveia113, J. Boyd32,I.R. Boyko68,A.J. Bozson80,J. Bracinik19,A. Brandt8, G. Brandt177,O. Brandt60a,F. Braren45, U. Bratzler158,B. Brau89, J.E. Brau118,W.D. Breaden Madden56, K. Brendlinger45,A.J. Brennan91, L. Brenner109,R. Brenner168, S. Bressler175,D.L. Briglin19, T.M. Bristow49,D. Britton56,D. Britzger60b, I. Brock23,R. Brock93,G. Brooijmans38,T. Brooks80, W.K. Brooks34b, E. Brost110, J.H Broughton19, P.A. Bruckman de Renstrom42, D. Bruncko146b, A. Bruni22a,G. Bruni22a,L.S. Bruni109, S. Bruno135a,135b, BH Brunt30, M. Bruschi22a, N. Bruscino127, P. Bryant33, L. Bryngemark45,T. Buanes15,Q. Buat144, P. Buchholz143, A.G. Buckley56, I.A. Budagov68,F. Buehrer51,M.K. Bugge121, O. Bulekov100, D. Bullock8, T.J. Burch110,S. Burdin77,C.D. Burgard109,A.M. Burger5, B. Burghgrave110, K. Burka42, S. Burke133, I. Burmeister46, J.T.P. Burr122,D. Büscher51,V. Büscher86, E. Buschmann58,P. Bussey56,J.M. Butler24, C.M. Buttar56, J.M. Butterworth81, P. Butti32,W. Buttinger27,A. Buzatu153, A.R. Buzykaev111,c,

S. Cabrera Urbán170, D. Caforio130, H. Cai169, V.M.M. Cairo2,O. Cakir4a,N. Calace52,P. Calafiura16, A. Calandri88, G. Calderini83,P. Calfayan64,G. Callea40a,40b,L.P. Caloba26a, S. Calvente Lopez85, D. Calvet37,S. Calvet37, T.P. Calvet88,R. Camacho Toro33,S. Camarda32, P. Camarri135a,135b, D. Cameron121,R. Caminal Armadans89,C. Camincher57, S. Campana32,M. Campanelli81,

A. Camplani94a,94b, A. Campoverde143,V. Canale106a,106b,M. Cano Bret36b, J. Cantero116, T. Cao155, M.D.M. Capeans Garrido32,I. Caprini28b, M. Caprini28b, M. Capua40a,40b, R.M. Carbone38,

R. Cardarelli135a, F. Cardillo51,I. Carli131,T. Carli32, G. Carlino106a, B.T. Carlson127,L. Carminati94a,94b, R.M.D. Carney148a,148b, S. Caron108, E. Carquin34b,S. Carrá94a,94b, G.D. Carrillo-Montoya32,D. Casadei19, M.P. Casado13,j,A.F. Casha161,M. Casolino13,D.W. Casper166, R. Castelijn109,V. Castillo Gimenez170, N.F. Castro128a,k,A. Catinaccio32, J.R. Catmore121, A. Cattai32,J. Caudron23,V. Cavaliere27,

E. Cavallaro13, D. Cavalli94a, M. Cavalli-Sforza13,V. Cavasinni126a,126b,E. Celebi20d, F. Ceradini136a,136b, L. Cerda Alberich170, A.S. Cerqueira26b,A. Cerri151,L. Cerrito135a,135b, F. Cerutti16, A. Cervelli22a,22b, S.A. Cetin20d,A. Chafaq137a, D. Chakraborty110,S.K. Chan59,W.S. Chan109,Y.L. Chan62a,P. Chang169, J.D. Chapman30,D.G. Charlton19, C.C. Chau31, C.A. Chavez Barajas151, S. Che113,A. Chegwidden93, S. Chekanov6, S.V. Chekulaev163a, G.A. Chelkov68,l, M.A. Chelstowska32, C. Chen36c, C. Chen67, H. Chen27,J. Chen36c,J. Chen38, S. Chen35b, S. Chen157, X. Chen35c,m, Y. Chen70, H.C. Cheng92, H.J. Cheng35a,35d,A. Cheplakov68,E. Cheremushkina132,R. Cherkaoui El Moursli137e,E. Cheu7, K. Cheung63, L. Chevalier138,V. Chiarella50, G. Chiarelli126a,G. Chiodini76a, A.S. Chisholm32,

A. Chitan28b,Y.H. Chiu172, M.V. Chizhov68, K. Choi64, A.R. Chomont37, S. Chouridou156,Y.S. Chow109, V. Christodoulou81, M.C. Chu62a,J. Chudoba129,A.J. Chuinard90,J.J. Chwastowski42,L. Chytka117, D. Cinca46,V. Cindro78, I.A. Cioar˘a23,A. Ciocio16, F. Cirotto106a,106b, Z.H. Citron175,M. Citterio94a, A. Clark52,M.R. Clark38, P.J. Clark49,R.N. Clarke16, C. Clement148a,148b,Y. Coadou88,M. Cobal167a,167c, A. Coccaro52, J. Cochran67, L. Colasurdo108,B. Cole38,A.P. Colijn109,J. Collot57, P. Conde Muiño128a,128b, E. Coniavitis51, S.H. Connell147b, I.A. Connelly87, S. Constantinescu28b,G. Conti32, F. Conventi106a,n, A.M. Cooper-Sarkar122,F. Cormier171,K.J.R. Cormier161,M. Corradi134a,134b_{, E.E. Corrigan}84_,

F. Corriveau90,o, A. Cortes-Gonzalez32,M.J. Costa170, D. Costanzo141, G. Cottin30, G. Cowan80,

B.E. Cox87,K. Cranmer112,S.J. Crawley56,R.A. Creager124, G. Cree31, S. Crépé-Renaudin57,F. Crescioli83, M. Cristinziani23,V. Croft112, G. Crosetti40a,40b,A. Cueto85, T. Cuhadar Donszelmann141,

A.R. Cukierman145, J. Cummings179, M. Curatolo50, J. Cúth86,S. Czekierda42,P. Czodrowski32,

G. D’amen22a,22b,S. D’Auria56,L. D’eramo83,M. D’Onofrio77, M.J. Da Cunha Sargedas De Sousa128a,128b, C. Da Via87, W. Dabrowski41a, T. Dado146a,S. Dahbi137e, T. Dai92,O. Dale15, F. Dallaire97,

C. Dallapiccola89, M. Dam39,J.R. Dandoy124,M.F. Daneri29,N.P. Dang176,e,N.S. Dann87, M. Danninger171,M. Dano Hoffmann138,V. Dao32, G. Darbo53a,S. Darmora8,J. Dassoulas3, A. Dattagupta118,T. Daubney45,W. Davey23,C. David45, T. Davidek131,D.R. Davis48,P. Davison81, E. Dawe91,I. Dawson141, K. De8,R. de Asmundis106a, A. De Benedetti115, S. De Castro22a,22b, S. De Cecco83,N. De Groot108, P. de Jong109,H. De la Torre93,F. De Lorenzi67, A. De Maria58, D. De Pedis134a, A. De Salvo134a,U. De Sanctis135a,135b,A. De Santo151, K. De Vasconcelos Corga88, J.B. De Vivie De Regie119,C. Debenedetti139,D.V. Dedovich68, N. Dehghanian3, I. Deigaard109, M. Del Gaudio40a,40b, J. Del Peso85, D. Delgove119, F. Deliot138,C.M. Delitzsch7, A. Dell’Acqua32, L. Dell’Asta24, M. Della Pietra106a,106b, D. della Volpe52,M. Delmastro5, C. Delporte119,P.A. Delsart57, D.A. DeMarco161, S. Demers179, M. Demichev68,S.P. Denisov132, D. Denysiuk138, D. Derendarz42, J.E. Derkaoui137d,F. Derue83,P. Dervan77,K. Desch23, C. Deterre45, K. Dette161,M.R. Devesa29, P.O. Deviveiros32,A. Dewhurst133,S. Dhaliwal25, F.A. Di Bello52,A. Di Ciaccio135a,135b,L. Di Ciaccio5, W.K. Di Clemente124,C. Di Donato106a,106b,A. Di Girolamo32,B. Di Micco136a,136b,R. Di Nardo32, K.F. Di Petrillo59, A. Di Simone51, R. Di Sipio161,D. Di Valentino31, C. Diaconu88, M. Diamond161, F.A. Dias39,M.A. Diaz34a, J. Dickinson16,E.B. Diehl92,J. Dietrich17,S. Díez Cornell45,A. Dimitrievska16, J. Dingfelder23,P. Dita28b,S. Dita28b,F. Dittus32,F. Djama88,T. Djobava54b,J.I. Djuvsland60a,

M.A.B. do Vale26c, M. Dobre28b,D. Dodsworth25,C. Doglioni84,J. Dolejsi131, Z. Dolezal131,

M. Donadelli26d, S. Donati126a,126b, J. Donini37,J. Dopke133, A. Doria106a, M.T. Dova74,A.T. Doyle56, E. Drechsler58,E. Dreyer144,M. Dris10,Y. Du36a, J. Duarte-Campderros155, F. Dubinin98,A. Dubreuil52, E. Duchovni175, G. Duckeck102, A. Ducourthial83,O.A. Ducu97,p,D. Duda109, A. Dudarev32,

A.Chr. Dudder86,E.M. Duffield16, L. Duflot119,M. Dührssen32, C. Dulsen177, M. Dumancic175, A.E. Dumitriu28b,q, A.K. Duncan56, M. Dunford60a, A. Duperrin88,H. Duran Yildiz4a,M. Düren55,

A. Durglishvili54b,D. Duschinger47,B. Dutta45,D. Duvnjak1,M. Dyndal45, B.S. Dziedzic42,C. Eckardt45, K.M. Ecker103, R.C. Edgar92,T. Eifert32,G. Eigen15, K. Einsweiler16, T. Ekelof168,M. El Kacimi137c, R. El Kosseifi88, V. Ellajosyula88, M. Ellert168,F. Ellinghaus177,A.A. Elliot172,N. Ellis32,J. Elmsheuser27, M. Elsing32, D. Emeliyanov133, Y. Enari157, J.S. Ennis173,M.B. Epland48,J. Erdmann46, A. Ereditato18, S. Errede169, M. Escalier119,C. Escobar170, B. Esposito50, O. Estrada Pastor170,A.I. Etienvre138, E. Etzion155,H. Evans64, A. Ezhilov125,M. Ezzi137e, F. Fabbri22a,22b,L. Fabbri22a,22b,V. Fabiani108, G. Facini81,R.M. Fakhrutdinov132, S. Falciano134a, R.J. Falla81,J. Faltova131, Y. Fang35a,M. Fanti94a,94b, A. Farbin8,A. Farilla136a,E.M. Farina123a,123b,T. Farooque93, S. Farrell16, S.M. Farrington173,

P. Farthouat32,F. Fassi137e, P. Fassnacht32,D. Fassouliotis9, M. Faucci Giannelli49, A. Favareto53a,53b, W.J. Fawcett122, L. Fayard119, O.L. Fedin125,r, W. Fedorko171, M. Feickert43, S. Feigl121,L. Feligioni88, C. Feng36a, E.J. Feng32,M. Feng48, M.J. Fenton56,A.B. Fenyuk132, L. Feremenga8,

P. Fernandez Martinez170,J. Ferrando45,A. Ferrari168, P. Ferrari109,R. Ferrari123a,

D.E. Ferreira de Lima60b, A. Ferrer170, D. Ferrere52,C. Ferretti92,F. Fiedler86,A. Filipˇciˇc78, F. Filthaut108, M. Fincke-Keeler172,K.D. Finelli24,M.C.N. Fiolhais128a,128c,s, L. Fiorini170,C. Fischer13,J. Fischer177, W.C. Fisher93,N. Flaschel45, I. Fleck143,P. Fleischmann92, R.R.M. Fletcher124, T. Flick177, B.M. Flierl102, L.M. Flores124,L.R. Flores Castillo62a,N. Fomin15, G.T. Forcolin87, A. Formica138, F.A. Förster13,

A. Forti87,A.G. Foster19, D. Fournier119, H. Fox75,S. Fracchia141, P. Francavilla126a,126b, M. Franchini22a,22b, S. Franchino60a,D. Francis32,L. Franconi121,M. Franklin59,M. Frate166, M. Fraternali123a,123b, D. Freeborn81, S.M. Fressard-Batraneanu32,B. Freund97,W.S. Freund26a, D. Froidevaux32, J.A. Frost122, C. Fukunaga158, T. Fusayasu104, J. Fuster170, O. Gabizon154,

A. Gabrielli22a,22b,A. Gabrielli16, G.P. Gach41a,S. Gadatsch52,S. Gadomski80,G. Gagliardi53a,53b, L.G. Gagnon97,C. Galea108,B. Galhardo128a,128c,E.J. Gallas122,B.J. Gallop133,P. Gallus130, G. Galster39, K.K. Gan113, S. Ganguly175, Y. Gao77,Y.S. Gao145,g, F.M. Garay Walls34a, C. García170,