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Physics Letters B 780 (2018) 578–602

Contents lists available atScienceDirect

Physics

Letters

B

www.elsevier.com/locate/physletb

Measurement

of

the

cross

section

for

isolated-photon

plus

jet

production

in

pp collisions

at

s

=

13 TeV

using

the

ATLAS

detector

.

The

ATLAS

Collaboration



a

r

t

i

c

l

e

i

n

f

o

a

b

s

t

r

a

c

t

Articlehistory:

Received30December2017

Receivedinrevisedform27February2018 Accepted13March2018

Availableonline15March2018 Editor: W.-D.Schlatter

The dynamicsofisolated-photonproductioninassociation withajetinproton–proton collisions ata centre-of-massenergyof13 TeVarestudiedwiththeATLASdetectorattheLHCusingadatasetwithan integratedluminosityof3.2 fb−1.Photonsarerequiredtohavetransverseenergiesabove125 GeV.Jets areidentifiedusingtheanti-kt algorithmwithradiusparameterR=0.4 andrequiredtohavetransverse

momenta above 100 GeV. Measurements ofisolated-photon plus jet cross sections are presented as functionsoftheleading-photontransverseenergy,theleading-jettransversemomentum,theazimuthal angularseparation betweenthe photonand the jet, thephoton–jet invariant massand the scattering angleinthephoton–jet centre-of-masssystem.Tree-levelplusparton-showerpredictionsfrom Sherpa and Pythia aswellasnext-to-leading-orderQCDpredictionsfrom Jetphox and Sherpa arecomparedto themeasurements.

©2018TheAuthor.PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense (http://creativecommons.org/licenses/by/4.0/).FundedbySCOAP3.

1. Introduction

Theproductionofprompt photonsinassociation withatleast onejetinproton–proton(pp)collisionsprovidesatestingground forperturbativeQCD(pQCD).In pp collisions,allphotonsthatare notsecondariesfromhadrondecaysareconsideredtobe“prompt”. Themeasurementsofangularcorrelationsbetweenthephotonand thejet canbe usedto probethedynamicsofthe hard-scattering process. The dominant source in pp collisions at the LHC is the

qg

q

γ

process. Thesemeasurements are alsousefulfortuning MonteCarlo(MC)modelsandtestingt-channelquarkexchange [1,

2].Furthermore,precisemeasurementsoftheseprocessesvalidate thegeneratorsusedforbackgroundstudiesinsearchesforphysics beyond the Standard Model which involve photons, such as the search for new phenomena in final states with a photon and a jet [3,4].

The productionof pp

γ

+

jet

+

X events proceedsvia two processes: direct, in which the photon originates from the hard process, andfragmentation, in which thephoton arisesfromthe fragmentationofacolouredhightransversemomentum1 (pT)

par- E-mailaddress:atlas .publications @cern .ch.

1 ATLASusesaright-handed coordinatesystemwith itsoriginat thenominal

interactionpoint(IP)inthecentreofthedetectorandthez-axisalongthebeam pipe.Thex-axispointsfromtheIPtothecentreoftheLHCring,andthe y-axis

pointsupwards.Cylindricalcoordinates(r,φ)areusedinthetransverseplane,φ beingtheazimuthalanglearoundthez-axis.Thepseudorapidityisdefinedinterms ofthepolarangleθasη= −ln tan(θ/2).Theangulardistanceismeasuredinunits ofR≡(η)2+ (φ)2.Therapidityisdefinedasy=0.5ln[(E+p

z)/(Epz)],

ton [5,6].Thedirectandfragmentationcontributionsareonlywell defined at leading order (LO) in QCD; at higher orders this dis-tinctionisnolongerpossible.Thesetwoprocessesexhibitdistinct behaviours in the observables considered here. Precise measure-mentstesttheinterplayofdirectandfragmentationprocesses.

Measurements of prompt-photon production in a final state with accompanying hadrons necessitate an isolation requirement onthephotontoavoidthelargecontributionfromneutral-hadron decaysintophotons.Theproductionofisolatedphotonsin associ-ation withjetsin pp collisionsat

s

=

7 and8 TeV was studied by theATLAS [1,2,7] andCMS [8–10] Collaborations.Theincrease inthecentre-of-massenergyofpp collisionsattheLHCto13 TeV allows theexploration ofthedynamicsofphoton

+

jet production inanewregime withthegoaloftestingthepQCDpredictionsat higherenergytransfers thanachievedbefore.Itisalsopossibleto investigate whetherthe data in the newenergy regime are well described by the predictions of parton-shower event generators, suchas Sherpa [11] and Pythia [12].

The dynamics of the underlying processes in 2

2 hard collinear scattering can be investigated using the variable

θ

∗, wherecos

θ

tanh

(

y

/

2

)

and



y isthedifference betweenthe rapidities of the two final-state particles. The variable

θ

∗ coin-cides withthe scatteringpolarangle inthecentre-of-massframe forcollinearscatteringofmasslessparticles,anditsdistributionis sensitivetothespinoftheexchangedparticle.Forprocesses

dom-whereE istheenergyandpzisthez-componentofthemomentum,andtransverse

energyisdefinedasET=E sinθ. https://doi.org/10.1016/j.physletb.2018.03.035

0370-2693/©2018TheAuthor.PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense(http://creativecommons.org/licenses/by/4.0/).Fundedby SCOAP3.

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inatedbyt-channelgluonexchange,suchasdijetproductioninpp

collisions,thedifferentialcrosssectionbehavesas

(

1

− |

cos

θ

|)

−2

when

|

cos

θ

|

1.Incontrast,processesdominatedby t-channel

quark exchange are expected to exhibit a

(

1

− |

cos

θ

|)

−1 be-haviour when

|

cos

θ

|

1. This fundamental prediction of QCD can be tested in photon plus jet production in pp collisions.

Thedirect-photoncontribution,dominatedbyt-channelquark ex-change,isexpectedtoexhibita

(

1

− |

cos

θ

|)

−1dependencewhen

|

cos

θ

|

1,whereasthatoffragmentationprocessesispredicted tobethesameasindijetproduction,namely

(

1

− |

cos

θ

|)

−2.For bothprocesses, there arealso s-channel contributionswhich are, however,non-singularwhen

|

cos

θ

|

1.Asa result,a measure-mentof the crosssection forprompt-photon plus jet production asa functionof

|

cos

θ

|

providesa handleontherelative contri-butionsofthedirectandfragmentationcomponentsaswellasthe possibilityoftestingthedominanceoft-channelquarkexchange.

The results presented here include a study of the kinematics ofthephotonplus one-jet systemviameasurements ofthecross sectionsasfunctionsoftheleading-photontransverseenergy(EγT) andtheleading-jet transverse momentum(pjet-leadT ). The dynam-icsof the photon plus one-jet systemare studied by measuring theazimuthalangularseparationbetweentheleadingphotonand theleading jet (

γ−jet),the invariant massofthe leading pho-ton and the leading jet (mγ−jet) and cos

θ

∗. The distribution in

−jet ispredictedtobemonotonicallydecreasinginQCD dueto theabsenceofresonancesthatdecayintoaphotonandajet.The analysisisperformedusing3

.

2 fb−1 of

s

=

13 TeV pp collision datarecordedby ATLAS.Next-to-leading-order(NLO)QCD predic-tions from Jetphox [13,14] and Sherpa as well asthe tree-level predictions of Pythia and Sherpa arecompared to the measure-ments.

2. ATLASdetector

The ATLAS detector [15] is a multi-purpose detector with a forward–backward symmetric cylindrical geometry. It consists of an inner trackingdetectorsurrounded by a thinsuperconducting solenoid, electromagneticandhadroniccalorimeters,anda muon spectrometer incorporating three large superconducting toroid magnets. The inner-detector system is immersed in a 2 T axial magneticfield andprovidescharged-particletrackingintherange

|

η

|

<

2

.

5. The high-granularitysilicon pixel detectoris closest to theinteractionregionandprovidesfourmeasurements pertrack; theinnermostlayer,knownastheinsertableB-layer [16],provides high-resolutionhitsatsmallradiustoimprovethetracking perfor-mance. The pixel detector is followed by the silicon microstrip tracker, which typically provides four three-dimensional space pointmeasurementspertrack.Thesesilicondetectorsare comple-mentedby thetransitionradiationtracker,whichenablesradially extended track reconstruction up to

|

η

|

=

2

.

0. The calorimeter system covers the range

|

η

|

<

4

.

9. Within the region

|

η

|

<

3

.

2, electromagnetic(EM) calorimetry is providedby barreland end-caphigh-granularitylead/liquid-argon(LAr)EMcalorimeters,with anadditionalthinLArpresamplercovering

|

η

|

<

1

.

8 tocorrectfor energylossinmaterialupstreamofthecalorimeters;for

|

η

|

<

2

.

5 theEMcalorimeterisdividedintothreelayers indepth.Hadronic calorimetryisprovidedbyasteel/scintillator-tilecalorimeter, seg-mented into three barrel structures within

|

η

|

<

1

.

7, and two copper/LAr hadronic endcap calorimeters, which cover the re-gion 1

.

5

<

|

η

|

<

3

.

2. The solid-angle coverage is completed out to

|

η

|

=

4

.

9 withforwardcopper/LArandtungsten/LArcalorimeter modules,whichareoptimisedforEMandhadronicmeasurements, respectively. Events are selected using a first-level trigger imple-mentedincustom electronics,whichreducesthemaximumevent rateof 40 MHz to a design value of 100 kHz using a subset of

detector information.Software algorithms withaccess tothe full detector information are then used in the high-level trigger to yieldarecordedeventrateofabout1 kHz [17].

3. DatasampleandMonteCarlosimulations

The data used inthis analysiswere collected withthe ATLAS detectorduringthe pp collisionrunningperiodof2015,whenthe LHC operated with a bunch spacing of 25 ns and at a centre-of-massenergyof 13 TeV.Onlyevents takenduring stablebeam conditions andsatisfying detectorand data-quality requirements, which include the calorimeters and inner tracking detectors be-ing innominaloperation, are considered.The average numberof

pp interactionsper bunchcrossing inthedatasetis 13.Thetotal

integratedluminosity ofthecollected sampleis 3

.

16

±

0

.

07 fb−1. Theuncertaintyintheintegratedluminosityis2

.

1% andisderived, followingamethodologysimilartothatdetailedinRef. [18],from a calibration of the luminosity scale using x– y beam-separation

scansperformedinAugust2015.

Samples of MC events were generated to study the charac-teristics of signal events. The MC programs Pythia 8.186 and Sherpa2.1.1 were usedtogenerate thesimulatedevents.Inboth generators,thepartonicprocesseswere simulatedusingtree-level matrixelements,withtheinclusionofinitial- andfinal-state par-tonshowers.Fragmentationintohadronswasperformedusingthe Lund stringmodel [19] inthecaseof Pythia,andin Sherpa bya modifiedversion oftheclustermodel [20].TheLONNPDF2.3 [21] partondistributionfunctions(PDF) setwasused for Pythia while the NLO CT10 [22] PDF set was usedfor Sherpa toparameterise the proton structure. Both samples include a simulation of the underlying event (UE). The event-generator parameters were set accordingtotheATLAS2014tuneseries(A14tune)for Pythia [23] andtothetunedevelopedinconjunctionwiththeNLO CT10PDF set for Sherpa. The Pythia simulation of the signal includes LO photon-plus-jetevents fromboth directprocesses (the hard sub-processes qg

q

γ

and qq

¯

g

γ

, called the “hard” component) and photon bremsstrahlung in LO QCD dijet events (called the “bremsstrahlung” component). The bremsstrahlung component is modelledby final-stateQEDradiationarisingfromcalculationsof all 2

2 QCDprocesses. Intheparticle-level phasespaceof the presentedmeasurements thefractionofthebremsstrahlung com-ponent decreases from 35% at T

=

125 GeV to 15% at T

=

1 TeV. The Sherpa samples were generated with LO matrix ele-ments forphoton-plus-jetfinalstateswithup tothree additional partons (2

n processes with n from 2 to 5); the matrix el-ements were merged with the Sherpa parton shower using the ME+PS@LO prescription [24]. The bremsstrahlung component is accounted for in Sherpa through the matrix elements of 2

n

processeswithn

3.In thegeneration ofthe Sherpa samples,a requirement on the photon isolation at the matrix-element level wasimposedusingthecriteriondefinedinRef. [25].Thiscriterion, commonlycalledFrixione’scriterion, requiresthetotal transverse energy inside a cone of size

V

around the generated final-state photon,excluding thephotonitself,tobe belowa certain thresh-old, Emax

T

(V)

=



E

γ

T

((

1

cos

V)/(

1

cos

R))

n,forall

V < R

.The parameters forthe threshold were chosen to be

R

=

0

.

3, n

=

2 and



=

0

.

025.The Sherpa predictionsfromthiscomputationare referredtoasLO Sherpa.

All the samplesof generatedevents were passed through the Geant4-based [26] ATLASdetectorandtriggerfullsimulation pro-grams [27]. They are reconstructed and analysed withthe same program chain as the data. Pile-up from additional pp collisions

inthe sameand neighbouringbunch crossingswas simulatedby overlayingeachMCeventwithavariablenumberofsimulated in-elastic pp collisionsgeneratedusing Pythia 8.153withtheATLAS

(3)

580 The ATLAS Collaboration / Physics Letters B 780 (2018) 578–602

setoftuned parametersforminimumbias events(A2tune) [28]. The MCevents areweighted to reproducethe distributionof the averagenumberofinteractionsperbunchcrossing(



μ



)observed inthedata,referredtoas“pile-upreweighting”.Inthisprocedure, the



μ



valuefromthedataisdividedby afactorof1

.

16

±

0

.

07, a rescalingwhichmakesthenumberofreconstructedprimary ver-ticesagreebetterbetweendataandsimulationandreproducesthe visiblecross sectionof inelastic pp collisions asmeasured inthe data [29].

4. Eventselection

Events were recorded using a single-photon trigger, with a transverse energy threshold of 120 GeV and “loose” identifica-tionrequirementsbasedontheshowershapesinthesecondlayer ofthe EM calorimeteras well as onthe energy leaking intothe hadroniccalorimeterfromtheEMcalorimeter [17].Eventsare re-quiredtohaveareconstructedprimaryvertex.Ifmultipleprimary verticesarereconstructed,theonewiththehighestsumofthep2T

oftheassociatedtracksisselectedastheprimaryvertex.

Photon candidates are reconstructed from clusters of energy deposited in the EM calorimeter and classified [30] as uncon-vertedphotons(candidateswithoutamatchingtrackormatching reconstructed conversion vertex in the inner detector) or con-vertedphotons(candidateswithamatchingreconstructed conver-sion vertexor a matchingtrack consistent withoriginating from a photon conversion). The measurement of the photon energyis based on the energy collected in calorimeter cells in an area of size



η

× φ =

0

.

075

×

0

.

175 in the barrel and 0

.

125

×

0

.

125 in the endcaps. A dedicated energy calibration [31] is then ap-plied to thecandidates to account forupstream energy loss and bothlateral andlongitudinal leakage.The photonidentificationis basedprimarilyonshowershapesinthecalorimeter [30].An ini-tialselection is derived using the informationfrom the hadronic calorimeter andthe lateral shower shape in the second layer of theEMcalorimeter,wheremostofthephotonenergyiscontained. Thefinaltightselectionappliesstringentcriteria [30] tothesame variablesusedintheinitialselection,separatelyforconvertedand unconvertedphotoncandidates.Italsoplacesrequirementsonthe showershapeinthefinelysegmentedfirstcalorimeterlayerto en-surethe compatibility of the measured shower profile with that originatingfromasinglephotonimpacting thecalorimeter.When applyingthephotonidentificationcriteriatosimulatedevents, cor-rections are made forsmall differences in the average values of the shower-shape variables between dataand simulation. Events withatleastonephotoncandidatewithcalibrated T

>

125 GeV, wherethe trigger is maximally efficient,and

|

η

γ

|

<

2

.

37 are

se-lected.Candidatesintheregion1

.

37

<

|

η

γ

|

<

1

.

56,whichincludes

thetransitionregionbetweenthebarrelandendcapcalorimeters, are not considered. The photon candidate is required to be iso-latedbasedon theamount oftransverse energyinsidea cone of size



R

=

0

.

4 inthe

η

φ

planearoundthephotoncandidate, ex-cludingan area ofsize



η

× φ =

0

.

125

×

0

.

175 centred onthe photon. The isolation transverse energy is computed from topo-logical clusters of calorimeter cells [32] and is denoted by Eiso

T . Topologicalclustersare built fromneighbouring calorimetercells containingenergysignificantlyabovea noisethresholdthatis es-timated from measurements of calorimeter electronic noise and simulatedpile-up noise. The measured value of Eiso

T iscorrected forthe expected leakage of thephoton energyinto the isolation coneas well asfortheestimatedcontributions fromthe UE and pile-up [33,34]. The corrections forpile-up andthe UE are com-putedsimultaneouslyonanevent-by-eventbasisusingthejet-area method [35,36] asfollows:thekjetalgorithm [37,38] withjet ra-diusR

=

0

.

5 isusedtoreconstructalljets,takingtopological

clus-tersofcalorimetercellsasinput;noexplicittransversemomentum threshold is applied. The ambient transverse energy density for the event (

ρ

), from pile-up and the UE, is computed using the medianof thedistributionof theratioofthe jet’s transverse en-ergytoitsarea.Finally,

ρ

ismultipliedbytheareaoftheisolation conetocomputethecorrectiontoEisoT .Thecombinedcorrectionis typically2 GeV anddependsweaklyon T.Inaddition,for simu-latedevents,data-drivencorrectionsto EisoT are appliedsuch that the peak position in the Eiso

T distribution coincides in data and simulation. Afterall these corrections, EisoT is requiredto be less than EisoT,cut

4

.

2

·

10−3

·

T

+

4

.

8GeV [39].Theisolation require-mentsignificantlyreducesthemainbackground,whichconsistsof multi-jet events whereone jet typically contains a

π

0 or

η

me-son that carries most of the jet energy and is misidentified as a photon because it decays intoan almost collinearphoton pair. A smallfractionoftheeventscontainmorethanonephoton candi-datesatisfyingtheselectioncriteria.Insuchevents,thehighest-EγT (leading)photonisconsideredforfurtherstudy.

Jetsare reconstructedusingtheanti-kt algorithm [40,41] with

a radius parameter R

=

0

.

4, using topological clusters as input. The calorimeter cell energies are measured atthe EM scale, cor-responding to the energy deposited by electromagnetically inter-actingparticles.Thejetfour-momentaarecomputedfromthesum ofthejet-constituentfour-momenta,treatingeachasafour-vector with zero mass. The jets are then further calibrated using the method described in Ref. [42] and these jets are referred to as detector-leveljets.The four-momentumofeach jetisrecalculated topointtotheselectedprimaryvertexoftheeventratherthanthe centreofthedetector.ThecontributionfromtheUEandpile-upis then subtracted on a jet-by-jet basis using the jet-area method. A jet-energy calibrationisderived fromMC simulations asa cor-rectionrelatingthecalorimeterresponsetothetruejetenergy.To determine thesecorrections, thejet reconstruction procedure ap-plied to the topological clusters is alsoapplied to the generated stable particles, which are defined as those witha decaylength of c

τ

>

10 mm, excluding muons and neutrinos; these jets are referred toasparticle-leveljets.Inaddition,sequentialjet correc-tions, derived from MC simulated events andusing global prop-erties ofthe jet such astracking information,calorimeterenergy depositsandmuonspectrometerinformation,areapplied [43]. Fi-nally, thedetector-leveljetsarefurthercalibratedwithadditional correction factors derived in situfrom a combinationof

γ

+

jet,

Z

+

jet andmulti-jetpT balancemethods [44,45].2

Jetsreconstructedfromcalorimetersignalsnotoriginatingfrom

a pp collisionarerejectedby applyingjet-qualitycriteria [45,46].

These criteriasuppressspurious jetsfrom electronic noisein the calorimeter, cosmic rays andbeam-related backgrounds. Remain-ingjetsarerequiredtohavecalibratedtransversemomentagreater than 60 GeV and rapidity

|

yjet

|

<

2

.

37. Jetsoverlapping withthe candidate photon are not considered if the jet axis lies within a cone of size



R

=

0

.

8 around the photon candidate; this re-quirementpreventsanyoverlapbetweenthephotonisolationcone (



R

=

0

.

4) andthe jet cone (



R

=

0

.

4). Finally, theeventis re-tained if thejet withhighesttransverse energy (leadingjet) has

pjetT

>

100 GeV.

Thetotalnumberofdataeventsselectedbyusingthe require-ments discussed aboveis 895726.Thissample ofeventsis used to measure the cross section as a function of T, pjet-leadT and

γ−jet.Forthemeasurements ofthecrosssectionsasfunctions

2 The effectofthecorrelation betweenthe eventsusedinthe insitu γ+jet

analysisandtheeventsselectedherehasanegligibleeffectontheexperimental uncertaintiesassociatedtothemeasurements.

(4)

Fig. 1. Eiso

T distributionfortight(blackdots)andnon-tight(dashedhistogram,normalisedaccordingtothefit,seetext)photoncandidatesindatawith|ηγ|<0.6 indifferent

T regions.TheMCsimulationofthesignalusing Pythia isalsoshown(dottedhistogram).ThesolidhistogramisthesumofthecontributionsoftheMCsimulationofthe

signalusing Pythia andthatofthenon-tightphotoncandidatesnormalisedaccordingtothefit. of−jetand

|

cos

θ

|

,theadditionalconstraints

|

η

γ

+

yjet-lead

|

<

2

.

37,

|

cos

θ

|

<

0

.

83 and −jet

>

450 GeV are imposed to re-movethebias [1,2] duetotherapidityandtransverse-momentum requirementsonthephotonandthejet3;thenumberofevents

se-lectedinthedataaftertheseadditionalrequirementsis137738. 5. Backgroundestimationandsignalextraction

Afterthe requirements on photon identification andisolation areappliedto thesampleofevents,thereisstill aresidual back-groundcontribution,whicharisesprimarilyfromjetsidentifiedas photons in multi-jet events. This background contribution is es-timated andsubtracted bin-by-bin using a data-driven technique whichmakes useofthe sametwo-dimensional sidebandmethod employedinapreviousanalysis [47].Inthisapproach,thephoton isclassifiedas:

“Isolated”,ifEisoT

<

EisoT,cut.

“Non-isolated”,ifEisoT

>

EisoT,cut

+

2GeV and EisoT

<

50 GeV.The non-isolated region is separated by 2 GeV from the isolated regiontoreducethesignalcontamination.Theupperboundis appliedtoavoidhighlynon-isolatedphotons.4

“Tight”,ifitsatisfiesthetightphotonidentificationcriteria.

“Non-tight”, ifit failsat leastone of fourtight requirements ontheshower-shapevariablescomputedfromtheenergy de-positsinthefirstlayeroftheEMcalorimeter,butsatisfiesthe tightrequirementonthetotallateralshowerwidthinthefirst layerandalltheothertightidentificationcriteriainother lay-ers [30].

Thedistributions in EisoT fortightandnon-tight photon candi-dateswith

|

η

γ

|

<

0

.

6 inthedataareshownseparatelyinFig.1for

tworegions in T.TheMC simulationoftheprompt-photon sig-nalusing Pythia isalsoshown.Afitofthesumofthedistributions ofthe Pythia signal photonsandthenon-tight photoncandidates

3 Thefirsttwoconstraintsavoidthebiasinduced byrequirementsonηγ and

yjet-lead,yieldingslicesofcos

θ∗withthesamelengthalongtheηγ+yjet-leadaxis.

ThethirdconstraintavoidsthebiasduetotheT>125 GeV requirement. 4 Inthisway,thedeterminationofthesignalyielddoesnotdependonthe

de-scriptionbytheMCgeneratorsofthedistributionofEiso

T forpromptphotonswith

highvaluesofEiso T .

tothedistributionofthetightphotoncandidatesisalsoincluded. A clearsignalofpromptphotonscentredat EisoT aboutzerois ob-served.

Fortheestimationofthebackgroundcontaminationinthe sig-nalregionatwo-dimensionalplaneisformedby ETisoandabinary variable(“tight”vs. “non-tight”photoncandidate)sincethesetwo variables are expected to be largely uncorrelatedfor background events.Inthisplane,fourregionsare defined:the“signal”region ( A), containing tight and isolated photon candidates; the “non-isolated”backgroundcontrolregion(B),containingtightand non-isolatedphotoncandidates;the“non-tight”backgroundcontrol re-gion(C ),containingisolatedandnon-tightphotoncandidates;the background control region containing non-isolated and non-tight photoncandidates(D).

Thesignal yieldNsigA inregion A isestimatedby usingthe re-lation

NsigA

=

NA

Rbg

· (

NB

fBNsigA

)

·

(

NC

fCNsigA

)

(

ND

fDNsigA

)

,

(1)

whereNK,with K

=

A

,

B

,

C

,

D,isthenumberofeventsinregion K andRbg

=

NbgA

·

NbgD

/(

NbgB

·

NCbg

)

istheso-calledbackground cor-relationandistakenasRbg

=

1 forthenominalresults; NbgK with

K

=

A

,

B

,

C

,

D is the unknown number of background events in each region. Equation (1) takes into account the expected num-ber of signal events in each of the three backgroundcontrol re-gions (NsigK ) via the signal leakage fractions, fK

=

NsigK

/

NsigA with K

=

B

,

C

,

D,whichareestimatedusingtheMCsimulationsofthe signal.

The only assumption underlying Eq. (1) is that the isolation andidentificationvariablesareuncorrelatedforbackgroundevents, thus Rbg

=

1.Thisassumption isverified indata typicallywithin

±

10% invalidationregions,5 whicharedominatedbybackground. Deviations of Rbg from unity in the validation regions, after ac-countingforsignal leakage usingeither the Pythia orLO Sherpa simulations,are propagated throughEq. (1) andtakenas system-atic uncertainties.The signal purity,definedas NsigA

/

NA,isabove

90% in all bins of the measured distributions. The use of Pythia

5 ThevalidationregionsaredefinedwithinthecontrolregionsB andD by

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582 The ATLAS Collaboration / Physics Letters B 780 (2018) 578–602

Table 1

Summaryoftherequirementsatparticlelevelthatdefinethefiducialphase-space regionofthemeasurements.

Requirements on photons T>125 GeV,|ηγ| <2.37 (excluding 1.37<|ηγ| <1.56) Eiso T <4.2·10−3·E γ T+10 GeV Requirements on jets

anti-ktalgorithm with R=0.4

the leading jet within|yjet| <2.37 andRγ−jet>0.8 is selected

pjet-leadT >100 GeV

UE subtraction using kalgorithm with R=0.5 (cf. Section4) Additional requirements for dσ/dmγ−jetand dσ/d|cosθ|

|ηγ+yjet-lead| <2

.37,|cosθ| <0.83 and mγ−jet

>450 GeV

orLO Sherpa toextract thesignal leakage fractionsleadto simi-larsignalpurities;thedifferenceinthesignalpurityistakenasa systematicuncertainty.

Thebackgroundfromelectronsmisidentifiedasphotons,mainly producedinDrell–YanZ(∗)

/

γ

e+e−andW(∗)

e

ν

processes, isalsostudied.Suchmisidentifiedelectronsarelargelysuppressed by the photon selection. This backgroundis estimated using MC samplesoffullysimulatedeventsandfoundtobenegligibleinthe phase-spaceregionoftheanalysispresentedhere.Theseprocesses weresimulatedusingthe Sherpa 2.2.1generator.Matrix-elements werecalculatedforuptotwoadditionalpartonsatNLOandupto fourpartonsatLO [48,49].

6. Fiducialphasespaceandunfolding

6.1. Fiducialphasespace

The crosssections are unfolded toa phase-space region close to theapplied eventselection. The fiducialphase-space regionis defined atthe particle level. A summary of the requirements at particle level that define the fiducial phase-space region of the measurementsisgiveninTable1.Thecrosssectionsasfunctions of

|

cos

θ

|

and−jet aremeasured inafiducialphase-space re-gion withadditional requirements,asdetailed inthe last row of Table 1. The particle-level isolation requirement on the photon is builtby summing the transverse energyof all stable particles (seeSection4), exceptformuonsandneutrinos,inaconeofsize



R

=

0

.

4 aroundthephotondirectionafterthecontributionfrom theUE issubtracted.The sameunderlying-event subtraction pro-cedure used atthe reconstruction level isapplied at theparticle level.The particle-levelrequirement on Eiso

T isoptimised to best matchtheacceptanceatreconstructionlevelusingthe Pythia and LO Sherpa MC samples by comparing the calorimeter isolation transverse energy withthe particle-level isolation transverse en-ergyonanevent-by-eventbasis.Theparticle-levelrequirementon

EisoT thus optimised is EisoT

(

particle

)

<

4

.

2

·

10−3

·

Eγ

T

+

10 GeV; thesamerequirementisobtainedwhether Pythia orLO Sherpa is used.Particle-level jetsarereconstructed usingtheanti-kt jet

al-gorithm withradiusparameter R

=

0

.

4 and are builtfromstable particles,excludingmuonsandneutrinos.Atparticlelevel,the par-ticles associatedwiththe overlaid pp collisions (pile-up)are not considered.

6.2. Unfolding

The distributions ofthe background-subtracted signal yield as functionsofT, pjet-leadT ,

γ−jet,−jetand

|

cos

θ

|

areusedto measurethecorrespondingdifferentialcrosssectionsfor isolated-photon plusjet production.The distributions are unfolded tothe

particle level using MC samples of events via a bin-by-bin tech-nique which corrects for resolution effects andthe efficiency of thephotonandjetreconstructionthroughtheformula

d

σ

dO

(

i

)

=

NsigA

(

i

)

CMC

(

i

)

L



O

(

i

)

,

where d

σ

/

dO

(

i

)

is the crosssection as a function ofobservable

O in bin i, NsigA

(

i

)

isthe number of background-subtracted data events inbin i, CMC

(

i

)

is thecorrection factor inbin i,

L

is the integrated luminosity and



O

(

i

)

is the width of bin i. The cor-rection factors are computed from the MC samples as CMC

(

i

)

=

NMCpart

(

i

)/

NMC

reco

(

i

)

,where NMCpart

(

i

)

is thenumberofeventsthat sat-isfy the kinematic constraints of the phase-space region at the particle level, and NMC

reco

(

i

)

is the number of events which meet alltheselectioncriteriaatthereconstructionlevel.

The distributions of the signal yields as functions of T,

pjet-leadT ,

γ−jet, −jet and

|

cos

θ

|

in data after background subtraction are well described by the LO Sherpa MC simula-tions, butsome differences are observed when compared to the Pythia MC simulations, in particular in the tail of the pjet-leadT distribution.Abetterdescriptionofthedatadistributionsas func-tions of T, pjet-leadT ,

γ−jet, −jet and

|

cos

θ

|

by Pythia is obtained by increasing/decreasing the relative contribution from direct processes with respect to bremsstrahlung processes [1,2]; theresulting Pythia simulationsarereferredtoas Pythia-adjusted simulations.

Theunfoldedcrosssectionsaremeasuredusingthesignal leak-agefractionsfrom Pythia-adjustedsimulationssincetheseinclude an unbiased sample ofnon-isolated photons,6 andthe correction

factors, CMC, fromLO Sherpa sincethesesimulations give some-whatbetter agreementwiththedatadistributionsasfunctionsof

T, pjet-leadT ,

γ−jet,−jet and

|

cos

θ

|

.The correction factors varybetween1

.

08 and1

.

21 dependingontheobservable.The re-sults of the bin-by-bin unfolding procedure are checked withan iterativeBayesianunfoldingmethod [50] basedonLO Sherpa sim-ulations,givingconsistentresults.

7. Uncertaintiesinthecross-sectionmeasurements

Photonenergyscaleandresolution. A detailedassessmentofthe uncertainties in the photon energy scale and resolution is made using the methodreported inRef. [47]. The photon energy scale uncertainties come mostly from calibration studies using 8 TeV data [31],withadditionalsystematicuncertaintiestotakeinto ac-count thedifferencesbetweenthe 2012and2015configurations. The uncertainties are split into independent components to ac-count forcorrelations oftheuncertainties betweendifferent bins of the measured cross sections.The individual sources of uncer-tainty arevaried by

±

1

σ

inthe MC simulations andpropagated through the analysis separately to maintain the full information aboutthecorrelationsoftheuncertainties betweendifferentbins ofthe measured crosssections.Theimpact ofthephoton energy resolutionuncertaintyismuchsmallerthanthatofthephoton en-ergy scaleuncertainty. Theresulting uncertaintyinthemeasured crosssectionsisobtainedbyaddinginquadratureall the individ-ualcomponentsandincreasesfrom1% atT

=

125 GeV to4

.

5% at

T

1

.

5 TeV.

6 IntheLO Sherpa samples,theapplicationoftheFrixione’scriteriontothe

pho-tonisolationatmatrix-elementlevelpreventstheradiatedphotonfrombeingclose toaparton. Inthe Pythia samples,the bremsstrahlungcomponentissimulated withapartonshowerapproachand,asaresult,theradiatedphotoncanbeclose toaparton.

(6)

Jetenergyscaleandresolution. Adetailedassessmentofthe un-certainties in the jet energy scale and resolution is made us-ing the method reported in Ref. [42]. The individual sources of uncertainty [42] are varied by

±

1

σ

in the MC simulations and propagated through the analysis separately, to maintain the full information about the correlations of the uncertainties between different bins of the measured cross sections. The resulting un-certaintyinthemeasured crosssectionsisobtainedbyaddingin quadraturealltheindividualcomponentsandincreasesfrom1

.

9% atpjet-leadT

=

100 GeV to7

.

5% at pjet-leadT

1 TeV.

Parton-showerandhadronisationmodeldependence. Theeffects duetotheparton-showerandhadronisationmodelsonthesignal purityanddetector-to-particle-levelcorrection factorsare studied separately.The effects on the signal purity are estimatedas the differencesobserved between the nominal results andthose ob-tained using either the (non-adjusted) Pythia or LO Sherpa MC samplesforthedeterminationofthesignalleakage fractions.The differencebetweenthe nominalresultsandthose obtainedusing the Pythia-adjustedMCsamplesforthedeterminationofthe un-foldingcorrectionfactorsistakenasasystematicuncertainty.The resultinguncertaintiesinthemeasuredcrosssectionsaretypically smallerthan 2%.

Photonidentification efficiency. The uncertainty in the photon identificationefficiencyisestimatedfromtheeffectofdifferences betweenshower-shape variabledistributions in data and simula-tion.FromthestudiespresentedinRefs. [30,51],thisprocedureis foundtoprovideaconservativeestimateoftheuncertainties.The resultinguncertaintyinthemeasuredcrosssectionsisintherange 1–2%.Theeffectsonthemeasuredcrosssectionsduetothe uncer-taintyinthephotonreconstructionefficiency,whichareevaluated byrepeatingthefullanalysisusingadifferentdetectorsimulation withincreasedmaterialinfrontofthecalorimeter,arefoundtobe negligible.

Photonisolationmodelling. The differences between the nomi-nal results and those obtained without applying the data-driven correctionstoEiso

T insimulatedeventsaretakenassystematic un-certainties inthe measurements dueto the modellingof Eiso

T in theMCsimulation.Theresultinguncertaintyinthemeasuredcross sectionsislessthan 1

.

1%.

Definitionofthebackgroundcontrolregions. The estimation of thebackground contamination inthe signal region isaffected by the choice of background control regions. The control regions B

andD aredefinedby thelowerandupperlimitson Eiso

T andthe choiceofinvertedphotonidentificationvariablesusedinthe selec-tionofnon-tightphotons.Tostudythedependenceonthespecific choices,thesedefinitionsarevariedovera widerange.The lower limit on EisoT inregions B and D isvaried by

±

1 GeV, which is largerthananydifference betweendataandsimulations andstill provides a sufficient sample to perform the data-driven subtrac-tion.Theupperlimiton Eiso

T inregions B andD is removed.The resultinguncertaintyinthemeasured crosssectionsisnegligible. Likewise, thechoice of invertedphoton identificationvariables is varied. The analysis is repeated using differentsets of variables: tighter(looser)identificationcriteriaaredefinedbyapplyingtight requirementstoanextended(restricted)setofshower-shape vari-ables in the first calorimeter layer [30,51]. The resulting uncer-taintyinthemeasuredcrosssectionsissmallerthan1

.

3%. Photonidentificationandisolationcorrelationinthebackground. The photon isolation and identification variables used to define

theplaneinthetwo-dimensionalsidebandmethodtosubtractthe backgroundareassumedtobeindependentforbackgroundevents (Rbg

=

1 in Eq. (1)).Any correlation between thesevariables af-fectstheestimationofthepurityofthesignalsampleandleadsto systematicuncertaintiesinthebackground-subtraction procedure. Arangein Rbgissettocoverthedeviationsfromunitymeasured inthevalidationregions aftersubtracting thesignalleakage with either Pythia-adjustedorLO Sherpa MCsamples.Theresulting un-certaintyinallmeasuredcrosssectionsislessthan 2%.

Pile-up. The uncertainty is estimated by changing the nominal rescaling factor of 1

.

16 to 1

.

09 or 1

.

23 and re-evaluating the reweighting factors. The resulting uncertainty in the measured crosssectionsistypicallylessthan0

.

5%.

Unfoldingprocedure. Theuncertaintyis estimatedbycomparing the nominal results with those obtained by unfolding with LO Sherpa MC samples reweigthed to match the data distributions. Theresulting uncertaintyinthemeasuredcrosssectionsis negli-gible.

The total systematic uncertainty is computed by adding in quadrature the uncertainties from the sources listed above, the statistical uncertainty ofthe MC samples, the uncertainty inthe triggerefficiency(1%)andtheuncertaintyintheintegrated lumi-nosity, which isfullycorrelated betweenall bins ofall the mea-suredcrosssections.Therearelargecorrelationsinthesystematic uncertaintiesacrossbinsofoneobservable,particularlyinthe un-certainties due to the photon and jet energy scales, which are dominant. The total systematicuncertainty, excluding that inthe luminosity,islessthan 5% for T, 4% for

γ−jet, 6% for−jet and 4% for

|

cos

θ

|

andincreases from4% at pjet-leadT

=

100 GeV to10% at pjet-leadT

1

.

5 TeV.Fig.2showsthetotalsystematic un-certainty for each measured cross section, excluding that in the luminosity;thedominantcomponentsareshownseparatelyinthis Figure.Thesystematicuncertaintydominatesthetotal experimen-tal uncertaintyfor T



700 GeV and−jet



1

.

5 TeV,whereas for higher T and −jet values, the statistical uncertainty of the data limits the precision of the measurements. For pjet-leadT ,

γ−jet and

|

cos

θ

|

,thesystematicuncertaintydominatesinthe wholemeasuredrange.

8. Theoreticalpredictions

The NLO pQCD predictions presented in this Letter are com-puted using two programs, namely Jetphox 1.3.1_2 and Sherpa 2.2.2.The Jetphox programincludesafullNLOpQCDcalculationof both thedirectandfragmentationcontributions tothe cross

sec-tion for the pp

γ

+

jet

+

X process. The numberof massless

quark flavours is set to five. The renormalisation scale

μ

R, fac-torisation scale

μ

F and fragmentationscale

μ

f are chosen to be

μ

R

=

μ

F

=

μ

f

=

T [14].Thecalculationsareperformedusingthe MMHT2014 [52] PDFset and the BFG set II of parton-to-photon fragmentation functions [53], both at NLO. The strong coupling constantissetto

α

s

(

mZ

)

=

0

.

120.Thecalculationsareperformed

using a parton-level isolation criterion which requires the total transverseenergyfromthepartonsinsideaconeofsize



R

=

0

.

4 aroundthephotondirectiontobebelow4

.

2

·

10−3

·

Eγ

T

+

10GeV. The NLO pQCD predictions from Jetphox are at the parton level whilethemeasurements are atthe particlelevel.Thus,there can bedifferencesbetweenthetwolevelsconcerning thephoton iso-lationaswellasthephotonandjetfour-momenta.Sincethedata are correctedforpile-upandUE effectsandthedistributions are unfoldedtoaphase-spacedefinitioninwhichtherequirementon

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584 The ATLAS Collaboration / Physics Letters B 780 (2018) 578–602

Fig. 2. Totalrelativesystematicuncertainty(solidlines),excludingthatintheluminositymeasurement,asafunctionofT,p jet-lead

T ,φγ−jet,−jetand|cosθ∗|.Thethree

dominantcontributionsarealsoincludedseparately:thejetenergyscale(dashedlines),thephotonenergyscale(dottedlines)andthephotonidentification(dot-dashed lines).Theshadedbanddisplaystherelativestatisticaluncertainty;forthelastpointinT (mγ−jet)therelativestatisticaluncertaintyis32% (30%).

(8)

EisoT at particle level is applied after subtractionof the UE, it is expectedthatparton-to-hadroncorrectionstotheNLO pQCD pre-dictionsaresmall.Correctionfactorstothe Jetphox predictionsare estimatedby computing the ratio ofthe particle-level cross sec-tionfora Pythia samplewithUE effectstotheparton-levelcross sectionwithoutUEeffects.Thesefactorsareclosetounitywithin

±

5% fortheobservablesstudied,exceptforpjet-leadT



600 GeV;in thisregion,whichisdominatedbythebremsstrahlungcomponent, thefactorscandifferbyupto30% fromunitysincehadronisation ofanearbypartoncansignificantlychangetheparticle-level isola-tioncomparedtotheparton-levelisolation.

The Sherpa 2.2.2 program consistently combines parton-level calculationsof

γ

+ (

1

,

2

)

jet eventsatNLOand

γ

+ (

3

,

4

)

jet events at LO [48,49] supplemented with a parton shower [54] whileavoidingdouble-countingeffects [55].Arequirementonthe photonisolationatthematrix-elementlevelisimposedusing Frix-ione’scriterion with

R

=

0

.

1,n

=

2 and



=

0

.

1.Dynamic factori-sationandrenormalisationscalesareadoptedaswellasa dynam-icalmerging scale with Q

¯

cut

=

20 GeV [56]. The strongcoupling constantissetto

α

s

(

mZ

)

=

0

.

118.Fragmentationintohadronsand

simulationoftheUEareperformedusingthesamemodelsasfor theLO Sherpa samples.Thenext-to-next-to-leading-order(NNLO) NNPDF3.0PDFset [57] isusedinconjunctionwiththe correspond-ing Sherpa tuncorrespond-ing.All the NLO Sherpa predictions are based on theparticle-levelobservablesfromthiscomputationafterapplying therequirementslistedinTable1.

8.1.Uncertaintiesinthepredictions

TheuncertaintyintheNLOpQCDpredictionsfrom Jetphox due to terms beyond NLO is estimated by repeating the calculations using values of

μ

R,

μ

F and

μ

f scaled by the factors 0

.

5 and 2. The three scales are either varied simultaneously, individually or byfixingoneandvaryingtheothertwo.Inallcases,thecondition 0

.

5

μ

A

/

μ

B

2 is imposed,where A

,

B

=

R

,

F

,

f.The final

un-certaintyistakenasthelargestdeviationfromthenominalvalue amongthe14 possiblevariations. Inthe caseoftheNLO Sherpa prediction,whichdoesnotincludethefragmentationcontribution,

μ

Rand

μ

F arevaried asaboveandthelargestdeviationfromthe nominalvalueamongthe6possiblevariationsistakenasthe un-certainty.

TheuncertaintyintheNLOpQCDpredictionsfrom Jetphox due tothechoice ofprotonPDFsis estimatedby repeatingthe calcu-lationsusingthe50 sets fromtheMMHT2014erroranalysis [52] andapplying theHessian method [58] for evaluationof the PDF uncertainties.InthecaseofNLO Sherpa,itisestimatedusing100 replicasfromtheNNPDF3.0analysis [57].

The uncertainty in the NLO pQCD predictions from Jetphox (NLO Sherpa) due to the uncertainty in

α

s is estimated by re-peatingthe calculationsusingtwo additionalsets ofprotonPDFs fromtheMMHT2014(NNPDF3.0)analysis,forwhichdifferent val-uesof

α

s atmZ were assumedin thefits, namely 0

.

118 (0

.

117)

and0

.

122 (0

.

119);inthisway,thecorrelationbetween

α

sandthe PDFsispreserved.

Theuncertaintyintheparton-to-hadroncorrectionisestimated bycomparingthevaluesobtainedusingdifferenttunesof Pythia: theATLAS setoftuned parametersfortheunderlyingevent(tune AU2) [28] with the CTEQ6L1 PDF set [59], the A14 tune with theLO NNPDF2.3PDF set aswell as thetunes inwhich the pa-rametersettings ofthe latter relatedto the modellingof the UE arevaried [23].Larger differencesareobtainedfromthe compari-sonofthetwo centraltunes thanfromthevariations aroundthe A14tune. The nominal correction is takenas theaverage of the correctionsusing the two central tunes, while the uncertaintyis estimatedashalfofthedifferencebetweenthetwocentraltunes.

The dominant theoretical uncertainty is that arising from the terms beyond NLO and, inthe case of Jetphox (NLO Sherpa), is

10% (15–25%)forT,−jetand

|

cos

θ

|

andincreasesfrom5%

(15%)at pjet-leadT

=

130 GeV to30% (30%)forpjet-leadT

=

1

.

5 TeV.In the caseof theNLO Sherpa predictionfor d

σ

/

d

γ−jet,the un-certaintyincreasesfrom10% at

γ−jet

π

to40% at

γ−jet

π

/

2.Theuncertainty inthepredictions of Jetphox (NLO Sherpa) arising from that in the PDFs is



2% (3%) for all observables. The uncertainty arising from the value of

α

s

(

mZ

)

is below 2%

(5%). Theuncertaintyintheparton-to-hadroncorrection isinthe range 1–3% except for pjet-leadT



600 GeV, where it increases to 20% at pjet-leadT

=

1

.

5 TeV; thisuncertaintyisincluded inthe Jet-phox predictions, but not in the caseof NLO Sherpa since it is a particle-level Monte Carlo generator.7 The total theoretical

un-certainty is obtained by adding in quadrature the individual un-certaintieslistedabove and,inthecaseof Jetphox (NLO Sherpa), is 10–15% (15–25%) except for pjet-leadT , where it is in the range 10–40% (15–30%); in the caseof the NLO Sherpa prediction for d

σ

/

d

γ−jet,thetotaluncertaintyis10–40%.

9. Results

The measurements presented here apply to isolated prompt photonswithEisoT

<

4

.

2

·

10−3

·

T

+

10GeV atparticleleveland jetsof hadrons. The measured fiducial cross section for isolated-photonplusone-jetproductioninthephase-spaceregiongivenin Table 1is

σ

meas

=

300

±

10

(

exp

.)

±

6

(

lumi

.)

pb, where “exp.” denotes the sum in quadrature of the statistical and systematic uncertaintiesexcludingthatduetotheluminosityand“lumi.” de-notes the uncertainty due to that in the integrated luminosity. ThefiducialcrosssectionspredictedbyNLO QCD Jetphox (multi-leg NLO QCD plus parton-shower Sherpa) using the MMHT2014 (NNPDF3.0)PDFsetare

σ

Jetphox

=

291+2521

(

scale

)

+23

(

PDF

)

+45

(

α

s

)

±

6

(

non-perturb.

)

pb and

σ

NLOSherpa

=

319+5445

(

scale

)

±

3

(

PDF

)

+−1011

(

α

s

)

pb

,

whichareconsistentwiththemeasurementwithinthetheoretical uncertainties.

Fig.3showstheisolated-photonplusjetcrosssectionsas func-tions of T, pjet-leadT ,

γ−jet,−jet and

|

cos

θ

|

.Themeasured

d

σ

/

dEγT decreases by almost six orders of magnitude over the

T range studied. Values of T up to 1

.

5 TeV are measured. The measured d

σ

/

dpjet-leadT decreases by more than four orders ofmagnitudefrom pjet-leadT

=

100 GeV uptothehighestmeasured value, pjet-leadT

1

.

5 TeV.Themeasurementofd

σ

/

d

γ−jet is re-strictedto

γ−jet

>

π

/

2 toavoidthe phase-spaceregion domi-natedbyphotonproductioninassociationwithamulti-jetsystem. The measured d

σ

/

d

γ−jet increases as

γ−jet increases.The measuredd

σ

/

dmγ−jetdecreasesbymorethanfourordersof mag-nitudeup to thehighestmeasured value,−jet

=

3

.

25 TeV.The measuredd

σ

/

d

|

cos

θ

|

increasesas

|

cos

θ

|

increases.

The tree-level predictions of the Pythia and LO Sherpa MC models are compared to the measurements inFig. 3. These pre-dictionsare normalised to themeasured integratedfiducial cross

7 Anuncertaintyrelatedtothemodelling ofthehadronisationprocessshould

alsobeassignedtotheNLO Sherpa predictions,butnotuneotherthanthedefault oneisavailable.Itisexpectedthattheuncertaintyshouldbeofsimilarsizeasthat evaluatedusing Pythia.

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586 The ATLAS Collaboration / Physics Letters B 780 (2018) 578–602

Fig. 3. Measuredcrosssectionsforisolated-photonplusjetproduction(dots)asfunctionsofT,p jet-lead

T ,φγ−jet,−jetand|cosθ∗|;theobservablesareconstructedusing

theleadingphotonandtheleadingjet.Forcomparison,thetree-levelplusparton-showerpredictionsfromLO Sherpa (solidlines)and Pythia (dashedlines)normalisedto theintegratedmeasuredcrosssections(usingthefactorsindicatedinparentheses)arealsoshown.Thetheoreticaluncertaintiesassociatedwiththetree-levelpredictions arenotincluded.ThebottompartofeachfigureshowstheratiosoftheMCpredictionstothemeasuredcrosssection.Theinner(outer)errorbarsrepresentthestatistical uncertainties(thestatisticalandsystematicuncertaintiesaddedinquadrature).Formostofthepoints,theinnererrorbarsaresmallerthanthemarkersizeand,thus,not visible.

(10)

Fig. 4. Measuredcrosssectionforisolated-photonplusjetproduction(dots)asa functionof|cosθ∗|;theobservableisconstructedusingtheleadingphotonandthe leadingjet.Forcomparison,theLOQCDpredictionsfrom Jetphox,normalisedto theintegratedmeasuredcrosssectionbythefactorsshowninparentheses,ofdirect (dashedlines)andfragmentation(dottedlines)processesareshownseparately.The errorbarsaresmallerthanthemarkersizeand,thus,notvisible.

section.Thedifference innormalisationbetweendataand Pythia (LO Sherpa) is

∼ +

10%

(

+

40%

)

and attributed to the fact that thesegenerators are based on tree-level matrix elements, which are affected by a large normalisation uncertainty dueto missing higher-order terms; for this reason, the theoretical uncertainties arenot included inFig. 3.Both predictions give an adequate de-scriptionoftheshapeofthemeasuredd

σ

/

dEγT,although Pythia is slightlybetterthanLO Sherpa forT



600 GeV.Ford

σ

/

dpjet-leadT , the prediction from LO Sherpa gives an adequate description of thedatainthewholemeasuredrange,whereas thatfrom Pythia overestimatesthe dataforpjet-leadT



200 GeV;theoverestimation isattributed toa large contribution fromphoton bremsstrahlung predicted by the tune used in Pythia (see Section 3). The pre-dictionfromLO Sherpa givesa gooddescriptionofthemeasured d

σ

/

d

γ−jet,whereas Pythia underestimatesthedatafor3

π

/

5

<

γ−jet

<

4

π

/

5 rad;thisisexpectedfromthe inclusionof addi-tionalpartons in the matrixelements in Sherpa ascompared to Pythia,forwhich additionalpartonsmust necessarilycomefrom thepartonshower.Bothpredictionsgiveagooddescriptionofthe data for−jet

<

1

.

25 TeV and for all of the measured

|

cos

θ

|

range.

To illustrate the sensitivity to t-channel quark or gluon ex-change,thepredictedcross-sectionsd

σ

/

d

|

cos

θ

|

from Jetphox for LOdirectandfragmentationprocessesarecompared tothe mea-surementinFig.4.Eventhoughthetwocomponentsarenolonger distinguishableatNLO,the LOcalculationsareusefulin illustrat-ingthebasicdifferencesinthedynamicsofthetwoprocesses.The contribution from fragmentation, dominated by gluon exchange, showsasteeperincreaseas

|

cos

θ

|

1 thanthatfromdirect pro-cesses,dominatedbyquarkexchange.The shapeofthemeasured cross-sectiond

σ

/

d

|

cos

θ

|

isclosertothatofthedirectprocesses thanthatoffragmentation.Thisisconsistentwiththedominance ofprocessesinwhichtheexchangedparticleisaquark.

Thepredictionsofthefixed-orderNLOQCDcalculationsof Jet-phox basedon theMMHT2014 protonPDF set andcorrectedfor hadronisation andUE effectsas explained inSection 8 are com-paredtothemeasurements8inFig.5.Thepredictionsofthe multi-legNLOQCD plusparton-showercalculationsof Sherpa basedon theNNPDF3.0PDF setare alsocomparedtothemeasurementsin Fig.5.Both typesofpredictions describe thedatawithin the

ex-8 Asshownin Ref. [1], the NLOQCD predictionsof Jetphox cannotdescribe

dσ/dφγ−jetduetothelimitednumberoffinal-statepartons.

perimental andtheoretical uncertainties. Forthe cross section as a function of

γ−jet, the only well-founded prediction is that of NLO Sherpa, which is able to reproduce the data down to

γ−jet

=

π

/

2 due to the inclusion of the matrix elements for

2

n processes with n

=

4 and 5. For most of the points, the

theoreticaluncertaintiesarelargerthanthoseofexperimental ori-gin. Predictionsfor Jetphox (Sherpa NLO) arealso obtainedwith other PDF sets, namelyNLO CT14 [60] and NLO NNPDF3.0(CT14 andMMHT2014),anddifferbylessthan5% withrespecttothose using MMHT2014 (NNPDF3.0). Thus, the description of the data achievedby the predictionsdoes notdepend significantly on the specific PDF setused.It isconcluded that theNLO pQCD predic-tionsprovideanadequatedescriptionofthemeasurementswithin theuncertainties.

10. Summary

Measurements of the cross section for the production of an isolated photon in association withjets in pp collisions at

s

=

13 TeV, pp

γ

+

jet

+

X , are presented. These measurements are basedon an integratedluminosity of3

.

2 fb−1 of ATLAS data recordedattheLHC.ThephotonisrequiredtohaveT

>

125 GeV and

|

η

γ

|

<

2

.

37,excludingtheregion1

.

37

<

|

η

γ

|

<

1

.

56.Thejets

are reconstructedusing theanti-kt algorithm withradius

param-eter R

=

0

.

4.Thecrosssectionsaremeasured asfunctionsof T,

pjet-leadT and

γ−jet with pjet-lead

T

>

100 GeV; themeasurements extenduptovaluesof1

.

5 TeV inT andpjet-leadT .Thedependence on−jetand

|

cos

θ

|

ismeasuredfor−jet

>

450 GeV.

Thepredictions ofthetree-levelplusparton-showerMC mod-els by Pythia and LO Sherpa give a satisfactory description of theshapeofthedatadistributions,exceptfor pjet-leadT inthecase of Pythia. The fixed-order NLO QCD calculationsof Jetphox, cor-rectedforhadronisationandUEeffects,andthemulti-legNLOQCD plus parton-showercalculationsof Sherpa describe themeasured cross sectionswithin theexperimental andtheoretical uncertain-ties. The comparison of predictions based on different parame-terisations of the proton PDFs showsthat the description of the data achieved does not depend significantly on the specific PDF set used. The only well-founded prediction for d

σ

/

d

γ−jet is that of NLO Sherpa, which is able to reproduce the data down to

γ−jet

=

π

/

2 duetotheinclusionofthematrixelementsfor

2

n processeswithn

=

4 and 5.Themeasured dependenceon

|

cos

θ

|

isconsistentwiththedominanceofprocessesinwhicha quarkisexchanged.AllthesestudiesprovidetestsofthepQCD de-scriptionofthedynamicsofisolated-photonplusjetproductionin

pp collisionsat

s

=

13 TeV. Theexperimental uncertainties are,

ingeneral,muchsmallerthantheuncertaintiesinthepredictions and, thus, calculations withhigher precision will allow stringent testsofthetheory.

Acknowledgements

We thank CERN forthe very successfuloperation of the LHC, aswell as thesupport staff fromour institutionswithout whom ATLAScouldnotbeoperatedefficiently.

WeacknowledgethesupportofANPCyT,Argentina;YerPhI, Ar-menia; ARC, Australia; BMWFW and FWF, Austria; ANAS, Azer-baijan; SSTC, Belarus; CNPq andFAPESP, 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, and MPG, Germany; GSRT, Greece;RGC,HongKongSAR,China;ISF,I-COREandBenoziyo Cen-ter, Israel; INFN, Italy; MEXT and JSPS, Japan; CNRST, Morocco;

(11)

588 The ATLAS Collaboration / Physics Letters B 780 (2018) 578–602

Fig. 5. Measuredcrosssectionsforisolated-photonplusjetproduction(dots)asfunctionsofT,p jet-lead

T ,φγ−jet,−jetand|cosθ∗|;theobservablesareconstructedusing

theleadingphotonandtheleadingjet.Forcomparison,themulti-legNLOQCDpluspartonshowerpredictionsfromNLO Sherpa (dashedlines)andtheNLOQCDpredictions from Jetphox correctedforhadronisationandUEeffects(solidlines)arealsoshown.Thebottompartofeachfigureshowstheratiosofthepredictionstothemeasured crosssection.Theinner(outer)errorbarsrepresentthestatisticaluncertainties(thestatisticalandsystematicuncertaintiesaddedinquadrature)andthebandsdisplaythe theoreticaluncertainty.Formostofthepoints,theinnererrorbarsaresmallerthanthemarkersizeand,thus,notvisible.

Figure

Fig. 1. E iso T distribution for tight (black dots) and non-tight (dashed histogram, normalised according to the fit, see text) photon candidates in data with | η γ | &lt; 0
Fig. 2. Total relative systematic uncertainty (solid lines), excluding that in the luminosity measurement, as a function of E γ T , p jet-lead T , φ γ − jet , m γ − jet and | cos θ ∗ |
Fig. 3. Measured cross sections for isolated-photon plus jet production (dots) as functions of E γ T , p jet-lead T , φ γ − jet , m γ − jet and | cos θ ∗ | ; the observables are constructed using the leading photon and the leading jet
Fig. 4. Measured cross section for isolated-photon plus jet production (dots) as a function of | cos θ ∗ | ; the observable is constructed using the leading photon and the leading jet
+2

References

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