Measurement of the cross-section for electroweak production of dijets in association with a Z boson in pp collisions at √

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Physics Letters B

www.elsevier.com/locate/physletb

Measurement of the cross-section for electroweak production of dijets in association with a Z boson in pp collisions at √

s = ^{13 TeV} with the ATLAS detector

.The ATLAS Collaboration

^

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

Articlehistory:

Received2October2017

Receivedinrevisedform19October2017 Accepted19October2017

Availableonline27October2017 Editor:W.-D.Schlatter

The cross-section for the productionof two jetsinassociation with aleptonically decaying Z boson (Z jj)ismeasuredinproton–protoncollisionsatacentre-of-massenergyof13 TeV,usingdatarecorded with the ATLAS detector atthe LargeHadron Collider, corresponding to an integrated luminosity of 3.2 fb⁻¹. The electroweak Z jj cross-section is extracted in a fiducial region chosen to enhance the electroweak contribution relative to the dominant Drell–Yan Z jj process, which is constrained using adata-drivenapproach. The measuredfiducialelectroweak cross-sectionis σ_EW^Zjj ₌ 119±¹⁶ (stat.)± 20(syst.)±²(lumi.)fbfordijetinvariantmassgreaterthan250 GeV,and34.2±⁵.8(stat.)±⁵.5(syst.)± 0.7(lumi.)fbfordijetinvariantmassgreaterthan1 TeV.StandardModelpredictionsareinagreement withthemeasurements.TheinclusiveZ jj cross-sectionisalsomeasuredinsixdifferentfiducialregions withvaryingcontributionsfromelectroweakandDrell–YanZ jj production.

©^{2017TheAuthor(s).PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense} (http://creativecommons.org/licenses/by/4.0/).FundedbySCOAP³.

1. Introduction

AttheLargeHadronCollider(LHC)eventscontainingaZ boson andatleasttwojets( Z jj)areproducedpredominantlyviainitial- state QCD radiation from the incoming partons in the Drell–Yan process (QCD- Z jj), asshownin Fig. 1(a).Incontrast,the produc- tionofZ jj eventsviat-channelelectroweakgaugebosonexchange (EW- Z jj events),including the vector-bosonfusion (VBF) process showninFig. 1(b),isamuchrarerprocess.SuchVBFprocessesfor vector-bosonproductionareofgreatinterestasa‘standardcandle’

forother VBF processesatthe LHC: e.g.,the productionof Higgs bosons or thesearch forweakly interacting particles beyondthe StandardModel.

Thekinematicpropertiesof Z jj eventsallowsomediscrimina- tionbetweentheQCDandEWproductionmechanisms.Theemis- sionofavirtualW bosonfromthequarkinEW- Z jj eventsresults inthepresenceoftwohigh-energyjets,withmoderatetransverse momentum(p_T),separatedbyalargeintervalinrapidity( y)¹ and

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

1 ATLASusesaright-handed coordinatesystemwith itsoriginat thenominal interaction point inthe centre ofthe detector and the z-axisalong the beam pipe.Inthetransverseplane,the x-axispointsfromtheinteractionpointtothe centreofthe LHCring,the y-axispoints upward,andφ isthe azimuthalangle aroundthe z-axis.Thepseudorapidityisdefinedintermsofthepolarangleθas η= −ln tan(θ/2).Therapidityisdefinedasy=0.5ln[(E+pz)/(E−pz)],whereE andpzaretheenergyandlongitudinalmomentumrespectively.Anangularsepara-

thereforewithlargedijetmass(mj j)thatcharacterisestheEW- Z jj signal.AconsequenceoftheexchangeofavectorbosoninFig. 1(b) is that there is no colour connection between the hadronic sys- temsproducedbythebreak-upofthetwoincomingprotons.Asa result,EW- Z jj eventsarelesslikelytocontainadditionalhadronic activityintherapidityintervalbetweenthetwohigh-pT jetsthan correspondingQCD- Z jj events.

The first studies of EW- Z jj productionwere performed [1]in pp collisionsatacentre-of-massenergy(√

s)of7 TeVbytheCMS Collaboration,wherethebackground-onlyhypothesiswasrejected atthe2.6

σ

level.ThefirstobservationoftheEW- Z jj processwas performedbytheATLAS Collaborationatacentre-of-massenergy (√

s)of8 TeV[2].Thecross-sectionmeasurementisinagreement withpredictionsfromthe Powheg-box eventgenerator[3–5]and allowed limitsto beplaced onanomalous triplegauge couplings.

The CMS Collaboration has also observed and measured [6] the cross-sectionforEW- Z jj productionat8 TeV.ThisLetterpresents measurements ofthecross-section forEW- Z jj productionandin- clusive Z jj productionathighdijetinvariantmassinpp collisions at√

s=13 TeV usingdatacorrespondingtoanintegratedluminos- ityof3.2 fb⁻¹ collectedby theATLAS detectorattheLHC.These measurements allow the dependence of the cross-section on √

s

tionbetweentwoobjectsisdefinedasR=

(φ)²+ (η)²,whereφandη aretheseparationsinφandηrespectively.Momentuminthetransverseplaneis denotedbypT.

https://doi.org/10.1016/j.physletb.2017.10.040

0370-2693/©^{2017TheAuthor(s).PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense}(http://creativecommons.org/licenses/by/4.0/).Fundedby SCOAP³.

Fig. 1. Examplesofleading-orderFeynmandiagramsforthetwoproductionmech- anismsforaleptonicallydecayingZ bosonandatleasttwojets( Z jj)inproton–

proton collisions: (a) QCD radiation from the incoming partons (QCD- Z jj) and (b) t-channelexchangeofanEWgaugeboson(EW- Z jj).

tobestudied.Theincreased√

s allowsexplorationofhigherdijet masses, where the EW- Z jj contribution to the total Z jj rate be- comesmorepronounced.

2. ATLASdetector

TheATLASdetectorisdescribed indetailinRefs. [7,8].Itcon- sistsofaninnerdetectorfortracking,surroundedbyathinsuper- conducting solenoid, electromagnetic and hadronic calorimeters, andamuonspectrometerincorporatingthreelargesuperconduct- ingtoroidalmagnetsystems.Theinnerdetectorisimmersedina 2 Taxial magneticfield and providescharged-particle trackingin therange|

η

_|<2.5.

The calorimeters cover the pseudorapidity range |

η

|< 4.9.

Electromagnetic calorimetry is provided by barrel and end-cap lead/liquid-argon(LAr)calorimetersintheregion|

η

_|<3.2.Within

|

η

|<2.47 the calorimeter is finely segmented in the lateral di- rection of the showers, allowing measurement of the energy and position of electrons, and providing electron identification in conjunction with the inner detector. Hadronic calorimetry is provided by the steel/scintillator-tile calorimeter, segmented into three barrel structures within |

η

_|<1.7, and two hadronic end-cap calorimeters. A copper/LAr hadronic calorimeter covers the 1.5<|

η

| <³.2 region, and a forward copper/tungsten/LAr calorimeterwithelectromagnetic-showeridentificationcapabilities coversthe3.1<|

η

_{| <}4.9 region.

The muon spectrometer comprises separate trigger and high- precisiontrackingchambers. The trackingchamberscoverthere- gion|

η

_|<2.7 withthreelayersofmonitoreddrifttubes,comple- mentedby cathodestrip chambersinpartof theforwardregion, wherethehitrateishighest. Themuontriggersystemcoversthe range|

η

|<2.4 withresistiveplatechambersinthebarrelregion, andthingapchambersintheend-capregions.

A two-level trigger system is used to select events of inter- est[9]. TheLevel-1 triggeris implementedinhardware anduses a subset of the detectorinformation to reduce the event rateto around100 kHz.Thisisfollowedbythesoftware-basedhigh-level triggersystemwhichreducestheeventratetoabout1 kHz.

3. MonteCarlosamples

The production of EW- Z jj events was simulated at next- to-leading-order (NLO) accuracy in perturbative QCD using the Powheg-box v1 Monte Carlo (MC) event generator [4,5,10] and, alternatively, at leading-order (LO) accuracy in perturbative QCD usingthe Sherpa 2.2.0eventgenerator[11].Formodellingofthe partonshower,fragmentation,hadronisation andunderlyingevent (UEPS), Powheg-box wasinterfacedto Pythia 8[12] witha ded- icated set of parton-shower-generator parameters (tune) denoted AZNLO[13] andthe CT10 NLO partondistributionfunction (PDF) set[14].The renormalisation andfactorisationscales were set to

the Z boson mass. Sherpa predictions used the Comix [15] and OpenLoops [16] matrix elementevent generators,and theCKKW method was used to combine the various final-state topologies from the matrixelement andmatch them to the partonshower [17].The matrix elements were merged withthe Sherpa parton shower [18] using the ME+PS@LO prescription[19,20], andusing Sherpa’snativedynamicalscale-settingalgorithmtosettherenor- malisation and factorisation scales. Sherpa predictions used the NNPDF30NNLO PDFset[21].

The production of QCD- Z jj events was simulated usingthree event generators, Sherpa 2.2.1, Alpgen 2.14 [22] and MadGraph5_aMC@NLO 2.2.2 [23]. Sherpa provides Z+^n-parton predictionscalculatedforup totwopartonsatNLO accuracyand up to four partons at LO accuracy in perturbative QCD. Sherpa predictionsusedthe NNPDF30NLO PDFsettogether withthetun- ingoftheUEPSparametersdevelopedbythe Sherpa authorsusing the ME+PS@NLO prescription[19,20]. Alpgen isanLOeventgener- atorwhichusesexplicitmatrixelementsforuptofivepartonsand was interfacedto Pythia 6.426[24] usingthe Perugia2011Ctune [25]andtheCTEQ6L1PDFset[26].Onlymatrixelementsforlight- flavourproductionin Alpgen areincluded,withheavy-flavourcon- tributionsmodelledbythepartonshower. MadGraph5_aMC@NLO 2.2.2(MG5_aMC)usesexplicitmatrixelementsforuptofourpar- tonsatLO,andwasinterfacedto Pythia 8withthe A14tune[27]

and using the NNPDF23LO PDF set [28]. Forreconstruction-level studies,total Z bosonproductionratespredictedbyallthreeevent generators used to produce QCD- Z jj predictions are normalised usingthenext-to-next-to-leading-order (NNLO)predictionscalcu- lated withthe FEWZ 3.1 program [29–31] using the CT10 NNLO PDF set [14]. However, when comparing particle-leveltheoretical predictionstodetector-correctedmeasurements,thenormalisation ofquotedpredictions isprovidedbytheeventgeneratorinques- tionratherthananexternalNNLOprediction.

TheproductionofapairofEWvectorbosons(diboson),where onedecaysleptonicallyandtheotherhadronically, orwhereboth decay leptonically and are produced in association with two or more jets, through W Z or Z Z production with at least one Z boson decaying to leptons, was simulated separately using Sherpa2.1.1andthe CT10 NLO PDFset.

Thelargestbackgroundtotheselected Z jj samplesarisesfrom tt and¯ single-top (W t) production. These were generated using Powheg-box v2and Pythia 6.428withthePerugia2012tune[25], andnormalisedusingthecross-section calculatedatNNLO+^NNLL (next-to-next-to-leading log) accuracy using the Top++2.0 pro- gram[32].

All the above MC samples were fully simulated through the Geant4[33] simulationoftheATLAS detector[34].The effectof additional pp interactions (pile-up)in thesame ornearbybunch crossingswasalsosimulated,using Pythia v8.186withthe A2tune [35] and the MSTW2008LO PDF set [36]. The MC samples were reweightedsothatthedistributionoftheaveragenumberofpile- upinteractionsper bunchcrossingmatchesthat observedindata.

ForthedataconsideredinthisLetter,theaveragenumberofinter- actionsis 13.7.

4. Eventpreselection

The Z bosonsaremeasuredintheirdielectronanddimuonde- cay modes.Candidate eventsare selectedusingtriggers requiring atleastone identifiedelectronormuon withtransversemomen- tum thresholds of pT =^{24 GeV and 20 GeV} respectively, with additional isolation requirements imposed in these triggers. At higher transverse momenta, the efficiency of selecting candidate events is improved through the use of additional electron and

muontriggerswithoutisolationrequirementsandwiththresholds ofpT=^{60 GeV and50 GeV}respectively.

Candidateelectronsarereconstructedfromclustersofenergyin the electromagneticcalorimeter matched toinner-detector tracks [37].TheymustsatisfytheMedium identificationrequirementsde- scribedinRef.[37]andhavep_T > 25 GeV and|

η

| <^2.47,exclud- ingthetransitionregionbetweenthebarrelandend-capcalorime- tersat1.37<|

η

| <^{1.52.Candidatemuonsareidentifiedastracks} intheinner detectormatchedandcombinedwithtracksegments inthemuonspectrometer. TheymustsatisfytheMedium identifi- cationrequirementsdescribedinRef.[38],andhavep_T > 25 GeV and|

η

_{| <}2.4. Candidate leptons mustalso satisfya set ofisola- tioncriteriabasedonreconstructedtracksandcalorimeteractivity.

Events are required to contain exactly two leptons of the same flavour butof opposite charge.The dilepton invariant massmust satisfy81<m_<101 GeV.

Candidate hadronic jets are required to satisfy pT > 25 GeV and|^y| < ^{4.4. Theyare} reconstructed fromclustersofenergy in the calorimeter[39] usingthe anti-k_t algorithm [40,41] with ra- dius parameter R=⁰.4. Jet energies are calibrated by applying p_T- and y-dependent correctionsderived from MonteCarlosim- ulationwithadditionalinsitucorrectionfactorsdetermined from data [42]. To reduce the impact ofpile-up contributions, all jets with |^y|<2.4 and p_T<60 GeV are required to be compatible withhaving originatedfromthe primary vertex (the vertexwith the highest sum of track p²_T), as defined by the jet vertex tag- geralgorithm[43].Selected electronsandmuonsarediscarded if theylie within R=⁰.4 of areconstructedjet. Thisrequirement isimposed to removenon-prompt non-isolated leptons produced in heavy-flavourdecays orfrom thedecay in flight ofa kaon or pion.

5. MeasurementofinclusiveZ j j fiducialcross-sections 5.1. Definitionofparticle-levelcross-sections

Cross-sections are measured for inclusive Z jj production that includes the EW- Z jj and QCD- Z jj processes, as well as diboson events.Theparticle-levelproductioncross-sectionforinclusiveZ jj productioninagivenfiducialregion f isgivenby

σ

^f

=

^N

f

obs

−

N_bkg^f

L

·

C^f

,

(1)

where N_obs^f is the number of events observed in the data pass- ing theselection requirements ofthefiducial regionunder study at detectorlevel, N_bkg^f is the corresponding number of expected background(non- Z jj)events,L istheintegratedluminositycorre- spondingtotheanalyseddatasample,andC^{f isacorrectionfactor} appliedtotheobserveddatayields,whichaccountsforexperimen- tal efficiencyanddetector resolutioneffects, andis derived from MCsimulationwithdata-drivenefficiencyandenergy/momentum scalecorrections.Thiscorrectionfactoriscalculatedas:

C^f

=

^N

f det

N_particle^f

,

where N_det^f is the numberof signal events that satisfy the fidu- cial selection criteriaatdetectorlevel in theMC simulation, and N_particle^f isthenumberofsignaleventsthatpasstheequivalentse- lectionbut atparticle level. These correction factors havevalues between0.63 and0.77,dependingonthefiducialregion.

Withtheexception ofbackgroundfrommultijetandW+^jets processes(henceforthreferredtotogether simplyasmultijetpro- cesses),contributionsto N_bkg^f areestimatedusingtheMonteCarlo

samples described in Section 3.Background from multijetevents is estimated fromthe data by reversing requirements on lepton identification or isolation to derive a template for the contribu- tion of jets mis-reconstructedas lepton candidates asa function ofdileptonmass.Non-multijet backgroundis subtractedfromthe template usingsimulation.The normalisationisderived byfitting thenominaldileptonmassdistributionineachfiducialregionwith the sumofthe multijettemplate andatemplate comprisingsig- nalandbackgroundcontributionsdeterminedfromsimulation.The multijetcontributionisfoundtobelessthan0.3%ineachfiducial region.ThecontributionfromW+jets processeswascheckedus- ing MC simulation andfound to be much smaller than the total multijetbackgroundasdeterminedfromdata.

At particlelevel,only final-stateparticles withproperlifetime c

τ

>10 mm areconsidered.Promptleptonsaredressedusingthe four-momentumcombinationofanelectronormuonandallpho- tons (not originating from hadron decays) within a cone of size

R=⁰.1 centred on the lepton. These dressed leptons are re- quiredto satisfy pT>25 GeV and |

η

|<2.47.Events arerequired tocontain exactlytwodressedleptons ofthesameflavourbutof oppositecharge,andthedileptoninvariantmassmustsatisfy81<

m<101 GeV. Jetsarereconstructed usingthe anti-kt algorithm with radius parameter R=⁰.4. Prompt leptons andthe photons used to dresstheseleptons are not includedin theparticle-level jet reconstruction. All remaining final-stateparticles are included in theparticle-leveljet clustering. Promptleptons witha separa- tionRj,<0.4 fromanyjetarerejected.

The cross-section measurements are performed in the six phase-space regions definedinTable 1. Theseregions arechosen tohavevaryingcontributionsfromEW- Z jj andQCD- Z jj processes.

5.2. Eventselection

Following Ref. [2], events are selected in sixdetector fiducial regions. Asfaraspossible,theseare definedwiththesamekine- matic requirements asthe six phase-space regions in which the cross-sectionismeasured(Table 1).Thisminimisessystematicun- certaintiesinthemodellingoftheacceptance.

Thebaselinefiducialregionrepresentsaninclusiveselectionof eventscontainingaleptonicallydecayingZ bosonandatleasttwo jetswithpT>45 GeV,atleastoneofwhichsatisfiespT>55 GeV.

The two highest-pT (leading and sub-leading) jets in a given event define the dijet system. The baseline region is dominated by QCD- Z jj events.The requirementof 81<m_<101 GeV sup- presses other sources ofdileptonevents,such astt and¯ Z→

τ τ

, aswellasthemultijetbackground.

Becausetheenergyscaleofthedijetsystemistypicallyhigher ineventsproducedbytheEW- Z jj processthaninthoseproduced bytheQCD- Z jj process,twosubsetsofthebaselineregionarede- fined which probe the EW- Z jj contribution in differentways: in thehigh-massfiducialregionahighvalueoftheinvariantmassof thedijetsystem(mj j>1 TeV)isrequired,andinthehigh-pTfidu- cialregiontheminimumpToftheleadingandsub-leadingjetsis increasedto85 GeVand75 GeVrespectively.TheEW- Z jj process typicallyproduces harderjettransversemomentaandresultsina harderdijetinvariantmassspectrumthantheQCD- Z jj process.

Three additional fiducial regions allow the separate contribu- tionsfromtheEW- Z jj andQCD- Z jj processestobemeasured.The EW-enriched fiducial region is designed to enhance the EW- Z jj contribution relative to that from QCD- Z jj, particularly at high m_{j j}. The EW-enriched region is derived from the baseline re- gion requiring m_{j j}>250 GeV, a dilepton transverse momentum of p^_T > 20 GeV,andthatthenormalisedtransverse momentum balance betweenthe twoleptons andthe two highesttransverse

Table 1

Summaryoftheparticle-levelselectioncriteriadefiningthesixfiducialregions(seetextfordetails).

Fiducial region

Object Baseline High-mass High-pT EW-enriched EW-enriched, QCD-enriched mj j>1 TeV

Leptons |η| <2.47, pT>25 GeV,Rj,>0.4

Dilepton pair 81<m<101 GeV

– p^_T >20 GeV

Jets |^y| <⁴.4

p_T^j1 >55 GeV p_T^j1>85 GeV p_T^j1>55 GeV p_T^j2 >45 GeV p_T^j2>75 GeV p_T^j2>45 GeV

Dijet system – mj j>1 TeV – mj j>250 GeV mj j>1 TeV mj j>250 GeV

Interval jets – N^interval_jet(p

T>25 GeV)=^{0 N}jet^interval(p_T>25 GeV)≥¹

Z jj system – p^balance_T <0.15 p^balance_T ^,3<0.15

momentumjetssatisfy p^balance_T <0.15.Thelatterquantityisgiven by

p^balance_T

=

 

^p_T^1

+ 

p_T^2

+ 

p_T^j1

+ 

p_T^j2

 

 

^pT^1

  +  

^pT^2

  +  

^pT^j1

  +  

^pT^j2

  ,

(2)

where ^p_T^{i is thetransversemomentum vector ofobjecti,} 1 and

2labelthetwoleptonsthatdefinethe Z bosoncandidate,and j1 and j2 refer to the leading andsub-leading jets. These require- ments help remove events in which the jets arise from pile-up ormultiple partoninteractions. The requirementon p^balance_T also helps suppress events in which the pT of one or more jets is badlymeasured andit enhancesthe EW- Z jj contribution,where the lower probability of additional radiation causes the Z boson and the dijet system to be well balanced. The EW-enriched re- gion requires a veto [44] on any jets with p_T>25 GeV recon- structed within the rapidity interval bounded by the dijet sys- tem(N_jet^interval_(p

T>25 GeV)=^{0). A second fiducial region,denoted EW-} enriched(m_{j j}>1 TeV),hasidenticalselectioncriteria,exceptfora raisedm_{j j} thresholdof1 TeVwhichfurtherenhancestheEW- Z jj contributiontothetotal Z jj signalrate.

Incontrast,theQCD-enrichedfiducialregionisdesignedtosup- pressthe EW- Z jj contributionrelativetoQCD- Z jj byrequiringat leastonejetwith pT>25 GeV tobereconstructedwithinthera- pidityintervalboundedbythedijetsystem(N^interval_jet(p

T>25 GeV) ≥^1).

IntheQCD-enrichedregion,thedefinitionofthenormalisedtrans- versemomentumbalanceismodifiedfromthatgiveninEq.(2)to includeinthe calculationofthe numeratoranddenominator the p_T of thehighest p_T jet within therapidity interval bounded by thedijetsystem(p^balance_T ^,3).Inallotherrespects,thekinematicre- quirements in the EW-enriched region and QCD-enriched region areidentical.

5.3.Detector-levelresults

Inthebaselineregion,30686 eventsareselectedinthedielec- tronchanneland36786 eventsareselected inthedimuonchan- nel.Thetotalobservedyieldsare inagreementwiththeexpected yieldswithinstatisticaluncertaintiesineachdileptonchannel.The largestdeviationacrossallfiducialregionsisa2

σ

(statistical)dif- ference between the expected to observed ratio in the electron versusmuonchannelinthehigh-p_T region.

Theexpectedcomposition ofthe selecteddata samplesinthe sixZ jj fiducialregionsissummarisedinTable 2,averagingacross thedielectronanddimuonchannelsasthesecompositionsinthe

two dilepton channels are in agreement within statistical uncer- tainties.The numbersofselectedeventsindataandexpectations fromtotalsignalplusbackgroundestimatesarealsogivenforeach region. The largest discrepancy between observed and expected yieldsisseeninthehigh-massregion,andresultsfromamismod- elling ofthe mj j spectrum in the QCD- Z jj MC simulations used, whichisdiscussedbelowandaccountedforintheassessmentof systematicuncertainties inthemeasurement.

5.4. SystematicuncertaintiesintheinclusiveZ jj fiducialcross-sections

Experimentalsystematicuncertainties affectthe determination of the C^{f correction factor and the background estimates. The} dominantsystematicuncertaintyintheinclusiveZ jj fiducialcross- sections arises from the calibration of the jet energy scale and resolution. This uncertainty varies from around 4% in the EW- enriched region to around 12% in the QCD-enriched region. The largeruncertaintyintheQCD-enrichedregionisduetothehigher average jet multiplicity (an average of 1.7 additional jets in ad- dition to the leading and sub-leading jets) compared with the EW-enriched region (anaverage of0.4additionaljets). Other ex- perimentalsystematicuncertaintiesarisingfromleptonefficiencies relatedto reconstruction, identification, isolation andtrigger, and leptonenergy/momentumscaleandresolutionaswellasfromthe effectofpile-up,amounttoatotalofaround1–2%,depending on thefiducialregion.

The systematic uncertainty arising from the MC modelling of the mj j distributionin the QCD- Z jj and EW- Z jj signal processes is around 3% in theEW-enriched region, around 1% in theQCD- enriched region, 2% inthe high-mass region, andbelow1% else- where. This is assessed by comparing the correction factors ob- tained by usingthe differentMC event generators listed in Sec- tion3andbyperformingadata-drivenreweightingoftheQCD- Z jj MCsampletodescribethem_{j j}distributionoftheobserveddatain agivenfiducialregion.Additionalcontributionsarisefromvarying theQCDrenormalisationandfactorisationscalesupanddownby a factor of two independently, andfrom the propagation of un- certaintiesinthePDFsets.Thenormalisationofthedibosoncon- tribution isvaried accordingto PDF andscale variations inthese predictions[45],andresultsinuptoa0.1% effectonthemeasured Z jj cross-sections depending on the fiducial region. The uncer- taintyfromvaryingthenormalisationandshapeinm_{j j}oftheesti- matedbackgroundfromtop-quarkproductionisatmost1%(inthe high-massregion),arisingfromchangesintheextractedZ jj cross- sectionswhen usingmodified top-quarkbackground MC samples withPDFandscalevariations, suppressedorenhanced additional

Table 2

Estimatedcomposition(inpercent)ofthedatasamplesselectedinthesixZ jj fiducialregionsforthedielectronanddimuonchan- nelscombined,usingtheEW- Z jj samplefrom Powheg,andtheQCD- Z jj samplefrom Sherpa (normalisedusingNNLOpredictions fortheinclusiveZ cross-sectioncalculatedwith FEWZ).Uncertaintiesinthesamplecontributionsarestatisticalonly.Alsoshown arethetotalexpectedyieldsandthetotalobservedyieldsineachfiducialregion.Uncertaintiesinthetotalexpectedyieldsare statistical(first)andsystematic(second),seeSection5.4fordetails.

Process Composition [%]

Baseline High-mass High-pT EW-enriched EW-enriched, QCD-enriched

mj j>1 TeV

QCD-Z jj 94.2±⁰.4 86.8±¹.6 92.3±⁰.4 93.4±⁰.9 72.9±².1 95.4±⁰.8 EW-Z jj 1.5± <0.1 10.6±0.2 2.6± <0.1 4.8± <0.1 26.1±0.5 1.6± <0.1 Diboson 1.6± <0.1 1.5±0.7 2.0±0.5 1.0±0.5 0.8±0.4 1.8±0.4 t¯t 2.6± <⁰.1 1.1±⁰.1 3.1±⁰.1 0.7± <⁰.1 0.1±⁰.1 1.2±⁰.1

Single-t <0.2 <0.2 <0.2 <0.1 <0.1 <0.1

Multijet <0.3 <0.3 <0.3 <0.3 <0.3 <0.3

Total expected 64800 2220 21900 11100 640 7120

±¹³⁰±⁵²²⁰ ±²⁰±²⁰⁰ ±⁴⁰±¹²¹⁰ ±⁵⁰±⁵²⁰ ±¹⁰±⁴⁰ ±³⁰±⁸⁸⁰

Total observed 67472 1471 22461 11630 490 6453

radiation (generated with the Perugia2012radHi/Lo tunes [25]), or using an alternative top-quark production sample from Mad- Graph5_aMC@NLOinterfacedto Herwig++ v2.7.1[23,46].

Thesystematicuncertaintyintheintegratedluminosityis2.1%.

This is derived following a methodology similar to that detailed inRef. [47],froma calibration ofthe luminosity scaleusing x– y beam-separationscansperformedinJune2015.

5.5. InclusiveZ jj results

The measured cross-sections in the dielectron and dimuon channels are combined and presented here as a weighted aver- age(takingintoaccounttotaluncertainties)acrossboth channels.

Thesecross-sections aredetermined using each ofthe correction factors derived from the six combinations of the three QCD- Z jj (Alpgen, MG5_aMC, and Sherpa) and two EW- Z jj (Powheg and Sherpa)MCsamples.Foragivenfiducialregion(Table 1)thecross- section averaged over all six variations is presented in Table 3.

The envelope of variation betweenQCD- Z jj and EW- Z jj models isassignedasasourceofsystematicuncertainty(1%inallregions excepttheEW-enrichedregion wherethevariationis3% andthe high-massregionwherethevariationis2%).

The theoretical predictions from Sherpa (QCD- Z jj)+ Powheg (EW- Z jj), MG5_aMC (QCD- Z jj) + Powheg (EW- Z jj), and Alpgen (QCD- Z jj)+ Powheg (EW- Z jj)arefoundtobeinagreementwith themeasurementsinmostcases.Theuncertaintiesinthetheoreti- calpredictionsaresignificantlylargerthantheuncertaintiesinthe correspondingmeasurements.

The largestdifferences betweenpredictions andmeasurement are in the high-mass and EW-enriched (mj j >250 GeV and

>1 TeV) regions. Predictions from Sherpa (QCD- Z jj) + Powheg (EW- Z jj) and MG5_aMC (QCD- Z jj) + Powheg (EW- Z jj) exceed measurements in the high-mass region by 54% and 34% respec- tively,where the predictions have relative uncertainties withre- spect tothe measurement of 36% and32%. Forthe EW-enriched region, Sherpa (QCD- Z jj) + Powheg (EW- Z jj) describes the ob- served rates well, but MG5_aMC (QCD- Z jj) + Powheg (EW- Z jj) overestimatesmeasurementsby28%witharelativeuncertaintyof 11%. In the EW-enriched (mj j >1 TeV) region the same predic- tions overestimate measured ratesby 33% and57%, withrelative uncertaintiesof16%and15%.Someofthesedifferencesarisefrom a significant mismodellingofthe QCD- Z jj contribution, asinves- tigated and discussed in detail in Section 6.1. Predictions from

Alpgen(QCD- Z jj)+ Powheg (EW- Z jj)are inagreementwiththe data for the high-mass and EW-enriched (mj j >250 GeV and

>1 TeV)regions.

6. MeasurementofEW- Z j j fiducialcross-sections

The EW-enriched fiducial region (defined in Table 1) is used to measure the production cross-section of the EW- Z jj process.

The EW-enriched region has an overall expected EW- Z jj signal fraction of4.8% (Table 2) andthissignal fraction grows within- creasing m_{j j} to 26.1% form_{j j}>1 TeV. The QCD-enriched region has an overall expectedEW- Z jj signal fractionof 1.6%increasing to 4.4%form_{j j}>1 TeV.The dominantbackgroundto theEW- Z jj cross-sectionmeasurementisQCD- Z jj production.Itissubtracted inthesamewayasnon- Z jj backgroundsintheinclusivemeasure- mentdescribedinSection5.Althoughdibosonproductionincludes contributionsfrompurelyEWprocesses,inthismeasurementitis consideredaspartofthebackgroundandisestimatedfromsimu- lation.

A particle-level production cross-section measurement of EW- Z jj productioninagivenfiducialregion f isthusgivenby

σ

_EW^f

₌

^N

f

obs

−

^N_QCD-Zjj^f

−

^N_bkg^f

L

·

C_EW^f

,

(3)

with the samenotations asin Eq.(1) andwhere N_{QCD- Zjj}^f is the expectednumberofQCD- Z jj eventspassingtheselectionrequire- mentsofthefiducialregionatdetectorlevel,N_bkg^f istheexpected number ofbackground(non- Z jj and diboson)events,and C_EW^f is acorrection factorappliedtotheobservedbackground-subtracted datayields that accountsforexperimental efficiencyanddetector resolutioneffects,andisderivedfromEW- Z jj MCsimulationwith data-drivenefficiencyandenergy/momentumscalecorrections.For the mj j>250 GeV (mj j >1 TeV) region this correction factor is determined to be 0.66 (0.67) when using the Sherpa EW- Z jj prediction,and 0.67 (0.68) whenusingthe Powheg EW- Z jj pre- diction.

Detector-levelcomparisonsofthemj j distributionbetweendata and simulation in (a) the EW-enriched region and(b) the QCD- enriched region are shown in Fig. 2. It can be seen in Fig. 2(a)

Table 3

Measuredand predictedinclusive Z jj productioncross-sectionsinthesixfiducialregionsdefinedinTable 1.Forthemeasuredcross-sections,the firstuncertaintygivenisstatistical,thesecondissystematicandthethirdisduetotheluminositydetermination.Forthepredictions,thestatistical uncertaintyisaddedinquadraturetothesystematicuncertaintiesarisingfromthePDFsandfactorisationandrenormalisationscalevariations.

Fiducial region Inclusive Z jj cross-sections [pb]

Measured Prediction

value ±^stat. ±^syst. ±^{lumi. Sherpa(QCD-Z jj)} MG5_aMC (QCD-Z jj) Alpgen(QCD-Z jj) +Powheg (EW-Z jj) +Powheg (EW-Z jj) +Powheg (EW-Z jj)

Baseline 13.9 ±^0.1 ±^1.1 ±^{0.3 13}.5±¹.9 15.2±².2 11.7±¹.7

High-pT 4.77 ±^0.05 ±^0.27 ±^{0.10 4}.7±⁰.8 5.5±⁰.9 4.2±⁰.7

EW-enriched 2.77 ±0.04 ±0.13 ±0.06 2.7±0.2 3.6±0.3 2.4±0.2

QCD-enriched 1.34 ±^0.02 ±^0.17 ±^{0.03 1}.5±⁰.4 1.4±⁰.3 1.1±⁰.3

High-mass 0.30 ±0.01 ±0.03 ±0.01 0.46±0.11 0.40±0.09 0.27±0.06

EW-enriched (mj j>1 TeV) 0.118 ±0.008 ±0.006 ±0.002 0.156±0.019 0.185±0.023 0.120±0.015

Fig. 2. Detector-levelcomparisonsofthedijetinvariantmassdistributionbetweendataandsimulationin(a) theEW-enrichedregionand(b) theQCD-enrichedregion,forthe dielectronanddimuonchannelcombined.Uncertaintiesshownonthedataarestatisticalonly.TheEW- Z jj simulationsamplecomesfromthe Powheg eventgeneratorand theQCD- Z jj MCsamplecomesfromthe Sherpa eventgenerator.ThelowerpanelsshowtheratioofsimulationtodataforthreeQCD- Z jj models,from Alpgen, MG5_aMC, and Sherpa.Thehatchedbandcentredatunityrepresentsthesizeofstatisticalandexperimentalsystematicuncertaintiesaddedinquadrature.

that in the EW-enriched region the EW- Z jj component becomes prominentatlargevaluesofmj j.However, Fig. 2(b)demonstrates that the shape ofthe mj j distribution for QCD- Z jj productionis poorlymodelledinsimulation.Thesametrendisseenforallthree QCD- Z jj eventgeneratorslistedinSection3. Alpgen providesthe best description of the data over the whole mj j range. In com- parison, MG5_aMCand Sherpa overestimatethedataby 80%and 120%respectively, formj j=^{2 TeV, well outsidethe} uncertainties onthesepredictionsdescribedinTable 3.Thesediscrepancieshave beenobserved previously in Z jj [2,48] and Wjj [49–51] produc- tionathighdijetinvariant massandathighjetrapidities.Forthe purposeofextractingthecross-sectionforEW- Z jj production,this mismodellingofQCD- Z jj iscorrected forusinga data-drivenap- proach,asdiscussedinthefollowing.

6.1.CorrectionsformismodellingofQCD- Z jj productionandfitting procedure

ThenormalisationoftheQCD- Z jj backgroundisextractedfrom a fit of the QCD- Z jj and EW- Z jj mj j simulated distributions to thedata in the EW-enriched region, aftersubtraction ofnon- Z jj anddibosonbackground,usingalog-likelihoodmaximisation[52].

FollowingtheprocedureadoptedinRef.[2],thedataintheQCD-

enriched region are used toevaluate detector-level shape correc- tion factors for the QCD- Z jj MC predictions bin-by-bin in m_{j j}. Thesedata-to-simulationratiocorrectionfactorsareappliedtothe simulation-predicted shapeinmj j oftheQCD- Z jj contribution in the EW-enriched region.This procedure ismotivated by two ob- servations:

(a) theQCD-enrichedregionandEW-enrichedregionaredesigned tobe kinematicallyverysimilar, differingonlywithregardto thepresence/absenceofjetsreconstructedwithintherapidity intervalboundedbythedijetsystem,

(b) the contributionofEW- Z jj totheregion ofhighm_{j j} issup- pressedintheQCD-enrichedregion(4.4%form_{j j}>1 TeV)rel- ativetothatintheEW-enrichedregion(26.1%form_{j j}>1 TeV) (also illustratedin Fig. 2);the impactofthe residualEW- Z jj contamination in the QCD-enriched region is assigned as a componentofthesystematicuncertaintyintheQCD- Z jj back- ground.

The shape correction factors in mj j obtained using the three different QCD- Z jj MC samplesare shown in Fig. 3(a). These are derived asthe ratio ofthe data to simulation in bins of m_{j j} af- ternormalisationofthetotalyieldinsimulationtothatobserved

Fig. 3. Binneddata-to-simulationnormalisedratioshapecorrectionfactorsasafunctionofdijetinvariantmassintheQCD-enrichedregion.(a) Ratioforthreedifferent QCD- Z jj MCsampleswithuncertaintiescorrespondingtothecombinedstatisticaluncertaintiesinthedataandQCD-ZjjMCsamplesaddedinquadrature.ScaleandPDF uncertaintiesin Sherpa predictionsareindicatedbytheshadedbands.Linesrepresentfitstotheratiosusingalinearfit.(b) RatioforsubregionsoftheQCD-enrichedregion forthe Alpgen MCsample.Curvesrepresenttheresultoffitswithaquadraticfunctionforthevarioussubregions.

indataintheQCD-enrichedregion.Abinnedfittothecorrection factorsderived indijetinvariant mass isperformedwithalinear fit function(and also witha quadratic fitfunction) toproduce a continuouscorrectionfactor.Thelinearfitisillustratedoverlaidon thebinnedcorrectionfactorsinFig. 3(a).Thenominalvalueofthe EW- Z jj cross-section correspondingtoaparticularQCD- Z jj event generatortemplateisdeterminedusingthecorrectionfactorsfrom the linearfit. The change inresultant EW- Z jj cross-section from using binned correction factors directly is assessed asa system- aticuncertainty.ThechangeintheextractedEW- Z jj cross-section when usinga quadraticfit was found tobe negligible.The vari- ations observed betweenevent generators may be partlydue to differencesinthemodelling ofQCD radiationwithin therapidity interval bounded by the dijet system, which affects the extrap- olationfrom thecentral-jet-enriched QCD-enrichedregion to the central-jet-suppressedEW-enrichedregion.The variationbetween eventgenerators ismuch larger than theeffect ofPDF andscale uncertaintiesinaparticularprediction(indicatedinFig. 3(a)bya shadedband onthepredictionsfrom Sherpa).Estimatingtheun- certainties associated with QCD- Z jj mismodelling from PDF and scale variations around a single generator predictionwould thus resultinan underestimate ofthe truetheoretical uncertaintyas- sociated with this mismodelling. In this measurement, the span ofresultantEW- Z jj cross-sectionsextractedfromtheuseofeach ofthethreeQCD- Z jj templates isassessedasasystematicuncer- tainty.ThevariationintheEW- Z jj cross-sectionmeasurementdue toa changeintheEW- Z jj signaltemplate usedinthederivation ofthemj j correctionfactors(from Powheg to Sherpa)isfoundto benegligible.

To test the dependence of the QCD- Z jj correction factors on the modelling of any additional jet emitted in the dijet rapidity interval, theQCD-enriched control region isdivided into pairs of mutuallyexclusivesubsetsaccordingto the |^y| ^{ofthehighest p}T jet within the rapidity interval bounded by the dijetsystem, the pT ofthatjet,orthevalueofN_jet^interval_(p

T>25 GeV).Thecontinuouscor- rectionfactors are determined fromeach subregion usingboth a linearandaquadraticfittothedata.Correctionfactorsderived in the subregions usingquadratic fits result inthe largest variation in the extractedcross-sections. These fits are shown in Fig. 3(b) forthe Alpgen QCD- Z jj sample, which displays the largest vari- ation between subregions of the three event generators used to produce QCD- Z jj predictions. Within statistical uncertainties the measuredEW- Z jj cross-sectionsarenotsensitivetothedefinition ofthecontrolregionused.

ThenormalisationsofthecorrectedQCD- Z jj templatesandthe EW- Z jj templatesareallowedtovaryindependentlyinafittothe background-subtractedmj j distributionintheEW-enrichedregion.

Themeasured electroweakproductioncross-sectionisdetermined from the data minus the QCD- Z jj contribution determined from thesefits(Eq.(3)).AsthechoiceofEW- Z jj templatecaninfluence the normalisation of the QCD- Z jj template in the EW-enriched regionfit,themeasuredEW- Z jj cross-sectiondeterminationisre- peated for each QCD- Z jj template using either the Powheg or SherpaEW- Z jj templateinthefit.Thecentralvalue oftheresult quoted isthe averageofthe measured EW- Z jj cross-sections de- terminedwitheachofthesixcombinationsofthethreeQCD- Z jj and two EW- Z jj templates, with the envelope of measured re- sultsfromthesevariationstakenasanuncertaintyassociatedwith the dependence on the modelling of the templates in the EW- enriched region.Separate uncertaintiesareassignedforthedeter- mination of the QCD- Z jj correction factors in the QCD-enriched region and their propagation into the EW-enriched region. The measurement ofthe EW- Z jj cross-sectionintheEW-enrichedre- gionform_{j j}>1 TeV isextractedfromthesamefitprocedure,with dataandQCD- Z jj yieldsintegratedformj j>1 TeV.

Fig. 4(a) shows a comparison in the EW-enriched region of the fittedEW- Z jj and m_{j j}-reweighted QCD- Z jj templates to the background-subtracted data, from which the measured EW- Z jj cross-section isextracted. Fig. 4(b)demonstrateshow thedatain the EW-enriched region is modelled with the fitted EW- Z jj and mj j-reweightedQCD- Z jj templates,forthethreedifferentQCD- Z jj event generators (and their corresponding correction factors de- rived in the QCD-enriched region shown in Fig. 3(a)). Despite significantly different modelling of the mj j distribution between event generators, anddifferent models for additional QCD radia- tion,theresultsofthecombinedcorrectionandfitproceduregive aconsistentdescriptionofthedata.

6.2. SystematicuncertaintiesintheEW- Z jj fiducialcross-section

Thetotalsystematicuncertaintyinthecross-sectionforEW- Z jj production intheEW-enriched fiducialregion is17% (16%inthe EW-enriched mj j>1 TeV region). The sources and size of each systematicuncertaintyaresummarisedinTable 4.

Systematic uncertainties associated with the EW- Z jj signal templateusedinthefitandEW- Z jj signalextractionareobtained from thevariation in the measured cross-section whenusing ei- ther ofthe individual EW- Z jj MC samples(Powheg and Sherpa)

Fig. 4. (a) ComparisonintheEW-enrichedregionofthesumofEW- Z jj andmj j-reweightedQCD- Z jj templatestothedata(minusthenon- Z jj backgrounds).Thenormal- isationofthetemplatesisadjustedtotheresultsofthefit(seetextfordetails).TheEW- Z jj MCsamplecomesfromthe Powheg eventgeneratorandtheQCD- Z jj MC samplecomesfromthe Alpgen eventgenerator.(b) TheratioofthesumoftheEW- Z jj andmj j-reweightedQCD- Z jj templatestothebackground-subtracteddatainthe EW-enrichedregion,forthreedifferentQCD- Z jj MCpredictions.Thenormalisationofthetemplatesisadjustedtotheresultsofthefit.Errorbarsrepresentthestatistical uncertaintiesinthedataandcombinedQCD- Z jj plusEW- Z jj MCsamplesaddedinquadrature.Thehatchedbandrepresentsexperimentalsystematicuncertaintiesinthe mj jdistribution.

Table 4

SystematicuncertaintiescontributingtothemeasurementoftheEW- Z jj cross-sectionsformj j>250 GeVand mj j>1 TeV.UncertaintiesaregroupedintoEW- Z jj signalmodelling,QCD- Z jj backgroundmodelling,QCD-EW interference,non- Z jj backgrounds,andexperimentalsources.

Source Relative systematic uncertainty [%]

σEW^{mj j>250 GeV} σEW^{mj j>1 TeV}

EW-Z jj signal modelling (QCD scales, PDF and UEPS) ±7.4 ±1.7

EW-Z jj template statistical uncertainty ±^0.5 ±^0.04

EW-Z jj contamination in QCD-enriched region −⁰.1 −⁰.2

QCD-Z jj modelling (mj jshape constraint / third-jet veto) ±11 ±11

Stat. uncertainty in QCD control region constraint ±6.2 ±6.4

QCD-Z jj signal modelling (QCD scales, PDF and UEPS) ±^4.5 ±^6.5

QCD-Z jj template statistical uncertainty ±^2.5 ±^3.5

QCD-EW interference ±1.3 ±1.5

¯

tt and single-top background modelling ±^1.0 ±^1.2

Diboson background modelling ±^0.1 ±^0.1

Jet energy resolution ±2.3 ±1.1

Jet energy scale +⁵.3/−⁴.1 +³.5/−⁴.2

Lepton identification, momentum scale, trigger, pile-up +¹.3/−².5 +³.2/−¹.5

Luminosity ±^2.1 ±^2.1

Total ±17 ±16

comparedtotheaverageofthetwo,takenasthecentralvalue.Un- certaintiesinthe EW- Z jj templates duetovariations ofthe QCD scales,ofthePDFs,andoftheUEPSmodelarealsoincludedasare statisticaluncertaintiesinthetemplatesthemselves.

FollowingtheextractionoftheEW- Z jj cross-sectionintheEW- enrichedregions,thenormalisationsoftheEW- Z jj MCsamplesare modified to agree with the measurements and the potential EW contamination of the QCD-enrichedregion is recalculated, which leads to a modification of the QCD- Z jj correction factors. The EW- Z jj cross-section measurement is repeatedwith these mod- ified QCD- Z jj templates and the change in the resultant cross- sections is assigned as a systematic uncertainty associated with theEW- Z jj contaminationoftheQCD-enrichedregion.

Asdiscussed inSection 6.1, theuse ofa QCD-enrichedregion provides away to correctforQCD- Z jj modelling issues andalso constrains theoretical and experimental uncertainties associated withobservablesconstructedfromthetwoleadingjets.Neverthe-

less, the largest contribution to the total uncertaintyarises from modelling uncertainties associated with propagation of the m_{j j} correctionfactorsforQCD- Z jj intheQCD-enrichedregionintothe EW-enriched region, andthese correction factors depend on the modellingoftheadditionaljetactivityintheQCD- Z jj MCsamples used inthemeasurement. Theuncertainty isassessed byrepeat- ing the EW- Z jj cross-section measurement with mj j-reweighted QCD- Z jj MCtemplates from Alpgen, MG5_aMC,and Sherpa, and assigning the variation of the measured cross-sections from the central EW- Z jj result as a systematic uncertainty. Statistical un- certaintiesfromdataandsimulationinthemj j correction factors derived inthe QCD-enriched region are also propagated through tothemeasuredEW- Z jj cross-sectionasasystematicuncertainty.

Uncertainties associated with QCD renormalisation and factori- sation scales, PDF error sets, and UEPS modelling are assessed by studying the change in the extracted EW- Z jj cross-sections whenrepeating themeasurement procedure,includingrederiving