Observation of electroweak W ± Z boson pair production in association with two jets in pp collisions at s=13 TeV with the ATLAS detector

Physics Letters B 793 (2019) 469–492

Contents lists available atScienceDirect

Physics

Letters

B

www.elsevier.com/locate/physletb

Observation

of

electroweak

W

±

Z boson

pair

production

in

association

with

two

jets

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

r

a

c

t

Articlehistory:

Received27December2018 Receivedinrevisedform16April2019 Accepted6May2019

Availableonline13May2019 Editor:M.Doser

Anobservationofelectroweak

W

±_{Z production inassociationwithtwojetsinproton–protoncollisions} is presented. The data collected by the ATLAS detector at the Large Hadron Collider in 2015 and 2016atacentre-of-mass energyof√s=13 TeV areused,corresponding to anintegratedluminosity of 36.1 fb−1.Eventscontaining three identifiedleptons, eitherelectrons ormuons, and two jetsare selected. The electroweak productionof W±Z bosons in association withtwo jetsis measured with anobservedsignificanceof5.3 standarddeviations.Afiducialcross-sectionforelectroweakproduction including interference effects and for a single leptonic decay mode is measured to be

σ

W Z j j−EW=

0.57+0.14 −0.13(stat.)+

0.07

−0.06(syst.)fb. Total and differential fiducial cross-sections of the sum of W±Z j j

electroweakandstrongproductionsforseveralkinematicobservablesarealsomeasured.

©2019TheAuthor(s).PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense (http://creativecommons.org/licenses/by/4.0/).FundedbySCOAP3_.

1. Introduction

The scattering of vector bosons (VBS), V V

→

V V with V

=

W

/

Z

/

γ

,isakeyprocesswithwhichtoprobetheSU

(

2

)

L

×

U

(

1

)

Y

gaugesymmetry ofthe electroweak(EW)theory that determines the self-couplings of the vector bosons. New phenomena be-yond the Standard Model (SM) can alter the couplings of vector bosons,generating additionalcontributions to quartic gauge cou-plings(QGC)comparedwiththeSMpredictions [1–3].

Inproton–protoncollisions,VBSisinitiatedbyaninteractionof twovectorbosonsradiatedfromtheinitial-statequarks,yieldinga finalstate withtwo bosonsandtwo jets, V V j j,ina purely elec-troweak process [4]. VBS diagrams are not independently gauge invariant and cannot be studied separately fromother processes leading to the same V V j j final state [5]. Twocategories of pro-cessesgive riseto V V j j final states.Thefirstcategory, which in-cludesVBScontributions,involvesexclusivelyweakinteractionsat Bornleveloforder

α

6

EWincludingthebosondecays,where

α

EWis

theelectroweakcouplingconstant.Itisreferredtoaselectroweak production.Thesecondcategoryinvolvesboththestrongand elec-troweakinteractionsatBornleveloforder

α

2

S

α

4EW,where

α

Sisthe

stronginteractioncouplingconstant.Itis referredtoasQCD pro-duction.AccordingtotheSM asmallinterferenceoccursbetween electroweakandQCDproduction.

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

Different searches for diboson electroweak production have beenperformedbytheATLAS andCMScollaborationsattheLHC. So far, electroweak V V j j production has only been observed in thesame-sign W±W±j j channelbyCMSusingdatacollectedata centre-of-massenergyof

√

s

=

13 TeV [6].Evidenceofelectroweak

V V j j production has also been obtained in the W±W±j j [7,8] and Z

γ

j j [9] channels by ATLAS and CMS, respectively, using smaller samplesof data recordedat

√

s

=

8 TeV.Limits on elec-troweakcross-sectionsfortheproductionoftwogaugebosonhave been reportedfor the W±Z j j [10,11], Z Z j j [12], Z

γ

j j [13] and

W

γ

j j [14] channelsbyATLASandCMS.

This Letter reports on an observation and measurement of electroweak W±Z j j production,exploitingthefullyleptonic final states where both the Z and W bosonsdecay into electrons or muons.Thepp collisiondatawerecollectedwiththeATLAS detec-torin2015 and2016 ata centre-of-massenergyof

√

s

=

13 TeV andcorrespondtoanintegratedluminosityof36

.

1 fb−1.

2. TheATLASdetector

The ATLAS detector [15] is a multipurpose detector with a cylindricalgeometry1 _{andnearly 4}

_π

_{coverage insolid angle.The}

collision point is surrounded by inner tracking detectors,

collec-1 _{ATLASuses aright-handedcoordinatesystemwith itsoriginat thenominal} interactionpoint(IP)inthecentreofthedetectorandthez-axisalongthebeam direction.Thex-axispointsfromtheIPtothecentreoftheLHCring,andthey-axis pointsupward.Cylindricalcoordinates

(

r, φ)areusedinthetransverse

(

x, y)plane, https://doi.org/10.1016/j.physletb.2019.05.012

0370-2693/©2019TheAuthor(s).PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense(http://creativecommons.org/licenses/by/4.0/).Fundedby SCOAP3_.

tivelyreferredtoastheinnerdetector(ID),locatedwithina super-conductingsolenoidprovidinga2 Taxialmagneticfield,followed byacalorimetersystemandamuonspectrometer(MS).

Theinner detectorprovides precisemeasurements of charged-particle tracks in the pseudorapidity range

|

η

|

<

2

.

5. It consists ofthree subdetectors arranged in a coaxialgeometryaround the beam axis: a silicon pixel detector, a silicon microstrip detector andatransitionradiationtracker.

Theelectromagneticcalorimetercoverstheregion

|

η

|

<

3

.

2 and isbasedonhigh-granularity,lead/liquid-argon(LAr)sampling tech-nology. The hadronic calorimeter uses a steel/scintillator-tile de-tector in the region

|

η

|

<

1

.

7 and a copper/LAr detector in the region 1

.

5

<

|

η

|

<

3

.

2. The mostforward region ofthe detector, 3

.

1

<

|

η

|

<

4

.

9,isequippedwithaforwardcalorimeter,measuring electromagnetic and hadronic energies in copper/LAr and tung-sten/LArmodules.

The muon spectrometer comprises separate trigger and high-precision tracking chambers to measure the deflection of muons in a magnetic field generated by three large superconducting toroidal magnetsarranged withan eightfold azimuthal coil sym-metryaroundthecalorimeters.Thehigh-precisionchamberscover the range

|

η

|

<

2

.

7 with three layers of monitored drift tubes, complemented by cathodestrip chambersin the forwardregion, wheretheparticlefluxishighest.Themuontriggersystemcovers therange

|

η

|

<

2

.

4 withresistive-platechambersinthebarreland thin-gapchambersintheendcapregions.

A two-level trigger system is used to select events in real time [16]. It consists of a hardware-based first-level trigger and asoftware-basedhigh-leveltrigger.The latteremploys algorithms similartothoseusedofflinetoidentifyelectrons,muons, photons andjets.

3. Phasespaceforcross-sectionmeasurements

The W±Z j j electroweak cross-section is measured in a fidu-cialphasespacethatisdefinedbythekinematicsofthefinal-state leptons,electronsormuons,associatedwiththeW±andZ boson

decays,andoftwojets.Leptonsproducedinthedecayofahadron, a

τ

-lepton,ortheir descendantsare notconsidered inthe defini-tion ofthe fiducial phase space. At particle level,the kinematics ofthechargedlepton afterquantum electrodynamics(QED) final-stateradiation(FSR)are‘dressed’by includingcontributionsfrom photons with an angular distance

R

≡



(

η

)

2

_{+ (φ)}

2

_<

₀

_.

₁

fromthelepton.Dressedchargedleptons,andfinal-stateneutrinos thatdonotoriginatefromhadronor

τ

-leptondecays,arematched tothe W± andZ bosondecayproductsusingaMonteCarlo(MC) generator-independent algorithmic approach, calledthe ‘resonant shape’algorithm.Thisalgorithmisbasedon thevalueofan esti-matorexpressingtheproductofthenominallineshapesoftheW

andZ resonancesasdetailedinRef. [10].

Thefiducialphasespaceofthemeasurementmatchestheone used in Refs. [10,17] and is defined at particle level by the fol-lowingrequirements: thecharged leptons from the Z boson de-cayare requiredtohavetransversemomentum pT

>

15 GeV,the

charged lepton from the W± decay is required to have trans-versemomentum p_T

>

20 GeV,thechargedleptonsfromtheW±

and Z bosons are required to have

|

η

|

<

2

.

5 and the invariant massofthetwoleptons fromthe Z boson decaymustbe within 10 GeV of the nominalZ boson mass,taken fromthe world av-eragevalue,mPDG_Z [18].The W bosontransversemass,definedas

mW_T

=



2

·

pν_T

·

p_T

· [

1

−

cos

φ (,

ν

)

]

, where

φ (,

ν

)

is the

an-φbeingtheazimuthalanglearoundthebeamdirection.Thepseudorapidityis de-finedintermsofthepolarangle

θ

asη= −ln[tan(θ/2)].

gle between thelepton andthe neutrinoin the transverseplane and pν_T is the transversemomentum of theneutrino, is required to be mW

T

>

30 GeV. The angular distance between the charged

lepton fromthe W± decayandeach ofthechargedleptonsfrom the Z decay is required to be

R

>

0

.

3, and the angular dis-tancebetweenthetwoleptonsfromthe Z decayisrequiredtobe

R

>

0

.

2.Requiring that thetransverse momentum of the lead-ingleptonbeabove27 GeVreducestheacceptanceofthefiducial phase spaceby only0

.

02% andisthereforenot addedto the def-inition of the fiducial phase space, although it is present in the selectionatthedetectorlevelpresentedinSection5.

Inadditiontotheserequirementsthatdefineaninclusivephase space, atleasttwo jets with pT

>

40 GeV and

|

η

j

|

<

4

.

5 are

re-quired.Theseparticle-leveljetsare reconstructedfromstable par-ticles witha lifetimeof

τ

>

30 ps inthesimulation afterparton showering, hadronisation, anddecayof particles with

τ

<

30 ps. Muons, electrons, neutrinos andphotonsassociated with W and Z decays are excluded. The particle-level jets are reconstructed using the anti-kt [10] algorithm with a radius parameter R =

0

.

4. The angular distance between all selected leptons and jets is required to be

R

(

j

,

)

>

0

.

3. If the

R

(

j

,

)

requirement is not satisfied,the jet isdiscarded. Theinvariant mass,mj j, ofthe

two highest-pT jetsin opposite hemispheres,

η

j1

·

η

j2

<

0,is

re-quired to be mj j

>

500 GeV to enhance the sensitivity to VBS

processes. These two jetsare referred to astagging jets. Finally, processes withab-quark intheinitial state, suchast Z j

produc-tion, are not considered assignal. The production of t Z j results

from a t-channel exchange of a W boson between a b- and a

u-quarkgivingafinalstatewithat-quark,a Z bosonanda light-quark jet, butdoesnot includediagrams withgauge boson cou-plings.

4. Signalandbackgroundsimulation

MonteCarlosimulationisusedtomodelsignalandbackground processes.AllgeneratedMCeventswerepassedthroughtheATLAS detector simulation [20], based on Geant 4 [21], and processed using thesamereconstruction softwareasusedforthe data.The eventsamplesincludethesimulationofadditionalproton–proton interactions (pile-up) generatedwith Pythia 8.186 [22] usingthe

MSTW2008LO

[23] parton distribution functions (PDF) and the A2 [24] setoftunedparameters.

Scalefactorsare appliedtosimulatedeventstocorrectforthe differencesbetweendataandMCsimulationinthetrigger, recon-struction,identification,isolationandimpactparameterefficiencies ofelectrons andmuons [25,26]. Furthermore,theelectronenergy andmuonmomentuminsimulatedeventsaresmearedtoaccount fordifferencesinresolutionbetweendataandMCsimulation [26,

27].

The Sherpa 2

.

2

.

2 MC event generator [28–35] was used to model W±Z j j events. It includes the modelling of hard scatter-ing, partonshowering, hadronisation andtheunderlyingevent. A MC eventsample,referredtoasW Z j j

−

EW,includesprocessesof order six(zero)in

α

EW (

α

S). In thissample, which includesVBS

diagrams, two additional jets originating from electroweak ver-tices frommatrix-elementpartons areincludedin thefinal state. Diagrams with a b-quark in either the initial or final state, i.e.

b-quarks in the matrix-element calculation, are not considered. This sample provides a LO prediction for the W Z j j

−

EW signal process. A second MC event sample, referred to as W Z j j

−

QCD, includes processes of order four in

α

EW in the matrix-element

of W±Z production with up to one jet calculated at next-to-leading order (NLO) and with a second or third jet calculated at leading order (LO). This W Z j j

−

QCD sample includes matrix-elementb-quarks.Both Sherpa samplesweregeneratedusingthe

The ATLAS Collaboration / Physics Letters B 793 (2019) 469–492 471

NNPDF3.0

[36] PDFset.Interferencesbetweenthetwoprocesses were estimated at LO using the MadGraph5_aMC@NLO 2

.

3 [37] MC eventgenerator withthe

NNPDF3.0

PDF set, includingonly contributions to the squared matrix-element of order one in

α

S. They are found to be positive and approximately 10% of

the W Z j j

−

EW cross-sectionin the fiducial phase spaceand are treatedasanuncertaintyinthemeasurement,asdiscussedin Sec-tion 8. For the estimation of modelling uncertainties, alternative MCsamplesofW Z j j

−

QCD andW Z j j

−

EW processeswere gener-atedwith MadGraph5_aMC@NLO 2

.

3 at LOinQCD, includingup totwo partons inthematrix-element for W Z j j

−

QCD, andusing the

NNPDF3.0

PDF set. MC samples of inclusive W±Z

produc-tiongenerated at NLO in QCD withthe Powheg-Box v2 [38–41] generator, interfaced to Pythia 8.210 or Herwig++ 2.7.1 [42] for simulation of parton showering and hadronisation are also used fortestsofthemodellingofW Z j j

−

QCD events.

The qq

¯

→

Z Z(∗) _{processes were generated with Sherpa 2}

_.

₂

_.

₂

and the

NNPDF3.0

PDF set. Similarly to W±Z simulation, the

Z Z j j

−

QCD and Z Z j j

−

EW processesaregeneratedseparatelywith the same matrix-element accuracy as for the W±Z Sherpa MC

samples.The Sherpa 2

.

1

.

1 MCeventgeneratorwasusedtomodel the gg

→

Z Z(∗) and V V V processesat LO using the

CT10

[43] PDFset.Thet

¯

t V processesweregeneratedatNLO withthe Mad-Graph5_aMC@NLO 2

.

3 MCgeneratorusingthe

NNPDF3.0

PDFset interfacedto the Pythia 8.186 parton shower model.The associ-atedproductionofasingletopquarkandaZ bosonwassimulated atLOwith MadGraph5_aMC@NLO 2

.

3 using the

NNPDF3.0

PDF setandinterfacedto Pythia 8

.

186 forpartonshower.

5. Eventselection

Candidateeventswereselectedusingsingle-leptonstriggers [16] that requiredat least one electron ormuon. The transverse mo-mentumthresholdoftheleptonsin2015 was24 GeVforelectrons and 20 GeV for muons satisfying a loose isolation requirement based only on ID track information. Due to the higher instan-taneous luminosity in 2016 the trigger threshold was increased to 26 GeV for both the electrons and muons and tighter iso-lation requirements were applied. Possible inefficiencies for lep-tons with large transverse momenta were reduced by including additional electron and muon triggers that did not include any isolation requirements with transverse momentum thresholds of

pT

=

60 GeV and 50 GeV, respectively. Finally, a single-electron

triggerrequiringpT

>

120 GeVorpT

>

140 GeVin2015 and2016,

respectively,withlessrestrictiveelectronidentificationcriteriawas used to increase the selection efficiency for high-pT electrons.

The combined efficiency of these triggers is close to 100% for

W±Z j j events. Only data recorded with stable beam conditions andwithall relevantdetectorsubsystems operationalare consid-ered.

Events are required to have a primary vertex reconstructed fromatleasttwocharged-particletracksandcompatiblewiththe pp interaction region. Ifseveral such vertices are present in the event, theone with thehighestsum ofthe p2_T ofthe associated tracksis selectedasthe productionvertexof the W±Z .All final stateswiththreechargedleptons(electronsormuons)and neutri-nosfromW±Z leptonicdecaysareconsidered.

Muon candidatesare identified by tracks reconstructedin the muon spectrometer and matched to tracks reconstructed in the inner detector. Muons are required to satisfy a ‘medium’ identi-fication selection that is based on requirements on the number ofhitsintheID andtheMS [26].The efficiencyofthisselection averagedover pT and

η

is

>

98%.Themuonmomentumis

calcu-latedbycombiningtheMSmeasurement,correctedfortheenergy depositedinthecalorimeters,withtheIDmeasurement.The

trans-verse momentum ofthe muonmust satisfy pT

>

15 GeV andits

pseudorapiditymustsatisfy

|

η

|

<

2

.

5.

Electron candidates are reconstructed fromenergy clusters in theelectromagneticcalorimetermatchedtoIDtracks.Electronsare identifiedusingalikelihoodfunctionconstructedfrominformation from the shape of the electromagnetic showers inthe calorime-ter,trackpropertiesandtrack-to-clustermatchingquantities [25]. Electrons must satisfy a ‘medium’ likelihood requirement, which provides an overall identification efficiency of 90%. The electron momentumiscomputedfromtheclusterenergyandthedirection ofthetrack.Thetransverse momentumoftheelectronmust sat-isfy pT

>

15 GeVandthepseudorapidityoftheclustermustbein

theranges

|

η

|

<

1

.

37 or1

.

52

<

|

η

|

<

2

.

47.

Electron and muon candidates are required to originate from the primary vertex. The significanceofthe track’stransverse im-pactparameter relative to the beamline mustsatisfy

|

d0

/

σ

d0

|

<

3

(

5

)

formuons(electrons),andthelongitudinal impact parame-ter,z0 (the differencebetweenthevalue ofz ofthepointon the

trackatwhich d0 isdefinedandthe longitudinal positionofthe

primaryvertex),isrequiredtosatisfy

|

z0

·

sin

(θ )

|

<

0

.

5 mm.

Electrons and muons are required to be isolated from other particles, according to calorimeter-cluster and ID-track informa-tion. The isolation requirementfor electrons varies with pT and

istuned foran efficiencyofatleast 90% for pT

>

25 GeVandat

least99% for pT

>

60 GeV [25]. Fixed thresholds valuesare used

forthemuonisolationvariables,providinganefficiencyabove90% forpT

>

15 GeVandatleast99% forpT

>

60 GeV [26].

Jets are reconstructed from clusters of energy depositions in the calorimeter [44] using the anti-kt algorithm [19] with a

ra-dius parameter R

=

0

.

4. Events with jets arising from detector noise or other non-collision sources are discarded [45]. All jets must have pT

>

25 GeV and be reconstructed in the

pseudora-pidity range

|

η

|

<

4

.

5. A multivariate combinationof track-based variables is usedto suppressjets originatingfrompile-up in the IDacceptance [46].Theenergyofjetsiscalibratedusingajet en-ergycorrectionderivedfromsimulationandinsitu methodsusing data [47]. Jets in the ID acceptance with pT

>

25 GeV

contain-ing a b-hadron are identified usinga multivariate algorithm [48,

49] thatusesimpact parameterandreconstructedsecondary ver-texinformationofthetrackscontainedinthejets.Jetsinitiatedby

b-quarksare selected bysetting thealgorithm’s output threshold suchthat a70% b-jetselectionefficiencyisachievedinsimulated

tt events.

¯

The transverse momentum of the neutrino is estimated from the missingtransversemomentum inthe event, Emiss_T , calculated as the negative vector sum of the transverse momentum of all identified hard (high pT) physics objects (electrons, muons and

jets), aswell asan additional softterm. A track-based measure-ment of the softterm [50,51], which accounts forlow-pT tracks

notassignedtoahardobject,isused.

Events are requiredtocontain exactlythree lepton candidates satisfyingtheselectioncriteriadescribedabove.Toensurethatthe triggerefficiencyiswelldetermined,atleastoneofthecandidate leptons is requiredto have pT

>

25 GeV or pT

>

27 GeV for the

2015 or2016 data,respectively,andtobegeometricallymatched toaleptonthatwasselectedbythetrigger.

To suppress background processes with at least four prompt leptons, events with a fourth lepton candidate satisfying looser selectioncriteriaarerejected. Forthislooserselection,the pT

re-quirement for the leptons is lowered to pT

>

5 GeV and ‘loose’

identification requirements are used for both the electrons and muons. Alessstringentrequirementisapplied forelectron isola-tionbasedonlyonIDtrackinformationandelectronswithcluster intherange1

.

37

≤ |

η

|

≤

1

.

52 arealsoconsidered.

Table 1

Expected and observed numbers ofeventsin the W±Z j j signalregion and inthe threecontrolregions, beforethefit.TheexpectednumberofW Z j j−EW eventsfrom Sherpa and the estimated number of background events from the other processes are shown. Thesum ofthebackgrounds containingmisidentified leptons islabelled ‘Misid.leptons’.Thecontributionarisingfrominterferencesbetween W Z j j−QCD and W Z j j−EW processesisnotincludedinthetable.Thetotaluncertaintiesarequoted.

SR W Z j j−QCD CR b-CR Z Z -CR Data 161 213 141 52 Total predicted 200±41 290±61 160±14 45.2±7.5 W Z j j−EW (signal) 24.9±1.4 8.45±0.37 1.36±0.10 0.21±0.12 W Z j j−QCD 144±41 231±60 24.4±1.7 1.43±0.22 Misid. leptons 9.8±3.9 17.7±7.1 30±12 0.47±0.21 Z Z j j−QCD 8.1±2.2 15.0±3.9 1.96±0.49 35±11 t Z j 6.5±1.2 6.6±1.1 36.2±5.7 0.18±0.04 t¯t+V 4.21±0.76 9.11±1.40 65.4±10.3 2.8±0.61 Z Z j j−EW 1.80±0.45 0.53±0.14 0.12±0.09 4.1±1.4 V V V 0.59±0.15 0.93±0.23 0.13±0.03 1.05±0.30

Candidateeventsarerequiredtohaveatleastone pairof lep-tonsofthesameflavourandofoppositecharge,withaninvariant mass that is consistent with the nominal Z boson mass [52] to within 10 GeV. Thispair isconsidered to be the Z boson candi-date.Ifmorethanonepaircanbeformed,thepairwhoseinvariant massisclosesttothenominalZ bosonmassistakenasthe Z

bo-soncandidate.

Theremaining thirdlepton isassignedtothe W bosondecay. The transverse mass of the W candidate, computed using Emiss_T

andthe pT oftheassociatedlepton,isrequiredtobegreaterthan

30 GeV.

Backgrounds originating from misidentified leptons are sup-pressed by requiring thelepton associated withthe W bosonto satisfy morestringentselection criteria. Thus, thetransverse mo-mentumoftheseleptons isrequiredto be pT

>

20 GeV.

Further-more,leptons associatedwiththe W bosondecayare requiredto satisfy the ‘tight’ identification requirements, which have an ef-ficiency between 90% and 98% for muons and an efficiency of 85% for electrons. Finally, muons must also satisfy a tighter iso-lation requirement, tuned foran efficiencyof at least 90% (99%) forpT

>

25

(

60

)

GeV.

ToselectW±Z j j candidates, eventsarefurther requiredtobe associatedwithatleasttwo ‘tagging’jets. Theleading taggingjet is selectedas thehighest-pT jet in theevent with pT

>

40 GeV.

Thesecond taggingjetisselectedastheonewiththehighestpT

amongtheremaining jetsthat havea pseudorapidity ofopposite sign to the first tagging jet and a pT

>

40 GeV. These two jets

are required to verify mj j

>

150 GeV, in order to minimise the

contaminationfromtribosonprocesses.

Thefinalsignal region(SR)forVBSprocessesisdefinedby re-quiring that the invariant mass of the two tagging jets, mj j, be

above500 GeVandthatnob-taggedjetbepresentintheevent.

6. Backgroundestimation

Thebackground sourcesare classifiedintotwo groups:events whereatleastone ofthe candidateleptons isnot a prompt lep-ton (reducible background) and events where all candidates are promptleptons orare producedin thedecayofa

τ

-lepton (irre-ducible background). Candidatesthat are not prompt leptons are alsocalled‘misidentified’or‘fake’leptons.

The dominantsourceof backgroundoriginatesfrom the QCD-inducedproductionofW±Z dibosonsinassociationwithtwojets,

W Z j j

−

QCD. Theshapesofdistributions ofkinematicobservables of this irreducible background are modelled by the Sherpa MC simulation.Thenormalisationofthisbackgroundis,however, con-strainedbydatainadedicatedcontrolregion.Thisregion,referred

to as W Z j j

−

QCD CR, is defined by selecting a sub-sample of

W±Z j j candidateeventswithmj j

<

500 GeVandnoreconstructed b-jets.

The other main sources of irreducible background arise from

Z Z andtt

¯

+

V (whereV

=

Z orW ).Theseirreduciblebackgrounds are also modelled using MC simulations. Data in two additional dedicatedcontrol regions,referredtoas Z Z -CR andb-CR, respec-tively,are usedtoconstrain thenormalisationsofthe Z Z j j

−

QCD andt

¯

t

+

V backgrounds.ThecontrolregionZ Z -CR,enrichedinZ Z

events,isdefinedby applyingtheW±Z j j eventselectiondefined in Section 5, withthe exception that instead of vetoinga fourth leptonitisrequiredthateventshaveatleastafourthlepton can-didatewithlooseridentificationrequirements.Thisregionis domi-natedbyZ Z j j

−

QCD eventswithasmallcontributionofZ Z j j

−

EW events.The controlregion b-CR,enriched int

¯

t

+

V events,is de-fined by selecting W±Z j j candidate events having at least one reconstructed b-jet. Remaining sources of irreducible background are Z Z j j

−

EW V V V and t Z j events. Their contributions in the controlandsignalregionsareestimatedfromMCsimulations.

The reducible backgrounds originate from Z

+

j, Z

γ

, tt,

¯

W t

andW W productionprocesses.Thereduciblebackgroundsare es-timated using a data-driven method basedon the inversion of a globalmatrixcontaining theefficienciesandthemisidentification probabilitiesforpromptandfakeleptons [10,53].The method ex-ploits theclassification ofthe leptonasloose ortight candidates and theprobability that a fake lepton ismisidentified asa loose ortight leptoncandidate.Tight leptonscandidates aresignal lep-ton candidates as defined in Section 5. Loose lepton candidates areleptonsthatdonotmeettheisolationandidentification crite-riaofsignalleptoncandidatesbutsatisfyonlyloosercriteria.The misidentificationprobabilitiesforfakeleptonsaredeterminedfrom data,usingdedicatedcontrolsamplesenrichedinnon-prompt lep-tons from heavy-flavour jets and in misidentified leptons from photon conversions or charged hadrons in light-flavour jets. The lepton misidentification probabilities are applied to samples of

W±Z j j candidate events in data where at least one and up to three of the lepton candidates are loose. Then, using a matrix inversion, the number of events with at least one misidentified lepton, which represents the amount of reduciblebackground in theselectedW±Z j j sample,isobtained.

The number of observed events together with the expected backgroundcontributionsaresummarisedinTable1forthesignal region andthethree controlregions. All sourcesofuncertainties, asdescribed inSection8,areincluded.Theexpectedsignalpurity in the W±Z j j signal regionis about13%, and72% of theevents arisefromW Z j j

−

QCD production.

The ATLAS Collaboration / Physics Letters B 793 (2019) 469–492 473

7.Signalextractionprocedure

GiventhesmallcontributiontothesignalregionofW Z j j

−

EW processes,amultivariatediscriminantisusedtoseparatethesignal from the backgrounds. A boosted decision tree (BDT), as imple-mentedintheTMVApackage [54],isusedtoexploitthekinematic differences between the W Z j j

−

EW signal and the W Z j j

−

QCD andotherbackgrounds.TheBDTistrainedandoptimisedon sim-ulatedeventsto separate W Z j j

−

EW eventsfromall background processes.

Atotalof15 variablesarecombinedintoonediscriminant,the BDT score output value in the range

[−

1

,

1

]

. The variables can beclassifiedintothree categories:jet-kinematicvariables, vector-bosons-kinematicsvariables,andvariablesrelatedtobothjetsand leptons kinematics. The variables related to the kinematic prop-erties ofthe two tagging jetsare the invariant mass of the two jets, mj j, the transverse momenta of the jets, the difference in

pseudorapidity and azimuthal angle between the two jets,

η

j j

and

φ

j j, the rapidity of the leading jet and the jet

multiplic-ity. Variables related to the kinematic properties of the vector bosons are the transverse momenta of the W and Z bosons,

the pseudorapidity of the W boson, the absolute difference be-tween the rapidities of the Z boson and the lepton from the decay of the W boson,

|

yZ

−

y,W

|

, and the transverse mass

of the W±Z system mW Z

T . The pseudorapidity of the W boson

is reconstructed using an estimate of the longitudinal momen-tum of the neutrino obtained using the W mass constraint as detailed in Ref. [55]. The mW Z_T observable is reconstructed fol-lowingRef. [10]. Variablesthat relate thekinematicpropertiesof jetsand leptons are the distance in the pseudorapidity–azimuth plane between the Z boson and the leading jet,

R

(

j1

,

Z

)

, the

eventbalance Rhard

pT , definedasthe transverse componentof the

vector sum of the W Z bosons and tagging jets momenta, nor-malised to their scalar pT sum, and, finally the centrality of

the W Z system relative to the tagging jets, defined as

ζ

lep.

=

min

(

η

₋

,

η

₊

)

, with

η

₋

=

min

(

η

W 

,

η

Z 2

,

η

Z

1

)

−

min

(

η

j1

,

η

j2

)

and

η

+

=

max

(

η

j1

,

η

j2

)

−

max

(

η

W 

,

η

Z2

,

η

Z

1

)

.Alargersetof

dis-criminatingobservableswas studiedbutonlyvariablesimproving signal-to-background were retained. The good modelling by MC simulations ofthe distribution shapesand the correlationsof all inputvariablestotheBDTisverifiedintheW Z j j

−

QCD CR,as ex-emplifiedbythegooddescriptionoftheBDTscoredistributionof dataintheW Z j j

−

QCD CRshowninFig.1.

Thedistribution ofthe BDT scoreinthe W±Z j j signal region is used to extract the significance of the W Z j j

−

EW signal and tomeasureitsfiducialcross-sectionviaamaximum-likelihoodfit. An extended likelihood is built from the product of four likeli-hoodscorresponding tothe BDTscore distributioninthe W±Z j j

SR,themj j distributionintheW Z j j

−

QCD CR,themultiplicityof

reconstructedb-quarksintheb-CRandthemj j distributioninthe Z Z -CR.Theinclusionofthethreecontrolregionsinthefitallows theyields oftheW Z j j

−

QCD,t

¯

t

+

V and Z Z j j

−

QCD backgrounds to be constrained by data. The shapes of these backgrounds are taken from MC predictions and can vary within the uncertain-ties affecting the measurement as described in Section 8. The normalisations of these backgrounds are introduced in the like-lihood as parameters, labelled

μ

W Z j j−QCD,

μ

t¯t+V and

μ

Z Z j j−QCD

forW Z j j

−

QCD,tt

¯

+

V and Z Z j j

−

QCD backgrounds, respectively. They are treated as unconstrained nuisance parameters that are determined mainly by the data in the respective control region. Thenormalisationandshapeoftheotherirreduciblebackgrounds are taken from MC simulations and are allowed to vary within their respective uncertainties. The distribution of the reducible backgroundisestimatedfromdata usingthematrixmethod

pre-Fig. 1. Post-fitdistributionoftheBDTscoredistributionintheW Z j j−QCD control region.Signalandbackgroundsarenormalisedtotheexpectednumberofevents af-terthefit.TheuncertaintybandaroundtheMCexpectationincludesallsystematic uncertaintiesasobtainedfromthefit.

sented in Section 6 and is allowed to vary within its uncer-tainty.

The determination of the fiducial cross-section is carried out usingthesignalstrengthparameter

μ

W Z j j−EW:

μ

W Z j j−EW

=

N_datasignal N_MCsignal

=

σ

fid. W Z j j−EW

σ

_{W Z j j−}fid.,MC_EW

,

where N_datasignal is the signal yield extracted from data by the

fit and Nsignal_MC is the number of signal events predicted by the

Sherpa MC simulation. The measured cross-section

σ

fid.

W Z j j−EW is

derived fromthe signal strength

μ

W Z j j−EW by multiplying it by

the Sherpa MC cross-section prediction

σ

_{W Z j j}fid.,MC_−EW inthe fiducial region. The W Z j j

−

QCD contribution that is considered as back-groundinthefitproceduredoesnotcontaininterferencebetween the W Z j j

−

QCD and W Z j j

−

EW processes. The measured cross-section

σ

fid.

W Z j j−EW therefore formally corresponds to the

cross-section of the electroweak production including interference ef-fects.

8. Systematicuncertainties

Systematic uncertainties in the signal and control regions af-fecting the shape and normalisation of the BDT score, mj j and N_b−jetsdistributionsfortheindividualbackgrounds,aswellasthe

acceptanceofthesignalandtheshapeofitstemplateare consid-ered. Ifthe variationofa systematicuncertaintyasa function of the BDT score is consistent withbeing dueto statistical fluctua-tions,thissystematicuncertaintyisneglected.

Systematicuncertaintiesduetothetheoreticalmodellinginthe eventgeneratorusedtoevaluatethe W Z j j

−

QCD and W Z j j

−

EW templates are considered. Uncertainties dueto higher orderQCD correctionsare evaluatedby varyingthe renormalisationand fac-torisation scales independently by factors of two and one-half, removing combinations wherethevariations differ by a factorof four.Theseuncertaintiesareof

−

20% to

+

30% ontheW Z j j

−

QCD backgroundnormalisation andupto

±

5% on the W Z j j

−

EW sig-nal shape. The uncertainties due to the PDF and the

α

S value

prescription [56]. They are of the order of 1% to 2% in shape of the predicted cross-section. A global modelling uncertainty in the W Z j j

−

QCD background template that includes effects of the parton shower model is estimated by comparing predic-tions ofthe BDT score distribution inthe signal region fromthe Sherpa _and MadGraph _{MC eventgenerators. The difference} be-tween the predicted shapes of the BDT score distribution from thetwo generators isconsidered asan uncertainty. Theresulting uncertainty ranges from 5% to 20% at medium and high values of the BDT score,respectively. Alternatively, using two MC sam-ples with different parton shower models, Powheg+Pythia8 and Powheg+Herwig_{, it was verified that for W Z j j}

−

_{QCD events the} variations oftheBDT scoreshape dueto differentpartonshower modelsarewithintheglobalmodellinguncertaintydefinedabove. Aglobalmodellinguncertaintyinthe W Z j j

−

EW signaltemplate isalso estimatedby comparingpredictions ofthe BDT score dis-tributioninthesignalregionfromthe Sherpa and MadGraph MC eventgenerators. Thismodelling uncertaintyaffects the shapeof theBDT scoredistribution by atmost14% at large valuesofthe BDTscore.TheSherpaW Z j j

−

EW sampleusedinthisanalysiswas recentlyfoundtoimplementacolourflowcomputationinVBS-like processes that increases central parton emissions from the par-tonshower [57].Itwas verifiedthatpossibleeffectsonkinematic distributionsandespeciallyontheBDT scoredistributionare cov-eredbythemodellinguncertaintyused.Theinterferencebetween electroweak- and QCD-induced processes is not included in the probabilitydistributionfunctionsofthefitbutisconsideredasan uncertainty affecting only the shape of the W Z j j

−

EW MC tem-plate.Theeffectisdeterminedusingthe MadGraph MCgenerator, resultingforthesignal regioninshape-onlyuncertaintiesranging from10% to5% at lowandhighvaluesoftheBDT score, respec-tively.The effectof interference on the shape of the W Z j j

−

EW MCtemplate intheW±Z j j-QCDCRisnegligibleandistherefore notincluded.

Systematic uncertainties affecting the reconstruction and en-ergy calibration of jets, electrons and muons are propagated through the analysis. The dominant sources of uncertainties are the jet energy scale calibration, including the modelling of pile-up. The uncertainties in the jet energy scale are obtained from

√

s

=

13 TeV simulationsandinsitu measurements [47].The un-certaintyin thejetenergyresolution [58] andinthesuppression ofjetsoriginatingfrompile-up arealso considered [46].The un-certaintiesintheb-taggingefficiencyandthemistagratearealso takenintoaccount.Theeffectofjetuncertaintiesontheexpected numberofeventsranges from10% to 3% atlow andhighvalues oftheBDTscore,respectively,withasimilareffectforW Z j j

−

QCD andW Z j j

−

EW events.

TheuncertaintyintheEmiss_T measurementisestimatedby prop-agating the uncertainties in the transverse momenta of hard physics objects andby applying momentum scale andresolution uncertaintiestothetrack-basedsoftterm [50,51].

The uncertainties due to lepton reconstruction, identification, isolationrequirementsandtriggerefficiencies areestimatedusing tag-and-probemethodsin Z

→ 

events [25,26].Uncertaintiesin theleptonmomentumscaleandresolutionarealsoassessedusing

Z

→ 

events [26,27]. These uncertainties impact the expected numberofeventsby 1

.

4% and 0

.

4% forelectrons andmuons, re-spectively, and are independent of the BDT score. Their effectis similarforW Z j j

−

QCD andW Z j j

−

EW events.

A40% yielduncertaintyisassignedtothereduciblebackground estimate.Thistakesintoaccountthelimitednumberofeventsin thecontrolregionsaswellasthedifferencesinbackground com-positionbetweenthecontrolregionsusedtodeterminethelepton misidentification rate and the control regions used to estimate theyield in thesignal region. The uncertaintydue toirreducible

Table 2

Summaryoftherelativeuncertaintiesinthemeasuredfiducial cross-sectionσfid.

W Z j j−EW.Theuncertaintiesarereportedas per-centages. Source Uncertainty [%] W Z j j−EW theory modelling 4.8 W Z j j−QCD theory modelling 5.2 W Z j j−EW and W Z j j−QCD interference 1.9 Jets 6.6 Pile-up 2.2 Electrons 1.4 Muons 0.4 b-tagging 0.1 MC statistics 1.9

Misid. lepton background 0.9

Other backgrounds 0.8

Luminosity 2.1

Total Systematics 10.9

backgroundsourcesotherthanW Z j j

−

QCD isevaluatedby propa-gating the uncertaintyin their MC cross-sections. These are 20% for V V V [59], 15% for t Z j [10] and tt

¯

+

V [60], and 25% for

Z Z j j

−

QCD toaccountforthepotentiallylargeimpactofscale vari-ations.

The uncertainty in the combined 2015+2016 integrated lumi-nosity is 2

.

1%. It is derived, following a methodology similar to that detailedinRef. [61], andusingthe LUCID-2detectorforthe baseline luminosity measurements [62], froma calibration ofthe luminosityscaleusingx– y beam-separationscans.

The effectof the systematic uncertainties on the final results after the maximum-likelihood fitis shown inTable 2 where the breakdown of the contributions to the uncertainties in the mea-suredfiducialcross-section

σ

fid.

W Z j j−EWispresented.The individual

sources ofsystematicuncertaintyarecombinedintotheory mod-ellingandexperimentalcategories.Asshowninthetable,the sys-tematicuncertaintiesinthejetreconstructionandcalibrationplay a dominant role, followed by the uncertainties in the modelling ofthe W Z j j

−

EW signalandofthe W Z j j

−

QCD background. Sys-tematic uncertainties inthe missing transversemomentum com-putationarisedirectlyfromthemomentumandenergycalibration of jets, electrons and muons and are included in the respective lines ofTable 2.Systematicuncertainties in themodelling ofthe reducibleandirreduciblebackgroundsother thanW Z j j

−

QCD are alsodetailed.

9. Cross-sectionmeasurements

The signal strength

μ

W Z j j−EW and its uncertainty are

deter-mined withaprofile-likelihood-ratioteststatistic [63].Systematic uncertainties in the input templates are treated asnuisance pa-rameterswithanassumedGaussiandistribution.Thedistributions ofmj j inthe Z Z -CRcontrol region,ofNb−jets intheb-CR,ofmj j

in the W Z j j

−

QCD control region and of the BDT score in the signal region, with background normalisations, signal normalisa-tionandnuisanceparametersadjustedbytheprofile-likelihoodfit areshowninFig.2.Thecorresponding post-fityieldsaredetailed in Table 3. The table presents the integral of the BDT score dis-tribution in the SR, but the uncertainty on the measured signal crosssectionisdominatedbyeventsathighBDTscore.Thesignal strengthismeasuredtobe

μ

_{W Z j j−}EW

=

1

.

77+₋00..4440

(

stat

.)

+ 0.15 −0.12

(

exp

.

syst

.)

+0.15 −0.12

(

mod

.

syst

.)

+ 0.15 −0.13

(

theory

)

+ 0.04 −0.02

(

lumi

.)

=

1

.

77+₋0₀._.51₄₅

,

The ATLAS Collaboration / Physics Letters B 793 (2019) 469–492 475

Fig. 2. Post-fitdistributionsof(a)mj jintheZ Z -CRcontrolregion,(b)Nb−jetsintheb-CR,(c)mj jintheW Z j j−QCD controlregionand(d)theBDTscoredistributioninthe signalregion.Signalandbackgroundsarenormalisedtotheexpectednumberofeventsafterthefit.TheuncertaintybandaroundtheMCexpectationincludesallsystematic uncertaintiesasobtainedfromthefit.

Table 3

ObservedandexpectednumbersofeventsintheW±Z j j signalregionandinthethree controlregions,afterthefit.TheexpectednumberofW Z j j−EW eventsfrom Sherpa and theestimatednumberofbackgroundeventsfromtheotherprocessesareshown.Thesum ofthebackgroundscontainingmisidentifiedleptonsislabelled‘Misid.leptons’.Thetotal correlatedpost-fituncertaintiesarequoted.

SR W Z j j−QCD CR b-CR Z Z -CR Data 161 213 141 52 Total predicted 167±11 204±12 146±11 51.3±7.0 W Z j j−EW (signal) 44±11 8.52±0.41 1.38±0.10 0.211±0.004 W Z j j−QCD 91±10 144±14 13.9±3.8 0.94±0.14 Misid. leptons 7.8±3.2 14.0±5.7 23.5±9.6 0.41±0.18 Z Z j j−QCD 11.1±2.8 18.3±1.1 2.35±0.06 40.8±7.2 t Z j 6.2±1.1 6.3±1.1 34.0±5.3 0.17±0.04 t¯t+V 4.7±1.0 11.14±0.37 71±15 3.47±0.54 Z Z j j−EW 1.80±0.45 0.44±0.10 0.10±0.03 4.2±1.2 V V V 0.59±0.15 0.93±0.23 0.13±0.03 1.06±0.30

where the uncertainties correspond to statistical, experimental systematic, theory modelling and interference systematic, theory

σ

_{W Z j j}fid.,MC_−EWnormalisationandluminosityuncertainties,respectively. Thebackground-onlyhypothesisisexcluded withasignificanceof

5

.

3 standard deviations, compared with 3

.

2 standard deviations expected.ThenormalisationparametersoftheW Z j j

−

QCD,tt

¯

+

V

and Z Z backgroundsconstrainedby data inthe control and sig-nalregionsaremeasuredtobe

μ

W Z j j−QCD

=

0

.

56

±

0

.

16,

μ

t¯t+V

=

1

.

07

±

0

.

28 and

μ

Z Z j j−QCD

=

1

.

34

±

0

.

44.TheobservedW Z j j

−

EW

productionintegratedfiducialcross-sectionderived fromthis sig-nalstrengthforasingleleptonicdecaymodeis

σ

fid. W Z j j−EW

=

0

.

57+ 0.14 −0.13

(

stat

.)

+ 0.05 −0.04

(

exp

.

syst

.)

+0.05 −0.04

(

mod

.

syst

.)

+ 0.01 −0.01

(

lumi

.)

fb

=

0

.

57+₋0₀._.16₁₄fb

.

It corresponds to the cross-section of electroweak W±Z j j

pro-duction, including interference effects between W Z j j

−

QCD and

W Z j j

−

EW processes,in thefiducial phasespacedefined in Sec-tion3usingdressed-levelleptons.

TheSM LOpredictionfrom Sherpa forelectroweakproduction withoutinterferenceeffectsis

σ

_{W Z j j}fid.,Sherpa_−EW

=

0

.

321

±

0

.

002

(

stat

.)

±

0

.

005

(

PDF

)

₋+0₀._.027₀₂₃

(

scale

)

fb

,

where the effects of uncertainties in the PDF and the

α

S value

used in the PDF determination, as well as the uncertainties due totherenormalisationandfactorisationscales,areevaluatedusing thesameprocedureastheonedescribedinSection8.

Alargercross-sectionof

σ

_{W Z j j−}fid.,MadGraph_EW

=

0

.

366

±

0

.

004

(

stat

.)

fb ispredicted by MadGraph.These predictions areat LO only and includeneither the effectsof interference,estimatedat LO tobe 10%, northeeffects ofNLO electroweakcorrectionsascalculated recentlyinRef. [64].

Fromthe numberofobserved eventsintheSR, theintegrated cross-sectionofW±Z j j productionintheVBSfiducialphasespace definedin Section 3, including W Z j j

−

EW and W Z j j

−

QCD con-tributionsandtheirinterference,ismeasured.Foragivenchannel

W±Z

→ 

±

ν



+



−, where



and



 indicates each type of lep-ton(e or

μ

),theintegratedfiducialcrosssectionthatincludesthe leptonic branchingfractionsofthe W and Z bosonsiscalculated as

σ

fid. W±Z j j

=

Ndata

−

Nbkg

L

·

CW Z j j

×



1

−

Nτ Nall



,

where Ndata and Nbkg are the number of observed events and

the estimated number of background events in the SR, respec-tively, and

L

is the integrated luminosity. The factor CW Z j j,

ob-tained from simulation, is the ratio of the number of selected signaleventsatdetectorleveltothenumberofeventsatparticle levelin thefiducial phasespace. This factorcorrects fordetector efficienciesandforQEDfinal-stateradiationeffects.The contribu-tion from

τ

-lepton decays, amounting to 4

.

7%, is removed from thecross-section definition by introducing thetermin parenthe-ses. This term is computed using simulation, where Nτ is the number of selected events at detector level in which at least one of the bosons decays into a

τ

-lepton and Nall is the

num-ber of selected W Z events with decays into any lepton. The

CW Z j j factorcalculatedwith Sherpa forthesumofthefour

mea-sured decay channels is 0

.

52 with a negligible statistical uncer-tainty. This factor is the same for W Z j j

−

QCD and W Z j j

−

EW events,aspredictedby Sherpa. Thetheory modellinguncertainty in this factor is 8%, as estimated from the difference between the Sherpa and MadGraph predictions.The uncertainties on this factorduetohigherorderQCDscalecorrectionsorPDFare negli-gible.

Themeasured W±Z j j cross-sectioninthefiducialphasespace forasingleleptonicdecaymodeis

σ

_Wfid±._{Z j j}

=

1

.

68

±

0

.

16

(

stat

.)

±

0

.

12

(

exp

.

syst

.)

±

0

.

13

(

mod

.

syst

.)

±

0

.

044

(

lumi

.)

fb

,

=

1

.

68

±

0

.

25 fb

,

wheretheuncertaintiescorrespondtostatistical,experimental sys-tematic, theory modelling systematic, and luminosity uncertain-ties, respectively. The corresponding prediction from Sherpa for strong and electroweak production without interference effects is

σ

_Wfid_±.,_{Z j j}Sherpa

=

2

.

15

±

0

.

01

(

stat

.)

±

0

.

05

(

PDF

)

₋+0₀._.65₄₄

(

scale

)

fb

.

EventsintheSRarealsousedtomeasuretheW±Z j j

differen-tial productioncross-sectionin theVBS fiducialphase space. The differential detector-level distributions are corrected for detector resolution using an iterative Bayesian unfolding method [65], as implemented inthe RooUnfoldtoolkit [66]. Three iterations were used fortheunfolding ofeach variable.The widthofthebins in each distribution ischosen accordingto theexperimental resolu-tion andtothe statisticalsignificanceofthe expectednumberof eventsinthatbin.ThefractionofsignalMC eventsreconstructed in the same bin as generated is always greater than 40% and around70% onaverage.

For each distribution, simulated W±Z j j events are used to obtain a response matrix that accounts for bin-to-bin migration effects between the reconstruction-level and particle-level distri-butions. The Sherpa MCsamplesfor W Z j j

−

EW and W Z j j

−

QCD production are added together to model W±Z j j production. To more closely model the data and to minimise unfolding uncer-tainties,their predictedcross-sectionsarerescaled bythe respec-tive signal strengths of 1

.

77 and 0

.

56 for the W Z j j

−

EW and

W Z j j

−

QCD contributions,respectively,asmeasuredindatabythe maximum-likelihoodfit.

Uncertainties in the unfolding due to imperfect modelling of the databy the MC simulationare evaluated usinga data-driven method [67],wheretheMCdifferentialdistributioniscorrectedto matchthedatadistributionandtheresultingweighted MC distri-butionatreconstructionlevelisunfoldedwiththeresponsematrix usedinthedataunfolding.Thenewunfoldeddistributionis com-paredwiththeweightedMCdistributionatgeneratorlevelandthe differenceistakenasthesystematicuncertainty.Theuncertainties obtainedrange from0

.

1% to 25% depending onthe resolutionof the unfoldedobservables andonthequality ofits descriptionby Sherpa_.

Measurements are performed asa function of three variables sensitive to anomalies in the quartic gauge coupling in W±Z j j

events [10], namelythescalarsumofthe transversemomentaof the three charged leptons associated with the W and Z bosons



p_T, the difference in azimuthal angle

φ (

W

,

Z

)

between the

W and Z bosons’directions,andthetransversemassoftheW±Z

system mW Z

T ,defined following Ref. [10]. Theseare presented in

Fig.3.

Measurements are also performed as a function of variables related to the kinematics of jets. The exclusive multiplicity of jets, Njets, is shown in Fig. 4. The absolute difference in

rapid-ity between the two tagging jets

yj j, the invariant mass of

the tagging jets mj j, the exclusive multiplicity Njetsgapof jets with pT

>

25 GeV in the gapin

η

betweenthe two tagging jets, and

theazimuthal anglebetweenthetwotaggingjets

φ

j jareshown

The ATLAS Collaboration / Physics Letters B 793 (2019) 469–492 477

Fig. 3. ThemeasuredW±Z j j differentialcross-sectionintheVBSfiducialphasespaceasafunctionof(a)p

T,(b)

φ(

W,Z)and(c)mW ZT .Theinnerandoutererrorbars onthedatapointsrepresentthestatisticalandtotaluncertainties,respectively.ThemeasurementsarecomparedwiththesumoftherescaledW Z j j−QCD andW Z j j−EW predictionsfrom Sherpa (solidline).TheW Z j j−EW andW Z j j−QCD contributionsarealsorepresentedbydashedanddashed-dottedlines,respectively.In(a)and(c),the righty-axisreferstothelastcross-sectionpoint,separatedfromtheothersbyaverticaldashedline,asthislastbinisintegrateduptothemaximumvaluereachedin thephasespace.Thelowerpanelsshowtheratiosofthedatatothepredictionsfrom Sherpa.Theuncertaintyonthe Sherpa predictionisdominatedbytheQCDscale uncertaintyontheW Z j j−QCD predictedcross-section,whoseenvelopeisof+30

−20% anditisnotrepresentedonthefigure.

Totaluncertaintiesinthemeasurementsaredominatedby sta-tisticaluncertainties.The differentialmeasurements arecompared withthepredictionfrom Sherpa,afterhavingrescaledtheseparate

W Z j j

−

QCD andW Z j j

−

EW componentsbytheglobal

μ

W Z j j−QCD

and

μ

W Z j j−EWparameters,respectively,obtainedfromthe

profile-likelihoodfittodata.InterferenceeffectsbetweentheW Z j j

−

QCD andW Z j j

−

EW processesare incorporatedviathe

μ

W Z j j−EW

pa-rameterasachangeoftheglobalnormalisationofthe Sherpa elec-troweakprediction.

10. Conclusion

An observationof electroweak productionof a diboson W±Z

systeminassociationwithtwojetsandmeasurementsofits pro-ductioncross-sectionin

√

s

=

13 TeV pp collisionsattheLHCare presented.The data were collected with the ATLAS detector and correspondtoanintegratedluminosityof36

.

1 fb−1.The measure-ments useleptonic decays ofthe gauge bosons into electrons or muonsandareperformedinafiducialphasespaceapproximating

the detector acceptance that increases the sensitivity to W±Z j j

electroweakproductionmodes.

TheelectroweakproductionofW±Z bosonsinassociationwith twojetsismeasuredwithobservedandexpectedsignificances of 5

.

3 and3

.

2 standarddeviations,respectively. Themeasured fidu-cialcross-sectionforelectroweakproductionincludinginterference effectsis

σ

W Z j j−EW

=

0

.

57+₋0₀._.14₁₃

(

stat

.)

+₋0₀._.05₀₄

(

exp

.

syst

.)

+0.05

−0.04

(

mod

.

syst

.)

+ 0.01

−0.01

(

lumi

.)

fb

.

ItisfoundtobelargerthantheLO SMpredictionof0

.

32

±

0

.

03 fb as calculated with the Sherpa MC event generator that includes neither interference effects, estimatedat LO to be 10%, nor NLO electroweakcorrections.Differentialcross-sectionsofW±Z j j

pro-duction,includingboththe strongandelectroweakprocesses,are also measured in thesame fiducial phase spaceas a function of severalkinematicobservables.

Fig. 4. Themeasured W±Z j j differentialcross-sectionintheVBSfiducialphase spaceasafunctionoftheexclusivejetmultiplicityofjetswithpT>40 GeV.The in-nerandoutererrorbarsonthedatapointsrepresentthestatisticalandtotal uncer-tainties,respectively.Themeasurementsarecomparedwiththesumofthescaled W Z j j−QCD and W Z j j−EW predictionsfrom Sherpa (solidline).TheW Z j j−EW andW Z j j−QCD contributionsarealsorepresentedbydashedanddashed-dotted lines,respectively.Theright y-axisreferstothelastcross-sectionpoint,separated fromtheothersbyaverticaldashedline,asthislastbinisintegrateduptothe maximumvaluereachedinthephasespace.Thelowerpanel showstheratioof thedatatothepredictionfrom Sherpa.Theuncertaintyonthe Sherpa predictionis dominatedbytheQCDscaleuncertaintyontheW Z j j−QCD predictedcross-section, whoseenvelopeisof+₋3020% anditisnotrepresentedonthefigure.

Acknowledgements

We thankCERN for the very successfuloperation of theLHC, aswell asthe support stafffrom ourinstitutions without 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,Hong KongSAR,China;ISF andBenoziyo Center, Is-rael; INFN, Italy; MEXT and JSPS, Japan; CNRST, Morocco; NWO, Netherlands;RCN, Norway;MNiSW andNCN, Poland;FCT, Portu-gal; MNE/IFA, Romania; MES of Russiaand NRC KI, Russian Fed-eration; JINR; MESTD, Serbia; MSSR, Slovakia; ARRS and MIZŠ, Slovenia;DST/NRF,SouthAfrica;MINECO,Spain;SRCand Wallen-berg Foundation, Sweden; SERI, SNSF and Cantons of Bern and Geneva, Switzerland; MOST, Taiwan; TAEK, Turkey; STFC, United Kingdom;DOEandNSF,UnitedStatesofAmerica. Inaddition, in-dividualgroupsandmembershavereceivedsupport fromBCKDF, Canarie,CRCandComputeCanada,Canada;COST,ERC,ERDF, Hori-zon 2020, andMarie Skłodowska-Curie Actions, European Union; Investissements d’ AvenirLabex and Idex, ANR, France; DFG and AvH Foundation, Germany; Herakleitos, Thales and Aristeia pro-grammesco-financedbyEU-ESFandtheGreekNSRF,Greece; BSF-NSF and GIF, Israel; CERCA Programme Generalitat de Catalunya, Spain;TheRoyalSocietyandLeverhulmeTrust,UnitedKingdom.

The crucial computing supportfrom all WLCG partnersis ac-knowledged gratefully, in particular from CERN, the ATLAS Tier-1 facilities at TRIUMF (Canada), NDGF (Denmark, Norway, Swe-den),CC-IN2P3(France),KIT/GridKA(Germany),INFN-CNAF(Italy), NL-T1(Netherlands),PIC(Spain),ASGC(Taiwan),RAL(UK)andBNL (USA),theTier-2facilitiesworldwideandlargenon-WLCGresource providers.Major contributorsofcomputingresources arelistedin Ref. [68].

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