Contents lists available atScienceDirect
Physics
Letters
B
www.elsevier.com/locate/physletb
Measurement
of
vector
boson
scattering
and
constraints
on
anomalous
quartic
couplings
from
events
with
four
leptons
and
two
jets
in proton–proton
collisions
at
√
s
=
13 TeV
.
The
CMS
Collaboration
CERN,Switzerland
a
r
t
i
c
l
e
i
n
f
o
a
b
s
t
r
a
c
t
Articlehistory:
Received9August2017
Receivedinrevisedform21September 2017
Accepted10October2017 Availableonline17October2017 Editor:M.Doser Keywords: CMS Physics SM ZZ VBS aQGC
Ameasurementofvectorbosonscatteringand constraintsonanomalousquarticgaugecouplingsfrom eventswithtwoZbosonsandtwojetsarepresented.Theanalysisisbasedonadatasampleofproton– proton collisionsat√s=13 TeV collectedwiththeCMS detectorand correspondingto anintegrated luminosity of35.9 fb−1.The search isperformed inthe fully leptonic finalstate ZZ→ , where ,=e or
μ.
The electroweakproductionoftwo Zbosonsinassociationwith twojetsismeasured with an observed (expected)significance of 2.7(1.6) standard deviations. A fiducialcross sectionfor theelectroweakproductionismeasuredtobeσ
EW(pp→ZZjj→ jj)=0.40+−00..2116(stat)+0.13 −0.09(syst) fb,
whichisconsistentwith thestandard modelprediction.Limitsonanomalousquarticgaugecouplings are determinedintermsoftheeffective fieldtheoryoperators T0,T1,T2,T8,andT9.Thisisthefirst measurementofvectorbosonscatteringintheZZ channelattheLHC.
©2017TheAuthor(s).PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense (http://creativecommons.org/licenses/by/4.0/).FundedbySCOAP3.
1. Introduction
Weakvector bosonscattering(VBS)plays acentral roleinthe standardmodel(SM)andisakeyprocesstoprobethenon-Abelian gaugestructureoftheelectroweak(EW)interaction.Intheabsence ofanyother contributions, the scatteringamplitude of longitudi-nallypolarizedvector bosonswouldviolateunitarityat center-of-massenergiesforthescatteringprocessoforder1 TeV [1,2].The discoveryofascalarbosonattheCERNLHC[3,4]withgauge cou-plingscompatiblewiththosepredictedfortheSMHiggsboson[5]
providesevidencethatcontributionsfromtheexchangeofthis bo-son maybe responsible forpreserving unitarity athighenergies, aspredictedintheSM.
UnitarityrestorationforlongitudinalbosonscatteringintheSM relies on theinterference of the VBS amplitudes andamplitudes thatinvolvetheHiggsboson.AnydeviationintheSMcouplingof theHiggsbosontothegaugebosonsbreaksthisdelicate cancella-tion,thuspermittingatestoftheEWsymmetrybreaking mecha-nism(EWSB)oftheSM.Thestudyofdifferentialcrosssectionsfor VBSprocessesatlargedibosoninvariantmassesprovidesa model-independent test of the Higgs boson couplings to vector bosons, complementing direct measurements of Higgs boson production
E-mailaddress:cms-publication-committee-chair@cern.ch.
anddecayrates.ManymodelsofphysicsbeyondtheSM alterthe couplingsofvectorbosons,andtheeffectscanbeparametrizedin an effectivefieldtheoryapproach [6].TheVBS topologyincreases the sensitivity to the contribution ofthe quartic interactions, al-lowingtestsforthepresenceofanomalousquarticgaugecouplings (aQGCs)[7].
AttheLHC,VBSisinitiatedbyquarksq fromthecolliding pro-tons; both quarks radiate vector bosons (V
=
W, Z) which then interact. Becauseoftherelativelysmalltransversemomentum pT carriedbythegaugebosonsandtheabsenceofanycolorexchange atleadingorder(LO),VBSischaracterizedbythepresenceoftwo forwardjetsjinadditiontotheoutgoinggaugebosons(qq→
VVjj) and little hadronic activitybetween the two jets [8,9]. The hard interaction inVBS only involvesthe EWinteraction. Fig. 1shows someoftheFeynmandiagramsthatcontributetotheEW produc-tionoftheVVjj signature,involvingquartic(topleft)andtrilinear vertices(topright),aswellasdiagramsinvolvingtheHiggsboson (bottomleft).Theqq→
VVjj processcanalsobemediatedthrough the stronginteraction(bottomrightinFig. 1), whichleads tothe samefinalstateastheVBSsignal,resultinginanirreducible back-ground.BoththeATLASandCMSCollaborationsperformedsearchesfor VBS usingproton–protoncollisions at
√
s=
8 TeV, notably inthe same-sign WWchannel [10–12].TheATLASCollaborationalsore-https://doi.org/10.1016/j.physletb.2017.10.020
0370-2693/©2017TheAuthor(s).PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense(http://creativecommons.org/licenses/by/4.0/).Fundedby SCOAP3.
Fig. 1. RepresentativeFeynmandiagrams forthe EW- (toprowand bottomleft) andQCD-inducedproduction(bottomright)oftheZZjj→ jj (,=e orμ) finalstate.Thescatteringofmassivegaugebosonsasdepictedinthetoprowis unitarizedbytheinterferencewithamplitudesthatfeaturetheHiggsboson(bottom left).
portedlimitsonafiducialcrosssectionforVBSintheWZchannel
[13].TheZZchannelremainedunprobed.LimitsonaQGCsare re-portedinRefs.[10–18].
Thispaperpresentsthefirstexperimental investigationofVBS intheZZchannelandexploitsthefullyleptonicfinalstate,where bothZ bosonsdecayintoelectronsormuons,ZZ
→
(
,
=
e or
μ
). Despite a low cross section, a small Z→
branching fraction,andalargeirreducibleQCDbackground,thischannel pro-videsafavorable laboratorytostudyEWSBbecauseallfinal-state particles are reconstructed. The clean leptonic final state results in a small reducible background, where one or more of the re-constructedleptoncandidatesoriginatefromthemisidentification ofjet fragments. Thischannel also provides a precise knowledge ofthescatteringenergy.Furthermore,thespin correlationsofthe reconstructed fermions permit the extraction of the longitudinal contributiontoVBS.Thesearch forthe EW productionof the
jj final state is carriedoutusing ppcollisions at
√
s=
13 TeV recordedwiththe CMSdetectorattheLHC.Thedatasetcorrespondstoanintegrated luminosityof35.9 fb−1 collectedin2016. Amultivariate discrim-inant, whichcombines observablessensitive to the kinematicsof theVBS process toseparate the EW- fromtheQCD-induced pro-duction,isusedto extractthe signalsignificance andto measure thecross section fortheEW production ina fiducialvolume. Fi-nally, the selectedjj events are used to constrain aQGCs describedby theoperators T0, T1, andT2aswell asthe neutral-currentoperatorsT8andT9[7].
2. TheCMSdetector
ThecentralfeatureoftheCMSapparatusisasuperconducting solenoidof 6 m internal diameter, providing a magnetic field of 3.8 T.Withinthesolenoidvolumearesiliconpixelandstrip track-ingdetectors,aleadtungstatecrystalelectromagneticcalorimeter (ECAL), and a brass and scintillator hadron calorimeter (HCAL),
each composed of a barrel and two endcap sections. Forward calorimetersextendthepseudorapidity
η
coverageprovidedbythe barrel andendcap detectors up to|
η
|
<
5. Muons are measured ingas-ionizationdetectorsembeddedinthesteelflux-returnyoke outsidethesolenoid.Thesilicontrackermeasureschargedparticleswithinthe pseu-dorapidity range
|
η
|
<
2.
5. It consists of 1440 silicon pixel and 15 148 silicon strip detector modules. For nonisolated particles with 1<
pT<
10 GeV and|
η
|
<
1.
4, the track resolutions are typically1.5%inpTand25–90(45–150) μm inthetransverse (lon-gitudinal)impactparameter[19].Electronsare measured inthe pseudorapidity range
|
η
| <
2.
5 usingboththetrackingsystemandtheECAL.Themomentum res-olution for electrons with pT≈
45 GeV from Z→
e+e− decays ranges from1.7%fornonshowering electrons inthebarrelregion (|
η
|
<
1.
479)to4.5%forshoweringelectronsintheendcaps[20].Muons are measured in the pseudorapidity range
|
η
| <
2.
4 using thesilicon trackerandmuon systems. The muon detectors are constructedusing threedifferenttechnologies:drift tubes for|
η
|
<
1.
2, cathode strip chambers for 0.
9<
|
η
|
<
2.
4, and resis-tive platechambersfor|
η
|
<
1.
6.Intheintermediate pT rangeof 20<
pT<
100 GeV, matching muons to tracks measured in the silicontrackerresultsinarelative pT resolutionof1.3–2.0%inthe barrel(|
η
|
<
1.
2), andbetter than6%inthe endcaps.The pT res-olutioninthebarrelis betterthan10% formuonswith pT up to 1 TeV[21].In theregion
|
η
|
<
1.
74,the HCALcells havewidths of0.087 inpseudorapidityand0.087inazimuth(φ
).Intheη
–φ
plane,and for|
η
|
<
1.
48,theHCALcellsmaponto5×
5 arraysofECAL crys-tals toformcalorimetertowers projectingradially outwardsfrom thenominalinteractionpoint.For|
η
|
>
1.
74,thesizeofthe tow-ersincreasesprogressivelytoamaximumof0.174inη
andφ
. Whencombininginformationfromtheentiredetector,thejet en-ergyresolutionamountstypicallyto15%at10 GeV,8%at100 GeV, and4% at1 TeV,to be comparedto about40%,12%, and5% ob-tainedwhentheECALandHCALcalorimetersaloneareused.Thefirstlevel ofthe CMStriggersystem, composedofcustom hardware processors, uses informationfromthe calorimetersand muondetectorstoselecteventsofinterestinafixedtimeinterval of3.2 μs. The high-level trigger processorfarm furtherdecreases theeventratefromaround100 kHz tolessthan1 kHz,beforedata storage[22].
AmoredetaileddescriptionoftheCMSdetector,togetherwith adefinitionofthe coordinatesystemusedandtherelevant kine-maticvariables,canbefoundinRef.[23].
3. Signalandbackgroundsimulation
SeveralMonteCarloeventgeneratorsare usedtosimulatethe signal and background contributions. The simulated samples are employed to optimizethe event selection, to develop the multi-variate discriminator, andto estimate the irreducible background yields.
TheEWproductionofZbosonpairsandtwofinal-statequarks, where the Z bosons decay leptonically, is simulated at LO using MadGraph5_amc@nlo v2.3.3(abbreviatedas MG5_aMC inthe fol-lowing) [24]. The sample includes triboson processes, where the Zboson pairisaccompanied by athird vectorboson that decays intojets,aswellasdiagramsinvolvingthequarticcouplingvertex. Thepredictionsfromthissamplearecross-checkedwiththose ob-tained fromtheLO generator Phantom v1.2.8[25],andexcellent agreementintheyieldsandthemultivariatedistributionexploited forthesignalextractionisfound.
The event samples of the QCD-induced production of two Z bosons are simulated with zero, one, and two outgoing partons
atBorn levelatnext-to-leadingorder (NLO)with MG5_aMC. The differentjet multiplicitiesaremergedusingtheFxFxscheme[26]
withamergingscaleof30 GeV,andleptonic Z bosondecaysare simulatedusing MadSpin [27]. The interferencebetweenthe EW andQCDdiagramsisevaluatedusingdedicatedsamplesproduced with MG5_aMC at LO. It is found to contribute less than 1% to the total yield andis thereforeneglected. The loop-induced pro-duction oftwo Z bosons,referred to asgg
→
ZZ, issimulated at LOwith mcfm v7.0.1[28].Adedicated MG5_aMC simulationofthe loop-inducedgg→
ZZjj processisused tocheck themodeling of theZZjj phase spaceinthe mcfm sample, andgoodagreementis found.Samples for ttZ and WWZ production, background processes that contain four prompt, isolated leptons and additional jetsin thefinalstate,aresimulatedwith MG5_aMC atNLO.
ThesimulationoftheaQGCprocessesisperformedatLOusing MG5_aMC and employs matrix element reweighting to obtain a finelyspacedgridineachofthefiveanomalouscouplingsprobed bytheanalysis.
The pythia v8.212 [29,30] package is used for parton show-ering, hadronization, and the underlying event simulation, with parameters set by the CUETP8M1 tune [31]. The NNPDF3.0 [32]
set ofparton distributionfunctions (PDFs)is used,and thePDFs are calculatedto thesame orderinQCD asthe hard process.All simulatedsamples are normalized to thecross sections obtained fromtherespectiveeventgenerator.
Thedetectorresponseissimulatedusingadetaileddescription oftheCMSdetectorimplementedinthe Geant4package [33,34]. Thesimulatedeventsarereconstructedusingthesamealgorithms asusedforthedata.Thesimulatedsamplesincludeadditional in-teractionsin thesame andneighboringbunch crossings, referred to as pileup. Simulated events are weighted so that the pileup distribution reproduces that observed in the data, which has an averageofabout23interactionsperbunchcrossing.
4. Eventselection
Thefinalstateshouldconsistofatleasttwopairsofoppositely chargedisolatedleptonsandatleasttwohadronicjets.TheZZ se-lectionissimilartothatusedintheCMSinclusiveZZcrosssection measurement[35].
The primary triggers requirethe presence ofa pairof loosely isolatedleptons. Thehighest pT electron (muon) musthave pT
>
23(
17)
GeV, andthe next-to-highest pT lepton must have pT>
12(
8)
GeV.The dilepton triggers require that the tracks associ-atedwith theleptons originate fromwithin 2 mm of each other along the beam axis. Triggers requiring a triplet of low-pT lep-tonswithnoisolation criterion,aswellasisolatedsingle-electron andsingle-muon triggers withminimal pT thresholds of 27 and 22 GeV,respectively,helptorecoverefficiency.Theoveralltrigger efficiencyforeventsthatsatisfy theZZselectiondescribed below isgreaterthan98%.Events are reconstructed using a particle-flow algorithm [36]
that reconstructs and identifies each individual particle with an optimized combination ofall subdetector information. The miss-ingtransversemomentumvector
pmissT isdefinedastheprojection ontotheplaneperpendiculartothebeamaxisofthenegative vec-torsumofthemomentaofallreconstructedparticle-flowobjects inanevent.Itsmagnitudeisreferredtoaspmiss
T .
The reconstructed vertex with the largest value of summed physics-object p2T is taken to be the primary pp interaction ver-tex.The physics objects are theobjects returned by ajet finding algorithm[37,38]appliedtoallchargedtracksassociatedwiththe vertex, plus the corresponding associated pmissT . Leptonsand jets arerequiredtooriginatefromtheprimaryvertex.
Electronsareidentifiedusingamultivariateclassifier,which in-cludes observablessensitiveto bremsstrahlungalongthe electron trajectory, the geometrical and energy-momentum compatibility between the electron track and the associated energy cluster in the ECAL,theshapeofthe electromagneticshower, andvariables thatdiscriminateagainstelectronsoriginatingfromphoton conver-sions[20].
Muons are reconstructed by combining information from the silicontrackerandthemuon system[21].Thematchingbetween theinnerandoutertracksproceedseitheroutside-in,startingfrom atrackinthemuonsystem,orinside-out,startingfromatrackin thesilicontracker.Themuonsareselectedfromthereconstructed muon trackcandidates by applyingminimal requirementson the trackinboththemuonsystemandsilicontracker,andtakinginto accountcompatibilitywithsmallenergydepositsinthe calorime-ters.
In order to suppress electrons from photon conversions and muons originating from in-flight decays of hadrons, we require thethree-dimensionalimpactparameterofeachleptontrack, com-putedwithrespecttotheprimary vertexposition,tobe lessthan fourtimestheuncertaintyontheimpactparameter.
Leptonsare requiredtobeisolated fromotherparticles inthe event.Therelativeisolationisdefinedas
Riso
=
charged hadrons pT
+
max 0,
neutral hadrons pT+
photons pT−
pPUT pT,
(1)where the sums run over the charged and neutral hadrons and photons,inaconedefinedby
R
≡
(
η
)
2+ (φ)
2=
0.
3 around theleptontrajectory.Tominimizethecontributionofcharged par-ticlesfrompileuptotheisolationcalculation,chargedhadronsare includedonly ifthey originate fromthe primaryvertex. The con-tributionofneutralparticlesfrompileupis pPUT .Forelectrons,pPUTis evaluated withthe jet area method described inRef. [39].For muons, pPU
T is taken to be half the pT sum of all charged par-ticles in the cone originating from pileup vertices. The factor of one-halfaccountsfortheexpectedratioofchargedtoneutral par-ticleenergyinhadronicinteractions.LeptonswithRiso
<
0.
35 are consideredisolated.Theefficiencyoftheleptonreconstructionandselectionis mea-suredinbinsofp
T and
η
usingthetag-and-probetechnique.The measured efficienciesareused tocorrectthesimulation.The lep-tonmomentumscalesarecalibratedinbinsofpTandη
usingthedecay products of known dilepton resonances. The electron mo-mentum scale for data iscorrected with a Z
→
e+e− sample by matchingthepeakofthereconstructeddielectronmassspectrum totheknownvalueofmZ.AGaussiansmearingoftheelectron en-ergies in the simulation is also applied to match the Z→
e+e− mass resolution in data. Muon momenta are calibrated using a Kalmanfilterapproach[40],usingJ/ψ
mesonandZ bosondecays. Analgorithmisusedtoidentifyfinal-stateradiation(FSR)from theleptons [41].Aphoton withpT>
2 GeV andwithin aconeofR
=
0.
5 aroundthe leptonmomentumdirectionisselectedifit satisfies quality requirements.The FSRphotons identified by the algorithmareexcludedfromtheleptonisolationcomputation.Jets are reconstructed fromparticle-flow candidates using the anti-kT clustering algorithm [37], asimplemented inthe FASTJET package [38],withadistanceparameterof0.4. Inordertoassure a good reconstruction efficiency and to reduce the instrumental backgroundaswell asthecontamination frompileup,loose iden-tification criteriabased onthe multiplicities andenergyfractions carriedby chargedandneutralhadronsare imposedon jets[42]. Onlyjetswith
|
η
|
<
4.
7 areconsidered.Jet energy corrections are extractedfrom data and simulated eventsto account forthe effectsof pileup,uniformity ofthe de-tector response, and residual differences between the jet energy scaleinthedataandinthesimulation.Thejet energyscale cali-bration[43–45]reliesoncorrectionsparameterizedintermsofthe uncorrected pT and
η
ofthejet,andisappliedasamultiplicative factor,scaling thefour-momentum vector ofeach jet.In orderto ensurethatjetsarewell measuredandtoreducethepileup con-tamination,alljetsmusthaveacorrectedpT largerthan30 GeV.A signal event must contain at least two Z candidates, each formed from pairs of isolated electrons or muons of oppo-site charges. Only reconstructed electrons (muons) with a pT
>
7(
5)
GeV areconsidered.Amongthefourleptons,thehighestpT leptonmusthave pT>
20 GeV, andthesecond-highest pT lepton musthavepT>
12(
10)
GeV ifitisanelectron(muon).Allleptons arerequired tobe separatedbyR
(
1,
2) >
0.
02, andelectrons arerequiredtobeseparatedfrommuonsbyR
(
e,
μ
) >
0.
05.Withineach event, all permutations of leptons giving a valid pair of Z candidates are considered. For each ZZ candidate, the leptonpair withtheinvariant mass closest tothe nominalZ bo-son mass is denoted Z1 andis required to have a mass greater than40 GeV.TheotherdileptoncandidateisdenotedZ2.BothmZ1
andmZ2 are required to be less than 120 GeV. All pairs of
op-positely chargedleptons, regardlessofflavor, in theZZcandidate arerequiredtosatisfym
>
4 GeV tosuppressbackgroundsfromhadrondecays.
Ifmultiple ZZ candidates in an event pass this selection, the candidatewithmZ1 closest to the nominalZ bosonmass is
cho-sen.Intherarecase(0.3%)offurtherambiguity,whichmayarise ineventswithmorethanfourleptons,theZ2candidatethat max-imizesthescalar pT sumofthefourleptonsischosen.Finally,the Z1 andZ2candidatesmusthavemassesbetween60 and120 GeV. ThisselectionisreferredtoastheZZ selection.
ThesearchfortheEWproductionoftwoZ bosonsisperformed onasubsetofeventsthatpasstheZZ selection,namelythosethat featureatleasttwojets.Thejetsarerequiredtobeseparatedfrom theleptonsoftheZZ candidateby
R
=
0.
4.Thetwohighest pT jetsare referredtoasthetaggingjetsandtheir invariantmassis requiredtobelargerthan100 GeV.Thisselectionisreferredtoas theZZjj selection.5. Backgroundestimation
The dominant background is the QCD-induced production of two Z bosons in association with jets, as shown in the bottom right diagram of Fig. 1. The yield and shape of the multivariate discriminantofthisirreduciblebackgroundaretakenfrom simula-tion,butultimatelyconstrainedbythedatainthefitthatextracts theEW signal, asdescribed inSection 7. Other irreducible back-groundsarise fromprocesses that produce fourgenuine high-pT isolatedleptons,pp
→
ttZ+
jets andpp→
WWZ+
jets.Thesesmall contributionsfeaturekinematicdistributionssimilartothatofthe dominantbackgroundandareestimatedusingsimulation.Reducible backgrounds arise from processes in which heavy-flavorjetsproducesecondary leptons orfromprocessesinwhich jetsaremisidentifiedasleptons.Theleptonidentificationand iso-lationrequirementssignificantly suppressthisbackground,which isverysmallcomparedtothesignalaftertheselection.
Thereduciblebackground,referredtoasZ
+
X,ispredominately composedofZ+
jets events,withminorcontributionsfromtt+
jets andWZ+
jets processes. Thisreduciblecontributionisestimated from data by inverting the lepton selection criteria and weight-ingeventsincontrolregions usingalepton misidentificationrate whichisalsodeterminedfromdata.Twocontrolregions servetoestimate the reducible background fromevents withone ortwo misidentifiedleptons,respectively.
Events inthecontrol regionwithone (two)misidentified lep-ton(s)satisfytheZZjj selection,withtheexceptionthatoneofthe Z boson candidates is constructed from one (two) lepton(s) that failtheidentificationorisolationcriteria.Thelepton misidentifica-tionrateismeasuredbyselectingeventsthatfeatureoneZ boson candidateanda thirdreconstructedlepton.Thefractionofevents forwhichthethirdleptonsatisfiestheidentificationandisolation criteriaistakenastheleptonmisidentificationrate.Theprocedure isidenticaltothatusedinRef.[35]andisdescribedinmoredetail inRef.[41].
6. Systematicuncertainties
Several sources of systematic uncertainty are considered and evaluated by varying each relevant parameter. The resulting changes tothe distributionof themultivariate discriminant,both inshapeandyield,aretakenintoaccount.Theimpactofthe vari-ationforeachsourceofuncertaintyissummarizedbelow.
Renormalization andfactorizationscale uncertainties are eval-uatedby varyingbothscales independentlybyfactorsoftwoand one-half, removing combinations where both variations differ by a factor of four, and amount to 10 (7)% for the dominant QCD background(EWsignal).ThePDF
+
α
svariationsareevaluatedfol-lowing the PDF4LHC prescription [46], and increase from 6% at low values of the multivariate discriminant to 9% in the signal-richregion.A40%uncertaintyintheyieldoftheloop-inducedZZjj backgroundisassigned.The impactofthejetenergyscale uncer-taintyamountsto20(4)%atlow(high)valuesofthemultivariate discriminant and the impact of the jet energy resolution uncer-taintyis8%[44,45].TheuncertaintiesintheQCDbackground nor-malization andthe jet energyscale are the dominant systematic uncertaintiesinthemeasurement.HigherorderEWcorrectionsin VBS processes areknown to be negative andatthe leveloftens ofpercent[47],butsuchcorrectionshavenotbeencalculatedfor thefinalstateconsideredinthispaper,andthereforearenot con-sideredhere.Nevertheless,theimpactofsuchNLOEWcorrections wouldbenegligibleinthisanalysis,whichislimitedbythelarge statistical uncertainty. The uncertainty in the lepton reconstruc-tion and selection efficiency is 6/4/2% in the 4e
/
2e2μ
/
4μ
final states, respectively. The uncertainty in the integrated luminosity is2.5% [48]. Thesystematicuncertaintyin thetriggerefficiencies isevaluatedby takingthedifference betweenthetrigger efficien-cies measured in data and in simulated events,and amounts to 2%.A 40%yielduncertaintyinthereduciblebackgroundestimate based ondata samplestakesinto account thelimitednumber of eventsinthecontrolregionsaswellasthemismatchinthe back-groundcomposition inthecontrol regionsused todeterminethe leptonmisidentificationratesandthecontrolregionsusedto esti-matetheyieldinthesignalregion.7. SearchforEWZZjjproduction
The expected signal purity in the ZZjj selection is about 5%, with 83% of eventscoming from QCD-induced production. Addi-tionalkinematicselectionsarethereforenecessarytoenhancethe contribution from EW production. Fig. 2 shows the absolute di-jet pseudorapidity separation
|
η
jj|
and the dijetinvariant massmjj for events passing the ZZjj selection. Table 1 shows the ex-pectedandobserved numberofeventsforthe ZZjj selectionand illustrates theincrease of theVBS signal purityobtainedwithan exemplaryselectionthatrequiresmjj
>
400 GeV and|
η
jj| >
2.
4.ThedeterminationofthesignalstrengthfortheEWproduction, i.e.,theratioofthemeasuredcrosssectiontotheSMexpectation
Fig. 2. Distributionofthedijetpseudorapidityseparation(left)anddijetinvariantmass(right)foreventspassingtheZZjj selection,whichrequiresmjj>100 GeV.Points representthedata,filledhistogramstheexpectedsignalandbackgroundcontributions.Nodatabeyond|ηjj|>7 (left)andmjj>1600 GeV (right)isobserved.
Table 1
SignalandbackgroundyieldsfortheZZjj selectionandforanillustrativeVBSsignal-enrichedselectionthatrequiresmjj>400 GeV and|ηjj|>2.4.
Selection ttZ and WWZ QCD ZZjj Z+X Total bkg. EW ZZjj Total expected Data ZZjj 7.1±0.8 97±14 6.6±2.5 111±14 6.2±0.7 117±14 99 VBS signal-enriched 0.9±0.2 19±4 0.7±0.3 20±4 4±0.5 25±4 19
Fig. 3. DistributionoftheBDToutputinthecontrolregionobtainedbyselectingZZjj eventswithmjj<400 GeV or|ηjj|<2.4 (left)andfortheZZjj selection(right).Points
representthedata,filledhistogramstheexpectedsignalandbackgroundcontributions.
μ
=
σ
/
σ
SM,employsamultivariatediscriminanttooptimally sep-aratethesignal andtheQCD background.Thescikit-learn frame-work [49] is used to train and optimize a boosted decisiontree (BDT)onsimulatedeventstoexploitthekinematicdifferences be-tweentheEWsignal andtheQCD background.Seven observables areusedintheBDT,includingmjj,|
η
jj|
,mZZ,aswellasthe Zep-penfeld variables [8]η
∗Zi=
η
Zi− (
η
jet 1+
η
jet 2)/
2 of the two Zbosons,andtheratiobetweenthepTofthetaggingjetsystemand the scalar pT sumof the taggingjets. The BDT also exploitsthe eventbalance Rphard
T , whichis definedasthe transverse compo-nentofthevectorsumoftheZ bosonsandtaggingjetsmomenta, normalizedtothescalar pTsumofthesameobjects[50].
Atotalof36discriminatingvariablesincludingobservables sen-sitive to parton emissions betweenthe tagging jets, the produc-tion anddecay angles of the leptons, Z bosons, and tagging jets aswellasquark–gluontagginginformationare consideredinthe
BDT training.Observablesthatdonotimprovetheareaunderthe signal-versus-backgroundefficiencycurve(AUC)areremovedfrom the BDT.The observablessensitivetoextra partonemissions pro-vide little marginal AUC increase and are not retained because of the limited modeling accuracy in the simulation. The tunable hyper-parameters oftheBDT trainingalgorithmare optimizedvia a grid-search algorithm. Finally,the BDT performance is checked using amatrix element approach[51–53] that provides a similar separationbetweenthesignalandbackgroundprocesses.
To validate the modeling of the backgrounds in the search, a QCD-enrichedcontrolregionisdefinedbyselectingeventswith
mjj
<
400 GeV or|
η
jj|
<
2.
4. Good agreement is observed be-tween the data and SM expectation in this control region, as shown in Fig. 3 (left). The classifier output distribution for all events inthe ZZjj selection includingthehigh signal purity con-tributionatlargeBDToutputvaluesisshowninFig. 3(right).Table 2
Expectedandobservedlowerandupper95%CLlimitsonthecouplingsofthequarticoperatorsT0,T1,andT2, aswellastheneutralcurrentoperatorsT8andT9.Theunitarityboundsarealsolisted.Allcouplingparameter limitsareinTeV−4,whiletheunitarityboundsareinTeV.
Coupling Exp. lower Exp. upper Obs. lower Obs. upper Unitarity bound
fT0/4 −0.53 0.51 −0.46 0.44 2.5
fT1/4 −0.72 0.71 −0.61 0.61 2.3
fT2/4 −1.4 1.4 −1.2 1.2 2.4
fT8/4 −0.99 0.99 −0.84 0.84 2.8
fT9/4 −2.1 2.1 −1.8 1.8 2.9
The BDT distribution of the events in the ZZjj selection is usedtoextract thesignificanceoftheEWsignalviaa maximum-likelihoodfit.Theexpecteddistributionsforthesignalandthe ir-reduciblebackgroundsaretakenfromthesimulationwhilethe re-duciblebackgroundisestimatedfromthedata.Theshapeand nor-malizationofeachdistributionareallowedtovaryinthefitwithin therespectiveuncertainties.Thisapproachconstrains theyieldof theQCD-inducedproductionfromthebackground-enrichedregion oftheBDTdistribution.
The systematic uncertainties are treated as nuisance parame-tersinthefitandprofiled[54].The post-fitvaluesare thenused toextract thesignal strength. Thesignal strength ismeasured to be
μ
=
1.
39+−00..7257(stat)−+00..4631(syst)=
1.
39+−00..8665andthe background-only hypothesis is excluded with a significance of 2.
7 standard deviations(1.
6 standarddeviationsexpected).The measured signal strength is used to determine the fidu-cial cross section for the EW production. The fiducial volume is almost identical to the selections imposed at the reconstruction level, the only difference being the lepton thresholds of pT
>
5 GeV and
|
η
|
<
2.
5.Thegenerator-levelleptonmomentaarecor-rectedby addingthe momentaof generator-levelphotons within
R
(,
γ
)
<
0.
1.The kinematicselection of theZ bosons andthe finalZZjj candidateproceedsasthereconstruction-levelselection. Theobservedsignalstrengthcorrespondstoafiducialcrosssection ofσ
EW(
pp→
ZZjj→
jj
)
=
0.
40+−00..2116(stat)+0.13
−0.09(syst) fb, com-patiblewiththeSMpredictionof0
.
29−+00..0203fb.8. Limitsonanomalousquarticgaugecouplings
TheeventsintheZZjj selectionareusedtoconstrainaQGCsin theeffectivefieldtheoryapproach.TheZZjj channelissensitiveto theoperatorsT0, T1,andT2,aswellastheneutralcurrent opera-torsT8andT9[7].Theformeroperatorsareconstructedfromthe SUL
(
2)
gaugefields,whilethelatteronlyinvolvetheUY(
1)
fields.Asaconsequence,theT8andT9operatorsareexperimentally ac-cessible only via final states involving the neutralgauge bosons. Theeffectof anonzero aQGC isto enhancethe productioncross sectionatlargemassesoftheZZ system.ThusthemZZdistribution isusedtoconstraintheaQGCparameters fTi
/
4.Theincreaseof theyieldexhibitsaquadraticdependenceontheanomalous cou-pling,andaparabolicfunctionisfittedtotheper-massbinyields, allowing for an interpolation between the discrete coupling pa-rametersofthe simulatedsignals. Thestatisticalanalysisemploys thesamemethodologyusedforthesignalstrength,includingthe profiling ofthe systematic uncertainties. The distributions of the backgroundmodel,including theEW component, are normalized totheir respectiveSMpredictions.TheWaldGaussian approxima-tionand Wilks’ theoremare used to derive 95% confidencelevel (CL)limitsontheaQGC parameters[55–57].The measurementis statisticallylimited.Fig. 4showstheexpectedmZZ distributionfortheSMandtwo aQGCscenarios. Table 2lists theindividuallower andupper lim-its obtainedby setting all other anomalous couplings to zero, as well as the unitarity bound. The unitarity bound is determined
Fig. 4. ThemZZdistributionintheZZjj selectiontogetherwiththeSMprediction
and twohypothesesfor the aQGCcouplingstrengths. Pointsrepresentthedata, filled histogramsthe expectedsignaland backgroundcontributions. Thelastbin includesallcontributionswithmZZ>1200 GeV.
using the VBFNLO framework [58] as the scattering energy mZZ at which the aQGC coupling strength set equal to the observed limitwouldresultinascatteringamplitudethatviolatesunitarity. Thesearethe moststringentlimitstodateontheaQGC parame-ters fT0,1,2
/
4and fT8,9/
4.9. Summary
A search was performed for vector boson scattering in the four-lepton andtwo-jet final state using proton–protoncollisions at 13 TeV. The data correspond to an integrated luminosity of 35.9 fb−1 collectedwiththeCMSdetectorattheLHC.
The electroweak production of two Z bosons in association withtwo jets was measured withan observed (expected) signif-icance of 2.7(1.6) standard deviations.The fiducialcross section is
σ
EW(
pp→
ZZjj→
jj
)
=
0.
40+−00..2116(stat)+−00..1309(syst) fb, con-sistentwiththestandardmodelpredictionof0.
29+−00..0203 fb.Limits on anomalous quartic gauge couplings were set atthe 95%confidencelevelintermsofeffectivefieldtheoryoperators,in unitsofTeV−4:
−
0.
46<
fT0/
4<
0.
44−
0.
61<
fT1/
4<
0.
61−
1.
2<
fT2/
4<
1.
2−
0.
84<
fT8/
4<
0.
84−
1.
8<
fT9/
4<
1.
8.
Thesearethefirstresultsfortheelectroweakproductionoftwo Z bosonsinassociationwithjetsattheLHCandthemoststringent limitsontheT0,T1, T2,T8,andT9anomalousquarticgauge cou-plingstodate.
Acknowledgements
WecongratulateourcolleaguesintheCERNaccelerator depart-ments for the excellent performance of the LHC and thank the technicalandadministrativestaffs atCERN andatother CMS in-stitutes for their contributions to the success of the CMS effort. Inaddition,wegratefullyacknowledgethecomputingcentresand personneloftheWorldwideLHCComputingGridfordeliveringso effectivelythe computinginfrastructureessential to ouranalyses. Finally, we acknowledge the enduring support for the construc-tionandoperation oftheLHCandthe CMSdetectorprovidedby thefollowingfundingagencies:BMWFWandFWF(Austria);FNRS and FWO (Belgium); CNPq, CAPES, FAPERJ, and FAPESP (Brazil); MES (Bulgaria); CERN; CAS, MOST, and NSFC (China); COLCIEN-CIAS(Colombia);MSESandCSF(Croatia);RPF(Cyprus);SENESCYT (Ecuador); MoER, ERC IUT, and ERDF (Estonia); Academy of Fin-land,MEC,andHIP(Finland);CEAandCNRS/IN2P3(France);BMBF, DFG, and HGF (Germany); GSRT (Greece); OTKA and NIH (Hun-gary);DAEandDST(India);IPM(Iran);SFI(Ireland);INFN(Italy); MSIPandNRF(RepublicofKorea);LAS (Lithuania);MOE andUM (Malaysia); BUAP, CINVESTAV,CONACYT, LNS, SEP, and UASLP-FAI (Mexico); MBIE (New Zealand); PAEC (Pakistan); MSHE and NSC (Poland);FCT(Portugal);JINR(Dubna);MON,RosAtom,RAS,RFBR andRAEP(Russia);MESTD (Serbia);SEIDI,CPAN,PCTI andFEDER (Spain);SwissFundingAgencies(Switzerland);MST(Taipei); ThEP-Center, IPST, STAR, and NSTDA (Thailand); TUBITAK and TAEK (Turkey);NASUandSFFR(Ukraine); STFC(United Kingdom);DOE andNSF(USA).
Individuals have received support from the Marie-Curie pro-gramme and the European Research Council and Horizon 2020 Grant,contract No. 675440 (EuropeanUnion);theLeventis Foun-dation;the A. P. Sloan Foundation; theAlexander von Humboldt Foundation; the Belgian Federal Science Policy Office; the Fonds pourlaFormationàlaRecherchedansl’Industrieetdans l’Agricul-ture (FRIA-Belgium); the Agentschapvoor Innovatie door Weten-schap en Technologie (IWT-Belgium); the Ministry of Education, YouthandSports(MEYS)oftheCzechRepublic;theCouncilof Sci-enceandIndustrialResearch,India;theHOMINGPLUSprogramme of the Foundation for Polish Science, cofinanced from European Union,Regional DevelopmentFund,the MobilityPlusprogramme oftheMinistryofScienceandHigherEducation,theNational Sci-ence Center (Poland), contracts Harmonia 2014/14/M/ST2/00428, Opus2014/13/B/ST2/02543,2014/15/B/ST2/03998,and2015/19/B/ ST2/02861, Sonata-bis 2012/07/E/ST2/01406; the National Priori-tiesResearchProgram byQatar NationalResearch Fund;the Pro-gramaClarín-COFUND del Principado de Asturias;the Thalis and Aristeia programmes cofinanced by EU-ESF andthe Greek NSRF; theRachadapisekSompotFundforPostdoctoralFellowship, Chula-longkornUniversityandtheChulalongkornAcademicintoIts 2nd Century Project Advancement Project (Thailand); and the Welch Foundation,contractC-1845.
References
[1] B.W. Lee,C.Quigg,H.B.Thacker,Strength ofweakinteractionsat veryhigh energies andthe Higgsboson mass, Phys.Rev.Lett. 38(1977)883, http:// dx.doi.org/10.1103/PhysRevLett.38.883.
[2] B.W.Lee,C.Quigg,H.B.Thacker,Weakinteractionsatveryhighenergies:the roleoftheHiggsbosonmass,Phys.Rev.D16(1977)1519,http://dx.doi.org/ 10.1103/PhysRevD.16.1519.
[3] ATLASCollaboration,Observationofanewparticleinthesearchforthe Stan-dardModelHiggsbosonwiththeATLASdetectorattheLHC,Phys.Lett.B716 (2012)1,http://dx.doi.org/10.1016/j.physletb.2012.08.020,arXiv:1207.7214. [4] CMSCollaboration,Observationofanewboson atamassof125GeVwith
theCMSexperimentattheLHC,Phys.Lett.B716(2012)30,http://dx.doi.org/ 10.1016/j.physletb.2012.08.021,arXiv:1207.7235.
[5] ATLAS and CMSCollaborations, Measurements ofthe Higgsboson produc-tionand decayratesand constraintson itscouplingsfrom acombined AT-LASand CMSanalysis ofthe LHCpp collisiondataat √s=7 and8 TeV, J. HighEnergyPhys.08(2016)045,http://dx.doi.org/10.1007/JHEP08(2016)045, arXiv:1606.02266.
[6] C.Degrande,N.Greiner,W.Kilian,O.Mattelaer,H.Mebane,T.Stelzer,S. Willen-brock,C.Zhang,Effectivefieldtheory:amodernapproachtoanomalous cou-plings,Ann.Phys. 335(2013) 21,http://dx.doi.org/10.1016/j.aop.2013.04.016, arXiv:1205.4231.
[7] O.J.P. Éboli, M.C. Gonzalez-Garcia, J.K. Mizukoshi, pp→ j je±μ±νν and
j je±μ∓ννatO(α6
em)andO(αem4 αs2)forthestudyofthequarticelectroweak gaugeboson vertexat CERN LHC,Phys. Rev.D 74 (2006) 073005, http:// dx.doi.org/10.1103/PhysRevD.74.073005,arXiv:hep-ph/0606118.
[8] D.Rainwater,R.Szalapski,D.Zeppenfeld,ProbingcolorsingletexchangeinZ+
2-jeteventsattheCERNLHC,Phys.Rev.D54(1996)6680,http://dx.doi.org/ 10.1103/PhysRevD.54.6680,arXiv:hep-ph/9605444.
[9] V.A. Khoze, M.G. Ryskin, W.J. Stirling, P.H. Williams, A Z-monitor to cali-brateHiggsproductionviavectorbosonfusionwithrapiditygapsattheLHC, Eur.Phys. J. C 26 (2003) 429,http://dx.doi.org/10.1140/epjc/s2002-01069-2, arXiv:hep-ph/0207365.
[10] ATLASCollaboration,EvidenceforelectroweakproductionofW±W±j j inpp
collisionsat√s=8 TeV withtheATLASdetector,Phys.Rev.Lett.113(2014) 141803,http://dx.doi.org/10.1103/PhysRevLett.113.141803,arXiv:1405.6241. [11] CMSCollaboration,Studyofvectorbosonscatteringandsearchfornewphysics
ineventswithtwosame-signleptonsandtwojets,Phys.Rev.Lett.114(2015) 051801,http://dx.doi.org/10.1103/PhysRevLett.114.051801,arXiv:1410.6315. [12] ATLAS Collaboration, Measurementof W±W± vector–boson scattering and
limits on anomalous quartic gauge couplings with the ATLAS detector, Phys.Rev.D96(2017)012007,http://dx.doi.org/10.1103/PhysRevD.96.012007, arXiv:1611.02428.
[13] ATLASCollaboration,MeasurementsofW±Z productioncrosssectionsinpp
collisionsat √s=8 TeV withthe ATLASdetector andlimits onanomalous gaugebosonself-couplings,Phys.Rev.D93(2016)092004,http://dx.doi.org/ 10.1103/PhysRevD.93.092004,arXiv:1603.02151.
[14] CMSCollaboration,Evidenceforexclusiveγ γ→W+W−productionand con-straints on anomalous quartic gaugecouplings in pp collisions at √s=7 and 8 TeV, J. High Energy Phys. 08 (2016) 119, http://dx.doi.org/10.1007/ JHEP08(2016)119,arXiv:1604.04464.
[15] ATLAS Collaboration, Search for anomalous electroweak production of
W W/W Z in associationwitha high-massdijetsystem inpp collisionsat
√
s=8 TeV withtheATLASdetector,Phys.Rev.D95(2017)032001,http:// dx.doi.org/10.1103/PhysRevD.95.032001,arXiv:1609.05122.
[16] CMSCollaboration,Measurementofthecrosssectionforelectroweak produc-tionofZγ inassociationwithtwojetsandconstraintsonanomalousquartic gaugecouplingsinproton–protoncollisionsat√s=8 TeV,Phys.Lett.B770 (2017)380,http://dx.doi.org/10.1016/j.physletb.2017.04.071,arXiv:1702.03025. [17] CMS Collaboration,Measurementofelectroweak-induced productionofWγ
withtwojetsinppcollisionsat√s=8 TeV andconstraintsonanomalous quarticgaugecouplings,J.HighEnergyPhys.06(2017)106,http://dx.doi.org/ 10.1007/JHEP06(2017)106,arXiv:1612.09256.
[18] ATLAS Collaboration, Studiesof Zγ production inassociationwith a high-massdijetsysteminpp collisionsat√s=8 TeV withtheATLASdetector,J. HighEnergy Phys.07(2017)107,http://dx.doi.org/10.1007/JHEP07(2017)107, arXiv:1705.01966.
[19] CMSCollaboration,Descriptionandperformanceoftrackandprimary-vertex reconstruction with the CMS tracker, J. Instrum. 9 (2014) P10009, http:// dx.doi.org/10.1088/1748-0221/9/10/P10009,arXiv:1405.6569.
[20] CMSCollaboration,Performanceofelectronreconstructionandselectionwith the CMS detector in proton–proton collisions at √s=8 TeV, J. Instrum. 10 (2015) P06005, http://dx.doi.org/10.1088/1748-0221/10/06/P06005, arXiv: 1502.02701.
[21] CMSCollaboration,PerformanceofCMSmuonreconstructioninppcollision eventsat√s=7 TeV,J.Instrum.7(2012)P10002,http://dx.doi.org/10.1088/ 1748-0221/7/10/P10002,arXiv:1206.4071.
[22] CMS Collaboration, The CMStrigger system,J. Instrum. 12 (2017) P01020, http://dx.doi.org/10.1088/1748-0221/12/01/P01020,arXiv:1609.02366. [23] CMSCollaboration,TheCMSexperimentattheCERNLHC,J.Instrum.3(2008)
S08004,http://dx.doi.org/10.1088/1748-0221/3/08/S08004.
[24] J.Alwall,R.Frederix,S.Frixione,V.Hirschi,F.Maltoni,O.Mattelaer,H.-S.Shao, T.Stelzer,P.Torielli,M. Zaro,Theautomatedcomputation oftree-leveland next-to-leadingorder differentialcrosssections,and theirmatching to par-tonshowersimulations,J.HighEnergyPhys.07(2014)079,http://dx.doi.org/ 10.1007/JHEP07(2014)079,arXiv:1405.0301.
[25] A.Ballestrero, A.Belhouari, G.Bevilacqua,V.Kashkan, E.Maina,PHANTOM: a MonteCarloeventgeneratorforsixpartonfinalstatesathighenergy col-liders,Comput.Phys.Commun.180(2009)401,http://dx.doi.org/10.1016/j.cpc. 2008.10.005,arXiv:0801.3359.
[26] R. Frederix,S. Frixione, Merging meetsmatching inMC@NLO, J. High En-ergy Phys. 12 (2012) 061,http://dx.doi.org/10.1007/JHEP12(2012)061, arXiv: 1209.6215.
[27] P.Artoisenet,R.Frederix,O.Mattelaer,R.Rietkerk,Automaticspin-entangled decaysofheavyresonancesinMonteCarlosimulations,J.HighEnergyPhys. 03(2013)015,http://dx.doi.org/10.1007/JHEP03(2013)015,arXiv:1212.3460. [28] J.M.Campbell,R.K.Ellis,MCFMfor thetevatronand theLHC,Nucl.Phys.B,
Proc.Suppl.205–206(2010)10,http://dx.doi.org/10.1016/j.nuclphysbps.2010. 08.011,arXiv:1007.3492.
[29] T.Sjöstrand, S. Mrenna,P.Skands, PYTHIA6.4 physics andmanual, J.High EnergyPhys.05(2006)026,http://dx.doi.org/10.1088/1126-6708/2006/05/026, arXiv:hep-ph/0603175.
[30] T.Sjöstrand,S.Ask,J.R.Christiansen,R.Corke,N.Desai,P.Ilten,S.Mrenna,S. Prestel,C.O.Rasmussen,P.Z.Skands,AnintroductiontoPYTHIA8.2,Comput. Phys. Commun. 191 (2015) 159, http://dx.doi.org/10.1016/j.cpc.2015.01.024, arXiv:1410.3012.
[31] CMS Collaboration, Event generator tunes obtained from underlying event and multiparton scattering measurements, Eur. Phys. J. C 76 (2016) 155, http://dx.doi.org/10.1140/epjc/s10052-016-3988-x,arXiv:1512.00815. [32] R.D.Ball,et al.,NNPDF,Partondistributions forthe LHCrun II,J.High
En-ergy Phys. 04 (2015)040, http://dx.doi.org/10.1007/JHEP04(2015)040, arXiv: 1410.8849.
[33] S.Agostinelli, et al., GEANT4, GEANT4—asimulation toolkit, Nucl. Instrum. MethodsA506(2003)250,http://dx.doi.org/10.1016/S0168-9002(03)01368-8. [34] J.Allison,etal.,GEANT4developmentsandapplications,IEEETrans.Nucl.Sci.
53(2006)270,http://dx.doi.org/10.1109/TNS.2006.869826.
[35] CMS Collaboration, Measurement of the ZZ production cross section and Z→ +−+− branchingfraction in pp collisions at √s=13 TeV, Phys. Lett.B763(2016)280,http://dx.doi.org/10.1016/j.physletb.2016.10.054,arXiv: 1607.08834.
[36] CMSCollaboration,Particle-flow reconstructionandglobalevent description withtheCMSdetector,J.Instrum.12(2017)P10003,http://dx.doi.org/10.1088/ 1748-0221/12/10/P10003,arXiv:1706.04965.
[37] M.Cacciari,G.P.Salam,G.Soyez,Theanti-ktjetclusteringalgorithm,J.High
EnergyPhys.04(2008)063,http://dx.doi.org/10.1088/1126-6708/2008/04/063, arXiv:0802.1189.
[38] M.Cacciari,G.P.Salam,G.Soyez,FastJetusermanual,Eur.Phys.J.C72(2012) 1896,http://dx.doi.org/10.1140/epjc/s10052-012-1896-2,arXiv:1111.6097. [39] M.Cacciari,G.P.Salam,Pileupsubtractionusingjetareas,Phys. Lett.B659
(2008)119,http://dx.doi.org/10.1016/j.physletb.2007.09.077,arXiv:0707.1378. [40] R. Frühwirth, Application of Kalman filtering to track and vertex fitting,
Nucl. Instrum. Methods A 262 (1987) 444, http://dx.doi.org/10.1016/0168-9002(87)90887-4.
[41] CMS Collaboration, Measurement of the properties of a Higgs boson in thefour-leptonfinalstate,Phys.Rev.D89(2014)092007,http://dx.doi.org/ 10.1103/PhysRevD.89.092007,arXiv:1312.5353.
[42] CMSCollaboration,Jetalgorithms performancein13 TeV data, CMSPhysics Analysis Summary CMS-PAS-JME-16-003, https://cds.cern.ch/record/2256875, 2017.
[43] CMSCollaboration,Determinationofjetenergycalibrationandtransverse mo-mentum resolutionin CMS, J. Instrum. 6(2011) P11002, http://dx.doi.org/ 10.1088/1748-0221/6/11/P11002,arXiv:1107.4277.
[44] CMSCollaboration,JetenergyscaleandresolutionintheCMSexperimentin ppcollisionsat8 TeV,J.Instrum.12(2017)P02014,http://dx.doi.org/10.1088/ 1748-0221/12/02/P02014,arXiv:1607.03663.
[45] CMS Collaboration, Jet energy scale and resolution performances with 13 TeV data,CMSDetectorPerformanceSummaryCMS-DP-2016-020,https:// cds.cern.ch/record/2160347,2016.
[46] J. Butterworth, et al., PDF4LHC recommendations for LHC Run II, J. Phys. G43(2016)023001,http://dx.doi.org/10.1088/0954-3899/43/2/023001,arXiv: 1510.03865.
[47] B.Biedermann,A.Denner,M.Pellen,Largeelectroweakcorrectionstovector– boson scattering at the large hadron collider, Phys. Rev. Lett. 118 (2017) 261801,http://dx.doi.org/10.1103/PhysRevLett.118.261801,arXiv:1611.02951. [48] CMSCollaboration,CMSluminositymeasurementsforthe2016datataking
pe-riod,CMSPhysicsAnalysisSummaryCMS-PAS-LUM-17-001,https://cds.cern.ch/ record/2257069,2017.
[49] F.Pedregosa,etal.,Scikit-learn:machinelearninginpython,J.Mach.Learn. Res. 12 (2011) 2825, http://www.jmlr.org/papers/volume12/pedregosa11a/ pedregosa11a.pdf,arXiv:1201.0490.
[50] CMSCollaboration,Measurementofelectroweakproductionoftwojetsin as-sociationwithaZbosoninproton–protoncollisionsat√s=8 TeV,Eur.Phys. J. C 75 (2015) 66, http://dx.doi.org/10.1140/epjc/s10052-014-3232-5, arXiv: 1410.3153.
[51] Y.Gao,A.V.Gritsan, Z.Guo,K. Melnikov,M. Schulze,N.V.Tran,Spin deter-minationofsingle-producedresonancesathadroncolliders,Phys. Rev.D81 (2010)075022,http://dx.doi.org/10.1103/PhysRevD.81.075022,arXiv:1001.3396, Erratum:Phys.Rev.D81(2010)079905,http://dx.doi.org/10.1103/PhysRevD.81. 079905.
[52] S. Bolognesi, Y. Gao, A.V. Gritsan, K. Melnikov, M. Schulze, N.V. Tran, A. Whitbeck,Spinandparityofasingle-producedresonanceat theLHC,Phys. Rev.D86(2012)095031,http://dx.doi.org/10.1103/PhysRevD.86.095031,arXiv: 1208.4018.
[53] I.Anderson,S.Bolognesi,F.Caola,Y.Gao,A.V.Gritsan,C.B.Martin,K.Melnikov, M.Schulze,N.V.Tran,A.Whitbeck,Y.Zhou,ConstraininganomalousH V V
in-teractionsatprotonandleptoncolliders,Phys.Rev.D89(2014)035007,http:// dx.doi.org/10.1103/PhysRevD.89.035007,arXiv:1309.4819.
[54] ATLASandCMSCollaborations,LHCHiggsCombinationGroup,Procedurefor theLHCHiggsbosonsearchcombinationinSummer2011, CMS-NOTE-2011-005,ATL-PHYS-PUB-2011-11,http://cdsweb.cern.ch/record/1379837,2011. [55] A.L.Read,Presentationofsearchresults:theCLstechnique,J.Phys.G28(2002)
2693,http://dx.doi.org/10.1088/0954-3899/28/10/313.
[56] T. Junk, Confidence level computation for combining searches with small statistics,Nucl.Instrum.MethodsA434(1999)435,http://dx.doi.org/10.1016/ S0168-9002(99)00498-2,arXiv:hep-ex/9902006.
[57] G.Cowan,K.Cranmer,E.Gross,O.Vitells,Asymptoticformulaefor likelihood-based testsofnewphysics,Eur.Phys.J.C71(2011)1554,http://dx.doi.org/ 10.1140/epjc/s10052-011-1554-0, arXiv:1007.1727, Erratum: https://doi.org/ 10.1140/epjc/s10052-013-2501-z.
[58] K.Arnold,etal.,VBFNLO:apartonlevelMonteCarloforprocesseswith elec-troweakbosons,Comput.Phys.Commun.180(2009)1661, http://dx.doi.org/ 10.1016/j.cpc.2009.03.006,arXiv:0811.4559.
TheCMSCollaboration
A.M. Sirunyan,
A. Tumasyan
YerevanPhysicsInstitute,Yerevan,Armenia
W. Adam,
F. Ambrogi,
E. Asilar,
T. Bergauer,
J. Brandstetter,
E. Brondolin,
M. Dragicevic,
J. Erö,
M. Flechl,
M. Friedl,
R. Frühwirth
1,
V.M. Ghete,
J. Grossmann,
J. Hrubec,
M. Jeitler
1,
A. König,
N. Krammer,
I. Krätschmer,
D. Liko,
T. Madlener,
I. Mikulec,
E. Pree,
D. Rabady,
N. Rad,
H. Rohringer,
J. Schieck
1,
R. Schöfbeck,
M. Spanring,
D. Spitzbart,
W. Waltenberger,
J. Wittmann,
C.-E. Wulz
1,
M. Zarucki
InstitutfürHochenergiephysik,Wien,Austria
V. Chekhovsky,
V. Mossolov,
J. Suarez Gonzalez
InstituteforNuclearProblems,Minsk,Belarus
E.A. De Wolf,
D. Di Croce,
X. Janssen,
J. Lauwers,
H. Van Haevermaet,
P. Van Mechelen,
N. Van Remortel
S. Abu Zeid,
F. Blekman,
J. D’Hondt,
I. De Bruyn,
J. De Clercq,
K. Deroover,
G. Flouris,
D. Lontkovskyi,
S. Lowette,
S. Moortgat,
L. Moreels,
Q. Python,
K. Skovpen,
S. Tavernier,
W. Van Doninck,
P. Van Mulders,
I. Van Parijs
VrijeUniversiteitBrussel,Brussel,Belgium
H. Brun,
B. Clerbaux,
G. De Lentdecker,
H. Delannoy,
G. Fasanella,
L. Favart,
R. Goldouzian,
A. Grebenyuk,
G. Karapostoli,
T. Lenzi,
J. Luetic,
T. Maerschalk,
A. Marinov,
A. Randle-conde,
T. Seva,
C. Vander Velde,
P. Vanlaer,
D. Vannerom,
R. Yonamine,
F. Zenoni,
F. Zhang
2UniversitéLibredeBruxelles,Bruxelles,Belgium
A. Cimmino,
T. Cornelis,
D. Dobur,
A. Fagot,
M. Gul,
I. Khvastunov,
D. Poyraz,
C. Roskas,
S. Salva,
M. Tytgat,
W. Verbeke,
N. Zaganidis
GhentUniversity,Ghent,Belgium
H. Bakhshiansohi,
O. Bondu,
S. Brochet,
G. Bruno,
C. Caputo,
A. Caudron,
S. De Visscher,
C. Delaere,
M. Delcourt,
B. Francois,
A. Giammanco,
A. Jafari,
M. Komm,
G. Krintiras,
V. Lemaitre,
A. Magitteri,
A. Mertens,
M. Musich,
K. Piotrzkowski,
L. Quertenmont,
M. Vidal Marono,
S. Wertz
UniversitéCatholiquedeLouvain,Louvain-la-Neuve,Belgium
N. Beliy
UniversitédeMons,Mons,Belgium
W.L. Aldá Júnior,
F.L. Alves,
G.A. Alves,
L. Brito,
M. Correa Martins Junior,
C. Hensel,
A. Moraes,
M.E. Pol,
P. Rebello Teles
CentroBrasileirodePesquisasFisicas,RiodeJaneiro,Brazil
E. Belchior Batista Das Chagas,
W. Carvalho,
J. Chinellato
3,
A. Custódio,
E.M. Da Costa,
G.G. Da Silveira
4,
D. De Jesus Damiao,
S. Fonseca De Souza,
L.M. Huertas Guativa,
H. Malbouisson,
M. Melo De Almeida,
C. Mora Herrera,
L. Mundim,
H. Nogima,
A. Santoro,
A. Sznajder,
E.J. Tonelli Manganote
3,
F. Torres Da Silva De Araujo,
A. Vilela Pereira
UniversidadedoEstadodoRiodeJaneiro,RiodeJaneiro,Brazil
S. Ahuja
a,
C.A. Bernardes
a,
T.R. Fernandez Perez Tomei
a,
E.M. Gregores
b,
P.G. Mercadante
b,
S.F. Novaes
a,
Sandra S. Padula
a,
D. Romero Abad
b,
J.C. Ruiz Vargas
aaUniversidadeEstadualPaulista,SãoPaulo,Brazil bUniversidadeFederaldoABC,SãoPaulo,Brazil
A. Aleksandrov,
R. Hadjiiska,
P. Iaydjiev,
M. Misheva,
M. Rodozov,
M. Shopova,
S. Stoykova,
G. Sultanov
InstituteforNuclearResearchandNuclearEnergyofBulgariaAcademyofSciences,Bulgaria
A. Dimitrov,
I. Glushkov,
L. Litov,
B. Pavlov,
P. Petkov
UniversityofSofia,Sofia,Bulgaria
W. Fang
5,
X. Gao
5BeihangUniversity,Beijing,China
M. Ahmad,
J.G. Bian,
G.M. Chen,
H.S. Chen,
M. Chen,
Y. Chen,
C.H. Jiang,
D. Leggat,
H. Liao,
Z. Liu,
F. Romeo,
S.M. Shaheen,
A. Spiezia,
J. Tao,
C. Wang,
Z. Wang,
E. Yazgan,
H. Zhang,
J. Zhao
Y. Ban,
G. Chen,
Q. Li,
S. Liu,
Y. Mao,
S.J. Qian,
D. Wang,
Z. Xu
StateKeyLaboratoryofNuclearPhysicsandTechnology,PekingUniversity,Beijing,China
C. Avila,
A. Cabrera,
L.F. Chaparro Sierra,
C. Florez,
C.F. González Hernández,
J.D. Ruiz Alvarez
UniversidaddeLosAndes,Bogota,Colombia
B. Courbon,
N. Godinovic,
D. Lelas,
I. Puljak,
P.M. Ribeiro Cipriano,
T. Sculac
UniversityofSplit,FacultyofElectricalEngineering,MechanicalEngineeringandNavalArchitecture,Split,Croatia
Z. Antunovic,
M. Kovac
UniversityofSplit,FacultyofScience,Split,Croatia
V. Brigljevic,
D. Ferencek,
K. Kadija,
B. Mesic,
A. Starodumov
6,
T. Susa
InstituteRudjerBoskovic,Zagreb,Croatia
M.W. Ather,
A. Attikis,
G. Mavromanolakis,
J. Mousa,
C. Nicolaou,
F. Ptochos,
P.A. Razis,
H. Rykaczewski
UniversityofCyprus,Nicosia,Cyprus
M. Finger
7,
M. Finger Jr.
7CharlesUniversity,Prague,CzechRepublic
E. Carrera Jarrin
UniversidadSanFranciscodeQuito,Quito,Ecuador
Y. Assran
8,
9,
S. Elgammal
9,
A. Mahrous
10AcademyofScientificResearchandTechnologyoftheArabRepublicofEgypt,EgyptianNetworkofHighEnergyPhysics,Cairo,Egypt
R.K. Dewanjee,
M. Kadastik,
L. Perrini,
M. Raidal,
A. Tiko,
C. Veelken
NationalInstituteofChemicalPhysicsandBiophysics,Tallinn,Estonia
P. Eerola,
J. Pekkanen,
M. Voutilainen
DepartmentofPhysics,UniversityofHelsinki,Helsinki,Finland
J. Härkönen,
T. Järvinen,
V. Karimäki,
R. Kinnunen,
T. Lampén,
K. Lassila-Perini,
S. Lehti,
T. Lindén,
P. Luukka,
E. Tuominen,
J. Tuominiemi,
E. Tuovinen
HelsinkiInstituteofPhysics,Helsinki,Finland
J. Talvitie,
T. Tuuva
LappeenrantaUniversityofTechnology,Lappeenranta,Finland
M. Besancon,
F. Couderc,
M. Dejardin,
D. Denegri,
J.L. Faure,
F. Ferri,
S. Ganjour,
S. Ghosh,
A. Givernaud,
P. Gras,
G. Hamel de Monchenault,
P. Jarry,
I. Kucher,
E. Locci,
M. Machet,
J. Malcles,
G. Negro,
J. Rander,
A. Rosowsky,
M.Ö. Sahin,
M. Titov
IRFU,CEA,UniversitéParis-Saclay,Gif-sur-Yvette,France
A. Abdulsalam,
I. Antropov,
S. Baffioni,
F. Beaudette,
P. Busson,
L. Cadamuro,
C. Charlot,
R. Granier de Cassagnac,
M. Jo,
S. Lisniak,
A. Lobanov,
J. Martin Blanco,
M. Nguyen,
C. Ochando,
G. Ortona,
P. Paganini,
P. Pigard,
S. Regnard,
R. Salerno,
J.B. Sauvan,
Y. Sirois,
A.G. Stahl Leiton,
T. Strebler,
Y. Yilmaz,
A. Zabi,
A. Zghiche
J.-L. Agram
11,
J. Andrea,
D. Bloch,
J.-M. Brom,
M. Buttignol,
E.C. Chabert,
N. Chanon,
C. Collard,
E. Conte
11,
X. Coubez,
J.-C. Fontaine
11,
D. Gelé,
U. Goerlach,
M. Jansová,
A.-C. Le Bihan,
N. Tonon,
P. Van Hove
UniversitédeStrasbourg,CNRS,IPHCUMR7178,F-67000Strasbourg,France
S. Gadrat
CentredeCalculdel’InstitutNationaldePhysiqueNucleaireetdePhysiquedesParticules,CNRS/IN2P3,Villeurbanne,France
S. Beauceron,
C. Bernet,
G. Boudoul,
R. Chierici,
D. Contardo,
P. Depasse,
H. El Mamouni,
J. Fay,
L. Finco,
S. Gascon,
M. Gouzevitch,
G. Grenier,
B. Ille,
F. Lagarde,
I.B. Laktineh,
M. Lethuillier,
L. Mirabito,
A.L. Pequegnot,
S. Perries,
A. Popov
12,
V. Sordini,
M. Vander Donckt,
S. Viret
UniversitédeLyon,UniversitéClaudeBernardLyon1,CNRS-IN2P3,InstitutdePhysiqueNucléairedeLyon,Villeurbanne,France
A. Khvedelidze
7GeorgianTechnicalUniversity,Tbilisi,Georgia
Z. Tsamalaidze
7TbilisiStateUniversity,Tbilisi,Georgia
C. Autermann,
S. Beranek,
L. Feld,
M.K. Kiesel,
K. Klein,
M. Lipinski,
M. Preuten,
C. Schomakers,
J. Schulz,
T. Verlage
RWTHAachenUniversity,I.PhysikalischesInstitut,Aachen,Germany
A. Albert,
E. Dietz-Laursonn,
D. Duchardt,
M. Endres,
M. Erdmann,
S. Erdweg,
T. Esch,
R. Fischer,
A. Güth,
M. Hamer,
T. Hebbeker,
C. Heidemann,
K. Hoepfner,
S. Knutzen,
M. Merschmeyer,
A. Meyer,
P. Millet,
S. Mukherjee,
M. Olschewski,
K. Padeken,
T. Pook,
M. Radziej,
H. Reithler,
M. Rieger,
F. Scheuch,
D. Teyssier,
S. Thüer
RWTHAachenUniversity,III.PhysikalischesInstitutA,Aachen,Germany
G. Flügge,
B. Kargoll,
T. Kress,
A. Künsken,
J. Lingemann,
T. Müller,
A. Nehrkorn,
A. Nowack,
C. Pistone,
O. Pooth,
A. Stahl
13RWTHAachenUniversity,III.PhysikalischesInstitutB,Aachen,Germany
M. Aldaya Martin,
T. Arndt,
C. Asawatangtrakuldee,
K. Beernaert,
O. Behnke,
U. Behrens,
A. Bermúdez Martínez,
A.A. Bin Anuar,
K. Borras
14,
V. Botta,
A. Campbell,
P. Connor,
C. Contreras-Campana,
F. Costanza,
C. Diez Pardos,
G. Eckerlin,
D. Eckstein,
T. Eichhorn,
E. Eren,
E. Gallo
15,
J. Garay Garcia,
A. Geiser,
A. Gizhko,
J.M. Grados Luyando,
A. Grohsjean,
P. Gunnellini,
M. Guthoff,
A. Harb,
J. Hauk,
M. Hempel
16,
H. Jung,
A. Kalogeropoulos,
M. Kasemann,
J. Keaveney,
C. Kleinwort,
I. Korol,
D. Krücker,
W. Lange,
A. Lelek,
T. Lenz,
J. Leonard,
K. Lipka,
W. Lohmann
16,
R. Mankel,
I.-A. Melzer-Pellmann,
A.B. Meyer,
G. Mittag,
J. Mnich,
A. Mussgiller,
E. Ntomari,
D. Pitzl,
A. Raspereza,
B. Roland,
M. Savitskyi,
P. Saxena,
R. Shevchenko,
S. Spannagel,
N. Stefaniuk,
G.P. Van Onsem,
R. Walsh,
Y. Wen,
K. Wichmann,
C. Wissing,
O. Zenaiev
DeutschesElektronen-Synchrotron,Hamburg,Germany
S. Bein,
V. Blobel,
M. Centis Vignali,
T. Dreyer,
E. Garutti,
D. Gonzalez,
J. Haller,
A. Hinzmann,
M. Hoffmann,
A. Karavdina,
R. Klanner,
R. Kogler,
N. Kovalchuk,
S. Kurz,
T. Lapsien,
I. Marchesini,
D. Marconi,
M. Meyer,
M. Niedziela,
D. Nowatschin,
F. Pantaleo
13,
T. Peiffer,
A. Perieanu,
C. Scharf,
P. Schleper,
A. Schmidt,
S. Schumann,
J. Schwandt,
J. Sonneveld,
H. Stadie,
G. Steinbrück,
F.M. Stober,
M. Stöver,
H. Tholen,
D. Troendle,
E. Usai,
L. Vanelderen,
A. Vanhoefer,
B. Vormwald
M. Akbiyik,
C. Barth,
S. Baur,
E. Butz,
R. Caspart,
T. Chwalek,
F. Colombo,
W. De Boer,
A. Dierlamm,
B. Freund,
R. Friese,
M. Giffels,
A. Gilbert,
D. Haitz,
F. Hartmann
13,
S.M. Heindl,
U. Husemann,
F. Kassel
13,
S. Kudella,
H. Mildner,
M.U. Mozer,
Th. Müller,
M. Plagge,
G. Quast,
K. Rabbertz,
M. Schröder,
I. Shvetsov,
G. Sieber,
H.J. Simonis,
R. Ulrich,
S. Wayand,
M. Weber,
T. Weiler,
S. Williamson,
C. Wöhrmann,
R. Wolf
InstitutfürExperimentelleKernphysik,Karlsruhe,Germany
G. Anagnostou,
G. Daskalakis,
T. Geralis,
V.A. Giakoumopoulou,
A. Kyriakis,
D. Loukas,
I. Topsis-Giotis
InstituteofNuclearandParticlePhysics(INPP),NCSRDemokritos,AghiaParaskevi,Greece
G. Karathanasis,
S. Kesisoglou,
A. Panagiotou,
N. Saoulidou
NationalandKapodistrianUniversityofAthens,Athens,Greece
I. Evangelou,
C. Foudas,
P. Kokkas,
S. Mallios,
N. Manthos,
I. Papadopoulos,
E. Paradas,
J. Strologas,
F.A. Triantis
UniversityofIoánnina,Ioánnina,Greece
M. Csanad,
N. Filipovic,
G. Pasztor,
G.I. Veres
17MTA-ELTELendületCMSParticleandNuclearPhysicsGroup,EötvösLorándUniversity,Budapest,Hungary
G. Bencze,
C. Hajdu,
D. Horvath
18,
Á. Hunyadi,
F. Sikler,
V. Veszpremi,
G. Vesztergombi
17,
A.J. Zsigmond
WignerResearchCentreforPhysics,Budapest,Hungary
N. Beni,
S. Czellar,
J. Karancsi
19,
A. Makovec,
J. Molnar,
Z. Szillasi
InstituteofNuclearResearchATOMKI,Debrecen,Hungary
M. Bartók
17,
P. Raics,
Z.L. Trocsanyi,
B. Ujvari
InstituteofPhysics,UniversityofDebrecen,Debrecen,Hungary
S. Choudhury,
J.R. Komaragiri
IndianInstituteofScience(IISc),Bangalore,India
S. Bahinipati
20,
S. Bhowmik,
P. Mal,
K. Mandal,
A. Nayak
21,
D.K. Sahoo
20,
N. Sahoo,
S.K. Swain
NationalInstituteofScienceEducationandResearch,Bhubaneswar,India
S. Bansal,
S.B. Beri,
V. Bhatnagar,
R. Chawla,
N. Dhingra,
A.K. Kalsi,
A. Kaur,
M. Kaur,
R. Kumar,
P. Kumari,
A. Mehta,
J.B. Singh,
G. Walia
PanjabUniversity,Chandigarh,India
Ashok Kumar,
Shah Aashaq,
A. Bhardwaj,
S. Chauhan,
B.C. Choudhary,
R.B. Garg,
S. Keshri,
A. Kumar,
S. Malhotra,
M. Naimuddin,
K. Ranjan,
R. Sharma
UniversityofDelhi,Delhi,India
R. Bhardwaj,
R. Bhattacharya,
S. Bhattacharya,
U. Bhawandeep,
S. Dey,
S. Dutt,
S. Dutta,
S. Ghosh,
N. Majumdar,
A. Modak,
K. Mondal,
S. Mukhopadhyay,
S. Nandan,
A. Purohit,
A. Roy,
D. Roy,
S. Roy Chowdhury,
S. Sarkar,
M. Sharan,
S. Thakur
SahaInstituteofNuclearPhysics,HBNI,Kolkata,India