Search for invisible decays of a Higgs boson produced through vector boson fusion in proton-proton collisions at √s=13 TeV

Contents lists available atScienceDirect

Physics

Letters

B

www.elsevier.com/locate/physletb

Search

for

invisible

decays

of

a

Higgs

boson

produced

through

vector

boson

fusion

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:

Received16September2018 Receivedinrevisedform7March2019 Accepted9April2019

Availableonline15April2019 Editor:M.Doser Keywords: CMS Physics Higgs VBF Invisibledecays

AsearchforinvisibledecaysofaHiggsbosonisperformedusingproton-protoncollisiondatacollected withtheCMSdetectorattheLHCin2016atacenter-of-massenergy√s=13TeV,correspondingtoan integratedluminosityof35.9 fb−1.ThesearchtargetstheproductionofaHiggsbosonviavectorboson fusion.Thedataarefoundtobeinagreementwiththebackgroundcontributionsfromstandardmodel processes. Anobserved(expected)upper limitof0.33 (0.25),at95%confidencelevel,isplacedonthe branchingfractionoftheHiggsbosondecaytoinvisibleparticles,assumingstandardmodelproduction rates and aHiggs boson mass of125.09 GeV. Results from acombination ofthis analysis and other direct searches forinvisible decays ofthe Higgsboson, performedusing data collectedat√s=7,8, and 13 TeV,arepresented.Anobserved(expected)upperlimitof0.19 (0.15),at95%confidencelevel,is setonthebranchingfractionofinvisibledecaysoftheHiggsboson.Thecombinedlimitrepresentsthe moststringentboundontheinvisiblebranchingfractionoftheHiggsbosonreportedtodate.Thisresult isalsointerpretedinthecontextofHiggs-portaldarkmattermodels,inwhichupperboundsareplaced onthespin-independentdark-matter-nucleonscatteringcrosssection.

©2019TheAuthor(s).PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense (http://creativecommons.org/licenses/by/4.0/).FundedbySCOAP3.

1. Introduction

SincethediscoveryoftheHiggsbosonattheCERNLHC [1–3], the ATLAS and CMS Collaborations have pursued a wide-ranging programtostudyitspropertiesandinteractions.Precise measure-mentsofthecouplingsoftheHiggsbosontostandardmodel(SM) particlesindicatethatthepropertiesofthenewparticleare consis-tentwiththeSMpredictions [4].Thesemeasurementsalsoprovide indirect constraints on additional contributions to the Higgs bo-sonwidthfrombeyondtheSM(BSM)decays.Basedontheresults presentedin Ref. [4],an indirect upperlimit on theHiggsboson branchingfractiontoBSMparticlesof0.34issetat95%confidence level(CL).

In the SM, the Higgs boson decays invisibly (H

→

inv) only through the H

→

ZZ

→

4

ν

process, with a branching fraction,

B

(

H

→

inv

)

, of about 10−3_{. The rate for invisible decays of the}

Higgsbosonmaybesignificantly enhancedinthecontext of sev-eralBSMscenarios [5–8],includingthose inwhichthe Higgs bo-son actsas a portal todark matter (DM) [9–12]. Direct searches forH

→

inv decaysincreasethesensitivityto

B

(

H

→

inv

)

beyond

 _{E-mailaddress:cms-publication-committee-chair@cern.ch.}

the indirect constraints. The ATLAS Collaboration [13] presented a combination of direct searches using

√

s

=

7 and 8 TeV data fromproton-proton(pp)collisions,yieldinganobserved(expected) upper limit of 0.25 (0.27) on

B

(

H

→

inv

)

at 95% CL [14]. The CMSCollaboration [15] performedasimilarcombinationbasedon

√

s

=

7,8,and13 TeV pp collisiondatacollected uptotheendof 2015,settinganobserved(expected)upperlimitof0.24(0.23)on

B

(

H

→

inv

)

at95%CL [16].

This Letter presents a search for invisible decays of a Higgs boson, using pp collision data at

√

s

=

13TeV collectedwith the CMSdetectorin2016,correspondingtoanintegratedluminosityof 35.9 fb−1.ThesearchtargetseventsinwhichaHiggsbosonis pro-ducedinassociation withjetsfromvectorboson fusion(VBF),as illustratedbytheFeynmandiagraminFig.1(left).Intheseevents, aHiggsbosonisproducedalongwithtwojetsthatexhibitalarge separation in pseudorapidity (

|

η

jj

|

) and a large dijet invariant

mass(mjj).Thischaracteristicsignatureallowsforthesuppression

of SM backgrounds, making the VBF channel the most sensitive modeforinvisibledecaysofaHiggsbosonathadroncolliders [16,

17]. The invisible particles produced by the Higgs boson decay can recoilwithhigh transversemomentum (pT) againstthe

visi-bleVBF-jetsystem,resultinginaneventwithlarge pTimbalance,

whichcanbeusedtoselectsignalenrichedregions.Inthisphase

https://doi.org/10.1016/j.physletb.2019.04.025

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

The CMS Collaboration / Physics Letters B 793 (2019) 520–551 521

Fig. 1. Leading order Feynman diagrams for the main production processes targeted in the combination: VBF (left), VH (middle), and ggH (right).

space, the main expected backgrounds originate from Z

(

νν

)

+jets and W

(

ν

)

+jets processes. They are estimated from data using dedicatedcontrolregions(CRs),whichconsistofhighpurity sam-plesofZ orW bosonsdecayingleptonically(



=

μ

,

e).While ear-lier searches probing this final state at the LHC were based on countingexperiments, the analysispresented in thisLetter more optimally exploits the distinctive kinematic features of the VBF topologybyfittingtheshapeofthemjjdistribution.Thisapproach

isreferredtoasthe“shapeanalysis”.Theshapeanalysishasbeen designedto provideasubstantially improvedsensitivityto invisi-bledecaysofthe SMHiggsboson,resultinginthemostsensitive VBF H

→

inv search reported to date. In addition, a simple but lesssensitivecountingapproach,referredtoasthe“cut-and-count analysis”,allowsforan easierinterpretation oftheresultsofthis searchinthecontextofotherphenomenologicalmodelspredicting thesamefinal-statesignature. Upperlimitsontheproductofthe cross section and branching fraction for an additional Higgs bo-sonwithSM-likecouplings,whichdoesnotmixwiththe125 GeV Higgsboson,arealsoreported.

Tofurther improvethesensitivity, resultsfrom acombination ofsearchesforinvisibledecaysoftheHiggsboson,usingdata col-lected at

√

s

=

7,8,and13 TeV, are alsopresented.The searches consideredinthiscombinationtargettheVBF,theassociated pro-duction(denoted by VH, whereV denotes a W orZ boson), and thegluon fusionmodes, whoserepresentative Feynmandiagrams areshowninFig.1.TheVH-tagincludesbothasearchforZH pro-duction,inwhichtheZ bosondecaystoapairofleptons(e

,

μ

)or bquarks,andone whereaLorentz-boostedW orZ bosondecays tolight-flavorquarks,whosecorrespondinghadronizationproducts arereconstructedasasinglelarge-radiusjet.Additionalsensitivity isachieved by including a search for gg

→

gH production (here-afterreferredtoasggH),whereahigh-pTHiggsbosoncandidateis

producedinassociationwithjetsfrominitial-stateradiation.When thesesearchesarecombinedtosetanupperlimiton

B

(

H

→

inv

)

, SMproductioncrosssectionsareassumed.Theresultofthis com-binationisalsointerpreted inthecontext ofHiggs-portalmodels ofDMinteractions [9–12],inwhichthe125 GeV Higgsbosonplays theroleofamediatorbetweentheSM andDMparticles,thereby allowingforthepossibilityofproducingDMcandidates.

ThisLetteris organized asfollows: aftera briefdescriptionof the CMS detector in Section 2, the event reconstruction in Sec-tion3,andthesimulatedsignalandbackgroundprocessesin Sec-tion4,Section5is dedicatedtotheeventselectionrequirements followedbya detaileddescriptionofthe analysisstrategy in Sec-tion6.Section 7reportstheresultsoftheVBFsearch intermsof upperlimitson

B

(

H

→

inv

)

.Section 8reportstheupperlimiton

B

(

H

→

inv

)

from a combination of the aforementioned searches forinvisible decaysofthe Higgsbosonbasedon13 TeV data col-lectedin 2016while,in Section9, resultsfroma morecomplete combination, involving also similar analyses performed on the 7 and8 TeV data sets, are presented. The Letter is summarized in Section10.

2. TheCMSdetector

The CMS detector is a multi-purpose apparatus designed to studyawiderangeofphysicsprocessesinbothpp andheavyion collisions.Thecentralfeatureoftheexperimentisa superconduct-ing solenoid of6 m internal diameter, providinga magnetic field of3.8 T paralleltothebeamdirection.Withinthesolenoidvolume a silicon pixel and strip tracker, a lead tungstate crystal electro-magnetic calorimeter (ECAL), and a brass and scintillator hadron calorimeter (HCAL) are installed, each composed of a barrel and two endcap sections. The tracker system measures the momen-tumofchargedparticlesupto

|

η

|

=

2

.

5,whiletheECALandHCAL providecoverageupto

|

η

| =

3

.

0.Inaddition,thesteeland quartz-fiberCherenkovhadronforwardcalorimeterextendsthecoverage to

|

η

| =

5

.

0. Muonsare detected ingas-ionization chambers em-bedded in thesteel flux-returnyoke outside thesolenoid, which coverupto

|

η

| =

2

.

4.

Events of interest are selected using a two-tiered trigger sys-tem [18]. The first level (L1) is composed of custom hardware processors,whichuseinformationfromthecalorimetersandmuon detectors toselectevents atarateof about100 kHz.The second level,knownashigh-leveltrigger(HLT),isasoftware-basedsystem which runs a version of the CMS full eventreconstruction opti-mizedforfastprocessing,reducingtheeventratetoabout1 kHz.

AmoredetaileddescriptionoftheCMSdetector,togetherwith adefinitionofthe coordinatesystemusedandtherelevant kine-maticvariables,canbefoundinRef. [15].

3. Eventreconstruction

The particle-flow (PF) algorithm [19] aims to reconstruct and identifyeach particleinan eventwithan optimizedcombination ofinformationfromthevariouselementsoftheCMSdetector.The energy of photonsis obtained fromthe ECALmeasurement. The energyofelectronsisdeterminedfromacombinationofthe mo-mentumoftheassociatedtrackatthe primaryinteractionvertex, theenergyofthecorrespondingECALcluster,andtheenergysum ofallbremsstrahlungphotonsspatiallycompatiblewithoriginating fromtheelectrontrack.Themomentumofmuonsisobtainedfrom the curvatureofthe correspondingtracks. Theenergy ofcharged hadrons is determined from a combination of their momentum measured inthetrackerandthematchedECALandHCALenergy deposits, corrected for the response function of the calorimeters tohadronicshowers. Finally,the energyofneutralhadronsis ob-tainedfromthecorrespondingcorrectedECALandHCALenergy.

The missingtransverse momentumvector (



pmiss_T ) iscomputed as the negative vector pT sum of all the PF candidates in an

event, and its magnitude is denoted as pmiss

T . Hadronic jets are

reconstructed by clustering PF candidates usingthe anti-kT

algo-rithm [20,21],withadistanceparameterof0.4.Thereconstructed vertex with the largest value of summed physics object p2

T is

takentobe theprimary pp interaction vertex,wherephysics ob-jects correspondtothejetsandthe pmiss

The chargedPF candidates originatingfrom anyother vertexare ignoredduring thejetfinding procedure.Jetmomentumis deter-mined as the vector sum of all particle momenta inside the jet, andisfoundfromsimulationto vary,on average,between5and 10%ofthetrue momentumoverthewhole pT spectrumand

de-tectoracceptance.Anoffsetcorrectionisappliedtojetenergiesto takeintoaccountthecontributionfromadditionalpp interactions withinthesameoradjacentbunchcrossings(pileup) [22].Jet en-ergy corrections are derived from simulation and are confirmed withinsitu measurementsoftheenergybalanceindijet,multijet,

γ

+jets, andleptonicallydecaying Z+jets events [23].Theseenergy correctionsarealsopropagatedtothe pmiss

T calculation [24].

Muoncandidates,withinthegeometricalacceptanceofthe sili-contracker andmuon subdetectors (

|

η

| <

2

.

4), are reconstructed by combining the information from the tracker and the muon chambers [25]. These candidates are required to satisfy a set of quality criteria based on the number of hits measured in the tracker andthe muon system, the properties ofthe fitted muon track, aswellasthe impactparameters ofthe trackwithrespect totheprimaryvertexoftheevent.

Electroncandidateswithin

|

η

|

<

2

.

5 arereconstructedusingan algorithm that associates fitted tracks inthe silicon tracker with electromagnetic energy clusters in the ECAL [26]. To reduce the misidentificationrate,thesecandidatesarerequiredtosatisfy iden-tificationcriteriabasedontheshowershapeoftheenergydeposit, the matching of the electron track to the ECAL energy cluster, the relative amount of energy deposited in the HCAL detector, and the consistency of the electron track with the primary ver-tex.Because of non-optimalreconstruction performance, electron candidates in the transitionregion between theECAL barrel and endcap,1

.

44

<

|

η

| <

1

.

57,arenotconsideredintheanalysis. Elec-tronsidentifiedascomingfromphotonconversionsinthedetector arediscarded [27].

Identifiedelectrons ormuonsarerequiredto beisolated from hadronic activity in the event. The isolation is defined by sum-ming the pT of all the PF candidates within a cone of radius

R

=

√

(

η

)

2

+ (φ)

2

=

0

.

4

(

0

.

3

)

aroundthemuon(electron)track, and is corrected for the contribution of neutral hadrons from pileupinteractions [25,26].

Hadronicallydecaying

τ

leptons(

τ

h)areidentifiedfrom

recon-structedjetsviathehadron-plus-stripalgorithm [28],thatrequires asubsetofparticlesinsidethejettobeconsistentwiththedecay productsofa

τ

lepton.Inaddition,the

τ

hcandidatemustbe

iso-latedfromotheractivityinthedetector.Theisolationiscomputed bysummingthe pT ofallthechargedPFcandidates andPF

pho-tonswithinaconeofradiusR

=

0

.

3 aroundthejetaxis.Hadronic

τ

leptons areselectedwithan averageefficiencybetween60and 65%.

4. Simulatedsamples

Thesignal andbackgroundprocesses aresimulatedusing sev-eral Monte Carlo (MC) generators. Higgs boson signal events, produced through ggH and VBF, are generated with powheg v2.0 [29–33] at next-to-leading order (NLO) approximation in perturbative quantum chromodynamics (QCD). Signal events are normalizedtotheinclusiveHiggsbosonproductioncrosssections takenfromtherecommendationsofRef. [34].TheggH production crosssectioniscomputedatnext-to-next-to-NLO(N3_LO)precision

in QCD, and at NLO in electroweak (EW) theory [35]. The cross section for Higgs boson production through VBF is calculated at next-to-NLO (NNLO) in QCD, includingalso NLO EW corrections. TheggH processis simulatedusingcalculationsinwhichthetop quarkloopisfullyresolved.The pTdistributionoftheHiggsboson

produced viaggH isreweightedtomatchtheNNLOplus next-to-next-to-leading-logarithmic (NNLL)predictionfrom hres v2.1 [36,

37]. When upperlimits are seton

B

(

H

→

inv

)

forthe SM Higgs boson, both ggH and VBF signal events are generated assuming a Higgsboson mass of 125.09 GeV, which is consistent with the combined ATLAS and CMS measurement [38] based on 7+8 TeV data, as well as the recent CMS measurement at 13 TeV in the H

→

ZZ

→

4



channel [39].

The Z

/

γ

∗

(

+



−

)

+jets, Z

(

νν

)

+jets,andW

(

ν

)

+jets backgrounds are simulated at leading order (LO) using MadGraph5_amc@nlo v2.2.2 [40], where up to four partons in the final state are in-cluded in the matrix element calculation. The background pro-cessesinvolvingtheproductionofavectorboson(V)inassociation with two jets exclusively through EW interactions, i.e. of order

α

4_{, are simulated at LO via MadGraph5_amc@nlo. In addition,}

the QCD multijetbackgroundisalso simulatedatLOusing Mad-Graph_{5_amc@nlo.Thett andsingletopquarkbackgroundsamples} are produced at NLO QCD using powheg v2.0 and v1.0, respec-tively [41–43]. Finally, the WZ and ZZ diboson productions are simulatedat LOwith pythia v8.205 [44], whilethe V

γ

andWW processes aresimulatedatNLO QCDusing MadGraph5_amc@nlo and powheg [45],respectively.

Inallcases,generatedeventsareinterfacedwith pythia v8.205 or higher for the simulation of fragmentation, parton shower-ing, and the underlying event description, using the parameters from the cuetp8m1 tune [46]. In the case of LO (NLO) Mad-Graph5_amc@nlo samples, partonsfromthematrixelements are matched to the parton shower description via the MLM [47] (FxFx [48])scheme.The nnpdf v3.0 [49] partondistribution func-tions (PDFs) are usedfor all thematrix element calculations. In-teractions of the final-state particles with the CMS detector are simulatedwith Geant4 [50]. Simulatedeventsincludethe effects ofpileup,andareweightedtoreproducetheobservedpileup dis-tribution.

5. Eventselection

Events inthesignal region(SR)are selectedinitiallybytheL1 trigger exploiting the pmiss

T information, whose threshold varies

between 60 and 90 GeV depending on the instantaneous lumi-nosity. The pmiss_T at the L1 trigger is computed from the vector pT sum of all the energy depositions in the calorimeters with

|

η

| <

3.Partial mistiming of signalsin the forwardregion of the ECALendcaps(2

.

5

<

|

η

| <

3

.

0)ledtoareductionintheL1trigger efficiency.Acorrectionforthiseffectwasdeterminedusingan un-biaseddatasample.Thiscorrection wasfound tobeabout1%for mjj of 200 GeV andit increases to about20% formjj larger than

3.5 TeV.

At theHLTlevel,eventsofinterest arecollected usingtriggers withthresholdsof110or120 GeV, depending onthedatataking period,appliedequallytoboththemissingtransversemomentum computedatthetriggerlevel(pmiss_{T, trig}) andthe Hmiss_{T, trig}variable.The Hmiss_{T, trig}isdefinedasthemagnitudeofthevector pT sumofthe

re-constructedjetsatthetriggerlevelintheeventwith pT

>

20 GeV

and

|

η

| <

5. The energyfraction attributedto neutralhadrons in jetswith

|

η

| <

3

.

0 isrequiredtobe lessthan90%,inorderto re-movespuriousjetsoriginatingfromdetectornoise.Both pmiss_{T, trig}and Hmiss_{T, trig}arecalculatedwithoutincludingmuoncandidates,allowing thesametriggerstobeusedalsoforselectingeventsinthemuon CRs, whichare usedin thebackground estimationprocedure de-scribedinSection6.

Offline, events considered in the VBF search are required to have at least two jets with pT larger than 80 (40) GeV for the

The CMS Collaboration / Physics Letters B 793 (2019) 520–551 523

Table 1

SummaryofthekinematicselectionsusedtodefinetheSRforboththeshapeandthecut-and-countanalyses. Observable Shape analysis Cut-and-count analysis Target background

Leading (subleading) jet pT>80(40)GeV,|η| <4.7 All

pmiss

T >250 GeV QCD multijet, tt,γ+jets, V+jets φ(pmissT ,p

jet

T) >0.5 rad QCD multijet,γ+jets

Muons (electrons) Nμ,e=0 with pT>10 GeV,|η| <2.4(2.5) W(ν)+jets τhcandidates Nτh=0 with pT>18 GeV,|η| <2.3 W(ν)+jets Photons Nγ=0 with pT>15 GeV,|η| <2.5 γ+jets, Vγ

b quark jet Njet=0 with pT>20 GeV, CSVv2>0.848 tt, single top quark ηj1ηj2 <0 Z(νν)+jets, W(ν)+jets

|φjj| <1.5 rad Z(νν)+jets, W(ν)+jets

|ηjj| >1 >4 Z(νν)+jets, W(ν)+jets mjj >200 GeV >1.3 TeV Z(νν)+jets, W(ν)+jets

useinformationfromthehadronicactivityintheforwardregion, at least one of the two leading jets in the event is required to have

|

η

| <

3.Toensureahighandstabletriggerefficiency,events arefurtherrequiredtohavepmiss_T

>

250 GeV.Thetriggerefficiency is measured as a function of Hmiss_T , computed from jets with pT

>

30 GeV and

|

η

| <

3.AftercorrectingfortheL1mistiming

in-efficiency,thesetriggers are foundto be fullyefficientforevents passingtheanalysisselectionwithHmiss

T

>

250 GeV.Inaddition,if

theleadingjetiswithinthegeometricalacceptanceofthetracker (

|

η

| <

2

.

4), its energy fraction attributed to charged hadrons is required to be greater than 10%, while the energy fraction at-tributed to neutral hadrons is required to be smaller than 80%. These requirements, along with quality filters applied to tracks, muoncandidates, andother physics objects,reduce the contami-nationarisingfromlargemisreconstructed pmiss_T fromnoncollision backgrounds [51].TofurthersuppressthecontaminationfromQCD multijet events, in which a large pmiss_T may arise froma severe mismeasurementofthejetmomentum,thejetsintheevent,with pT

>

30 GeV and

|

η

| <

4

.

7,arerequiredtonotbealignedwiththe



pmiss

T . The minimum value of the azimuthal angle between the



pmiss_T vector and each jet (min

φ (



p_Tmiss

,



pjet_T

)

) is required to be larger than 0.5 rad,where only the first fourleading jetsare in-cludedinthemin

φ (



pmiss_T

,



pjet_T

)

definition.Thisselectionreduces theQCDmultijetcontaminationtolessthan1%ofthetotal back-ground.

The two leading jets in VBF signal events typically show a largeseparation in

η

, largemjj anda smallazimuthal separation

(

|φ

jj

|

). The discriminatory power of

|φ

jj

|

results froma

com-binationofthespin-parity propertiesoftheHiggsbosonandthe high-pTregimeexploredbythissearch [17],inwhichthetwoVBF

jetstendtorecoilagainsttheinvisiblesystem.TheZ

(

νν

)

+jets and W

(

ν

)

+jets processes constitute the largest backgrounds in this search.Theshape analysisprimarilyemploys thelargeseparation powerofmjj todiscriminatebetweenVBFsignalandV+jets

back-grounds.Therefore,inthisscenario,asetoflooserequirementsis appliedonbothmjjand

|

η

jj

|

,i.e.

|

η

jj

|

>

1

.

0 andmjj

>

200GeV.

Tofurther reduce the V+jets contamination,

|φ

jj

|

isrequired to

besmallerthan1.5 rad andthetwojetsmustlieinopposite hemi-spheres,

η

j1

η

j2

<

0.Inthecut-and-countapproach,Z

(

νν

)

+jets and

W

(

ν

)

+jets processesaresuppressedbyamorestringentevent se-lectionrequiring

|

η

jj

| >

4

.

0 andmjj

>

1

.

3 TeV,whilethe

require-mentappliedon

|φ

jj

|

remainsunchanged.

TheW

(

ν

)

+jets backgroundis furthersuppressed by rejecting events that contain at leastone isolated electron or muon with pT

>

10GeV, ora

τ

h candidate with pT

>

18GeV and

|

η

|

<

2

.

3,

where the isolation is required to be less than 25 (16)% of the muon(electron) pT.Withthisstrategy, promptmuons(electrons)

are selected with an average efficiency of about 98 (95)%. In or-der to further reduce the contribution from

γ

+jets and V

γ

pro-cesses,eventscontaininganisolatedphotonwithpT

>

15GeV and

|

η

|

<

2

.

5,passingidentificationcriteriabasedon itsECALshower shape [27],arevetoed.

Topquark backgrounds(tt andsingle topquark processes)are suppressed by rejecting events in which at least one jet, with pT

>

20 GeV and

|

η

| <

2

.

4, is identified as a b quark jet using

the combined secondary vertex(CSVv2) algorithm [52]. A work-ingpointthatyieldsa60%efficiencyfortaggingab quarkjetand a 1 (10)% probability ofmisidentifying a light-flavor (c quark) jet asab quarkjetisused.

A summary of the selection criteria for the SR for both the shapeandthecut-and-countanalysesisshowninTable1.

6. Analysisstrategy

The search exploitsthe large mjj and

|

η

jj

|

that characterize

events from VBF Higgs boson production. In the shape analysis case, the signal is extractedby fittingthe sum ofthe signal and backgroundshapestothebinnedmjjdistributionobservedindata.

The signal isexpectedto accumulate asanexcess ofeventsover the background at large values of mjj. This strategy necessitates

a preciseestimationofthe shapeofthebackgroundmjj

distribu-tion.

About 95% ofthe total expected background in thissearch is duetotheV+jets processes,namelyZ

(

νν

)

+jets andW

(

ν

)

+jets.A fractionoftheV+jets background,referred toasV+jets (EW),can beattributedtotheEWproductionofaZ oraW bosonin associa-tionwithtwojets.ArepresentativeFeynmandiagramcontributing toV+jets(EW)productionisshowninFig.2(left).Theremaining V+jets contributionarisesfromtheproductionofavectorbosonin associationwithQCD radiation,asshownin Fig.2(right). Thisis referredtoastheV+jets (QCD)background.ForbothEWandQCD productions, theexpectedZ

(

νν

)

+jets rate inthe SRisabouttwo timeslargerthantheW

(

ν

)

+jets contribution.

Acomparison ofthe shapesofthe keydiscriminating observ-ables used in this analysis, obtained after applying the require-mentslistedinTable1exceptforthoseonmjj,

|

η

jj

|

and

|φ

jj

|

,is

showninFig.3forsimulatedsignalandV+jets backgroundevents. Fromthesedistributions,itcanbeseenthattheV+jets (EW) back-ground is kinematically similar to the VBF Higgs boson signal. Therefore,its contributiontothe totalV+jets background rate in-creaseswhen thetwo leading jetshave largemjj and

|

η

jj

|

.The

V+jets (EW)processconstitutesabout2% ofthetotalV+jets back-groundformjjaround200 GeV.Itscontributionincreasestoabout

20%formjj

≈

1

.

5TeV,andismorethan50%formjj

>

3TeV.

6.1. OverviewoftheV+jetsbackgroundestimation

The Z+jets and W+jets backgrounds are estimated using four mutuallyexclusive CRs.Theseinclude adimuon anda dielectron

Fig. 2. RepresentativeleadingorderFeynmandiagramsfortheproductionofaZ bosoninassociationwithtwopartonsarisingfromEW(left)andQCD(right)interactions. TheleftdiagramcontributestotheZ(νν)+jets (EW)production crosssection,whilethediagramontherighttotheZ(νν)+jets (QCD)one. DiagramsforEWand QCD productionofaW bosoninassociationwithtwojetsaresimilartothosereportedabovefortheZ(νν)+jets process.

Fig. 3. Comparisonbetweentheshapesofthemjj(left),|ηjj|(middle)and|φjj|(right)distributionsofsignalevents,producedbyVBF(solidblack)andggH (dashedblack)

mechanisms,andV+jets backgroundsfrombothQCD(solidred)andEW(solidblue)production.Bothsignalandbackgrounddistributionsarescaledinordertohaveunit area.DistributionsareobtainedfromsimulatedeventspassedthroughtheCMSeventreconstruction.

CR consisting mostly of Z

()

+jets events that are kinematically similartoZ

(

νν

)

+jets backgroundifthepresenceofthetwoleptons intheeventisignored.TheW+jets backgroundisestimatedusing CRs consisting of single-muon and single-electron events stem-ming mainly from leptonic decays of a W boson. In contrast to theW+jets backgroundintheSR, thesingle-leptonCRsconsist of leptonsthatfallwithinthedetectoracceptanceandpassthe iden-tification requirements. The pmiss

T in all the CRs is calculated by

excluding the contribution ofthe identified leptons. Therefore,it corresponds to the pT of the hadronic recoil system, which

re-sembles the pmiss

T expected from the V+jets backgrounds in the

SR.

TheeventyieldinthedileptonCRsisconsiderablysmallerthan the Z

(

νν

)

+jets contribution in the SR because the Z

()

branch-ingfraction,where



=

μ

ore,issixtimessmallerthantheZ

(

νν

)

branching fraction.Consequently, thedilepton CRshavea limited statisticalpowertoconstraintheZ

(

νν

)

+jets backgroundby them-selves. In contrast, the yield of the single-lepton CRs is compa-rable to the Z

(

νν

)

+jets background. Furthermore, the Z

(

νν

)

+jets andW

(

ν

)

+jets processesarekinematicallysimilarifthepresence ofthechargedleptonis ignored.The theoreticaluncertainties in-volved in the prediction of the Z+jets and W+jets cross sections largely cancelout in their ratio.Therefore, thisratiois predicted very reliably by the simulation andcan be used as a constraint toconnectthestatisticallyrichsingle-leptonCRstotheZ

(

νν

)

+jets backgroundintheSR.

The predictions for the V+jets processes obtained from simu-lationarereferredtoas“pre-fit”expectations,andareconsidered tobetheinitialestimatesfortheV+jets yieldsintheCRsandSR. TheseV+jets yieldsarethentreatedasfreelyfloatingparameters,

and are fit to the data in all CRs and the SR. The V+jets yields obtained fromthisfit are referred to as“post-fit” estimates,and serveasthefinalV+jets backgroundpredictionsintheanalysis. 6.2. Definitionofcontrolregions

Dimuon andsingle-muonCRs are selected using thesame L1 and HLT pmiss_T -based triggers that are used to collect events in the SR. Dimuon events are required to contain exactly two op-positely charged muonswith pT

>

10GeV thatforman invariant

mass (mμμ) between 60and 120 GeV, which is compatiblewith a Z boson decay.Events withadditionalelectrons or photonsare rejected. At least one ofthe two muonsmust have pT

>

20GeV,

andisrequiredtopasstighteridentificationcriteriabasedonthe number of measurements in the tracker andthe muon systems, thequalityofthemuontrackfit,andtheconsistencyofthemuon track with the primary vertex. The isolation, as defined in Sec-tion 3,isrequiredtobesmallerthan 15%ofthemuon pT.These

tightlyidentifiedmuonsareselectedwithanaverageefficiencyof 90%.

In the single-muon CR, events are required to contain ex-actly one muon with pT

>

20 GeV, passing both tight

identifica-tion andisolation requirements. The transversemass (mT) ofthe

muon-pmiss_T systemiscomputedasmT

=



2pmiss_T pμ_T

(

1

−

cos

φ)

, wherepμ_T isthepTofthemuon,and

φ

istheanglebetween



pμT

and



pmiss

T inthetransverseplane.ThemTisrequiredtobesmaller

than160 GeV, andnoadditionalelectrons orphotonsareallowed intheevent.

Events inthe dielectron and single-electronCRs are collected mainly using a single-electron trigger with a pT threshold of

The CMS Collaboration / Physics Letters B 793 (2019) 520–551 525

27 GeV. In the caseof dielectron events where the Z boson has pT

>

600GeV,thetwo electrons havea smallangularseparation,

andarelikelytogetincludedineachother’sisolationcones.This resultsinaninefficiencyforthechosentriggerthatimposes isola-tionrequirementsonelectroncandidates.Thisinefficiencyis mit-igated by including events collected by a single-electron trigger witha pT thresholdof105 GeV andnoisolation requirementson

theelectroncandidate.

Thedielectroneventsarerequiredtocontainexactlytwo oppo-sitelychargedelectronswithpT

>

10GeV andnoadditionalmuons

or photons. As in the case of the dimuon events, the invariant massof the dielectronsystemis required to be between60 and 120 GeV.AtleastoneofthetwoelectronsmusthavepT

>

40 GeV,

and is required to pass a tight identification criterion based on the shower shape of its ECAL energy deposit, the matching of theelectrontracktotheECALenergycluster, andtheconsistency of the electron track with the primary vertex. Furthermore, the isolation is required to be smaller than 6% of the electron pT.

These selection requirements for electrons have an average effi-ciencyof 70%.

Eventsinthesingle-electronCRarerequiredtocontainexactly onetightly identified andisolated electron with pT

>

40GeV;no

additionalmuonsorphotonsareallowed.Thecontaminationfrom QCD multijet events is reduced by requiring pmiss_T

>

60GeV and mT

<

160GeV.

Eventsin theCRsmust alsosatisfy therequirements imposed on events in the SR. When doing so, the negative pT of the

hadronicrecoilsystemisusedinsteadofthe pmiss

T intheevent.

6.3.EstimationofV+jetsbackgrounds

TheV+jets yields in theCRs are translatedto thebackground estimates in the SR using transfer factors that are derived from simulation. The transfer factors are defined as the ratio of the yieldsofagivenV+jets backgroundintheSRandthe correspond-ingprocessmeasuredineachCR.

ThetransferfactorsforthedileptonCRsaccountforthe differ-enceinthebranchingfractionsoftheZ

(

νν

)

andZ

()

decays,and the

γ

∗

()

contribution, as well as the impact of lepton accep-tance andselection efficiencies. In the case of dielectronevents, the transfer factors also account forthe difference in trigger ef-ficiencies. Transfer factors between the W

(

ν

)

+jets event yields inthe single-leptonCRs and the W+jets background estimate in the SR take into account the effect of lepton acceptance, selec-tionefficiencies,andleptonand

τ

hvetoefficiencies,aswellasthe

differenceintrigger efficiencies inthecaseofthe single-electron CR.

Theconstraint onthe ratioofthe cross sectionsofthe Z+jets andW+jets processes,whichisusedto connectthesingle-lepton CRsto the Z

(

νν

)

+jets inthe SR, is alsoimplemented asa trans-fer factor, and is computed as the ratio of the Z

(

νν

)

+jets and W

(

ν

)

+jets yields in the SR. In order to have the most pre-ciseestimate ofthisconstraint, the LOsimulationsforthe Z+jets (QCD)andtheW+jets (QCD) processesare correctedusingboson pT and mjj– dependent NLO QCD K -factors derived with

Mad-Graph5_amc@nlo. The Z+jets and W+jets simulations are also correctedas a function ofboson pT with NLO EW K -factors

de-rivedfromtheoreticalcalculations [53].Similarly,Z+jets (EW)and W+jets (EW)processesarecorrectedwithNLO QCD K -factors de-rived using the vbfnlo event generator [54,55] as a function of bosonpT andmjj.

The V+jets background yields are determined using a maxi-mum-likelihood fit, performedsimultaneously across all CRsand theSR.Thelikelihoodfunctionisdefinedas:

L

(

μ

,

κ

νν

, θ )

=



i P



di





Bi(θ )

+ (

1

+

fi(θ )Q

)

κ

iνν

+

RZ_i

(

1

+

fi(θ )E

)

κ

iνν

+

μ

Si(θ )





i P



dμμ_i





Bμμ_i

(θ )

+

κ

i νν Rμμ_i

(θ )

Q

+

RZi

κ

iνν Rμμ_i

(θ )

E





i P



dee_i



_

Bee_i

(θ )

+

κ

i νν Ree i

(θ )

Q

+

RZi

κ

iνν Ree i

(θ )

E





i P



dμ_i



_

Bμ_i

(θ )

+

fi(θ )Q

κ

i νν Rμ_i

(θ )

Q

+

RZifi(θ )E

κ

iνν Rμ_i

(θ )

E





i P



de_i



_

Be_i

(θ )

+

fi(θ )Q

κ

i νν Re_i

(θ )

Q

+

RZ_ifi(θ )E

κ

iνν Re_i

(θ )

E





j P

(θ )

(1)

where P

(

x

|

y

)

=

yxe−y

/

x

!

. The symbol i denotes each bin of the mjj distributionintheshapeanalysis, while,inthecut-and-count

case, i standsforasingle binthat representstheeventyields ob-tained at the end of the event selection. The symbolsdμμ_i , dee

i ,

dμ_i,de

i,anddi denotetheobserved numberofeventsineach bin

i ofthedimuon,dielectron,single-muon,single-electronCRs,and theSR,respectively.Thesymbols fi

(θ )

Qand fi

(θ )

Eindicatethe

ra-tiosbetweentheW

(

ν

)

+jets andZ

(

νν

)

+jets backgroundsintheSR fromQCDandEWproduction,respectively.Thesymbols Rμμ_i

(θ )

Q,

Ree_i

(θ )

Q, Rμ_i

(θ )

Q,and Re_i

(θ )

Q are thetransfer factorsrelating the

dimuon,dielectron, single-muon, andsingle-electronCRs, respec-tively,totheSRfortheV+jets (QCD)processes.Similarly, Rμμ_i

(θ )

E,

Ree_i

(θ )

E, Rμ_i

(θ )

E, and Re_i

(θ )

E indicate the transfer factors for the

V+jets (EW) processes. The parameters

κ

iνν represent the yield

ofthe Z

(

νν

)

+jets (QCD) backgroundin each bini ofthe SR, and are left to float freely in the fit. In a given bin, the Z

(

νν

)

+jets (EW)backgroundyieldisobtainedfrom

κ

iνν throughthetransfer

factor RZ_i thatrepresents theratiobetweenthe Z

(

νν

)

+jets (QCD) andZ

(

νν

)

+jets (EW)processes.Thecontributionsfromsubleading backgrounds in each region are estimated directly from simula-tion and they are denoted by Bμμ_i , Bee

i , B

μ

i , Bei and Bi. Finally,

the likelihoodalso includesa signal termin which Si represents

theexpectedsignalprediction,while

μ

= (

σ

/

σ

SM

)

B

(

H

→

inv

)

de-notesthesignalstrengthparameter.

Systematic uncertainties are modeled as constrained nuisance parameters(θ),forwhichlog-normalorGaussianpriors,indicated by Pj

(θ )

inpreviousequation, areconsidered.The systematic

un-certainties in the V+jets background estimates are introduced in the likelihood asvariations ofthe transfer factors. These include theoretical uncertainties inthe Z+jets toW+jets differential cross sectionratioforboththeQCDandEWprocessesduetothechoice oftherenormalizationandthe factorizationscales, aswell asthe choice of the PDFs. The QCD scale variations are assumedto be uncorrelatedbetweentheZ+jets and W+jets processes,and there-forethey donotcancelintheZ+jets toW+jets crosssectionratio. This results in larger uncertainties compared to those from NLO calculationsrecommendedinRef. [53].Theuncertaintyduetothe choice ofthe renormalizationscale variesbetween8 and12% as a function of mjj for both Z+jets/W+jets (QCD) and (EW) ratios.

Similarly, the uncertainty due to the choice of the factorization scale varies between 2 and 7%. This also covers the uncertainty intheZ+jets/W+jets crosssectionratioduetotheinterference be-tween the V+jets (QCD) andV+jets (EW) processes,which isnot includedinthesimulation.The PDFuncertainties are assumedto

Table 2

ExperimentalandtheoreticalsourcesofsystematicuncertaintiesontheV+jets transferfactors,whichenterinthesimultaneousfit,usedto es-timatetheV+jets backgrounds,asconstrainednuisanceparameters.Inaddition,theimpactonthefittedsignalstrength,(σ/σSM)B(H→inv), isreportedinthelastcolumnestimatedafterperformingthemjjshapefittotheobserveddataacrosssignalandcontrolregions.

Source of uncertainty Ratios Uncertainty vs. mjj Impact onB(H→inv)

Theoretical uncertainties

Ren. scale V+jets (EW) Z(νν)/W(ν)(EW) 9–12% 48% Ren. scale V+jets (QCD) Z(νν)/W(ν)(QCD) 9–12% 25% Fac. scale V+jets (EW) Z(νν)/W(ν)(EW) 2–7% 4% Fac. scale V+jets (QCD) Z(νν)/W(ν)(QCD) 2–7% 2% PDF V+jets (QCD) Z(νν)/W(ν)(QCD) 0.5–1% <1% PDF V+jets (EW) Z(νν)/W(ν)(EW) 0.5–1% <1%

NLO EW corr. Z(νν)/W(ν)(QCD) 1–2% <1%

Experimental uncertainties

Muon reco. eff. Z(μμ)/Z(νν), W(μν)/W(ν) ≈1% (per lepton) 8% Electron reco. eff. Z(ee)/Z(νν), W(eν)/W(ν) ≈1% (per lepton) 3% Muon id. eff. Z(μμ)/Z(νν), W(μν)/W(ν) ≈1% (per lepton) 8% Electron id. eff. Z(ee)/Z(νν), W(eν)/W(ν) ≈1.5% (per lepton) 4% Muon veto Z(νν)/W(ν), W(CRs)/W(ν) ≈2.5 (2)% for EW (QCD) 7% Electron veto Z(νν)/W(ν), W(CRs)/W(ν) ≈1.5 (1)% for EW (QCD) 5%

τveto Z(νν)/W(ν), W(CRs)/W(ν) ≈3.5 (3)% for EW (QCD) 13% Jet energy scale Z(CRs)/Z(νν), W(CRs)/W(ν) ≈1 (2)% for Z/Z (W/W) 4% Electron trigger Z(ee)/Z(νν), W(eν)/W(ν) ≈1% <1% pmiss

T trigger All ratios ≈2% 18%

be correlated across V+jets processes, resulting in a residual un-certainty smaller than 1% on the Z+jets/W+jets cross section ra-tio.The uncertaintiesrelatedtoNLO EWcorrectionstotheV+jets (QCD)processesare estimatedaccordingtotherecommendations inRef. [53],andarefoundtobeabout1–2%acrosstheentiremjj

spectrum.Additionaluncertaintiesincludedinthetransferfactors include uncertainties in the reconstruction efficiencies of leptons (around1%permuonorelectron),theselectionefficienciesof lep-tons(about1%permuon,1.5%perelectron),thevetoefficiencyof leptons(around2%per muon,1%perelectron)and

τ

hcandidates

(about3.5%per

τ

h),theknowledgeofthejetenergyscale(1–2%),

andthe efficiencyof the electron (around1%) and pmiss T triggers

(about2%).

The full set of systematic uncertainties related to the V+jets transfer factorsare listed in Table2. Before anyfitis performed, thetotaluncertaintyintheexpectedbackgroundintheSRranges between4.5and6% asa functionofmjj,dominatedby the

theo-reticaluncertainties intheZ+jets toW+jets crosssectionratiofor both QCDandEW production.The impactof each sourceof sys-tematicuncertainty, asreported in Table 2in the context ofthe shape analysis, isdefined as the maximumdifference inthe fit-tedvalueofthesignalstrength,

(

σ

/

σ

SM

)

B

(

H

→

inv

)

,obtainedby

varyingtheassociatednuisanceparameterwithinonestandard de-viationofitsmaximumlikelihoodestimate.Inthisprocedure,the per-bin

κ

iνν parameters are profiled when a given nuisance

pa-rameterisshiftedfromitsbestfitestimate.

Themjj distributions inthedileptonandsingle-leptonCRsare

showninFig.4.Thepre-fitpredictionsfortheV+jets processesare showninred.Theseindicatethelevelofagreementbetweendata andsimulationbeforeafitisperformed.AnestimateoftheV+jets backgroundsisthenobtainedbyfittingthedataacrossalltheCRs. ThisisdepictedbythebluelineinFig.4.Thisfitisreferredtoas the “CR-only” fit,since it doesnot impose anyconstraint onthe V+jets yieldsduetothedataintheSR.

Toassessthelevelofagreement betweendataandsimulation obtained through the application of pT–mjj dependent NLO

cor-rectionsto boththe V+jets (QCD)andV+jets (EW)processes,the ratiobetweenthenumberofZ+jets andW+jets eventsintheCRs in bins ofmjj is used asa benchmark. Fig. 5 showsthe ratio of

theZ+jets andW+jets eventyieldsinthemuon(left)andelectron (right) CRs, respectively. A good agreement is observed between

dataandsimulationandlocaldifferencesarecovered bythe sys-tematicuncertaintieslistedinTable2.

6.4. Otherbackgrounds

InadditiontotheV+jets processes,severalotherminorsources ofbackgroundcontributetothetotaleventyieldintheSR. These include QCD multijet events that typically have small genuine pmiss

T .However, jetmomentum mismeasurementsand

instrumen-taleffectsmaygiverisetolargepmiss_T tails.Amin

φ

extrapolation method [56] isusedtoestimatethisbackgroundfromdata,where a QCD multijet enriched CR is defined by selecting events that fail the min

φ

requirementbetweenthe jetsandthe



pmiss

T

vec-tor,butstillfulfilltheremainingeventselectioncriteria.Atransfer factor,derived fromsimulatedQCD multijetevents,isusedto es-timate the background in the SR from the event rate measured in thelow-

φ (



pmiss_T

,



pjet_T

)

sample. The low-

φ (



pmiss_T

,



pjet_T

)

region containsasignificantcontaminationfromV+jets production,which have genuine pmiss

T . Theycontribute about40%of thetotalevent

yieldformjj smallerthan 500 GeV,andabout80%formjj

>

3 TeV.

This contamination is estimated from simulation and subtracted fromtheeventyield measuredinthelow-

φ (

p



miss_T

,



pjet_T

)

sample. An uncertainty of20% is assigned whileperforming the subtrac-tion,whichresultsinanuncertaintyofabout30%intheestimated QCDmultijetbackgroundintheSR.TheMC statisticaluncertainty oftheQCDmultijetsamples,whichaffectsthetransferfactor pre-diction, isalso considered andis found to vary between 40and 100% asa function ofmjj. Lastly,a validation ofthe

φ

method

is performed using a purer sample of QCD multijet events that pass the analysis requirements, but have pmiss_T in the range of 100–175 GeV. In this validation region, the predicted QCD back-groundisfound toagreewiththeobservationwithin50%, which istakenasaconservativeestimateofanadditionaluncertainty.

The remaining background sources include top quark produc-tionanddibosonprocesses,whichare estimatedfromsimulation. The pT distributionofthetop quarkinsimulationiscorrected to

matchtheobservedpTdistributionindata [57].Anuncertaintyof

about10%isassignedtotheoveralltopquarkbackground normal-ization, while an additional 10% uncertainty is addedto account for the modeling of the top quark pT distribution in simulation.

un-The CMS Collaboration / Physics Letters B 793 (2019) 520–551 527

Fig. 4. Themjj distributionsinthedimuon(topleft),dielectron(topright),single-muon(bottomleft),andsingle-electron(bottomright)CRsascomputedintheshape

analysis.Predictionfromsimulation(pre-fitestimate)isshownbythedashedredline.ThesolidbluelineshowstheV+jets expectationafterfittingthedatainalltheCRs. ThefilledhistogramsindicateallprocessesotherthanV+jets (QCD).Thelastbinincludesalleventswithmjj>3.5 TeV.Ratiosofdataandthepre-fitbackground(redpoints)

andthepost-fitbackgroundprediction(bluepoints)areshown.Thegraybandintheratiopanelindicatesthetotaluncertaintyafterperformingthefit.Thelowestpanel showsthedifferencebetweendataandthepost-fitbackgroundestimaterelativetothepost-fitbackgrounduncertainty.

certaintyofabout15% [58,59]. Theuncertaintiesinthetop quark anddibosonbackgroundsarecorrelatedacrosstheSRandtheCRs. Severalexperimental sources of uncertainty are also assigned to thesebackgrounds.Anuncertaintyof2.5%intheintegrated

lumi-nositymeasurement [60] ispropagated to thebackgroundyields. The uncertainty in the efficiency ofthe b quarkjet vetois esti-matedtobearound3%forthetopquarkbackgroundandofabout 1% forthe other simulated processes. The uncertainty related to

Fig. 5. ComparisonbetweendataandsimulationoftheZ(μμ)+jets/W(μν)+jets (left)andZ(ee)+jets/W(eν)+jets (right)ratiosasfunctionsofmjj,computedintheshape

analysisphase-space.Inthebottompanels,ratiosofdatawiththepre-fitbackgroundpredictionarereported.Thegraybandsincludeboththetheoreticalandexperimental systematicuncertaintieslistedinTable2,aswellasthestatisticaluncertaintyinthesimulation.

thejetenergyscalevariesbetween8and15%,depending onboth theprocessandtheCR.

7. Results

Thissection presentstheresults obtainedfromtheshape and thecut-and-countanalyses.Theseinclude95% CL upperlimitson

B

(

H

→

inv

)

,andaninterpretationofthe searchinthecontext of a BSM model which allows for the presence of a SM-like Higgs bosonwithamassbetween110and1000 GeV.

7.1. Theshapeanalysis

Theobservedandtheexpectedmjjdistributions intheSR,

ob-tainedafterapplyingthefulleventselection,areshowninFig.6. ThebackgroundpredictionshowninFig.6(left)isobtainedfroma fittothedataintheCRs.SignaldistributionsfortheSMHiggs bo-son producedvia theggH andVBF modesareoverlaid, assuming

B

(

H

→

inv

)

=

1. The estimated background yields from the CR-onlyfitare listedinTable3,alongwiththeobserved eventyield in the SR. The large contamination from ggH production arises fromthe low-mjj bins, whichrepresent theleastsensitive region

toH

→

inv decays.Systematicuncertainties intheV+jets transfer factorsandintheminorbackgroundsintroducecorrelationsacross themjjbinsusedinthefit.Thecorrelationsinthepredicted

back-groundyieldsineachmjjbinarereportedinTable4.

An excess of about 4–10% is observed in the SR data when compared tothe estimated backgrounds.The discrepancy resides mainly in the bulk of the mjj distribution. The shape of the

ex-cessisinconsistentwiththecharacteristicfeaturesofaVBFsignal, whosepresenceisexpectedtoproduce anincreasing discrepancy betweendataandbackgroundsasmjj increases.Agoodness offit

test,basedonasaturated

χ

2 _{teststatistic [61,62],yieldsap-value}

ofabout6% indicating that thedataare compatiblewiththe SM prediction.

Fig. 6 (right)shows the background prediction obtained after includingeventsfromtheSRinthefit,butassumingtheabsence

of asignal. Such afit isreferred to asthe“b-onlyfit”. The com-parison betweenthe results of the b-only fit with that allowing for the presence of the signal is used to set an upper limit on

B

(

H

→

inv

)

. In the b-only fit, the V+jets estimate in the SR can vary withrespectto theprediction fromtheCRs within the sys-tematic uncertainties assigned to the transfer factors. Therefore, the additionalconstraint duetothe datain the SRmitigates the excessshowninFig.6(left),yieldingap-valuefortheb-onlyfitof about65%.

The resultsofthissearchare interpretedintermsofanupper limit on theproduct oftheHiggsboson productioncrosssection anditsbranchingfractiontoinvisibleparticles,

σ B

(

H

→

inv

)

, rel-ativetothepredictedcrosssectionassumingSMinteractions,

σ

SM.

Observedandexpected95%CL upperlimitsarecomputedusingan asymptoticapproximationoftheCLsmethod [63,64] withaprofile

likelihood ratio test statistic [65] in which systematic uncertain-ties are modeled as nuisance parameters following a frequentist approach [66].Theprofilelikelihoodratioisdefinedas:

q

= −

2



ln

L

= −

2 ln

L

(

data

|(

σ

/

σ

SM

)

B

(

H

→

inv

), ˆ

θ

a

,

κ

ˆ

a

)

L

(

data

|(

σ

/

σ

SM

) ˆ

B

(

H

→

inv

), ˆ

θ ,

κ

ˆ

)

(2)

where

(

σ

/

σ

SM

) ˆ

B

(

H

→

inv

)

represents the value of the signal

strengththatmaximizesthelikelihood

L

forthedata,while

ˆθ ( ˆ

κ

)

and

ˆθ

a

(

κ

ˆ

a

)

denotethebestfitestimatesforthenuisance

param-eters (Z

(

νν

)

+jets ratein each bin) andthe estimates fora given fixedvalueof

(

σ

/

σ

SM

)

B

(

H

→

inv

)

,respectively.

The relative contributions of the VBF and ggH production modes are fixed to the SM prediction within their uncertainties. The uncertaintiesinthe predictionsoftheinclusiveVBFandggH production cross sections due to PDF uncertainties, renormaliza-tionandfactorizationscalevariationsaretakenfromRef. [34].An additionaluncertaintyof40%isassignedtotheexpectedggH con-tribution.ThisaccountsforboththelimitedknowledgeoftheggH crosssection inassociation withtwo ormorejets,aswell asthe

The CMS Collaboration / Physics Letters B 793 (2019) 520–551 529

Fig. 6. TheobservedmjjdistributionoftheshapeanalysisSRcomparedtothepost-fitbackgroundsfromvariousSMprocesses.Ontheleft,thepredictedbackgroundsare

obtainedfromacombinedfittothedatainalltheCRs,butexcludingtheSR.Ontheright,thepredictedbackgroundsareobtainedfromacombinedfittothedatainallthe CRs,aswellasintheSR,assumingtheabsenceofanysignal.Expectedsignaldistributionsfora125 GeV HiggsbosonproducedthroughggH andVBFmodes,anddecaying toinvisibleparticleswithabranchingfractionB(H→inv)=1,areoverlaid.Thelastbinincludesalleventswithmjj>3.5 TeV.Thedescriptionoftheratiopanelsisthe

sameasinFig.4.

Table 3

Expectedeventyieldsineachmjj binforvariousbackgroundprocessesintheSRoftheshapeanalysis.Thebackgroundyieldsandthecorrespondinguncertaintiesare

obtainedafterperformingacombinedfitacrossalltheCRs,butexcludingdataintheSR.The“otherbackgrounds”includesQCDmultijetandZ()+jets processes.The expectedtotalsignalcontributionforthe125 GeV Higgsboson,decayingtoinvisibleparticleswithabranchingfractionB(H→inv)=1,andtheobservedeventyieldsare alsoreported.

Process mjjrange in TeV

0.2–0.4 0.4–0.6 0.6–0.9 0.9–1.2 1.2–1.5 1.5–2.0 2.0–2.75 2.75–3.5 >3.5 Z(νν)(QCD) 9311±388 5669±257 3884±179 1648±88 677±42 405±28 153±14 22.8±3.5 8.1±2.2 Z(νν)(EW) 201±8 228±10 273±13 198±11 129±8 112±8 70.6±6.6 20.2±3.1 10.8±2.9 W(ν)(QCD) 4755±267 3017±180 2090±130 928±63 361±28 227±19 80.4±9.1 13.7±2.7 4.5±1.9 W(ν)(EW) 102±14 118±16 133±18 100±13 61.2±8.1 61.4±7.6 39.4±4.9 12.6±1.9 5.6±1.4 Top quark 208±37 159±28 119±21 57.6±10.2 28.7±5.1 16.1±2.9 8.9±1.6 2.2±0.4 0.7±0.1 Dibosons 222±39 157±28 116±21 48.2±8.5 19.0±3.4 9.3±1.6 2.6±0.5 1.4±0.3 0.4±0.1 Others 78.6±19.5 51.0±11.6 42.8±11.5 13.6±2.9 6.5±1.5 3.3±0.8 2.4±0.6 0.7±0.2 0.3±0.4 Total bkg. 14878±566 9401±387 6658±271 2994±144 1283±69 834±51 358±29 73.8±9.4 30.3±7.4 Signal 590±244 559±199 547±151 447±109 276±58 304±66 201±36 68.6±11.7 30.0±6.4 Data 16177 10008 7277 3138 1439 911 408 87 29

uncertaintyinthepredictionofthe ggH differentialcross section forlarge Higgs boson transverse momentum, pH

T

>

250GeV. The

formercontributionisobtainedbyfollowingtherecipeoutlinedin Ref. [34] andisfoundtobeabout30%,whilethelatteruncertainty isestimatedbycomparingthepredictionfrom powheg+minlo [67] withthe onefrom MadGraph5_amc@nlo andranges between20 and25%. Furthermore,the uncertainties inthe signal acceptance duetothechoiceofthePDFsetarealsoevaluatedindependently forthedifferentsignal processes,andaretreatedasindependent nuisanceparametersinthefit.

Theobserved(expected)95% CL upperlimit on

B

(

H

→

inv

)

is measured to be 0.33 (0.25), andthe regions containing 68% and

95% ofthe distribution ofupper limits, expectedinabsence ofa signal,arefoundtobe0.18–0.35and0.14–0.47,respectively.

The backgroundestimatesreported inTable 3, along withthe correlationmatrixpresentedinTable4,canbeusedinthe simpli-fied likelihoodapproach detailedin Ref. [68] toreinterpret these resultsintheoreticalmodelsdifferentfromthosepresentedinthis Letter.

7.2. Thecut-and-countanalysis

Thecut-and-countanalysisispresentedbecauseitallowsforan easierreinterpretationofthissearchinthecontextofother theo-reticalmodelsthatpredict pmiss

ob-Table 4

CorrelationbetweentheuncertaintiesinpredictedbackgroundyieldsacrossthemjjbinsoftheshapeanalysisSR.Thebackgrounds

areestimatedbyfittingthedataintheCRs.BinrangesareexpressedinTeV. Correlation coefficients 0.2–0.4 0.4–0.6 0.6–0.9 0.9–1.2 1.2–1.5 1.5–2.0 2.0–2.75 2.75–3.5 >3.5 0.2–0.4 1.00 – – – – – – – – 0.4–0.6 0.88 1.00 – – – – – – – 0.6–0.9 0.85 0.84 1.00 – – – – – – 0.9–1.2 0.78 0.76 0.75 1.00 – – – – – 1.2–1.5 0.70 0.72 0.71 0.60 1.00 – – – – 1.5–2.0 0.62 0.57 0.63 0.59 0.54 1.00 – – – 2.0–2.75 0.38 0.40 0.43 0.43 0.45 0.43 1.00 – – 2.75–3.5 0.28 0.28 0.33 0.26 0.34 0.27 0.22 1.00 – >3.5 0.22 0.21 0.22 0.23 0.24 0.20 0.23 0.19 1.00 Table 5

ExpectedeventyieldsintheSRandintheCRsofthecut-and-countanalysisforvariousSMprocesses.Thebackgroundyieldsand thecorrespondinguncertaintiesareobtainedfromacombinedfittodatainalltheCRs,butexcludingdataintheSR.Theexpected totalsignalcontributionforthe125 GeV Higgsboson,decayingtoinvisibleparticleswithabranchingfractionB(H→inv)=1,and theobservedeventyieldsarealsoreported.

Process Signal region Dimuon CR Dielectron CR Single-muon CR Single-electron CR

Z(νν)(QCD) 810±71 – – – – Z(νν)(EW) 269±33 – – – – Z()(QCD) – 91.5±7.6 66.5±6.0 27.1±1.2 5.2±0.3 Z()(EW) – 32.5±4.1 24.1±3.2 5.7±0.3 2.4±0.2 W(ν)(QCD) 499±33 0.2±0.2 0.9±0.6 907±30 544±21 W(ν)(EW) 141±11 0.1±0.1 – 406±15 254±11 Top quark 37.8±8.8 4.8±1.4 2.9±1.0 112±22 74.2±13.6 Dibosons 18.6±6.2 2.3±1.1 0.7±0.4 21.3±4.4 14.4±3.7 Others 3.3±2.3 – – 22.9±13.9 2.1±1.9 Total bkg. 1779±96 131±8 95.0±6.3 1502±34 896±24 Signal mH=125.09 GeV 743±129 – – – – Data 2035 114 104 1504 902

servedeventyieldafterthecut-and-countselectionisreportedin Table5,alongwiththepredictedbackgroundsintheSR.The back-grounds are estimated by fitting the data in the CRs.An excess, characterized by a significance of about 2.5 standard deviations, isobservedintheSRcomparedtothebackgroundprediction ob-tainedfromtheCRs.Asfortheshapeanalysis,thisexcessismostly duetolowmjjevents.TheexcessisincompatiblewithaVBFHiggs

bosonsignaland,upondetailedscrutiny,isascribedtoastatistical fluctuation.

Theresultsofthecut-and-countanalysisarepresentedinterms ofa95%CLupperlimiton

B

(

H

→

inv

)

usingthestatistical proce-dure outlinedin Section7.1.The observed(expected)upperlimit isfoundtobe0.58(0.30),andtheregionscontaining68%and95% ofthedistributionofupperlimits,expectedinabsenceofasignal, arefoundtobe0.22–0.43and0.17–0.58,respectively.

7.3. ConstraintsonaSM-likeHiggsboson

Theresultspresentedarealsointerpreted inthecontextofan additionalSM-likeHiggsbosonthatdoesnotmixwiththe125 GeV bosonanddecaystoinvisibleparticles [69].Such abosonmaybe producedvia boththe ggH andVBFmechanisms.Thismodelhas already been studied in earlier CMS publications [70–72]. Upper limits,computedat95%CL on

(

σ

/

σ

SM

)

B

(

H

→

inv

)

,areshownin

Fig. 7as a function of theSM-like Higgsboson mass hypothesis (mH)forboththeshapeandthecut-and-countanalyses.

8. CombinedlimitsonH

→

inv from2016data

Thecommonfeature ofall thesearchesincluded inthis com-binationisalarge pmiss_T ,whereatleastonehigh-pT jetoraweak

bosonrecoilsagainsttheinvisibleparticlesproducedbytheHiggs bosondecay.Specifictopologicalselectionsaredesignedtoreduce

thecontamination fromlargeSM backgrounds,targetinga partic-ular Higgsboson productionmode. Theanalyses included inthis combinationarelistedinTable6,togetherwiththeirexpected sig-nal compositionandtheirindividual upperlimitson

B

(

H

→

inv

)

. TheresultsquotedfortheVBFchannelcomefromtheshape anal-ysisdescribedearlierinthisLetter.TheZ

(

+



−

)

H analysisis iden-ticalto theone described inRef. [72], wherethe expectedsignal comes entirelyfrominvisible decays oftheSM Higgs boson pro-ducedinassociationwitha leptonicallydecayingZ boson, via ei-therqq

→

ZH orgg

→

ZH production.Incontrast,theV

(

qq’

)

H and theggH-taggedsearchesaresimilartothosedescribedinRef. [73], buteventswhichoverlapwiththeVBFanalysishavebeenremoved to avoiddouble counting. Inboth the ggH and V

(

qq’

)

H searches, overlappingeventsrepresentabout6 (15)%ofthetotalbackground for a pmiss

T of about 250 (1000) GeV. The overlap removal

intro-ducesa5% lossintheexpectedexclusionsensitivitycomparedto that of Ref. [73]. Both the V

(

qq’

)

H and the ggH searches target eventswithatleastonehigh-pT centraljet,andtheirSRscontain

amixtureofdifferentproductionmodes.Thismixtureresultsfrom the limited discrimination powerof the substructureobservables exploitedtoselectboostedV

(

qq’

)

H candidates.

No significant deviations from the SM expectations are ob-served in any of the searches. The results are interpreted asan upper limit on

(

σ

/

σ

SM

)

B

(

H

→

inv

)

. These limits are calculated

following the same approach described in Section 7.1. The com-binedlikelihoodfitaccountsforcorrelationsbetweenthenuisance parameters ineach search.Theuncertainties inthediboson back-grounds (except for those considered in the Z

()

H channel), tt and single top quark cross sections, lepton efficiencies, momen-tum scales, integratedluminosity, b quark jet and

τ

h vetoes are

correlatedamongallthesearches.Inaddition,theuncertaintiesin theinclusivesignal productioncrosssections,dueto renormaliza-tion and factorizationscale variations, andthe PDF uncertainties

The CMS Collaboration / Physics Letters B 793 (2019) 520–551 531

Fig. 7. Expectedandobserved95%CL upperlimitson(σ/σSM)B(H→inv)foranSM-likeHiggsbosonasafunctionofitsmass(mH).Ontheleft,observed(solidblack)and

expected(dashedblack)upperlimitsareobtainedfromtheshapeanalysiswhile,ontheright,resultsfromthecut-and-countanalysisarereported.The68%(green)and95% (yellow)CLintervalsaroundtheexpectedupperlimitsarealsoshownforboththeshapeandthecut-and-countanalyses.

Table 6

Signalcompositionandupperlimits(observedandexpected)ontheinvisibleHiggsbosonbranchingfractionclassifiedaccordingto thefinalstateconsideredineachanalysis.TherelativecontributionsfromthedifferentHiggsproductionmechanismsarederived fromsimulation,fixingtheHiggsbosonmassto125.09 GeV andassumingSMproductioncrosssections.

Analysis Final state Signal composition Observed limit Expected limit VBF-tag VBF-jet+pmissT 52% VBF, 48% ggH 0.33 0.25

VH-tag Z()+pmissT [72] 79% qqZH, 21% ggZH 0.40 0.42

V(qq’)+pmiss

T [73] 39% ggH, 6% VBF, 33% WH, 22% ZH 0.50 0.48

ggH-tag jets+pmiss

T [73] 80% ggH, 12% VBF, 5% WH, 3% ZH 0.66 0.59

are alsocorrelated across the channels. Incontrast, since the jet kinematics inthe VBF search differ fromthat inthe other anal-yses, jet energy scale and resolution uncertainties are correlated onlyacrosstheggH andVH-taggedcategories.Thetheoretical un-certainties applied to the V+jets (QCD) ratios are assumed to be uncorrelatedbetweentheVBFanalysisandtheothersearches.

Observed and expected upper limits on

(

σ

/

σ

SM

)

B

(

H

→

inv

)

are computed at 95% CL and are presented in Fig. 8 (left). As-sumingSM crosssections for each productionmode, the combi-nationyieldsanobserved(expected)upperlimitof

B

(

H

→

inv

) <

0

.

26

(

0

.

20

)

. The profile likelihood ratios as a function of

B

(

H

→

inv

)

,forboththecombinedfitandeachindividualsearchchannel, arereportedinFig.8(right). Resultsareshownforbothdataand an Asimovdataset [65], defined by fixing the nuisances parame-terstotheir maximum likelihoodestimate obtainedfroma fitto thedatainwhich

B

(

H

→

inv

)

=

0 isassumed.

9. Combinationof7,8,and13 TeV searchesforH

→

inv decays

The analyses previously described and listed in Table 6 are furthercombinedwithearliersearchesperformedusingdata col-lected at

√

s

=

7, 8, and 13 TeV up to the end of 2015, as re-portedinRefs. [16,70,74].The7and8 TeV data,collected in2011 and2012,correspond tointegratedluminosities ofup to4.9and 19.7 fb−1 [75,76], respectively. The 13 TeV data collected in2015 correspondtoanintegratedluminosityof2.3 fb−1 [77].Systematic uncertainties inthe inclusive ggH,VBF, and VH productioncross sectionsare fullycorrelated across the 7,8, and13 TeV analyses. Theuncertaintyinthepredictionofthe Higgsboson pT

distribu-tioninggH production,includedinboththeggH andVH channels,

andthosearisingfromthelimitedknowledgeofthePDFs,arealso correlatedamongallsearches.Theuncertaintiesintheleptonand photonreconstruction andidentificationefficiencies,inthelepton momentumscales,andinthevetoefficiencyofleptons,

τ

h

candi-dates,andb quark jetsare uncorrelatedbetween7+8 and13 TeV searches. Similarly, uncertainties in the jet energy scale and res-olution, mistag rateof leptons, andmodeling of the unclustered particles are alsouncorrelated between7+8 and13 TeV searches. ThebjetenergyscaleandresolutionuncertaintiesfortheZ

(

bb

)

H analysis are estimated using different techniques, and therefore aretreatedasuncorrelatedwithotherchannels.Theoretical uncer-taintiesaffecting theratioofZ

(

νν

)

andW

(

ν

)

predictions inthe VBFsearches,forbothQCDandEWV+jets processes,are uncorre-latedacross datasets becausedifferentstrategiesare followedto quantifyandassigntheseuncertainties.Incontrast,thoseaffecting the Z

(

νν

)

/W

(

ν

)

andZ

(

νν

)

/

γ

+jets ratiosintheggH and V

(

qq

)

H channelsarecorrelatedacrossthe7+8andthe13 TeV (2015data) searches, asdescribed inRef. [16]. The uncertainties in thetune oftheunderlyingeventsimulationandinthepileupmodelingare uncorrelatedbetween7+8and13 TeV searches.Finally,theoretical uncertaintiesaffectingdibosonandtopquarkcrosssections,except forthoseconsideredontheZZ

/

WZ ratiointheZ

()

H channel,are correlatedacrossalldatasets.

Observedandexpectedupperlimitson

(

σ

/

σ

SM

)

B

(

H

→

inv

)

at

95% CL arepresentedinFig.9(left).Limitsare computedforthe combination of all data sets, as well as forpartial combinations basedeitheron7+8or13 TeV data.Therelativecontributionsfrom differentHiggsproductionmechanismsareconstrainedtotheirSM valueswithinthetheoreticaluncertainties.Thecombinationyields anobserved(expected)upperlimitof

B

(

H

→

inv

) <

0

.

19

(

0

.

15

)

at