Evidence for the Higgs boson decay to a bottom quark-antiquark pair

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DOI: 10.1016/j.physletb.2018.02.050

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©2018

by Elsevier. All rights reserved.

DIRETORIA DE TRATAMENTO DA INFORMAÇÃO

Cidade Universitária Zeferino Vaz Barão Geraldo

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http://www.repositorio.unicamp.br

Physics Letters B 780 (2018) 501–532

Contents lists available atScienceDirect

Physics

Letters

B

www.elsevier.com/locate/physletb

Evidence

for

the

Higgs

boson

decay

to

a

bottom

quark–antiquark

pair

.

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:

Received21September2017

Receivedinrevisedform17February2018 Accepted20February2018

Availableonline27February2018 Editor: M.Doser

Keywords:

CMS Physics Higgs

A searchforthe standard model (SM)Higgsboson(H)decaying tobb whenproducedin association with anelectroweakvectorbosonis reportedforthe followingprocesses: Z(

νν

)H,W(

μν

)H,W(e

ν

)H, Z(

μμ

)H,andZ(ee)H.Thesearchisperformedindatasamplescorrespondingtoanintegratedluminosity of35.9 fb−1at √s=13 TeV recordedby theCMS experiment atthe LHCduringRun 2 in2016. An excessofeventsis observedindata comparedtotheexpectation intheabsenceofaH→bb signal. Thesignificance ofthisexcessis3.3standard deviations,wheretheexpectationfromSMHiggsboson productionis2.8.Thesignalstrengthcorrespondingtothisexcess,relativetothatoftheSMHiggsboson production,is1.2±0.4.WhencombinedwiththeRun 1measurementofthesameprocesses,thesignal significanceis3.8standarddeviationswith3.8expected.Thecorrespondingsignalstrength,relativeto thatoftheSMHiggsboson,is1.06+₋0₀._.31₂₉.

©2018TheAuthor(s).PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense (http://creativecommons.org/licenses/by/4.0/).FundedbySCOAP3_.

1. Introduction

TheATLASandCMSCollaborationsreportedin2012the discov-eryofanewbosonwithamassnear125 GeV usingdatafromthe LargeHadronCollider(LHC)atCERN [1–3].Significantsignalshave beenobserved inchannels wherethe bosondecays into

γ γ

, ZZ, WW,or

τ τ

[4–13].Themeasuredproductionanddecayratesand spin-parityproperties of thisboson [14–20] are compatible with thoseofthestandardmodel(SM)Higgsboson(H) [21–26].

The H

→

bb decay tests directly the Higgsboson coupling to fermions,andmorespecificallytodown-typequarks,andhasnot yet been established experimentally. In the SM, for a Higgs bo-sonmass mH

=

125 GeV,thebranching fractionisapproximately

58% [27],byfarthelargest.Anobservationinthischannelis nec-essarytosolidifytheHiggsbosonasthesourceofmassgeneration inthefermionsectoroftheSM [28,29].

AttheTevatronpp colliderthesensitivityoftheSM Higgs bo-sonsearch,formassesbelow130 GeV,wasdominatedbyits pro-ductioninassociation witha weakvector boson(VH production) anditsdecaytobb [30].ThecombinedsearchesfromtheCDFand D0Collaborationsresultedinan excessofeventswithalocal sig-nificance, at mH

=

125 GeV, of 2.8 standard deviations, with an

expectedvalue of1.6. FortheH

→

bb searchatthe LHC,the fol-lowingHiggsbosonproductionprocesseshavebeenconsidered:in association witha top quark pair [31–34], through vector boson

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

fusion [35,36],throughVHproduction [37,38],and,morerecently, throughgluonfusion [39].Theprocesswiththelargestsensitivity isVHproduction.

The combined searches for H

→

bb by the ATLAS and CMS Collaborations in Run 1, at

√

s

=

7 and 8 TeV, evaluated for a Higgsbosonmassof125.09 GeV, resultedinasignificanceof2.6 standard deviations, with 3.7 standard deviations expected [18]. The corresponding signal strength, relative to the SM expecta-tion,is

μ

=

0

.

7

±

0

.

3.The significancefromthe individualsearch by the ATLAS (CMS) experiment is 1.7 (2.0) standard deviations, with2.7(2.5) standarddeviationsexpected, andasignalstrength

μ

=

0

.

6

±

0

.

4 (

μ

=

0

.

8

±

0

.

4).

Recent results by the ATLAS Collaboration [40] in the search for H

→

bb through VH production at

√

s

=

13 TeV, with data corresponding to an integrated luminosity of 36.1 fb−1, report a significance of3.5 standard deviations, corresponding to a signal strengthof

μ

=

1

.

20₋+0₀._.42₃₆.Thecombinationwiththeresultsfrom thesamesearchinRun 1 [37] yieldsasignificanceof3.6standard deviationsandasignalstrength

μ

=

0

.

90+₋0₀._.28₂₆.

This article reports on the search with the CMS experiment forthe decay ofthe SM Higgsboson to bottom quarks,H

→

bb, when producedthrough the pp

→

VH process,where V is either a W or a Z boson. This search is performedwith data samples from Run 2 of the LHC, recorded during 2016, corresponding to anintegratedluminosityof35.9 fb−1 at

√

s

=

13TeV.The follow-ingfiveprocessesareconsideredinthesearch:Z

(

νν

)

H,W

(

μν

)

H, W

(

e

ν

)

H,Z

(

μμ

)

H,andZ

(

ee

)

H.Thefinalstatesthatpredominantly correspond to these processes, respectively, are characterized by https://doi.org/10.1016/j.physletb.2018.02.050

0370-2693/©2018TheAuthor(s).PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense(http://creativecommons.org/licenses/by/4.0/).Fundedby SCOAP3_.

thenumberofleptons requiredintheeventselection,andare re-ferredtoasthe0-,1-,and2-leptonchannels.

Throughout this article the term “lepton” (denoted



) refers solely to muonsand electrons, but not to taus. The leptonic tau decays in WH and ZH processes are implicitly included in the W

(

μν

)

H, W

(

e

ν

)

H, Z

(

μμ

)

H, and Z

(

ee

)

H processes. Background processes originate from the production of W and Z bosons in association withjetsfromgluonsandfromlight- orheavy-flavor quarks (W

+

jets and Z

+

jets), from singly andpair-produced top quarks(singletopandtt),fromdibosonproduction(VV),andfrom quantumchromodynamicsmultijetevents(QCD).

Simulatedsamplesofsignalandbackgroundeventsareusedto optimizethesearch. Foreach channel,asignalregionenriched in VHevents is selectedtogether with severalcontrol regions, each enrichedineventsfromindividualbackgroundprocesses.The con-trolregionsareusedtotesttheaccuracyofthesimulatedsamples’ modelingforthevariablesrelevanttotheanalysis.Asimultaneous binned-likelihood fit to the shape and normalization of specific distributions for the signal and control regions for all channels combined is used to extract a possible Higgs boson signal. The distribution used inthe signal region is the output of a boosted decisiontree(BDT)eventdiscriminant [41,42] thathelpsseparate signal from background. For the control regions, a variable that identifiesjetsoriginatingfrombquarks,andthatdiscriminates be-tweenthedifferentbackgroundprocesses,isused.Tovalidatethe analysisprocedure,thesamemethodologyisusedtoextracta sig-nalfortheVZ process,withZ

→

bb,whichhasanearly identical final state to VH withH

→

bb,but witha productioncross sec-tion of5 to 15times larger, depending on thekinematic regime considered.Finally,theresultsfromthissearcharecombinedwith thoseofsimilarsearchesperformedbytheCMSCollaboration dur-ingRun 1 [18,36,38].

Thisarticleisstructured asfollows:Sections 2–3 describethe CMS detector, the simulated samples used for signal and back-groundprocesses, andthe triggers used to collect the data. Sec-tions4–5describethereconstructionofthedetectorobjectsused in theanalysis andthe selection criteriafor eventsin the signal andcontrolregions.Section6describesthesourcesofuncertainty intheanalysis,andSection7describestheresults,summarizedin Section8.

2. TheCMSdetectorandsimulatedsamples

Adetaileddescriptionof theCMSdetectorcan befound else-where in Ref. [43]. The momenta of charged particles are mea-suredusingasiliconpixelandstriptrackerthatcovers therange

|

η

|

<

2

.

5 andisimmersedina3.8 T axialmagneticfield.The pseu-dorapidity isdefined as

η

= −

ln

[

tan

(θ/

2

)

]

, where

θ

is the polar angleof thetrajectory ofa particle withrespect tothe direction ofthecounterclockwiseprotonbeam.Surroundingthetrackerare acrystalelectromagneticcalorimeter(ECAL)andabrassand scin-tillator hadroncalorimeter(HCAL),both usedto measureparticle energydepositsandbothconsistingofabarrelassemblyandtwo endcaps.TheECALandHCALextendtoarangeof

|

η

|

<

3

.

0.Asteel and quartz-fiber Cherenkov forward detector extends the calori-metriccoverageto

|

η

|

<

5

.

0.TheoutermostcomponentoftheCMS detectoristhemuonsystem,consistingofgas-ionizationdetectors placedinthesteelflux-returnyokeofthemagnettomeasurethe momentaofmuonstraversingthroughthedetector.Thetwo-level CMStriggersystemselects eventsofinterest forpermanent stor-age.Thefirsttriggerlevel,composed ofcustom hardware proces-sors, usesinformationfrom thecalorimetersandmuon detectors toselecteventsinlessthan3.2μs.Thehigh-leveltriggersoftware algorithms,executed on afarm ofcommercialprocessors,further reducethe eventrateusinginformationfromalldetector

subsys-tems.Thevariable

R

=



(

η

)

2

_{+ ( φ)}

2 _{isusedtomeasurethe}

separationbetweenreconstructedobjectsinthedetector,where

φ

istheangle(inradians)ofthetrajectoryoftheobjectintheplane transversetothedirectionoftheprotonbeams.

Samples of simulated signal and background events are pro-ducedusingthe MonteCarlo(MC) eventgenerators listed below. The CMS detector response is modeled with Geant4 [44]. The signal samples usedhave Higgsbosons withmH

=

125GeV

pro-duced in association with vector bosons. The quark-induced ZH and WH processes are generated at next-to-leading order (NLO) using the powheg [45–47] v2 eventgeneratorextended withthe MiNLO procedure [48,49], while the gluon-inducedZH processes (denoted ggZH)aregeneratedatleading-order(LO)accuracywith powheg v2. The MadGraph5_amc@nlo [50] v2.3.3 generator is used atNLO withtheFxFx mergingscheme [51] for thediboson background samples. The same generator is usedat LO accuracy withthe MLMmatching scheme [52] for theW

+

jetsandZ

+

jets in inclusive and b-quark enriched configurations, as well as the QCD multijet sample. The tt [53] production process, as well as the single top quark sample forthet-channel [54], are produced with powheg v2. The single top quark samples forthe tW- [55] and s-channel [56] are instead produced with powheg v1. The production cross sections for the signal samples are rescaled to next-to-next-to-leadingorder(NNLO)QCD

+

NLOelectroweak ac-curacycombiningthe vhnnlo [57–59], vh@nnlo [60,61] and hawk v2.0 [62] generatorsasdescribed inthedocumentation produced bytheLHCWorkingGrouponHiggsbosoncrosssections [63],and they areappliedasafunctionofthevectorbosontransverse mo-mentum(pT).Theproductioncrosssectionsforthett samplesare

rescaled totheNNLOwiththenext-to-next-to-leading-log(NNLL) predictionobtainedwith Top

++

v2.0 [64],whiletheW

+

jetsand Z

+

jetssamplesarerescaledtotheNLOcrosssectionsusing Mad-Graph5_amc@nlo. The parton distribution functions (PDFs) used toproducetheNLOsamplesaretheNLONNPDF3.0set [65],while theLONNPDF3.0setisusedfortheLOsamples.Forparton show-ering and hadronization the powheg and MadGraph5_amc@nlo samples are interfaced with pythia 8.212 [66]. The pythia8 pa-rameters for the underlying event description correspond to the CUETP8M1tunederived inRef. [67] basedontheworkdescribed inRef. [68].

During the2016data-taking periodtheLHCinstantaneous lu-minosityreachedapproximately1

.

5

×

1034 _cm−2_s−1 _andthe

av-eragenumberofpp interactionsper bunchcrossingwas approxi-mately23.Thesimulatedsamplesincludetheseadditionalpp in-teractions, referredtoaspileupinteractions (orpileup),that over-lapwiththeeventofinterestinthesamebunchcrossing. 3. Triggers

Severaltriggers are used to collectevents withfinal-state ob-jects consistent with the signal processes in the channels under consideration.

Forthe0-leptonchannel,thequantitiesusedinthetriggerare derived fromthe reconstructed objects in the detector identified by a particle-flow (PF) algorithm [69] that combines the online information fromall CMS subsystems toidentify andreconstruct individual particles emerging from the proton-proton collisions: chargedhadrons, neutralhadrons,photons, muons, andelectrons. The main trigger used requires that both the missing transverse momentum, pmiss_T , and the hadronicmissing transverse momen-tum, Hmiss_T ,intheeventbeaboveathresholdof110 GeV.Online pmiss

T isdefinedasthemagnitudeofthenegativevectorsumofthe

transverse momentaofall reconstructedobjects identifiedby the PFalgorithm,while Hmiss_T isdefinedasthemagnitudeofthe neg-ative vector sumof the transverse momenta ofall reconstructed

The CMS Collaboration / Physics Letters B 780 (2018) 501–532 503

jets(withpT

>

20GeV and

|

η

|

<

5

.

2)identifiedbythesame

algo-rithm.ForZ

(

νν

)

H eventswith pmiss_T

>

170GeV,evaluatedoffline, thetrigger efficiencyis approximately92%, andnear100% above 200 GeV.

Forthe1-leptonchannels, single-leptontriggers are used.The muontriggerpTthresholdis24 GeV andtheelectronpTthreshold

is27 GeV. For the 2-lepton channels, dilepton triggers are used. The muon pT thresholds are 17and 8 GeV,andthe electron pT

thresholds are 23 and 12 GeV. All leptons in these triggers are required to pass stringent lepton identification criteria. In addi-tion,to maintain an acceptable trigger rate, andto be consistent with what is expected from signal events, leptons are also re-quired to be isolated from other tracks and calorimeter energy deposits.ForW

(

μν

)

H eventsthatpassallofflinerequirements de-scribed in Section 5, the single-muon trigger efficiencyis

≈

95%. The corresponding efficiency for recording W

(

e

ν

)

H events with thesingle-electrontriggeris

≈

90%. ForZ

()

H signal eventsthat passallofflinerequirementsinSection5,thedileptontriggersare nearly100%efficient.

4. Eventreconstruction

ThecharacterizationofVHeventsinthechannelsstudiedhere requiresthereconstructionofthefollowingobjectsinthedetector, usingthePFalgorithm [69] andoriginatingfromtheprimary inter-actionvertex:muons,electrons,neutrinos(reconstructedaspmiss

T ),

andjets—includingthosethatoriginatefromthehadronizationof b quarks,referredtoas“b jets”.

The reconstructed vertex with the largest value of summed physics-objectp2_T istakentobetheprimarypp interactionvertex. Thephysics objectsare theobjects reconstructedby ajet finding algorithm [70,71] appliedtoallchargedtracksassociatedwiththe vertex, plusthe corresponding associated pmiss_T .The pileup inter-actionsaffectjet momentum reconstruction, pmiss_T reconstruction, lepton isolation, and b tagging efficiencies. To mitigate these ef-fects,all chargedhadronsthat donot originatefromtheprimary interaction vertex are removed from consideration in the event. In addition, the average neutral energy density from pileup in-teractions is evaluated from PF objects and subtracted from the reconstructed jetsin the eventand fromthe summed energy in theisolationcriteriausedforleptons [72].Thesepileupmitigation proceduresareappliedonanobject-by-objectbasis.

Muons are reconstructed using two algorithms [73]: one in whichtracksinthesilicontrackerarematchedtohitsinthemuon detectors,andanotherinwhichatrackfitisperformedusinghits inthesilicontrackerandinthemuonsystems.Inthelatter algo-rithm,themuonisseededbyhitsinthemuonsystems.Themuon candidatesusedintheanalysisarerequiredtobesuccessfully re-constructedby both algorithms. Furtheridentification criteriaare imposedon themuoncandidates toreduce thefractionoftracks misidentifiedas muons. Theseinclude thenumber ofhitsin the trackerandinthemuonsystems,thefitqualityoftheglobalmuon track, and its consistency withthe primary vertex. Muon candi-datesarerequiredtobeinthe

|

η

|

<

2

.

4 region.

Electronreconstruction [74] requires the matchingof a setof ECAL clusters, denoted supercluster (SC), to a track in the sili-con tracker. Electron identification [74] relies on a multivariate technique that combines observables sensitive to the amount of bremsstrahlung along the electron trajectory, such as the geo-metricalmatchingandmomentum consistencybetweenthe elec-tron trajectory and the associated calorimeter clusters, as well as various shower shape observables in the calorimeters. Addi-tional requirements are imposed to remove electrons that origi-natefromphoton conversions.Electronsarerequiredtobeinthe range

|

η

|

<

2

.

5,excluding candidatesforwhichtheSC liesinthe

1

.

444

<

|

η

SC

|

<

1

.

566 transition region between the ECAL barrel

andendcap,whereelectronreconstructionisnotoptimal. Charged leptons from W and Z bosondecays are expected to be isolatedfromother activityinthe event.Foreach lepton can-didate,aconein

η

—

φ

isconstructedaroundthetrackdirectionat theeventvertex. Thescalar sumof thetransversemomentum of eachreconstructedparticle,includingneutralparticles,compatible withthe primary vertexandcontained withinthe cone is calcu-lated, excludingthe contributionfromtheleptoncandidateitself. Thissumiscalledisolation.Inthepresence ofpileup,isolation is contaminated withparticles fromthe other interactions. A quan-tity proportionalto thepileup isused tocorrectthe isolation on averagetomitigatereductionsinsignalefficiencyatlargervalues of pileup.In the1-lepton channel, ifthe corrected isolation sum exceeds 6% of the lepton candidate pT, the lepton is rejected. In

the2-leptonchannel,thethresholdislooser;theisolationofeach candidatecanbeupto20(15%)ofthemuon(electron)pT.

Includ-ingtheisolationrequirement,thetotalefficiencyforreconstructing muonsis in the rangeof 85–100%,depending on pT and

η

.The

correspondingefficiencyforelectronsisintherangeof40–90%. Jets are reconstructed fromPF objects using the anti-kT

clus-teringalgorithm [70], witha distanceparameterof0.4,as imple-mented inthe FastJet package [71,75].Each jetis requiredtolie within

|

η

|

<

2

.

4, to have at least two tracks associated with it, and to haveelectromagnetic and hadronicenergy fractions of at least 1%.Thelastrequirementremovesjetsoriginatingfrom instru-mentaleffects.Jetenergycorrectionsareappliedasafunctionof

η

and pT ofthejet [76].The missingtransversemomentumvector,



pmiss

T ,is calculatedofflineasthe negativeof thevectorialsumof

transversemomenta ofallPFobjects identifiedinthe event [77], andthe magnitude ofthis vector is denoted pmiss_T inthe rest of thisarticle.

Theidentificationofb jetsisperformedusingacombined mul-tivariate(CMVA)b taggingalgorithm [78,79].Thisalgorithm com-bines, in a likelihood discriminant, information within jets that helpsdifferentiate between b jets andjets originatingfromlight quarks, gluons, or charm quarks. This information includes track impactparameters,secondary vertices,andinformationrelatedto low-pT leptons ifcontained within a jet. The output of this

dis-criminanthascontinuousvaluesbetween

−

1

.

0 and1.0.Ajetwith a CMVA discriminant value above a certain threshold is labeled as “b-tagged”. The efficiency for tagging b jets and the rate of misidentification of non-b jets depend on the threshold chosen, andare typicallyparameterized asafunction ofthe pT and

η

of

the jets. These performance measurements are obtained directly fromdatainsamplesthatcanbeenrichedinb jets,suchastt and multijet events (where, for example,requiring the presence ofa muoninthejetsenhancestheheavy-flavorcontentoftheevents). ThreethresholdsfortheCMVAdiscriminantvalueareusedinthis analysis: loose (CMVAL), medium (CMVAM), and tight (CMVAT).

Dependingon thethresholdused,theefficiencies fortaggingjets that originate from b quarks, c quarks, and light quarks or glu-ons areinthe50–75%,5–25%, and0.15–3.0%ranges,respectively. Theloose(tight)thresholdhasthehighest(lowest)efficiencyand allowsmost(least)contamination.

Inbackground events,particularly tt,there isoftenadditional, lowenergy,hadronicactivityintheevent.Measuringthehadronic activity associated with the main primary vertex provides addi-tional discriminating variables to reject background. To measure this hadronic activity only reconstructed charged-particle tracks are used, excluding those associated with the vector boson and the two b jets. A collection of “additional tracks” is assembled using reconstructed tracks that: (i) satisfy the high purity qual-ityrequirements definedin Ref. [80] and pT

>

300MeV; (ii)are

intheevent;(iii)haveaminimumlongitudinalimpactparameter,

|

dz

(

PV

)

|

,withrespectto themain PV,ratherthantootherpileup interaction vertices;(iv) satisfy

|

dz

(

PV

)

|

<

2 mm;and(v) are not intheregionbetweenthetwoselected b-taggedjets.Thisregion is definedasan ellipsein the

η

—

φ

plane, centered on the mid-pointbetweenthetwojets,withmajoraxisoflength

R

(

bb

)

+

1, where

R

(

bb

)

=



(

η

bb)2

_{+ ( φ}

_bb)2_{,orientedalongthedirection}

connectingthe two b jets, andwith minoraxis oflength 1.The additionaltracksarethenclusteredinto“soft-trackjets”usingthe anti-kT clustering algorithmwitha distanceparameterof0.4.The

useoftrackjetsrepresentsa cleanandvalidatedmethod [81] to reconstruct the hadronization of partons with energies down to a few GeV [82];an extensive studyofthe soft-track jet activity canbe found inRefs. [83,84]. Thenumberof softtrackjetswith pT

>

5GeV isusedinallchannelsasabackgrounddiscriminating

variable.

Eventsfromdataandfromthesimulatedsamplesarerequired tosatisfythesametriggerandeventreconstructionrequirements. Correctionsthataccountforthedifferencesintheperformanceof these algorithms between data and simulated samples are com-putedfromdataandusedintheanalysis.

5. Eventselection

AsignalregionenrichedinVHeventsisdeterminedseparately foreachchannel.Simulatedeventsinthisregionareusedtotrain aneventBDTdiscriminanttohelpdifferentiatebetweensignaland backgroundevents.Alsoforeachchannel,differentcontrolregions, eachenrichedineventsfromindividualbackgroundprocesses,are selected.Theseregions areusedtostudytheagreement between simulatedsamplesanddata,andtoprovide adistribution thatis combinedwiththe outputdistribution ofthesignal region event BDTdiscriminant intheH

→

bb signal-extractionfit.Thiscontrol region distribution is obtained fromthe second-highest value of theCMVAdiscriminantamongthetwojetsselectedforthe recon-structionoftheH

→

bb decay,denotedCMVAmin.

AsmentionedintheIntroduction,backgroundprocessestoVH production with H

→

bb are the production of vector bosons in associationwithone ormore jets(V

+

jets),tt production, single-top-quarkproduction,dibosonproduction, andQCD multijet pro-duction. These processes haveproduction cross sections that are severalorders of magnitudelarger than that ofthe Higgs boson, withtheexceptionoftheVZ processwithZ

→

bb,withan inclu-sivecrosssectiononlyabout15timeslargerthantheVH produc-tioncross section.Given thenearly identicalfinal state, this pro-cessprovidesa benchmarkagainst whichtheHiggsboson search strategycanbetested.Theresultsofthistestarediscussedin Sec-tion7.1.

Belowwedescribetheselectioncriteriausedtodefinethe sig-nal regions and the variables used to construct the event BDT discriminant.Alsodescribed arethe criteriausedto select appro-priate background-specific control regions andthe corresponding distributionsusedinthesignal-extractionfit.

5.1. Signalregions

ThesignalregionrequirementsarelistedinTable1.Eventsare selected to belong exclusively to onlyone ofthe three channels. Signaleventsare characterizedbythe presenceofavectorboson recoilingagainsttwob jetswithaninvariant massnear125 GeV. The event selection therefore relies on the reconstruction of the decayoftheHiggsbosonintotwob-taggedjetsandonthe recon-structionoftheleptonicdecaymodesofthevectorboson.

The reconstruction of the H

→

bb decay is based on the se-lection of the pair of jets that have the highest values of the

Table 1

Selectioncriteriathatdefine thesignalregion.Entriesmarkedwith“—”indicate thatthevariableisnotusedinthegivenchannel.Whereselectionsdifferfor dif-ferent pT(V)regions, therearecommaseparatedentriesofthresholds orsquare

bracketswitharangethatindicateeachregion’s selectionasdefinedinthe first rowofthetable.Thevalueslistedforkinematicvariablesareinunitsof GeV,and foranglesinunitsofradians.Whereselectiondiffersbetweenleptonflavors,the selectionislistedas(muon,electron).

Variable 0-lepton 1-lepton 2-lepton

pT(V) >170 >100 [50,150],>150 M() — — [75,105] p T — (>25, >30) >20 pT(j1) >60 >25 >20 pT(j2) >35 >25 >20 pT(jj) >120 >100 — M(jj) [60,160] [90,150] [90,150] φ(V,jj) >2.0 >2.5 >2.5 CMVAmax >CMVAT >CMVAT >CMVAL

CMVAmin >CMVAL >CMVAL >CMVAL

Naj <2 <2 — Na =0 =0 — pmiss T >170 — — φ(pmiss T ,j) >0.5 — — φ(pmiss T ,p miss T (trk)) <0.5 — — φ(pmiss T , ) — <2.0 — Lepton isolation — <0.06 (<0.25, <0.15) Event BDT >−0.8 >0.3 >−0.8

CMVA discriminant among all jetsin the event. The highestand second-highestvaluesoftheCMVAdiscriminantforthesetwojets aredenotedbyCMVAmax andCMVAmin,respectively.Both jetsare

requiredtobecentral(with

|

η

|

<

2

.

4),tosatisfystandard require-ments toremove jetsfrompileup [85], andto havea pT above a

minimumthreshold,thatcanbe differentforthehighest(j1)and

second-highest(j2)pTjet.Theselecteddijetpairisdenotedby“jj”

intherestofthisarticle.

The background from V

+

jets and diboson production is re-ducedsignificantly whenthe b tagging requirementsare applied. Asaresult,processeswherethetwojetsoriginatefromgenuineb quarks dominatethesample composition inthe signal region.To provideadditionalsuppressionofbackgroundevents,severalother requirementsareimposedoneachchannelafterthereconstruction oftheH

→

bb decay.

5.1.1. 0-leptonchannel

This channeltargetsmainly Z

(

νν

)

H events inwhichthe pmiss_T isinterpreted asthe transversemomentumoftheZbosoninthe Z

→

νν

decay. In order to overcome large QCD multijet back-grounds,arelativelyhighthresholdofpmiss_T

>

170GeV isrequired. TheQCD multijetbackgroundisfurtherreducedtonegligible lev-els in this channel when requiring that the pmiss

T doesnot

orig-inate from the direction of (mismeasured) jets. To that end, if there is a jet with

|

η

|

<

2

.

5 and pT

>

30 GeV, whoseazimuthal

angle is within 0.5 radians of the pmiss

T direction, the event is

rejected. The rejectionof multijetevents with pmiss

T produced by

mismeasured jetsisaidedby usingadifferentmissingtransverse momentumreconstruction,denotedpmiss_T

(

trk

)

,obtainedby consid-eringonlycharged-particletrackswithpT

>

0

.

5GeV and

|

η

|

<

2

.

5.

Foraneventtobeaccepted,itisrequiredthat pmiss_T

(

trk

)

andpmiss_T be alignedin azimuth within 0.5radians. Toreduce background eventsfromtt andWZ productionchannels,eventswithany addi-tionalisolatedleptonswithpT

>

20GeV arerejected.Thenumber

oftheseadditionalleptonsisdenotedbyNa.

5.1.2. 1-leptonchannel

ThischanneltargetsmainlyW

(

ν

)

H eventsinwhichcandidate W

→ 

ν

decaysareidentifiedbythepresenceofoneisolated lep-ton aswell asmissingtransversemomentum, whichisimplicitly

The CMS Collaboration / Physics Letters B 780 (2018) 501–532 505

required in the pT(V

)

selection criteria mentioned below, where pT(V

)

is calculated from the vectorial sum of



pmiss_T and the lep-ton



pT.Muons(electrons) arerequiredtohavepT

>

25

(

30

)

GeV.

It is also required that the azimuthal angle between the pmiss T

directionandthe leptonbe lessthan 2.0radians.The lepton iso-lationforeitherflavor ofleptonisrequiredtobesmallerthan6% of the lepton pT. These requirements significantly reduce

possi-blecontamination from QCD multijetproduction. Withthe same motivationasinthe0-lepton channel,eventswithanyadditional isolatedleptons are rejected.Tosubstantially reject tt events,the numberofadditionaljetswith

|

η

|

<

2

.

9 and pT

>

25GeV,Naj,is

allowedtobeatmostone. 5.1.3. 2-leptonchannel

ThischanneltargetsZ

→ 

decays,whicharereconstructedby combiningisolated,oppositelychargedpairsofelectronsormuons andrequiringthedileptoninvariant masstosatisfy75

<

M

()

<

105 GeV.The pT for each lepton is required to be greater than

20 GeV.Isolationrequirementsarerelaxedin thischannel asthe QCD multijet backgroundis practically eliminated afterrequiring compatibilitywiththeZbosonmass [86].

5.1.4. pT(V

)

requirements,H

→

bb massreconstruction,andeventBDT discriminant

Backgroundevents are substantially reduced by requiring sig-nificant large transverse momentum of the reconstructed vector boson, pT(V

)

, orofthe Higgsboson candidate [87]. Inthis kine-maticregion, the V and H bosons recoil fromeach other witha largeazimuthalopeningangle,

φ (

V

,

H

)

,betweenthem.Different pT(V

)

regions are selectedfor each channel. Because ofdifferent signalandbackgroundcontent,eachoftheseregionshasdifferent sensitivityandtheanalysisisperformedseparatelyineachregion. Forthe0-leptonchannel,asingleregionrequiringpmiss

T

>

170GeV

isstudied.The1-leptonchannelisalsoanalyzedinasingleregion, with pT(V

)

>

100 GeV. The 2-lepton channels consider two re-gions:low- andhigh-pT regionsdefinedby50

<

pT(V

)

<

150GeV

andpT(V

)

>

150GeV.

Afterall event selection criteria described in this section are applied,thedijetinvariantmassresolutionofthetwob jetsfrom theHiggsbosondecayisapproximately15%,dependingonthepT

ofthereconstructedHiggsboson,withafew percentshiftinthe valueofthemasspeakrelativeto125 GeV.TheHiggsbosonmass resolutionisfurtherimprovedbyapplyingmultivariateregression techniquessimilarto thoseused attheCDFexperiment [88] and usedfor severalRun 1 H

→

bb analysesby ATLAS and CMS [37, 38].Theregressionestimatesacorrectionthatisappliedafterthe jet energy correctionsdiscussed in Section 4. It is computedfor individual b jets in an attempt to improve the accuracy of the measuredenergywithrespecttotheb quarkenergy.Tothisend, a BDT is trained on b jets fromsimulated tt events with inputs that include detailed jet structure information, which differs in jets from b quarks from that of jets from light-flavor quarks or gluons.Theseinputsincludevariablesrelatedtoseveralproperties ofthe secondary vertex (when reconstructed), information about tracks,jet constituents,and other variables relatedto theenergy reconstructionofthejet.Becauseofsemileptonicb hadrondecays, jetsfromb quarkscontain,onaverage,moreleptonsandalarger fractionof missingenergy thanjets fromlight quarks or gluons. Therefore,inthecaseswherea low-pT lepton isfoundin thejet

orinits vicinity, thefollowing variables are alsoincluded inthe regressionBDT:thepTofthelepton,the

R distancebetweenthe

lepton and the jet directions, and the momentum of the lepton transversetothejetdirection.

Forthethree channelsunderconsideration, theH

→

bb mass resolution, measured on simulated signal samples when the

Fig. 1. DijetinvariantmassdistributionsforsimulatedsamplesofZ()H(bb)events (mH=125GeV),before(red)andafter(blue)theenergycorrectionfromthe

re-gressionprocedureisapplied.AsumofaBernsteinpolynomialandaCrystalBall functionisusedtofitthedistribution.Thedisplayedresolutionsarederivedfrom thepeakandRMSoftheGaussiancoreoftheCrystalBallfunction.(For interpreta-tionofthecolorsinthefigure(s),thereaderisreferredtothewebversionofthis article.)

regression-correctedjetenergiesareused,isinthe10–13%range, and it dependson the pT of the reconstructed Higgsboson.

Av-eraging overall channels, the improvementin massresolution is approximately 15%, resulting in an increase of about 10% in the sensitivityoftheanalysis.Theperformanceofthesecorrectionsis shownin Fig.1 forsimulated samplesof Z

()

H

(

bb

)

events.The validationofthetechniqueindataisdoneusingthe pT()/pT(jj

)

distributioninsamplesofZ

→ 

eventscontainingtwo b-tagged jets, andusing the reconstructed top quark mass distribution in the lepton

+

jets final state in tt-enriched samples. After the jets arecorrected,theroot-mean-squarevalueofbothdistributions de-creases,thepeak value ofthe pT()/pT(jj

)

distributionis shifted closer to 1.0, andthe peak value of the reconstructed top quark massgets closertothetop quarkmass.Thesedistributions show good agreement between data and the simulated samples be-fore and after the regression correction is applied. Importantly, thereconstructeddijetinvariantmassdistributionsforbackground processes do not develop a peak structure when the regression correctionisappliedtotheselectedb-taggedjetsintheevent.

As mentionedabove, to help separate signal frombackground in the signal region, an event BDT discriminant is trained using simulated samples for signal and all background processes. The set of eventinput variables used,listed inTable 2, is chosen by iterativeoptimizationfromalargernumberofpotentially discrim-inatingvariables.Among the mostdiscriminating variablesforall channelsarethedijetinvariantmassdistribution,M

(

jj

)

,the num-berofadditionaljets, Naj,thevalueofCMVAforthejetwiththe

second-highest CMVA value, CMVAmin, and the distance,

R

(

jj

)

,

betweenthetwojets. 5.2. Backgroundcontrolregions

To help determine the normalizationof the main background processes,andtovalidatehowwell thesimulatedsamplesmodel thedistributionsofvariablesmostrelevanttotheanalysis,several control regions are selected in data.Tables 3–5 list theselection criteria usedto define theseregions forthe 0-, 1-,and 2-lepton channels,respectively.Separate controlregionsarespecifiedfortt production andforthe productionof W and Z bosonsin associ-ation with either predominantly heavy-flavor (HF) or light-flavor

Table 2

VariablesusedinthetrainingoftheeventBDTdiscriminantforthedifferentchannels.Jetsarecountedasadditionaljets tothoseselectedtoreconstructtheH→bb decayiftheysatisfythefollowing:pT>30GeV and|η|<2.4 forthe0- and

2-leptonchannels,andpT>25GeV and|η|<2.9 forthe1-leptonchannel.

Variable Description 0-lepton 1-lepton 2-lepton

M(jj) dijet invariant mass   

pT(jj) dijet transverse momentum   

pT(j1), pT(j2) transverse momentum of each jet  

R(jj) distance inη–φbetween jets 

η(jj) difference inηbetween jets   φ(jj) azimuthal angle between jets 

pT(V) vector boson transverse momentum  

φ(V,jj) azimuthal angle between vector boson and dijet directions    pT(jj)/pT(V) pTratio between dijet and vector boson 

M() reconstructed Z boson mass 

CMVAmax value of CMVA discriminant for the jet  

with highest CMVA value

CMVAmin value of CMVA discriminant for the jet   

with second highest CMVA value

CMVAadd value of CMVA for the additional jet 

with highest CMVA value

pmissT missing transverse momentum   

φ(pmiss

T ,j) azimuthal angle betweenpmissT and closest jet (pT>30 GeV) 

φ(pmissT ,) azimuthal angle betweenp miss

T and lepton 

mT mass of leptonpT+ pmissT 

mtop reconstructed top quark mass 

Naj number of additional jets  

pT(add) transverse momentum of leading additional jet 

SA5 number of soft-track jets with pT>5 GeV   

Table 3

Definitionofthecontrolregionsforthe0-leptonchannel.LFandHFreferto light-andheavy-flavorjets.Thevalueslistedforkinematicvariablesareinunitsof GeV, andforanglesinunitsofradians.Entriesmarkedwith“—”indicatethatthevariable isnotusedinthatregion.

Variable tt Z+LF Z+HF V decay category W(ν) Z(νν) Z(νν) pT(j1) >60 >60 >60 pT(j2) >35 >35 >35 pT(jj) >120 >120 >120 pmiss T >170 >170 >170 φ(V,jj) >2 >2 >2 Na ≥1 =0 =0 Naj ≥2 ≤1 <1 M(jj) — — ∈ [/ 60–160]

CMVAmax >CMVAM <CMVAM >CMVAT

CMVAmin >CMVAL >CMVAL >CMVAL

φ(j,pmiss T ) — >0.5 >0.5 φ(pmiss T ,p miss T (trk)) — <0.5 <0.5 min φ(j,pmiss T ) <π/2 — — Table 4

Definitionofthecontrolregionsforthe1-leptonchannels.TheHFcontrolregionis dividedintolow- andhigh-massrangesasshowninthetable.Thesignificanceof

pmiss

T ,σ(pmissT ),ispmissT dividedbythesquarerootofthescalarsumofjetpTwhere

jet pT>30GeV. Thevalueslistedforkinematicvariablesareinunitsof GeV,

exceptforσ(pmiss

T )whoseunitsare √

GeV.Foranglesunitsareradians.Entries markedwith“—”indicatethatthevariableisnotusedinthatregion.

Variable tt W+LF W+HF

pT(j1) >25 >25 >25

pT(j2) >25 >25 >25

pT(jj) >100 >100 >100

pT(V) >100 >100 >100

CMVAmax >CMVAT [CMVAL,CMVAM] >CMVAT

Naj >1 — =0 Na =0 =0 =0 σ(pmiss T ) — >2.0 >2.0 φ(pmiss T , ) <2 <2 <2 M(jj) <250 <250 <90,[150,250]

(LF) jets. While some control regions are very pure in their tar-getedbackgroundprocess,otherscontainmorethanoneprocess.

Different backgroundprocessesfeature specific bjet composi-tions, e.g. two genuine b jets for tt and V

+

bb, one genuine b

Table 5

Definitionofthecontrolregionsforthe2-leptonchannels.Thesameselectionis usedforboththelow- andhigh-pT(V)regions.Thevalueslistedforkinematic

vari-ablesareinunitsof GeV andforanglesinunitsofradians.Entriesmarkedwith “—”indicatethatthevariableisnotusedinthatregion.

Variable tt Z+LF Z+HF

pT(V) [50,150],>150 [50,150],>150 [50,150],>150

CMVAmax >CMVAT <CMVAL >CMVAT

CMVAmin >CMVAL <CMVAL >CMVAL

pmiss

T — — <60

φ(V,jj) — >2.5 >2.5

M() ∈ [/ 0,10],∈ [/ 75,120] [75,105] [85,97] M(jj) — [90,150] ∈ [/ 90,150]

jet for V

+

b, no genuine b jet for V

+

udscg. This characteristic, togetherwiththeirdifferentkinematicdistributions,resultsin dis-tinctCMVAmindistributionsthatservetoextractthenormalization

scalefactorsofthevarioussimulatedbackgroundsampleswhenfit todatainconjunctionwiththeBDTdistributions inthesignal re-gion to search fora possible VH signal. In this signal-extraction fit, discussed further in Section 7, the shape and normalization of these distributions are allowed to vary, for each background component, withinthesystematicandstatisticaluncertainties de-scribed in Section 6. These uncertainties are treated as indepen-dent nuisance parameters.The simulated samplesfor theV

+

jets processes are split into independent subprocesses according to the number of MC generator-level jets (with pT

>

20 GeV and

|

η

|

<

2

.

4)containing atleastone b hadron.Table6liststhescale factors obtainedfromthefit.Theseaccount notonly forpossible cross section discrepancies, but alsofor potential residual differ-ences in the selection efficiency of the different objects in the detector. Scale factors obtained from a similar fit to the control regionsaloneareconsistentwiththoseinTable6.Giventhe signif-icantly differenteventselection criteria, each channelprobes dif-ferentkinematicandtopologicalfeaturesofthesamebackground processes andvariations in the value of the scale factors across channelsaretobeexpected.

Fig.2showspT(V

)

distributionstogetherwithexamplesof dis-tributionsforvariablesindifferentcontrolregionsandfordifferent channels after the scale factors in Table 6 have been applied to

The CMS Collaboration / Physics Letters B 780 (2018) 501–532 507

Fig. 2. Examplesofdistributionsforvariablesinthesimulatedsamplesandindatafordifferentcontrolregionsandfordifferentchannelsafterapplyingthedata/MCscale factorsinTable6.Thetoprowofplotsisfromthe0-leptonZ+HFcontrolregion.Themiddlerowshowsvariablesinthe1-leptontt controlregion.Thebottomrowshows variablesinthe2-leptonZ+HFcontrolregion.TheplotsontheleftarealwayspT(V).Plotsontherightshowakeyvariablethatisvalidatedinthatcontrolregion.These

variablesare,fromtoptobottom,theazimuthalanglebetweenthetwojetsthatcomprisetheHiggsboson,thereconstructedtopquarkmass,andtheratioofpT(V)and

Table 6

Data/MCscalefactorsforeachofthemainbackgroundprocessesineachchannel,asobtainedfromthecombinedsignal-extraction fittocontrolandsignalregiondistributionsdescribedinSection7.Electronandmuonsamplesinthe1- and2-leptonchannelsare fitsimultaneouslytodetermineaveragescalefactors.ThesamescalefactorsforW+jetsprocessesareusedforthe0- and1-lepton channels.

Process 0-lepton 1-lepton 2-lepton low-pT(V) 2-lepton high-pT(V)

W0b 1.14±0.07 1.14±0.07 — — W1b 1.66±0.12 1.66±0.12 — — W2b 1.49±0.12 1.49±0.12 — — Z0b 1.03±0.07 — 1.01±0.06 1.02±0.06 Z1b 1.28±0.17 — 0.98±0.06 1.02±0.11 Z2b 1.61±0.10 — 1.09±0.07 1.28±0.09 tt 0.78±0.05 0.91±0.03 1.00±0.03 1.04±0.05

the corresponding simulated samples. Fig. 3 shows examples of CMVAminandeventBDTdistributions,alsofordifferentcontrol

re-gionsandfordifferentchannels, wherenotonly thescalefactors areappliedbutalsotheshapesofthedistributionsareallowedto vary accordingto the treatment ofsystematic uncertainties from all nuisances in the signal-extraction fit. TheseBDT distributions are from control regions and do not participate in that fit. The signalregionBDTdistributionsusedinthefitarepresentedin Sec-tion7.

Ininclusivevectorbosonsamples,selectedforthisanalysis,the pT(V

)

spectrumindataisobservedtobesofterthaninsimulated samples,asexpectedfromhigher-orderelectroweakcorrectionsto theproductionprocesses [89].Theeventsinallthreechannelsare re-weighted to account for theelectroweak corrections to pT(V

)

. The correction is negligible for low pT(V

)

but is sizable at high pT(V

)

,reaching10%near400 GeV.

Afterthesecorrections,aresidualdiscrepancyinpT(V

)

between dataandsimulatedsamplesisobservedinsomecontrolregions.In the0-leptonchannel, tt samplesarere-weighted asafunction of thegeneratedtopquark’spTaccordingtotheobserved

discrepan-ciesindataandsimulatedsamplesindifferentialtop quarkcross sectionmeasurements [90].Thisre-weightingresolvesthe discrep-ancyin pT(V

)

intt controlregions. Inthe1-leptonchannel, addi-tionalcorrectionsareneededforW

+

jetssamples,andcorrections arederivedfromthedatain1-leptoncontrolregionsforthese pro-cesses:tt,W

+

udscg,andthesumofW

+

b,W

+

bb,andsingletop quark backgrounds. A re-weighting of simulated eventsin pT(V

)

isderived for each,such that the shapeof thesumof simulated processesmatchesthedata.Thecorrectionfunctionsareextracted through a simultaneous fit oflinear functions in pT(V

)

. The un-certaintiesinthefitparametersare usedtoassessthesystematic uncertainty. The pT(V

)

spectra resulting fromre-weighting in ei-therthetopquark pTorpT(V

)

areequivalent.

TheV

+

jetsLOsimulatedsamplesareusedintheanalysis be-cause, due to computingresource limitations,considerably more eventsareavailable thanfortheNLO samples.AnormalizationK factorisappliedtotheLOsamplestoaccountforthedifferencein cross sections. Kinematic distributions between the two samples are found to be consistent after matching the LO distribution of thepseudorapidityseparation

η

(

jj

)

betweenthetwoH

→

bb jet candidates to the NLO one. Different correctionsare derived de-pending onwhether thesetwo jetsare matched to zero,one, or two b quarks. Both the

η

(

jj

)

distributions of the NLO samples andthecorrectedLOsamplesagreewell withdataincontrol re-gions.

6. Systematicuncertainties

Systematic effects affect the H

→

bb mass resolution, the shapesoftheCMVAmindistributions,theshapesoftheeventBDT

distributions, and the signal and background yields in the most

sensitiveregionoftheBDTdistributions.Theuncertainties associ-atedwiththenormalizationscalefactorsofthesimulatedsamples forthemainbackgroundprocesseshavethelargestimpactonthe uncertaintyinthefittedsignalstrength

μ

.Thenextlargesteffects result from the size of the simulated samples and from uncer-tainties incorrectingmismodeling ofkinematicvariables,both in signal and in background simulated samples. The next group of significantsystematicuncertaintiesarerelatedtob tagging uncer-taintiesanduncertaintiesinjetenergy.Allsystematicuncertainties considered are listedin Table7 andaredescribed inmore detail below,inthesameorderastheyappearinthetable.

The sizes of simulated samples are sometimes limited. If the statisticaluncertaintyinthecontentofcertainbinsintheBDT dis-tributions forthesimulatedsamplesis large,Poissoniannuisance parameters areusedinthesignal extractionbinned-likelihood fit. ThesearerequiredmainlyintheV

+

jetssamplesandarealeading sourceofsystematicuncertaintyintheanalysis.

ThecorrectionstothepT(V

)

spectrainthett andW

+

jets sam-plesareappliedpersampleaccordingtotheuncertaintyinthe si-multaneous pT(V

)

fitdescribedinSection 5.2.Thisuncertaintyon thecorrectionisatmost5%onthebackgroundyieldnearpT(V

)

of 400 GeV.TheshapedifferenceintheeventBDTandCMVAmin

dis-tributions betweensimulations oftwo event generators are used toaccount forimperfectmodelinginthenominalsimulated sam-ples.FortheV

+

jets,thedifferencebetweentheshapesforevents generatedwiththe MadGraph5_amc@nlo MCgeneratoratLOand NLO is considered as a shape systematic uncertainty. For the tt process,thedifferencesintheshapesbetweenthenominalsample generatedwith powheg and thatobtainedfromthe mc@nlo [91] generatorare consideredasshapesystematicuncertainties. Varia-tions ontheQCD factorizationandrenormalizationscales andon the PDFchoice are consideredforthesimulated signaland back-ground samples. The scales are varied by factors of 0.5 and2.0, independently, whilethe PDF uncertaintyeffecton theshapesof theBDT distributionsisevaluatedby usingthePDF replicas asso-ciatedtotheNNPDFset [65].

The b taggingefficiencies andtheprobability totagasab jet a jet originatingfroma differentflavor (mistag)are measured in heavy-flavorenhancedsamplesofjetsthatcontainmuonsandare applied consistently to jetsin signal andbackgroundevents. The measured uncertainties for the b tagging scale factors are: 1.5% per b-quark tag,5% per charm-quark tag,and10%per mistagged jet(originatingfromgluonsandlightu,d,ors quarks) [79].These uncertainties are propagated tothe CMVAmin distributions by

re-weighting events.Theshape oftheeventBDTdistribution isalso affectedbytheshapeoftheCMVAdistributionsbecauseCMVAmin

is an input to the BDT discriminant. For the 2-lepton channel CMVAmaxisalsoaninputtothisdiscriminant.Thesignalstrength

uncertaintyincreasesby8%and5%, respectively,duetob tagging efficiencyandmistagscalefactoruncertaintiespropagatedthrough theCMVAdistributionsandfinallytotheeventBDTdistributions.

The CMS Collaboration / Physics Letters B 780 (2018) 501–532 509

Fig. 3. Distributionsincontrolregionsaftersimulatedsamplesarefittothedatainthesignalextractionfit.OntheleftareexamplesofCMVAmindistributions,whileonthe

rightarecorrespondingeventBDTdistributionsofthesamecontrolregionsastheplotsontheleft.NotethattheseBDTdistributionsarenotpartofthefitandareprimarily forvalidation.Thecontrolregionsshownfromtoptobottomare:tt forthe0-leptonchannel,low-massHFforthesingle-muonchannel,andHFforthedielectronchannel.

Table 7

Effectofeachsourceofsystematicuncertaintyintheexpectedsignalstrengthμ.Thethirdcolumnshowstheuncertaintyinμ

fromeachsourcewhenonlythatparticularsourceisconsidered.Thelastcolumnshowsthepercentagedecreaseintheuncertainty whenremovingthatspecificsourceofuncertaintywhileapplyingallothersystematicuncertainties.Duetocorrelations,thetotal systematicuncertaintyislargerthanthesuminquadratureoftheindividualuncertainties.Thesecondcolumnshowswhetherthe sourceaffectsonlythenormalizationorboththeshapeandnormalizationoftheeventBDToutputdistribution.Seetextfordetails.

Source Type Individualcontributionto theμuncertainty(%)

Effectofremovaltotheμ

uncertainty(%) Scale factors (tt, V+jets) norm. 9.4 3.5

Size of simulated samples shape 8.1 3.1 Simulated samples’ modeling shape 4.1 2.9

b tagging efficiency shape 7.9 1.8

Jet energy scale shape 4.2 1.8

Signal cross sections norm. 5.3 1.1 Cross section uncertainties (single-top, VV) norm. 4.7 1.1 Jet energy resolution shape 5.6 0.9 b tagging mistag rate shape 4.6 0.9 Integrated luminosity norm. 2.2 0.9

Unclustered energy shape 1.3 0.2

Lepton efficiency and trigger norm. 1.9 0.1

The uncertainties in the jet energyscale andresolution have an effect on the shape of the eventBDT output distribution be-cause the dijet invariant mass is a crucial input variable to the BDTdiscriminant.Theimpactofthejetenergyscaleuncertaintyis determinedbyrecomputingtheBDToutputdistributionafter shift-ingtheenergyscaleupanddownbyitsuncertainty.Similarly,the impactofthejetenergyresolutionisdeterminedby recomputing theBDT output distributionafterincreasing ordecreasing thejet energyresolution.Theuncertaintiesinjetenergyscaleand resolu-tionaffectnotonlythejetsintheeventbutalsothepmiss

T ,which

is recalculated when these variations are applied. The individual contributiontotheincreaseinsignalstrengthuncertaintyisfound to be around 6% for the jet energy scale and4% for the jet en-ergyresolutionuncertainty.Theuncertaintyinthejetenergyscale andresolution varyas functionsofjet pT and

η

. Forthe jet

en-ergyscalethereareseveralsourcesofuncertaintythatarederived andappliedindependentlyasthey arefullyuncorrelatedbetween themselves [92],whileforthejetenergyresolutionasingleshape systematicisevaluated.

The total VH signal cross section has been calculated to NNLO

+

NNLL accuracy in QCD, combined with NLO electroweak corrections, and the associated systematic uncertainties [63] in-clude the effect of scale variations and PDF uncertainties. The estimateduncertaintiesintheNLOelectroweakcorrectionsare7% fortheWH and 5%fortheZH productionprocesses,respectively. The estimate for the NNLO QCD correction results in an uncer-tainty of1% fortheWH and 4%forthe ZH productionprocesses, whichincludestheggZHcontribution.

Anuncertaintyof15%isassignedtotheeventyields obtained fromsimulatedsamplesforbothsingletopquarkanddiboson pro-duction.Theseuncertaintiesare about25%largerthanthosefrom theCMSmeasurementsoftheseprocesses [93–95],toaccountfor thedifferent kinematicregime inwhich thosemeasurements are performed.

Anothersourceofuncertaintythataffectsthepmiss

T

reconstruc-tionistheestimateoftheenergythatisnotclusteredinjets [77]. Thisaffectsonlythe0- and1-leptonchannels, withan individual contributiontothesignalstrengthuncertaintyof1.3%.

Muonandelectrontrigger,reconstruction,andidentification ef-ficienciesinsimulatedsamplesarecorrectedfordifferencesindata and simulation using samples ofleptonic Z boson decays. These corrections are affected by uncertainties coming from the effi-ciencymeasurementmethod,theleptonselection,andthelimited size ofthe Z boson samples.Theyare measured andpropagated as functions of lepton pT and

η

. The parameters describing the

turn-on curve that parametrizes the Z

(

νν

)

H trigger efficiency as

afunctionof pmiss_T arevariedwithintheirstatisticaluncertainties, andare alsoestimatedfor differentassumptions onthe methods used toderive theefficiency.The totalindividual impactofthese uncertaintiesonleptonidentificationandtriggerefficienciesonthe measuredsignalstrengthisabout2%.

TheuncertaintyintheCMSintegratedluminositymeasurement is estimated to be 2.5% [96]. Events in simulated samples must be re-weighted such that the distribution ofpileup in the simu-latedsamplesmatchesthatestimatedindata.A5%uncertaintyon pileupre-weightingisassigned,buttheimpactofthisuncertainty isnegligible.

Thecombinedeffectofthesystematicuncertaintiesresultsina 25%reductionoftheexpectedsignificancefortheSMHiggsboson rate.

7. Results

Results are obtained from combined signal and background binned-likelihood fits,simultaneouslyforallchannels, toboththe shapeoftheoutputdistributionoftheeventBDTdiscriminantsin the signal region and to the CMVAmin distributions for the

con-trolregions correspondingtoeachchannel.TheBDTdiscriminants aretrainedseparatelyforeachchanneltosearchforaHiggsboson with a mass of 125 GeV. To remove the background-dominated portion of the BDT output distribution, only events with a BDT outputvalue abovethresholdslistedinTable1areconsidered.To achieve a better sensitivity in the search, this threshold is opti-mizedseparatelyforeachchannel.Inthissignal-extractionfit,the shapeandnormalizationofalldistributionsforsignalandforeach backgroundcomponentareallowed tovarywithinthesystematic and statistical uncertainties described in Section 6. These uncer-taintiesaretreatedasindependentnuisanceparametersinthefit. Nuisanceparameters,thesignalstrength,andthescalefactors de-scribedinSection 5.2areallowedto floatfreely andare adjusted bythefit.

In total, seven eventBDT output distributions are included in the fit: one for the 0-lepton channel, one for each lepton flavor for the1-lepton channels, andtwo foreach lepton flavor forthe 2-lepton channels (correspondingto the two pT(V

)

regions). The number of CMVAmin distributions included is 24, corresponding

to thecontrolregions listed inTables3–5: threeforthe0-lepton channel,fourforeachleptonflavorforthe1-leptonchannels,and six for each lepton flavor for the 2-lepton channels (each corre-sponding to one of two pT(V

)

regions). Fig. 4 shows the seven BDT distributions after they havebeen adjusted bythe fit.Fig. 5 combinestheBDT outputvaluesofallchannelswheretheevents

The CMS Collaboration / Physics Letters B 780 (2018) 501–532 511

Fig. 4. Post-fiteventBDToutputdistributionsforthe13 TeV data(pointswitherrorbars),forthe0-leptonchannel(top),forthe1-leptonchannels(middle),andforthe 2-leptonlow-pT(V)andhigh-pT(V)regions(bottom).Thebottominsetshowstheratioofthenumberofeventsobservedindatatothatofthepredictionfromsimulated

samplesfortheSMHiggsbosonsignalandforbackgrounds.

aregathered inbins ofsimilar expectedsignal-to-background ra-tio,asgivenbythevalueoftheoutputoftheircorrespondingBDT discriminant.The observed excessof eventsinthe bins withthe largest signal-to-background ratio is consistent with what is ex-pectedfromtheproductionoftheSMHiggsboson.Todetailthis excess,thetotalnumbersofeventsforallbackgrounds,fortheSM Higgs boson signal, andfor data are shown in Table 8 for each channel, for the rightmost 20% region of the BDT output distri-bution, where the sensitivity is large. The simulation yields are adjustedusingtheresultsoffit.

Thesignificanceoftheobservedexcess ofeventsin thesignal extraction fit is computed using the standard LHC profile

likeli-hood asymptotic approximation [97–100]. For mH

=

125

.

09 GeV,

it corresponds to a local significance of 3.3 standard deviations away fromthe background-onlyhypothesis.Thisexcessis consis-tentwiththeSMpredictionforHiggsbosonproductionwithsignal strength

μ

=

1

.

19+₋0_0..₂₀21(stat)+₋0₀._.34₃₂(syst). The expected significance is2.8standarddeviationswith

μ

=

1

.

0.Togetherwiththisresult, Table 9alsolists theexpectedandobserved significancesforthe 0-leptonchannel,forthe1-leptonchannelscombined,andforthe 2-leptonchannelscombined.

Theobserved signalstrength

μ

isshowninthelower portion of Fig. 6 for 0-, 1- and 2-lepton channels. The observed signal strengths ofthethreechannelsareconsistent withthecombined

Table 8

Thetotalnumbersofeventsineachchannel,fortherightmost20%regionoftheeventBDT outputdistribution,areshownforallbackgroundprocesses,fortheSMHiggsbosonVHsignal, andfordata.Theyieldsfromsimulatedsamplesarecomputedwithadjustmentstotheshapes andnormalizationsoftheBDTdistributionsgivenbythesignalextractionfit.The signal-to-backgroundratio(S/B)isalsoshown.

Process 0-lepton 1-lepton 2-lepton low-pT(V) 2-lepton high-pT(V)

Vbb 216.8 102.5 617.5 113.9

Vb 31.8 20.0 141.1 17.2

V+udscg 10.2 9.8 58.4 4.1

tt 34.7 98.0 157.7 3.2

Single top quark 11.8 44.6 2.3 0.0 VV(udscg) 0.5 1.5 6.6 0.5 VZ(bb) 9.9 6.9 22.9 3.8 Total background 315.7 283.3 1006.5 142.7 VH 38.3 33.5 33.7 22.1 Data 334 320 1030 179 S/B 0.12 0.12 0.033 0.15

Fig. 5. CombinationofallchannelsintoasingleeventBDTdistribution.Eventsare sortedinbinsofsimilarexpectedsignal-to-backgroundratio,asgivenbythevalue oftheoutputoftheircorrespondingBDTdiscriminant(trainedwithaHiggsboson masshypothesisof125 GeV).Thebottomplotsshowtheratioofthedatatothe background-onlyprediction.

Table 9

TheexpectedandobservedsignificancesforVHproductionwithH→bb areshown, formH=125.09GeV,foreachchannelfitindividuallyaswellasforthe

combina-tionofallthreechannels.

Channels Significance expected Significance observed 0-lepton 1.5 0.0 1-lepton 1.5 3.2 2-lepton 1.8 3.1 Combined 2.8 3.3

bestfitsignal strengthwithaprobabilityof5%.Intheupper por-tion of Fig. 6 the signal strengths for the separate WH and ZH production processes are shown. The two production modes are consistent withthe SM expectationswithin uncertainties.The fit for the WH and ZH production modesis not fully correlated to theanalysischannelsbecausetheanalysischannelscontainmixed processes.The WH processcontributes approximately15% ofthe Higgsbosonsignaleventyields inthe0-leptonchannel,resulting

Fig. 6. Thebestfitvalueofthesignalstrengthμ,atmH=125.09GeV,isshown

inblackwithagreenuncertaintyband.Alsoshownaretheresultsofaseparatefit whereeachchannelisassignedanindependentsignalstrengthparameter.Above thedashedlinearetheWH andZH signalstrengthsderivedfromafitwhereeach productionmodeisassignedanindependentsignalstrengthparameter.

fromeventsinwhichtheleptonisoutsidethedetectoracceptance, andtheZHprocesscontributeslessthan3%tothe1-lepton chan-nelwhenoneoftheleptonsisoutsidethedetectoracceptance.

Fig.7showsadijetinvariantmassdistribution,combinedforall channels,fordataandfortheVHandVZ processes,withallother background processes subtracted. The distribution is constructed fromalleventsthatpopulatethesignalregioneventBDT distribu-tionsshowninFig.4.Thevaluesofthescalefactorsandnuisance parameters fromthe fit used to extract the VH signal are prop-agatedto thisdistribution.Tobetter visualizethe contributionof events fromsignal, all events are weighted by S

/(

S

+

B

)

,where S andBare thenumbersofexpectedsignal andtotalpost-fit back-groundeventsinthebinoftheoutputoftheBDT distributionin which each event is contained. The data are consistent with the productionofastandardmodelHiggsbosondecayingtobb.Inthe Figure, aside from the weights, which favor the VH process, the eventyield fromVZ processesis reducedsignificantlydueto the pT(V

)

and M

(

jj

)

selection requirements forthe VHsignal region,

The CMS Collaboration / Physics Letters B 780 (2018) 501–532 513

Fig. 7. Weighteddijetinvariantmassdistributionforeventsinallchannels com-bined.Shownaredataandthe VHand VZ processeswithallotherbackground processessubtracted.WeightsarederivedfromtheeventBDToutputdistribution asdescribedinthetext.

Table 10

ValidationresultsforVZ productionwithZ→bb.Expectedandobserved signifi-cances,andtheobservedsignalstrengths.Significancevaluesaregiveninnumbers ofstandarddeviations. Channels Significance expected Significance observed Signalstrength observed 0-lepton 3.1 2.0 0.57±0.32 1-lepton 2.6 3.7 1.67±0.47 2-lepton 3.2 4.5 1.33±0.34 Combined 4.9 5.0 1.02±0.22

andfromthetrainingoftheBDTthatfurtherdiscriminatesagainst dibosonprocesses.

7.1.ExtractionofVZ withZ

→

bb

The VZ process with Z

→

bb, having a nearly identical final state asVH with H

→

bb, serves as a validation ofthe method-ology used in the search for the latter process. To extract this dibosonsignal, eventBDT discriminants are trainedusing as sig-nal the simulated samples for this process. All other processes, includingVHproduction(atthepredictedSMrate),aretreatedas background.The only modificationmade is therequirement that thesignalregionM

(

jj

)

beinthe

[

60

,

160

]

GeV range.

Theresultsfromthecombinedfitforallchannelsofthecontrol andsignalregion distributions,asdefinedinSections5.1and5.2, aresummarizedinTable10forthesame

√

s

=

13TeV datausedin theVHsearchdescribedabove. Theobservedexcessofeventsfor thecombinedWZ andZZ processeshasasignificanceof5.0 stan-darddeviationsfromthebackground-onlyeventyieldexpectation. Thecorrespondingsignalstrength,relativetothepredictionofthe MadGraph_{5_amc@nlo generatoratNLOmentionedinSection2,is} measuredtobe

μ

VV

=

1

.

02₋+00..2223.

Fig.8showsthecombinedeventBDToutputdistributionforall channels,withthecontentofeachbin,foreachchannel,weighted bytheexpectedsignal-to-backgroundratio.Theexcessofeventsin data,over background,isshownto be compatiblewiththe yield expectationfromVZ productionwithZ

→

bb.

Fig. 8. CombinationofallchannelsintheVZ search,withZ→bb intoasingle event BDTdistribution. Events aresorted inbins ofsimilarexpected signal-to-backgroundratio,asgivenbythevalueoftheoutputoftheircorrespondingBDT discriminant.Thebottominsetshowstheratioofthedatatothepredicted back-ground,with aredlineoverlayingthe expectedSMcontribution fromVZ with Z→bb.

Table 11

TheexpectedandobservedsignificancesandtheobservedsignalstrengthsforVH productionwithH→bb forRun 1data [18],Run 2(2016)data,andforthe combi-nationofthetwo.Significancevaluesaregiveninnumbersofstandarddeviations.

Data used Significance expected Significance observed Signalstrength observed Run 1 2.5 2.1 0.89+0.44 −0.42 Run 2 2.8 3.3 1.19+₋00..4038 Combined 3.8 3.8 1.06+₋00..3129

7.2. CombinationwithRun 1VH(bb)analysis

Theresultsfromthesearch forVHwithH

→

bb,presentedin thisarticle,arecombinedwiththosefromthesimilarsearches per-formed by the CMS experiment [18,36,38] during Run 1 of the LHC, using proton-proton collisions at

√

s

=

7 and 8 TeV with datasamplescorrespondingtointegratedluminositiesofupto5.1 and 18.9 fb−1, respectively. The combination yields an observed signal significance, at mH

=

125

.

09 GeV, of 3.8 standard

devia-tions,where3.8areexpected.Thecorrespondingsignalstrengthis

μ

=

1

.

06₋+0_0..31₂₉.Allsystematicuncertaintiesareassumedtobe un-correlated inthecombination, exceptforcrosssection uncertain-tiesderivedfromtheory,whichareassumedtobefullycorrelated. Treatingalluncertaintiesasuncorrelatedhasanegligibleeffecton thesignificance.Table11liststheseresults.

8. Summary

A search for the standard model (SM) Higgs boson (H)when producedinassociationwithanelectroweakvectorbosonand de-cayingtoabb pairisreportedfortheZ

(

νν

)

H,W

(

μν

)

H,W

(

e

ν

)

H, Z

(

μμ

)

H, and Z

(

ee

)

H processes. The search is performed in data samplescorrespondingtoanintegratedluminosityof35.9 fb−1 at

√

s

=

13 TeV, recorded by the CMS experiment at the LHC. The observedsignalsignificance,formH

=

125

.

09GeV,is3.3standard

deviations,where theexpectationfrom theSM Higgsboson pro-ductionis2.8.Thecorrespondingsignalstrengthis

μ

=

1

.

2

±

0

.

4.