Observation of the Higgs boson decay to a pair of τ leptons with the CMS detector

Contents lists available atScienceDirect

Physics

Letters

B

www.elsevier.com/locate/physletb

Observation

of

the

Higgs

boson

decay

to

a

pair

of

τ

leptons

with

the

CMS

detector

.

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: Received1August2017

Receivedinrevisedform1February2018 Accepted2February2018

Availableonline7February2018 Editor: M.Doser Keywords: CMS Physics Tau Higgs Observation LHC

A measurement ofthe H_→

τ τ

signal strengthis performedusingevents recorded inproton–proton

collisions by the CMS experiment at the LHC in 2016 at a center-of-mass energy of 13 TeV. The

data set corresponds to an integrated luminosity of 35.9 fb−1. The H→

τ τ

signal is established

with a significance of 4.9 standard deviations, to be compared to an expected significance of 4.7

standarddeviations.ThebestfitoftheproductoftheobservedH→

τ τ

signalproductioncrosssection

and branching fraction is1.09₋+₀0._.27₂₆ times the standard model expectation.The combinationwith the

corresponding measurement performedwith data collectedbythe CMS experimentatcenter-of-mass

energiesof7and8 TeV leadstoanobservedsignificanceof5.9standarddeviations,equaltotheexpected

significance.ThisisthefirstobservationofHiggsbosondecaysto

τ

leptonsbyasingleexperiment.

©2018TheAuthor(s).PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense

(http://creativecommons.org/licenses/by/4.0/).FundedbySCOAP3_.

1. Introduction

In the standard model (SM) of particle physics [1–3], elec-troweak symmetry breaking is achieved via the Brout–Englert– Higgs mechanism [4–9], leading, in its minimal version, to the predictionoftheexistence ofonephysicalneutralscalarparticle, commonlyknown as the Higgs boson (H).A particle compatible withsuch a boson was observed by theATLAS andCMS experi-ments attheCERN LHC inthe ZZ,

γ γ

,and W+W− decay chan-nels [10–12],duringtheproton–proton(pp)datatakingperiodin 2011and2012atcenter-of-massenergiesof

√

s

=

7 and8 TeV, re-spectively.Subsequentresultsfrombothexperiments,describedin Refs. [13–18],establishedthatthemeasuredpropertiesofthenew particle,includingitsspin,CPproperties,andcouplingstrengthsto SMparticles,areconsistentwiththoseexpectedfortheHiggs bo-sonpredicted bythe SM. The massofthe Higgsboson hasbeen determined to be 125

.

09

±

0

.

21 (stat)

±

0

.

11 (syst) GeV, from a combinationofATLASandCMSmeasurements [19].

Toestablishthemassgenerationmechanismforfermions,itis necessarytoprobethedirectcouplingoftheHiggsbosontosuch particles.Themostpromisingdecaychannel is

τ

+

τ

−,becauseof thelarge eventrateexpected inthe SM comparedto the

μ

+

μ

−

decaychannel(

B(

H

→

τ

+

τ

−

)

=

6

.

3% fora massof125

.

09 GeV),

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

andofthe smallercontributionfrombackgroundevents with re-specttothebb decaychannel.

Searches for a Higgs boson decaying to a

τ

lepton pair were performedattheLEP [20–23],Tevatron [24,25],andLHCcolliders. Using pp collisiondataat

√

s

=

7 and 8 TeV,the CMS Collabora-tionshowedevidenceforthisprocesswithanobserved(expected) significanceof3.2(3.7) standarddeviations(s.d.) [26].TheATLAS experimentreportedevidenceforHiggsbosonsdecayingintopairs of

τ

leptonswithanobserved (expected)significanceof4.5(3.4) s.d. foraHiggsboson massof125 GeV [27].The combinationof the results fromboth experiments yields an observed (expected) significanceof5.5(5.0)s.d. [28].

This Letter reports on a measurement of the H

→

τ τ

signal strength.Theanalysistargetsboththegluonfusionandthevector bosonfusionproductionmechanisms.Theanalyzeddataset corre-spondstoanintegratedluminosityof35

.

9 fb−1,andwascollected in2016in pp collisions atacenter-of-massenergyof 13 TeV.In thefollowing,thesymbol



referstoelectronsormuons,the sym-bol

τ

h refers to

τ

leptons reconstructedintheir hadronicdecays,

andH

→

τ

+

τ

− andH

→

W+W− are simplydenoted asH

→

τ τ

andH

→

WW,respectively. All possible

τ τ

final states are stud-ied,exceptforthosewithtwomuonsortwoelectronsbecauseof thelowbranchingfractionandlargebackgroundcontribution.The analysiscoversabout94%ofallpossible

τ τ

finalstates.

https://doi.org/10.1016/j.physletb.2018.02.004

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

2. TheCMSdetector

Thecentralfeature oftheCMSapparatusisasuperconducting solenoid of6 m internal diameter, providing a magnetic field of 3.8 T. Withinthe solenoidvolume, there are a silicon pixel and strip tracker,a lead tungstate crystalelectromagnetic calorimeter (ECAL), and a brass and scintillator hadron calorimeter (HCAL), each composed of a barrel and two endcap sections. Forward calorimetersextend thepseudorapidity coverage providedby the barrelandendcapdetectors.Muonsaredetectedingas-ionization chambers embedded in the steel flux-return yoke outside the solenoid.

Events of interest are selected using a two-tiered trigger sys-tem [29]. Thefirstlevel (L1),composedofcustom hardware pro-cessors, usesinformationfromthe calorimetersandmuon detec-tors to select events ata rateof around 100 kHz within a time intervaloflessthan4 μs.Thesecondlevel,knownasthehigh-level trigger(HLT),consistsofafarmofprocessorsrunningaversionof thefull eventreconstruction softwareoptimized forfast process-ing,andreducestheeventratetoabout1 kHzbeforedatastorage. SignificantupgradesoftheL1triggerduringthefirstlong shut-down of the LHC have benefited this analysis, especially in the

τ

h

τ

hchannel.Theseupgradesimprovedthe

τ

hidentificationatL1

by giving more flexibility to object isolation, allowing new tech-niquestosuppressthecontributionfromadditionalpp interactions perbunchcrossing, andtoreconstructtheL1

τ

h objectina

fidu-cial region that matches more closely that of a true hadronic

τ

decay.Theflexibilityisachievedbyemployinghighbandwidth op-ticallinks fordata communication andlarge field-programmable gatearrays(FPGAs)fordataprocessing.

AmoredetaileddescriptionoftheCMSdetector,togetherwith adefinitionofthecoordinatesystemused andthe relevant kine-maticvariables,canbefoundinRef. [30].

3. Simulatedsamples

Signalandbackgroundprocessesare modeledwithsamplesof simulatedevents.ThesignalsampleswithaHiggsbosonproduced through gluon fusion (ggH), vector boson fusion (VBF), or in as-sociation with a W or Z boson (WH or ZH), are generated at next-to-leading order (NLO) in perturbative quantum chromody-namics(pQCD)withthe powheg 2.0 [31–35] generator.The minlo hvJ[36] extensionof powheg 2.0isusedfortheWH andZH sim-ulatedsamples.The setof partondistributionfunctions(PDFs)is NNPDF30_nlo_as_0118 [37].ThettH processisnegligible.The var-iousproductioncrosssectionsandbranchingfractionsfortheSM Higgsbosonproduction,andtheircorrespondinguncertaintiesare takenfromRefs. [38–40] andreferencestherein.

The MG5_amc@nlo [41] generator is used for Z

+

jets and W

+

jets processes. Theyaresimulatedatleading order(LO)with theMLMjetmatchingandmerging [42].The MG5_amc@nlo gen-erator is also used fordiboson production simulated at next-to-LO(NLO) withthe FxFx jet matchingand merging [43], whereas powheg _{2.0 and 1.0 are used for tt and single top quark} pro-duction, respectively. The generators are interfaced with pythia 8.212 [44] to model the partonshoweringand fragmentation, as wellasthedecayofthe

τ

leptons.The pythia parametersaffecting thedescription oftheunderlying eventare set totheCUETP8M1 tune [45].

Generated events are processed through a simulation of the CMS detectorbased on Geant4 [46], and are reconstructed with thesamealgorithmsusedfordata.Thesimulatedsamplesinclude additionalpp interactionsperbunchcrossing,referredtoas “pile-up”.The effectofpileupistakenintoaccountby generating con-currentminimumbiascollisioneventsgeneratedwith pythia.The

simulated events are weighted such that the distribution of the numberofadditionalpileupinteractions,estimatedfromthe mea-sured instantaneous luminosity foreach bunch crossing, matches thatindata,withanaverageofapproximately27interactionsper bunchcrossing.

4. Eventreconstruction

The reconstructionofobserved andsimulatedeventsrelieson the particle-flow (PF) algorithm [47], which combines the infor-mationfromtheCMSsubdetectorstoidentifyandreconstructthe particles emerging from pp collisions: charged hadrons, neutral hadrons,photons, muons,andelectrons.CombinationsofthesePF objectsareusedtoreconstructhigher-levelobjectssuchasjets,

τ

h

candidates, or missing transverse momentum. The reconstructed vertexwiththelargestvalueofsummedphysics-objectp2_Tistaken to be the primary pp interactionvertex. The physics objects are the objectsconstructedby ajet findingalgorithm [48,49] applied to all charged tracks associated withthe vertex, including tracks fromleptoncandidates,andthecorrespondingassociatedmissing transversemomentum.

Muons are identified withrequirements on thequality of the track reconstruction andon thenumber ofmeasurements in the trackerandthemuonsystems [50].Electronsareidentifiedwitha multivariate discriminant combiningseveral quantities describing thetrackquality,theshapeoftheenergydepositsintheECAL,and the compatibility ofthe measurements from the trackerand the ECAL [51].Torejectnon-promptormisidentifiedleptons,a relative leptonisolationisdefinedas:

I

≡



chargedpT

+

max



0

,



_neutralpT

−

12



charged, PUpT



p T

.

(1)

Inthisexpression,



_chargedpT isthescalarsumofthetransverse

momenta of the charged particles originating from the primary vertex and located in a cone of size



R

=

√

(

η

)

2

+ (φ)

2

=

0

.

4

(

0

.

3

)

centered on the muon (electron) direction. The sum



neutralpT representsa similarquantity forneutralparticles. The

contribution of photons and neutral hadrons originating from pileupverticesisestimatedfromthescalarsumofthetransverse momenta ofchargedhadronsintheconeoriginatingfrompileup vertices,



_{charged, PU}pT.Thissumismultipliedbyafactorof1

/

2,

whichcorrespondsapproximatelytotheratioofneutraltocharged hadronproductioninthehadronizationprocessofinelasticpp col-lisions,asestimatedfromsimulation.Theexpression p_Tstandsfor the pT ofthelepton.Isolationrequirementsusedinthisanalysis,

basedonI_{,arelistedinTable1.}

Jetsarereconstructedwithananti-kT clusteringalgorithm

im-plementedinthe FastJet library [49,52].Itisbasedonthe cluster-ingofneutralandchargedPFcandidateswithinadistance param-eterof0.4.ChargedPFcandidatesnotassociatedwiththeprimary vertexoftheinteractionarenotconsideredwhenbuildingjets.An offsetcorrectionisappliedtojetenergiestotakeintoaccountthe contribution from additional pp interactions within the same or nearbybunchcrossings.Theenergyofajetiscalibratedbasedon simulation anddata throughcorrection factors [53]. In this anal-ysis, jets are required to have pT greater than 30 GeV and

|

η

|

less than 4.7, and are separated from the selected leptons by a



R of at least 0.5. The combined secondary vertex (CSV) algo-rithm isusedtoidentifyjetsthat arelikelytooriginate fromab quark(“b jets”).Thealgorithmexploitsthetrack-basedlifetime in-formationtogetherwiththesecondaryverticesassociatedwiththe jet toprovidealikelihoodratiodiscriminator forthebjet identi-fication. A set of pT-dependent correction factors are applied to

Table 1

Kinematicselectionrequirementsforthefourdi-τ decaychannels.Thetriggerrequirementisdefinedbyacombination oftriggercandidateswithpToveragiventhreshold(inGeV),indicatedinsideparentheses.Thepseudorapiditythresholds comefromtriggerandobjectreconstructionconstraints.ThepTthresholdsfortheleptonselectionaredrivenbythetrigger requirements,exceptfortheleadingτhcandidateintheτhτhchannel,theτhcandidateintheμτhandeτhchannels,and themuonintheeμchannel,wheretheyhavebeenoptimizedtoincreasethesignificanceoftheanalysis.

Channel Trigger requirement Lepton selection

pT(GeV) η Isolation

τhτh τh(35)&τh(35) pTτh>50 & 40 |ητh| <2.1 MVAτhID

μτh μ(22) pμT>23 |ημ| <2.1 Iμ<0.15 pτh T >30 |ητh| <2.3 MVAτhID μ(19)&τh(21) 20<pμT<23 |ημ| <2.1 Iμ<0.15 pτh T >30 |ητh| <2.3 MVAτhID eτh e(25) peT>26 |η e_{| <2} .1 Ie <0.1 pτh T >30 |ητh| <2.3 MVAτhID eμ e(12)&μ(23) pe T>13 |η e_{| <2} .5 Ie <0.15 pμT>24 |ημ| <2.4 Iμ<0.2 e(23)&μ(8) pe T>24 |ηe| <2.5 Ie<0.15 pμ_T>15 |ημ_{| <2.4 I}μ_<0.2

simulatedeventsto account fordifferencesin the btagging effi-ciencybetweendataandsimulation.Theworkingpointchosenin thisanalysisgivesanefficiencyforrealbjetsofabout70%,andfor about1%oflightflavororquarkjetsbeingmisidentified.

Hadronically decaying

τ

leptons are reconstructed with the hadron-plus-strips(HPS) algorithm [54,55], which isseeded with anti-kT jets. The HPS algorithm reconstructs

τ

h candidates on

the basis of the number of tracks and of the number of ECAL strips in the

η

–

φ

plane with energy deposits, in the 1-prong, 1-prong

+

π

0

₍

_s

₎

_{,and3-prongdecaymodes.A multivariate(MVA)}

discriminator [56], includingisolation andlifetimeinformation,is usedto reduce therate forquark- and gluon-initiatedjets to be identifiedas

τ

h candidates. The workingpoint usedin this

anal-ysis has an efficiency of about 60% for genuine

τ

h, with about

1%misidentificationrateforquark- andgluon-initiatedjets, fora pT range typical of

τ

h originatingfrom a Z boson. Electrons and

muonsmisidentifiedas

τ

h candidatesare suppressed using

dedi-catedcriteriabasedontheconsistencybetweenthemeasurements inthe tracker, the calorimeters, andthe muon detectors [54,55]. The workingpoints ofthese discriminatorsdepend on thedecay channelstudied.The

τ

henergyscaleinsimulationiscorrectedper

decaymode,onthebasisofameasurementinZ

→

τ τ

events.The rateandtheenergyscaleofelectronsandmuonsmisidentifiedas

τ

h candidates are also corrected in simulation,on the basis of a

tag-and-probemeasurement [57] inZ

→ 

events.

Allparticles reconstructedin theeventare usedto determine themissing transversemomentum,



pmiss_T . The missingtransverse momentumisdefinedasthenegativevectorialsumofthe trans-verse momenta of all PF candidates [58]. It is adjusted for the effectofjetenergycorrections.Correctionstothep



miss_T areapplied toreducethemismodelingofthesimulatedZ

+

jets,W

+

jets and Higgsbosonsamples.Thecorrectionsareappliedtothesimulated events on the basis of the vectorial difference of the measured missingtransversemomentumandtotaltransversemomentumof neutrinosoriginatingfromthedecayoftheZ,W,orHiggsboson. Their average effect is the reduction of the pmiss

T obtained from

simulationbyafewGeV.

Thevisible mass ofthe

τ τ

system, mvis, can be used to

sep-arate the H

→

τ τ

signal events from the large contribution of irreducible Z

→

τ τ

events. However, the neutrinos from the

τ

leptondecayscarryalargefractionofthe

τ

leptonenergyand re-ducethediscriminatingpowerofthisvariable.The svfit algorithm combinesthe



pmiss_T withthe four-vectorsofboth

τ

candidatesto calculateamoreaccurate estimate ofthemass oftheparent

bo-son,denotedasmττ .Theresolutionofmττ isbetween15and20% depending onthe

τ τ

final state.A detaileddescription ofthe al-gorithm canbe found inRef. [59].Both variablesare usedin the analysis, asdetailedin Section 6,andmvis ispreferred overmττ

whenthebackgroundfromZ

→ 

eventsislarge. 5. Eventselection

Selected events are classified into the various decay channels according to the number of selected electrons, muons, and

τ

h

candidates.Theresultingeventsamplesaremademutually exclu-sive by discarding events that have additional loosely identified and isolated muons or electrons. Leptons must meet the mini-mum requirement that the distance of closest approach to the primary vertex satisfies

|

dz

|

<

0

.

2 cm along the beam direction,

and

|

dxy

|

<

0

.

045 cm inthetransverseplane.Thetwoleptons

as-signedtotheHiggsbosondecayarerequiredtohaveopposite-sign electric charges. In the

μτ

h channel, events are selected witha

combination of online criteria that require at least one isolated muontriggercandidate,oratleastoneisolatedmuonandone

τ

h

trigger candidate, depending on the offline muon pT. In the e

τ

h

channel,the triggersystemrequiresatleastoneisolatedelectron object,whereas inthe e

μ

channel, thetriggers relyon the pres-ence of both an electron anda muon, allowing lower online pT

thresholds.Inthe

τ

h

τ

hchannel,thetriggerselectseventswithtwo

looselyisolated

τ

h objects.The selection criteriaare summarized

inTable1.

Inthe



τ

h channels,the largeW

+

jets backgroundisreduced

byrequiringthetransversemass,mT,tosatisfy

mT

≡



2p_Tpmiss_T

[

1

−

cos

(φ)

] <

50 GeV

,

(2)

where p

Tisthetransversemomentumofthelepton



,and

φ

is

theazimuthalanglebetweenitsdirectionandthe



pmiss T .

In the e

μ

channel, the tt background is reduced by requir-ing pζ

−

0

.

85pζvis

>

−

35 or

−

10 GeV dependingonthecategory,

where pζ isthecomponentofthe



pmissT alongthebisectorofthe

transversemomentaofthetwoleptonsandpvis

ζ isthesumofthe

componentsoftheleptontransversemomentaalongthesame di-rection [60]. This selection criterion has a high signal efficiency becausethe



pmiss

T istypicallyorientedinthesamedirectionasthe

visibledi-

τ

systeminsignal events.In addition,eventswitha b-taggedjet are discardedto furthersuppressthett background in thee

μ

channel.

Table 2

Categoryselectionandobservablesusedtobuildthe2Dkinematicdistributions.Theeventsneitherselectedinthe0-jet norintheVBFcategoryareincludedintheboostedcategory,asdenotedby“Others”.

0-jet VBF Boosted

Selection

τhτh No jet ≥2 jets, pτ τT >100 GeV,ηjj>2.5 Others μτh No jet ≥2 jets, mjj>300 GeV, pτ τT >50 GeV, p

τh

T >40 GeV Others eτh No jet ≥2 jets, mjj>300 GeV, pτ τT >50 GeV Others

eμ No jet 2 jets, mjj>300 GeV Others

Observables

τhτh mτ τ mjj, mτ τ pτ τT , mτ τ

μτh τhdecay mode, mvis mjj, mτ τ pτ τT , mτ τ eτh τhdecay mode, mvis mjj, mτ τ pτ τT , mτ τ

eμ pμT, mvis mjj, mτ τ pτ τT , mτ τ

6. Categorization

The event sample is split into three mutually exclusive cat-egories per decay channel. In each category the two variables that maximize the H

→

τ τ

sensitivity are chosen to build two-dimensional(2D)distributions.

Thethreecategoriesaredefinedas:

•

0-jet: Thiscategory targets Higgs bosonevents produced via gluon fusion.The two variables chosen to extract the results are mvis andthe reconstructed

τ

h candidatedecay mode (in

the

μτ

h and e

τ

h decay channels) or the pT of the muon

(in the e

μ

channel). The Z

→ 

background is large in the 1-prongand1-prong

+

π

0

₍

_s

₎

_τ

hdecaymodesinthe

μτ

hand

e

τ

h channels. The mvis variable is used as a final

discrimi-nantinthe fitinsteadofmττ becauseit separatesthesignal fromtheZ

→ 

background,whichpeaksaroundtheZ boson mass.The reconstructed

τ

h candidatedecaymode isused as

theotherdiscriminantinthe

μτ

hande

τ

hdecaychannels

be-causetheZ

→ 

backgroundisnegligiblefor

τ

hreconstructed

inthe3-prongdecaymode,leading toan increased signal-to-backgroundratio for thisparticular decaymode, and several systematicuncertainties relatedtothe

τ

h decaymodecanbe

constrainedwithmoreprecision.The 2Ddistributions forthe signalandZ

→ 

backgroundinthe0-jetcategoryofthe

μτ

h

decay channel are shown in Fig. 1 (top). In the

τ

h

τ

h decay

channel, only one observable, mττ , is considered because of thelow eventyields duetotherelatively high pT thresholds

on the

τ

h attrigger level,and becauseof thesharply falling

τ

h pT distribution.Simulationsindicatethatabout98%of

sig-naleventsinthe0-jetcategorycorrespondtothegluonfusion productionmechanism.

•

VBF: This category targets Higgs boson events produced via VBF. Events are selected with atleast two (exactly two) jets with pT

>

30 GeV in the

τ

h

τ

h,

μτ

h, and e

τ

h (e

μ

) channels.

Inthe

μτ

h,e

τ

h,ande

μ

channels,thetwoleading jetsare

re-quired to have an invariant mass, mjj, larger than 300 GeV.

The variable pτ τ_T , defined as the magnitude of the vectorial sum of the



pT of the visible decay products of the

τ

lep-tonsand



pmiss_T , is required to be greater than 50

(

100

)

GeV inthe

μτ

hande

τ

h(

τ

h

τ

h)channelstoreducethecontribution

fromW

+

jets backgrounds. Thisselection criterionalso sup-presses the background from SM events composed uniquely ofjetsproducedthroughthestronginteraction,referredtoas quantumchromodynamics (QCD)multijetevents.Inaddition, the pT threshold onthe

τ

h candidateis raised to 40 GeV in

the

μτ

hchannel,andthetwoleadingjetsinthe

τ

h

τ

hchannel

shouldbe separatedin pseudorapidityby



η

>

2

.

5. Thetwo observablesintheVBFcategoryaremττ andmjj.The2D

dis-tributions forthe signal and Z

→

τ τ

background inthe VBF

category ofthe

μτ

h decaychannel areshownin Fig.1

(cen-ter).Integratingoverthewholemjj phasespace,upto57%of

thesignaleventsintheVBFcategoryareproducedintheVBF productionmode,butthisproportionincreaseswithmjj.

•

Boosted:Thiscategorycontainsalltheeventsthat donot

en-teroneofthepreviouscategories,namelyeventswithonejet andeventswithseveraljetsthatfailthespecificrequirements oftheVBFcategory. Itcontainsgluon fusioneventsproduced inassociationwithoneormorejets(78–80%ofsignalevents), VBFeventswhereoneofthejetshasescapeddetectionorhas low mjj (11–13%),aswell asHiggsbosons produced in

asso-ciationwitha W or a Z boson decayinghadronically (4–8%). While mττ is chosen asone ofthe dimensionsofthe distri-butions, pτ τ_T istakenasthe second dimensionto specifically target Higgs boson events produced in gluon fusion, with a Lorentz-boostedbosonrecoilingagainstjets.Mostbackground processes, including W

+

jets and QCD multijet events, typi-cally have low pτ τ_T . The 2D distributions for the signal and W

+

jets backgroundintheboostedcategoryofthe

μτ

hdecay

channelareshowninFig.1(bottom).

Thecategoriesandthevariablesusedtobuildthe2D distribu-tions are summarized in Table 2. The results of the analysis are extracted witha globalmaximumlikelihood fitbased on the2D distributionsinthevarioussignalregions,andonsomecontrol re-gions, detailedin Section 7, that constrain the normalizations of themainbackgrounds.

7. Backgroundestimation

The largest irreducible source of background is the Drell–Yan production of Z

/

γ

∗

→

τ τ

,



. In order to correct the yield and distributions of the Z

/

γ

∗

→

τ τ

,



simulations to better repro-duce theDrell–Yanprocessindata,a dedicatedcontrol sampleof Z

/

γ

∗

→

μμ

eventsiscollectedindatawithasingle-muontrigger, and compared to simulation.The control sample is composed of eventswithtwo well-identifiedandwell-isolatedopposite-charge muons with pT greater than 25 GeV and an invariant mass

be-tween 70 and110 GeV. More than 99% ofevents in this region comefromZ

/

γ

∗

→

μμ

decays.Differencesinthedistributionsof m/τ τ and pT(/

τ τ

)

indataandinsimulationsare observedin this control region,and 2D weights basedon these variablesare derivedandappliedtosimulatedZ

/

γ

∗

→

τ τ

,



eventsinthe sig-nal region of the analysis. In addition, corrections depending on mjj are derived fromthe Z

/

γ

∗

→

μμ

region and applied to the

Z

/

γ

∗

→

τ τ

,



simulationforevents withatleasttwo jets pass-ingtheVBFcategoryselectioncriteria.Afterthisreweighting,good agreement betweendata in the Z

/

γ

∗

→

μμ

region and simula-tionisfoundforallother variables.Thesimulatedsampleissplit, onthebasisofthematchingbetweenobjectsatthegeneratorand

Fig. 1. Distributionsforthesignal(left)andforsomedominantbackgroundprocesses(right)ofthetwoobservableschoseninthe0-jet(top),VBF(center),andboosted (bottom)categoriesintheμτhdecaychannel.Thebackgroundprocessesarechosenforillustrativepurposefortheirseparationfromthesignal.TheZ→μμbackgroundin the0-jetcategoryisconcentratedintheregionswherethevisiblemassiscloseto90 GeV andisnegligiblewhentheτhcandidateisreconstructedinthe3-prongdecay mode.TheZ→τ τ backgroundintheVBFcategorymostlyliesatlowmjj valueswhereasthedistributionofVBFsignaleventsextendstohighmjj values.Intheboosted category,theW+jetsbackground,whichbehavessimilarlytotheQCDmultijetbackground,isratherflatwithrespecttomτ τ,andisconcentratedatlowpτ τT values.These distributionsarenotusedassuchtoextracttheresults.

Fig. 2. ControlregionsenrichedintheW+jets backgroundusedinthemaximumlikelihoodfit,togetherwiththesignalregions,toextracttheresults.Thenormalizationof thepredictedbackgrounddistributionscorrespondstotheresultoftheglobalfit.Theseregions,definedwithmT>80 GeV,controltheyieldsoftheW+jets backgroundin theμτhandeτhchannels.TheconstraintsobtainedintheboostedcategoriesarepropagatedtotheVBFcategoriesofthecorrespondingchannels.

atthedetectorlevels,intoeventswithpromptleptons (muonsor electrons),hadronicdecays ofthe

τ

leptons, andjetsor misiden-tifiedobjectsatthedetectorlevelthatdonothavecorresponding objectsat generatorlevel within



R

<

0

.

2. The electroweak pro-ductionofZ bosonsinassociationwithtwojetsisalsotakeninto accountintheanalysis;itcontributesupto8%oftheZ boson pro-ductionintheVBFcategory.

The background fromW

+

jets production contributes signifi-cantlytothe

μτ

hande

τ

hchannels,whentheW bosondecays

lep-tonicallyandajetismisidentifiedasa

τ

h candidate.TheW

+

jets

distributionsare modeled using simulation,whiletheiryields are estimatedusing data, asdetailed below.In the boosted andVBF categories,statisticalfluctuationsinthedistributionsfrom simula-tionsarereducedby relaxingtheisolation ofthe

τ

h and



candi-dates, whichhas beenchecked not to biasthe distributions. The simulatedsample isnormalizedinsuchawayastoobtain agree-mentbetweentheyieldsindataandthepredictedbackgroundsin acontrolregionenrichedintheW

+

jets background,whichis ob-tainedbyapplyingallselectioncriteria,withtheexceptionthatmT

isrequiredtobegreaterthan80 GeV insteadoflessthan50 GeV. TheW

+

jets eventpurityinthisregionvariesfromabout50%in the boosted category to 85% in the 0-jet category. The high-mT

sidebands described above, for each category, are considered as controlregionsinthisfit.Theconstraintsobtainedintheboosted categoryareextrapolatedtotheVBFcategoryofthecorresponding decaychannelbecausethetopologyoftheboostedandVBFevents issimilar, andfew dataeventswouldpass thehigh-mT sideband

selectionintheVBFcategory.Fig.2showsthecontrolregionswith mT

>

80 GeV in the0-jet andboostedcategoriesofthe

μτ

h and

e

τ

h channels.Thesecontrolregionsarecomposedofonlyonebin

becausetheyareusedsolelytoconstrainthenormalizationofthe W

+

jets process.Inthee

μ

and

τ

h

τ

hdecaychannels,theW

+

jets

backgroundissmallcomparedtootherbackgrounds,andits con-tributionisestimatedfromsimulations.

The QCD multijet events constitute another important source of reducible background in the



τ

h channels, and it is entirely

estimated from data. Various control samples are constituted to estimatethe shapeandtheyieldoftheQCDmultijetbackground inthesechannels,asexplainedbelow:

1. Therawyieldisextractedusingasamplewherethe



andthe

τ

hcandidateshavethesamesign.Usingthissample,theQCD

multijetprocessisestimatedfromdatabysubtractingthe con-tributionoftheDrell–Yan,tt,diboson,andW

+

jets processes. 2. The yield obtained above is corrected to account for differ-encesbetweenthebackgroundcomposition in thesame-sign and opposite-sign regions. The extrapolation factor between the same-sign and opposite-sign regions is determined by

comparingtheyieldoftheQCDmultijetbackgroundforevents with



candidates passing inverted isolation criteria, in the same-sign and opposite-sign regions. It is constrained and measured byaddingtotheglobalfittheopposite-signregion where the



candidates pass invertedisolation criteria, using theQCDmultijetbackgroundestimatefromthesame-sign re-gion with



candidates passinginverted isolation criteria.For the samereasonsasin thecaseofthe W

+

jets background, theconstraintsarealsoextrapolatedtotheVBF signalregion. Fig. 3 showsthese control regions for the 0-jet andboosted categoriesofthe

μτ

hande

τ

hchannels;theobservableismvis

or mττ to provide discrimination between the QCD multijet andtheZ

→

τ τ

processes.

3. The2D distributionsoftheQCDmultijetbackgroundare esti-mated froma regionwithsame-signleptons, asforthe yield estimate, but theisolation ofthe



and

τ

h candidates is

ad-ditionally relaxed to reduce the statisticalfluctuationsin the distributions.AgainthecontributionoftheDrell–Yan,tt, dibo-son,andW

+

jets processesaresubtractedfromdatatoextract theQCDmultijetcontributioninthisregion.

Thesametechniqueisusedinthee

μ

decaychannel,butno con-trolregionisincludedinthefitbecauseQCDmultijetevents con-tributelittletothetotalbackgroundinthisdecaychannel.

Inthe

τ

h

τ

hchannel,thelargeQCDmultijetbackgroundis

esti-mated witha slightlydifferentmethod,froma samplecomposed of events withopposite-sign

τ

h satisfying a relaxedisolation

re-quirement, disjointfromthesignalregion.Inthisregion,theQCD multijet backgroundshape and yield are obtainedby subtracting thecontributionoftheDrell–Yan, tt,andW

+

jets processes, esti-mated asexplainedabove, fromthe data.The QCDmultijet back-ground yield in the signal region is obtainedby multiplying the yield previously obtainedin the control region by an extrapola-tionfactor.Theextrapolationfactorismeasuredineventspassing identicalselectioncriteriaasthoseinthesignalregion,andinthe relaxedisolationregion,exceptthatthe

τ

hcandidatesarerequired

to havethesamesign. The eventsselectedwithopposite-sign

τ

h

candidatespassingrelaxedisolationrequirementsformcontrol re-gions,showninFig.4,andareusedinthefittoextracttheresults. The tt productionprocess is one of the main backgrounds in the e

μ

channel. The 2D distributions in all decay channels are predictedbysimulation.Thenormalizationisadjustedtotheone observed inatt-enriched sample orthogonal tothesignal region. Thiscontrolregion,showninFig.5,isaddedtotheglobalfitto ex-tracttheresults,andisdefinedsimilarlyasthe e

μ

signal region, exceptthat the pζ requirementisinvertedandtheeventsshould

Fig. 3. ControlregionsenrichedintheQCDmultijetbackgroundusedinthemaximumlikelihoodfit,togetherwiththesignalregions,toextracttheresults.Thenormalization ofthepredictedbackgrounddistributionscorrespondstotheresultoftheglobalfit.Theseregions,definedbyselectingeventswithopposite-signandτhcandidateswith

passinginvertedisolationconditions,controltheyieldsoftheQCDmultijetbackgroundintheμτh andeτhchannels.Theconstraintsobtainedintheboostedcategories arepropagatedtotheVBFcategoriesofthecorrespondingchannels.

Fig. 4. ControlregionsenrichedintheQCDmultijetbackgroundusedinthemaximumlikelihoodfit,togetherwiththesignalregions,toextracttheresults.Thenormalization ofthepredictedbackgrounddistributionscorrespondstotheresultoftheglobalfit.Theseregions,formedbyselectingeventswithopposite-signτh candidatespassing relaxedisolationrequirements,controltheyieldsoftheQCDmultijetbackgroundintheτhτhchannel.

Fig. 5. Controlregionenrichedinthett background,usedinthemaximum likeli-hoodfit,togetherwiththesignalregions,toextracttheresults.Thenormalization ofthepredictedbackgrounddistributionscorrespondstotheresultoftheglobalfit. Thisregion,definedbyinvertingthepζ requirementandrejectingeventswithno jetintheeμfinalstate,isusedtoestimatetheyieldsofthett backgroundinall channels.

Thecontributionsfromdibosonandsingletopquarkproduction areestimatedfromsimulation,asistheH

→

WW background. 8. Systematicuncertainties

8.1. Uncertaintiesrelatedtoobjectreconstructionandidentification The overall uncertainty in the

τ

h identification efficiency for

genuine

τ

h leptons is 5%, which has beenmeasured witha

tag-and-probe method in Z

→

τ τ

events. This number is not fully correlated among the di-

τ

channels because the

τ

h candidates

are required to pass different working points of the discrimina-torsthatreducethemisidentificationrateofelectronsandmuons as

τ

h candidates.The triggerefficiency uncertaintyper

τ

h

candi-date amounts to an additional 5%, which leads to a total trigger uncertaintyof10%forprocessesestimatedfromsimulationinthe

τ

h

τ

hdecaychannel.Thisuncertaintyhasalsobeenmeasuredwith

atag-and-probemethodinZ

→

τ τ

events.

An uncertainty of 1.2% in the visible energy scale of genuine

τ

h leptons affectsboththedistributions andthesignal and

back-groundyields.Itisuncorrelatedamongthe1-prong,1-prong

+

π

0_,

and3-prongdecaymodes.The magnitudeoftheuncertaintywas determinedinZ

→

τ τ

eventswithone

τ

leptondecaying hadroni-callyandtheotheronetoamuon,byperformingmaximum likeli-hoodfitsfordifferentvaluesofthevisibleenergyscaleofgenuine

τ

h leptons. Among these events,less than half overlap withthe

events selected inthe

μτ

h channel ofthis analysis. The fit

con-strainsthevisible

τ

henergyscaleuncertaintytoabout0.3%forall

decaymodes.Theconstraintmostlycomesfromhighlypopulated regionswithahigh

τ

hpurity,namelythe0-jetandboosted

cate-goriesof the

μτ

hand

τ

h

τ

h channels. The decreasein thesize of

the uncertainty is explained by the addition of two other decay channelswith

τ

hcandidates(

τ

h

τ

hande

τ

h),bythehighernumber

of eventsin the MC simulations, and by the finer categorization that leads to regions with a high Z

→

τ τ

eventpurity. Even in themostboostedcategories, reconstructed

τ

hcandidatestypically

have moderate pT (pT less than 100 GeV) and are found inthe

barrelregion ofthe detector.As tracks are well measured inthe CMSdetectorforthisrangeof pT,thevisibleenergyscaleof

gen-uine

τ

hleptons isfullycorrelated forall

τ

h leptonsreconstructed

inthesamedecaymode,irrespectiveoftheirpT and

η

.The

uncer-taintiesinthevisibleenergyscaleforgenuine

τ

hleptonstogether

contribute anuncertaintyof5%tothemeasurement ofthesignal strength.

Inthe0-jetcategoryofthe

μτ

h ande

τ

hchannels, therelative

contributionof

τ

hinagivenreconstructeddecaymodeisallowed

to fluctuate by 3% to account for the possibility that the recon-structionandidentificationefficienciesaredifferentforeachdecay mode.Thisuncertaintyhasbeenmeasuredinaregionenrichedin Z

→

τ τ

events withone

τ

lepton decaying hadronically andthe other one decayingto a muon, by comparing the levelof agree-ment inexclusive binsofthe reconstructed

τ

h decaymode,after

adjusting the inclusive normalization of the Z

→

τ τ

simulation to its best-fit value. The effect of migration between the recon-structed

τ

h decay modes isnegligible in other categories, where

alldecaymodesaretreatedtogether.

For events where muons or electrons are misidentified as

τ

h

candidates, essentially Z

→

μμ

eventsin the

μτ

h decay channel

and Z

→

ee eventsinthee

τ

hdecaychannel,the

τ

hidentification

leads torateuncertaintiesof25and12%,respectively, per recon-structed

τ

hdecaymode.Usingmvisandthereconstructed

τ

hdecay

modeastheobservablesinthe0-jetcategoryofthe

μτ

h ande

τ

h

channels helpsreduce theuncertainty after the signal extraction fit:theuncertaintyintherateofmuonsorelectronsmisidentified as

τ

h becomes of the order of 5%. The energy scale uncertainty

formuonsorelectronsmisidentifiedas

τ

hcandidatesis1.5or3%,

respectively, andis uncorrelatedbetween reconstructed

τ

h decay

modes. The fit constrains these uncertainties to about one third of their initial values.Forevents wherequark- or gluon-initiated jets are misidentified as

τ

h candidates, a linear uncertainty that

increases by 20% per 100 GeV in

τ

h pT accounts fora potential

mismodeling of the jet

→

τ

h misidentification rateasa function

ofthe

τ

h pT insimulations.Theuncertaintyhasbeendetermined

from a region enriched in W

+

jets events, using events with a muonanda

τ

hcandidateinthefinalstate,characterizedbyalarge

transversemassbetweenthe pmiss_T andthemuon [54,55]. Inthedecaychannelswithmuonsorelectrons,the uncertain-ties in the muon and electron identification, isolation, and trig-gerefficiencieslead totherateuncertaintyof2%forbothmuons andelectrons.Theuncertaintyintheelectronenergyscale,which amountsto2.5%intheendcapsand1%inthebarrelofthe detec-tor, isrelevantonlyinthee

μ

decaychannel,whereitaffectsthe final distributions.Inall channels,theeffectoftheuncertaintyin themuonenergyscaleisnegligible.

Theuncertaintiesinthejetenergyscaledependonthe pTand

η

ofthe jet [53]. Theyare propagated tothe computation ofthe numberofjets,whichaffectstherepartitionofeventsbetweenthe 0-jet,VBF, andboostedcategories, andto thecomputationofmjj,

whichisoneoftheobservablesintheVBFcategory.

The rate uncertainty related to discarding events with a b-tagged jet in the e

μ

decay channel is up to 5% forthe tt back-ground.Theuncertaintyinthemistaggingrateofgluonand light-flavorjetsisnegligible.

The



pmiss_T scaleuncertainties [61], whicharecomputed event-by-event,affectthenormalizationofvariousprocessesthroughthe event selection, as well astheir distributions through the prop-agation of these uncertainties to the di-

τ

mass mττ . The



pmiss

T

scale uncertainties arising from unclustered energy deposits in the detector come from four independent sources related to the tracker,ECAL,HCAL,andforwardcalorimeterssubdetectors. Addi-tionally,



pmiss_T scaleuncertaintiesrelatedtotheuncertaintiesinthe jet energyscale measurement,which leadto uncertainties inthe



pmiss

T calculation,aretakenintoaccount.Thecombinationofboth

sources ofuncertaintiesinthe



pmiss

T scaleleadsto anuncertainty

8.2.Backgroundestimationuncertainties

The Z

→

τ τ

background yield and distribution are corrected based on the agreement between data and the background pre-diction in a control region enriched in the Z

→

μμ

events, as explained in Section 7. The extrapolation uncertainty related to kinematic differences in the selections in the signal and control regionsrangesbetween3and10%,depending onthecategory.In addition,shapeuncertaintiesrelatedtotheuncertaintiesinthe ap-pliedcorrectionsareconsidered; they reach 20%forsome ranges of mjj in the VBF category. These uncertainties arise from the

differentlevel of agreement betweendata andsimulation in the Z

→

μμ

control region obtainedwhen varying the threshold on themuon pT.

TheuncertaintiesintheW

+

jets eventyielddetermined from thecontrol regions in the

μτ

h ande

τ

h channelsaccount forthe

statisticaluncertainty of the observed data, the statistical uncer-tainty ofthe W

+

jets simulated sample, andthe systematic un-certaintiesassociated withbackgroundprocessesin thesecontrol regions. Additionally, an uncertainty in the extrapolation of the constraints from the high-mT (mT

>

80 GeV) control regions to

thelow-mT (mT

<

50 GeV)signalregionsisadditionallytakeninto

account.Thelatterrangesfrom5to10%,andisobtainedby com-paring the mT distributions of simulated andobserved Z

→

μμ

eventswhereoneofthemuonsisremovedandthe



pmiss_T adjusted accordingly,tomimicW

+

jets events.Thereconstructedinvariant massoftheparentbosonintherestframeismultipliedbythe ra-tioof theW and Z bosonmasses beforeremoving themuon. In the

τ

h

τ

h ande

μ

channels, wheretheW

+

jets backgroundis

es-timatedfromsimulation,theuncertaintyintheyieldofthissmall backgroundis equal to 4 and 20%, respectively. The larger value forthe e

μ

channel includesuncertainties inthemisidentification ratesof jetsaselectrons and muons, whereas the uncertaintyin themisidentificationrateofjetsas

τ

hcandidatesinthe

τ

h

τ

h

chan-nelisaccountedforby thelinearuncertaintyasafunctionofthe

τ

h pTdescribedearlier.

The uncertainty in the QCD multijet background yield in the e

μ

decaychannelrangesfrom10to20%,depending onthe cate-gory.Itcorresponds totheuncertaintyintheextrapolationfactor from the same-sign to opposite-sign region, measured in events withanti-isolatedleptons.Inthe

μτ

hande

τ

hdecaychannels,

un-certaintiesfromthefitofthecontrolregionswithleptonspassing relaxedisolation conditions are considered, together with an ad-ditional20%uncertainty thataccounts fortheextrapolationfrom therelaxed-isolationcontrolregiontotheisolatedsignalregion.In the

τ

h

τ

hdecaychannel,theuncertaintyintheQCDmutlijet

back-groundyieldisa combinationofthe uncertaintiesobtainedfrom fitting the dedicated control regions with

τ

h candidates passing

relaxedisolation criteria,andofextrapolationuncertaintiestothe signalregionrangingfrom3to15%andaccountingforlimited dis-agreementbetweenpredictionanddatainsignal-freeregionswith variouslooseisolationcriteria.

Theyieldofeventsinatt-enrichedregionisaddedtothe max-imumlikelihoodfittocontrolthenormalizationofthisprocessin thesignalregion,asexplainedinSection7.The uncertaintyfrom thefitinthecontrolregionisautomaticallypropagatedtothe sig-nalregions,resultinginanuncertaintyofabout5%onthett cross section.Per-channeluncertaintiesrelatedtotheobject reconstruc-tionandidentificationareconsideredwhenextrapolatingfromthe e

μ

finalstatetotheothers.Thett simulationiscorrectedfor dif-ferencesinthe topquark pT distributionsobservedbetweendata

andsimulation,andan uncertaintyinthecorrection istakeninto account.

Thecombined systematicuncertainty in thebackground yield arisingfromdibosonandsingletopquark productionprocessesis

estimatedtobe5%onthebasisofrecentCMSmeasurements [62,

63].

8.3. Signalpredictionuncertainties

The rateandacceptanceuncertainties forthe signal processes relatedto the theoretical calculationsare due to uncertainties in thePDFs,variations oftheQCD renormalizationandfactorization scales, anduncertainties in the modeling ofpartonshowers. The magnitudeoftherateuncertaintydependsontheproduction pro-cessandontheeventcategory.

The inclusive uncertaintyrelated to the PDFsamounts to 3.2, 2.1, 1.9,and1.6%,respectively,fortheggH,VBF,WH, andZH pro-duction modes [38].The corresponding uncertaintyforthe varia-tionoftherenormalizationandfactorizationscalesis3.9,0.4,0.7, and 3.8%, respectively [38]. The acceptance uncertainties related to the particular selection criteria used in this analysis are less than1%fortheggH andVBFproductionsforthePDFuncertainties. TheacceptanceuncertaintiesfortheVBFproductioninthe renor-malizationandfactorizationscale uncertaintiesare alsolessthan 1%,whilethecorrespondinguncertainties fortheggH processare treatedasshapeuncertaintiesastheuncertaintyincreaseslinearly withpτ τ_T andmjj.

The pT distributionoftheHiggsbosoninthe powheg 2.0

sim-ulations is tuned tomatch moreclosely thenext-to-NLO (NNLO) plus next-to-next-to-leading-logarithmic (NNLL) prediction in the HRes2.1generator [64,65].Theacceptancechangeswiththe varia-tionofthepartonshowertune in herwig++ 2.6samples [66] are consideredasadditionaluncertainties,andamounttoup to7%in theboostedcategory.Thetheoreticaluncertaintyinthebranching fractionoftheHiggsbosonto

τ

leptonsisequalto2.1% [38].

The theoretical uncertainties in the signal production depend onthejetmultiplicity;thiseffectisincludedbyfollowingthe pre-scriptionsin Ref. [67].Thiseffect needsto be takenintoaccount becausethedefinitionsofthethreecategoriesusedintheanalysis arebasedpartiallyonthenumberofreconstructedjets.Additional uncertaintiesforboostedHiggsbosons,relatedtothetreatmentof the top quark mass in thecalculations, are considered forsignal eventswithpτ τ_T

>

150 GeV.

Theoryuncertaintiesinthesignalpredictioncontributean un-certaintyof10%tothemeasurementofthesignalstrength. 8.4. Otheruncertainties

The uncertainty inthe integratedluminosity amounts to2.5% [68].

Uncertaintiesrelatedtothe finitenumberofsimulatedevents, or to the limited number of events in data control regions, are takenintoaccount. Theyareconsidered forall binsofthe distri-butionsusedtoextracttheresultsiftheuncertaintyislargerthan 5%.Theyareuncorrelatedacrossdifferentsamples,andacrossbins ofa singledistribution. Takentogether,they contributean uncer-tainty of about12% to the signal strength measurement, coming essentiallyfromtheVBFcategory,wherethebackgroundtemplates arelesspopulatedthanintheothercategories.

The systematic uncertainties considered in the analysis are summarizedinTable3.

9. Results

The extractionof theresults involvesa globalmaximum like-lihood fit based on 2D distributions in all channels, shown in Figs.6–17,togetherwiththecontrolregionsforthett,QCD multi-jet,andW

+

jets backgrounds.Thechoiceofthebinningisdriven by thestatisticalprecisionofthebackgroundanddatatemplates,

Table 3

Sourcesofsystematicuncertainty.Iftheglobalfittothesignalandcontrolregions,describedinthenextsection, signifi-cantlyconstrainstheseuncertainties,thevaluesoftheuncertaintiesaftertheglobalfitareindicatedinthethirdcolumn. TheacronymsCRandIDstandforcontrolregionandidentification,respectively.

Source of uncertainty Prefit Postfit (%)

τhenergy scale 1.2% in energy scale 0.2–0.3

e energy scale 1–2.5% in energy scale 0.2–0.5

e misidentified asτhenergy scale 3% in energy scale 0.6–0.8 μmisidentified asτhenergy scale 1.5% in energy scale 0.3–1.0

Jet energy scale Dependent upon pTandη –



pmiss

T energy scale Dependent upon pTandη –

τhID & isolation 5% perτh 3.5

τhtrigger 5% perτh 3

τhreconstruction per decay mode 3% migration between decay modes 2

e ID & isolation & trigger 2% –

μID & isolation & trigger 2% –

e misidentified asτhrate 12% 5

μmisidentified asτhrate 25% 3–8

Jet misidentified asτhrate 20% per 100 GeVτh pT 15

Z→τ τ/estimation Normalization: 7–15% 3–15

Uncertainty in m/τ τ, pT(/τ τ), – and mjjcorrections

W+jets estimation Normalization (eμ,τhτh): 4–20% – Unc. from CR (eτh,μτh):5–15 – Extrap. from high-mTCR (eτh,μτh): 5–10% – QCD multijet estimation Normalization (eμ): 10–20% 5–20%

Unc. from CR (eτh,τhτh,μτh):5–15% – Extrap. from anti-iso. CR (eτh,μτh): 20% 7–10 Extrap. from anti-iso. CR (τhτh): 3–15% 3–10

Diboson normalization 5% –

Single top quark normalization 5% –

tt estimation Normalization from CR:5% –

Uncertainty on top quark pTreweighting –

Integrated luminosity 2.5% –

b-tagged jet rejection (eμ) 3.5–5.0% –

Limited number of events Statistical uncertainty in individual bins –

Signal theoretical uncertainty Up to 20% –

Fig. 6. Observedandpredicted2DdistributionsintheVBFcategoryoftheτhτhdecaychannel.Thenormalizationofthepredictedbackgrounddistributionscorrespondsto theresultoftheglobalfit.Thesignaldistributionisnormalizedtoitsbestfitsignalstrength.Thebackgroundhistogramsarestacked.The“Others”backgroundcontribution includeseventsfromdibosonandsingletopquarkproduction,aswellasHiggsbosondecaystoapairofW bosons.Thebackgrounduncertaintybandaccountsforallsources ofbackgrounduncertainty,systematicaswellasstatistical,aftertheglobalfit.Thesignalisshownbothasastackedfilledhistogramandanopenoverlaidhistogram.

Fig. 7. Observed and predicted 2D distributions in the VBF category of theμτhdecay channel. The description of the histograms is the same as in Fig.6.

Fig. 8. Observed and predicted 2D distributions in the VBF category of the eτhdecay channel. The description of the histograms is the same as in Fig.6.

Fig. 10. Observed and predicted 2D distributions in the boosted category of theτhτhdecay channel. The description of the histograms is the same as in Fig.6.

Fig. 11. Observed and predicted 2D distributions in the boosted category of theμτhdecay channel. The description of the histograms is the same as in Fig.6.

Fig. 13. Observed and predicted 2D distributions in the boosted category of the eμdecay channel. The description of the histograms is the same as in Fig.6.

Fig. 14. Observed and predicted distributions in the 0-jet category of theτhτhdecay channel. The description of the histograms is the same as in Fig.6.

Fig. 16. Observed and predicted 2D distributions in the 0-jet category of the eτhdecay channel. The description of the histograms is the same as in Fig.6.

Fig. 17. Observed and predicted 2D distributions in the 0-jet category of the eμdecay channel. The description of the histograms is the same as in Fig.6.

Table 4

Backgroundandsignalexpectations,togetherwiththenumberofobservedevents,forbinsinthesignalregionforwhich log10(S/(S+B))>−0.9,whereS andB are,respectively,thenumberofexpectedsignaleventsforaHiggsbosonwith amassmH=125.09 GeV and ofexpectedbackgroundevents,inthosebins.Thebackgrounduncertaintyaccountsfor allsourcesofbackgrounduncertainty,systematicaswellasstatistical,aftertheglobalfit.Thecontributionfrom“other backgrounds”includeseventsfromdibosonandsingletopquarkproduction.ThecontributionfromHiggsbosondecaysto apairofW bosonsiszerointhesebins.

Process eμ eτh μτh τhτh Z→τ τ 5.8±2.2 21.2±3.3 34.6±4.9 89.1±6.9 Z→ee/μμ 0.0±0.0 2.9±0.2 3.7±0.2 5.0±0.2 tt+jets 1.9±0.1 10.4±0.3 22.2±1.8 13.9±0.5 W+jets 0.8±0.02 4.0±0.3 6.6±1.3 7.6±0.8 QCD multijet 2.1±0.3 3.3±2.5 5.0±1.3 35.5±2.1 Other backgrounds 1.4±0.1 5.2±0.2 6.1±0.2 7.3±0.2 ggH,H→τ τ 0.6±0.1 5.0±0.6 6.0±0.6 27.4±2.1 VBF H→τ τ 2.8±0.3 5.1±0.5 12.55±1.0 17.5±1.0 VH,H→τ τ 0.0±0.0 0.3±0.0 0.2±0.0 1.3±0.1 Total backgrounds 12.1±2.2 46.5±4.1 77.7±5.5 156.2±7.3 Total signal 3.4±0.4 10.9±0.8 19.2±1.4 48.3±2.6 Observed 11 54 91 207

Fig. 18. Distributionofthedecimallogarithmoftheratiobetweenthe expected signalandthesumofexpectedsignalandexpectedbackgroundineachbinofthe massdistributionsusedtoextracttheresults,inallsignalregions.Thebackground contributionsareseparatedbydecaychannel.Theinsetshowsthecorresponding differencebetweentheobserveddataandexpectedbackgrounddistributions di-videdbythebackgroundexpectation,aswellasthesignalexpectationdividedby thebackgroundexpectation.

leading to wider bins in the poorly-populated VBF category. The most sensitive category, VBF, is shown first and is followed by theboostedand0-jetcategories.ThesignalpredictionforaHiggs boson withmH

=

125

.

09 GeV is normalized to its best fit cross

sectiontimesbranchingfraction.Thebackgrounddistributionsare adjustedtotheresultsoftheglobalmaximumlikelihoodfit.

The 2D distributions of the final discriminating variables ob-tainedfor each category andeach channel in the signal regions, along withthe control regions, are combined in a binned likeli-hoodinvolving the expected andobserved numbers ofevents in each bin. The expected number of signal events is the one pre-dicted for the production of a SM Higgs boson of mass mH

=

125

.

09 GeV decayingintoapairof

τ

leptons,multipliedbya sig-nalstrengthmodifier

μ

treatedasafreeparameterinthefit.

The systematic uncertainties are represented by nuisance pa-rameters that are varied in the fit according to their probability densityfunctions.A log-normal probabilitydensityfunctionis as-sumed for the nuisance parameters affecting the event yields of the various background contributions, whereas systematic uncer-taintiesthat affectthe shape ofthedistributions are represented by nuisance parameters whose variation results in a continuous perturbationofthespectrum [69] andwhichareassumedtohave aGaussianprobabilitydensityfunction.Overall,thestatistical un-certainty inthe observed eventyields isthe dominant sourceof uncertaintyforallcombinedresults.

Groupingeventsinthesignalregionbytheirdecimallogarithm of the ratio of the signal (S) to signal-plus-background (S

+

B) in each bin (Fig. 18), an excess of observed events with respect to the SM background expectation is clearly visible in the most sensitive bins of the analysis. The expected background and sig-nalcontributions, aswell asthe observednumber ofevents, are indicated per process and category in Table 4 for the bins with log₁₀

(

S

/(

S

+

B

))

>

−

0

.

9.Thechannelthatcontributesthemostto thesebinsis

τ

h

τ

h.

Anexcessofobservedeventsrelativetothebackground expec-tationisalsovisibleinFig.19,whereeverymassdistributionfora constantrangeoftheseconddimensionofthesignaldistributions

Fig. 19. Combinedobservedandpredictedmτ τdistributions.Thetop panelincludes theVBFcategoryoftheμτh,eτhandeμchannels,andthebottom panelincludes allotherchannelsthatmakeuseofmτ τ insteadofmvisforthesignalstrengthfit. Thebinningreflectstheoneusedinthe2Ddistributions,anddoesnotallow merg-ingofthetwofigures.Thenormalizationofthepredictedbackgrounddistributions correspondstotheresultoftheglobalfit,whilethesignalisnormalizedtoitsbest fitsignalstrength.Themassdistributionsforaconstantrangeofthesecond di-mensionofthesignaldistributionsareweightedaccordingtoS/(S+B),whereS

andB arecomputed,respectively,asthesignalorbackgroundcontributioninthe massdistributionexcludingthefirstandlastbins.The“Others”background contri-butionincludeseventsfromdiboson,tt,andsingletopquarkproduction,aswellas HiggsbosondecaytoapairofW bosonsandZ bosonsdecayingtoapairoflight leptons.Thebackgrounduncertaintybandaccountsforallsourcesofbackground uncertainty,systematicaswellasstatistical,aftertheglobalfit.Theinsetshowsthe correspondingdifferencebetweentheobserveddataandexpectedbackground dis-tributions,togetherwiththesignalexpectation.Thesignalyieldisnotaffectedby thereweighting.

hasbeensummedwithaweightofS

/(

S

+

B

)

toincreasethe con-tributionofthemostsensitivedistributions. Inthiscase, S and B are computed,respectively, asthesignal orbackground contribu-tion inthe mass distributionexcluding the first andlast bins, in which theamount of signal isnegligible. The signal regions that usemvisinsteadofmττ ,namelythe0-jetcategoryofthe

μτ

h,e

τ

h

Fig. 20. Localp-valueandsignificanceasafunctionoftheSMHiggsbosonmass hy-pothesis.Theobservation(red,solid)iscomparedtotheexpectation(blue,dashed) foraHiggsbosonwithamassmH=125.09 GeV.ThebackgroundincludesHiggs bosondecaystopairsofW bosons,withmH=125.09 GeV.

ande

μ

channels,arenotincluded.ThetwopanesofFig.19group thecompatiblebinsofFigs.6–17.

The excess in data is quantified by calculating the corre-spondinglocal p-valueusinga profilelikelihood ratiotest statis-tic [70–73]. As shownin Fig. 20, the observed significance fora SMHiggsbosonwithmH

=

125

.

09 GeV is4.9standarddeviations,

foranexpectedsignificanceof4.7standarddeviations.

The corresponding best fit value for the signal strength

μ

is 1

.

09+₋0₀._.27₂₆ at mH

=

125

.

09 GeV. The uncertainty in the best fit

signal strength can be decomposed into four components: the-oretical uncertainties, bin-by-bin statistical uncertainties on the backgrounds, other systematic uncertainties, and the statistical uncertainty. In this format, the best fit signal strength is

μ

=

1

.

09+₋0_0..₁₅15 (stat)+₋0₀._.16₁₅ (syst)+₋₀0._.10₀₈ (theo)₋+₀0._.13₁₂ (bin-by-bin). The indi-vidualbestfitsignalstrengthsperchannelandpercategory,using the constraints obtainedon the systematic uncertainties through theglobalfit,aregiveninFig.21;theydemonstratethe channel-and category-wise consistency of the observation with the SM Higgsbosonhypothesis.

A likelihood scan is performed for mH

=

125

.

09 GeV in the

(

κ

V,

κ

f) parameter space, where

κ

V and

κ

f quantify, respectively,

the ratio between the measured and the SM value for the cou-plingsoftheHiggsbosontovectorbosonsandfermions,withthe methodsdescribedinRef. [26].Forthisscanonly,Higgsboson de-cays to pairs of W bosons are considered as part of the signal. All nuisance parameters are profiled for each point of the scan. AsshowninFig.22,theobservedlikelihoodcontourisconsistent withtheSMexpectationof

κ

Vand

κ

fequaltounity.

The results are combined with the results of the search for H

→

τ τ

performed withthe datacollected with theCMS detec-toratcenter-of-massenergies of7 and8 TeV [14], usinga com-mon signal strength for all data taking periods. All uncertainties areconsideredasfullyuncorrelatedbetweenthedifferent center-of-mass energies. The combination leads to an observed and an expectedsignificance of5.9standard deviations.The correspond-ing best fit value for the signal strength

μ

is 0

.

98

±

0

.

18 at mH

=

125

.

09 GeV.Thisconstitutesthemostsignificantdirect

mea-surement of the coupling of the Higgs boson to fermions by a singleexperiment.

Fig. 21. Bestfitsignalstrengthpercategory(top)andchannel(bottom),formH= 125.09 GeV.Theconstraintsfromthe globalfit areusedtoextracteachofthe individualbest fitsignalstrengths.Thecombinedbestfitsignalstrengthisμ= 1.09+0.27

−0.26.

10. Summary

A measurement of the H

→

τ τ

signal strength, using events recordedinproton–protoncollisionsbytheCMSexperimentatthe LHC in2016ata center-of-massenergyof13 TeV, hasbeen pre-sented. EventcategoriesaredesignedtotargetHiggsbosonsignal eventsproduced by gluonorvector boson fusion.Theresults are extractedviamaximumlikelihood fitsintwo-dimensionalplanes, and give an observed significance for Higgs boson decays to

τ

lepton pairs of 4.9standard deviations, to be compared withan expectedsignificanceof4.7standard deviations.Thecombination withthecorrespondingmeasurementperformedatcenter-of-mass energies of7 and8 TeV withthe CMSdetectorleads tothe first observationbyasingleexperimentofdecaysoftheHiggsbosonto pairsof

τ

leptons,withasignificanceof5.9standarddeviations.

Fig. 22. Scanofthenegativelog-likelihooddifferenceasafunctionofκV andκf, formH=125.09 GeV.Allnuisanceparametersareprofiledforeachpoint.Forthis scan,thepp→H→WW contributionistreatedasasignalprocess.

Acknowledgements

WecongratulateourcolleaguesintheCERNaccelerator depart-ments for the excellent performance of the LHC and thank the technicalandadministrativestaffs atCERN andatother CMS in-stitutes for their contributions to the success of the CMS effort. Inaddition,wegratefullyacknowledgethecomputingcentersand personneloftheWorldwideLHCComputingGridfordeliveringso effectivelythecomputinginfrastructure essential toour analyses. Finally, we acknowledge the enduring support for the construc-tionandoperationofthe LHCandtheCMSdetectorprovided by thefollowingfundingagencies:BMWFWandFWF(Austria);FNRS and FWO (Belgium); CNPq, CAPES, FAPERJ, and FAPESP (Brazil); MES (Bulgaria); CERN; CAS, MOST, and NSFC (China); COLCIEN-CIAS(Colombia);MSESandCSF(Croatia);RPF(Cyprus);SENESCYT (Ecuador); MoER, ERC IUT, and ERDF (Estonia); Academy of Fin-land,MEC,andHIP(Finland);CEAandCNRS/IN2P3(France);BMBF, DFG, and HGF (Germany); GSRT (Greece); OTKA and NIH (Hun-gary);DAEandDST (India);IPM(Iran);SFI(Ireland);INFN (Italy); MSIPandNRF (RepublicofKorea);LAS(Lithuania);MOE andUM (Malaysia); BUAP,CINVESTAV, CONACYT, LNS, SEP, and UASLP-FAI (Mexico); MBIE (New Zealand); PAEC (Pakistan); MSHE and NSC (Poland);FCT(Portugal);JINR(Dubna);MON,ROSATOM,RAS,RFBR andRAEP (Russia);MESTD(Serbia); SEIDI,CPAN,PCTI andFEDER (Spain);SwissFundingAgencies(Switzerland);MST(Taipei); ThEP-Center, IPST, STAR, and NSTDA (Thailand); TUBITAK and TAEK (Turkey);NASUandSFFR(Ukraine);STFC (UnitedKingdom);DOE andNSF(USA).

Individuals have received support from the Marie-Curie pro-gramandtheEuropeanResearchCouncilandHorizon2020Grant, contract No. 675440 (European Union); the Leventis Foundation; theAlfredP.SloanFoundation;theAlexandervonHumboldt Foun-dation;the BelgianFederal Science PolicyOffice; the Fonds pour laFormation àla Recherche dansl’Industrie etdans l’Agriculture (FRIA-Belgium); the Agentschap voor Innovatie door Wetenschap en Technologie (IWT-Belgium); the Ministry of Education, Youth and Sports (MEYS) of the Czech Republic; the Council of Sci-ence and Industrial Research, India; the HOMING PLUS program of the Foundation for Polish Science, cofinanced from European Union,Regional DevelopmentFund, theMobilityPlus programof

theMinistryofScienceandHigherEducation,theNationalScience Center (Poland), contracts Harmonia 2014/14/M/ST2/00428, Opus 2014/13/B/ST2/02543, 2014/15/B/ST2/03998, and 2015/19/B/ST2/ 02861,Sonata-bis2012/07/E/ST2/01406;theNationalPriorities Re-search Program by Qatar National Research Fund; the Programa Clarín-COFUND del Principado de Asturias; the Thalis and Aris-teia programs cofinanced by EU-ESF and the Greek NSRF; the Rachadapisek Sompot Fund for Postdoctoral Fellowship, Chula-longkornUniversityandtheChulalongkornAcademic intoIts2nd Century Project Advancement Project (Thailand); and the Welch Foundation,contractC-1845.

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