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DOI: 10.1016/j.physletb.2019.01.069
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by Elsevier. All rights reserved.
DIRETORIA DE TRATAMENTO DA INFORMAÇÃO
Cidade Universitária Zeferino Vaz Barão Geraldo
CEP 13083-970 – Campinas SP
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Contents lists available atScienceDirect
Physics
Letters
B
www.elsevier.com/locate/physletb
Search
for
a
W
boson
decaying
to
a
τ
lepton
and
a
neutrino
in
proton-proton
collisions
at
√
s
=
13
TeV
.
The
CMS
Collaboration
CERN,Switzerland
a
r
t
i
c
l
e
i
n
f
o
a
b
s
t
r
a
c
t
Articlehistory:
Received30July2018
Receivedinrevisedform30January2019 Accepted31January2019
Availableonline15March2019 Editor:M.Doser Keywords: CMS Physics Tau MET
A search for a new high-mass resonance decaying to a
τ
lepton and a neutrino is reported. The analysisusesproton-protoncollisiondata collectedbytheCMSexperimentattheLHCat√s=13TeV, corresponding to an integrated luminosity of 35.9 fb−1. The search utilizes hadronically decayingτ
leptons. No excess in the event yield is observed at high transverse masses of theτ
and missing transverse momentum.Aninterpretation ofresultswithinthe sequentialstandard modelexcludesW boson massesbelow 4.0 TeV at 95% confidencelevel. Existinglimits are also improvedonmodels in whichthe W bosondecays preferentiallytofermions ofthethird generation.HeavyW bosonswith masseslessthan1.7–3.9 TeV,dependingonthecouplinginthenon-universalG(221)model,areexcluded at95%confidencelevel.Thesearethemoststringentlimitsonthismodeltodate.©2019TheAuthor(s).PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense
(http://creativecommons.org/licenses/by/4.0/).FundedbySCOAP3.
1. Introduction
Newchargedheavy gauge bosons, generallyreferred to asW bosons,arepredictedbyvariousextensionsofthestandardmodel (SM). An example is the sequential standard model (SSM) [1], featuring an extended gauge sector, which is often used as a benchmarkmodel.LeptonuniversalityholdsintheSSM;however, there exist models without this assumption. Nonuniversal gauge interaction models (NUGIMs) [2–6] predict an enhanced W bo-son branching fraction to the third generation fermions. In this approach,thehightopquarkmassisassociatedwiththelarge vac-uumexpectationvalueofthecorrespondingHiggsfield.
The analysis presented in this Letter searches for W
→
τ ν
events,wheretheτ
leptondecayshadronically.Theleadingorder FeynmandiagramisshowninFig.1.InthisLetter,thesymbolτ
hwillbeusedtodenotethevisiblepartofthehadronicdecayofthe
τ
,whichisreconstructedasaτ
jetinthedetector.The hadronic decaysoftheτ
leptonareexperimentallydistinctivebecausethey result in low charged-hadron multiplicity, unlike jets originating fromthehadronizationofpartonsproducedinthehardscattering process,which havehigh charged-hadronmultiplicity.The signa-tureofaW bosoneventissimilartothatofa W bosoneventin whichtheW bosonisproduced“off-shell”withahighmass.SearchesforaWbosondecayingtoa
τ
leptonandaneutrino havebeenperformedpreviouslybytheCMS [7] andATLAS [8]col- E-mailaddress:cms-publication-committee-chair@cern.ch.
Fig. 1. Leading order Feynman diagram of the expected signal process W→τ ν.
laborationsatthe CERNLHC.Searches fora W boson havebeen performedalsoine
+
pmissT ,μ
+
pmissT [9,10],WZ [11,12],qq [13, 14] and tb [15,16] channels.The ATLAS experimenthasexcluded anSSMWformassesbelow3.7 TeV intheτ
h+
pmissT channel.TheCMSexperimenthasexcludedanSSMWformassesbelow5.2 TeV inthecombinationofelectronandmuonchannels.ThisLetter de-scribes a search fora W boson inthe
τ
h+
pmissT channel usingproton-proton (pp)collisionscollectedin2016atacenter-of-mass energyof13 TeV.Thedatasetcorrespondstoan integrated lumi-nosity of 35.9 fb−1.The results are interpreted in the context of twomodels,theSSMandtheNUGIM.
2. Physicsmodels
2.1. ThesequentialstandardmodelWboson
In theSSM, the W boson is a heavy analog ofthe W boson. Itisaresonancewithfermionicdecaymodesandbranching frac-https://doi.org/10.1016/j.physletb.2019.01.069
0370-2693/©2019TheAuthor(s).PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense(http://creativecommons.org/licenses/by/4.0/).Fundedby SCOAP3.
tions similar to those of the SM W boson, with the addition of thedecayW
→
tb,whichbecomesrelevantforW bosonmasses largerthan180 GeV.IftheWbosonisheavyenough todecayto topandbottom quarks,theSSMbranchingfractionforthe decay W→
τ ν
is8.5% [1].Undertheseassumptions, therelativewidth/
M ofthe W bosonis∼
3.3%. Withincreasingmass,a growing fractionofeventsisproduced off-shell andshifted tolowermass values.Assumingeventswithinawindowof±
10%aroundthe ac-tualmassto beon-shell,theoff-shellfractionsare approximately 9,22and66%forWmassesof1,3and5 TeV,respectively.Decays intoWZ depend onthe specificmodelassumptions andare usu-allyconsidered to be suppressed in theSSM, asassumedby the currentsearch.Inaccordancewithpreviousanalyses, itisassumedthatthere isnointerferencebetweentheproductionofthenewparticleand theproductionoftheSMW boson.Suchanabsenceofinterference wouldoccur,forexample,iftheWinteractsviaV+Acoupling [17]. Signal events forthe SSM W boson are simulatedat leading order (LO) with pythia 8.212 [18], using the NNPDF 2.3 [19,20] parton distribution function (PDF) set and tune CUETP8M1 [21]. The W samples are normalized to next-to-next-to-leading-order (NNLO)crosssectionsfrom fewz [22,23].
2.2. Couplingstrength
The W bosoncouplingstrength, gW, isgivenintermsofthe
SM weak coupling strength gW
=
e/
sin2θ
W≈
0.65. Here,θ
W isthe weak mixing angle. If the W is a heavier copy of the SM W boson, their coupling ratio is gW
/
gW=
1 and the SSM Wtheoretical cross sections,signal shapes, andwidths apply. How-ever,different couplingsare possible. Becauseof the dependence ofthewidthofa particleonitscoupling,andtheconsequent ef-fectonthetransversemassdistribution,alimitcanalsobeseton the couplingstrength. For thisstudy, a reweighting procedure is used.SomeselectedsignalsamplesaresimulatedatLOwith Mad-Graph(version 1.5.11)[24],forarangeofcouplingratios gW
/
gWfrom0.01 to 3.These signals exhibit different widths aswell as different cross sections. The generated distributions of the SSM pythiasampleswith gW
/
gW=
1 arereweighted to takeintoac-countthedecaywidthdependence,thusprovidingtheappropriate reconstructed transverse mass distributions for gW
/
gW=
1. ForgW
/
gW=
1,thetheoreticalLOcrosssectionsapply andthiscou-plingstrengthisusedtocomparethestandardSSMsampleswith thereweightedones,allowingthereweightingmethodtobe veri-fied.
2.3. Nonuniversalgaugeinteractionmodel
Models with nonuniversal couplings predict an enhanced branchingfractionforthethirdgenerationoffermionsandexplain thelarge massof thetop quark. The nonuniversalgauge interac-tionmodels(NUGIMs)exhibitaSU
(2)
l×
SU(2)
h×
U(1)
symmetry,andthusareoftencalledG(221)models.Heretheindiceslandh refertolightandheavy,respectively.TheweakSM SU
(2)
W groupis a low-energy limit oftwo gauge groups, a light SU
(2)
l andaheavy SU
(2)
h, which govern the couplings to the light fermionsofthefirsttwogenerationsandtotheheavyfermionsofthethird generation,respectively.Thesetwogroupsmix,resultinginan SM-likeSU
(2)
Wandanextendedgroup SU(2)
E.TheSU(2)
Eextendedgauge group gives rise to additionalgauge bosons such asa W. The mixing of the two gauge groupsinvolves a mixing angle of theextendedgroup,
θ
E,whichmodifiesthecouplingstotheheavyboson.Consequently,themixingmodifiestheproductioncross sec-tion and, as illustrated in Fig. 2, the branching fractions of the
Fig. 2. BranchingfractionsB(W)asafunctionofthemixinganglecotθE,forW
bosondecaysintheNUGIMG(221)framework,ascalculatedinRefs. [2,25,26].For cotθE=1 thevaluescorrespondtothoseintheSSM,rescaledtoaccommodatethe
WH decaychannel.
W. For cotθE
3 the W decayspredominantly to thirdgenera-tion fermions. The branching fraction to WH issmaller than the branchingfractiontothirdgenerationfermions,asshowninFig.2. ForcotθE
=
1 thebranchingfractionsarethesameasthoseoftheSSM,andtheW bosoncouplesdemocraticallytoallfermions.For cot
θ
E<
1 thedecaysintolightfermionsaredominant.IntheNUGIMG(221),theratioofthecouplings gW
/
gW isre-latedtotheparametercot
θ
Ebythefollowingequation [26]:W
=
SSMW(
4+
14)
cot2θ
E+
8 tan2θ
E 12+
14=
SSM W gW gW 2 (1) Becauseofthisfunctionalrelationship,areinterpretation oflimits oncouplingstrengthwillyieldlimitsonNUGIMG(221),andthus itwasnotnecessarytogenerateasignalsampleforthismodel.3. TheCMSdetector
The central feature of the CMS apparatus is a superconduct-ing solenoid of6 m internal diameter, providing a magneticfield of 3.8 T. Withinthesolenoidvolume are a siliconpixeland strip tracker,aleadtungstatecrystalelectromagneticcalorimeter(ECAL), andabrassandscintillatorhadron calorimeter(HCAL),each com-posed ofa barrelandtwo endcapsections. Forwardcalorimeters extendthepseudorapidity(
η
)coverageprovidedbythebarreland endcapdetectors. Muonsaredetected ingas-ionization chambers embeddedinthesteelflux-returnyokeoutsidethesolenoid.Thesilicontrackermeasureschargedparticleswithintherange
|
η
|
<
2.5.It consistsof1440siliconpixel and15 148silicon strip detector modules. For nonisolated particles with transverse mo-mentum 1<
pT<
10GeV and|
η
|
<
1.4,the trackresolutions aretypically 1.5% in pT and 25–90 μm in the transverse impact
pa-rameterand45–150 μminthelongitudinalimpactparameter.The ECALconsistsof75 848leadtungstatecrystals,whichprovide cov-erage of
|
η
|
<
1.48 in a barrel region (EB) and 1.48<
|
η
|
<
3.0 in two endcapregions (EE). The HCALis a samplingcalorimeter, whichutilizesalternating layersofbrassasan absorberand plas-ticscintillatorasactivematerial,coveringtherange|
η
|
<
3.Inthe forward region, the calorimetric coverage is extended to|
η
|
<
5 byasteelandquartzfiberCherenkovhadronforwardcalorimeter. Muonsaremeasuredintherange|
η
|
<
2.4,withdetectionplanes madeusingthreetechnologies:drifttubes,cathodestripchambers,andresistiveplatechambers. Eventsofinterestareselectedusing atwo-tieredtriggersystem [27].
AmoredetaileddescriptionoftheCMSdetector,togetherwith adefinitionofthecoordinatesystemusedandtherelevant kine-maticvariables,canbefoundinRef. [28].
4. Backgroundsimulation
ThedominantSMbackgroundistheproductionofW+jets.This background is generated at LO using MadGraph5_amc@nlo ver-sion2.2.2withtheMLM merging [24,29] andtheNNPDF 3.0 [19, 20,30] PDF set for on-shell W boson production and using pythia8.212withtheNNPDF 2.3 PDFsetforoff-shellproduction. The differential cross section is reweighted as a function of the invariantmass ofthe SM W bosondecay products,incorporating NNLOquantumchromodynamics(QCD)andnext-to-leading-order (NLO)electroweak(EW)corrections.Theeffectwithrespecttothe LOcalculationcorrespondstoacorrectionfactor(K factor)forthe W bosontransversemassspectrum.TocombinetheQCDandEW differentialcrosssections,two differentmathematicalapproaches could be taken [31]:an additive or a multiplicative combination. Their effects differ by around 5%. The K factor assumed in this analysisisobtainedbytakingtheadditive combinationas recom-mended by Ref. [32] and the difference from the multiplicative combinationistreatedasasystematicuncertainty.The K factoris 1.15ata W massof 0.3 TeV and dropsmonotonically forhigher massesdown to0.6foramassof6 TeV. Thecalculation usesthe generators fewz 3.1 and mcsanc 1.01 [33] for theQCD and elec-troweakcorrections.
Other background processes are: Z/
γ
∗
→
generated with MadGraph5_amc@nlo version 2.3.2.2 [24] with the NNPDF 3.0 PDFset,dibosonprocessesgeneratedwith pythia 8.212andwith theNNPDF 2.3 PDF set, andtop quark processes generated with powheg 2.0 [34–39] and the NNPDF 3.0 PDF set. Background from jets that are falsely identified asτ
h candidates isdomi-nated by Z
→
νν
+
jets events,which are simulated with Mad-Graph5_amc@nlo version2.3.2.2andwiththeNNPDF 3.0PDFset. Parton fragmentation and hadronization are performed with pythia8.212 withtheunderlyingeventtune CUETP8M1.The de-tector response is simulated using a detailed description of the CMSdetectorimplementedwiththe Geant4package [40].All sim-ulatedeventsamplesare normalizedto theintegratedluminosity of the recorded data, using the theoretical cross section values. Additional pp collisions during thesame bunch crossing (pileup) istakeninto account by superimposingsimulated minimumbias interactions onto all simulated events. The simulated events are weightedsothatthepileupdistributionmatchesthatofthedata, withanaverageofabout27interactionsperbunchcrossing.5. Reconstructionandidentificationofphysicsobjects
Aparticle-flow(PF)algorithm [41] isusedtocombine informa-tionfromallCMSsubdetectorsinordertoreconstructandidentify individual particles in the event:muons, electrons, photons, and chargedandneutralhadrons.Theresultingsetofparticlesisused to reconstruct the
τ
h candidates, missing transverse momentum(pmissT ),andjets.Thevector p
Tmissisdefinedasthenegativevector
pT sumofall PFcandidates reconstructedintheevent.The
mag-nitudeofthisvectorisreferredtoaspmiss
T .TherawpmissT valueis
modifiedto account forcorrectionstotheenergy scaleofall the reconstructed jetsin the event [42]. The jets are clusteredusing theanti-kT jetfindingalgorithm [43,44].The reconstructedvertex
withthelargestvalueofsummedphysics-objectp2T istakenasthe primaryvertex.
Electrons [45,46] arereconstructedbymatchingenergydeposits intheECALwithtracksegmentsintheinnertracker.Muon recon-struction [47] is performed by matching a track segment recon-structed in the inner trackerwitha track segmentreconstructed inthemuondetectorandperformingaglobalfitofthecharge de-positsfromthetwotracksegments.
The
τ
hreconstructioninCMSstartsfromjetsclusteredfromPFcandidates,usingtheanti-kT algorithmwithadistanceparameter
of 0.4. The
τ
h candidates are reconstructed using thehadrons-plus-strips algorithm [48,49], which is designed to optimize the performance of
τ
h reconstruction and identification byconsider-ingspecific
τ
leptondecaymodes.Individualτ
hdecaymodesarereconstructedseparately.Thesignaturesdistinguishedbythe algo-rithm are: a single chargedhadron, a charged hadron andup to twoneutralpions,andthreechargedhadrons.
Requiring
τ
hcandidatestopassisolationrequirementsreducesthe jet
→
τ
h misidentificationprobability.The multivariant-based(MVA-based)
τ
h identificationdiscriminantcombineisolation andother variables with sensitivity to the
τ
lifetime, to provide the bestpossiblediscriminationforτ
hdecaysagainstquarkandgluonjets. Hadronicallydecaying
τ
leptons inthisanalysisare required to satisfy the very loose working point of the MVA-based isola-tion [50]. This workingpoint has an efficiency of about 70% for genuineτ
h, withabout0.4% misidentificationrateforquark- andgluon-initiatedjets,forapTrangetypicalof
τ
horiginatingfromaWbosonofmassof2 TeV.Isolatedelectronshaveahigh probabil-itytobemisidentifiedas
τ
hobjectsthatdecaytoasinglechargedhadron(h±orh±
π
0).Electronscanemitenergeticbremsstrahlungphotonsastheytraversethematerialofthesilicontracker.When thisoccurs, theelectronandaccompanying photonsmaybe mis-takenly reconstructed as a hadronically decaying
τ
. Muons can also be reconstructed asτ
h objects in the h± decay mode. Theτ
hcandidatesinthisanalysisarerequiredtopasstheloosework-ingpointoftheantielectrondiscriminator,whichhasanefficiency ofabout85%forgenuine
τ
hevents,andamisidentificationrateofabout1.5%forelectrons.The
τ
hcandidatesarefurtherrequiredtopassthelooseworkingpointoftheantimuondiscriminator,which hasanefficiencyof
>
99% forgenuineτ
hevents,withamisiden-tificationrateofabout0.3%formuons [50,51].
6. Analysisstrategy
The discriminating variable used in thisanalysis is the trans-versemass,definedasfollows:
mT
=
2pτTpmiss
T
[
1−
cosφ (
pTτ
,
pTmiss
)
],
(2)where pτT is the magnitude of the transverse momentum vector ofthe
τ
hcandidatepτT,and
φ
isthedifferenceintheazimuthalanglebetweenpτ
T and
pTmiss.
Thestrategyofthisanalysisistoselectaheavybosoncandidate decayingalmostatresttoahadronicjetconsistentwitha
τ
hcan-didate andneutrinos, the latter manifesting themselves as pmissT . Signaleventsareselectedonlinewitha
τ
h+
pmissT triggerthatre-quires the pT ofthe
τ
h candidate tobe greater than 50 GeV andthe value of pmissT to be greater than 90 GeV. To ensurethat the triggerismaximallyefficientforselectedevents,theoffline selec-tion requires one isolated
τ
h candidate to have pτT greater than80 GeV andpmiss
T tobegreaterthan200 GeV.
Althoughthere are two neutrinosin thefinal state, pmissT and the isolated
τ
h candidate are largely produced inoppositedirec-tions, which helps to distinguish signal from background events especiallythosecomingfromQCDmultijetproduction.Two selec-tion criteria exploit this behavior to reduce the background: the ratioofthepτT topmiss
Fig. 3. (Left)ThemTdistributionafterthefinalselection.Theblacksymbolswitherrorbarsshowdata,whilethefilledhistogramsrepresenttheSMbackgrounds.Signal
examplesforSSMWbosonswithmassesof0.6,1.0,4.0,and5.0 TeV areshownwiththeopenhistograms.(Right)Theintegraltransversemassdistribution,wherethevalue ineachbinisequaltothenumberofeventswithtransversemassequaltoorgreaterthantheleftofthebin.Thelowerpanelsshowtheratioofdatatoprediction,andthe graybandrepresentsthesystematicuncertainties.
andthe angle
φ (
pτT
,
pTmiss
)
has to be greater than 2.4radians. Consequently, the lowest mT value is about 300 GeV. To avoidan overlap with the W boson search in the electron channel, events are rejected if they contain a loosely identified electron withpT
>
20GeV and|
η
|
<
2.5,wherethelooseworkingpointis≈
90% efficientforreal electrons.For similarreasons,events con-tainingalooselyidentified muonwith pT>
20GeV and|
η
|
<
2.4arenotconsideredinthisanalysis,wherethelooseworkingpoint
is
>99%
efficientforrealmuons.Afterallselections, themT distributions fortheobserved data
and expected background events are presented in Fig. 3 (left). Fig.3 (right)showsthe integral distribution,which isformed by fillingeachbinofthehistogramwiththesumofthatbinandall followingbins.Thesystematicuncertainties,whicharedetailedin Section7,areillustratedasagray bandinthelowerpanelsofthe plots.TheproductofthesignalefficiencyandacceptanceforSSM W
→
τ ν
eventsdependson theW bosonmass.The totalsignal efficiencyforthestudiedrangeofmT>
300GeV variesfrom14%toabout24%asMW increasesfrom1to3 TeV.ForhigherWboson
masses,eventsshifttolowermTbecauseoftheincreasingfraction
ofoff-shell production(as showninFig. 3for a fewsignal mass points).Forexample,foraW bosonwithamassof5 TeV,the to-talsignalefficiencyisaround17%.Thetriggerthresholdaffectsthe signalefficiencyinthelow-massrange.Theseefficiencyvaluesare obtained assuming the W
→
τ ν
branching fraction to be unity. Theefficiencyvaluesare estimatedusing simulatedeventswhere theτ
leptondecayshadronically.The dominantbackground is fromthe off-shelltail ofthe mT
distributionoftheSMW boson, andisobtainedfromsimulation. ThebackgroundcontributionsfromZ(
→
νν
)
+
jets andQCD mul-tijeteventsarealsoobtainedfromsimulation.Thesebackgrounds primarilyariseasaconsequenceofjetsmisidentifiedasτ
hcandi-dates.ThecontributionofQCDmultijetbackgroundissmall com-paredtoZ(
→
νν
)
+
jets inthesignalregion.Followingthestrategy inRef. [52],toensurethatthemisidentifiedτ
backgroundis sim-ulated properly, the agreement between data and simulation is checkedinacontrolregiondominatedbyZ(→
μμ
)
+
jets events, whereajetismisidentifiedasaτ
hcandidate.ThepmissT isrecalcu-latedexcludingthemuonsfromtheZdecayinordertoreproduce the pmissT distribution of Z
→
νν
events. Specifically, the control region is defined as follows. Events are selected online using a dimuon trigger with muon pT thresholds of 17 and 8 GeV.Theymust contain two oppositely charged muons with pT
>
20GeVand
|
η
|
<
2.4, both passing loose identificationand isolation re-quirements.The invariantmass ofthedimuonsystemisrequired to be between 81 and 101 GeV. In addition, the events are re-quired to contain exactly oneτ
h candidate passing the samese-lectionrequirementsasinthesignalregion,withpτT
>
20GeV and|
η
τ|
<
2.1. To remove the overlap between muon andτ
hcandi-dates, theseparation betweenthem mustfulfill
R
(
μ
,
τ
h)
>
0.1,where
R isdefinedas
R
=
(
η
)
2+ (φ)
2.Dataandsimula-tion arecompared usingdistributions ofthedimuonmass, pmissT ,
pT/pmissT ,mT,
η
τ and pτT.Fig. 4showsthe pτT distributionin thecontrol region.Data andsimulation agree within 50% in all bins except inone bin inthe tailofthe pτT distribution, giving confi-dencethat themisidentified
τ
h backgroundsource—about22% ofthetotalbackground—iscorrectlymodeledinthesimulation.
7. Systematicuncertainties
The uncertaintyinthe modelingofthemT distributioncan be
split into threecategories: uncertainties affecting shapeand nor-malization, uncertainties affectingonly normalizationandan un-certaintyduetolimitednumbersofeventsinsimulatedsamples.
The dominantuncertaintyofthe firstcategory comesfrom
τ
hreconstruction and identification, affecting background anda po-tential signal in the same way. The uncertainty associated with the
τ
h identification is 5% [48]. An additional systematicuncer-tainty, which dominates for high-pT
τ
h candidates, is related tothedegreeofconfidencethattheMCsimulationcorrectlymodels the identification efficiency. This additional uncertainty increases linearlywithpτT andamountsto
+
5%/−
35% at pτT=
1TeV.The un-certainty isasymmetric becausestudiesindicate that theτ
iden-tification efficiencyissmaller indatathanin simulation,andthe difference increasesasthe pT oftheτ
increases.TheuncertaintyFig. 4. DistributionofpτT inthecontrolregion.Theblacksymbolswitherrorbars
showthedata,whilethehistogramsrepresenttheSMbackgrounds.Thelowerpanel showstheratioofdatatoprediction.
pmissT uncertainty from jets are the jet energy scale and jet en-ergyresolution [53].Fortheenergymeasurementsofotherobjects thefollowinguncertainties areapplied:3% [48] for
τ
h,0.6%inEBand1.5% in EE, respectively, for electrons andphotons [54]; and 0.2%formuons [47].The contributiontothe uncertaintyin pmissT
associated with unclustered energy is estimated by varying this energyby
±
10%.Fortheτ
plus pmissT trigger,ascalefactorof0.9 isapplied.Thescale factorhasan uncertaintyof10%.The uncer-tainty associatedwiththe choice ofthe PDF inthesimulation is evaluatedaccordingtothePDF4LHCprescription [55–57].The val-uesincrease withmT,rangingfromanuncertaintyof1to10%atmT
=
0.5 to4.0 TeV.Forthe K factoroftheW bosonbackground,the difference between additive and multiplicative combination, which is around 5%, is taken to be the systematic uncertainty. Thesimulatedeventsareweighted sothatthepileupdistribution matches the measured one, using a value for the total inelastic crosssectionof69.2 mb,whichhasanuncertaintyof
±
4.6% [58].Uncertainties of the second category influence only the nor-malizationof the mT distribution. Kinematic distributions in the
Z(
→
μμ
)
+
jets control region demonstratethat dataand simu-lationagreewithin 50%formisidentifiedτ
h background,whichiscomposedofZ(
→
νν
)
+
jets andQCDmultijetevents.Thisguides theassignmentofa50% systematicuncertaintyinthe normaliza-tionofthesebackgrounds.Theuncertaintyintheelectron identifi-cationefficiency(veto)is2%andtheuncertaintyintheintegrated luminositymeasurementis2.5% [59].Uncertaintiesin the third category arise fromlimited sizes of eventsamplesinthesimulationofbackgroundprocesses.In con-trasttoallotheruncertainties,theyarenotcorrelatedbetweenthe binsoftheinvariantmassdistribution.
Inthehigh-massregion,whereboththeexpectedandthe ob-served numbers of events are consistent with zero,the effect of thesystematicuncertaintyontheexclusionlimitsisnegligible.
Therelevantsystematicuncertaintiestakenintoaccountinthe estimation of potential signals include those associated with
τ
hidentification and energyscale, pmiss
T , trigger, pile-up simulation,
andintegratedluminosity. Theuncertainty inthe signal K factor
arisesfromthechoicesofPDFand
α
S.Thecombineduncertaintyis evaluated using the PDF4LHC prescription,where in the com-putation of each PDF set, the strong couplingconstant isvaried. Uncertaintiesfromdifferent PDFsets and
α
S variation are addedinquadrature.
8. Results
Thetransversemassdistribution inFig. 3showsnosignificant deviationsfromtheexpectedSMbackground.Signaleventsare ex-pected to be particularlyprominent atthe upper end of themT
distribution, where the expected SM background is low. The ex-pected andmeasured yields are summarized inTable 1 together withthedetailedsystematicuncertaintiesdescribedinSection7.
8.1. Statisticalanalysis
Upperlimitsontheproductoftheproductioncrosssectionand branchingfraction,
σ
(pp
→
W)
B(
W→
τ ν
),
aredeterminedusing aBayesianmethod [60,61] withauniformpositiveprior probabil-ity densityfor the signal cross section (known to have excellent frequentistpropertieswhenusedasatechnicaldevicefor generat-ing frequentistupperlimits).Alllimitspresentedhereareat95% confidencelevel(CL).Thenuisanceparametersassociatedwiththe systematicuncertaintiesaremodeledthroughlog-normal distribu-tions foruncertainties in the normalization. Uncertainties in the shapeofthedistributionsaremodeledthrough“template morph-ing” techniques [62]. The limitsare obtained fromthe entiremTspectrumformT
>
320GeV,asdisplayed inFig.3.Thisprocedureis performedfordifferentvaluesof parameters ofeach signal, to obtainlimitsintermsontheseparameters,suchastheW boson mass.
Table 1
Expectedyieldsfor thesignalandbackgroundeventscomparedtothemeasured event yieldsindata,forthreeregionsofmT.Alsoshownarethetotalsystematicuncertaintiesin
theestimateoftheeventnumbers.
Range of mT mT<0.5 TeV 0.5<mT<1 TeV mT>1 TeV
W+jets 786 ± 110 355 ± 68 21.8 ± 6.2 Z→νν+jets 238 ± 120 68 ± 35 0.9 ± 0.5 Multijet 68 ± 35 18 ± 10 <0.1 tt 68 ± 15 14.5 ± 4.5 <0.1 Z→ +jets 35.8 ± 8.7 10.4 ± 5.1 <0.1 Diboson (WW, WZ, Z Z) 24.9 ± 6.4 9.6 ± 3.5 0.7 ± 0.1 Single top quark 21.5 ± 6.5 7.0 ± 2.9 <0.1 Total background 1243 ± 160 485 ± 77 23.4 ± 6.2 SSM WM=600 GeV 28229 ± 4388 14012 ± 2798 45.6 ± 7.7 SSM WM=1 TeV 3767 ± 590 10079 ± 1581 355 ± 98 SSM WM=4 TeV 0.7 ± 0.1 3.0 ± 1.8 11.4 ± 3.9
Fig. 5. Expected(blackdashedline)andobserved(blacksolidline)95%CL upper limitsonthecrosssectionfortheproductionofSSMWboson.Theshadedbands aroundtheexpectedlimitrepresenttheoneandtwostandarddeviation(s.d.) un-certaintyintervals.TheNNLOtheoreticalcrosssectionwiththecorrespondingPDF uncertaintybandisalsoshown.
To determine a model-independent upper limit on the prod-uct of the cross section and branching fraction, all events above a threshold mminT are summed. From the number of background events,signal events,andobserveddataevents,the crosssection limitcanbecalculated.Theresultinglimitcanbereinterpretedin the framework of other models witha
τ
h and pmissT in the finalstate.
8.2. ThesequentialstandardmodelW
The parameter of interest is the product of the signal cross section and the branching fraction,
σ
B(
W→
τ ν
).
The branch-ing fractionincludes allτ
lepton decay modes, to allow adirect comparisonwiththeWsearchesintheelectronandmuon chan-nels [9].The upper limit on
σ
B(
W→
τ ν
)
as a function of the SSM W boson massis shown inFig. 5. The observed limit is consis-tent withthe expected limit. The SSM W boson isexcluded for masses 0.4<
MW<
4.0TeV at 95% CL where the lower limit ismainlydeterminedbythetriggerthresholdandtheupperoneby theavailabledata.Thisresultinthe
τ
channelmaybecompared with the lower mass limit of 5.2 TeV for an SSM W boson, ob-tained from the combination of electron and muon channels [9, 10].8.3. Limitsonthecouplingstrength
Theupperlimitson thecross sectiondepend not onlyonthe massofa potentialexcess,butalsoon thewidth. Becauseofthe relationbetweenthecoupling ofaparticle anditswidth, a limit canalsobesetonthecouplingstrength.Inordertocomputethe limitforcouplings gW
/
gW=
1,reweightedsamplesareusedthattakeintoaccounttheappropriatesignalwidthandthedifferences in reconstructed mT shapes. For gW
/
gW=
1 the theoretical LOcross sectionsapply. Fora givenmass, the crosssection limit as afunctionofthecouplingstrength gW
/
gW isdetermined.ForeachsimulatedW bosonmass,theexcluded crosssection isdeterminedfromtheintersectionofthetheoreticalcrosssection curve withthe observed cross section limit. The resulting inter-section pointsprovide theinput forthe exclusionlimitin a two-dimensionalplanemadeofgW
/
gW andMW,asdepictedinFig.6.Fig. 6. Expected(blackdashedline)andobserved(blacksolidline)95%CL upper limits on the ratioofcouplings as afunction ofthe W bosonmass. The val-uesabovetheobservedlimitcontourareexcluded.Theshadedbandsaroundthe expectedlimitrepresenttheoneandtwostandarddeviation(s.d.)uncertainty in-tervals.
Thephasespaceabovetheobservedlimitcontourisexcluded.For lowmasses, gW
/
gW valuesdownto7×
10−2 areexcluded.8.4. Thenonuniversalgaugeinteractionmodellimits
In the NUGIM G(221) framework, the ratio of the couplings
gW
/
gW is related to the parameter cotθ
E through Eq. (1). Thuscot
θ
EcanbeextractedforeachvalueofgW/
gW.Basedonthelim-itsoncouplingstrengthspresentedinFig.6,thetwo-dimensional limitoncotθEisshownasafunctionoftheWbosonmass.Fig.7
(left) shows the width of the W boson as a function of cotθE
and MW. For cotθE
>
6.5, the width becomes so large that themodelisnolongervalid.Thelimit,showninFig.7(right),focuses on theparameter spacecot
θ
E≥
1 where theτ
hchannel sets themoststringentbounds, asillustratedinFig.2.Forlowervaluesof cot
θ
E,other channelsare moresensitive.Dependingonthevalueofcot
θ
E,themassoftheW bosoncanbeexcludedat95%CL upto3.9 TeV intheNUGIMG(221)framework.
8.5. Themodel-independentcrosssectionlimit
TheshapeanalysisassumesacertainsignalshapeinmT.
How-ever, alternative new physics processes yielding a
τ
h+
pmissTfi-nal state could cause an excess of a different shape. A model-independent cross section limit isdetermined usinga single bin rangingfromalowerthresholdonmT toinfinity.Noassumptions
ontheshapeofthesignalmT distributionhavetobe madeother
than that of a flatproduct of acceptancetimes efficiency, A
,as a functionofW mass.Inordertodeterminethelimit fora spe-cific model from the model-independent limit shown here, only the model-dependent part of the efficiency needs to be applied. The experimentalefficienciesforthesignalare alreadytakeninto account, includingthe effectof thekinematic selection ofevents containing
τ
h and pmissT (the selectionson pT/
pmissT andφ
),thegeometrical acceptance (selection on
η
), and the trigger thresh-old.A factor fmT that reflects the effectof the thresholdm
min T on
the signal is determinedby counting theevents withmT
>
mminTanddividingtheresultbythenumberofgeneratedevents.The re-constructionefficiencyisnearlyconstantovertheentire mTrange
Fig. 7. Left:ThewidthoftheWbosonasafunctionofMWandmixinganglecotθE intheNUGIMG(221)framework.Right:Expected(blackdashedline)andobserved
(blacksolidline)95%CL upperlimitsonthemixinganglecotθEasafunctionoftheWbosonmass.Theregionleftofthesolidlineisexcluded.Theshadedbandsrepresent
theoneandtwostandarddeviation(s.d.)uncertaintybands.
Fig. 8. Expected(blackdashedline)andobserved(blacksolidline)95%CL model-independentupperlimitsontheproductofcrosssection,branchingfraction,and acceptanceforaresonancedecayingintotheτ νchannel.Theshadedbands repre-senttheoneandtwostandarddeviation(s.d.)uncertaintybands.
probed here, therefore fmT can be evaluated at generator level.
A limitontheproductofthecrosssectionandbranchingfraction
(
σ
B
A)
excl canbeobtainedbydividingtheexcludedcrosssectionofthe model-independentlimit
(
σ
B
A)
MI given inFig. 8by thecalculatedfraction fmT
(
m min T):
(
σ
B
A)
excl=
(
σ
B
A)
MI(
mminT)
fmT(
m min T)
(3) Here,B
isthe branchingfractionofthenewparticle decayingtoτ
+
ν
.Modelswithatheoreticalcrosssection(
σ
B)
theo largerthan(
σ
B)
excl can be excluded. The procedure described here can beappliedto all models involvingthe two-bodydecayofa massive state,whichexhibit back-to-backkinematics similartothose ofa generic W.If the kinematicpropertiesare different, thefraction ofevents fmT
(
mmin
T
)
mustbedeterminedfortheparticularmodelconsidered.
Theresultingcrosssectionlimitasafunctionofmmin
T isshown
inFig.8.ThehighestmT eventindatawas foundat1.65 TeV,
af-terwhichthe limit becomes flat.The results dependstrongly on thethreshold mminT . Values of theproduct
σ
B
Abetween 50fb (mminT
>
400GeV) and 0.4fb (mminT>
2TeV) are excluded forthemmin
T thresholdsgiveninbrackets.
9. Summary
Asearchfornewphysicsinfinalstateswithahadronically de-caying
τ
leptonandmissingtransversemomentumhasbeen per-formedbytheCMSexperiment,usingproton-protoncollisiondata atthecenter-of-massenergy√
s=
13TeV withanintegrated lumi-nosityof35.9 fb−1.Nosignificantexcesscomparedtothestandard model expectation is observed in the transverse mass of theτ
andmissing transverse momentum.A sequential standard model W boson is excluded in the mass range 0.4<
MW<
4.0TeV at95% confidencelevel.Couplingsthatare weakerthan assumedin thesequentialstandardmodelcanbe excludeddowntovaluesof 7
×
10−2 for MW
=
1TeV. Within the nonuniversal gaugeinter-action SU
(2)
×
SU(2)
×
U(1)
model, the lower limit on the W bosonmassdependsonthecouplingconstantandvariesfrom1.7 to3.9 TeV at95%confidencelevel.Forcotθ
E>
1,theseresultsob-tainedinthe
τ
channelprovidethemoststringentconstraintson thismodeltodate.Inaddition,amodel-independentlimitis pro-videdallowingtheresultstobeinterpretedinothermodelsgiving thesamefinalstatewithsimilarkinematicdistributions.Acknowledgements
WecongratulateourcolleaguesintheCERNaccelerator depart-ments for the excellent performance of the LHC and thank the technicalandadministrative staffsatCERN andatother CMS in-stitutes for their contributions to the success of the CMS effort. Inaddition,wegratefullyacknowledgethecomputingcentersand personneloftheWorldwideLHCComputingGridfordeliveringso effectivelythe computinginfrastructureessential to ouranalyses. Finally, we acknowledge the enduring support for the construc-tionandoperation oftheLHC andtheCMSdetectorprovidedby thefollowingfundingagencies:BMWFWandFWF(Austria);FNRS and FWO(Belgium); CNPq,CAPES, FAPERJ, FAPERGS, and FAPESP (Brazil); MES (Bulgaria); CERN; CAS, MOST, and NSFC (China); COLCIENCIAS (Colombia); MSES andCSF (Croatia); RPF (Cyprus); SENESCYT(Ecuador);MoER,ERCIUT,andERDF(Estonia);Academy ofFinland,MEC,andHIP(Finland);CEAandCNRS/IN2P3(France); BMBF, DFG, and HGF (Germany); GSRT (Greece); NKFIA (Hun-gary);DAEandDST(India);IPM(Iran);SFI(Ireland);INFN(Italy); MSIPandNRF (RepublicofKorea); MES(Latvia);LAS (Lithuania); MOE and UM (Malaysia); BUAP, CINVESTAV, CONACYT, LNS, SEP, andUASLP-FAI(Mexico);MOS(Montenegro);MBIE(NewZealand); PAEC (Pakistan); MSHE and NSC (Poland); FCT (Portugal); JINR (Dubna);MON,ROSATOM,RAS,RFBR,andNRCKI(Russia);MESTD (Serbia);SEIDI,CPAN,PCTI,andFEDER(Spain);MoSTR (SriLanka);
Swiss Funding Agencies (Switzerland); MST (Taipei); ThEPCenter, IPST, STAR, and NSTDA (Thailand); TÜBITAK and TAEK (Turkey); NASU andSFFR(Ukraine); STFC (United Kingdom);DOE andNSF (USA).
Individuals have received support from the Marie-Curie pro-gramme and the European Research Council and Horizon 2020 Grant,contract No. 675440 (EuropeanUnion);theLeventis Foun-dation;the Alfred P. Sloan Foundation; the Alexander von Hum-boldt Foundation; the Belgian Federal Science Policy Office; the Fonds pour la Formation à la Recherche dans l’Industrie etdans l’Agriculture (FRIA-Belgium); the Agentschapvoor Innovatie door Wetenschap en Technologie (IWT-Belgium); the F.R.S.-FNRS and FWO (Belgium) under the “Excellence of Science - EOS” - be.h projectn.30820817; theMinistryofEducation,Youth andSports (MEYS) of the Czech Republic; the Lendület (“Momentum”) Pro-gramme and the János Bolyai Research Scholarship of the Hun-garian Academy of Sciences, the New National Excellence Pro-gram ÚNKP, the NKFIA research grants 123842, 123959, 124845, 124850 and 125105 (Hungary); the Council of Science and In-dustrial Research, India; the HOMING PLUS programme of the Foundation for Polish Science, cofinanced from European Union, Regional DevelopmentFund, theMobility Plusprogrammeofthe Ministry of Science and Higher Education, the National Science Centre (Poland), contractsHarmonia 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 EstataldeFomento delaInvestigación CientíficayTécnica de Ex-celencia María de Maeztu, grant MDM-2015-0509 and the Pro-grama Severo Ochoa del Principado de Asturias; the Thalis and Aristeia programmes cofinanced by EU-ESF andthe Greek NSRF; theRachadapisekSompotFundforPostdoctoralFellowship, Chula-longkornUniversityandtheChulalongkornAcademicintoIts 2nd CenturyProjectAdvancement Project(Thailand);theWelch Foun-dation,contractC-1845;andtheWestonHavensFoundation(USA).
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InstituteforNuclearProblems,Minsk,Belarus
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D. Di Croce,
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UniversiteitAntwerpen,Antwerpen,Belgium
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UniversitéLibredeBruxelles,Bruxelles,Belgium
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M. Kovac
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UniversityofCyprus,Nicosia,Cyprus
M. Finger
8,
M. Finger Jr.
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E. Ayala
EscuelaPolitecnicaNacional,Quito,Ecuador
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NationalInstituteofChemicalPhysicsandBiophysics,Tallinn,Estonia
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DepartmentofPhysics,UniversityofHelsinki,Helsinki,Finland
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UniversitédeLyon,UniversitéClaudeBernardLyon1,CNRS-IN2P3,InstitutdePhysiqueNucléairedeLyon,Villeurbanne,France
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8GeorgianTechnicalUniversity,Tbilisi,Georgia
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UniversityofHamburg,Hamburg,Germany