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DOI: 10.1016/j.physletb.2014.06.076
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©2014
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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http://www.repositorio.unicamp.br
Contents lists available atScienceDirect
Physics
Letters
B
www.elsevier.com/locate/physletbMeasurement
of
the
ratio
B
(
t
→
Wb
)/
B
(
t
→
Wq
)
in
pp
collisions
at
√
s
=
8 TeV
.
CMS
Collaboration
CERN,Switzerland
a
r
t
i
c
l
e
i
n
f
o
a
b
s
t
r
a
c
t
Articlehistory: Received8April2014Receivedinrevisedform5June2014 Accepted29June2014
Availableonline3July2014 Editor: M.Doser Keywords: CMS Top CKM Width
The ratio of the top-quark branching fractions R=B(t→Wb)/B(t→Wq),where the denominator includesthesumoveralldown-typequarks(q=b,s,d),ismeasuredinthet¯t dileptonfinalstatewith proton–protoncollisiondataat√s=8 TeV fromanintegratedluminosityof19.7 fb−1,collectedwiththe
CMSdetector.Inordertoquantifythepurityofthesignalsample,thecrosssectionismeasuredbyfitting theobservedjetmultiplicity,therebyconstrainingthesignalandbackgroundcontributions.Bycounting thenumber ofbjetsperevent,anunconstrained valueofR=1.014±0.003(stat.)±0.032(syst.) is measured,inagoodagreementwithcurrentprecisionmeasurementsinelectroweakandflavoursectors. AlowerlimitR>0.955 atthe95%confidencelevelisobtainedafterrequiringR≤1,andalowerlimit onthe Cabibbo–Kobayashi–Maskawamatrix element|Vtb|>0.975 isset at95% confidencelevel. The
resultiscombinedwithapreviousCMSmeasurementofthet-channelsingle-top-quarkcrosssectionto determinethetop-quarktotaldecaywidth,Γt=1.36±0.02(stat.)+−00..1411 (syst.) GeV.
©2014TheAuthors.PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense (http://creativecommons.org/licenses/by/3.0/).FundedbySCOAP3.
1. Introduction
Because of its large mass [1], the top quark decays before fragmentingor forminga hadronic bound state [2].According to thestandard model (SM), thetop quark decaysthrough an elec-troweak interaction almost exclusively to an on-shell W boson andab quark. Themagnitudeofthetop–bottom chargedcurrent is proportional to
|
Vtb|
, an element of the Cabibbo–Kobayashi–Maskawa(CKM)matrix.Undertheassumptionthatthe CKM ma-trixisunitaryandgiventhemeasuredvaluesforVubandVcb(or
Vts and Vtd),
|
Vtb|
isexpectedtobe closetounityanddominateover the off-diagonal elements, i.e.
|
Vtb|
|
Vts|,
|
Vtd|
. Thus, thedecaymodesofthetopquarktolighterdown-typequarks(d or s) are allowed, but highly suppressed. The indirect measurement of
|
Vtb|
,fromtheunitarityconstraintoftheCKMmatrix,is|
Vtb|
=
0
.
999146+−00..000046000021 [3].Any deviationfromthisvalueorinthe par-tialdecaywidthofthetopquarktob quarks,wouldindicatenew physics contributions such as those from new heavy up- and/or down-typequarksora chargedHiggs boson,amongst others [4]. DirectsearchesattheLargeHadronCollider(LHC)havesetlower limitsonthemassofthesehypotheticalnewparticles[5–15],and the observation of a SM Higgs boson candidate [16–18] places stringentconstraintson theexistence ofa fourth sequential gen-eration of quarks. These results support the validity of both theE-mailaddress:cms-publication-committee-chair@cern.ch.
unitarityhypothesisandthe3
×
3 structureoftheCKMmatrixfor theenergy scaleprobed bythe LHCexperiments.However, other newphysicscontributions,includingthosedescribedabove,could invalidatetheboundsestablishedsofaron|
Vtb|
[3].In this Letter, we present a measurement of
R
=
B(
t→
Wb)/B(
t→
Wq)
, wherethe denominator includes the sum over the branching fractions of the top quark to a W boson and a down-type quark (q=
b,
s,
d). Under the assumption of the uni-tarity of the 3×
3 CKM matrix,R
= |
Vtb|
2, and thus toindi-rectly measure
|
Vtb|
. In addition, the combination of adetermi-nation of
R
andameasurementofthet-channelsingle-topcross section can provide an indirect measurement of the top-quark width (Γ
t) [19]. The most recent measurement ofΓ
t based onthis approach [20] is found to be compatible with the SM pre-dictions with a relative uncertainty of approximately 22%. The value of
R
has been measured at the Tevatron, and the most precise result is obtained by the D0 Collaboration, whereR
=
0.
90±
0.
04(
stat.+
syst.)
[21] indicates a tension with the SM prediction.Thistensionisenhancedforthemeasurementinthet¯
t dilepton decaychannel, whereboth W bosonsdecayleptonically andR
=
0.
86−+00..041042(stat.)±
0.
035 (syst.) isobtained.Themost re-centmeasurementsbytheCDFCollaborationaregivenin[22,23].Owing toits purity, the t
¯
t dilepton channel is chosen forthis measurement.Events are selectedfromthe datasample acquired in proton–protoncollisions at√
s=
8 TeV bythe Compact Muon Solenoid(CMS)experimentattheLHCduring2012.Theintegrated luminosity of the analysed data sample is 19.
7±
0.
5 fb−1 [24]. http://dx.doi.org/10.1016/j.physletb.2014.06.0760370-2693/©2014TheAuthors.PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense(http://creativecommons.org/licenses/by/3.0/).Fundedby SCOAP3.
The selected eventsare used to measure the t
¯
t production cross section by fitting the observed jet multiplicity distribution, con-straining the signal and background contributions. The b-quark contentoftheeventsisinferredfromthedistributionofthe num-ber of b-tagged jets per event as a function of jet multiplicity foreach of thedilepton channels. Data-based strategiesare used toconstrainthe mainbackgroundsandthecontributionsofextra jetsfrom gluon radiation in t¯
t events. TheR
value is measured by fittingthe observedb-tagged jet distributionwith a paramet-ric modelthat dependson theobserved cross section,correcting forthe fractionofjets that cannot be matchedto a t→
Wq de-cay.Themodelalsodependsontheefficiencyforidentifyingb jets anddiscriminatingthem fromother jets.Lastly,themeasurement ofR
iscombined witha previously published CMSresultofthet-channelproductioncrosssectionofsingletopquarksinpp colli-sions[25]toyieldanindirectdeterminationofthetop-quarktotal decaywidth.
2. TheCMSdetector
The central feature ofthe Compact Muon Solenoid (CMS) ap-paratus is a superconducting solenoid of 6 m internal diame-ter, providing a magnetic field of 3.8 T. Within the supercon-ducting solenoid volume are a silicon pixel and strip tracker, a leadtungstatecrystalelectromagneticcalorimeter(ECAL), anda brass/scintillator hadron calorimeter(HCAL), each composed of a barrelandtwo endcapsections.Muonsare measured in gas-ion-isation detectors embedded in the steel flux-return yoke outside thesolenoid. Extensiveforwardcalorimetrycomplementsthe cov-erageprovidedbythebarrelandendcapdetectors.
Thesilicontrackermeasureschargedparticleswithinthe pseu-dorapidityrange
|
η
|
<
2.
5,wherethepseudorapidityη
isdefined asη
= −
ln[
tan(θ/
2)
]
andθ
isthepolarangleofthetrajectory of theparticlewithrespecttotheanticlockwise-beamdirection.The trackerconsistsof 1440siliconpixel and15 148 siliconstrip de-tectormodules andislocated inthefield ofthesuperconducting solenoid. It provides an impact parameter resolution of∼
15 μm and a transverse momentum (pT) resolution of about 1.5% for100 GeV particles. The electron energyis measured by the ECAL anditsdirectionis measuredby thetracker.The massresolution forZ
→
ee decaysis1.6%whenbothelectronsareintheECAL bar-rel, and2.6% when both electrons are in the ECAL endcap [26]. Matchingmuonsto tracksmeasured inthesilicontrackerresults ina pT resolutionbetween1and10%,for pT valuesupto 1 TeV.Thejetenergyresolution(JER)amountstypicallyto15%at10 GeV, 8%at100 GeV,and4%at1 TeV[27].
A more detailed description of the detector can be found in Ref.[28].
3. Simulationofsignalandbackgroundevents
The top-quark pair production cross section has been calcu-latedatnext-to-next-to-leadingorder(NNLO)and next-to-next-to-leadinglogarithmicsoftgluonterms(NNLL)[29].Inproton–proton collisions at
√
s=
8 TeV,andforatop-quarkmass of172.5 GeV, the expected cross section isσ
NNLO+NNLL(
t¯
t)
=
253+−68 (scale)±
6 (PDF) pb, where the first uncertainty is from the factorisation and renormalisation scales, and the second is from the parton distribution functions (PDFs). Signal events are simulated for a top-quarkmass of172.5 GeV with theleading-order (LO) Monte Carlo(MC)generator MadGraph (v5.1.3.30)[30]matchedto pythia (v6.426)[31],where the
τ
lepton decays are simulatedwiththe tauola package (v27.121.5) [32]. The CTEQ6L1 PDF set is used in the event generation [33]. Matrix elements describing up to three partons, andincluding b quarks, in addition to the t¯
t pairare includedin thegenerator usedto producethesimulated sig-nal samples. An alternative simulation at next-to-leading order (NLO) basedon powheg (v1.0,r1380)[34–36],usingtheCTEQ6M PDF set [33] andinterfaced with pythia, is used to evaluate the signal description uncertainty. Acorrection to thesimulated top-quark pT is applied, based on the approximate NNLO
computa-tion [37]: the events are reweighted at the generator level to matchthetop-quarkpTprediction,andthefulldifferencebetween
the reweighted andunweighted simulationsis assignedasa sys-tematicuncertainty.
Themostrelevantbackgroundprocessesforthedilepton chan-nel arefromtheproductionoftwo genuineisolated leptonswith large pT.This includesDrell–Yan(DY) productionofcharged
lep-tons, i.e.froma Z
/
γ
∗ decay,which is modelledwith MadGraph fordileptoninvariant massesabove 10 GeV,andisnormalised to aNNLOcrosssectionof4.393 nb,computedusing fewz[38].The Z+
γ
processisalsosimulatedwith MadGraph andnormalised to the LOpredictedcrosssection of123.9 pb. Single-top-quark pro-cesses aremodelledatNLO with powheg[39,40]andnormalised tocrosssectionsof22±
2 pb, 86±
3 pb,and5.
6±
0.
2 pb forthe tW,t-,ands-channelproduction,respectively[37].Thetheory un-certainties are dueto the variation ofthe PDFs andfactorisation and renormalisationscales. Diboson processes are modelledwith MadGraph and normalised to the NLO cross section computed with mcfm [41].ThegenerationofWW,WZ,andZZ pairsis nor-malisedtoinclusivecrosssectionsof54.8 pb,33.2 pb,and17.7 pb, respectively. For WZ and ZZ pairs a minimum dilepton invari-ant massof12 GeVisrequired.AssociatedproductionofW orZ bosonswitht¯
t pairsismodelledwith MadGraph,andnormalised to the LO cross sections of 232 fb and208 fb, respectively. The productionofa W bosonin associationwithjets, whichincludes misreconstructedandnon-promptleptons,ismodelledwith Mad-Graphandnormalisedtoatotalcrosssectionof36.3 nbcomputed with fewz. Multijet processes are also studied in simulation but arefoundtoyieldnegligiblecontributionstotheselectedsample.A detector simulation based on Geant4 (v.9.4p03) [42,43] is applied after the generator step for both signal and background samples.Thepresenceofmultipleinteractions(pileup)per bunch crossingisincorporatedbysimulatingadditionalinteractions(both in-time and out-of-time with the collision) with a multiplicity matchingthatobservedinthedata.Theaveragenumberofpileup eventsinthedatais21interactionsperbunchcrossing.
4. Eventselectionandbackgrounddetermination
The event selection is optimised for t
¯
t dilepton final states that contain two isolated oppositely charged leptons(electrons or muons), missingtransverse energy (EmissT ) definedbelow, and at least two jets. Events in which the electrons or muons are fromintermediate
τ
leptondecaysareconsideredassignalevents. Dilepton triggers are used to acquire the data samples, where a minimumtransverse momentumof8 GeVisrequiredforeachof theleptons,and17 GeVisrequiredforatleastoneoftheleptons. Electron-based triggers include additional isolation requirements, bothinthetrackerandcalorimeterdetectors.Allobjectsintheeventsarereconstructedwithaparticle-flow (PF) algorithm [44,45]. Reconstructed electron and muon candi-dates are requiredtohave pT
>
20 GeV andto bein thefiducialregion
|
η
|
≤
2.
4 of the detector. A particle-based relative isola-tion parameter iscomputed foreach lepton andcorrected onan event-by-event basis forthecontribution frompileup events.We require that the scalar sum of the pT of all particle candidatesreconstructed in an isolation cone built around the lepton’s mo-mentum vector is less than 15% (12%) of the electron (muon) transverse momentum. The isolation cone is defined using the
Table 1
Predictedandobservedeventyieldsafterthefulleventselection.Thecombinationofstatisticaluncertainties withexperimentalandtheoretical systematicuncertaintiesisreported.Non-dileptonic t¯t channels,identified usingagenerator-levelmatching,aswellasassociatedproductionwithvectorbosons(W orZ),isdesignated as“other tt”¯ andgroupedwiththeexpectedcontributionfromsingleW bosonandmultijetsproductions.The expectedcontributionfromvectorbosonpairprocessesisdesignatedas“VV”.
Source ee μμ eμ
W→ ν, multijets, other t¯t 134±91 43±10 (38±20)×10
VV 292±15 333±16 995±39
Z/γ∗→ (297±63)×10 (374±79)×10 (184±39)×10 Single top quark 526±26 583±26 1834±64 t¯t dileptons (signal) (1003±50)×10 (1104±54)×10 (349±17)×102
Total (1395±81)×10 (1574±96)×10 (400±17)×102
Data 13 723 15 596 38 892
radius R
=
(
η
)
2+ (φ)
2=
0.
4,whereη
andφ
arethedif-ferencesinpseudorapidityandazimuthalanglebetweenthe parti-clecandidate andthe lepton. Foreach eventwe require atleast two lepton candidates originating from a single primary vertex. Among the vertices identified in the event, the vertex with the largest
p2T,wherethesumrunsoverall tracksassociatedwith thevertex,ischosenastheprimaryvertex. Thetwoleptons with thehighest pT arechosen toformthedileptonpair.Same-flavourdileptonpairs(eeor
μμ
)compatiblewithZ→
decaysare re-movedbyrequiring|
MZ−
M|
>
15 GeV,whereMZistheZ bosonmass[3]andM istheinvariantmassofthedileptonsystem.For all dileptonchannels it isfurther required that M
>
12 GeV in ordertovetolow-massdilepton resonances,andthatthe leptons haveoppositeelectriccharge.Jetsare reconstructed by clustering all the PF candidates us-ingtheanti-kTalgorithm[46]withadistanceparameterof0.5.Jet
momentumisdefinedasthevectorsumofallparticlemomentain thejet,andinthesimulationitisfoundtobewithin 5to10%of thehadron-levelmomentumovertheentire pT spectrumand
de-tectoracceptance.Acorrection isapplied bysubtractingtheextra energyclusteredinjetsduetopileup,followingtheprocedure de-scribedinRefs.[47,48].Theenergiesofcharged-particlecandidates associatedwithother reconstructedprimary verticesinthe event are alsosubtracted. Jet energyscale (JES)corrections are derived fromsimulation, andare validated within-situ measurements of theenergybalanceofdijetandphoton
+
jetevents[27].Additional selectioncriteriaareappliedtoeventstoremove spuriousjet-like features originatingfrom isolated noise patterns in certain HCAL regions.In theselection oft¯
t events,atleasttwo jets, each with acorrectedtransversemomentum pT>
30 GeV and|
η
|
≤
2.
4,arerequired.The jetsmustbe separatedfromtheselectedleptons by
R
( ,
jet)
=
(
η
)
2+ (φ)
2≥
0.
3. Events with up to four jets,selectedunderthesecriteria,areused.
Themagnitudeofthevectorsumofthetransversemomentaof allparticlesreconstructedintheeventisusedastheestimatorfor the momentum imbalance inthe transverse plane, EmissT .All JES correctionsappliedtotheeventarealsopropagatedintothe EmissT
estimate.Fortheeeand
μμ
channels, EmissT>
40 GeV isrequired inordertoreduce thecontamination fromlepton pairsproduced throughtheDYmechanisminassociationwithatleasttwojets.The DY contribution to the same-flavour dilepton channels is estimatedfromthedataafterthefulleventselectionthroughthe modellingoftheangle
Θ
betweenthetwoleptons.TheΘ
dis-tributiondiscriminatesbetweenleptonsproducedinDYprocesses and leptons from the top-quark pair decay cascade. In the first caseanangular correlationis expected, whileinthe secondcase the leptons are nearly uncorrelated. The probability distribution function forΘ
is derived from data using a DY-enriched con-trol region selected after inverting the EmissT requirement of the
standard selection. Studies of simulated events indicate that the shapeofthe
Θ
distributioniswell describedwiththismethod, and that the contamination from other processes in the control region can be neglected. Compatibility testsperformed in simu-lations usingdifferent channelsandjet multiplicities are usedto estimate an intrinsic10%uncertainty inthefinal DY background. Theother sourcesofuncertaintyinthemethodarerelatedtothe simulation-based description ofthe probability distribution func-tion for theΘ
distribution fromother processes. Uncertainties areestimatedeitherbypropagatingtheuncertaintiesinpileupor JESandJER,orbytrying alternativefunctionsforthet¯
t contribu-tionwithvariedfactorisation/renormalisationscales(μ
R/
μ
F)withrespect to their nominal values given by the momentum trans-ferintheevent,matrixelement/partonshower(ME-PS)matching threshold,orgeneratorchoice(powheg vs. MadGraph).Theshapes ofkinematicdistributionsforDYandotherprocessesareusedina maximum-likelihoodfittoestimatetheamountofDYbackground in the selected sample. A total uncertainty of 21% is estimated fromthedataintherateofDYeventsforthesame-flavour chan-nels.
Forthee
μ
channel,a similarfit procedureisadoptedusinga differentvariable:thetransversemassMT=
2EmissT pT
(
1−
cosφ)
of each lepton, where
φ
is the difference in azimuthal an-gle between the lepton and the missing transverse momentum. The distribution of the sum MT is used as the distributionin the fit. In this case the probability distribution function for Z
/
γ
∗→
τ τ
→
eμ
is derived fromsimulation. The determination of the uncertainty associatedwith thismethod follows a similar prescription to that described above for the same-flavour chan-nels. Atotal uncertainty of21% isassigned tothe amount ofDY contaminationintheeμ
channel.Thesecond-largestbackgroundcontributionisfrom single-top-quark processes (in particular the tW channel) that is relevant for this measurement since the decay products of a single top quark(insteadofapair)areselected.Thecontributionofthis pro-cessisestimatedfromsimulation.Otherbackgroundprocessesare alsoestimatedfromsimulation.Uncertaintiesinthenormalisation stemmingfrominstrumentaluncertainties intheintegrated lumi-nosity,triggerandselectionefficiencies,andenergyscales,aswell asgenerator-specificuncertainties,aretakenintoaccount.
Table 1 shows the yields in the data andthose predicted for signal and background events after the full event selection. The systematicuncertainties assignedtothe predictionsofsignal and background events include the uncertainties in the JES and JER, pileupmodelling,crosssectioncalculations,integratedluminosity, and trigger and selection efficiencies. A conservative uncertainty isassignedto thepredictedyields ofmultijetandW
→
ν
back-groundeventssincethesecontributionsarefrommisidentified lep-tonsandhavebeenestimatedsolelyfromsimulation.Goodoverallagreement is observed for all three dilepton categories between theyieldsindataandthesumofexpectedyields.
5. Crosssectionmeasurement
Theselectedeventsarecategorised bythedileptonchanneland thenumberofobservedjets. Fig. 1showstheexpected composi-tionforeacheventcategory.Goodagreementisobservedbetween thedistributionsfromthedataandtheexpectations,includingthe control regions, definedas events with fewer than two ormore than four jets. The chosen categorisation not only allows one to study the contamination from initial- and final-state gluon radi-ation (ISR/FSR) in the sample, but also to constrain some of the uncertaintiesfromthedata.
The t
¯
t dilepton signal strength,μ
, definedas theratio ofthe observed to the expected signal rate, is measured from the jet multiplicitydistributionbyusingaprofilelikelihoodmethod[49]. A likelihoodis calculatedfromtheobservednumberofeventsin thek dileptonchannelsandjetmultiplicitycategoriesasL
(μ, θ )
=
kP
Nk, ˆ
Nk(μ, θ
i)
·
iρ
(θ
i),
(1)where
P
is the Poisson probability density function, Nk is thenumber of events observed in the k-th category, N
ˆ
k is the totalnumber of expected events from signal and background, and
θ
iarethenuisanceparameters,distributedaccordingtoaprobability densityfunction
ρ
.The nuisance parameters are used to modify theexpectednumberofeventsaccordingtothedifferent system-aticuncertaintysources,which includeinstrumentaleffects(such asintegratedluminosity,pileup,energyscaleandresolution, lep-tontriggerandselectionefficiencies)andsignalmodelling(μ
R/
μ
F,ME-PS scale, top-quark mass,leptonic branching fractions of the W boson)amongstothers.ThePDFuncertaintyisestimatedusing thePDF4LHCprescription[50,51].Theuncertaintyfromthechoice ofthet
¯
t signalgeneratorisestimatedbyassigning thedifference betweenthe MadGraph-based andthe powheg-basedpredictions asanextrauncertaintyinthefit.Thenuisanceparametersare as-sumed tobe unbiased anddistributed accordingto a log-normal function.Based onthelikelihood expressedinEq.(1),theprofile likelihoodratio(PLR)λ
isdefinedasλ(μ)
=
L
(μ, ˆˆ
θ )
L
(
μ, ˆ
ˆ
θ )
,
(2)wherethedenominatorhasestimators
μ
ˆ
andˆθ
thatmaximisethe likelihood,andthenumeratorhasestimatorsˆˆθ
thatmaximisethe likelihoodforthe specifiedsignal strengthμ
.Thesignal strength isobtainedaftermaximisingλ(
μ
)
inEq.(2).Thisapproachallows ustoparameterisetheeffectofthesystematicuncertaintiesinthe fit.The signal strength
μ
is determined independently in each category, i.e. for each dilepton channel and jet multiplicity. For each category, the purity of the selected sample ( ft¯t) is definedasthe fraction of “true” t
¯
t signal events in the selected sample,ft¯t
=
μ
·
Nt¯texp/
Nobs, where Nt¯texp is the number of expected t¯
tevents,and Nobs isthe totalnumberof observedevents.By
per-formingthe fitforeach category,the purityofthe sampleis ob-tained.Theresultsaresummarised inTable 2.Asexpected,thee
μ
categoryhasthehighestpurity(
≈
90%).Becauseofthe contamina-tionfromDY events,thesame-flavourchannelshavelowerpurity (≈
70%).Overall, thesignalpurityincreaseswithhigherjet multi-plicity.Asa cross-check,a fitincludingall categories, givesthe range 0
.
909<
μ
<
1.
043 atthe68%confidencelevel(CL).Thisleadstoa t¯
t productioncrosssectionofFig. 1. Theupperplotsshowtheobservedjetmultiplicityafterthefullevent se-lection,exceptfortherequirementonthenumberofjets,inthesame-flavour(top) anddifferent-flavour(bottom)channels.Theexpectationsareshownasstacked his-tograms,whilethe observeddatadistributionsarerepresentedasclosedcircles. Thepredicteddistributionsforthesimulatedt¯t andsingle-top-quarkevents corre-spondtoascenariowithR=1.Thelowerpanelsshowtheratioofthedatatothe expectations.Theshadedbandsrepresentthesystematicuncertaintyinthe deter-minationofthemainbackground(DY)andtheintegratedluminosity,andvaryfrom 31%(16%)to5%(3%)inthesame- (different-)flavour channelswhengoingfromthe 0 jetsto≥5 jetsbin.
σ
(
t¯t)
=
238±
1 (stat.)±
15 (syst.) pb,
in good agreement withNNLO
+
NNLL expectation [29] and the latestCMSmeasurement [52].Theresultisalsofoundto be con-sistentwiththeindividualresultsobtainedineacheventcategory. An extrauncertaintyis assignedintheextrapolationof thecross section tothe fullphase spacebecauseofthe dependenceoftheFig. 2. Theupperplotshowsthenumberofb-taggedjetspereventforthedifferentt¯t dileptonchannels.Foreachfinalstate,separatesubsetsareshowncorresponding toeventswithtwo,three,orfourjets.Thesimulatedt¯t andsingle-top-quarkeventscorrespondtoascenariowithR=1.Thelowerpanelshowstheratioofthedatato theexpectations.Theshadedbandsrepresenttheuncertaintyowingtothefinitesizeofthesimulationsamples,themainbackgroundcontribution(DY),andtheintegrated luminosity.
Table 2
Fractionoft¯t events( ft¯t)andrelativecontributionfromsingle-top-quarkprocesses
(kst)for variousjet multiplicitiesanddileptonchannels,asdeterminedfromthe
profilelikelihoodfit.Thetotaluncertaintyisshown. Parameter Jet multiplicity Dilepton channel ee μμ eμ ft¯t 2 0.67±0.07 0.65±0.08 0.85±0.06 3 0.79±0.06 0.78±0.07 0.90±0.07 4 0.81±0.11 0.82±0.11 0.94±0.10 kst 2 0.062±0.004 0.063±0.004 0.062±0.003 3 0.040±0.003 0.040±0.003 0.041±0.002 4 0.036±0.004 0.036±0.006 0.029±0.003
acceptanceon
μ
R/
μ
F,ME-PSthresholdchoices,andthetop-quarkmass.
Therelative single-top-quark contribution(kst), definedasthe
ratiooftheexpectednumberofsingle-top-quarkeventstothe es-timatednumberofinclusivet
¯
t events,isalsoshowninTable 2for eachcategory.Forthisdeterminationweusetheexpectednumber of single-top-quark events obtained after maximising the PLR in Eq.(2).Thecontributionduetosingle-top-quarkeventstendstobe mostsignificantinthetwo-jet category(<
7%relativetoinclusive t¯
t events).Sincetheestimateisobtainedforaspecificscenarioin whichR
=
1,anextralineardependenceofkst onR
isintroducedinordertoaccountfortheincreaseinthetW crosssectionas
|
Vtb|
becomes smaller while
|
Vtd|
and|
Vts|
become larger [4]. In thisparameterisation,themeasuredratio
|
Vtd|/|
Vts|
=
0.
211±
0.
006 isused[3],andtheuncertaintyisconsideredasanintrinsic system-aticuncertaintyinthemeasurementof
R
.6. Probingtheb-flavourcontent
Inthissectiontheb-flavourcontentoftheselectedevents(both signalandbackground)isdetermined fromthe b-taggedjet mul-tiplicitydistribution.Theprobability ofincorrectly assigning a jet
mustbe evaluated(Section6.1)inordertocorrectlyestimate the heavy-flavourcontentoftop-quarkdecays(Section6.2).
Theb-taggingalgorithmthat isused(thecombinedsecondary vertex,CSVmethoddescribedinRef.[53])isamultivariate proce-dure inwhichboth informationonthe transverseimpact param-eter withrespect to the primary vertexof the associated tracks, andthereconstructedsecondaryverticesisusedtodiscriminateb jetsfromc,light-flavour(u,d,s),andgluonjets.Theb-tagging ef-ficiency(
ε
b)ismeasured[54]usingmultijeteventswhereamuonis reconstructed inside a jet; a data-to-simulation scale factor is derived and is used to correct the predicted
ε
b value in the t¯
tdileptonsamplefromsimulation.Aftercorrection,theexpected ef-ficiencyintheselectedt
¯
t sampleis≈
84%,andtheuncertaintyin thescalefactorfromthedatais1–3%, dependingonthe kinemat-icsofthejets[54].Thesamescalefactorisappliedtotheexpected c-taggingefficiencybutwithadoubleduncertaintywithrespectto theoneassignedtob jetsowingtothefactthatnodirect measure-mentofthec-taggingefficiencyisperformed. Forjetsoriginating from the hadronisation of light-flavourjets, the misidentification efficiency(ε
q)isevaluated[53]fromso-callednegative tagsinjetsamples,whichareselectedusingtracksthat haveanegative im-pactparameterorsecondaryverticeswithanegativedecaylength. The scalar product of the jet direction with the vector pointing from the primary vertex to the point of closest approach of a trackwithnegative impactparameterhastheoppositesignofthe scalarproducttakenwithrespecttothepointofclosestapproach. The data-to-simulation correction factor for the misidentification efficiency is known with an uncertainty of about 11%, and the expectedmisidentificationefficiencyintheselectedsampleis ap-proximately12%[54].
Fig. 2showsthenumberofb-taggedjetsintheselected dilep-ton data sample, compared to the expectations from simulation. Themultiplicityisshownseparatelyforeachdileptonchanneland jet multiplicity.The expectedeventyields are correctedafter the PLR fitforthe signalstrength (describedin theprevious section)
and also incorporate the data-to-simulation scale factors for
ε
band
ε
q.Data andsimulation agreewithin 5%.The residualdiffer-encescanberelatedtothedifferentnumberofjetsselectedfrom top-quarkdecays in dataand simulation,the modellingof gluon radiation(ISR/FSR) and if
R
is differentfromunity (which is an assumptionusedinthesimulation).6.1. Jetmisassignment
Thereisa non-negligibleprobability thatatleastonejet from at
¯
t decayismissed,eitherbecauseitfallsoutsideofthedetector acceptanceoris notreconstructed, andanotherjet froma radia-tive processis chosen instead.Inthe followingdiscussion,thisis referredtoasa“misassignedjet”.Conversely,jetsthatcomefrom atop-quarkdecaywill bereferred toas“correctlyassigned”.The rateofcorrectjetassignmentsisestimatedfromthedatausinga combinationofthreedifferentcategories:•
eventswithnojetsselectedfromtop-quarkdecays,whichalso include backgroundeventswithnotopquarks;•
events withonly one jet froma top-quarkdecay, which in-cludes some t¯
t events and single-top-quark events (mainly producedthroughthetW channel);•
eventswithtwojetsproducedfromthetwotop-quarkdecays. Inorder toavoidmodel uncertainties,the numberofselected jetsfromtop-quarkdecaysisderivedfromthelepton-jet invariant-mass(M j)distribution,reconstructedbypairingeachleptonwithall selected jets. For lepton-jet pairs originating from the same top-quark decay, the endpoint of the spectrum occurs at M j
≈
M2t
−
M2W≈
153 GeV [55], where Mt (MW) is the top-quark(W boson) mass(Fig. 3, top, open histogram).The predicted dis-tribution forcorrectpairings is obtainedaftermatching the sim-ulated reconstructed jets to the b quarks from t
→
Wb at the generator level using a cone of radius R=
0.
3. The same quan-titycalculatedfora leptonfroma top-quarkdecaypairedwitha jetfromthetopantiquarkdecayandviceversa(“wrong”pairing) showsadistributionwithalongtail(Fig. 3,top,filledhistogram), which can be used as a discriminating feature. A similar tail is observed for “unmatched” pairings: either background processes withouttopquarks,orleptons matchedto otherjets. The combi-nationswith M j>
180 GeV are dominatedby incorrectly pairedjets,andthiscontrolregionisusedtonormalisethecontribution frombackground.
Inordertomodelthelepton-jet invariant-massdistributionof the misassigned jets, an empirical method is used based on the assumptionofuncorrelatedkinematics.Thevalidityofthemethod hasbeentestedusingsimulation.Foreacheventindata,the mo-mentum vectorofthe selectedlepton is“randomlyrotated” with uniform probability in the
(
cos(θ ),
φ)
phase space, and the M jis recomputed. This generates a combinatorial distribution that is used to describe the true distribution of M j for misassigned
jets. Fig. 3 (bottom)compares the data distributionwiththe two componentsof the M j spectrum, i.e.“correct assignments”from
simulationand“wrongassignments”modelledfromthedata.The background modelprovides a goodestimate of theshape ofthe spectrumofthemisassignedlepton-jetpairs.Afterfittingthe frac-tions ofthetwo components tothe data,the“misassigned” con-tributionissubtractedfromtheinclusivespectrum,andtheresult is compared to the expectedcontribution from the correctly as-signed lepton-jet pairs. The resultof this procedure is shown in theinsetofFig. 3(bottom).Thismethodisusedtodeterminethe fraction( fcorrect)ofselectedjetsfromtop-quarkdecaysintheM j
spectrum.Consequently,bymeasuring fcorrect,weestimatedirectly
Fig. 3. Thetopplot showsthecorrectandmisassignedlepton-jetinvariant-mass spectrainsimulatedt¯t dileptonevents.Bothdistributionsarenormalisedtounity. Theendpointofthespectrumforcorrectlyassignedpairsisshownbythedashed line.Inthebottomplottheobserveddataiscomparedwiththecorrect(from sim-ulation)andmisassigned(fromthedata)componentsforthelepton-jet invariant-massspectraineμeventswithexactlytwojets.Thelepton-jetmassdistributionis shownintheinset,afterthemisassignedpairsaresubtracted.
Table 3
Fractionoflepton-jetpairscorrectlyassignedintheselectedeventsestimatedfrom the dataandpredictedfromsimulation.Thelastcolumnshowsthe ratioofthe fractionmeasuredindatatothepredictionfromsimulation.Thetotaluncertainty isshown.
Dilepton channel # jets fdata
correct fcorrectMC data/MC
ee 2 0.28±0.05 0.277±0.001 1.03±0.19 3 0.22±0.07 0.223±0.001 0.99±0.29 4 0.19±0.07 0.175±0.001 1.09±0.43 μμ 2 0.28±0.06 0.276±0.001 1.00±0.21 3 0.24±0.06 0.227±0.001 1.05±0.25 4 0.20±0.07 0.181±0.001 1.08±0.37 eμ 2 0.36±0.06 0.3577±0.0007 1.01±0.16 3 0.26±0.05 0.2625±0.0007 1.00±0.18 4 0.21±0.06 0.2047±0.0008 1.00±0.27
fromthedata thenumberoftop-quarkdecaysreconstructedand selected. Noticethat fcorrect cannot belarger than 1
/
n for eventswithn jets,asitincludesthecombinatorialcontributionby defini-tion.
In Table 3 the values of fcorrect found in the data are
Fig. 4. Fractionofeventswith0,1,or2top-quarkdecaysselected,asdetermined fromthedata:thesefractions,shownfordifferenteventcategories,arelabelledα0, α1,andα2,respectively.
contamination from background events as well as the effect of missingoneortwojetsfromtop-quarkdecaysafterselection.The systematic uncertainties affecting the estimate of fcorrect can be
splitintotwosources:
•
distortion ofthe M jshape duetotheJESandJERofthere-constructedobjects[27];
•
calibrationuncertainties(derivedintheprevioussection) ow-ing tothe uncertainty intheμ
R/
μ
F scale, the simulationofgluon radiationandtheunderlyingevent,thetop-quarkmass value used in simulation, and the contributions from back-groundprocesses.
Foreachcasethefitisrepeatedwithdifferentsignalprobability distributionfunctions. The systematicuncertainty is estimatedto be 3–10%,depending on the jet multiplicity in the event, andis dominatedbytheME-PSmatchingthresholdandthe
μ
R/
μ
Fscaleuncertainties.
By combining the measured fcorrect from the data with the
fraction of tt and
¯
single-top-quark events, a parameterisation of thethree classesofevents isobtained, i.e.the numberofevents with0,1,or2selectedtop-quarkdecays.Therelativeamountsof thethreeeventclasses areparameterised by theprobabilitiesα
i,where i corresponds to the number of jets from top-quark de-cays selectedin an event.The probabilities
α
i are constrainedtoi
α
i=
1.Fig. 4summarises thevaluesofα
i obtainedforthein-dividualeventcategories, wherethedifferencesaredominatedby theeventselectionefficienciesandthebackgroundcontributionin eachcategory.
6.2.Heavy-flavourcontent
Foragivennumberofcorrectlyreconstructedandselectedjets, theexpectedb-taggedjet multiplicitycanbemodelledasa func-tionof
R
and theb-tagging andmisidentificationefficiencies. In the parameterisation, we distinguish events containing jetsfrom 0,1,or2top-quarkdecays.Themodelisanextension oftheone proposedinRef. [56].Forillustration, themostsignificantcaseis considered,i.e.modellingtheobservationoftwo b-taggedjetsin aneventwithtworeconstructedjets.Forthecasewheretwojets fromtop-quarkdecaysareselectedintheevent,theprobabilityto observetwob-taggedjetscanbewrittenasP2j,2t,2d
=
R
2ε
2b+
2R
(
1−
R
)ε
bε
q+ (
1−
R
)
2ε
q2,
(3)wherethesubscripts(2j,2t,2d)indicateatwo-jetevent,withtwo b-tagged jets, and two top-quark decays.If instead, only one jet fromatop-quarkdecayispresentintheevent, theprobability is modified totake thesecondjet intoaccountinthemeasurement of
R
. Inthiscase, theprobability ofobserving two b-taggedjets isP2j,2t,1d
=
R
2ε
bε
q∗+
R
(
1−
R
)(ε
b+
ε
q)ε
q∗+ (1
−
R
)
2ε
qε
q∗,
(4)where
ε
q∗ istheeffectivemisidentificationrate, andiscomputed by taking into account the expected flavour composition of the “extra”jetsintheevents(i.e.thosenotmatchedtoatop-quark de-cay). Theeffectivemisidentificationrateisderived specificallyfor eacheventcategory.Fromsimulation,theseextrajetsareexpected to comemostly fromlight-flavourjets(≈
87%). For completeness, forthecaseinwhichnojetfromtop-quarkdecayisreconstructed, theprobabilityofobservingtwob-taggedjetsisP2j,2t,0d
=
ε
2q∗.
(5)For each dilepton channel and jet multiplicity, analogous ex-pressions are derived and combined using the probabilities
α
iof having i reconstructed jetsfrom top-quark decays. Additional terms are added to extend the modelto events with morethan two jets. All efficiencies are determinedper event category, after convolvingthe correctionsfromdijeteventsinthedata withthe expected efficiencies (
ε
q andε
b) andthe simulated jet pTspec-trum.
For the measurement of
R
, a binned-likelihood function is constructed using the model described above and the observed b-taggingmultiplicity ineventswithtwo, three,orfourobserved jets in the different dilepton channels. A total of 36event cate-gories, corresponding to different permutations of three lepton-flavour pairs, three jet multiplicities, and up to four observed b-tagged jets are used (see Fig. 2). The likelihood is generically writtenasL
(
R
,
ft¯t,
kst,
fcorrect,
ε
b,
ε
q,
ε
q∗, θ
i)
=
Njets=2...4 Njets k=0P
N ,evNjets(
k), ˆ
N ,Njets ev(
k)
i
G
θ
i0, θ
i,
1,
(6) where N ,evNjets (Nˆ
,Njetsev ) is the number of observed (expected)
events with k b-tagged jets in a given dilepton channel (
=
ee
,
μμ
,
eμ
) with a given jet multiplicity (Njets),θ
i are thenui-sance parameters (a total of 33, which will be discussed later), and
G
isaGaussiandistribution.Forthenominalfit,thenuisance parameters are assumed to be unbiased (θ
i0=
0) and normally distributed. The nuisance parameters parameterise the effect of uncertainties,such asJESandJER,b-taggingandmisidentification rates,andμ
R/
μ
Fscales,amongst others,ontheinputparametersof the likelihood function. The mostlikely value for
R
is found after profilingthe likelihood usingthe same technique described in Section 5. The result of the fit is verified to be unbiased in simulation,byperformingpseudo-experimentswithdedicatedMC sampleswhereR
isvariedinthe[
0,
1]
interval.Theresidual dif-ference found fromthesetestsis assignedasamodelcalibration uncertainty.6.3. Measurementof
R
In the fit,
R
is allowed to vary without constraints. The pa-rametersofthemodelarealltakenfromthedata: ft¯t andkst areFig. 5. Expectedeventfractionsofdifferentb-taggedjetmultiplicitiesindilepton eventsasafunctionofR.
Fig. 6. Variationofthelogoftheprofilelikelihoodratio(λ)usedtoextractRfrom thedata.Thevariationsobservedinthecombinedfitandintheexclusiveee,μμ, andeμchannels,areshown.Theinsetshowstheinclusiveb-taggedjetmultiplicity distributionandthefitdistribution.
takenfromTable 2, fcorrect istakenfromTable 3,
ε
b andε
q fromdijet-based measurements [53],and
ε
q∗ is derived following themethoddescribed intheprevioussection.Fig. 5showsthe result-ingpredictionforthefractionofeventswithdifferentnumbersof observedb-tagged jetsasa functionof
R
.The individual predic-tionsforallcategoriesaresummedtobuildtheinclusivemodelfor theobservationofuptofourb-taggedjetsintheselectedevents.Fig. 6 shows the results obtained by maximising the profile likelihood. The combined measurement of
R
givesR
=
1.
014±
0.
003(stat.)±
0.
032 (syst.),ingood agreementwiththeSM pre-diction. Fits to the individual channels give consistent results. For these, we obtain values ofR
ee=
0.
997±
0.
007 (stat.)±
0
.
035 (syst.),R
μμ=
0.
996±
0.
007 (stat.)±
0.
034 (syst.), andR
eμ=
1.
015±
0.
003 (stat.)±
0.
031 (syst.) for the ee,μμ
, ande
μ
channels, respectively. The measurement in the eμ
channel dominatesinthefinalcombinationsincethemainsystematic un-certainties are fully correlated and this channel has the lowest statisticaluncertainty.Thetotalrelativeuncertaintyinthemeasurementof
R
is3.2%, andisdominatedbythesystematicuncertainty,whoseindividual contributionsare summarised inTable 4.Thelargest contributionTable 4
SummaryofthesystematicuncertaintiesaffectingthemeasurementofR.The val-uesoftheuncertaintiesarerelativetothevalueofRobtainedfromthefit.
Source Uncertainty (%) Experimental uncertainties: εb 2.4 εq 0.4 ft¯t 0.1 DY 0.2 misidentified lepton 0.1 JER 0.5 JES 0.5 unclustered Emiss T 0.5 integrated luminosity 0.2 pileup 0.5 simulation statistics 0.5 fcorrect 0.5 model calibration 0.2 selection efficiency 0.1 Theoretical uncertainties: top-quark mass 0.9 top-quark pT 0.5 ME-PS 0.5 μR/μF 0.5 signal generator 0.5 underlying event 0.1 colour reconnection 0.1 hadronisation 0.5 PDF 0.1 t→Wq flavour 0.4 |Vtd|/|Vts| <0.01
relative single-top-quark fraction (tW) 0.1 VV (theoretical cross section) 0.1 extra sources of heavy flavour 0.4
Total systematic 3.2
tothesystematicuncertaintyisfromtheb-taggingefficiency mea-surement. Additionalsourcesofuncertaintyarerelatedtothe de-termination ofthe purity of thesample ( ft¯t) and the fractionof correct assignments ( fcorrect) from the data; thesequantities are
affected by theoretical uncertainties relatedto the description of t
¯
t events, which have similar impact on the final measurement, suchasμ
R/
μ
F,ME-PS,signalgenerator,top-quarkmass,andtop-quark pT.Instrumental contributionsfromJESandJER,modelling
oftheunclusteredEmiss
T componentinsimulation,andthe
contri-butionfromtheDYandmisidentified-leptonbackgroundsareeach estimated to contribute a relative systematic uncertainty
<
0.6%. Anothersourceofuncertaintyisduetothecontributionfrom ex-tra sources of heavy-flavour production,either fromgluon split-tinginradiatedjetsorfromdecaysinbackgroundeventssuchas W→
c¯
s.Thiseffecthasbeenestimatedinthecomputationofε
q∗by assigning a conservative uncertainty of 100% to the c and b contributions.Theeffectoftheuncertaintyinthemisidentification efficiencyisestimatedtobesmall(
<
1%),aswellasothersources ofuncertainty,suchaspileupandintegratedluminosity.Afterthe fit isperformedno nuisanceparameter isobservedto changeby morethan 1.
5σ
.The mostrelevantsystematicuncertainty(ε
b) ismovedby
∼
0.
5σ
asaresultofthefit.If the three-generationCKM matrix is assumedto be unitary, then
R
= |
Vtb|
2[4].Byperformingthefitintermsof|
Vtb|
,avalueof
|
Vtb|
=
1.
007±
0.
016(
stat.+
syst.)
ismeasured.Upperandlowerendpointsofthe95%CLintervalfor
R
areextractedbyusingthe Feldman–Cousins(FC)frequentistapproach[57].The implementa-tion of the FC methodin RooStats [58] is used to compute the interval.Allthenuisanceparameters(includingε
b)areprofiledinordertotakeintoaccountthecorrespondinguncertainties (statis-ticalandsystematic).Ifthecondition
R
≤
1 isimposed,weobtainFig. 7. Expectedlimitbandsatdifferentconfidencelevelsasafunctionofthe mea-suredRvalue.TherangeofmeasuredvaluesofRthatareallowedforeachtrue valueofRis shownascolouredbandsfordifferentconfidencelevels.Theobserved valueofRisshownasthedashedline.
bands for 68% CL, 95% CL, and 99.7% CL, obtained from the FC method.Theexpectedlimitbandsaredeterminedfromthe distri-butionof the profilelikelihood obtainedfrom simulated pseudo-experiments.Theupperandloweracceptanceregionsconstructed in this procedure are used to determine the endpoints on the allowed interval for
R
. In the pseudo-experiments the expected signalandbackgroundyields are variedusing Poissonprobability distributions for the statistical uncertainties and Gaussian distri-butionsforthesystematicuncertainties.Byconstraining|
Vtb|
≤
1,a similarprocedureisusedtoobtain
|
Vtb|
>
0.
975 atthe95% CL.6.4.Indirectmeasurementofthetop-quarktotaldecaywidth
The result obtained for
R
can be combined with a mea-surementofthe single-top-quark production crosssection in thet-channeltoyieldanindirectdeterminationofthetop-quarktotal width
Γ
t.AssumingthatqB(
t→
Wq)
=
1,thenR
=
B(
t→
Wb)
and
Γ
t=
σ
t-ch.B
(
t→
Wb)
·
Γ (
t→
Wb)
σ
theor. t-ch.,
(7)where
σ
t-ch. (σ
ttheor-ch..) is the measured (theoretical) t-channel single-top-quark cross section andΓ (
t→
Wb)
is the top-quark partial decay width to Wb. If we assume a top-quark mass of 172.5 GeV,thenthetheoreticalpartialwidthofthetopquark de-cayingtoWbisΓ (
t→
Wb)
=
1.
329 GeV[3].Afittotheb-tagged jetmultiplicity distributioninthedataisperformed,leavingΓ
t asa free parameter. Inthe likelihood function we use the theoreti-calpredictionforthe t-channelcrosssection at
√
s=
7 TeV from Ref.[59]andthecorrespondingCMSmeasurementfromRef.[25]. The uncertainties in the predicted and measured cross sections are taken into account as extra nuisance parameters in the fit. The uncertainty in the theoretical cross section is parameterised by convolving a Gaussian function for the PDF uncertainty with a uniform prior describing the factorisation and renormalisation scale uncertainties. Some uncertainties in the experimental cross sectionmeasurementsuchasthosefromJESandJER,b-tagging ef-ficiency,μ
R/
μ
F scales,andME-PSthresholdfort¯
t productionarefullycorrelatedwiththeonesassignedtothemeasurementof
R
. All othersare summed in quadratureand assumedto be uncor-related.Afterperformingthemaximum-likelihoodfit,wemeasureTable 5
SummaryofthesystematicuncertaintiesinthemeasurementofΓt.Thevaluesof
theuncertaintiesarerelativetothevalueofΓtobtainedfromthefit.The“other
sources”categorycombinesalltheindividualcontributionsbelow0.5%.
Source Uncertainty (%)
Single-top quark t-channel cross section 9.2
εb 4.3 JES 0.7 pileup 0.8 ME-PS 0.8 μR/μF 0.8 top-quark mass 0.6 other sources 1.5 Total systematic 10.4
Γ
t=
1.
36±
0.
02 (stat.)−+00..1411 (syst.) GeV, in good agreement withthe theoretical expectation[3]. The dominant uncertainty comes from the measurement of the t-channel cross section, as sum-marised inTable 5.
7. Summary
A measurement of the ratio ofthe top-quark branching frac-tions
R
=
B(
t→
Wb)/B(
t→
Wq)
, where the denominator in-cludesthesumoverthebranchingfractionsofthetopquarktoa W bosonandadown-typequark(q=
b,
s,
d),hasbeenperformed using a sample of t¯
t dilepton events. The sample has been se-lected fromproton–proton collision data at√
s=
8 TeV from an integrated luminosity of 19.7 fb−1, collected with the CMSde-tector.The b-taggingandmisidentificationefficienciesarederived from multijet control samples. The fractions of events with0, 1, or 2 selected jets from top-quark decays are determined using the lepton-jet invariant-mass spectrum and an empirical model forthe misassignment contribution.The unconstrained measured value of
R
=
1.
014±
0.
003 (stat.)±
0.
032 (syst.) is consistent with the SM prediction, and the main systematic uncertainty is fromthe b-tagging efficiency(≈
2.4%). All other uncertainties are<
1%.A lower limit ofR
>
0.
955 at 95% CLis obtainedafter re-quiringR
≤
1 and taking into account both statistical and sys-tematical uncertainties. This result translates into a lower limit|
Vtb|
>
0.
975 at95%CLwhenassumingtheunitarityofthethree-generationCKM matrix.Bycombiningthisresultwithaprevious CMS measurement of the t-channel production cross section for single topquarks,anindirectmeasurementofthetop-quarktotal decay width
Γ
t=
1.
36±
0.
02 (stat.)+−00..1411 (syst.) GeV is obtained,inagreementwiththeSM expectation.Thesemeasurementsof
R
andΓ
t arethe mostprecise todateandthe firstobtainedattheLHC.
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,wegratefullyacknowledgethecomputingcentresand personneloftheWorldwideLHCComputingGridfordeliveringso effectivelythe computinginfrastructureessential to ouranalyses. Finally, we acknowledge the enduring support for the construc-tionandoperation oftheLHC andtheCMSdetectorprovidedby thefollowingfundingagencies:BMWFWandFWF(Austria);Fonds De La Recherche Scientifique - FNRS andFWO (Belgium); CNPq, CAPES, FAPERJ, and FAPESP (Brazil); MES (Bulgaria); CERN; CAS, MOST,andNSFC(China);COLCIENCIAS(Colombia);MSESandCSF (Croatia);RPF (Cyprus);MoER,SF0690030s09andERDF(Estonia);
AcademyofFinland,MEC,andHIP(Finland);CEAandCNRS/IN2P3 (France); BMBF, DFG, and HGF (Germany); GSRT (Greece); OTKA and NIH (Hungary); DAE and DST (India); IPM (Iran); SFI (Ire-land);INFN(Italy);NRFandWCU(RepublicofKorea);LAS (Lithua-nia); MOE and UM (Malaysia); CINVESTAV, CONACYT, SEP, and UASLP-FAI (Mexico);MBIE(New Zealand);PAEC(Pakistan);MSHE andNSC (Poland);FCT (Portugal); JINR (Dubna); MON, RosAtom, RASandRFBR(Russia); MESTD(Serbia); SEIDI andCPAN(Spain); Swiss Funding Agencies (Switzerland); MST (Taipei); ThEPCenter, IPST, STAR and NSTDA (Thailand); TUBITAK and TAEK (Turkey); NASU andSFFR(Ukraine); STFC (United Kingdom);DOE andNSF (USA).
Individuals have received support from the Marie-Curie pro-grammeandthe European ResearchCouncil andEPLANET (Euro-peanUnion);theLeventisFoundation;theAlfredP.Sloan Founda-tion; the Alexander von Humboldt Foundation; the Belgian Fed-eral Science Policy Office; the Fonds pour la Formation à la Recherchedansl’Industrieetdansl’Agriculture(FRIA-Belgium);the AgentschapvoorInnovatiedoorWetenschapenTechnologie (IWT-Belgium);the Ministry ofEducation,Youth andSports (MEYS) of Czech Republic; the Council of Science and Industrial Research, India; the Compagnia di San Paolo (Torino); the HOMING PLUS programmeofFoundationForPolishScience,cofinancedbyEU, Re-gionalDevelopmentFund;andtheThalisandAristeiaprogrammes cofinancedbyEU–ESFandtheGreekNSRF.
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CMSCollaboration
V. Khachatryan,
A.M. Sirunyan,
A. Tumasyan
YerevanPhysicsInstitute,Yerevan,Armenia
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T. Bergauer,
M. Dragicevic,
J. Erö,
C. Fabjan
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M. Friedl,
R. Frühwirth
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V.M. Ghete,
C. Hartl,
N. Hörmann,
J. Hrubec,
M. Jeitler
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W. Kiesenhofer,
V. Knünz,
M. Krammer
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I. Krätschmer,
D. Liko,
I. Mikulec,
D. Rabady
2,
B. Rahbaran,
H. Rohringer,
R. Schöfbeck,
J. Strauss,
A. Taurok,
W. Treberer-Treberspurg,
W. Waltenberger,
C.-E. Wulz
1InstitutfürHochenergiephysikderOeAW,Wien,Austria
V. Mossolov,
N. Shumeiko,
J. Suarez Gonzalez
NationalCentreforParticleandHighEnergyPhysics,Minsk,Belarus
S. Alderweireldt,
M. Bansal,
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T. Cornelis,
E.A. De Wolf,
X. Janssen,
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S. Ochesanu,
B. Roland,
R. Rougny,
M. Van De Klundert,
H. Van Haevermaet,
P. Van Mechelen,
N. Van Remortel,
A. Van Spilbeeck
UniversiteitAntwerpen,Antwerpen,Belgium
F. Blekman,
S. Blyweert,
J. D’Hondt,
N. Daci,
N. Heracleous,
A. Kalogeropoulos,
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A. Olbrechts,
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D. Strom,
S. Tavernier,
W. Van Doninck,
P. Van Mulders,
G.P. Van Onsem,
I. Villella
VrijeUniversiteitBrussel,Brussel,Belgium
C. Caillol,
B. Clerbaux,
G. De Lentdecker,
L. Favart,
A.P.R. Gay,
A. Grebenyuk,
A. Léonard,
P.E. Marage,
A. Mohammadi,
L. Perniè,
T. Reis,
T. Seva,
L. Thomas,
C. Vander Velde,
P. Vanlaer,
J. Wang
UniversitéLibredeBruxelles,Bruxelles,Belgium