Measurement of CKM matrix elements in single top quark t-channel production in proton-proton collisions at s=13 TeV

Physics Letters B 808 (2020) 135609

Contents lists available atScienceDirect

Physics

Letters

B

www.elsevier.com/locate/physletb

Measurement

of

CKM

matrix

elements

in

single

top

quark

t-channel

production

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: Received25April2020

Receivedinrevisedform13June2020 Accepted2July2020

Availableonline8July2020 Editor: M.Doser Keywords: CMS Physics CKMmatrix Topquark

The first direct, model-independent measurement is presented of the modulus of the Cabibbo– Kobayashi–Maskawa (CKM) matrix elements |Vtb|,|Vtd|,and |Vts|,in final statesenriched insingle topquarkt-channelevents.Theanalysisusesproton-protoncollisiondatafromtheLHC,collectedduring 2016 by the CMS experiment, at acentre-of-mass energy of13 TeV, corresponding to an integrated luminosity of 35.9 fb−1_{.Processes directlysensitive to thesematrix elements are considered atboth} theproductionanddecayverticesofthetopquark.InthestandardmodelhypothesisofCKMunitarity, a lowerlimit of|Vtb|

>

0.970 is measured atthe 95% confidence level. Severaltheories beyond the standard model are considered, and by releasing all constraints among the involved parameters,the values _|Vtb|=0.988±0.024,and |Vtd|2+ |Vts|2=0.06±0.06,where theuncertainties includeboth statisticalandsystematiccomponents,aremeasured.

©2020TheAuthor.PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense (http://creativecommons.org/licenses/by/4.0/).FundedbySCOAP3.

1. Introduction

A distinctive feature of the electroweak sector of top quark physics is the relative magnitude of the Cabibbo–Kobayashi– Maskawa(CKM) [1] matrixelement Vtb withrespectto Vtd and

Vts, which leads to a strong suppression of processes involving mixingbetween the third and the first two quark families. This featurecanbe probedattheCERNLHCbystudyingthecouplings oftopquarkstod,s,andb quarksinelectroweakcharged-current interactions, wheresuch couplings play a role at either the pro-ductionordecayverticesofthetopquark. Ingeneral, topquarks areproduced inproton-proton(pp) collisions through thestrong interaction,predominantlyviagluon fusion,creatingatop quark-antiquark(tt )pair.Topquarkscanalsobesinglyproducedviathe electroweak interaction, in which casethe dominantmechanism involves an exchange of a W boson in the t channel, a process whichhasbeenprecisely measuredatthe LHC [2–11]. The dom-inant decay process for a top quark is to a W boson and a b quark via an electroweak charged-current interaction. All single topquarkprocessesthereforeallowthedirectprobingofthetWq vertex, with q representing a b, d, or s quark, both in produc-tionanddecayofthe topquark. In the

t channel,

a topquark is producedrecoilingagainstalightquark,henceforthreferred toas q. Fig.1 shows typical Feynman diagrams atleading order (LO)



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

for the differentproduction and decaymodes considered in this analysis.

The elements Vtb, Vtd, and Vts of the CKM matrix can be indirectly constrained from measurements in the B and K me-sonsectors [12],butthosedeterminationsrelycruciallyonmodel assumptions, such as the existence of only three generations of quarks and the absence of particles beyond the standard model (SM) [13].Thismodeldependencemotivatesalternativeinferences based on different sets of hypotheses. In particular, given that thesethreeCKM elementsconnectthetopquark withdown-type quarks, it is natural to use events enriched in top quarks to set constraints on them. Twocomplementary approaches have been pursued by the Tevatron and LHC experiments to extract

|

Vtb|: the first method measures the branching fraction

B(

t

→

Wb

)

=

|

V_tb

|

2

/



|

Vtd|2

+ |

Vts|2

+ |

Vtb|2 intt events [14–17].The

B(

t

→

Wb

)

measurement is sensitive to the CKM elements of interest throughthedecayvertexofthetopquark,andcanbeturnedinto ameasurementofthevalueof

|

V_tb

|

onlyunderthehypothesisof theunitarityofthe3

×

3 CKMmatrix.Thesecondmethodisbased on thesingle topquark productioncross section andissensitive in principle through both the production and decay of the top quark. Todisentangletheeffects ofthe twoverticesinpast mea-surements atthe Tevatron [18–27] andthe LHC [2,3,5–10,28,29],

|

V_tb

|

was extracted in the t channel by assuming that the val-ues of

|

Vts

|

and

|

Vtd| are negligible. Some theoretical proposals havesuggestedthesimultaneousextractionofthethreeCKM ma-trixelementsfromacombinationofmeasurementsof

B(

t

→

Wb

)

andeitherinclusive [13,30] ordifferential [31,32] crosssectionsof

https://doi.org/10.1016/j.physletb.2020.135609

0370-2693/©2020TheAuthor.PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense(http://creativecommons.org/licenses/by/4.0/).Fundedby SCOAP3.

Fig. 1. Leading-orderFeynmandiagramsforsingletopquarkproductionviathet channelfeaturing:(a)atWb vertexinproductionanddecay,(b)atWb vertexinproduction andatWq indecay,withq beingans ord quark,(c)atWq vertexinproductionandatWb indecay,and(d)aprocessinitiatedbyad quarkandenhanceddueto contributionsfromthesevalencequarks.Thereferstoe orμ leptons.

singletopquarkproductioninthe

t channel.

Otherstudies specifi-callyaddressthedeterminationof

|

Vtd|[31,33] throughareliance onthereinterpretationofexistingmeasurements,buttheydonot makeuseoffullexperimentaldetectorsimulationsanddonot ex-ploit the discriminating power of multivariate analyses (see, for example,discussioninRef. [34]).

Thedata usedin thisLettercomefrom pp collisionsat

√

s

=

13 TeV,correspondingtoanintegratedluminosityof35.9 fb−1and collectedbytheCMSexperimentwithtriggersrequiringeitherone muonorelectroninthefinalstate.Wepresentthefirstdirectand model-independentsimultaneousmeasurementof

|

Vt b|,

|

Vtd

|

,and

|

Vts

|

,byconsideringtheirrespectivecontributionstothetopquark

t-channel productionanddecay.

2. TheCMSdetector

The central feature of the CMS apparatus is a superconduct-ing solenoidof 6 m internal diameter, providinga magnetic field of3.8 T. Withinthe solenoidvolume area siliconpixel andstrip tracker, a lead tungstate crystal electromagnetic calorimeter, and a brass and scintillator hadron calorimeter, each composed of a barrelandtwo endcapsections.Forward calorimetersextendthe pseudorapidity(

η

) [35] coverageprovidedbythebarreland end-capdetectors.

Events of interest are selected using a two-tiered trigger sys-tem [36].Thefirstlevel,composedofcustomhardwareprocessors, uses information from the calorimeters and muon detectors to select events. The second level, known as the high-level trigger, consistsofafarmofprocessorsrunningaversionofthefullevent

reconstruction softwareoptimised forefficientprocessing.Amore detaileddescriptionoftheCMSdetector,togetherwithadefinition ofthecoordinatesystemusedandtherelevantkinematicvariables, canbefoundinRef. [35].

3. Simulatedsamples

Monte Carlo (MC) eventgenerators are used to simulate sig-nal and background samples. Single top quark t-channel events are generated at next-to-leading-order (NLO) in quantum chro-modynamics (QCD) with powheg 2.0 [37–39]. The four-flavour scheme [40] isusedforeventswiththe V_tb vertexinproduction, whilethefive-flavourscheme [41] isusedforeventswithone

V

td or Vts vertexinproduction.Topquarkdecaysare simulatedwith madspin [42]. The tt background process [43], aswell asdouble vector boson production [44,45] (VV, where V stands for either a W or a Z boson), are generated with powheg 2.0. Associated top quark and W bosonproduction are simulated with powheg inthefive-flavourscheme [46].Single topquark s-channel events (t, s-ch) are simulated with MadGraph5_amc@nlo 2.2.2 [47] at NLO.Thevalueofthetopquarkmassusedinthesimulated sam-ples is 172.5 GeV. For all samples pythia 8.180 [48] with tune CUETP8M1 [49] is used to simulate the parton shower, quark hadronisation,andunderlyingevent,exceptfortt ,wherethetune CUETPM2T4isused [50].SimulatedeventsampleswithW andZ bosonsinassociationwithjets(W+jets,Z+jets)aregeneratedusing MadGraph5_amc@nlo 2.2.2. For theseprocesses, events withup to twoadditionalpartonsemitted inthehard scatteringare sim-ulated,andtheFxFxmergingscheme [51] isusedtoavoiddouble

The CMS Collaboration / Physics Letters B 808 (2020) 135609 3

countingwithpartonemissionsgeneratedinthepartonshowering. SimulatedQCDmultijetevents,generatedatLOwith pythia 8.180, areusedtovalidatetheestimationofthisbackgroundwitha tech-niquebasedoncontrolsamplesindata.

Thedefaultparametrisationofthepartondistributionfunctions (PDFs) used in all simulations is NNPDF3.0 [52] at LO or NLO QCD, withthe ordermatching that ofthe matrix element calcu-lation.Allgeneratedeventsundergoafullsimulationofthe detec-torresponse according to the modelof the CMSdetector within Geant4_{[53].Additionalpp interactionswithinthesameornearby} bunchcrossings (pileup)are included inthe simulation withthe samedistributionasobserved indata.ExceptfortheQCD multi-jetprocess, whichis determined fromafit todata, allsimulated samplesarenormalisedtotheexpectedcrosssections.

4. Eventselectionandreconstruction

Thesignaleventselectionisbasedonfinalstateswherethetop quarkdecaystoab,s,ord quark,andaW boson,whichthen de-cays to a lepton-neutrino pair.Events withexactly one muon or electron andat least two jets are considered in this analysis, as was done in the latest CMS single top quark cross section mea-surement [10]. The neutrino accompanying the lepton cannot be directly detected, and manifests itself in the detector as a mea-suredmomentumimbalanceintheevent.DependingontheCKM matrixelementinvolvedinthedecay,thefinal statemayinclude a jet from the hadronisation of either a b, s, or d quark. A jet recoilingagainstthetopquarkispresent,anditisproduced usu-allyat low angle with respect to the beamaxis. A third jet can stem fromthe second quark produced in the gluon splitting (as showninFig.1(c)).Thequarkfromgluonsplittinggeneratesajet thatusuallyhasasoftertransversemomentum(pT)spectrumthan thatof thejet fromthetop quark decayproducts. Dependingon the numberof tWb vertices in the event process, one can have onejetcoming fromthehadronisation ofab quark(b jet)ifthe tWb vertex occursinproduction orindecaybut notin both,or twob jetsifthetWb vertexoccursbothinproductionanddecay. Eventsareretainedfortheofflineanalysisiftheywereselected onlinebyrequiringthepresenceofanisolated,high-pT lepton: ei-thera muon with pT

>

24GeV or an electron with pT

>

32GeV. Fromthesampleoftriggeredevents,onlythosewithatleastone primaryvertexreconstructedfromatleastfourtracks,witha lon-gitudinaldistanceoflessthan24 cm andaradial distanceofless then2 cm fromthe centreofthedetector,are consideredforthe analysis. The candidate vertexwiththe largest value of summed physics-object

p

2T istakentobetheprimarypp interactionvertex. Thephysicsobjectsarethejets, clusteredusingthejet-finding al-gorithm [54,55] with the tracksassignedto candidatevertices as inputs,andtheassociatedmissing p_T (pmiss_T ),takenasthe magni-tudeofthenegativevectorsumofthep



_Tmiss ofthosejets.

Theparticle-flow(PF)algorithm [56] isusedtoreconstructand identifyindividualparticlesintheeventusingcombined informa-tionfromthesubdetectorsoftheCMSexperiment, allowing iden-tification of muons, electrons, photons, andcharged and neutral hadrons. After triggering, muons are considered forfurther anal-ysisif they have pT

>

26GeV and

|

η

|

<

2

.

4, while electrons are required to have p_T

>

35GeV and

|

η

|

<

2

.

1. Additional isolation requirements are used to discriminate between prompt leptons and those coming from hadronic decays within jets, by defin-ing I_rel, asthe scalarsum ofthe p_T of chargedhadrons, neutral hadrons, and photons divided by the p_T of lepton in a cone of



R

=



(

η

)

2

+ (φ)

2

=

0

.

4 aroundthemuonand0.3aroundthe electron, where

φ

is the azimuthal angle in radians. The contri-butionofhadronsfrompileupinteractions issubtractedfromthe scalarsumwith thetechniques detailedinRefs. [57,58]. The

pa-rameter I_rel isrequired to be less than6.0% for muons, 5.9% for barrelelectrons,and5.7%forendcapelectrons.

Jetsarereconstructedusingtheanti-k_T clusteringalgorithm de-scribed in Refs. [54,55] with a distance parameter of 0.4on the collectionofPFcandidates.Tobeincluded,chargedparticle candi-dates mustbe closeralongthe zaxistothe primary vertexthan toanyothervertex.

Acorrectionto accountforpileupinteractions isestimatedon an event-by-event basis using the jet area method described in Ref. [58], and is applied to the reconstructed jet pT. Further jet energy corrections [59], derived from the study of dijet events andphotonplusjet eventsindata,are applied.Twotypesofjets are defined: high-pT jets are definedby requiring

|

η

|

<

4

.

7 and

pT

>

40GeV, andlow-pT jets are defined by requiring

|

η

|

<

4

.

7 and20

<

p_T

<

40GeV.

Oncethejetshavebeenselected accordingtotheabove crite-ria,theycanbefurthercategorisedusingab taggingdiscriminator variable in orderto distinguish between jetsstemming from the hadronisation of b quarks and those from the hadronisation of light partons.A multivariate (MVA) discriminator algorithm uses track-basedlifetimeinformation,togetherwithsecondary vertices inside the jet, to provide a MVA discriminator for b jet identifi-cation [60,61]. Forvalues of the discriminator above the chosen threshold,theefficiencyofthetaggingalgorithmtocorrectlyfind b jetsisabout45%,witharateof0.1%formistagginglight-parton jets [60,61].

Eventsare dividedintomutuallyexclusive“categories” accord-ing tothe numberofselectedhigh-pT jetsandb-taggedhigh-pT jets.Inthefollowing,categoriesarelabelledas“njmt”,referringto eventswithexactly

n high-p

Tjets,

m of

whicharetaggedasb jets, regardlessofthenumberoflow-pT jets. Thethresholdonthejet momentumforhigh-p_T jetslessenstheimpactonthe categorisa-tionofadditionaljetscomingfrominitial- orfinal-stateradiation, whichis fullysimulatedandtakeninto accountinthe modelling systematicuncertainties.

TorejecteventsfromQCDmultijetbackgroundprocesses,a re-quirementonthetransversemassoftheW bosonof

m

W_T

>

50GeV isimposed,where mW_T

=



pT,

+

pmissT



2

−



px,

+

pmissx



2

−



py,

+

pmissy



2

.

(1) Here,

p

missT isdefinedasthemagnitudeof



p

miss

T ,whichisthe neg-ativeofthevectorial



p_T sumofallthePFparticles.The pmiss_x and

pmiss_y quantities are the p



_T componentsalong the x and y axes,

respectively,and pT,, px,,and py, arethecorrespondinglepton

momentumcomponentsinthetransverse,

x,

andy directions.

To analysethe kinematics of single top quark production, the four-momentum of a top quark candidate is reconstructed from the decayproducts:leptons, neutrinos,and b jetcandidates.The

pT of the neutrino can be inferred from p miss

T . The longitudinal momentum of the neutrino, pz,ν, is calculated assuming energy-momentum conservationatthe W



ν vertex andconstraining the W bosonmassto

m

W

=

80

.

4GeV [12]:

p±_z,ν

=



pz, p2_T,

±

1 p2_T,





2p2_z,

−

p2_T,

(

p2_p2_T,ν

− 

2

),

(2) where



=

m 2 W 2

+ 

pT,

· 

p miss T

,

(3)

and p2_

=

p2_T,

+

p2_z, denotes the square of the lepton momen-tum. In most of the cases, this leads to two real solutions for

Table 1

Valuesofthethird-rowelementsoftheCKMmatrixinferredfromlow-energy mea-surements,takenfromRef. [12],withtherespectivevaluesofthetopquarkdecay branchingfractions.Theq in|Vtq|andB(t→Wq)inthefirstcolumnreferstob,

s,andd quarks,accordingtothequarklabelshownintheheaderrow.

Quark b s d |Vtq| 0.999119+ 0.000024 −0.000012 0.04108+ 0.00030 −0.00057 0.008575+ 0.000076 −0.000098 B(t→Wq) 0.998239+₋00..000048000024 0.0016876+ 0.0000025 −0.0000047 0.000074+ 0.000013 −0.000017 Table 2

Foreachoftheproductionanddecayvertices,thecrosssectiontimesbranching fractionfor the corresponding signalprocess fromsimulation. The uncertainties shownincludethosefromthefactorisationandrenormalisationscales,thePDFs, andanyexperimentaluncertainties,whereappropriate.

Production Decay Crosssection×branching fraction(pb)

tWb tWb 217.0±8.4

tWb (tWs+tWd) 0.41±0.05

tWd tWb 0.102±0.015

tWs tWb 0.92±0.11

pz,ν and the solution with the smallest absolute value is cho-sen [21,23].Forsome events,thediscriminantinEq. (2) becomes negative, leading to complex solutions for p_z,ν. In this case, the imaginary component is eliminated by modification of px,ν and

p_y,ν so that

m

W_T

=

m_W,while still respecting the

m

W constraint. Thisisachievedbyrequiringthedeterminant,andthusthe square-rootterminEq. (2),toequalzero.Thisconditiongivesaquadratic relation between p_x,ν and p_y,ν with two possible solutions and oneremaining degreeoffreedom.Thesolutionischosenby find-ing the



pT,ν thathas theminimumvectorialdistancefrom



pTmiss inthe pmiss_x

−

pmiss_y plane.

Areconstructed top quark candidateis definedby associating one jet withan accompanying W boson, and the respective top quark four-momentum is evaluated asdescribed above.For each ofthesignalcategoriesselected,multipletopquarkcandidatescan bedefinedinthesamecategory,depending onthehypothesis for theoriginofthejetintheevent.

5. Signaldescriptionandeventcategorisation

Thepredictedbranchingfractionsoftop quarkstod, s,andb quarks can be written as a function of the overall magnitudeof

B(

t

→

Wq

)

= |

Vtq|2

/



|

Vtd|2

+ |

Vts

|

2

+ |

Vtb

|

2

.Thevaluesof

|

Vtq

|

and

B(

t

→

Wq

)

usedtoderive theinitial normalisationofsignal processesaretakenfromRef. [12],andshowninTable1.

ThequantitiesreportedinTable1comefromlow-energy mea-surementsthat assume unitarity in theCKM matrix andno new loopsin the relevant Feynman diagrams. This analysis will relax suchassumptionsandpresentdifferentscenariosforinterpretation oftheprovidedresults.

Thesignaturesfor

t-channel

processes involvingVtb, Vtd,and

V_ts eitherinproductionordecaydifferinthreeaspects:the num-berofreconstructedb-taggedjets,thefeaturesofthejetinvolved inthe reconstruction ofthecorrecttop quark candidate,andthe kinematicfeaturesoftheeventsasaresultofdifferentPDF contri-butionsto productionmodesinvolvingab,s,ord quark. Hence-forth,the

t-channel

process involvingVtb inbothproductionand decaywill be referred toas S T_b,b, while

t-channel

processes in-volving Vtb in only production or decay will be referred to as

S Tb,q and

S T

q,b,respectively.Thesignalchannelsandtheir corre-spondingcrosssectionstimesbranchingfractionsfromsimulation arereportedinTable2.ThecrosssectionsareevaluatedatNLOin thefive-flavourschemeusing powheg for

σ

t-ch,d,

σ

t-ch,s,andwith HATHOR[62] for

σ

_t-ch,b.

Multiplecategoriesaredefinedinordertoextractthe contribu-tion ofthe differentt-channel processes,whileatthe sametime discriminating against the background processes, mainly tt and W+jets production.Themajorityof

t-channel

eventspopulate cat-egories with2or3jets,asdefinedabove.Themain backgrounds arise from tt (all categories), W+jets (in the 2j1t and 3j1t cat-egories), and QCD multijet (in the 2j1t category) processes. The signal processes takeninto consideration give different contribu-tions to the three categories, and it is possible to identify the most sensitive categories with respect to each process based on the respective signatures, assummarised in Table 3.The physics motivationsleadingtothisstrategyaredescribedbelow.

Events from strong interaction tt production, where one top quarkdecaysthroughthetWd ortWs vertex(tt_b,q),populatethe 2j1tand3j1tcategories.Theirsmallcontributiontothet t yieldin suchcategoriesiscoveredbytheb-tagginguncertainty.Their sig-nature in those categories is also found to be indistinguishable, within systematic uncertainties, from that of tt when each top quarkdecaysthroughthetWb vertexandoneb jetdoesnotpass eitherthekinematicorb taggingrequirements.Forthosereasons, alltopquarkdecaymodesoftt pairsaretreatedasasingle back-groundsource.

ThediscriminationbetweenthethreesignalsS T_b,q,

S T

q,b,and

S T_b,b isbasedonthreecharacteristics.First,for

S T

b,q events,only asingleb quarkispresentinthefinalstatestemmingfromgluon splitting, thus resulting in a low-energy b-tagged jet, while the jet comingfromthetop quarkdecayis usuallynot b tagged.For

S Tq,b events,a single b-taggedjet is produced in thetop quark decay, and additional jets from gluon splitting are usually not b tagged. Both S Tq,b and S Tb,q processes therefore differ from

S Tb,b by having a single b quark in the final state, as opposed to two for the latter process. However, thisfeature can only be exploited when the jet from gluon splitting is energetic enough to bereconstructed.Second,furtherdiscrimination isachievedby exploitingthefeatures ofthereconstructed topquark candidates. The kinematic and angular propertiesof the decay products ex-hibitsignificant differencesdepending onwhetherthecorrectjet is chosen, or ifthe jet that originated from the quark produced inthegluon splittingisused.For S Tb,q events,thetopquark re-constructed withthe correctjet assignmentusually doesnot use the b-taggedjet intheevent, whilefor S Tb,b and S Tq,b,thetop quark candidateisreconstructedby usingtheb-taggedjet inthe majorityof cases.It isthereforepossibleto differentiatebetween the S Tb,b and S Tb,q processesby comparingthe features of top quark candidatesreconstructed withorwithout b-taggedjets. Fi-nally, different PDFs are involved in S T_b,b and S T_q,b processes, the latter drawing contributions from valence d quarks as well. Therefore,thekinematicpropertiesoffinal-stateparticlesmay dif-fer fromthe other channels. The second characteristic, relatedto thecorrectnessofthetopquarkreconstructionhypothesis,proves to be thestrongest amongst the three mentioned criteria. While the S T_b,q andthe S T_b,b processescanbe differentiated byusing thischaracteristic,the

S T

q,b andthe

S T

b,b productionscannot, be-causetheirfinal-statesignaturesexhibitthesamefeatures.

The 2j1t category ispopulated by events that depend on Vtb inbothproductionanddecay,wherethesinglereconstructedb jet comes inthe majorityofcases(85%) fromtopquark decays,and for the remaining cases from the second b jet from gluon split-ting.Thismeansthatthejet fromthesecond b quark failseither the jet p_T requirementorthe b tagrequirement, orboth. Events comingfromaprocessforwhich

V

td or

V

ts areinvolved,eitherin productionorindecay,populatethiscategoryaswell,witheither theb-taggedjetcomingfromtopquark decayorthesecondaryb quarkfromgluonsplitting.

For t-channel signal events from all four processes in Fig. 1, themostdistinctivefeaturesthatallowthediscriminationagainst

The CMS Collaboration / Physics Letters B 808 (2020) 135609 5

Table 3

Foreachcategory,thecorrespondingsignalprocess,thecrosssectiontimesbranchingfractionexpression,and thespecificFeynmandiagramfromFig.1areshown.

Category Enriched in Cross section×branching fraction Feynman diagram 2j1t S Tb,b σt-ch,bB(t→Wb) 1a

3j1t S Tb,q, S Tq,b σt-ch,bB(t→Wq),σt-ch,qB(t→Wb) 1b,1c,1d

3j2t S Tb,b σt-ch,bB(t→Wb) 1a

backgroundsinthe2j1tcategoryrelyon thefactthatthe second jet stems from the recoiling quark. For this reason the non-b-taggedjet isnot used forthe topquark reconstruction.This cat-egoryistheonewherethehighestdiscriminationpowerfor

S T

b,b againstbackgroundsis achievedby makinguseofthe featuresof thetopquarkdecayproducts,suchasthereconstructedtopquark massand

m

W_T ,and ofthe recoilingjet. However, the discrimina-tion power with respect to other t-channel mechanisms is poor sincejetsfrom gluonsplitting are typically notenergetic enough topassthe pT threshold,makingit impossibletoreconstructtwo differenttopquarkcandidates.

The3j1t categoryis alsopopulated byall

t-channel

processes ofinterest,butitdiffersfrom2j1tinthefactthatitaccommodates eventsinwhichthejetfromgluonsplittinghasahigher

p

T on av-erage.Forboth the2j1t and3j1tcategories, whenthe top quark decaysthroughtWd,s vertices,thejetcomingfromthetopquark usually does not pass the b tagging requirement since it stems fromthehadronisationofalightquark.Inallother cases,thisjet passesthe b taggingrequirement,giventheefficiencyofthe tag-gingalgorithm.

The3j1tcategory isenriched in

t-channel

eventsbyrequiring

|

η

_j

|

>

2

.

5,where

η

_j isthepseudorapidityofthemostforwardjet. Thetwojetsother thanthemostforwardone areusedto recon-structthetwotopquarkcandidates.Iftheeventisfromthe

S T

b,q process,theb-taggedjetinthe3j1tcategorywillstemfromgluon splitting,andtheadditionaljetwillhaveahigherchanceofbeing theonecomingfromthetopquarkdecaytoans ord quark. Vari-ablesofinterestinthiscaseareconstructedbymakinguseofthe b jetandtheleastforwardjetoftheremainingtwo,referredtoas theextrajet.Suchvariablesincludetheinvariantmassofthe lep-tonplusjet system(either theb jetortheextrajet), andseveral topquark kinematicvariablesconstructedusinga combinationof theextrajet,thelepton,and

p

missT .

In both the 2j1t and the 3j1t categories, mW_T is also used to discriminatebetweentheQCDmultijetbackgroundandother pro-cesses.AneventcategorydepletedofQCDmultijetbackgroundis definedbyaddingtherequirement

m

WT

>

50GeV.Fig.2showsthe

mW_T distribution from data and simulations in the 2j1t and 3j1t categoriesfor the muon (upper plots) and electron (lower plots) channels,wheretheQCDmultijetbackgroundisnormalisedtothe resultofthefit.

Inthe 3j2tcategory, there are two b jets,one produced from thetop quarkdecayandanotherfromgluon splitting.Both b jets areusedtoreconstructatopquark candidateandits correspond-ing variables. In this case, the mW_T

>

50GeV requirement is un-necessarysince theQCD multijet contamination isnegligible and thedominantbackgroundprocess is tt .No requirementon

η

_j is neededeithersincethe categoryis dominatedby the S T_b,b pro-cessandthecombinatorialtopquarkbackgroundissmall.

Multivariateanalysesarethenperformedbyusingboosted de-cision trees (BDT) in order to obtain appropriate discriminating variables,henceforthreferredtoasBDTdiscriminators,inthethree categories, for both muons and electrons. The processes used as signalorbackgroundinthetrainingarethefollowing:

•

Inthe2j1tcategory,thesingletopquark

S T

b,b processis con-sideredassignalandtt andW+jets processesasbackground.

•

Inthe3j1tcategory,thesingletopquark

S T

q,b processis

con-sideredassignal andthe S Tb,b,tt , and W+jets processesas background.

•

Inthe3j2tcategory,thesingletopquark

S T

b,b processis con-sideredassignalandtt asbackground.

Thevariables usedinthe 2j1tcategorytrainingare: the

|

η

|

of thenon-b-taggedjet,thereconstructedtopquarkmass,thecosine ofthe angle betweentheW boson momentum inthe top quark restframeandthemomentumofthelepton intheW boson rest frame, the cosine of the polarisation angle defined asthe angle betweenthedirectionoftheleptonandthelight-quarkmomenta inthetop quarkrestframe, theinvariantmassofthe leptonand b-taggedjetsystem,andtheinvariantmassoftheleptonand for-wardjetsystem.

The variables used in the 3j1t category training are: the

|

η

|

ofthe mostforward non-b-taggedjet,the massofthetop quark whenit isreconstructedwiththeb-taggedjet (b-topquark),the cosine ofthe angle betweenthe W boson momentum in the b-top quarkrest frameandthemomentum ofthelepton intheW boson restframe, the cosineof the polarisationangle definedas theanglebetweenthedirectionoftheleptonandthelight-quark momentain theb-top quarkrestframe, pmissT ,

m

W

T ,theinvariant massoftheleptonandb-taggedjetsystem,theinvariantmassof the leptonandextra jetsystem, the invariantmass ofthelepton and forwardjet system, the number oflow-pT jets, the mass of thetopquark whenitisreconstructed withthenon-b-taggedjet (non-b-topquark),thecosineofthe anglebetweentheW boson momentum in the non-b-top quark rest frame and the momen-tum ofthe lepton in the W boson rest frame, the cosine of the polarisation angle definedas the angle betweenthe direction of the lepton andthe light-quark momentain the non-b-top quark restframe,andthevalueoftheMVAb taggerdiscriminatorwhen appliedtothenon-b-taggedjet.

Thevariables usedinthe 3j2tcategorytrainingare: the

|

η

|

of thenon-b-taggedjet,themassofthetopquarkwhenitis recon-structedwiththehighest-pT b-taggedjet(leadingtopquark),the cosineoftheanglebetweentheW bosonmomentuminthe lead-ingtop quarkrestframeandthemomentumoftheleptoninthe W bosonrestframe,thecosineofthepolarisationangledefinedas theanglebetweenthedirectionoftheleptonandthelight-quark momenta intheleading top quark restframe, pmissT ,m

W T , the in-variantmassoftheleptonandthehighest-pT b-taggedjetsystem, theinvariantmassoftheleptonandlower-pTb-taggedjetsystem, theinvariantmassoftheleptonandlight-jetsystem,thenumber oflow-pTjets,themassofthetopquark whenitisreconstructed withthelower-p_Tb-taggedjet(non-leadingtopquark),thecosine oftheanglebetweentheW bosonmomentuminthenon-leading top quarkrest frameandthemomentum ofthelepton intheW boson restframe, the cosineof the polarisationangle definedas theanglebetweenthedirectionoftheleptonandthelight-quark momentainthenon-leadingtopquark restframe,andthe differ-encein

η

betweenthetwob-taggedjets.

Fig. 2. ThemWT distributionfromdata(points)andsimulation(shadedhistograms)inthe2j1t(left)and3j1t(right)categoriesforthemuon(upper)andelectron(lower)

channels.TheverticallinesonthepointsandthehatchedbandsshowtheexperimentalandMCstatisticaluncertainties,respectively.Theexpecteddistributionfromthe S Tq,b+S Tb,qprocesses(multipliedbyafactorof1000)isshownbythesolidblueline.ThelowerpanelsshowtheratioofthedatatotheMCprediction.

Figs. 3–5 show the distributions of the most discriminating variablesinthe2j1t,3j1t,and3j2tcategories,respectively.

6. Systematicuncertainties

Several sources of systematic uncertainties are considered in the analysis, divided intwo groupsdepending onthe treatment: uncertaintieslabelledas“profiled”aretreatedasnuisance param-etersandprofiledinthefitproceduredescribedinSection7,while thoselabelledas“nonprofiled”areestimatedasthedifference be-tween the result of the fit procedure by varying the systematic scenario.Theselatter uncertainties includethesources relatedto themodellingofthe signalprocess, whichcannot be constrained fromthemeasurementsincetheyapplytothefullphasespaceand not only to the region in which the measurement is performed. Also included are the jet energy scale andresolution uncertain-ties,whichplay amajorrole ineventsfeaturing hadronicactivity in the high-pseudorapidity region of the detector. They are also intertwinedwiththeuncertaintiesinthemodellingofthe hadro-nisation and causea larger uncertainty inthe signal acceptance, which was not the case for previous measurements [10,11]. For thesereasons,amoreconservativeapproachispreferredandthese uncertaintiesarenotprofiledinthefit.

The impact of nonprofiled uncertainties is determined by re-peating theanalysis usingvaried templates accordingto the sys-tematicuncertaintysources understudy inthe fit,insteadofthe nominaltemplates.Theuncertaintyduetoacertainsourceisthen takenashalfthedifference betweentheresultsforupanddown

variations oftheeffect.Inthefollowing,thedifferentuncertainty sources that are considered in the analysis are briefly described. Forthesakeofsimplicityandbetterreadability, theyaregrouped intoprofiledandnonprofileduncertainties.

Profileduncertainties

•

Limited size of simulated event samples: The statistical uncer-tainty due to the limited size of the simulated event sam-plesisevaluatedforeachbinwiththeBarlow–Beeston“light” method[63,64].

•

Lepton trigger and reconstruction: Single-muon and single-electron trigger andreconstruction efficiencies are estimated with a “tag-and-probe” method [65] from Drell–Yan events withthedileptoninvariantmassintheZ bosonpeak.

•

Pileup: The uncertainty in the average expected number of

pileupinteractionsispropagatedasasourceofsystematic un-certainty by varying the total pp inelastic cross section by

±

4

.

6% [66].

•

t

¯

t modelling: Thefollowinguncertaintysourcescoverpotential mismodellingof thett process. Theireffect isconsidered on boththeacceptanceandthecrosssection.

– t

¯

t renormalisation and factorisation scale uncertainties (

μ

R

/

μ

F): The uncertainties caused by variations in the renormalisa-tion andfactorisationscales are considered byreweighting theBDT response distributionswithdifferentcombinations of doubled/halved renormalisation and factorisation scales withrespecttothenominalvalueof172.5 GeV.

The CMS Collaboration / Physics Letters B 808 (2020) 135609 7

Fig. 3. Distributionsofthetwomostdiscriminatingvariablesfromdata(points)andsimulation(shadedhistograms)inthe2j1tcategory:the|η|ofthenon-b-taggedjet

η

j

(left)andtheinvariantmassofleptonandb jetmomentasystem(right),shownforthemuon(upper)andelectron(lower)channels,respectively.Theverticallinesonthe pointsandthehatchedbandsshowtheexperimentalandMCstatisticaluncertainties,respectively.TheexpecteddistributionfromtheS Tq,b+S Tb,q processes(multiplied

byafactorof1000)isshownbythesolidblueline.ThelowerpanelsshowtheratioofthedatatotheMCprediction.

– Matching

of matrix element and parton shower (ME-PS

match-ing): Theparameterthatcontrolsthematchingbetweenthe matrixelementlevelcalculationandthepartonshower,and thatregulatesthehigh-pTradiationinthesimulationis var-iedwithinitsuncertainties.

– Initial- and

final-state radiation: The

impact of variations in theinitial-stateandfinal-stateradiationisstudiedby com-paringthenominalsamplewithdedicatedtt samples.

– Underlyingevent: The effectofuncertaintiesinthemodelling oftheunderlyingeventisstudiedbycomparingthenominal samplewithdedicatedtt samples.

•

QCD multijet background process normalisation: The QCD multi-jet backgroundyield is assigned a 50% uncertainty, which is chosen conservativelytobe muchlargerthantheuncertainty fromthe

m

WT fit.

•

W+jets composition: Aseparate uncertaintyisdedicatedtothe fraction ofW+jets eventswherethe forwardjet isgenerated bythepartonshowering.

•

Other backgrounds μR

/

μ

F: In addition to tt , the uncertain-ties due to variations in the renormalisation and factorisa-tion scales are studied forthe tW and W+jets processes by reweighting the distributions with weights corresponding to differentcombinationsofhalvedordoubledfactorisationand renormalisationscales.Theeffectisestimatedforeachprocess separately.

•

PDF for background processes: Theuncertaintyduetothechoice ofPDFisestimatedusingreweightedhistogramsderivedfrom allPDFsetsofNNPDF 3.0 [67].

•

b tagging: The uncertainties inthe b tagging andmistagging efficiency measurements are split into different components andpropagatedtotheefficiencyoftaggingb jets.

Nonprofileduncertainties

•

Luminosity: Theintegratedluminosityisknownwitharelative uncertaintyof

±

2

.

6% [68].

•

Jet energy scale (JES): All reconstructed jet four-momenta in simulated events are simultaneously varied according to the

η

- and pT-dependentuncertaintiesintheJES [59].This varia-tioninjetfour-momentaisalsopropagatedto pmiss_T .

•

Jet energy resolution (JER): Asmearingisappliedtoaccountfor the difference in the JER between simulation and data [59], and its uncertainty is estimated by increasing or decreasing theresolutionsbytheiruncertainties.

•

Signal modelling: The following uncertaintysources cover po-tentialmismodellingof thesingle top quark

t-channel

signal processes.Theeffectofthoseuncertaintiesontheacceptance, andnot on the crosssection, is considered. In thefit proce-dure,theuncertaintiesarenotconsideredasnuisance parame-tersinthefitbutevaluatedbyrepeatingthefullanalysisusing samples ofsimulated signal events that feature variations in

Fig. 4. Distributionsofthetwomostdiscriminatingvariablesfromdata(points)andsimulation(shadedhistograms)inthe3j1tcategory:the pmissT inthetransverseplane

(left)andthevalueoftheMVAb taggerdiscriminatorwhenappliedtotheextrajet(right)areshownforthemuon(upper)andelectron(lower)channels,respectively.The verticallinesonthepointsandthehatchedbandsshowtheexperimentalandMCstatisticaluncertainties,respectively.Theexpecteddistributionfromthe S Tq,b+S Tb,q

processes(multipliedbyafactorof1000)isshownbythesolidblueline.ThelowerpanelsshowtheratioofthedatatotheMCprediction.

themodellingparameterscoveringthesystematicuncertainty sourcesunderstudy.

– Signal

μ

R

/

μ

F: The uncertainties causedbyvariations inthe renormalisation and factorisation scales are considered by reweighting the BDT response distributions according to weightscorrespondingtodoubling/halvingthenominal val-uesofthescales [40,41].

– Matching

of matrix element and parton shower (ME-PS

match-ing): The parameterthatcontrolsthematchingbetweenthe matrixelementlevelcalculationandthepartonshower,and thatregulatesthehigh-p_Tradiationinthesimulationis var-iedwithinitsuncertainties.

– Parton

shower factorisation scale: The

renormalisation scales of the initial- and final-state parton shower are varied by factors of two and one half with respect to the nominal valueof172.5 GeV.

– PDF

for signal process:

The uncertaintydue tothe choice of PDFisestimatedusingreweightedhistogramsderivedfrom all PDF sets of NNPDF 3.0. The measurements in the fol-lowingreportonlytheexperimentaluncertainties,whilethe uncertaintiesonthepredictedcrosssectionsarereportedin Table2.Effects on thefitdueto correlation betweenPDFs areconsiderednegligible.

7. Fitprocedure

The three CKM matrix elements are extracted by measuring the production cross sections and branching fractions of single

top quark

t-channel

processes that depend on Vtb, Vtd, and Vts in production and decay. The vast majority of single top quark

t-channel events come from the S T_b,b process, while S T_b,q and

S T_q,b constitute subdominant productionmechanisms. The tt_b,q contributionistakenintoaccountinthebackgroundestimation.

The fitprocedureisdivided intotwo steps.Inthefirst step,a maximumlikelihood(ML)fittothe

m

WT distributionisperformed separately forthe2j1t and3j1t categoriesinordertoextract the QCDmultijetcontribution.TheQCDmultijetnormalisationandthe relativeuncertaintyareextrapolatedtotheQCDmultijetdepleted categoriesandusedasaninputtothesecond step.Inthesecond step, in order to discriminate between S Tb,b, S Tq,b, and S Tb,q, themultivariate discriminatorsdescribedinSection 5areusedin asimultaneousMLfittothethreeeventcategories,whiletheQCD multijetprioruncertaintyandcentralvaluearetakenfromthefirst step.

The t-channel single top quark signalsare parametrised with a flatprior representingthecoupling strength,andallsystematic uncertainties are treated as described in Section 6. The smaller background yields are allowed to vary in the fit, along with the respectivescaleuncertainties.The QCDmultijetbackgroundis fit-ted witha flat prior nuisance,while tt and W+jets backgrounds areleftfloatingwithintherespectivesystematicuncertainties.The

t-channel S T_b,q and tt_b,q processes do not distinguish between topologies depending on Vtd or Vts inthe decay,while S Tq,b is sensitivetothedifferentPDFscontributingtotheprocesses.Fig.6

The CMS Collaboration / Physics Letters B 808 (2020) 135609 9

Fig. 5. Distributionsofthetwomostdiscriminatingvariablesfromdata(points)andsimulation(shadedhistograms)inthe3j2tcategory:the|η|ofthenon-b-taggedjet

ηj (left)andtheinvariantmassofleptonandnon-b-taggedjetsystem(right)areshownforthemuon(upper)andelectron(lower)channels,respectively.Thevertical

linesonthepointsandthehatchedbandsshowtheexperimentalandMCstatisticaluncertainties,respectively.TheexpecteddistributionfromtheS Tq,b+S Tb,qprocesses

(multipliedbyafactorof1000)isshownbythesolidblueline.ThelowerpanelsshowtheratioofthedatatotheMCprediction.

Table 4

Thesourcesandrelativevaluesinpercentofthesystematicuncertaintyinthe mea-surementoftheS Tb,bcrosssection.Theuncertaintiesarebrokenupintoprofiled

andnonprofiledsources.

Treatment Uncertainty σS T_b,b/σ(%)

Profiled Lepton trigger and reconstruction 0.50 Limited size of simulated event samples 3.13

tt modelling 0.66

Pileup 0.35

QCD background normalisation 0.08

W+jets composition 0.13

Other backgroundsμR/μF 0.44

PDF for background processes 0.42

b tagging 0.73

Total profiled 3.4

Nonprofiled Integrated luminosity 2.5

JER 2.8

JES 8.0

PDF for signal process 3.8

SignalμR/μF 2.4

ME-PS matching 3.7

Parton shower scale 6.1

Total nonprofiled 11.5

Total uncertainty 12.0

themuon(left) andtheelectron (right)channels. Thepartialand totalcontributionsoftheprofiledandnonprofileduncertaintiesare giveninTable4.

8. Resultsandinterpretation

ThecontributionsofeachofthethreeCKMmatrixelementsto thedifferent

S T

b,b,

S T

b,q,and

S T

q,b crosssections,extractedfrom thefitprocedure,areconsidered.IntheSM,topquarksonlydecay toW bosonsplus b,s,ord quarks,andtheirbranching fractions areproportionaltothemagnitudesquaredoftherespectivematrix element,asgiveninTable2.The fitresultsare givenintermsof two signal strengthparameters:the first,

μ

b, refers tothe S Tb,b process,andthesecond,

μ

sd,tothesumofthe S Tq,b and S Tb,q contributions.

By neglecting terms proportional to

|

Vtd|4,

|

V_ts

|

4, the S T_q,b

termcanbewrittenasproportionalto

|

Vtd|2

+ |

Vts|2,witha con-tribution oforder5% thatdependson

|

Vtd|2

/

|

V_ts

|

2.We consider variations on the latter contribution as negligible in the analy-sis. These assumptions can be justified because of the hierarchy observed in the first two rows of the CKM matrix. The signal strengthsthusbecome:

μ

_b

=

σ

obs t-ch,b

B

(

t

→

Wb

)

obs

σ

_t-ch,b

B

(

t

→

Wb

)

μ

_sd

=

σ

obs t-ch,b

B

(

t

→

Ws

,

d

)

obs

+

σ

_t-ch,obs_s,d

B

(

t

→

Wb

)

obs

σ

_t-ch,b

B

(

t

→

Ws

,

d

)

+

σ

_t-ch,s,d

B

(

t

→

Wb

)

,

(4)

where

B(

t

→

Ws

,

d

)

is thebranching fractionfora top quark to decayto a W bosonandeitheran s or d quark. Henceforth,the “obs”labelwillrefertothemeasuredvalue ofaquantity,andthe

Fig. 6. Distributionofthemultivariatediscriminators,comparingdatatosimulationnormalisedafterthefitprocedure,forthemuonchannelontheleftandfortheelectron channelontheright,for2j1t(upper),3j1t(middle),and3j2t(lower).Theverticallinesonthepointsandthehatchedbandsshowtheexperimentalandfituncertainties, respectively.TheexpecteddistributionfromtheS Tq,b+S Tb,q processes(multipliedbyafactorof1000)isshownbythesolidblueline.Thelowerpanelsshowtheratioof

thedatatothefit.

absence ofthis labelwill meanthe expected value. Equation (4) shows that the signal strengths are the ratios of the measured valueofaquantitytotheexpectedvalue.

One can write Eq. (4) more generally in terms of the top quark decay amplitudes or partial widths. We factorise out the modulus of the matrix element from the partial width for each quark. Thus, the top quark partial width to Wq can be written as

q

=

q

|

Vtq

|

2

, where

q is the top quark partial width for

|

V_tq

|

=

1. We further assume that

_q

=

_b, i.e. that any

differ-encesother thantheCKMelementsare negligible.Using thisand thetotalwidth

t ofthetopquark,wecanwriteEq. (4) as:

μ

_b

=

|

Vtb

|

4 obs

obs q

t

|

Vtb

|

4

q

obst

μ

sd

=

|

Vtb

|

2obs



|

Vts

|

2obs

+ |

Vtd

|

2obs



obsq

t

|

V_tb

|

2



|

V_ts

|

2

+ |

V_td

|

2



q

obs t

.

The CMS Collaboration / Physics Letters B 808 (2020) 135609 11

The first fit extractsthe signal strengths

μ

b and

μ

sd, whose valuescanbe interpretedunderdifferentmodelassumptions.The signalstrengthsobtainedare:

μ

_b

=

0

.

99

±

0

.

03

(

stat+prof

)

±

0

.

12

(

nonprof

)

μ

_sd

<

87 at 95% confidence level (CL), (6) withacorrelationfactorof

ρ

_μb,μs d

= −

0

.

25.Thefirstuncertainty

on

μ

b isthecombinationofthestatisticalandprofiledsystematic uncertainties,whilethe secondis dueto thenonprofiled system-aticcomponents.Theupperlimiton

μ

sd takesintoaccount both profiledandnonprofiledsystematicuncertainties.

In the following, we describe the signal extraction using the valuesoftheCKM elements directlyasparameters inthefit and applyingconstraintsfromtheSM scenarioandthen twopossible beyond-the-SM(BSM)extensions.

8.1. Measurement in the SM scenario

One can simplify Eq. (4) by assuming the SM unitarity con-straint

|

V_tb

|

2

+ |

Vtd|2

+ |

V_ts

|

2

=

1.Thefitisrepeated,taking

|

V_tb

|

as the single free parameter and replacing

|

Vtd|2

+ |

V_ts

|

2 with 1

− |

V_tb

|

2.Inthiscase,Eq. (4) becomes:

μ

b

=

|

V_tb

|

4_obs

|

V_tb

|

4

μ

sd

=

|

Vtb

|

2obs



1

− |

Vtb

|

2obs



|

V_tb

|

2



1

− |

V_tb

|

2

 .

(7)

Thefit isonly allowed to returnvalues of

|

V_tb

|

≤

1, andthe constraint

|

Vtd|2

+ |

V_ts

|

2

=

1

− |

V_tb

|

2 isimposed.Becauseofthese constraints,Gaussian behaviouroftheuncertaintiescannotbe as-sumed.Instead,pseudo-experimentsaregeneratedtoevaluatethe impactofnonprofileduncertainties onthemeasurement,andthe followingconfidenceintervalsaremeasuredat95%CL:

|

Vtb

| >

0

.

970

|

V_td

|

2

+ |

V_ts

|

2

<

0

.

057

.

(8)

Thismeasurement is comparable with theprevious mostprecise estimateusingtt eventsfromRef. [17],andwiththeresultofthe combinationofsingletopquarkmeasurementsinRef. [29].

8.2. Measurements for two BSM scenarios

Any BSM contribution potentially enhancing

|

Vtb

|

2

,

|

Vts

|

2

,or

|

Vtd|2 canaffecttopquark production,decay,orboth.SomeBSM scenariospredictthepresenceofadditionalquark families.Inthis case,theCKMmatrixisextendedduetothemixingbetweenthe SMquarksandthenewhypothesisedones.Thiswouldimplythat theCKMmatrixelements

|

Vtb

|

,

|

Vts|,and

|

Vtd|wouldnot neces-sarilysatisfytheunitarityconstraintof

|

Vtb

|

2

+ |

Vts

|

2

+ |

Vtd|2

=

1. Ifthese BSMquarks are heavier than the top quark, they would altertheCKMmatrixelementswithoutappearingastopquark de-cay products.They wouldthus not contribute directlyto the top quark decay width

t, but only indirectlybecause of the reduc-tionin theabsolutevalues ofthecorresponding SM CKM matrix elements.

For the first BSM scenario, we assume the top quark decays throughthesamechannelsasintheSMcase,andthatthepartial widthofeachdecayonlyvariesbecauseofamodifiedCKMmatrix

element.Inthiscase,bywriting

_t and

_q asafunctionof

|

V_tb

|

2

and

|

Vtd|2

+ |

V_ts

|

2,Eq. (5) becomes:

μ

_b

=

|

Vtb

|

4 obs

|

V_tb

|

4



|

V_tb

|

2_obs

+ |

V_ts

|

2_obs

+ |

V_td

|

2_obs



μ

_sd

=

|

Vtb

|

2 obs



|

V_ts

|

2_obs

+ |

V_td

|

2_obs





|

V_ts

|

2

+ |

V_td

|

2



|

V_tb

|

2_obs

+ |

V_ts

|

2_obs

+ |

V_td

|

2_obs

.

(9)

In this scenario, the measurement is performed leaving

|

Vtb|

and

|

Vtd|2 +

|

Vts|2 asfreeparametersinthefit,resultingin:

|

V_tb

| =

0

.

988

±

0

.

027

(

stat+prof

)

±

0

.

043

(

nonprof

)

|

V_td

|

2

+ |

V_ts

|

2

=

0

.

06

±

0

.

05

(

stat+prof

)

+₋00..0403

(

nonprof

).

(10) In the second BSM scenario, the top quark partial width is unchanged, but the total width increases due to additional, un-detecteddecays.Inthefit,thepartialwidthsfordecaystoknown quarks arefixed, andthe total widthisa free parameter and al-lowedtovary.Theeffectson

t duetovariationsin

|

Vtb

|

2 ,

|

Vtd|2, and

|

Vts

|

2

areneglected.

Inthisscenario,Eq. (5) ismodifiedto:

μ

b

=

|

V_tb

|

4_obs

t

|

V_tb

|

4

obs_t

μ

sd

=

|

Vtb

|

2obs



|

Vts

|

2obs

+ |

Vtd

|

2obs



t

|

V_tb

|

2



|

V_ts

|

2

+ |

V_td

|

2



obst

.

(11) Using

|

Vtb

|

2 ,

|

Vtd

|

2

+ |

Vts

|

2

,andR

=

obst

/

t asthefree pa-rametersinthefit,weobtain:

|

V_tb

| =

0

.

988

±

0

.

011

(

stat+prof

)

±

0

.

021

(

nonprof

)

|

V_td

|

2

+ |

V_ts

|

2

=

0

.

06

±

0

.

05

(

stat+prof

)

±

0

.

04

(

nonprof

)

R

=

0

.

99

±

0

.

42

(

stat+prof

)

±

0

.

03

(

nonprof

).

(12)

The measured correlation factors between the three parameters are

ρ

_|V

tb|,|Vtd|

2

= −

0

.

19,

ρ

_|V

t b|,R

= −

0

.

78,and

ρ

R ,|Vtd|

2

= −

0

.

21.

Thismeasurementisingood agreementwiththeother measure-ments fromRefs. [17,29,69,70], which howevermake use of the SM assumptions. Theresults forthesecond BSM scenariohavea higherstatisticalprecisionthanthoseforthefirstscenariobecause oftheweaker dependenceofthesignal strengthon

|

Vtb

|

forthe firstscenario.

AsmentionedinSection1,constraintson

|

V_td

|

and

|

Vts|from precisionlow-energymeasurementsdonotnecessarilyholdwhen BSMparticlesarepresentintherelevantFeynmandiagramloops. Theoretical studies have shown that values of

|

V_ts

|

up to about 0

.

2 are possible insome BSMscenarios [13]. The measurements presentedhereestablishamodel-independentupperlimiton

|

Vtd|

and

|

V_ts

|

by removing any assumed theoretical hypotheses. This willnowallownewinterpretationsforpossiblemixingofSMand BSMprocesses.

Alternativeapproachesinterpretthe available singletop quark measurements in terms of different scenarios for modifying the CKM matrix elements (see, for example,Ref. [32]),obtaining re-sults that are comparable with the measurements presented in this Letter. Such approaches, however, do not allow changes in the decay vertexof the top quark, anddo not consider possible similaritiesinthefeaturesofthe S T_b,q signalandbackground pro-cesses.

The current analysis improves the precision on

|

V_tb

|

by 50% withrespecttopreviousstudies [10] byexploitingthetWb vertex

in the top quark decay, and is more precise than the combined ATLASandCMSmeasurementusingdataat

√

s

=

7 and8 TeV [29].

9. Summary

AmeasurementoftheCabibbo–Kobayashi–Maskawa(CKM) ma-trix elements

|

Vtb

|

,

|

Vtd|, and

|

Vts

|

has been performed in an eventsampleenrichedin

t-channel

singletopquarkevents, featur-ingone muonorelectronandjetsinthefinal state.Thedataare fromproton-protoncollisionsat

√

s

=

13 TeV,acquiredattheLHC bytheCMSexperimentandcorrespondtoanintegrated luminos-ityof35.9 fb−1.Thecontributionsfromsingletopquarkprocesses featuringall threematrixelements intheproductionvertexhave beenconsideredasseparate signalprocesses,aswellas contribu-tions from decays of single top quarks involving all three quark families. The yields of the signal processes have been extracted throughasimultaneousfittodataindifferentselectedevent cat-egories, and the values of the CKM matrix elements have been inferredfromthesignalstrengths,whicharetheratiosofthe mea-suredtopquark

t-channel

crosssectionstimesbranchingratiosto theexpectedvalues.Thesignalstrengthsobtainedfromthefitare

μ

b

=

0

.

99

±

0

.

12,wheretheuncertaintyincludesboththe statis-ticalandsystematiccomponents,and

μ

sd

<

87at 95% confidence level(CL).

Under the standard model assumption of CKM unitarity, the valuesarefound tobe

|

Vtb

|

>

0

.

970 and

|

Vtd|

2

+ |

Vts

|

2

<

0

.

057, bothat95% CL.

Fits were also performed under two different beyond-the-standard-model scenarios. In the first, we assume the presence ofadditional quark families that are heavier than the top quark. The unitarity constraint for the three CKM matrix elements no longerholds,butthetopquark decaysthroughthesamechannels as in the standard model. We assume the partial width of each top quark decay only varies because of a modified CKM matrix element.Thefitgives:

|

Vtb

| =

0

.

988

±

0

.

051

|

V_td

|

2

+ |

V_ts

|

2

=

0

.

06

±

0

.

06

,

wheretheuncertaintiesincludeboththestatisticalandsystematic components.

In the second scenario, the top quark width is left uncon-strainedundertheassumption that thecontributionsto thetotal widthfromthemixingofthethreefamiliesarenegligible.The cor-respondingmeasuredvaluesare:

|

V_tb

| =

0

.

988

±

0

.

024

,

|

V_td

|

2

+ |

V_ts

|

2

=

0

.

06

±

0

.

06

,

obst

t

=

0

.

99

±

0

.

42

,

whereagain, both the statisticalandsystematicuncertainties are included.Thedifferencesamongtheuncertaintiesinthepresented scenarios are driven by the difference in the functional depen-dence of the observed event yields from the CKM matrix ele-ments. This resultsin smaller uncertainties in

|

Vtb|for the case where a fourth–power dependenceis considered with respectto thesecond–powerdependencecase.

Allresultsare consistentwitheachother,andshow no devia-tion withrespect to extrapolations oflow-energy measurements. These results are the first direct, model-independent measure-mentsoftheCKMmatrixelementsforthethird-generationquarks, andprovidethebestdetermination ofthesefundamentalSM pa-rametersviasingletopquarkmeasurements.

Declarationofcompetinginterest

Theauthorsdeclarethattheyhavenoknowncompeting finan-cialinterestsorpersonalrelationshipsthatcouldhaveappearedto influencetheworkreportedinthispaper.

Acknowledgements

WecongratulateourcolleaguesintheCERNaccelerator depart-ments for the excellent performance of the LHC and thank the technical andadministrativestaffs atCERNand atother CMS in-stitutes for their contributions to the success of the CMS effort. Inaddition,wegratefullyacknowledgethecomputingcentresand personneloftheWorldwideLHCComputingGridfordeliveringso effectively thecomputinginfrastructure essentialto our analyses. Finally, we acknowledge the enduring support for the construc-tion andoperationofthe LHCandtheCMSdetectorprovided by the followingfundingagencies: BMBWFandFWF(Austria);FNRS and FWO (Belgium); CNPq, CAPES,FAPERJ, FAPERGS, andFAPESP (Brazil); MES (Bulgaria); CERN; CAS, MOST, and NSFC (China); COLCIENCIAS (Colombia); MSES and CSF (Croatia); RPF (Cyprus); SENESCYT (Ecuador); MoER, ERC IUT, PUT and ERDF (Estonia); AcademyofFinland,MEC,andHIP(Finland);CEAandCNRS/IN2P3 (France); BMBF, DFG, and HGF (Germany); GSRT (Greece); NK-FIA (Hungary); DAE and DST (India); IPM (Iran); SFI (Ireland); INFN (Italy);MSIPandNRF(RepublicofKorea);MES(Latvia);LAS (Lithuania);MOEandUM(Malaysia);BUAP,CINVESTAV,CONACYT, LNS,SEP,andUASLP-FAI(Mexico);MOS(Montenegro);MBIE(New Zealand); PAEC (Pakistan); MSHE and NSC (Poland); FCT (Portu-gal);JINR(Dubna);MON,ROSATOM, RAS,RFBR,andNRCKI (Rus-sia);MESTD(Serbia);SEIDI,CPAN,PCTI,andFEDER(Spain);MoSTR (Sri Lanka); Swiss Funding Agencies (Switzerland); MST (Taipei); ThEPCenter,IPST,STAR, andNSTDA(Thailand);TUBITAKandTAEK (Turkey); NASU (Ukraine); STFC (United Kingdom); DOEand NSF (USA).

Individuals have received support from the Marie-Curie pro-gramme and the European Research Council and Horizon 2020 Grant, contract Nos. 675440, 752730, and 765710 (European Union); the Leventis Foundation; the Alfred P. Sloan Foundation; theAlexandervon HumboldtFoundation;theBelgianFederal Sci-ence Policy Office; the Fonds pour la Formation à la Recherche dansl’Industrieetdansl’Agriculture(FRIA-Belgium);theAgentschap voor Innovatie door Wetenschap en Technologie (IWT-Belgium); the F.R.S.-FNRS andFWO(Belgium) under the“Excellence of Sci-ence – EOS” – be.h project n. 30820817; the Beijing Municipal Science & Technology Commission, No. Z191100007219010; The Ministry of Education, Youth and Sports (MEYS) of the Czech Republic;theDeutscheForschungsgemeinschaft(DFG)under Ger-many’s Excellence Strategy – EXC 2121 “Quantum Universe” – 390833306;theLendület(“Momentum”)ProgrammeandtheJános BolyaiResearchScholarshipoftheHungarianAcademyofSciences, the New National Excellence Program ÚNKP, the NKFIA research grants123842,123959,124845,124850,125105,128713,128786, and129058 (Hungary); theCouncil of Scienceand Industrial Re-search, India; the HOMING PLUS programme of the Foundation for Polish Science, cofinanced from European Union, European Regional Development Fund, the Mobility Plus programme of the Ministry of Science and Higher Education, the National Sci-ence 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;theNational Priori-tiesResearchProgrambyQatar NationalResearchFund;the Min-istryofScienceandEducation,grantno.14.W03.31.0026(Russia); the Tomsk Polytechnic University Competitiveness Enhancement Programand“Nauka”Project FSWW-2020-0008(Russia);the Pro-gramaEstatalde Fomento de laInvestigaciónCientífica yTécnica