Measurement of spin correlations in tf production using the matrix element method in the muon plus jets final state in pp collisions at root S=8 TeV

(1)

Contents lists available atScienceDirect

Physics

Letters

B

www.elsevier.com/locate/physletb

Measurement

of

spin

correlations

in

tt production

using

the

matrix

element

method

in

the

muon+jets

ﬁnal

state

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: Received19November2015

Receivedinrevisedform14March2016 Accepted2May2016

Availableonline6May2016 Editor:M.Doser

Keywords: CMS LHC Topquark

Matrixelementmethod Spin

Theconsistencyofthespincorrelationstrengthintopquarkpairproductionwiththestandardmodel (SM)predictionistestedinthemuon+jetsﬁnalstate.Theeventsareselectedfromppcollisions,collected bytheCMSdetector,atacentre-of-massenergyof8 TeV,correspondingtoanintegratedluminosityof 19.7 fb−1_._The _data _are _compared_with _the _expectation_for _the_spin _correlation _predicted _by_the _SM

and with the expectation of nocorrelation. Usinga template ﬁtmethod, the fraction of events that showSMspincorrelationsismeasuredtobe0.72±0.08(stat)+₋0₀._.15₁₃(syst),representingthemostprecise measurementofthisquantityinthemuon+jetsﬁnalstatetodate.

1. Introduction

At the CERN LHC top quarks are predominantly produced in pairs(tt), mainly viagluon fusion, witheach top quark decaying almost 100% ofthe time intoa W boson anda b quark. The ﬁ-nal statescan be categorised asdilepton, where both W’sdecay intoaleptonandaneutrino, hadronic,wherebothW’sdecayinto quarks,andlepton+jets otherwise.TheW decayintoataulepton andneutrinoisonlyconsideredleptonicifthe

τ

decaysincludea muonorelectron.

Inquantum chromodynamics(QCD), the quark spinsin heavy quark productionare correlated.Since the lifetimeof top quarks is smaller than the hadronisation timescale (1

/

QCD), which in turnis smallerthan the spin decorrelation timescale mt

/

2_QCD

∼

3

×

10−21_s, _the _top _quarks _decay _before _their _spins _decorrelate. Thisspincorrelationisthereforepropagated tothetopquark de-cayproducts andonecaninfer thett spincorrelationstrength A

bystudyingtheangularcorrelationsbetweenthedecayproducts, where

A

=

(N

↑↑

+

N↓↓

)

− (

N↑↓

+

N↓↑

)

(N

_↑↑

+

N_↓↓

)

+ (

N_↑↓

+

N_↓↑

)

(1)

_E-mail_address:_{cms-publication-committee-chair@cern.ch}_.

istheasymmetrybetweenthenumberoftt pairswithalignedand antialignedspins.Thevalueof

A depends

onthespinquantization axischosenandontheproductionmodes.

Giventhe highcentre-of-mass energyat theLHC, the helicity basisisusedwherethespinquantizationaxisisdeﬁnedasthetop quark orantiquarkdirectioninthett restframe.The correspond-ing value ofthe spin correlation strength in the helicitybasis is referredtoasAhel.Sincethespincorrelationstrengthisprecisely, butnon-trivially, predictedby the standardmodel (SM) an accu-ratemeasurementofthisvariabletestsvariousaspectsoftheSM, includingthestrengthoftheQCDcouplingandtherelative contri-butionoftt productionmodes,althoughnewphysicscaninﬂuence thespincorrelationstrength[1,2].

Tevatron experimentsmade measurements of the tt spin cor-relation strength using template ﬁts to the angular distributions ofthe top quark decayproducts andextractingthe fractionof tt eventswiththeSMpredictionofspincorrelation f deﬁned as

f

=

N tt SM Ntt_SM

+

Nuncortt

,

(2) where Ntt

SM is the number of SM tt events, whereas Nuncortt rep-resentsthenumberofeventswithuncorrelatedtt.Thetopquark andantiquarkintheuncorrelatedtt eventsdecayspherically.The assumption isthat thereare onlySM anduncorrelated tt events,

http://dx.doi.org/10.1016/j.physletb.2016.05.005

(2)

witha fractionof

(

1

−

f

)

ofuncorrelatedtt events. The physical rangeofthisparameter f is restrictedto[0, 1],with f

=

1 fora sampleoftt eventsproduced bytheSM. However,quiteoftenan unconstrainedtemplatefitisperformed,allowingfornon-physical valuesofthisparameter.TheCDFCollaborationextractedthe frac-tion f of eventswiththeSM predictionofspincorrelation using the lepton+jetsfinal state [3]andthe D0 Collaboration extracted thisfractionusingthedilepton finalstates [4,5].The D0 Collabo-rationalsomadeaspincorrelationmeasurementusingthematrix element method(MEM) [6]in thedilepton final state andfound directevidence oftt spin correlation by combiningthe measure-mentsusingMEM inthedileptonandlepton+jetsfinal states[7]. The combined measurement yielded f

=

0

.

85

±

0

.

29(stat + syst) usingadatasampleofpp collisionsat

√

s

=

1

.

96TeV, correspond-ingtoanintegratedluminosityof5.3 fb−1.

AttheLHC,theATLASCollaborationhasreportedobservationof spincorrelationsintopquark pairproduction[8].Inthemost re-centmeasurementbytheATLASCollaboration,thespincorrelation measurement was performed usingtemplate ﬁts to the distribu-tionof thedifference inazimuthal anglebetweenthe two oppo-sitelychargedleptonsinthedileptonﬁnalstate.Thismeasurement at

√

s

=

8TeV,using20.3 fb−1ofintegratedluminosity,resultedin

f

=

1

.

20

±

0

.

05(stat)

±

0

.

13(syst)[9].AnotherresultbyATLAS in thedileptonchannelhasbeenreportedin[10].Theonly measure-mentinthelepton+jetsﬁnal stateattheLHCsofarwasmadeby theATLASCollaborationusingtheopeningangledistributions be-tweenthedecayproductsofthetopquarkandantiquark[11], giv-ing f

=

1

.

12

±

0

.

11(stat)

±

0

.

22(syst) at

√

s

=

7TeV,using4.6 fb−1 ofintegratedluminosity.

Here, a measurement of the top quark spin correlations in eventscharacterisedbythepresence ofamuonandjets(

μ

+jets) is described using a MEM at

√

s

=

8TeV with 19.7 fb−1 of inte-grated luminosity. Events with a muon coming from a

τ

decay arenotconsideredaspartofthesignal.Inthisanalysis, the tradi-tionaldiscretehypothesesareinvestigated:SManduncorrelatedtt productionanddecay.Inthe MEM,thelikelihoodofan observed eventto be produced by a giventheoretical model is calculated. The likelihood ratioof the sample allows to distinguish between the two hypotheses. In addition, the distribution of event likeli-hood ratiosis used ina template ﬁt to extract the fraction f of

eventswiththeSMpredictionofspincorrelation.

The restof thisLetter is organised asfollows.In Section 2,a description ofthe apparatusused in thismeasurement, the CMS detector,isgiven.Following,inSection3,adescriptionofthe sim-ulationsamplesusedinthisanalysisisgiven.Theeventselection and reconstruction procedure of the physics objects in an event aregiveninSection 4.InSection 5,theMEMisbrieﬂy explained. Section 6describesthe ﬁrstpartof thisanalysis, the hypothesis-testingprocedure,followedbytheextractionofthevariable f with

atemplateﬁtinSection7.Thesourcesofsystematicuncertainties arediscussedinSection8.Adescriptiononthetreatmentofthese uncertaintiesinbothpartsoftheanalysisandtheresultsaregiven inSection9.Finally,asummaryoftheanalysisispresentedin Sec-tion10.

2. TheCMSdetector

The central feature of the CMS apparatus [12] is a 3.8 T su-perconductingsolenoidof6 m internaldiameter.Thesiliconpixel andstriptrackerusedformeasuring charged-particle trajectories, a lead tungstate crystal electromagnetic calorimeter (ECAL), and the brass and scintillator hadron calorimeter (HCAL) are located within the superconducting solenoid volume. The calorimeters, ECALandHCAL,bothofwhichconsistofabarrelandtwoendcap sections,surroundthe silicontrackingvolume.Forward

calorime-tryextendsthecoverageprovidedbythebarrelandendcap detec-torstoapseudorapidityof

|

η

|

=

5.

Muons are measured using the tracker andthe muon system that consists of gas-ionization detectors embedded in the steel ﬂux-return yoke outside the solenoid. Muons are measured in therange

|

η

|

<

2

.

4,usingthreedetectortechnologies:drifttubes, cathode strip chambers, and resistive-plate chambers. Matching muonstotracksmeasuredinthesilicontrackerresultsinarelative transversemomentum(pT)resolutionof1.3–2.0%inthebarreland betterthan6%intheendcapsformuonswith20

<

pT

<

100GeV. The

p

Tresolutioninthebarrelisbetterthan10%formuonswith

pT upto1 TeV[13].

The ﬁrstleveloftheCMStriggersystem,composed ofcustom hardware processors, uses informationfromthe calorimetersand muon detectors to select the most interesting events. The high-leveltriggerprocessorfarm furtherdecreasestheeventratefrom around100 kHz toaround400 Hz,beforedatastorage.

A more detailed description of the CMS detector, together witha deﬁnitionof thecoordinatesystemused, canbe found in Ref.[12].

3. Signalandbackgroundmodeling

The signal processes (tt events in the

μ

+jets ﬁnal state, SM and uncorrelated) as well as other tt decay channels (SM and uncorrelated) are simulated on the basis of a next-to-leading-order (NLO) calculation using the generator mc@nlo v3.41 [14]

with a top quark mass of 172.5 GeV. Parton showering is simu-latedusing herwig 6.520[15]andthedefault herwig6underlying eventtune was used.The NLOpartondistribution function (PDF) set used is cteq6m [16]. The background samplesof W+jetsand Z/

γ

*+jets processes are generated using MadGraph 5.1.3.30 [17], pythia 6.426, and tauola v27.121.5 [18]. The backgrounds from singletopquarkprocessesaregeneratedusing powheg v1[19–21]

and tauola[22].TheZ2*underlyingeventtuneisused.Themost recent pythia Z2* tune is derived from the Z1 tune [23], which uses the CTEQ5L parton distributions set, whereas Z2* adopts CTEQ6L[24].ThegeneratedeventsareprocessedthroughtheCMS detector simulation based on Geant4[25] andevent reconstruc-tion. To estimate the size of the effect of the top quark mass andfactorisationandrenormalisationscaleuncertainties, mc@nlo samples with varied top quark mass and scales are used. The signal event yields are scaled to match the predicted top quark pair productioncrosssection inproton–protoncollisions at

√

s

=

8TeV, which is

σ

NNLO+NNLL tt

=

245

.

8

+6.2

−8.4(scales)+ 6.2

−6.4(PDF) pb for a topquarkmassequaltotheworldaverageof173.3 GeV[26], com-puted withnext-to-next-to-leading-order(NNLO) QCDcorrections and next-to-next-to-leading-logarithmic (NNLL) resummation ac-curacy [27]. Thesimulated samplesforthe backgroundprocesses are normalised using cross section calculations, generally atNLO accuracy [27]. Where necessary, systematically varied cross sec-tionshavebeenusedforthenormalisation.Thesimulationis cor-rected tothe pileup conditionsseen inthe data.Pileup refers to theadditionalproton–protoninteractionsrecordedsimultaneously from the same bunch crossing. During 2012 data taking, there wereonaverage20interactionsperbunchcrossing.

4. Eventreconstructionandselection

The event selection has been optimised to identify tt events in the

μ

+jets ﬁnal state. A single-muontrigger witha muon pT thresholdof24 GeV and arestrictiononthepseudorapidity

|

η

|

<

2

.

1 isusedtocollectthedatasamples.Isolationandidentiﬁcation criteriaareappliedatthetriggerleveltoachievemanageablerates withminimallossofeﬃciency.

(3)

Thephysicsobjectsusedinthisanalysisarereconstructedwith theCMSparticle-ﬂow(PF)algorithm[28,29].ThePFalgorithm re-constructsandidentiﬁeseachindividualparticleinaneventusing combined information fromall CMS subdetectors. The energy of photonsisdirectlyobtainedfromtheECALmeasurement.The en-ergyofelectronsisdeterminedfromacombinationoftheelectron momentum measured at the primary interaction vertex by the tracker,theenergyofthematchedECALcluster,andthetotal en-ergyoftheassociatedbremsstrahlungphotons.Themomentumof muonsis obtained fromthe curvature of the trackassociated to the muon. The energy of chargedhadrons is determined from a combinationof their momenta measured in the tracker and the matchingenergydepositsintheECALandHCAL,correctedforthe calorimeterresponse to hadronic showers. Finally, the energy of neutralhadronsisobtainedfromthecorrespondingcorrectedECAL andHCALenergy.

Thereconstructedmuon candidatesare requiredtohave pT

>

26GeV and

|

η

|

<

2

.

1, as to be in a region where the trigger is fullyeﬃcient. The trackassociated to the muon candidate is re-quiredtohaveaminimumnumberofhitsinthesilicontracker,to beconsistentwiththeprimaryvertex, andtohaveahigh-quality ﬁtwhich combines a trackin the trackerand a minimum num-berof hitsinthe muon detectorsinto one track.Foreach muon candidate,aPF-basedrelativeisolation iscalculated,correctedfor pileupeffectsonanevent-by-eventbasis.Thetransversemomenta ofallreconstructedparticlecandidates(excludingthemuonitself) aresummed ina coneof size

R

<

0

.

4 around themuon direc-tion,with

R

=

(

η

)

2

_{+ (φ)}

2 _where

_φ

_is_the_azimuthal_angle expressedinradians.Thepileupcontributioninthisscalarsumis correctedforby summingonly overthe chargedparticles associ-atedtotheeventvertexinthechargedparticlecontribution,and subtractingtheaverageenergyduetopileupintheneutral parti-clecontribution.After subtractionofthe pileup contribution,the scalarsumisrequiredtobesmallerthan12%ofthemuon pT.Itis requiredthatexactlyoneofthesewell-identiﬁedmuoncandidates ispresentintheevent.Inaddition,alooserselectiononmuonsis appliedwhichrequiresarelativeisolation oflessthan20%ofthe muon pT, a selection of pT

>

10GeV and

|

η

|

<

2

.

5. Events with additionalmuonspassing looser identificationcriteria, aswell as eventswithan electronarediscarded.Events selectedfromother tt finalstatesaredenotedas“tt other”andconsistofroughly70% tt eventsin thedileptonfinal state and30% eventsinthe

τ

+jets ﬁnalstate.

For each event, hadronic jets are clustered from the recon-structedparticle-flowparticleswiththeanti-kT algorithm[30,31], withadistanceparameterof0.5.Thejetmomentumisdetermined asthe vector sum of all particle momenta inthe jet, which has beendetermined from simulationto be within 5% to 10% of the truemomentumoverthewhole pT spectrumanddetector accep-tance.Contributionsfrompileuparetakenintoaccountbyan off-setcorrectiontothejetenergies.Jetenergyscalecorrections(JES) uptoparticle-levelarederivedfromsimulation,andareconfirmed within-situmeasurementsoftheenergybalanceindijetand pho-ton+jetevents.Thejetenergyresolution(JER)insimulationis cor-rectedtomatchtheresolutionobservedindata.Additional selec-tioncriteriaare appliedtoeacheventtoremovespurious jet-like features originating from isolated uncharacteristic noise patterns incertainHCALregions[32]andinthesiliconavalanche photodi-odesusedinthe ECALbarreldetector.Thefirst threejetsleading inpTarerequiredtohavea

p

Tofatleast30 GeV,thefourth lead-ingjetofatleast25 GeV andtheremainingjetsatleast20 GeV.At leasttwoselectedjetsshouldbeidentiﬁedascomingfromthe de-cayofB-hadrons,based onthecombinedsecondary vertex(CSV) algorithmwithmediumworkingpoint(CSVM)[33].TheCSV algo-rithmmakes useofsecondary vertices,whenavailable,combined

Table 1

Eventyieldaftereventselection,withthestatistical uncertainties.Thecontributionsfromvariousphysics processesaregiven,withacomparisonbetweenthe dataandthetotalsimulationatthebottom.

Process Yield W+jets 722±20 Z/γ*+jets 139±18 t,t (s channel) 41±3 t,t (t channel) 314±10 t,t (tW) 935±20 tt other 3896±24 ttμ+jets 31 992±69 Total simulation 38 039±81 Data 37 775

withtrack-basedb-lifetimeinformation.Asthetrackercoverage is limitedto

|

η

|

<

2

.

4,all selected jets(both taggedand untagged) arerestrictedtothispseudorapidityrange.Themissingtransverse momentumvector

pmiss

T isdeﬁnedastheprojectionontheplane perpendiculartothebeamsofthenegativevectorsumofthe mo-menta ofall reconstructedparticles inan event. Itsmagnitudeis referred to as Emiss_T .Toreduce the effectof FinalState Radiation (FSR), while not statisticallylimitingthe analysis, we restrict the data set to eventswith fouror ﬁve selected jets. Toensure that theselectedjetsintheeventdescribethett kinematicquantities, werejecteventsiftheyhaveadditionalforwardjetsintheregion of2

.

4

<

|

η

|

<

4

.

7 andthesehave pT

>

50GeV.

Tofurtherincreasethequalityoftheeventselectionandreduce thebackgroundcontribution,weuseakinematicfitter, HitFit[34], designedto reconstructthekinematicquantities ofthett system inthelepton+jetsfinalstate.Thekinematicquantitiesobservedin theeventarevariedwithinthedetectorresolutiontosatisfysome predefinedconstraints,i.e.thereconstructedhadronicallydecaying Wbosonmassisrequiredtobeconsistentwith80.4 GeV andthe reconstructed topquark andantiquark massesarerequired tobe equal.The HitFit algorithmtrieseveryjet-quarkpermutationand thesolutionwiththehighestgoodness-of-fit(orequivalently, low-est

χ

2

_/

_{ndof with}_ndof_being_the_number_of_degrees_of_freedom)_is chosen asthebestestimate ofthecorrectjet-quarkpermutation. We do not rely on HitFit to estimate the jet-quarkpermutation correctly,however, HitFit isusedtodecidewhichfourjetsinthe eventto use inthe reconstruction ofthe tt final state in five-jet events. It is required that two of the jets selected by HitFit are identified asoriginatingfromB-hadrons.Theselection ofthejets intheeventcouldbedonewithsimplermethods,e.g.selectingthe highest-pTjets,but HitFit offersthepossibilitytoapplyadditional qualitycriteria.Inordertoreducethebackgroundfractionandthe fractionofmismodeledevents,weonlyselecteventswitha HitFit

χ

2

_/

_ndof

_<

_{5 or,} _{equivalently,}_with _the _ﬁt _probability _larger _than 0.08. The value of the

χ

2

_/

_{ndof-selection} _is _chosen _to _maximise theseparationpowerdeﬁnedbyEq.(7)inSection 6.Mismodeled eventscanbeduetotheinclusionofradiatedjetsinthett recon-struction or events with poorly reconstructed jet quantities. The

χ

2 _probability _distribution _is _shown _for _data _and _simulation _in

Fig. 1, wherethe relative contributions ofthe simulationare de-terminedfromthetheoreticalcrosssections.

The event yield after the full event selection is displayed in

Table 1.Thecontributionsareestimatedfromsimulationand nor-malisedtotheobservedluminosityusingtheoreticalcrosssections. TheselectioneﬃciencyfortheSManduncorrelatedsignalsamples areverysimilarsothattheeventselectiondoesnotbiasthedata towardsonehypothesis.Thebackgroundcontributiondueto mul-tijetprocesseshasbeenestimatedfromsimulationandisfoundto benegligible.

(4)

Fig. 1. The

χ

2_probability_distribution_of_the_selected_solutions_of_the_kinematic_ﬁt

inthe

μ

+jetschannel,showingashapecomparisonbetweendataandsimulation includingthestatisticaluncertainties.Therelativecontributionsinsimulationare calculatedusingthetheoretical crosssectionswith thetotalyieldnormalisedto data.Fortheanalysis,weonlyconsidereventswithaprobabilitylargerthan0.08, asindicatedbythearrow.

5. Matrixelementmethod

Thematrixelementmethod[35–38]isatechniquethatdirectly relatestheory withexperimental events.Thecompatibilityofthe data recorded with the leading-order (LO) matrix element (ME) ofacertain process isevaluated. Theprobability that aneventis producedbythisprocessiscalculatedusingthefullkinematic in-formationintheevent.

The probability P

(

xi

|

H

)

to observe an eventi with kinematic

properties

x for

acertainhypothesis

H is

givenby:

P(xi

|

H)

=

1

σ

obs

(

H)

fPDF

(q

1

)

fPDF

(q

2

)

dq1dq2

(

2π

)

4

|

M(y,H)

|

2 q1q2s W

(x

i

,

y)d

6

.

(3)

The given probability is equivalent to an event likelihood. In thisequation, q1 and

q

2 representthe partonenergyfractions in thecollision, fPDF

(

q1

)

and fPDF

(

q2

)

arethePDFs,

s is

the centre-of-massenergysquaredofthecollidingprotons,andd

6 represents the phase spacevolume element. The transfer function, W

(

x

,

y

)

, relatesobserved kinematic quantities x with parton-level quanti-ties y. For every y, the transfer function is normalised to unity by integratingover all possible values of x. The LO ME is repre-sentedby M

(

y

,

H

)

,where H denotes thehypothesis used.Thett spincorrelationstrengthisnotaparameteroftheSMLagrangian, therefore H is not a continuous parameter. The MEs M

(

y

,

H

cor

)

andM

(

y

,

H

uncor

)

both describett productionandsubsequent de-cay in the

μ

+jets channel valid for both on- and off-shell top quarks.In thisanalysis, the hypotheses are eitherthe SM (Hcor), givingriseto aﬁnitevalue ofthespin correlationstrength A (as

discussed in Section 1) or the spin-uncorrelatedhypothesis with

A

=

0 (Huncor). Finally,

σ

obs

(

H

)

represents the observed tt cross

section of the hypothesis, which ensures that the probability is normalised. The quantity

σ

obs

(

H

)

consists of the product of the production crosssection

σ

, whichis identicalforour considered hypotheses,andtheoverallselectioneﬃciency

(

H

)

.Theselection eﬃciency foreventsfrom both hypothesesare very similar, with aneﬃciencyof

(

S M

)

=

0

.

0448

±

0

.

0001(stat) fortheSM

tt signal

hypothesis,and

(

uncor

)

=

0

.

0458

±

0

.

0001(stat) forthe uncorre-latedsignal hypothesis,whichcauses acceptanceeffectstonearly cancel in the likelihood ratio. The likelihood calculation is per-formedusing MadWeight[39],inthe MadGraph5framework[17]. Since, inour convention,the likelihoodfor asingle eventis rep-resented by P

(

xi

|

H

)

, thelikelihood of asample withn events is

then

L(x1

, . . . ,x

n

|

H)

=

ni=1P(xi

|

H). (4)

Thetransferfunctionofagiveninteractingparticledependson thespecificsofthedetector.Inthisanalysis, thetransferfunction is usedto correctthe jet kinematicquantities. The reconstructed jet energy information, corrected for JES and JER, is mapped ontoparton-level quantitiesby integratingoverthepartonenergy withinthetransferfunctionresolutionduringthelikelihood calcu-lation.Allotherkinematicquantities(suchasangularinformation or lepton quantities) are unmodified by the transfer function as thesearemeasuredwithsufficientaccuracywiththeCMSdetector todescribeafinalstatethatdoesnotincludeadileptonresonance. The description of these variables with a Dirac delta function speedsuptheintegration.The Emiss_T isalsodescribedwithaDirac deltafunctionandisonlyusedtocorrectthekinematicquantities of the eventfor thetransverse Lorentz boost.The eventtransfer function istheproduct oftheobjecttransfer functions,assuming no correlation between thereconstructed objects. The jet energy transferfunctionisdeterminedfromtt simulationtowhichtheJES andJERcorrectionshavebeenapplied.Foreachjetinthe simula-tion, unambiguouslymatched to apartonwith

R

(

jet

,

parton

) <

0

.

3,the Ejetand

E

partonarecompared(separatelyforjetsmatched tobandlight-ﬂavourpartons).The

E

jetdistributionisﬁttedwitha Gaussianfunction,wheretheGaussianmeanandwidthdependon

Epartonandaregivenby

μ

(

Ejet

)

=

m0

(

η

parton

)

+

m1

(

η

parton

)

Eparton and

σ

(

Ejet

)

=

σ

0

(

η

parton

)

+

σ

1

(

η

parton

)

Eparton

+

σ

2

(

η

parton

)

Eparton respectively. The ﬁtofthe Ejet distribution isconverted toa sin-gle Gaussiantransferfunction,whichisa functionofthevariable

E

=

Eparton

−

Ejet andthe parameters are a function of Eparton. The transfer function, which is determined inthe full kinematic phasespace,isgivenby

W

(E

parton

,

Ejet

)

=

1

√

2π

σ

0

+

σ

1Eparton

+

σ

2

Eparton

×

exp

⎡

⎣−

1 2

E

+

m0

+

m1Eparton

σ

0

+

σ

1Eparton

+

σ

2

Eparton

2

⎤

⎦,

(5)

wheretheparametersaredeterminedindependentlyforbjetsand light-ﬂavourjets,inthreeslicesof

|

η

parton

|

givenby0

<

|

η

parton

|

<

0

.

87, 0

.

87

<

|

η

parton

|

<

1

.

48 and 1

.

48

<

|

η

parton

|

<

2

.

5. In Fig. 2, the

E distribution isshownforthe

E

=

Eparton

−

Ejetfrom sim-ulation forall valuesof Eparton and

|

η

parton

|

.This iscompared to the

E distribution obtained by folding the Eparton spectrum of matched partonswiththe transferfunction. The reasonablygood agreementoftheresolutionandthetailsofthetwodistributions showsthatthedeterminedtransferfunctionsareadequate.

The disadvantage of using a LO ME is that there is no ex-plicit treatment for ﬁnal state radiation in the MEs. As a result, the ME doesnot always coverthe full eventinformationleading

(5)

Fig. 2.E distributionsbasedonthevaluesobtainedfromsimulation(circles) com-paredtotheE distributionobtainedbyfoldingtheEpartonspectrumofmatched

partonswiththetransferfunction(squares)summedoverallvaluesofEpartonand

|ηparton|.ThemeanandRMSshownontheplotsareobtainedfromsimulation.The

ﬁgureisshownforbquarkjets(top)andforlightquarkjets(bottom).

toa slightlyreduced discrimination betweenbothhypotheses. In addition,backgroundevents evaluated undera tt hypothesis will morecloselyresemble theuncorrelatedhypothesisasthere isno correlation between the decay products. In the template fit part ofthisanalysis, thesmall bias dueto thiseffect iscorrected for witha calibrationcurve (described in Section 7), whereas inthe hypothesistestingthebackgroundcontributionisfixedtothe pre-dictionsfromsimulation,so nobias ispresent. MadWeight [39], thetoolusedtoperformtheMEMlikelihoodcalculations,can par-tiallycorrectfortheinitialstateradiation(ISR)effectbyevaluating the LO ME at an overall partonic pT of the tt system equal to the reconstructed pT of the system, thus properly treating five-jeteventswhereonejetisduetoISR.Duetofinalstateradiation (FSR), the matchingwith theLO ME,which requires fourjets as input,becomesmoredifficultandmoresensitivetosystematic un-certaintiesrelatedto variationson thejet energyscale oronthe renormalisation/factorisationscales.Thett systemisreconstructed usingthefourselectedjetsbasedon HitFit intheevent,the lep-tonandthe

pmiss_T .The

pmiss_T quantityisassignedtotheundetected neutrinofromthett muon+jetsﬁnalstate.Inthe MadWeight like-lihoodcalculations,everyjet-quarkpermutationcompatiblewithb tagginginformationistakenintoaccount.

6. Hypothesistesting

The compatibilityofthe datawiththeSM hypothesis andthe fully uncorrelated hypothesis is tested. The likelihood for each event is calculated under these two hypotheses, as described in Section 5. According to the Neyman–Pearson lemma, the test statistic with maximum separation power for a sample coming fromeitheroftwo simplehypothesesisthe likelihoodratio.This analysisuses

λ

event asthediscriminatingvariable,deﬁnedas

λ

event

=

P(Huncor

)

P(Hcor

)

,

(6)

where P

(

Hcor

)

is the likelihood for the eventunder the SM hy-pothesisandsimilarly

P

(

Huncor

)

fortheuncorrelatedhypothesis.

Followingthe prescriptionproposedby Cousinsetal.[40],we use

−

2ln

λ

event as test statistic, a quantity hereafter referred to asthe eventlikelihood ratio.The distributions of

−

2ln

λ

event are shownin

Fig. 3

forthe SM tt sample(Fig. 3-top)andthe uncor-related tt sample (Fig. 3-bottom). The plots show a shape com-parison between data and simulation. The differences between the SM and uncorrelated distribution are statistically signiﬁcant. The expected distribution of the sample likelihood ratio, deﬁned as

−

2ln

λ

sample

= −

2ln

λ

event,is calculatedby drawing pseudo-experimentswiththedatasamplesize.Inthepseudo-experiments, the relative signal and background ratios are kept ﬁxed based on the theoretical cross sections. These pseudo-experiments are performed with the SM and uncorrelated event likelihood ratio distributions, respectively. The bin width of the eventlikelihood ratio distribution is chosen as 0

.

14 and the range of the dis-tribution used is

[−

0

.

70

,

1

.

26

]

. Events outside this

−

2ln

λ

event rangeof

[−

0

.

70

,

1

.

26

]

arediscarded. Theshapedifferencesofthe

−

2ln

λ

event distribution between the SM and uncorrelatedsignal hypothesis outside of this range are not statistically signiﬁcant. The distribution of the sample likelihood ratios, using pseudo-experiments drawn at the data set size of 36800 events within therange

−

2ln

λ

event

= [−

0

.

70

,

1

.

26

]

,isshownin

Fig. 4

.Thesolid lineshowstheexpectedGaussian distributionofthesample like-lihoodratiosforthissizeusingtheSM tt simulationassignaland thedashed lineshowstheGaussian distributionusingthe uncor-related tt simulation assignal. A way ofquantifying the overlap betweenthe sample likelihood ratio distributions of thetwo hy-pothesesisgivenbytheseparationpower

S

=

μ

1

−

μ

2

α

₁2

+

α

2₂

,

(7)

with

μ

1,2 being the means of the distributions and

α

1,2 their width [40]. The separation power is a measure for the discrimi-nation obtainable, forthe size of the data set,between the two hypothesesexpressedinstandarddeviations(

σ

).

Fig. 4

showsthat aseparationpowerof8.8

σ

canbeobtainedwiththeMEMwhen onlystatisticaleffectsaretakenintoaccount.Thedistributionswill be modiﬁed by the inclusion of the systematic uncertainties de-scribed in Section 8. The rangeof the

−

2ln

λ

event distribution is chosen to maximise the separation power, while the binning is chosen ﬁnely enough to preserve the available separationpower. Inaddition,theeventselection(inparticulartheselectiononthe HitFit

χ

2

/

ndof)has been optimised to maximise the separation power.

7. ExtractionoffractionofeventswithSMspincorrelation

Weextractthefraction f of tt signaleventswiththeSMspin correlation byperforming atemplate ﬁttothe

−

2ln

λ

event distri-bution.TheﬁtmodelM

(

fobs

,

β

obs

)

isgivenby

(6)

Fig. 3. Distributionof−2lnλevent.TheSMtt simulationisusedinthetopplotand theuncorrelatedtt simulationinthebottomplot.Bothdataandsimulationare nor-malisedtounity.Thehatcheduncertaintybandincludesstatisticalandsystematic uncertainties.Theerrorbarsintheratioplotatthebottomonlyconsider statisti-caluncertainties(ofbothdataandsimulation),whiletheuncertaintybandcovers bothstatisticalandsystematicuncertainties.Systematicuncertaintiesaredescribed inSection8.Theoverlapofthegreenuncertaintyband,whichisconstructedaround themarkerposition,withtheratiovalueof1indicatesagreementbetweenthedata andthesimulationwithinthetotaluncertainty.

M

(

fobs

, β

obs

)

=

(

1

− β

obs

)

[ fobsTcor

+ (

1

−

fobs

)

Tuncor]

+ β

obsTbkg

,

(8)

where fobs isthefractionofeventswiththeSM spincorrelation, and

β

obs isthefractionofbackgroundinthedata.Thett signalSM template,thett signaluncorrelatedtemplate,andthebackground template are denoted by Tcor, Tuncor, and Tbkg, respectively. The

Fig. 4. Theexpected−2lnλsampledistributionestimatedusingsimulation,evaluated atthedatasamplesize.Thesamplesinsimulationcontainsignalandbackground mixedaccordingtothetheoreticalcrosssections,withthesolidGaussianfunction usingSMtt simulationandthedashedGaussianfunctionusinguncorrelatedtt sim-ulation.Fromthisﬁgure,theseparationpowercanbeassessedinthecasewhen systematiceffectsarenotconsidered.

backgroundtemplate contains theaveragedcontributionof thett other backgroundwithSM spincorrelation andthett otherwith nospincorrelationasthesecontributionsarethesamewithin sta-tistical uncertainties.Systematicuncertainties are not includedin the fit model.The parameter estimation is done using a binned maximum likelihood fit in RooFit [41], using Minuit [42]. The totalnormalisationisfixedtotheobserveddatayield,butthe rel-ativebackgroundcontributionandthefraction fobs areallowedto vary unconstrainedin thefit. Thebinning andrangeof the tem-platedistributionsarefixedtothoseusedinthehypothesistesting, where they have been chosen to optimize the separation power betweenthetwohypotheses.

There isa smallbiasin theextractionof fobs inthe template ﬁt dueto the presence of background in the sample. The back-ground shape resembles morethe behaviour ofthe uncorrelated template, andthe sizeofthe sample fromwhich thebackground templateisderivedissmall.Thesmallbiasiscorrectedforwitha calibrationfunction.Thebiasisestimatedfromthesimulationvia pseudo-experiments with the observed data set size for a range ofworkingpoints( finput,

β

input).Ateachworkingpoint,themean observed fobs and

β

obs areextractedtoconstructa2Dcalibration function, used to derive fcalibrated as a function of the observed

fobs and

β

obs. The fobs- and

β

obs-variables have been shiftedby theweighted averageoftheevaluatedworkingpointsto decorre-latetheﬁtparameters.Thecalibrationfunctionisgivenby

f

=

p0

+

p1fobs

+

p2fobs

β

obs

,

(9) with f_obs

=

fobs

−

0

.

502 and

β

_obs

= β

obs

−

0

.

150.Theﬁtparameters ofthecalibrationfunctionarelistedin

Table 2

.

Table 2

Fitparameters ofthe 2D calibration function. The residualcorrelationbetweentheﬁtparametersis be-low10%andisignored.

Parameter Value p0 0.5004±0.0003 p1 0.9207±0.0008 p2 −0.56±0.01 χ2 /ndof 80/95

(7)

Fig. 5. Resultofthetemplatefittodata.Thesquaresrepresentthedatawiththe statisticaluncertaintysmallerthanthemarkersize,thedottedcurveistheoverall resultofthefit,thesolidcurveisthecontributionoftheSMsignaltemplatetothe fit,thedashedcurveisthecontributionoftheuncorrelatedsignal,andthedash–dot curveisthebackgroundcontribution.

It has been checked that the initial valuesof the parameters in the fit model have no influence on the template fit result. The result of the template fit on the data is shown in Fig. 5

with fobs,data

=

0

.

747

±

0

.

092,

β

obs,data

=

0

.

168

±

0

.

024, and a

χ

2

_/

_ndof

₌

₁

_.

_552. _From _simulation, _a _background _fraction

_β

_of 15.5% is expected in the ﬁt range. After calibration of both the nominalresultandthestatisticaluncertainty,theresultis:

f

=

0

.

724

±

0

.

084 (stat)

.

(10) In the ﬁt to the

−

2ln

λ

event distribution in the range

[−

0

.

7

,

1

.

26

]

,thecorrelationbetween fobs,dataand

β

obs,data isaround54%. 8. Sourcesofsystematicuncertainty

Systematicuncertaintiesaffectingthisanalysiscomefrom vari-oussources,suchasdetectoreffects,theoreticaluncertainties,and mismodelinginthesimulation.Thesimulationiscorrectedwhere necessary by the use of event weights to account for efficiency differences in the data and simulation, e.g. muon identification, isolation efficiency, trigger efficiencies, b tagging andmistagging rates and pileup modeling. The systematic uncertainties are de-termined, independently of each other, by varying the efficiency correction,resolution, orscalecorrection factors within their un-certainties. For some uncertainties, this is equivalent to varying theeventweights,forothers,thisrequiresrecalculatingtheevent likelihoods.Inbothcases,the

−

2ln

λ

eventdistributionsfromwhich pseudo-experimentsaredrawn tocalculate thesample likelihood ratiosin simulationorthat are used astemplates forthefit, are modified.The sources ofsystematicuncertaintiescommonto the hypothesis testing and template fit are listed and explained be-low.The order of the list of contributions givesan indication of therelativeimportanceofthecontributioninboththetemplatefit andthehypothesis testing. The explicittreatment ofthe system-aticuncertaintiesisexplainedinmoredetailinSection9.1forthe hypothesistestingandinSection9.2forthetemplatefit.

Limitedstatisticalprecisionofsimulation: The

−

2ln

λ

event dis-tributionsareobtainedfromsimulationwithfinitestatistical pre-cision. To estimate the effect of the statistical precision in this distribution on the observed significance or on the template fit, each binofthe

−

2ln

λ

event distributionis varied randomlyusing

a Poisson distribution within the statistical uncertainties. This is doneindependentlyforeachsimulationsamplethatcontributesto the

−

2ln

λ

eventdistribution.

Scaleuncertainty: SManduncorrelatedtt sampleswithvaried renormalisation andfactorisation scales are used to estimate the uncertainty caused by the scale uncertainty. The renormalisation andfactorisationscalesaresimultaneouslydoubledorhalvedwith respect to their nominal valuesset to the sumof thetransverse massessquaredoftheﬁnal-stateparticles(inthecaseoftt events this is the top quark pair and anyadditional parton) divided by two.Theeffectofthescalevariationontheeventselectionis in-cluded.

JESandJEReffects: Thefour-momentaofalljetsreconstructed in simulated events are varied simultaneously within the uncer-taintiesofthe pT- and

η

-dependentJES[43,44]priortotheevent selection.Theadditionalresolutioncorrectionappliedtothe simu-lationtotakeintoaccounttheresolutiondifferencebetweendata and simulation is varied within the uncertainties in the simula-tion.Thelikelihoodcalculationsareperformedwiththevariedjet quantities,usingthenominaltransferfunction.TheJESuncertainty entersthemeasurement intwo ways:(i)acceptanceeffects mod-ifytherelativecontributionsofthebackgroundsand(ii)theevent likelihood values vary due to the modiﬁed quantities. The latter effectisdominant.

Partondistributionfunctions: ThePDFisvariedwithinits un-certainty eigenvectors (CT10)in signal and background, and the effectsarepropagatedthroughtheeventweights[45,46].The pro-cedure to propagate the effect to the

−

2ln

λ

event distribution is describedin[45].

Topquarkmassuncertainty: SM and uncorrelatedtt samples withvariedtopquark massvalueshavebeenproduced,including the effect on the event selection. The nominal sample is simu-lated with a top quark mass of 172.5 GeV, whereas the system-atically varied samples are simulated with mt

=

169

.

5GeV and

mt

=

175

.

5GeV.The

−

2ln

λ

event distributionis varied within 1

/

3 ofthedeviationobtainedwith

m

t

=

175

.

5GeV and

m

t

=

169

.

5GeV inordertomimicthe

−

2ln

λ

event variationcausedbya1 GeV un-certaintyinthetopquarkmassworldaveragevalue[26].

Thetop quark pt_T modeling: The model of tt production in MadGraph as well as in mc@nlo predicts a harder transverse momentum spectrum forthe top quark pt_T than observed in the data [47,48]. The top quark pairs might be reweighted based on the pT spectrum of generator-level top quarks to obtain bet-ter agreement to the measured differential cross section. This reweighting is not applied in this analysis, butwe do assign an uncertaintytothe tt modelingby changingtheeventweightand propagatingtheeffecttothe

−

2ln

λ

eventshape.

Backgroundmodelingandtheoreticalcrosssections: We de-termine the relative contribution of the backgrounds using the theoretical crosssectionsforthebackgroundprocesses.The cross sections are varied within the theoretical uncertainties [27] and the effects are propagated to the analysis. The total background shapewillchangeduetothechangeinrelativecontributionsand, inthehypothesistesting, thetotalbackgroundfractionisfixedto the systematically varied value, whereas in the template fit, this fractioncanvaryfreelyinthefit.FortheW+jetscontribution,we varythebackgroundyieldby50%andpropagatetheeffectstothe analysis,whichisampletocovertheuncertaintiesonthe theoreti-calcrosssections.TheshapeoftheW+jetsbackgroundtemplateis alsovaried byevaluating the

−

2ln

λ

event distributionwithout the W+jetsshapeincluded,butkeepingthetotal backgroundfraction ﬁxedtothenominalvalue.

Pileup: A 5% uncertainty on the inelastic pp cross section is takenintoaccountandpropagatedtotheeventweights[49].

(8)

Thebtaggingeﬃciencyandmistagrates: The pT- and

η

-de-pendenttaggingandmistagging eﬃcienciesforlight- and heavy-ﬂavour jetsare varied within their uncertainties and are propa-gatedtotheeventweightsinthesimulation[50].

Leptontrigger, identiﬁcation, andisolation eﬃciencies: pT -and

η

-dependentscalefactorsareappliedtothesimulationto cor-rect for eﬃciency differencesin the data and simulation forthe singleleptontrigger,leptonidentiﬁcationandisolation.Thesescale factorsarevariedindependentlywithintheiruncertaintiesandthe effectsarepropagatedtotheeventweights.

The contribution of the individual systematic uncertainty sources is evaluated in the template ﬁtting procedure described in Section 9.2 andreported in Table 3. The relative size of each systematicuncertaintycontributionisconsistentinthehypothesis testingprocedureandthetemplateﬁtting.

9. Results

9.1. Hypothesis testing

Toevaluatethecompatibilityofthedatawitheitherofthe hy-potheses, thesystematicvariationsof the

−

2ln

λ

event distribution needtobepropagatedtothe

−

2ln

λ

sample distribution.Weassess theeffect ofthiseventlikelihood ratioﬂuctuation by a Gaussian templatemorphingtechniqueinwhichallsystematicuncertainties areevaluatedsimultaneously.Ineachpseudo-experiment,wedraw asamplefromthemorphedtemplatewithasizeequaltothatof thedataset,andevaluatethesamplelikelihoodratio.

The

−

2ln

λ

event distributionis morphedinthe following way. Wedrawavector

x of randomnumbersfromaGaussian distribu-tionwithmean0andwidth1.Persystematicuncertaintysource k, wehavean independententry

x

kinthevector. Ineachbinofthe

morphedtemplate, the bin content Ni is calculated asshown in

thefollowing equation with H

(

xk

)

a Heaviside step function and N_inomtheoriginalbincontent:

Ni

=

Nnom_i

+

k

|

xk

|

H(xk

)

Nk_i,up

−

Nnom_i

+

H(

−

xk

)

Nk_i,down

−

Nnom_i

.

(11)

Here, Nk,up _and_Nk,down _are_the_bin_contents_of_the systemati-callyvaried

−

2ln

λ

eventdistributionfortheupwardanddownward variationrespectively.Thesummationrunsoverallsystematic un-certaintysources.Thesystematicupward ﬂuctuationischosen for asystematicsourcewhen

x

k ispositiveandthedownward

ﬂuctu-ationis chosenwhen xk isnegative. Thisequation showsthat all

systematicuncertaintysourcesarevariedsimultaneouslywhilethe bin-to-bincorrelationsofthesystematiceffectispreserved. Ifthe systematicup- anddown-effectsareasymmetricinsize,this asym-metryis preserved.Ifthesystematicup- anddown-effects givea changeinthesamedirection,thelargestofthetwocontributions ischosenasaone-sideduncertaintywhilezeroisusedforthe op-positeside.Pertemplatemorphingiteration,wedrawone

x which

gives us a varied

−

2ln

λ

event distribution. From this distribution withthisparticular

x, wedrawonepseudo-experimentwithasize equal tothat of the dataset. Thisis done independently forthe SManduncorrelated

−

2ln

λ

event distribution.

We perform repeated pseudo-experiments with the template morphing technique to obtain the systematically varied sample likelihood ratio distribution shown in Fig. 6. The comparison of

Figs. 4 and 6showsthedegradation oftheseparation power be-tween the SM distribution and theuncorrelated distribution due tothesystematicuncertainties.Inaddition,theresultofthe asym-metricbehaviourofsomesystematicuncertaintysourcesisclearly visible.Performing107 _{pseudo-experiments}_is_enough_to_populate

Fig. 6. The−2lnλsample distributioninsimulation,evaluatedforthedatasetsize. Thesamplesinsimulationcontainsignalandbackgroundmixedaccordingtothe theoreticalcrosssections,withthesoliddistributionobtainedusingSMtt simula-tionandthedasheddistributionobtainedusinguncorrelatedtt simulation, includ-ingsystematicuncertainties.Thearrowindicatesthe−2lnλsampleobservedindata. Thedottedcurveshowsamixtureof72%SMtt eventsand28%uncorrelatedtt events.

theGaussiantailsinthetemplatemorphingphasespace,ensuring asmooth

−

2ln

λ

sample distributionwithlowstatisticaluncertainty eveninthetails.

Fromthevalueofthedatasamplelikelihoodratio,weﬁndthat 98.7% of the SM simulated area is above the data value, leading toanobservedagreementwiththeSMhypothesisof2.2standard deviations.Weﬁndthat0.2%oftheuncorrelatedsimulatedareais abovethedatavalue,leadingtoanobservedagreementofthe un-correlatedhypothesisof2.9standarddeviations.Fromthiswecan concludethatthedataismorecompatiblewiththeSMhypothesis than withtheuncorrelatedhypothesis.The dominantuncertainty sourcesaretheJES,scalevariation,andthetopquarkmass uncer-tainties.TheJESuncertaintyisresponsiblefortheasymmetrictails inthedistribution.

As a test ofthe compatibilityof the result in the hypothesis testing and the extraction of f , the hypothesis testing has been performed with a tt sample constructed such that 72% of the events contained SM correlations while the remainder 28% had no correlation. As a resultwe ﬁnd a sample likelihoodratio dis-tribution, shown in Fig. 6, in between the SM and uncorrelated scenario,withadatacompatibilityof0.6standarddeviations.The value measured indata, whichisslightly belowthemean ofthe distribution, is within the expectation of statistical and system-atic effects. We wouldhaveachieved even better agreementhad we usedinsimulationavalueofthetopquarkmassequaltothe worldaveragemeasurementof173.3 GeV[26].

9.2. Extraction of fraction of events with SM spin correlation

In the extraction of f using a template ﬁt to the variable

−

2ln

λ

event, we have the same list of systematic uncertainty sources as described earlier, butin addition a systematic uncer-tainty duetothecalibrationofthemethodistakenintoaccount. The calibrationuncertaintyis obtainedbypropagating the uncer-tainties in the calibration fit parameters shown in Table 2 and propagatingthefituncertaintyofthefitparameter

β

obs,data.

Thesystematicuncertaintiesaredeterminedbyﬁttingthedata with systematically varied templates and taking the difference from the nominal ﬁt result. The systematic contributions, taking

(9)

Table 3

Sourcesofsystematicuncertaintyinthefraction f ofeventswiththeSMspin cor-relation.Thereisnodownwardvariationforthept

Tmodeling.

Source of syst. uncer. Up variation Down variation Simulation stat. 0.042 −0.042 Scale −0.068 0.124 JES 0.051 −0.090 JER −0.023 −0.004 PDF 0.018 0.045 mt 0.001 −0.034 top quark pt Tmodeling 0.023 — Background modeling 0.017 −0.016 Pileup 0.012 −0.015 b tagging eﬃciency −0.001 0.001 Mistag rate 0.005 −0.006 Trigger <0.001 <0.001 Lepton ID/Iso <0.001 <0.001 Calibration 0.003 −0.003 Total syst. uncer. +₋00..1513

into account the effect of the nominal calibration function, are shown in Table 3 where the fit uncertainty of the nominal re-sultisalsoshown.Thesystematicuncertaintyrelatedtothefinite sizeofthesimulationsamplesisevaluatedbyfittingone pseudo-dataset in the simulation by 1000Poisson-fluctuated templates. TheGaussian width ofthefit result fobs is takenasthe system-atic uncertainty value. This is done for each simulation sample independentlywiththeuncertainties addedin quadrature.Inthe templatefitmethod,allsystematicuncertaintiesaretreatedas in-dependentofeachother.

Thetotalsystematicuncertaintyisobtainedbyaddingthe pos-itive and negative contributions in Table 3 in quadrature. When bothupanddownsystematicvariationsgiveanuncertaintyinthe samedirection,onlythelargestvalueistakenintoaccountinthe givendirection,andnouncertaintyisassignedintheopposite di-rection.Thisgivesusatotal systematicuncertaintyof

+

0

.

15 and

−

0

.

13.Thetotalresultofthetemplateﬁtisthen:

f

=

0

.

72

±

0

.

08 (stat)₋+₀0._.15₁₃(syst)

.

(12) Inthe assumption that there are only the SM tt pairs or un-correlated tt pairs, this results in an indirect extraction of Ahel. By making use of the relation Ameasured_hel

=

fSMASM_hel,MC where

ASM_hel,MC

=

0

.

324

±

0

.

003 obtained in simulation, which is in good agreement withthe theoretically predicted value of ASM

hel

=

0

.

319 [51,52] which includes NLO QCD and electroweak correc-tions, Ameasured_hel

=

0

.

23

±

0

.

03(stat)+₋0₀._.05₀₄(syst) is obtained. It is foundthatthe systematicuncertainties duetoJER,trigger,lepton identificationandisolationefficiencies,andbtaggingefficiencyare not relevant compared to the statistical uncertainties associated to them. The dominant uncertainties are the JES and renormal-isation/factorisation scale variation. The relative contributions of systematicuncertainty are very similar in the hypothesis testing andtemplatefitresults.

10. Summary

The hypothesis that tt events are produced with correlated spins as predicted by the SM is tested using a matrix element methodinthe

μ

+jetsﬁnalstate at

√

s

=

8TeV,usingppcollisions corresponding to an integratedluminosity of 19.7 fb−1. The data agree with the uncorrelated hypothesis within 2.9 standard de-viations, whereas agreement with the SM is within 2.2 standard deviations.Ourhypothesesareonly consideredup toNLO effects inthesimulation,withLOmatrix elements inthelikelihood cal-culations.

Usingatemplateﬁtmethod,thefractionofeventswhichshow SMspincorrelationshasbeenextracted.Thisfractionismeasured to be f

=

0

.

72

±

0

.

08(stat)₋+₀0._.15₁₃(syst), leading to a spin correla-tionstrength of Ameasured_hel

=

0

.

23

±

0

.

03(stat)+₋0₀._.05₀₄(syst) using the valueobtainedinsimulationwhichiscompatiblewiththe theoret-icalpredictionforASM_helfrom[51,52].Theresultisthemostprecise determinationofthisquantityinthemuon+jetsﬁnalstatetodate andis competitive with themost accurate resultin the dilepton ﬁnalstate[9].

Acknowledgements

WethankWerner BernreutherforkindlyprovidingtheLO ma-trixelementsdescribingtt productionandsubsequentdecayinthe

μ

+jetschannel,validforbothon- andoff-shelltopquarks. 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);FNRS and FWO (Belgium); CNPq, CAPES, FAPERJ, and FAPESP (Brazil); MES(Bulgaria);CERN;CAS,MoST,andNSFC(China);COLCIENCIAS (Colombia);MSESandCSF(Croatia);RPF(Cyprus);MoER,ERCIUT andERDF(Estonia);Academy ofFinland,MEC,andHIP (Finland); CEA and CNRS/IN2P3 (France); BMBF, DFG, and HGF (Germany); GSRT (Greece); OTKA and NIH (Hungary); DAE and DST (India); IPM (Iran); SFI (Ireland); INFN (Italy); MSIP and NRF (Republic of Korea); LAS (Lithuania); MOE and UM (Malaysia); CINVESTAV, CONACYT,SEP,andUASLP-FAI(Mexico);MBIE(NewZealand);PAEC (Pakistan);MSHEandNSC (Poland);FCT(Portugal);JINR(Dubna); MON,RosAtom,RASandRFBR(Russia);MESTD(Serbia);SEIDIand CPAN(Spain);SwissFundingAgencies(Switzerland);MST(Taipei); ThEPCenter,IPST, STARandNSTDA(Thailand);TUBITAKandTAEK (Turkey);NASUandSFFR(Ukraine); STFC(United Kingdom);DOE andNSF(USA).

Individuals have received support from the Marie-Curie pro-gramme and the European Research Council and EPLANET (Eu-ropean Union); the Leventis Foundation; the A.P. 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); theMinistry ofEducation, YouthandSports (MEYS) of the Czech Republic; the Council of Scientific and Industrial Re-search,India;theHOMINGPLUSprogrammeoftheFoundationfor Polish Science, cofinanced fromEuropean Union,Regional Devel-opmentFund;theOPUS programmeofthe NationalScience Cen-tre (Poland); the Compagniadi SanPaolo (Torino); MIUR project 20108T4XTM (Italy); the Thalis and Aristeia programmes cofi-nancedbyEU-ESFandtheGreekNSRF;theNationalPriorities Re-searchProgrambyQatarNationalResearchFund;theRachadapisek SompotFundforPostdoctoralFellowship,ChulalongkornUniversity (Thailand);andtheWelchFoundation,contractC-1845.

References

[1] D.Krohn,T.Liu,J.Shelton,L.-T.Wang,Apolarizedviewofthetopasymmetry, Phys.Rev.D84(2011)074034,http://dx.doi.org/10.1103/PhysRevD.84.074034, arXiv:1105.3743.

(10)

[2] W. Bernreuther,Z.-G. Si,Topquarkspincorrelationsandpolarizationatthe LHC:standard modelpredictionsandeffectsofanomaloustopchromo mo-ments,Phys.Lett.B725(2013)115,http://dx.doi.org/10.1016/j.physletb.2013. 06.051,arXiv:1305.2066.

[3] T.Aaltonen,etal.,CDF Collaboration,Measurementoftt spin correlationin pp collisionsusingtheCDFIIdetectorattheTevatron,Phys.Rev.D83(2011) 031104,http://dx.doi.org/10.1103/PhysRevD.83.031104,arXiv:1012.3093. [4] B.Abbott,et al.,D0Collaboration,Spincorrelationintt productionfrompp

collisionsat √s= 1.8TeV, Phys.Rev.Lett.85(2000)256,http://dx.doi.org/ 10.1103/PhysRevLett.85.256,arXiv:hep-ex/0002058.

[5] V.M.Abazov,et al.,D0 Collaboration,Measurementofspincorrelationintt production using dileptonﬁnal states,Phys. Lett. B 702(2011) 16, http:// dx.doi.org/10.1016/j.physletb.2011.05.077,arXiv:1103.1871.

[6] V.M. Abazov, et al., D0 Collaboration, Measurement of spin correlation in tt productionusingamatrix elementapproach,Phys. Rev.Lett. 107(2011) 032001,http://dx.doi.org/10.1103/PhysRevLett.107.032001,arXiv:1104.5194. [7] V.M.Abazov,etal.,D0Collaboration,Evidenceforspincorrelationintt

produc-tion,Phys.Rev.Lett.108(2012)032004,http://dx.doi.org/10.1103/PhysRevLett. 108.032004,arXiv:1110.4194.

[8] ATLASCollaboration,Observationofspincorrelationintt eventsfrompp col-lisionsat√(s)=7 TeV usingtheATLASdetector,Phys.Rev.Lett.108(2012) 212001,http://dx.doi.org/10.1103/PhysRevLett.108.212001,arXiv:1203.4081. [9] ATLAS Collaboration, Measurementofspin correlationintop–antitop quark

eventsandsearchfortopsquarkpairproductioninppcollisionsat√s=8TeV usingtheATLASdetector,Phys.Rev.Lett.114(2015)142001,http://dx.doi.org/ 10.1103/PhysRevLett.114.142001,arXiv:1412.4742.

[10] ATLASCollaboration,Measurementofthecorrelationsbetweenthepolar an-gles ofleptons from topquarkdecays in thehelicity basisat √s=7 TeV usingthe ATLAS detector,Phys. Rev.D 93(2016)012002, http://dx.doi.org/ 10.1103/PhysRevD.93.012002,arXiv:1510.07478.

[11] ATLASCollaboration,Measurementsofspincorrelationintop–antitopquark eventsfromproton–protoncollisionsat√s=7TeV usingtheATLASdetector, Phys.Rev.D90(2014)112016,http://dx.doi.org/10.1103/PhysRevD.90.112016, arXiv:1407.4314.

[12] CMSCollaboration,TheCMSexperimentattheCERNLHC,J.Instrum.3(2008) S08004,http://dx.doi.org/10.1088/1748-0221/3/08/S08004.

[13] CMSCollaboration,PerformanceofCMSmuonreconstructioninppcollision eventsat√s=7TeV, J.Instrum.7(2012)P10002,http://dx.doi.org/10.1088/ 1748-0221/7/10/P10002,arXiv:1206.4071.

[14] S.Frixione,B.R.Webber,MatchingNLOQCDcomputationsandpartonshower simulations, J. High Energy Phys. 06 (2002) 029, http://dx.doi.org/10.1088/ 1126-6708/2002/06/029,arXiv:hep-ph/0204244.

[15] S.Frixione,F.Stoeckli,P.Torrielli,B.R.Webber,NLOQCDcorrectionsin Her-wig++withMC@NLO, J.HighEnergyPhys. 01(2011)053,http://dx.doi.org/ 10.1007/JHEP01(2011)053,arXiv:1010.0568.

[16] H.-L.Lai,M.Guzzi,J.Huston,Z.Li,P.M.Nadolsky,J.Pumplin,C.-P.Yuan,New partondistributionsforcolliderphysics,Phys.Rev.D82(2010)074024,http:// dx.doi.org/10.1103/PhysRevD.82.074024,arXiv:1007.2241.

[17] J.Alwall,R.Frederix,S.Frixione,V.Hirschi,F.Maltoni,O.Mattelaer,H.-S.Shao, T.Stelzer,P.Torrielli,M.Zaro,Theautomatedcomputationoftree-leveland next-to-leading orderdifferentialcross sections,and theirmatching to par-tonshowersimulations,J.HighEnergyPhys.07(2014)079,http://dx.doi.org/ 10.1007/JHEP07(2014)079,arXiv:1405.0301.

[18] Z. Was, TAUOLA the library for tau lepton decay, and KKMC/KORALB/KO-RALZ/...statusreport,Nucl.Phys.B,Proc.Suppl.98(2001)96,http://dx.doi.org/ 10.1016/S0920-5632(01)01200-2,arXiv:hep-ph/0011305.

[19] P.Nason,AnewmethodforcombiningNLOQCDwithshowerMonteCarlo algorithms, J. High Energy Phys. 11 (2004) 040, http://dx.doi.org/10.1088/ 1126-6708/2004/11/040,arXiv:hep-ph/0409146.

[20] S.Frixione,P.Nason,C.Oleari,MatchingNLOQCDcomputationswithparton showersimulations:thePOWHEGmethod,J.HighEnergyPhys.11(2007)070, http://dx.doi.org/10.1088/1126-6708/2007/11/070,arXiv:0709.2092.

[21] S. Alioli, P. Nason, C. Oleari, E. Re, A general framework for implement-ing NLOcalculations inshower MonteCarloprograms: the POWHEG BOX, J. HighEnergyPhys.06(2010)043,http://dx.doi.org/10.1007/JHEP06(2010)043, arXiv:1002.2581.

[22] N.Davidson,G.Nanava,T.Przedzinski,E.Richter-Was,Z.Was,Universal inter-faceofTAUOLAtechnicalandphysicsdocumentation,Comput.Phys.Commun. 183(2012)821,http://dx.doi.org/10.1016/j.cpc.2011.12.009,arXiv:1002.0543. [23]R.Field,EarlyLHCunderlyingeventdata–ﬁndingsandsurprises,in:Hadron

ColliderPhysics,Proceedings,22ndConference,HCP2010,Toronto,Canada, Au-gust23–27,2010,2010,arXiv:1010.3558.

[24] J.Pumplin,D.R.Stump,J.Huston,H.-L.Lai,P.Nadolsky,W.-K.Tung,New gen-eration ofpartondistributionswith uncertaintiesfromglobalQCDanalysis, J.HighEnergyPhys.07(2002)012,http://dx.doi.org/10.1088/1126-6708/2002/ 07/012,arXiv:hep-ph/0201195.

[25] S.Agostinelli, et al., GEANT4, GEANT4—a simulation toolkit,Nucl. Instrum. MethodsPhys.Res.,Sect.A,Accel.Spectrom.Detect.Assoc.Equip.506(2003) 250,http://dx.doi.org/10.1016/S0168-9002(03)01368-8.

[26]ATLAS,CDF,CMSandD0Collaborations,FirstcombinationofTevatronandLHC measurementsofthetop-quarkmass,arXiv:1403.4427,2014.

[27] M.Czakon, P.Fiedler, A.Mitov, The totaltopquark pair production cross-sectionathadroncollidersthroughO(α4

S),Phys.Rev.Lett.110(2013)252004, http://dx.doi.org/10.1103/PhysRevLett.110.252004,arXiv:1303.6254.

[28] CMSCollaboration,Particle–ﬂoweventreconstructioninCMSandperformance forjets,taus,andEmiss

T ,CMSPhysicsAnalysisSummaryCMS-PAS-PFT-09-001,

URL:http://cdsweb.cern.ch/record/1194487,2009.

[29] CMS Collaboration,Commissioning oftheparticle-ﬂowevent reconstruction with the ﬁrst LHC collisions recorded in the CMS detector, CMS Physics Analysis Summary CMS-PAS-PFT-10–001, URL: http://cdsweb.cern.ch/record/ 1247373,2010.

[30] M.Cacciari,G.P.Salam,G.Soyez,Theanti-ktjetclusteringalgorithm,J.High

EnergyPhys.04(2008)063,http://dx.doi.org/10.1088/1126-6708/2008/04/063, arXiv:0802.1189.

[31] M.Cacciari,G.P.Salam,G.Soyez,FastJetusermanual,Eur.Phys.J.C72(2012) 1896,http://dx.doi.org/10.1140/epjc/s10052-012-1896-2,arXiv:1111.6097. [32] CMSCollaboration,Identiﬁcationandﬁlteringofuncharacteristicnoiseinthe

CMShadroncalorimeter,J.Instrum.5(2010)T03014,http://dx.doi.org/10.1088/ 1748-0221/5/03/T03014,arXiv:0911.4881.

[33] CMS Collaboration,Identiﬁcation ofb-quarkjetswiththe CMS experiment, J.Instrum.8(2013)P04013,http://dx.doi.org/10.1088/1748-0221/8/04/P04013, arXiv:1211.4462.

[34] B.Abbott,etal.,D0Collaboration,Directmeasurementofthetopquarkmass bythe D0 Collaboration, Phys. Rev.D 58 (1998) 052001, http://dx.doi.org/ 10.1103/PhysRevD.58.052001,arXiv:hep-ex/9801025.

[35] K.Kondo,Dynamicallikelihoodmethodforreconstructionofeventswith miss-ingmomentum.1.Methodandtoymodels,J.Phys.Soc.Jpn.57(1988)4126, http://dx.doi.org/10.1143/JPSJ.57.4126.

[36] K.Kondo,Dynamicallikelihoodmethodforreconstructionofeventswith miss-ingmomentum. 2.Mass spectrafor 2→2 processes,J.Phys. Soc. Jpn.60 (1991)836,http://dx.doi.org/10.1143/JPSJ.60.836.

[37] R.H. Dalitz,G.R. Goldstein, Analysisoftop–antitop productionand dilepton decayeventsandthetopquarkmass, Phys.Lett.B287(1992) 225,http:// dx.doi.org/10.1016/0370-2693(92)91904-N.

[38] M.Abazov,etal.,D0Collaboration,Aprecisionmeasurementofthemassof thetopquark,Nature429(2004)638,http://dx.doi.org/10.1038/nature02589, arXiv:hep-ex/0406031.

[39] P. Artoisenet,V. Lemaître,F.Maltoni, O. Mattelaer, Automationof the ma-trixelementreweightingmethod,J.HighEnergyPhys.12(2010)068,http:// dx.doi.org/10.1007/JHEP12(2010)068,arXiv:1007.3300.

[40] R.Cousins,J.Mumford,J.Tucker,V.Valuev,Spindiscriminationofnewheavy resonancesat theLHC,J.HighEnergy Phys.11(2005)46,http://dx.doi.org/ 10.1088/1126-6708/2005/11/046.

[41]W.Verkerke,D. Kirkby,TheRooFittoolkitfor datamodeling,arXiv:physics: data-an/0306116,2003.

[42] F.James,M.Roos,Minuit:asystemforfunctionminimizationandanalysisof theparametererrorsandcorrelations,Comput.Phys.Commun.10(1975)343, http://dx.doi.org/10.1016/0010-4655(75)90039-9.

[43] CMSCollaboration,Determinationofjetenergycalibrationandtransverse mo-mentumresolution in CMS,J. Instrum. 6(2011) P11002, http://dx.doi.org/ 10.1088/1748-0221/6/11/P11002,arXiv:1107.4277.

[44] CMS Collaboration, 8 TeV jetenergycorrections and uncertaintiesbased on 19.8 fb−1_of_data_in_CMS,_CMS_Detector_Performance_Note_{CMS-DP-2013-033.}

URL:https://cds.cern.ch/record/1627305,2013.

[45]S.Alekhin,etal.,ThePDF4LHCWorkingGroupinterimreport,arXiv:1101.0536, 2011.

[46]M.Botje,J.Butterworth,A.Cooper-Sarkar,A.deRoeck,J.Feltesse,S.Forte,A. Glazov,J.Huston,R.McNulty,T.Sjöstrand,R.S.Thorne,ThePDF4LHCWorking Groupinterimrecommendations,arXiv:1101.0538,2011.

[47] CMS Collaboration, Measurement of differential top-quark pair production crosssectionsinppcollisionsat√s=7TeV,Eur.Phys.J.C73(2013)2339, http://dx.doi.org/10.1140/epjc/s10052-013-2339-4,arXiv:1211.2220[hep-ph]. [48] CMSCollaboration,Measurementofthedifferentialcrosssectionfortopquark

pairproductioninppcollisionsat√s=8TeV,Eur.Phys.J.C75(2015)542, http://dx.doi.org/10.1140/epjc/s10052-015-3709-x,arXiv:1505.04480. [49] G.Antchev,etal.,TOTEMCollaboration,Firstmeasurementofthetotalproton–

protoncrosssectionattheLHCenergyof√s=7TeV,Europhys.Lett.96(2011) 21002,http://dx.doi.org/10.1209/0295-5075/96/21002,arXiv:1110.1395. [50] CMSCollaboration,Performanceofbtaggingat√s=8 TeV inmultijet,tt and

boostedtopologyevents,CMSPhysicsAnalysisSummaryCMS-PAS-BTV-13-001, URL:https://cds.cern.ch/record/1581306,2013.

[51] W.Bernreuther,A.Brandenburg,Z.G.Si,P.Uwer,Topquarkpair production anddecayathadroncolliders,Nucl.Phys.B690(2004)81,http://dx.doi.org/ 10.1016/j.nuclphysb.2004.04.019,arXiv:hep-ph/0403035.

[52] W.Bernreuther,D.Heisler,Z.-G. Si,Asetoftopquarkspincorrelationand polarizationobservables for the LHC:standard model predictionsand new physicscontributions, J.HighEnergy Phys.12 (2015)026,http://dx.doi.org/ 10.1007/JHEP12(2015)026,arXiv:1508.05271.