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Search for top squark pair production in
compressed-mass-spectrum scenarios in proton-proton
collisions at sqrt(s) = 8 TeV using the alphaT variable
V. Khachatryan, M. Besançon, F. Couderc, M. Dejardin, D. Denegri, B.
Fabbro, J.L. Faure, C. Favaro, F. Ferri, S. Ganjour, et al.
To cite this version:
Contents lists available atScienceDirect
Physics
Letters
B
www.elsevier.com/locate/physletb
Search
for
top
squark
pair
production
in
compressed-mass-spectrum
scenarios
in
proton–proton
collisions
at
√
s
=
8 TeV using
the
α
T
variable
.
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: Received29May2016Receivedinrevisedform22January2017 Accepted6February2017
Availableonline10February2017 Editor:M.Doser Keywords: CMS Physics SUSY Jets
Missingtransversemomentum AlphaT
An inclusive search is performed for supersymmetry in final states containing jetsand an apparent imbalance in transverse momentum, pmissT , due to the production of unobserved weakly interacting particlesinppcollisionsatacentre-of-massenergyof8 TeV.Thedata,recordedwiththeCMSdetectorat theCERNLHC,correspondtoanintegratedluminosityof18.5 fb−1.Thedimensionlesskinematicvariable
α
TisusedtodiscriminatebetweeneventswithgenuinepmissT associatedwithunobservedparticlesandspuriousvaluesof pmiss
T arisingfromjetenergymismeasurements.Noexcessofeventyieldsabovethe
expectedstandardmodelbackgroundsisobserved.Theresultsareinterpretedintermsofconstraintson theparameterspaceofseveralsimplifiedmodelsofsupersymmetrythatassumethepairproductionof top squarks.Thesearchprovidessensitivitytoabroadrangeoftopsquark(˜t)decaymodes,including thetwo-bodydecay˜t→c
χ
˜01,wherec isacharmquarkand
χ
˜ 01 isthelightestneutralino,aswellasthe
four-bodydecay˜t→b f¯f
χ
˜01,where b isabottomquarkand f and ¯f arefermions producedinthe
decayofanintermediateoff-shellWboson.Thesemodesdominateinscenariosinwhichthetopsquark andlightestneutralinoarenearlydegenerateinmass.Forthesemodes,topsquarkswithmassesaslarge as260and225 GeVareexcluded,respectively,forthetwo- andfour-bodydecays.
©2017TheAuthor.PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense (http://creativecommons.org/licenses/by/4.0/).FundedbySCOAP3.
1. Introduction
Thestandardmodel(SM)iswidelyregardedasaneffective ap-proximation,validatlow energies, ofa morecompletetheory of particleinteractions, such assupersymmetry (SUSY)[1–8],which wouldsupersedethe SMat higherenergyscales. Arealisationof SUSYwithTeV-scalethird-generationsquarks ismotivatedbythe cancellationofquadraticallydivergentloopcorrectionstothemass of the Higgs boson [9,10] avoiding the need for significant fine tuning [7,8,11]. In R-parity-conserving SUSY [12], supersymmet-ricparticles(sparticles)suchassquarksandgluinos areproduced inpairs anddecay to thelightest stable supersymmetricparticle (LSP),whichisgenerallyassumedto bea weaklyinteracting and massiveneutralino,
χ
˜
01.A characteristicsignature oftheseevents
isa final state withjetsaccompanied by an apparent, significant imbalanceintransversemomentum, p
missT ,duetounobservedχ
˜
0 1particlesthatcancarrysubstantialmomentum.
E-mailaddress:cms-publication-committee-chair@cern.ch.
The lack of evidence to date for SUSY at the CERN LHC has led to the careful consideration of regions of the SUSY parame-terspacethathavearelativelyweakcoverageintheexperimental programme.Onesuchclassofmodelsisthatofcompressedmass spectra,inwhichtheLSPliescloseinmasstotheparentsparticle produced in thecollisions. Models inwhich both the top squark (
˜
t)andneutralinoLSParelightandnearlydegenerateinmassare phenomenologically well motivated [13–20]. For a mass splittingm
=
m˜t−
mχ˜01
<
mW,wheremW isthemassoftheWboson,the decaymodesavailable to thetop squarkare eitherloop-induced, flavour-changingneutralcurrentdecaystoa charm(c)quark and a neutralino,˜
t→
cχ
˜
10, or four-body decays,˜
t→
b f¯
fχ
˜
10, where b is a bottom quark with f and¯
f fermions from, for example, anoff-shellWbosondecay.Improvedexperimentalacceptancefor systemswithcompressedmassspectracanbeachievedby requir-ing the sparticles to be produced in association with jets from initial-stateradiation(ISR).Thesparticledecayproductsfromthese systems can be Lorentz boostedto valuesof transverse momen-tum pT within theexperimental acceptanceifthey recoilagainsta sufficiently high-pT jet from ISR. This topology is exploitedby
searchesthat consider“monojet”
+
pmissT final states[21–23].The http://dx.doi.org/10.1016/j.physletb.2017.02.007relianceonISR isreducedforsystemswithlarger
m, asinthis casethesparticledecayproductscanhavesufficientlylargevalues of pT tolie withintheexperimentalacceptanceevenwithoutthe
LorentzboostfromISR.
Thisletterpresentsan inclusivesearch forthepairproduction of massive coloured sparticles in final states with two or more energeticjets and
pmissT inpp collisions at
√
s
=
8 TeV. The data correspondtoanintegratedluminosityof18.
5±
0.
5 fb−1 [24] col-lectedwiththeCMSdetectorattheLHC.Thesearchisbasedupon akinematicvariableα
T,describedinSection3,whichofferspow-erful discrimination against SM multijet production, andadheres toa strategy ofmaximisingexperimental acceptancethroughthe application ofloose selection requirements to provide sensitivity toa wide rangeofSUSY models.Previous versionsofthissearch werereportedat
√
s=
7 TeV[25–27],andforaninitialsample of datacorrespondingto11.
7 fb−1 at8 TeV[28].OtherLHCsearches formanifestations of SUSY in all-jetfinal states are presentedin Refs.[21–23,29–54].Recentsearchesfortop squarkproductionin leptonic final states can be found in Refs. [55] (and references therein)and[56,57].Thesearch makesuseofthenumberofreconstructedjetsper event
(
Njet)
,thenumberofthesejetsidentifiedasoriginatingfrombquarks
(
Nb)
,andthesumofthetransverseenergiesofthesejets(
HT)
,wherethetransverseenergyofajetisgivenby ET=
E sinθ
,with E the energy of the jet and
θ
its polar angle withrespectto the beam axis. The three discriminants provide sensitivity to differentproductionmechanismsofmassivecolouredsparticlesat hadron colliders (i.e. squark–squark, squark–gluino, and gluino– gluino), to a large range of mass splittings between the parent sparticle and the LSP, and to third-generation squark signatures. While the search results can be interpreted with a broad range of models involving the strong production of coloured sparticles leadingtofinalstateswithbothlowandhighbquarkcontent,we focus on the parameter space of simplified models [58–60] that assumesthe pairproduction oftop squarks, includingthe nearly mass-degeneratescenariosdescribedabove.Furthermore, interpre-tations are provided fortop squarks that decay to the
χ
˜
01 either
directlyinassociationwithatopquark(
˜
t→
tχ
˜
01),orviaan
inter-mediatelightestchargino
χ
˜
1± inassociationwithabottomquark, withthe subsequentdecayof theχ
˜
1± to theχ
˜
10 anda W boson (˜
t→
bχ
˜
1±→
bW±(∗)χ
˜
01).Allmodelsassumeonlythepair
produc-tionofthelow-masseigenstate
˜
t1,withthe˜
t2decoupledtoahighmass.
Severalaspects ofthe presentsearch are improvedrelative to theresultsofRef.[28]inordertoincreasethesensitivityto mod-els with nearly mass-degenerate
˜
t andχ
˜
01 states.The signal
re-gion is extended to incorporate events with a low level of jet activity using a parked data set collected witha dedicated trig-gerstream[61],where“parked”meansthat,duetolimitationsin the available processingcapability, the data were recorded with-outbeingprocessedthroughthereconstructionsoftware,andwere processedonlysubsequenttotheendofthe2012datacollection period.Furthermore,tightrequirementsonacombinationof kine-matic variables are employed to suppressmultijet production to the sub-percent level relative to the total remaining number of backgroundeventsfromotherSMprocesses.Finally,aneventveto basedonisolatedtracksisusedtofurthersuppressSMbackground contributionsfrom
τ
→
hadrons+
ν
decaysandmisreconstructed electronsandmuons.Thesefeaturesyieldanincreased experimen-tal acceptanceto eventswithlow jetactivity, andimprovements inthecontrolofSMbackgrounds,whicharecrucialforenhancing sensitivitytonewsourcesofphysicswithnearlydegeneratemass spectra.2. TheCMSdetector
The central feature of the CMS detectoris a superconducting solenoid providingan axial magnetic field of3.8 T. The CMS de-tector is nearly hermetic, which allows for accurate momentum balancemeasurementsintheplanetransversetothebeamaxis.
Charged particle trajectories are measured by a silicon pixel and strip tracker system, with full azimuthal (
φ
) coverage and a pseudo-rapidity acceptance|
η
|
<
2.
5. Isolated particles of pT=
100 GeV emittedat
|
η
|
<
1.
4 havetrackresolutionsof2.8%in pTand10(30) μminthetransverse(longitudinal)impactparameter
[62].
Aleadtungstatecrystalelectromagneticcalorimeter(ECAL)and a brass and scintillator hadron calorimeter (HCAL) surround the tracking volume and provide coverage over
|
η
|
<
3.
0. A forward HCAL extends the coverage to|
η
|
<
5.
0. In the barrel section of theECAL,anenergyresolutionofabout1%isachievedfor uncon-verted or late-converting photons with energies on the order of severaltensofGeV.Intheη
–φ
plane,andfor|
η
|
<
1.
48,theHCAL cells map onto 5×
5 arrays ofECAL crystalsto formcalorimeter towersprojectingradiallyoutwardsfromalocationnearthe nom-inalinteractionpoint.Atlargervaluesof|
η
|
,thesizeofthetowers increases and the matching ECAL arrays contain fewer crystals. Withineachtower,theenergydepositsinECALandHCALcellsare summed to define the calorimeter tower energies, subsequently used toprovide theenergies anddirectionsofreconstructedjets. The HCAL, whencombined withtheECAL, measures jet energies witharesolutionofapproximately40%at12 GeV,5%at100 GeV, and4%at1 TeV.Muons are identified in gasionisation detectors embedded in the steelflux-returnyokeofthemagnet. Muonsaremeasured in the range
|
η
|
<
2.
4.Bymatchingtracksegments reconstructedin the muon detectors to segments measured in the silicontracker, a relativetransversemomentum resolutionof1.3–2.0%and<
10% is achievedformuonswith, respectively,20<
pT<
100 GeV andpT
<
1 TeV[63].Thefirstlevel(L1)oftheCMStriggersystem,composedof cus-tom hardware processors,uses informationfromthecalorimeters andmuondetectorstoselecteventsofinterestwithinafixedtime interval ofless than 4 μs. The high-level trigger (HLT) processor farm further decreases the event rate from around 100 kHz to about600 Hz,beforedatastorage.Oftheseevents,abouthalfare reconstructed promptly. Theother half representtheparked data setreferredtoabove.
AmoredetaileddescriptionoftheCMSdetector,togetherwith a definitionofthecoordinatesystemusedandtherelevant kine-maticvariables,canbefoundinRef.[64].
3. The
α
TvariableThe
α
T kinematic variable, first introduced in Refs. [25,65],is used to efficiently reject events that do not contain signifi-cant
pmissT orthat contain large pmissT only becauseof transverse momentum mismeasurements,whileretainingsensitivityto new-physics events with significant pmissT . Theα
T variable dependssolelyonthetransverseenergiesandazimuthalanglesofjets,and is intrinsically robustagainst the presenceofjet energy mismea-surementsinmultijetsystems.
For events containing only two jets,
α
T is defined asα
T=
Ej2
T
/
MT,where ETj2 isthetransverseenergyofthejetwithsmallerET,andMTisthetransversemassofthedijetsystem,definedas:
whereEji
T,p ji
x,andpjyi are,respectively,thetransverseenergyand
x or y components ofthe transverse momentum ofjet ji.For a
perfectlymeasured dijeteventwith Ej1
T
=
E j2T andthe jetsinthe
back-to-back configuration (
φ
=
π
), and in the limit in which themomentum of each jet is large compared withits mass, the value ofα
T is0.5. For an imbalanceinthe ET valuesofthe twoback-to-backjets,whetherduetoanover- orunder-measurement of the ET of either jet, then ETj2
<
0.
5MT. This in turn impliesα
T<
0.
5,givingthevariableits intrinsicrobustness.Values ofα
Tsignificantlygreater than0.5are observedwhen thetwo jetsare notback-to-backandrecoilagainstsignificant,genuinep
missT from weaklyinteractingparticlesthatescapethedetector,suchas neu-trinos.Thedefinitionofthe
α
T variablecanbe generalisedforeventswithmore than two jets[25].The mass scale for anyprocess is characterisedthroughthe scalar ET sumofjets, definedas HT
=
Njeti=1E ji
T,whereNjetisthenumberofjetswithETabovea
prede-finedthreshold.Theestimatorfor
|
pmissT
|
isgivenbythemagnitudeofthevector pTsumofallthejets,definedby HmissT
= |
Njet
i=1p
T ji|
.Foreventswiththreeormorejets,apseudo-dijetsystemisformed bycombining thejetsin theeventinto two pseudo-jets.The to-tal HT foreach of thetwo pseudo-jets is givenby the scalar ET
sumof its contributing jets. The combination chosen is the one thatminimises
HT,definedasthedifferencebetweenthe HTof
thetwopseudo-jets.Thisclusteringcriterionassumesa balanced-momentum hypothesis,
|
pmissT|
≈
0 GeV, which provides the best separation betweenSM multijetevents and eventswith genuinepmiss
T .The
α
T definitioncanthenbegeneralisedto:α
T=
1 2 HT−
HT(
HT)
2− (
HmissT)
2.
(2)When jet energies are mismeasured, or there are neutrinos fromheavy-flavourquarkdecays,themagnitudeofHmiss
T and
HT
arehighlycorrelated.Thiscorrelationismuchweakerfor R-parity-conservingSUSYevents,whereeachofthetwodecaychains pro-ducesanundetectedLSP.
4. Eventreconstructionandselection
Theeventreconstructionandselectioncriteriadescribedbelow are discussed in greater detail in Ref. [28]. To suppressSM pro-cesses with genuine
pmissT from neutrinos, events containing an
isolated electron [66] or muon [63] with pT
>
10 GeV areve-toed. Furthermore, events containing an isolated track [67] with
pT
>
10 GeV are vetoed. Events containing isolated photons [68]withpT
>
25 GeV arealsovetoedtoensureaneventsamplecom-prisingonlymultijetfinalstates.
Jetsarereconstructedfromtheenergydepositsinthe calorime-tertowers,clusteredusingtheanti-kTalgorithm[69]witharadius
parameter of 0.5. The jet energies measured in the calorimeters are corrected to account for multiple pp interactions within an event(pileup),and to establish a uniformrelative response in
η
anda calibrated absoluteresponse in pT [70].Jets are identifiedasoriginating fromb quarks using the “medium” working point of the combined secondary vertex algorithm [71], such that the probability to misidentify jets originating from light-flavour par-tons(gluonsandu,d,orsquarks)asbquarkjetsisapproximately 1%forjetswithpT
=
80 GeV.The“medium”workingpointresultsin a b-tagging efficiency, i.e. the probability to correctlyidentify jetsasoriginatingfrombquarks,intherange60–70% depending onthejetpT.
All jets are required to satisfy
|
η
|
<
3.
0, and the jet with largest ET is also required to satisfy|
η
|
<
2.
5. All jets and theTable 1
HT-dependentthresholdsontheETvaluesofjetsandαTvalues.
HT(GeV) 200–275 275–325 325–375 >375
Highest ETjet (GeV) 73 73 87 100
Next-to-highest ETjet (GeV) 73 73 87 100
ETof other jets (GeV) 37 37 43 50
αT 0.65 0.60 0.55 0.55
two jets with largest ET are, respectively, subjected to a
nomi-nal (ET
>
50 GeV) and higher (ET>
100 GeV) threshold. Eventsarerequiredtocontainatleasttwojetsthatsatisfythe aforemen-tioned ET and
η
requirements.The valueof HT foreach eventisdeterminedfromthesejets.IfHT
<
375 GeV,therespectivejetETthresholdsare loweredto 43and87 GeV, HT isrecalculated,and
the event is reconsidered forselection. If the recalculated HT is
less than 325 GeV, the respective ET thresholds are lowered yet
further,to37and73 GeVandHT againrecalculated.Ifthisnewly
recalculated HT is lessthan 200 GeV, the event is rejected. The
schemeissummarisedinTable 1.Eventscanbeselectedwiththis iterativeprocedure even ifthey donot satisfy the sets oftighter requirements onthe ET thresholds. Thereason whylower jet ET
thresholds are employed for200
<
HT<
375 GeV is to maintaina similar backgroundcomposition inall HT bins, andtoincrease
theacceptanceforSUSYmodelscharacterisedbycompressedmass spectra.Significantjetactivityintheeventisestablishedby requir-ing HT
>
200 GeV,whichalsoensureshighefficiencyforthetrig-gerconditions,describedbelow,usedtorecordtheevents.Events arevetoedifrare,anomaloussignalsareidentifiedinthe calorime-ters [72] or if any jet satisfies ET
>
50 GeV and has|
η
|
>
3, inorder to enhance the performance of HTmiss as an estimator of
|
pmissT|
.Events are categorised according to the number of jets per event, 2
≤
Njet≤
3 or Njet≥
4, andthe numberof reconstructedbquark jetsper event, Nb
=
0,
1,
2,
3,or≥
4.Foreventscontain-ingexactlyzerooronebquarkjet,weemployelevenbinsin HT:
threebinsatlowjetactivityintherangeof200
<
HT<
375 GeV,as detailed in Table 1, an additional seven bins 100 GeV wide in the range of 375
<
HT<
1075 GeV, and an open final binHT
>
1075 GeV.Foreventscontaining twoorthree(atleastfour)b quark jets, a totalof nine (four) bins are used in HT, withan
open final bin HT
>
875(
375)
GeV. Thiscategorisation accordingtoNjet,Nb,andHT resultsinatotalofeight
(
Njet,
Nb)
eventcate-goriesand75bins.Anoverviewofthebinningschemeisprovided byTable 3.
For events satisfyingthe above selection criteria, the multijet background dominatesover all other SM sources. Multijet events populate the region
α
T0.
5, andtheα
T distribution ischarac-terised by a sharp edge at 0.5, beyond whichthe multijet event yield falls by several orders of magnitude. Multijet events with extremely rarebut large stochastic fluctuations inthe calorimet-ricmeasurements ofjetenergiescan leadtovaluesof
α
T slightlyabove0.5.Theedgeat0.5sharpenswithincreasing HTfor
multi-jetevents,primarilyduetoacorrespondingincreaseintheaverage jetenergyandaconsequentimprovementinthejetenergy resolu-tion.Thecontributionfrommultijeteventsissuppressedbymore than fiveordersof magnitudebyimposing the HT-dependent
α
TrequirementssummarisedinTable 1.
Severalbeam- anddetector-relatedeffects,suchasinteractions from beamhalo, reconstruction failures,detector noise, or event misreconstructionduetodetectorinefficiencies,canleadtoevents with large,unphysicalvaluesof
pmissT andvaluesofα
Tgreaterthan0.55. These types of events are rejected with high efficiency by applyingarangeofvetoes[73].
Twofinaleventvetoescompletethedefinitionofthesignal re-gion.Anestimatorfor
pmisssumofthetransversemomentaofallreconstructedparticlesinan event, as determined by the particle-flow (PF)algorithm [74,75]. ThemagnitudeofthisvectorialsummationisreferredtoasEmiss
T .
The first veto concerns the rare circumstance in which several jets,collinear in
φ
andeach with pT belowits respectivethresh-old,resultinsignificant Hmiss
T .Thistypeofbackground,typical of
multijet events, is suppressed while maintaining high efficiency for SM or new-physics processes with genuine
pmissT by requir-ing HmissT/
EmissT<
1.
25. The second vetoconsiders the minimum azimuthal separation betweena jet and thenegative ofthe vec-tor sum derived from the transverse momenta of all other jets inthe event, whichis referred to asφ
min∗ [25]. Thisvariable is employedtosuppresspotentialcontributionsfromenergetic mul-tijetevents that havesignificant pmissT throughthe production of neutrinosinsemileptonicheavy-flavourdecays.Suchneutrinosare typically collinearwiththe axisofa jet. We imposethe require-mentφ
∗min>
0.
3, which effectivelysuppresses thisbackground asdeterminedusingcontroldata.5. Triggersanddatacontrolsamples
Candidatesignal events arerecorded undermultiplejet-based trigger conditions that require both HT and
α
T to satisfyprede-termined thresholds. The trigger-level jet energies are corrected to account for energy scale and pileup effects. The trigger effi-cienciesfortheSM backgrounds aremeasured usinga sampleof
μ
+
jets events,whichprovidesanunbiasedcoverage ofthe kine-maticphasespacewhenthemuonisignored.Theefficienciesare determined as a function of Njet and HT, and lie in the range79–98% and
>
99% for 200<
HT<
375 GeV and HT>
375 GeV,respectively.The inefficienciesatlowvaluesof HT,whichare
ac-countedforin the final result, arise fromconditionsimposed on L1triggerquantities.Statistical uncertaintiesofa fewpercentare considered.Simulation-based studiesdemonstratethat trigger in-efficienciesforsignaleventsaretypicallynegligible.
AsetofprescaledHTtriggerconditionsisusedtorecordevents
foramultijet-enrichedcontrolsample,definedbyrelaxed require-ments on
α
T,φ
∗min, and HmissT/
EmissT withrespect to the signalregion. This eventsample is used to estimate the multijet back-groundcontribution.
SignificantbackgroundinthesignalregionisexpectedfromSM processeswithgenuine
pmissT inthefinalstate.Thedominant pro-cesses are the associated production of W orZ bosons and jets, withthedecaysZ→
νν
orW±→
ν
(=
e,μ
,τ
),andtopquark pair productionfollowed by semileptonic top quark decay. Three separatedatacontrolregions areusedtoestimatethebackground fromtheseprocesses.Thecontrol regionsaredefinedthroughthe selection ofμ
+
jets,μμ
+
jets,orγ
+
jets events [28]. The se-lection criteriaare chosen such that the SM processes and their kinematicpropertiesresemble ascloselyaspossibletheSM back-ground behaviour in the signal region, once the muon, dimuon system, orphoton are ignored in thedetermination ofquantities suchasHT andα
T.Theeventselectioncriteriaaredefinedtoen-surethat thepotential contribution frommultijeteventsor from awidevarietyofSUSYmodels(i.e.so-calledsignalcontamination) isnegligible.EventsarecategorisedaccordingtoNjet,Nb,andHT,
identicallyto theschemeused foreventsinthe signal region,as definedinSection4.
The
μ
+
jets sample is recorded using a trigger that requires an isolated muon.The eventselection criteriaarechosen so that thetrigger ismaximally efficient(≈
90%). Furthermore,themuon is required to be well separatedfrom the jets inthe event, and thetransverse massformed bythe muonand EmissT systemmust liebetween30and125 GeVtoensureasamplerichinWbosons (producedpromptlyorfromthe decayoftop quarks).Theμμ
+
jets sampleusesthesametriggercondition(efficiency
≈
99%)and similarselectioncriteriaastheμ
+
jets sample,specifically requir-ingtwooppositelychargedisolatedmuonsthatarewellseparated from the jets in the event, and with a dilepton invariant mass withina±
25 GeV windowaroundthenominalmassoftheZ bo-son. For both the muon anddimuon samples, norequirement is made onα
T, in order to increase the statisticalprecision of thepredictions fromthesesamples.The
γ
+
jets eventsare recorded usinga single-photontriggercondition.The eventselection crite-riarequireanisolated photonwith pT>
165 GeV, HT>
375 GeV,and
α
T>
0.
55,yieldingatriggerefficiencyof99%.6. Multijetbackgroundsuppression
The signal region is definedin a manner to suppressthe ex-pected contributionfrommultijeteventsto thesub-percent level relative to theexpectedbackground fromother SM processesfor alleventcategoriesandHTbins.Thisisachievedthroughvery
re-strictiverequirementsonthe
α
Tandφ
∗minvariables,asdescribedabove. In thissection, we discusstheserequirements further, to-gether with the procedure for estimatingthe remaining multijet background.
Independentestimatesaredeterminedperbininthesignal re-gion,definedintermsofNjet,Nb,andHT.Themethodutilisesthe
multijet-enriched controlsample introduced inSection 5,defined by 0
.
505<
α
T<
0.
55 and no threshold requirements onφ
∗minor HmissT
/
EmissT . The event counts in this data sideband are cor-rected to account for contamination from nonmultijet processes, whichareestimatedusingthemethoddescribedinSection7.The method exploitsthe evolutionofthe ratioR(
α
T)
,definedby thenumber of (corrected) event counts that satisfy the requirement
HmissT
/
EmissT<
1.
25 to the number that fail, as a function ofα
T.Theratio
R(
α
T)
isobservedtomonotonicallyfallasafunctionofα
Tandismodelled,independentlyforeachbin,withanexponen-tialfunction
F(
α
T)
.Anadditionalmultijet-enricheddatasideband,definedby HTmiss
/
EmissT>
1.
25 andα
T>
0.
55,isusedtodeterminethe numberof(corrected)events
N (
α
T>
α
Tmin)
perbinthatsat-isfy aminimumthresholdrequirementon
α
T.Finally,anestimateof themultijetbackground foreach binisdetermined asa func-tionofthethreshold
α
minT basedontheproductof
N (
α
T>
α
Tmin)
andtheextrapolatedvalueoftheratiofromthecorrespondingfit,
F(
α
T>
α
minT)
.The
α
Tvaluerequiredtosuppressthepredictedmultijetcontri-butiontothesub-percentlevelrelativetothetotalSMbackground isdeterminedindependentlyforeachbinofthesignalregion.The
α
minT thresholdsdetermined fromthismethodare summarisedin
Table 1 and, forsimplicity, are chosen tobe identicalfor all Njet
and Nb categories. Higher
α
T thresholds are required than thoseusedforRef.[28]becauseofhigherpileupconditionsinthelatter half ofthedatacollected in 2012andbecauseoftheaddition of thelow HT bins.
Various checks are performed in simulation and in data to assure closure, which, in simulation refers to the ability of the method tocorrectly predictthe backgroundrates foundin simu-lateddata,and,indata,referstotheconsistencybetweenthe data-derivedpredictionsfor,andcountsin,aseparatemultijet-enriched validationsample indata.The exponentialfunctionsarefound to adequately modeltheobservedbehaviourindataandsimulation. Systematicuncertainties inthe predictionsare obtainedfromthe differencesobserved usingalternative fitfunctionsandcan beas largeas
∼
100%.Following application ofthe
α
T requirements,residual0
.
3,asdiscussedinSection4.Thissuppressionisvalidatedin sim-ulationandindatausingacontrolsampledefinedbythe require-mentsHT>
775 GeV andeither0.
51<
α
T<
0.
55 orHTmiss/
EmissT>
1
.
25.TheseeventsareselectedwithanunprescaledHTtrigger,al-lowingastudyoftheperformanceoftheselectionrequirementsin thelow
α
Tregionaround0.51,whichcorrespondstosimilarHmissTvaluesasemployedinthelowest HT bins.Fromthesestudies,the
remaining multijetbackground isfound to be atthe sub-percent level.Withthislevelofsuppression,anyresidualcontributionfrom multijetevents isassumed tobe negligible compared to the un-certaintiesassociatedwiththenonmultijetbackgrounds(described below)andisignored.
7.Estimationofnonmultijetbackgrounds
Inevents withfew jetsor few b quark jets, the largest back-groundsareZ
→
νν
+
jets orW±→
ν
+
jets.Athigherjetorb quarkjet multiplicities, tt andsingle topproduction alsobecome animportantsourceofbackground.ForWbosondecaysthatyield anelectronormuon(possiblyoriginatingfromleptonicτ
decays), the background arises when the e orμ
is not rejected through the dedicated lepton vetoes. Background also ariseswhen theτ
leptondecaystoneutrinosandhadrons, whichareidentifiedasa jet.Thevetoofeventscontainingatleastoneisolatedtrackis ef-ficientat further suppressing thesebackgrounds, including those fromsingle-prongτ
-leptondecays,byasmuchas∼
50%for cate-goriesenrichedintt.Theproduction ofW and Zbosons in association withjetsis simulatedwiththeleading-order(LO) MadGraph 5.1.1.0[76]event generator,withuptofouradditionalpartonsconsideredinthe ma-trixelementcalculation.Theproductionoftt andsingletopquark eventsisgeneratedwiththenext-to-leading-order (NLO) powheg 1.0[77–80]program.TheLO pythia 6.4.26[81]programisusedto generateWW,WZ,andZZ(diboson)events,andto describe par-tonshoweringandhadronisationforallsamples.TheCTEQ6L1[82]
andCT10 [83]partondistribution functions(PDFs)are usedwith MadGraph and powheg, respectively. The description of the de-tector response is implemented using the Geant4 [84] package. Thesimulatedsamplesarenormalisedbythemostaccuratecross sectioncalculationscurrentlyavailable,usuallyupto next-to-next-to-leading-order (NNLO) accuracy in QCD [85–89]. To model the effectsofpileup,thesimulatedeventsare generatedwitha nom-inaldistribution of pp interactions per bunch crossing and then reweightedtomatchthepileupdistributionmeasuredindata.
Fig. 1showsthedistributionsofthe
α
T variableobtainedfromsamplesofeventsthatsatisfytheselectioncriteriausedtodefine the
μ
+
jets controlregionandthesignalregion.Theinclusive re-quirements Njet≥
2, Nb≥
0, and HT>
200 and 375 GeV forthetwosamples,respectively,areimposed.Thedistributionsillustrate the background composition of the two samples as determined fromsimulation.While thefigure alsodemonstrates an adequate modellingof the
α
T variablewith simulated events,the methodemployedby the search toestimate thenonmultijet backgrounds isdesignedtomitigatetheeffectsofsimulationmismodelling.
Themethodrelies onthe useoftransfer factorsthat are con-structedperbin,withabinningschemedefinedidenticallytothat ofthesignalregionintermsofNjet, Nb,andHT,foreachcontrol
sample in data. The transfer factors are determined using simu-lated events,and are given by the ratios of the expected yields in the corresponding bins of the signal region and control sam-ples. The transfer factors are used to extrapolate from the event yield measured in a data control sample to the expectation for backgroundfroma particularSM processorprocesses inthe sig-nalregion.Themethodaimstominimisetheeffectsofsimulation mismodelling, as manysystematic biases are expected to largely
Fig. 1. TheαT distributionobservedindataforevent samplesthatarerecorded
withaninclusivesetoftriggerconditionsandsatisfy(top)theselectioncriteria thatdefinetheμ+jets controlregionor(bottom)thecriteriathatdefinethe sig-nalregion,withtheadditionalrequirementHT>375 GeV.Eventyieldsobserved
indata(solidcircles)andSMexpectationsdeterminedfromsimulation(solid his-tograms)areshown.Contributionsfromsingletopquark,diboson,Drell–Yan,and tt+gaugebosonproductionarecollectivelylabelled“ResidualSM”.Thefinalbin containstheoverflowevents.Thelowerpanelsshowtheratiosofthebinnedyields obtainedfromdataandMonteCarlo(MC)simulationasafunctionofαT.The
sta-tisticaluncertaintiesintheSMexpectationsarerepresentedbythehatchedareas.
cancelintheratiosusedtodefine thetransferfactors. Uncertain-ties in the transfer factors are determined from a data-derived approach,describedbelow.
The
μ
+
jets data sample provides an estimate of the total contribution from tt and W boson production, as well as of the residual contributions fromsingle top quark, diboson, andDrell– Yan(qq→
Z/
γ
∗→
+−)production.Twoindependentestimates ofthebackgroundfromZ
→
νν
+
jets eventswithNb≤
1 arede-termined,one fromthe
γ
+
jets datasample andtheother from theμμ
+
jets data sample, whichare considered simultaneously inthelikelihoodfunctiondescribedinSection8.Theγ
+
jets and Z→
μμ
+
jets processeshavesimilar kinematicproperties when the photon or muons are ignored in the determination of Emissand HmissT [90], although the acceptances differ. An advantage of the
γ
+
jets process is its much larger production cross section comparedtotheZ→
νν
+
jets process.InthecaseofeventswithNb
≥
2,theμ
+
jets sampleis alsousedto estimate the smallZ
→
νν
+
jets background because of thelimitedeventcountsintheμμ
+
jets andγ
+
jets control sam-ples.ThemethodreliesontheuseofW→
μν
+
jets eventsto pre-dicttheZ→
μμ
+
jets background[25,27,28].Themethodcorrects fortt contaminationintheμ
+
jets sample,whichcanbe signifi-cantinthepresenceofjetsidentifiedasoriginatingfrombquarks. However,whilethett contaminationincreaseswithincreasingNb,theZ
→
μμ
+
jets backgroundisreducedtoasub-dominantlevel relativetootherbackgrounds.Themethodisvalidatedindata con-trolregionsdefinedbysamplesofeventscategorisedaccordingtoNb.Insummary,onlythe
μ
+
jets sampleisusedtoestimatethetotalSMbackgroundforeventswithNb
≥
2,whereasallthreedatacontrolsamplesareusedforeventswithNb
≤
1.Tomaximisesensitivitytonew-physicssignatureswithalarge numberofbquarks,amethodisemployedthatallowseventyields foragivenbquark jet multiplicity tobepredictedwitha higher statisticalprecisionthanobtaineddirectlyfromsimulation, partic-ularlyforeventswithalargenumberofbquarkjets(Nb
≥
2)[28].Themethodreliesongenerator-levelinformationcontainedinthe simulation to determine the distribution of Nb for a sample of
eventscategorisedaccordingtoNjetandHT.First,simulatedevents
are categorised according to the number of jets per event that are matched to underlyingb quarks (Nbgen), c quarks(Ngenc ), and
light-flavoured quarks or gluons (Ngenq ). Second, the efficiency
withwhich b quark jets are identified, and themisidentification probabilitiesforcquarksandlight-flavourpartons, fc and fq,
re-spectively,arealsodeterminedfromsimulation,witheachquantity averaged over jet pT and
η
per eventcategory. Correctionsto,
fc, and fq are applied on a jet-by-jet basis asa function of pT
and
η
sothattheymatchthecorrespondingquantitymeasuredin data[71].Finally, Ntagb , Ntagc ,and Ntag
q are,respectively, the
num-ber ofjets identified (“tagged”)as originatingfromb quarks per eventwhentheunderlyingpartonisabquark,cquark,ora light-flavoured quark or gluon, and P
(
Ntagb;
Nbgen,
)
, P(
Ntagc;
Ngen c
,
fc)
,andP
(
Ntagq;
N genq
,
fq)
arethebinomialprobabilitiesforthistohap-pen. These quantities are sufficient to estimate how events are distributed according to Nb per (Njet, HT) category when
sum-mingover allrelevantcombinationsthat satisfytherequirements
Njet
=
Nbgen+
Ngen
c
+
Ngenq andNb=
Ntagb+
N tag c+
Ntagq .Theeventyields determinedwiththemethoddescribedabove aresubsequentlyusedtodeterminethetransferfactorsbinned ac-cordingtoNb (inadditiontoNjetandHT).Theuncertaintiesinthe
transfer factors obtained from simulation are evaluated through sets of closure tests based on events from the data control re-gions[28].Eachsetusestheobservedeventcountsinuptoeleven bins in HT for a given sample of events, along with the
corre-sponding (HT-dependent) transfer factors obtained from
simula-tion,todetermine HT-dependentpredictions Npred
(
HT)
foryieldsinanother eventsample.The two samplesare takenfrom differ-entdata control regions, orare subsetsofthe same datacontrol sample with differing requirements on Njet or Nb. The
predic-tionsNpred
(
HT)
arecomparedwiththeHT-binnedobservedyieldsNobs
(
HT)
andthe level of closure is definedby the deviationoftheratio
(
Nobs−
Npred)/
Npred fromzero.Alarge numberoftestsareperformedtoprobekeyaspectsofthemodellingthatmay in-troduce an Njet- or HT-dependent source of bias in the transfer
factors[28].
Systematicuncertaintiesare determinedfromcoresetsof clo-suretests, ofwhich the results are shown in Fig. 2. Fivesets of tests are performed independently foreach of the two Njet
cat-egories, and a further three sets that are common to both Njet
Fig. 2. Ratio(Nobs−Npred)/NpredasafunctionofHTfordifferenteventcategories
and/orcontrolregionsfor(upper)eventswithtwoorthreejets,and(lower)events withfourormorejets;“btag”referstoareconstructedbquarkcandidate.Error barsrepresentstatisticaluncertaintiesonly,whilethegreyshadedbandsrepresent theNjet- andHT-dependentuncertaintiesassumedinthetransferfactors,as
deter-minedfromtheproceduredescribedinthetext.
categories. The testsaimto probeforthepresenceofstatistically significantbiasesthatcouldariseduetolimitationsinthemethod. ForeachNjet category,thefirstthreesetsofclosuretestsare
per-formed using the
μ
+
jets sample.The first setprobes the mod-elling of theα
T distribution for events containing genuine pmissTfrom neutrinos(open circlemarkers). Twosets (crosses, squares) probe the relative composition betweenW
+
jets and top events andthemodellingofthereconstructionofbquarkjets.Thefourth set (triangles)validatesthemodellingofvector bosonproduction by connectingtheμ
+
jets andμμ
+
jets controlsamples,which are enriched in W+
jets and Z+
jets events, respectively. The fifth set (swiss crosses) deals with the consistency between theγ
+
jets andμμ
+
jets samples, whichare both usedto provide an estimate ofthe Z→
μμ
+
jets background. Threefurther sets ofclosuretests(stars,invertedtriangles,diamonds),oneper data control sample,probethesimulation modellingofthe Njetdistri-butionforarangeofbackgroundcompositions.
Theclosuretestsrevealnosignificantbiasesordependencyon
Njet nor HT. Systematic uncertainties in the transfer factors are
determined from the variance in
(
Nobs−
Npred)/
Npred, weightedto accountforstatisticaluncertainties, forallclosuretestswithin an individual HT bin in the range 200
<
HT<
375 GeV and foreach Njet category. Forthe region HT
>
375 GeV,all tests within200 GeV-wide intervals in HT,defined by pairs ofadjacent bins,
arecombinedtodeterminethesystematicuncertainty,whichis as-sumedtobefullycorrelatedforbinswithineachinterval,andfully uncorrelated for different HT intervals and Njet categories. The
magnitudesofthesystematicuncertaintiesareindicatedbyshaded greybandsinFig. 2andsummarisedinTable 2.Thesame (uncor-related) value of systematic uncertainty is assumed for each Nb
Table 2
Systematicuncertainties(%)inthetransferfactors,inintervalsofNjetandHT.
Njet HTregion (GeV)
200–275 275–325 325–375 375–575 575–775 775-975 >975
2–3 4 6 6 8 12 17 19
≥4 6 6 11 11 18 20 26
Table 3
Observedeventyieldsindataandthe“apriori”SMexpectationsdeterminedfromeventcountsinthedatacontrolsamplesandtransferfactorsfromsimulation,inbins ofHT,andcategorisedaccordingtoNjetandNb.AlsoshownaretheSMexpectations(labelled“SM”)obtainedfromacombinedfittocontrolandsignalregionsunderthe
SMhypothesis.Thequoteduncertaintiesincludethestatisticalaswellassystematiccomponents.Foreachrowthatlistsfewerthanthefullsetofcolumns,thefinalentry representsvaluesobtainedforanopenfinalHTbin.
Category (Njet,Nb) HT(GeV) 200–275 275–325 325–375 375–475 475–575 575–675 675–775 775–875 875–975 975–1075 1075–∞ (2–3, 0) Data 13090 5331 3354 2326 671 206 76 29 10 9 2 (2–3, 0) a priori 12410+370 −410 5540+ 340 −230 3330+ 130 −170 2400+ 120 −90 663+ 34 −26 225+ 21 −17 68.5+ 6.9 −6.7 26.5+ 3.9 −3.0 10.3+ 1.9 −2.1 5.1+ 1.0 −1.1 4.5+ 0.9 −0.9 (2–3, 0) SM 13030+−90120 5348+ 85 −67 3351+ 56 −50 2351+ 38 −45 655+ 14 −11 218+ 12 −17 68.5+ 4.9 −4.8 27.2+ 3.0 −3.0 10.4+ 1.5 −1.6 5.6+ 1.0 −1.0 4.3+ 0.7 −1.0 (2–3, 1) Data 1733 833 527 356 90 31 6 4 1 0 1 (2–3, 1) a priori 1669+65 −67 853+ 50 −46 525+ 37 −24 391+ 23 −21 94.3+ 6.0 −5.6 24.5+ 2.5 −3.6 9.0+ 1.2 −1.4 2.8+ 0.6 −0.8 2.5+ 0.8 −0.9 0.3+ 0.2 −0.1 0.2+ 0.1 −0.1 (2–3, 1) SM 1711+−3733 839+ 21 −25 526+ 20 −17 372+ 12 −14 90.6+ 5.1 −4.6 25.8+ 2.9 −2.6 8.7+ 0.8 −1.4 3.0+ 0.7 −0.6 2.2+ 0.8 −0.6 0.3+ 0.2 −0.1 0.2+ 0.1 −0.2 (2–3, 2) Data 172 116 101 55 16 9 0 0 0 (2–3, 2) a priori 187+−78 118+ 7 −7 98.7+ 7.1 −7.0 61.3+ 5.9 −5.5 12.3+ 1.7 −1.0 2.8+ 0.5 −0.6 0.7+ 0.2 −0.2 0.2+ 0.1 −0.1 <0.1 (2–3, 2) SM 184+5 −7 117+ 7 −5 99.4+ 5.4 −4.6 60.2+ 3.5 −3.8 12.4+ 1.2 −1.0 3.3+ 0.6 −0.5 0.7+ 0.2 −0.2 0.2+ 0.1 −0.1 <0.1 (≥4, 0) Data 99 568 408 336 211 117 38 13 9 4 6 (≥4, 0) a priori 108+−1012 497+ 34 −36 403+ 36 −33 327+ 25 −22 193+ 14 −13 95+ 13 −11 40.3+ 5.9 −4.4 14.5+ 3.5 −2.4 7.1+ 1.7 −1.4 3.2+ 0.7 −1.0 2.9+ 0.7 −0.5 (≥4, 0) SM 104+6 −8 544+ 21 −18 407+ 18 −18 337+ 15 −10 202+ 10 −8 105+ 9 −7 42.5+ 4.5 −3.3 14.3+ 1.7 −2.5 7.5+ 1.4 −1.5 3.5+ 0.8 −0.8 3.4+ 1.0 −0.7 (≥4, 1) Data 38 195 210 159 83 33 7 10 4 1 1 (≥4, 1) a priori 39.2+−3.03.5 215+ 12 −16 208+ 24 −22 150+ 15 −11 75.8+ 7.8 −6.6 28.6+ 3.8 −3.7 10.3+ 2.1 −1.4 5.1+ 1.3 −0.9 2.0+ 0.7 −0.5 0.8+ 0.4 −0.3 0.9+ 0.6 −0.4 (≥4, 1) SM 38.9+2.2 −3.7 206+ 12 −10 209+ 13 −10 157+ 9 −9 79.3+ 5.2 −4.7 29.4+ 3.8 −2.2 9.9+ 1.9 −1.3 6.2+ 1.2 −1.1 2.3+ 0.7 −0.7 0.9+ 0.3 −0.3 0.9+ 0.3 −0.4 (≥4, 2) Data 16 81 88 64 43 14 5 1 1 (≥4, 2) a priori 12.3+−1.01.0 76.7+ 5.6 −5.2 93+ 11 −9 63.0+ 7.8 −5.7 34.0+ 3.6 −3.4 10.1+ 2.6 −1.8 3.4+ 0.9 −0.6 1.0+ 0.2 −0.2 0.7+ 0.1 −0.2 (≥4, 2) SM 12.5+−1.01.0 77.8+ 4.7 −4.6 90.2+ 9.0 −6.5 66.1+ 4.6 −4.8 36.3+ 3.4 −2.9 11.4+ 1.8 −1.9 3.9+ 0.8 −0.7 1.0+ 0.2 −0.3 0.7+ 0.1 −0.2 (≥4, 3) Data 0 7 5 5 6 1 1 0 0 (≥4, 3) a priori 1.1+−0.20.1 8.2+ 0.6 −0.9 11.1+ 2.0 −1.6 7.4+ 1.1 −1.0 4.0+ 0.5 −0.6 1.1+ 0.3 −0.3 0.4+ 0.2 −0.1 0.1+ 0.1 −0.0 <0.1 (≥4, 3) SM 1.1+−0.20.2 8.1+ 0.9 −0.9 9.9+ 1.5 −1.3 7.2+ 0.9 −0.7 4.1+ 0.6 −0.6 1.1+ 0.3 −0.3 0.4+ 0.1 −0.1 0.1+ 0.1 −0.0 <0.1 (≥4,≥4) Data 0 0 0 2 (≥4,≥4) a priori <0.1 0.2+−0.10.1 0.5+ 0.3 −0.3 0.3+ 0.2 −0.2 (≥4,≥4) SM <0.1 0.1+−0.10.1 0.4+ 0.2 −0.3 0.4+ 0.2 −0.2 misidentificationratesforjetsoriginatingfrombquarksandfrom light-flavouredquarksorgluons.These uncertaintiesare foundto beatthesub-percentlevel,subdominantrelativetothevaluesin
Table 2,andthereforeconsideredtobenegligible.
8. Resultsandinterpretation
Foragivencategoryofeventssatisfyingrequirementsonboth
Njet and Nb, a likelihood model of the observations in all data
samplesisusedto obtainaconsistentpredictionoftheSM back-groundsandtotestforthepresenceofavarietyofsignalmodels. Thisiswrittenas:
LNjet,Nb
=
LSRLμLμμLγ, (0
≤
Nb≤
1)LNjet,Nb
=
LSRLμ,
(
Nb≥
2)(3)
where LSR
=
iPois
(
ni|
bi+
si)
is a likelihood functioncompris-ingaproductofPoissontermsthat describetheyieldsineachof the HT binsof thesignal region forgivenvaluesof Njet and Nb.
Ineach binof HT (index i), the observationni is modelled asa
PoissonvariabledistributedaboutthesumoftheSM expectation
bianda potentialcontributionfromasignalmodelsi (assumedto bezerointhefollowingdiscussion).Thecontributionfrommultijet
productionisassumedtobezero,basedonthestudiesdescribed inSection6.The SMexpectationsinthesignal regionarerelated totheexpectedyieldsinthe
μ
+
jets,μμ
+
jets,andγ
+
jets con-trolsamplesviathetransferfactorsderivedfromsimulation. Anal-ogoustoLSR,thelikelihoodfunctionsLμ,Lμμ,andLγ describetheyieldsintheHTbinsofthe
μ
+
jets,μμ
+
jets,andγ
+
jets controlsamplesfor thesamevalues of Njet and Nb asthe signal region.
Forthecategory ofeventswithNb
≥
2,only theμ
+
jets controlsampleisusedinthelikelihoodtodeterminethetotalcontribution fromallnonmultijetSMbackgroundsinthesignalregion.The sys-tematicuncertainties inthetransferfactors,determined fromthe ensemble of closure tests described above and withmagnitudes intherange4–26%(Table 2), areaccommodatedinthelikelihood functionthroughanuisanceparameterassociatedwitheach trans-fer factor used in the background estimation for each (Njet, Nb)
category and HT interval. The HT intervals are defined by pairs
ofadjacent HT bins forthe region HT
>
375 GeV,asdescribed inSection 7,andso adjacentbinssharethesamenuisance parame-ter.Themeasurementsoftheseparametersareassumedtofollow alognormaldistribution.
Table 3 summarises the observed event yields and expected
deter-minedfromeventcountsinthedatacontrolsamplesandtransfer factorsfromsimulation,andarethereforeindependentofthe sig-nalregion.No significantdiscrepancies areobserved betweenthe “a priori” SM expectations andthe observed eventyields. In ad-dition,a simultaneous fitto datain the signal region andin up to three control regions is performed. The likelihood function is maximised over all fit parameters under the SM-only hypothesis inorderto estimate theyields fromSM processesineach binin allregions,intheabsenceofanassumedcontributionfromsignal events.Table 3summarisestheseestimates(labelled“SM”)forthe signal region. Agoodness-of-fit test isperformed to quantifythe degree ofcompatibilitybetweenthe observed yields andthe ex-pectationsunderthebackground-onlyhypothesis.Thetestisbased onaloglikelihoodratioandthealternativehypothesis isdefined bya “saturated”model[91].The p-valueprobabilities forall Njet
and Nb categories are found to be uniformly distributed,with a
minimumvalueof0.19.
Theresultsofthissearchare interpretedintermsoflimitson theparentsparticleandLSPmassesintheparameterspaceof sim-plifiedmodels[58–60]thatrepresentthedirectpairproductionof topsquarksandthedecaymodes
˜
t→
cχ
˜
01,
˜
t→
b f¯
fχ
˜
10,˜
t→
bχ
˜
1±followedby
χ
˜
1±→
W±χ
˜
01,and
˜
t→
tχ
˜
01.The CLs method[92,93]
isusedtodetermineupperlimitsatthe95%confidencelevel(CL) ontheproductioncrosssection ofa signalmodel,usingthe one-sided(LHC-style)profile likelihood ratioasthe test statistic[94]. Thesamplingdistributionsfortheteststatisticaregeneratedfrom pseudo-experimentsusingtherespectivemaximumlikelihood val-uesofnuisanceparametersdeterminedfromasimultaneousfitto the pseudo-data, in the 75 bins of the signal region and in the corresponding binsofup tothree controlsamples,underthe SM background-onlyandsignal
+
backgroundhypotheses.The poten-tialcontributionsofsignaleventstoeachofthesignalandcontrol samples are considered, butthe only significant contribution oc-cursinthesignalregionandnotthecontrolsamples.Theeventsamplesforthesimplifiedmodelsaregeneratedwith the LO MadGraph 5.1.1.0 generator, which considers up to two additional partons in the matrix element calculation. Inclusive, process-dependent,NLOcalculationsofSUSYproductioncross sec-tions, with next-to-leading-logarithmic (NLL) corrections, are ob-tained with the program prospino 2.1 [95–100]. All events are generatedusingthe CTEQ6L1PDFs.AsforSMprocesses,the simu-latedeventsaregeneratedwithanominalpileupdistributionand then reweighted to matchthe distribution observed in data.The detector response is provided by the CMS fast simulation pack-age[101].
Experimental uncertainties in the expected signal yields are considered. Contributions to the overall systematic uncertainty arise from various sources such as the uncertainties from the choiceofPDFs,thejetenergyscale,themodellingoftheefficiency and misidentification probability of b quark jets in simulation, the integratedluminosity [24], andvarious event selection crite-ria. The magnitude of each contribution depends on the model, the masses of the parent sparticle and LSP, and the event cate-goryunderconsideration.Uncertaintiesinthejetenergyscaleare typically dominant (
∼
15%) for models with mass splittings that satisfym
>
mt,wheremt isthetop quarkmass.The acceptanceformodelswithmasssplittingssatisfying
m
<
mt isdueinlargeparttoISR,themodellingofwhichcontributesthedominant sys-tematicuncertaintyforsystemswithacompressedmassspectrum. Anuncertaintyof
∼
20%isdeterminedbycomparingthesimulated andmeasured pT spectra ofthe systemrecoiling against the ISRjets in tt events, using the technique described in Ref. [67]. For the aforementionedsimplified models, the effectof uncertainties in the distribution of signal events is generally small compared with the uncertainties in the experimental acceptance. The total
systematicuncertaintyintheyieldofsignalisfoundtobe inthe range5–36%,dependingonNjetandNb,andistakenintoaccount
through a nuisanceparameter that follows a lognormal distribu-tion.
Fig. 3showstheobservedupperlimitontheproductioncross sectionat95%confidencelevel(CL),asafunctionofthetopsquark and
χ
˜
10 masses,forarangeofsimplifiedmodelsbasedonthepair productionoftopsquarks,togetherwithexcludedmassregions.Figs. 3 (upperleft andright)show thesensitivityofthis anal-ysis to the decay modes
˜
t→
cχ
˜
01 and
˜
t→
b f¯
fχ
˜
10, respectively.Models with
m as smallas10 GeVareconsidered, andthe top squarks areassumedtodecaypromptly.The excludedregionsare determined usingtheNLO
+
NLLcrosssectionsfortopsquarkpair production,assuming that bsquarks, light-flavoured squarks,and gluinos are too heavy to be produced in the pp collisions. Also shown are the excluded regions observed when the production crosssectionischangedbyitstheoreticaluncertainty,andthe ex-pected region ofexclusion, aswell asthose determined for both±
1 and±
2 standard deviation (σ
) changes in experimental un-certainties. The range ofexcluded top squarkmasses is sensitive to boththedecaymodeandm. Forthedecay
˜
t→
cχ
˜
01,the
ex-pected excluded region is relatively stable as a function of
m,
with
˜
t masses below285and325 GeVexcluded,respectively,form
=
10 and80 GeV.Theobservedexclusion,assuming the the-oretical production cross section reduced by its 1σ
uncertainty, is weaker, with˜
t masses below 240 and 260 GeV excluded form
=
10 and 80 GeV. Forthe decay t˜
→
b f¯
fχ
˜
01, the expected
excluded mass region is strongly dependent on
m, weakening considerably for increasing values of
m due to the increased momentumphasespaceavailabletoleptonsproducedinthe four-body decay. Topsquark masses below265 and 165 GeVare ex-cluded based on the expected results, respectively, for
m
=
10 and80 GeV.Theobservedexclusionisagainweaker,withmasses below 225 and 130 GeV excluded. The nonsmooth behaviour of the exclusioncontours is theresultof statisticalfluctuationsand the sparseness of the scan over the mass parameter space, and doesnotrepresentakinematicaleffect.Figs. 3(middle left andright)show the limitson theallowed cross section forthe decay
˜
t→
bχ
˜
1±,followed bya decay ofthe˜
χ
1± to theχ
˜
01 and to either an on- or off-shell W boson,
de-pending on the mass difference betweenthe
χ
˜
1± andχ
˜
10. For a modelwithmχ˜±1
=
0.
25m˜t+
0.
75mχ˜10,showninFig. 3(middleleft), the analysis has sensitivityin the region mχ˜±1
−
mχ˜10<
mW, ex-cludingχ
˜
01 massesup to 225 GeV andt masses
˜
up to 350 GeV.Models that satisfy mχ˜±
1
<
91.
9 GeV, or mχ˜1±<
103.
5 GeV andmχ˜±
1
−
mχ˜10<
5 GeV,arealreadyexcludedbyacombinationof re-sultsobtainedfromtheALEPH,DELPHI,L3,andOPALexperiments at LEP [102,103]. For a model with mχ˜±1
=
0.
75m˜t+
0.
25mχ˜10, shown in Fig. 3 (middle right),˜
t masses up to 400 GeV can be excludedbutthereachinχ
˜
01 massisreduced.
Fig. 3(lowerleft)showstheresultsoftheanalysisforthe de-cay
˜
t→
tχ
˜
01.Bothtwo- andthree-bodydecaysareconsidered,for
whichthelatterscenarioinvolvesanoff-shelltopquark.The polar-izationsofthetopquarksaremodeldependentandarenon-trivial functionsofthetop-squarkandneutralinomixingmatrices[104]. Simulatedeventsoftheproductionanddecayoftopsquarkpairs aregeneratedwithoutpolarizationofthetopquarks.Modelswith
m˜t
<
200 GeV arenot considered,duetosignificant signal contri-butions inthe controlregions. Topsquarkmassesup to500GeV are excluded,andχ
˜
01 massesupto100and50 GeVare excluded
Fig. 3. Observedupperlimitsontheproductioncrosssectionat95%CL(indicatedbythecolourscale)asafunctionofthetopsquarkandχ˜0
1 massesfor(upperleft) ˜
t→cχ˜0
1,(upperright)˜t→b f¯fχ˜ 0
1,(middleleft)t˜→bχ˜1±withm˜χ±
1 =0.25m˜t+0.75m˜χ10,(middleright)˜t→bχ˜
±
1 withm˜χ±
1 =0.75m˜t+0.25m˜χ10,and(lowerleft)˜t→tχ˜
0 1.
TheblacksolidthickcurvesindicatetheobservedexclusionassumingtheNLO+NLLSUSYproduction crosssections;thethinblackcurvesshow corresponding±1σ
theoreticaluncertainties.Theredthickdashedcurvesindicatemedianexpectedexclusionsandthethindashedanddottedcurvesindicate,respectively,their±1σand±2σ
experimentaluncertainties.Asummaryoftheobserved(solid)andmedianexpected(dotted)exclusioncontoursispresented(lowerright).Thegreydotteddiagonallines delimittheregionforwhichm˜t>m˜χ0
observedcountsindatainthe Nb
=
2 categoriesintheregion of500
<
HT<
700 GeV, whichis compatible witha statisticalfluc-tuation. The observed limits lie closerto the expected values at low top squark masses, which correspond to lower values of HT
forwhichgood agreementbetweenthedata andSM background predictionsisobserved.
Fig. 3 (lower right) presents a summary of all the expected and observed exclusion contours and indicates that the analysis hasgoodsensitivityacrossmanydifferentdecaysignaturesinthe
m˜t–mχ˜0
1 plane.Thesensitivityforthesemodelsistypicallydriven by categoriesinvolvingeventssatisfying Njet
≥
4 and1≤
Nb≤
2,whileeventswithlowerNjetandNbmultiplicitiesbecome
increas-inglyimportantfornearlymass-degeneratemodels.
9. Summary
AninclusivesearchforsupersymmetrywiththeCMSdetectoris reported,basedondatafromppcollisionscollectedat
√
s=
8 TeV, correspondingtoan integratedluminosity of18.
5±
0.
5 fb−1.The final states analysed contain two or more jets with large trans-verseenergiesanda significantimbalanceintheeventtransverse momentum,as expectedinthe production anddecayof massive squarksandgluinos.Dedicatedtriggersmadeitpossibletoextend thephasespacecoveredinthissearch tovaluesofHT and HmissTaslowas200and130 GeV,respectively.Theseregionsoflow HT
and HmissT correspond to regions of phase space that are highly populatedin models withlow-masssquarks andnearly degener-atemassspectra.Thesignal regionisbinnedaccordingtoHT,the
numberofreconstructedjets,andthenumberofjetsidentifiedas originatingfrombquarks.Thesumofstandardmodelbackgrounds ineachbinisestimatedfromasimultaneousbinned likelihoodfit totheeventyieldsinthesignalregionandin
μ
+
jets,μμ
+
jets, andγ
+
jets controlsamples.Theobservedyieldsinthesignal re-gionarefoundtobeinagreementwiththeexpectedcontributions fromstandardmodelprocesses.Limitsare determinedin themassparameter spaceof simpli-fiedmodelsthatassumethedirectpairproductionoftopsquarks. A comprehensivestudy oftop squark decay modesis performed andinterpretedin theparameter spaceoftheloop-induced two-body decays to the neutralino and one c quark (
˜
t→
cχ
˜
01);
four-bodydecaystotheneutralino,onebquark,andanoff-shellW bo-son(
˜
t→
b f¯
fχ
˜
01);decaystoonebquarkandthelightestchargino
(
˜
t→
bχ
˜
1±), followed by the decay of the chargino to the light-estneutralinoandan (off-shell)W boson;andthedecaytoatop quarkandneutralino(˜
t→
tχ
˜
10).Intheregionm˜t−
mχ˜01
<
mW,top squarkswithmassesaslargeas260and225 GeV, andneutralino massesupto240and215 GeV,areexcluded,respectively,forthe two- and four-bodydecay modes.For topsquark decaysto bχ
˜
1±, top squark masses up to 400 GeV and neutralino masses up to 225 GeVareexcluded,dependingonthemassofthechargino.For topsquarks decayingto atop quarkanda neutralino,topsquark massesupto 500 GeVandneutralino massesupto 105 GeVare excluded.Insummary,theanalysisprovidessensitivityacrossalarge re-gion of parameterspace in the (m˜t
,
mχ˜01) plane, covering several relevanttop squarkdecaymodes. Inparticular,the applicationof lowthresholds tomaximisesignalacceptanceprovides sensitivity to models withcompressed mass spectra. Fortop squarkdecays to b
χ
˜
1±, wherethe W boson fromtheχ
˜
1± decay isoff-shell,the presentedstudies improveonexisting limits.Mass exclusionsare reported in previously unexplored regions of the(
m˜t,
mχ˜±1
,
mχ˜ 0 1)
parameter spacethat satisfy 100 GeV<
m<
mt, ofup to m˜t=
325,mχ˜±
1
=
250,andmχ˜10=
225 GeV.For the regionm
<
mW, thesearchprovidesthestrongestexpectedmassexclusions,uptom˜t
=
325 GeV, forthe two-bodydecay t˜
→
cχ
˜
10 when 30 GeV<
m
<
mW.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,weacknowledgetheenduringsupportfortheconstruction and operationof the LHCand theCMS detectorprovided by the followingfundingagencies:BMWFWandFWF(Austria);FNRSand FWO (Belgium); CNPq, CAPES, FAPERJ, and FAPESP (Brazil); MES (Bulgaria); CERN; CAST Innovation Foundation, MoST, and NSFC (China); COLCIENCIAS (Colombia); MSES and CSF (Croatia); RPF (Cyprus); MoER,ERCIUTandERDF(Estonia);AcademyofFinland, Nokia, and HIP (Finland); CEA and CNRS/IN2P3 (France); BMBF, DFG, and HGF (Germany); GSRT (Greece); OTKA and NIH (Hun-gary);DAEandDST(India);IPM(Iran);SFI(Ireland);INFN (Italy); MSIPandNRF (RepublicofKorea);LAS(Lithuania);MOE andUM (Malaysia);BUAP,CINVESTAV,CONACYT,InstitutodeCienciay Tec-nología del Distrito Federal, SEP, and UASLP-FAI (Mexico); MBIE (New Zealand); PAEC (Pakistan); MSHE and NSC (Poland); FCT (Portugal); JINR(Dubna); MON,RosAtom, RASandRFBR (Russia); MESTD (Serbia); SEIDIandCPAN(Spain); SwissFundingAgencies (Switzerland); MST (Taipei); ThEPCenter, IPST, STAR and NSTDA (Thailand);TUBITAKandTAEK(Turkey);NASUandSFFR(Ukraine); STFC(UnitedKingdom);DOEandNSF(USA).
Individuals have received support from the Marie-Curie pro-gramme andtheEuropean Research Council andEPLANET (Euro-peanUnion);theLeventisFoundation;theAlfredP.Sloan Founda-tion; the Alexander von Humboldt Foundation; the Belgian Fed-eral Science Policy Office; the Fonds pour la Formation à la Recherchedansl’Industrieetdansl’Agriculture(FRIA-Belgium);the AgentschapvoorInnovatiedoorWetenschapenTechnologie (IWT-Belgium); the MinistryofEducation, Youth andSports(MEYS) of the Czech Republic; the Council of Scientific and Industrial Re-search, India; the HOMING PLUS programme of the Foundation forPolish Science,cofinancedfromEuropeanUnion, Regional De-velopment Fund;theMobilityPlusprogrammeoftheMinistryof Science andHigher Education (Poland);the OPUS programme of theNationalScienceCentreofPoland (Poland);theThalisand Aris-teia programmescofinanced by EU-ESF andthe Greek NSRF; the National Priorities Research Program by Qatar National Research Fund; the Programa Clarín-COFUND del Principado de Asturias; the Rachadapisek Sompot Fund forPostdoctoral Fellowship, Chu-lalongkornUniversity(Thailand);theChulalongkornAcademicinto Its 2nd CenturyProject Advancement Project (Thailand);and the WelchFoundation,contractC-1845.
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