Search for supersymmetry in the multijet and missing transverse momentum final state in pp collisions at 13 TeV

Physics Letters B 758 (2016) 152–180

Contents lists available atScienceDirect

Physics Letters B

www.elsevier.com/locate/physletb

Search for supersymmetry in the multijet and missing transverse momentum final state in pp collisions at 13 TeV

.CMS Collaboration

^

CERN,Switzerland

a r t i c l e i n f o a b s t ra c t

Articlehistory:

Received21February2016 Receivedinrevisedform8April2016 Accepted2May2016

Availableonline6May2016 Editor:M.Doser

Keywords:

CMS Physics Supersymmetry Multijets

A search for new physics is performed based on all-hadronic events with large missing transverse momentumproducedinproton–protoncollisionsat√

s=^{13 TeV.Thedatasample,}correspondingtoan integratedluminosityof2.3 fb⁻¹,wascollectedwiththeCMSdetectorattheCERNLHCin2015.Thedata areexaminedinsearchregionsofjetmultiplicity,taggedbottomquarkjetmultiplicity,missingtransverse momentum, and the scalar sum of jet transverse momenta. The observed numbers of events in all searchregionsarefoundtobeconsistentwiththeexpectationsfromstandardmodelprocesses.Exclusion limitsarepresentedforsimplifiedsupersymmetricmodelsofgluinopairproduction.Dependingonthe assumedgluinodecaymechanism,andforamassless,weaklyinteracting,lightestneutralino,lowerlimits onthegluinomassfrom1440to1600 GeVareobtained,significantlyextendingpreviouslimits.

©^{2016TheAuthor.PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense} (http://creativecommons.org/licenses/by/4.0/).FundedbySCOAP³.

1. Introduction

The standard model (SM) of particle physics successfully de- scribes a wide range of phenomena. However, in the SM, the Higgsbosonmassisunstabletohigher-ordercorrections,suggest- ing that the SM is incomplete. Manyextensions to the SM have beenproposedto provideamorefundamental theory.Supersym- metry (SUSY)[1–8],one such extension, postulates that each SM particle is paired with a SUSY partner from which it differs in spin by one-half unit. As examples, squarks and gluinos are the SUSY partnersof quarks andgluons, respectively, while neutrali- nos

χ

⁰ (charginos

χ

^±)arisefromamixtureoftheSUSYpartners ofneutral(charged)Higgsandelectroweakgaugebosons.Radiative corrections involving SUSY particles can compensate the contri- butions from SM particles and thereby stabilize the Higgsboson mass.Forthiscancellationtobe “natural”[9–12],thetop squark, bottomsquark,andgluinomusthavemassesontheorderofafew TeV orless, possiblyallowing them to be produced atthe CERN LHC.

Amongst SUSY processes, gluino pair production, typically yielding four or more hadronic jets in the final state, has the

 E-mailaddress:[email protected].

largest potentialcross section,making itan aptchannel forearly SUSY searchesintherecentlystartedLHCRun 2.Furthermore,in R-parity[13]conservingSUSYmodels,asare consideredhere,the lightest SUSY particle (LSP) is stable and assumed to be weakly interacting, leading to potentially large undetected, or “missing”, transverse momentum. Supersymmetry events at the LHC might thus be characterized by significant missing transverse momen- tum,numerousjets, and —in thecontext ofnaturalSUSY —jets initiatedbytopandbottomquarks.

ThisLetterdescribesasearch forgluinopairproductioninthe all-hadronic final state. The data, corresponding to an integrated luminosity of 2.3 fb⁻¹ of proton–protoncollisions ata center-of- massenergyof√

s=^{13 TeV,werecollectedwiththeCMSdetector} in 2015, the initial year of the LHC Run 2. Recent searches for gluino pairproductionat √

s=^{8 TeV,based on datacollected in} LHC Run 1, are presented in Refs. [14–16]. Because of the large massscalesandtheirall-hadronicnature,thetargetedSUSYevents areexpectedtoexhibitlargevaluesofHT,whereHTisthescalar sumofthetransverse momenta(pT)ofthejets. Asa measureof missingtransversemomentum,weusethevariableH^miss_T ,whichis themagnitudeofthevectorsumofthejet pT.Wepresentagen- eralsearch forgluino pairproductionleading tofinal stateswith large HT,large H^miss_T ,andlarge jet multiplicity.The dataare ex- amined in bins of Njet, Nb-jet, HT, and H^miss_T , where Njet is the http://dx.doi.org/10.1016/j.physletb.2016.05.002

0370-2693/©^{2016TheAuthor.PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense}(http://creativecommons.org/licenses/by/4.0/).Fundedby SCOAP³.

Fig. 1. Eventdiagramsforthenew-physicsscenariosconsideredinthisstudy:the(upperleft)T1bbbb,(upperright)T1tttt,(lowerleft)T1qqqq,and(lowerright)T5qqqqVV simplifiedmodels.FortheT5qqqqVVmodel,thequarkq andantiquarkq donothavethesameflavorifthegluinog decaysasg→qqχ₁^±,withχ₁^±achargino.

numberofjetsandN_b-jet thenumberoftaggedbottomquarkjets (b jets).The search is performed in exclusive bins of thesefour observables.

We consider SUSY scenarios in the context of four simplified models[17–20]ofnewparticleproduction.Diagramsforthefour models are shown in Fig. 1. Simplified models contain the min- imal particle content to representa topological configuration. As SUSYproductionscenarios, thefour simplifiedmodels canbe in- terpreted asfollows.Inthe firstscenario, showninFig. 1 (upper left),gluinopairproductionisfollowedbythedecayofeachgluino to a bottom quark and an off-shell bottom squark. The off-shell bottomsquark decaysto a bottomquark andthe LSP, wherethe LSPisassumedtobethelightestneutralino

χ

₁⁰ andtoescapede- tection, leading to significant H_T^miss. The second scenario,shown in Fig. 1 (upper right), is the same as the first scenario except withtopquarks andoff-shelltop squarksin placeofthe bottom quarks and squarks. The third scenario, shown in Fig. 1 (lower left),isthe corresponding situationwith gluinodecayto a light- flavoredquarkandoff-shell-squark:up,down,strange,andcharm with equal probability, for each gluino separately. In the fourth scenario,showninFig. 1 (lowerright), alsobasedon gluinopair production,each gluinosimilarly decaystoa light-flavored quark andcorrespondingoff-shellsquark.Theoff-shellsquarkdecaystoa quarkandtoeitherthenext-to-lightestneutralino

χ

₂⁰ orthelight- estchargino

χ

₁^±.The probabilityforthedecaytoproceedviathe



χ

₂⁰,

χ

₁⁺,or

χ

₁⁻,integratedovertheeventsample,is 1/3foreach possibility.The

χ

₂⁰(

χ

₁^±)subsequentlydecaystothe

χ

₁⁰ LSPandto a on- or off-shellZ (W^±) boson. We refer to thefour simplified models as the T1bbbb, T1tttt, T1qqqq, and T5qqqqVV scenarios, respectively[21]. Thus the first two scenarios explicitly presume either bottom or top squark production. The latter two scenar- iosrepresentmoreinclusivesituationsandprovidecomplementary sensitivitytotopsquarkproductionforlargevaluesof N_jet.Weas- sumeallSUSY particlesother thanthegluino,theLSP, and —for theT5qqqqVV models —the

χ

₂⁰ and 

χ

₁^±, to be too heavy to be directlyproduced,andthegluinotobeshort-lived.

The principal sources of background arise from the SM pro- duction of top quarks, a W or Z boson in association with jets (W+^{jets orZ}+jets events),andmultiplejetsthroughthestrong interaction. We refer to the latter class of background as quan- tumchromodynamics(QCD) multijetevents.The eventswithtop quarksmostly arisefromtopquark–antiquark(tt)production,but also from single top quark processes. The W and Z bosons in W+^{jets and Z}+jets events can be either on- or off-shell.For

top quark andW+jets events, significant H^miss_T can arise ifa W bosondecaysleptonically,producinganeutrinoandanundetected chargedlepton,whileZ+jets eventscanexhibit significant H_T^miss ifthe Z bosondecays totwo neutrinos.For QCD multijetevents, significant H^miss_T can arise if theevent contains a charm or bot- tomquark that undergoesasemileptonicdecay,buttheprincipal sourceofH^miss_T isthemismeasurementofjet pT.

This study combines and extends search strategies developed forthe analysisof CMSdatacollected at √

s=^{8 TeV,} specifically the studyofRef. [22],which examined datainbins of N_b-jet but not Njet andproved to be sensitive to the T1bbbb scenario, and the study of Ref. [23], which examined data in bins of N_jet but not Nb-jet and proved to be sensitive to the T1tttt, T1qqqq, and T5qqqqVV scenarios. Here, the two approaches are combined in aunifiedframeworkto yieldamorecomprehensiveandinclusive studywithimprovedsensitivity.

2. Detector,trigger,andeventreconstruction

TheCMSdetectorisbuiltaroundasuperconductingsolenoidof 6 minternaldiameter,providingamagneticfieldof3.8 T.Within the solenoid volume are a silicon pixel andstrip tracker, a lead tungstate crystalelectromagnetic calorimeter(ECAL), anda brass and scintillator hadron calorimeter (HCAL). The ECAL and HCAL, eachcomposedofabarrelandtwoendcapsections,extendovera pseudorapidityrange|

η

_|<3.0.Forwardcalorimetersoneachside of the interaction point encompass 3.0<|

η

_|<5.0. The tracking detectors cover |

η

|<2.5. Muons are measured within |

η

|<2.4 bygas-ionizationdetectorsembeddedinthesteelflux-returnyoke outside the solenoid. The detector is nearly hermetic, permitting accurate measurements of H^miss_T . A more detailed description of theCMSdetector,togetherwithadefinitionofthecoordinatesys- temandrelevantkinematicvariables,isgiveninRef.[24].

Signal event candidates are recorded using trigger conditions based on thresholds on H_T and missing transverse momentum.

The triggerefficiency,whichexceeds98% followingapplicationof the eventselection criteriadescribed below,is measured in data andisaccountedforintheanalysis.Separatedatasamplesrequir- ingthepresenceofeitherchargedleptonsorphotonsareusedfor thedeterminationofbackgroundsfromSMprocesses,asdiscussed below.

Physics objects are defined using the particle-flow (PF) algo- rithm[25,26],whichreconstructsandidentifiesindividualparticles through an optimized combination ofinformation from different detectorcomponents.ThePFcandidatesare classifiedasphotons,

154 CMS Collaboration / Physics Letters B 758 (2016) 152–180

charged hadrons, neutral hadrons, electrons [27], or muons[28].

Additionalqualitycriteriaareimposedonelectronandmuoncan- didates.Forexample,morerestrictiveconditionsareplacedonthe ECALshowershape andontheratioofenergies depositedinthe HCAL andECAL for electron candidates, and on the matching of tracksegmentsbetweenthesilicontrackerandmuondetectorfor muoncandidates.Theeventprimaryvertexistakentobe there- constructedvertexwiththelargestsumofcharged-trackp²_T values andis required to lie within 24 cm (2 cm)of the center ofthe detectorin the directionalong (perpendicularto) thebeam axis.

Charged tracks from extraneouspp interactions within the same or a nearby bunch crossing (“pileup”) are removed [29]. The PF objectsserveasinput forjetreconstruction,basedon theanti-k_T algorithm[30,31]withadistanceparameterof 0.4.Jetqualitycri- teriaasdescribedinRef.[32]areappliedtoeliminate,forexample, spurious events causedby calorimeter noise. Contributionsto an individualjet’s pTfrompileupinteractionsaresubtracted[33],and correctionsareappliedasafunctionofjetpTand

η

toaccountfor residual effects of nonuniform detector response [34]. Jets must havep_T>30 GeV.

Theidentificationofb jetsisperformedby applyingthecom- bined secondary vertexalgorithm (CSVv2)at the medium work- ing point [35] to reconstructed jets. The b tagging efficiency is measuredboth ina datasample ofmultijeteventswitharecon- structedmuon,andinadatasampleoftt events,withconsistent results,and the probability to misidentify a light-flavor quark or gluonjet asa b jetinadata sample ofinclusivemultijetevents, all asa function of jet pT and

η

. The signal efficiencyfor b jets (misidentification probability for light-flavor quark or gluon jets) is approximately 55% (1.6%) for jets with pT≈^{30 GeV. The cor-} responding misidentification probability for a charm quark jet is estimatedfromsimulationtobe 12%.

Electrons and muons are required to be isolated in order to reduce background from events with bottom and charm quarks.

The isolation criterion is based on the variable I, which is the scalar p_T sum of all PF charged hadrons, neutral hadrons, and photonswithin aconeofradius R=

(φ)²+ (

η

)² aroundthe lepton direction, divided by the lepton pT, where φ is the az- imuthal angle. The sum excludesthe lepton under consideration andiscorrected forthecontributionofpileup [29]. Thecone ra- dius is R=⁰.2 (0.05) for lepton pT≤^{50 GeV (}>200 GeV), and R=^{10 GeV}/p_Tfor50≤^pT≤^{200 GeV.Thereasonforthedecrease} inR withincreasingleptonpTistoaccountfortheincreasedcolli- mationoftheleptonparentparticle’sdecayproductsastheobjec- t’sLorentzboostincreases.WerequireI<0.1 (<0.2)forelectrons (muons).

Charged tracks not identifiedas an isolated electron ormuon are also subjected to an isolation criterion. To be considered an isolatedcharged-particletrack,thescalarsumofcharged-track p_T values(excludingthetrackunderconsideration)inaconeofradius R=⁰.3 aroundthetrackdirection, dividedbythe track pT,must belessthan 0.2ifthetrackisidentifiedbythePFprocedureasan electronormuon,andlessthan0.1otherwise.

3. Eventselectionandsearchregions

Thefollowingrequirementsdefinetheselectioncriteriaforsig- naleventcandidates:

• ^Njet≥^{4,wherethejetsmust satisfy} |

η

_|<2.4; we requireat leastfourjetsbecauseofourfocusongluinopairproduction;

• ^HT>500 GeV, where H_T is the scalar p_T sum of jets with

|

η

_|<2.4;

• ^HmissT >200 GeV,where H^miss_T isthemagnitudeof H^miss_T ,the negativeofthevector p_Tsumofjetswith|

η

|<5;the

η

range

Fig. 2. SchematicillustrationofthesearchintervalsintheH^miss_T versus HTplane.

EachofthesixHTandH_T^missintervalsisexaminedinthreeNjetandfourNb-jetbins foratotalof72searchregions.

is extended in this case so that H^miss_T better represents the totalmissingtransversemomentuminanevent;

•^{no identified,isolated electronormuon candidatewith p}T>

10 GeV;electron(muon)candidatesarerestrictedto|

η

|<2.5 (<2.4);

•^noisolatedcharged-particletrackwith|

η

_|<2.4,mT<100 GeV, and pT>10 GeV (pT>5 GeV ifthe trackis identifiedasan electronormuoncandidatebythePFalgorithm),wheremTis thetransversemass[36] formedfromthe p^miss_T andisolated- track pT vector, withp^miss_T thenegative ofthevector pT sum ofallPFobjects;

• φ_H^miss

T ,ji>0.5 (>0.3) forthe two highest pT jets j1 andj2 (the next two highest pT jetsj3 and j4), withφ_Hmiss

T ,ji the anglebetweenH^miss_T andthepTvectorofjetji.

The isolated-trackrequirement eliminates events witha hadron- ically decaying

τ

lepton, as well as isolated electrons or muons in cases where the lepton is not identified; the m_T requirement restrictsthisvetototracksconsistentwithaW bosondecayinor- der tominimize the impact on signal efficiency. Forall-hadronic events,^p^miss_T ^andH^miss_T aresimilar,butH_T^missislesssusceptibleto uncertainties in themodeling ofsoftenergydeposits.We choose



p^miss_T for the m_T calculation for consistency with previous prac- tice.Theφ_Hmiss

T ,ji requirementsreducethebackgroundfromQCD multijet processes,forwhich H^miss_T isusually aligned along ajet direction.

The searchisperformedinthefollowingexclusiveintervalsof thefoursearchvariables:

• ^Njet:4–6,7–8,≥^9;

• ^Nb-jet:0,1,2,≥^3;

• ^HT:500–800,800–1200,≥^{1200 GeV;}

• ^HmissT :200–500,500–750,≥^{750 GeV.}

Bins withboth H_T<800 GeV and H_T^miss>750 GeV are discarded becauseeventswithH^miss_T ^HT areverylikelytobebackground.

Additionally, for 500< H_T^miss<750 GeV, an expanded interval 500<HT<1200 GeV is used,and for H^miss_T >750 GeV a single interval H_T>800 GeV, because of the low expected number of signal eventsatlarge H^miss_T .Thesixsearch intervalsinthe H^miss_T versus H_T plane are illustrated schematically in Fig. 2. The total numberofsearchregionsis 72.

Theresultsareaveragedoverallsearchregions.Thevariationscorrespondtodiffer- entsignalmodelsandchoicesofthegluinoandLSPmasses.

Item Relative uncertainty (%)

Trigger efficiency 0.5–1.1

Pileup reweighting 0.1–0.5

Jet quality requirements 1.0

Renormalization and factorization scales 0.1–3.0

Initial-state radiation 0.02–10.0

Jet energy scale 0.5–4.0

Isolatedleptonandtrackvetoes(T1tttt andT5qqqqVVonly)

2.0

Total 1.5–11.0

A breakdown of the efficiency at different stages of the se- lectionprocess for threerepresentative signal models is givenin Table A.1ofAppendix A.

4. Eventsimulation

The background is mostly evaluated using data control re- gions, as described below (Section 5). Simulated samples of SM events are used to construct and validate the procedures and to estimate a few of the smaller background components. The MadGraph5_amc@nlo 2.2.2[37] eventgenerator atleadingorder isusedtosimulatett,W+^jets,Z+^jets,

γ

+^{jets,andQCDmultijet} events.Thissamegeneratoratnext-to-leading(NLO)orderisused todescribesingletopeventsinthes channel,eventswithdibosons (WW,ZZ,andWH production,etc.,withH aHiggsboson),andrare processes(ttW,ttZ,andWWZ production,etc.),exceptWW events inwhichbothW bosonsdecayleptonicallyaredescribedwiththe powhegv1.0 [38–42] programatNLO. Single top eventsin thet andtW channelsarealsodescribedwith powheg atNLO.Simula- tionofthedetectorresponseisbasedonthe Geant4[43]package.

The simulated samples are normalized using the most accurate crosssectioncalculationscurrentlyavailable[37,41,42,44–52],gen- erallywithNLOornext-to-NLOaccuracy.

Signal T1bbbb, T1tttt, T1qqqq, andT5qqqqVV eventsare gen- erated fora rangeof gluino m_g and LSP m_χ₁⁰ mass values, with m_χ₁⁰<m_g.FortheT5qqqqVVmodel,themassesoftheintermedi- ate

χ

₂⁰ and

χ

₁^± states aretakento be themean ofmχ_1⁰ andm_g. Thesignal samplesaregenerated withthe MadGraph5_amc@nlo programat leading order,withup to two partonspresent inad- ditionto the gluino pair. The decaysof the gluinoare described witha pure phase-spacematrixelement [53].The signal produc- tion cross sections are computed [54–58] with NLO plus next- to-leading-logarithm (NLL)accuracy. To reduce computational re- quirements,thedetectorismodeledwiththeCMSfastsimulation program [59,60], which yields consistent results compared with the Geant4-based simulation, except that we apply a correction of1%toaccountfordifferencesintheefficiencyofthejetquality requirements[32],andcorrectionsof3–10%toaccountfordiffer- encesintheb jettaggingefficiency.

The NNPDF3.0LO [61] parton distribution functions (PDF) are usedforthesimulatedsamplesgeneratedatleadingorder,andthe NNPDF3.0NLO[61]PDFsforthesamplesgeneratedatNLO.Allsim- ulatedsamplesusethe pythia 8.2[53]programtodescribeparton showeringandhadronization.To modelthe effectsof pileup,the simulatedeventsare generatedwitha nominaldistribution ofpp interactionsperbunchcrossingandthenreweightedtomatchthe correspondingdistributionindata.

Weevaluate systematicuncertainties inthe signal modelpre- dictions. Those that are relevant for the selection efficiency are listedinTable 1.Theuncertaintyassociatedwiththerenormaliza-

independentlybyfactorsof2.0and0.5[62,63].Anuncertaintyre- latedtothemodelingofinitial-stateradiation(ISR)isdetermined by comparingthesimulatedandmeasured p_T spectraofthesys- temrecoilingagainsttheISRjetsintt events,usingthetechnique describedinRef.[64].Thetwospectraareobservedtoagree.The statistical precision of the comparison is used to define an un- certainty of 15% (30%) for 400<pT<600 GeV (pT>600 GeV), whileno uncertaintyisdeemed necessaryfor pT<400 GeV.The uncertaintiesassociatedwiththerenormalizationandfactorization scales, and with ISR, integrated over all search regions, typically lie below 0.1% but can be as large as 1–3%, and 3–10%, respec- tively, for mχ_1⁰ ∼^mg (we use the notation mχ_1⁰ ∼^mg to mean mχ_1⁰+^2mX≈^mg,withm_X the bottomquark mass,the topquark mass,orthe massofthe “V”boson, respectively,fortheT1bbbb, T1tttt, andT5qqqqVV models; forthe T1qqqq model,m_χ₁⁰ ∼^m^g meansm_χ₁⁰≈^m^g). Theuncertaintyassociatedwiththejet energy scale is evaluated as a function of jet pT and

η

. Note that the isolated lepton and track vetoes have a minimal impact on the T1bbbbandT1qqqqmodelsbecauseeventsinthesemodelsrarely contain an isolated lepton,andthat the associateduncertaintyis negligible(^0.1%).

Wealsoevaluatesystematicuncertainties inthesignal predic- tionsrelatedtotheb jettaggingandmisidentificationefficiencies and to the statistical uncertainties in the signal event samples.

These sources of uncertainty do not affect the signal efficiency but can potentially alter the signal distribution shapes. Similarly, the sources of systematicuncertainty associatedwith the trigger efficiency, pileup reweighting, renormalization and factorization scales, ISR, andjet energyscale canaffect theshapesof thesig- naldistributions. Thesepotential changesinshape, i.e.,migration ofeventsbetweensearch regions, are accountedforinthelimit- settingproceduredescribedinSection6.

The systematic uncertainty in the determination of the inte- gratedluminosityis4.6%.

5. Backgroundevaluation

In thissection, we describe the evaluationof the background fromSM processes.Thisevaluationrelies ondatacontrol regions (CRs) selected using similar criteria to the search regions. Signal eventsmaycontributetotheCRs.The impactofthis“signalcon- tamination”onthefinalresultsisevaluatedinthecontextofeach individual SUSY model, as described in Section 6. However, the levelofsignalcontaminationisnegligibleforallCRsexceptthose used to evaluate the top quark and W+jets background (Sec- tion 5.1), andis nonnegligible only forthe T1tttt and T5qqqqVV models.The levelofsignal contamination forthesenonnegligible casesisdiscussedinSections5.1.1and5.1.2.

5.1. BackgroundfromtopquarkandW+jets events

BackgroundfromSM tt,single topquark, andW+jets events arises when a W boson decays leptonically, yielding a neutrino (thus, genuine H^miss_T ) andanon-vetoed chargedlepton.Thenon- vetoedlepton canbean electronormuon(including from

τ

lep- tondecay)that doesnotsatisfytheidentificationrequirementsof Section3(so-called“lostleptons”),oritcanbeahadronicallyde- caying

τ

lepton.

5.1.1. Lost-leptonbackground

Lost-lepton background can arise if an electron or muon lies outside the analysis acceptance, is not isolated, or is not recon- structed. The lost-lepton background is evaluated following the

156 CMS Collaboration / Physics Letters B 758 (2016) 152–180

proceduresestablishedinRefs.[23,65,66].Briefly,single-leptonCRs are selectedby inverting the electron andmuon vetoes.Each CR eventisentered intoone ofthe72search regions withaweight that represents the probability fora lost-lepton event to appear withthecorrespondingvaluesof HT,H^miss_T ,Njet,andNb-jet.

TheCRsare selectedby requiringeventstosatisfy thecriteria ofSection3exceptexactlyoneisolatedelectronormuonmustbe presentandtheisolated-trackvetois notapplied. Thetransverse mass formed fromthe p^miss_T and lepton pT vector is requiredto satisfy mT<100 GeV: this requirementis effectiveatidentifying SM events, which primarily arise from leptonic W boson decay, while reducing signal contamination. After applyingthis require- ment, the fraction ofCR events due to T1tttt (T5qqqqVV) signal contamination is generally negligible, viz., ⁰.1%, but it can be ashighas around 30–40%(5–20%) for thelargest valuesof Njet, N_b-jet, H_T,and/or H^miss_T ,depending onm_g and mχ_1⁰.Theweights, accountingforthe probabilityfora leptontobe “lost”,aredeter- mined fromthe tt, W+^{jets, single top quark, and rare process} simulationsthroughevaluationoftheefficiencyoftheacceptance, reconstruction, and isolation requirements as a function of HT, H^miss_T , Njet,lepton pT,andotherkinematicvariables.Sincetheef- ficiencies areparametrized interms ofkinematicandtopological quantities, the method is insensitive to the specific mix of pro- cesses, i.e., it doesnot requirethe relative fractions of tt, single top,andW+jets eventsintheCRstobethesameasinthesearch regions (nonetheless,thesefractionsagree towithin lessthan 1%

in simulation). A correction derived from data is applied to the weightstoaccountforthetriggerefficiency,whilecorrectionsfrom simulationaccountforcontaminationduetononpromptelectrons, contaminationduetodileptoneventsinwhichone oftheleptons islost,andtheselection efficiencyofthemT requirement. Corre- spondingefficiencies areevaluated fordileptoniceventsinwhich bothleptonsarelost.Thislattersourceofbackgroundispredicted to account for <2% of the total lost-lepton background. Finally, a correction is applied to account for the selection efficiency of theisolated-trackveto.

The weighted distributions of the search variables, summed overtheeventsintheCRs,definethelost-leptonbackgroundpre- diction.The procedureisperformedseparately forsingle-electron and single-muon events. The two independent predictions yield consistentresultsandare averagedto obtainthefinal lost-lepton backgroundprediction.Themethodisvalidatedwithaclosuretest, namelybydeterminingtheabilityofthemethod,appliedtosimu- latedsamples,topredictcorrectlythetruenumberofbackground events.Theresultsoftheclosuretestareshownintheupperplot ofFig. 3.Asacheck,werepeatedtheclosuretestaftervaryingthe fractionsoftt,singletop,andW+jets events,withnodiscernible changeintheoutcome.

Thedominantuncertaintiesinthelost-leptonbackgroundpre- diction are statistical,due tothe limitednumberofCRevents in themostsensitivesearchregions.As asystematicuncertainty,we take the larger ofthe observed nonclosurein Fig. 3(upper plot) or the statistical uncertainty in the nonclosure, for each search region, where “nonclosure” refers to the difference between the solidpointsandhistogram.Additionalsystematicuncertaintiesare assignedbased ona comparisonbetweendata andsimulationof theleptonreconstruction,leptonisolation,andisolatedtrackveto efficiencies.Withinthestatisticalprecision,therearenosuch dif- ferencesobserved,andthestatisticaluncertaintyintherespective comparisonis assignedasa systematicuncertainty. Uncertainties in the acceptance associated with the PDFs, including those re- latedtotherenormalizationandfactorizationscales,areevaluated by varying the PDF sets used to produce the simulated samples.

These uncertainties are defined by the maximum deviations ob- served from 100 variations of the NNPDF3.0LO PDFs for tt and

W+jets events. The uncertainty in the jet energy correction is propagated to p^miss_T ,andtheresultingchangeinthemT selection efficiencyisusedtodefineasystematicuncertainty.Smallsystem- atic uncertainties relatedto thepurity ofthe electronandmuon CRs and to thestatistical uncertainties in the simulatedefficien- ciesarealsoevaluated.

5.1.2. Hadronicallydecaying

τ

leptonbackground

To evaluate thebackground dueto W bosonsthat decay to a neutrino and a hadronically decaying

τ

lepton (

τ

h), we employ a template method [23,65,66].The

τ

h background is determined fromasingle-muonCR,composedalmostentirelyoftt,single top quark, andW+jets events, selectedusinga triggerthat requires HT>350 GeV andatleastonemuoncandidatewithpT>15 GeV.

TheCReventsarerequiredtocontainexactlyoneidentifiedmuon with p_T>20 GeV and |

η

|<2.1.Since

μ

+^{jets and}

τ

h+^{jets pro-} ductionarisefromthesameunderlyingprocess,thehadroniccom- ponent of the eventsis expected tobe thesame aside from the responseofthedetectortoa

μ

or

τ

h.Themuon pTinthesingle- muon CRis smeared according to the response functions (“tem- plates”) derived from tt and W+jets simulation. The templates expresstheexpectedvisible-pT distributionofa

τ

hcandidateasa function ofthetrue

τ

-lepton pT value,takentobethe measured muon pT.ThefractionofT1tttt(T5qqqqVV) eventsintheCRdue to signal contamination is generally ⁰.1%, butcan be as large asaround15–25%(4–8%)forthelargestvaluesofN_jet,N_b-jet, H_T, and/or H^miss_T ,dependingonm_gand m_χ₁⁰.

Followingthesmearing,thevaluesofHT,H_T^miss,Njet,andNb-jet are calculated fortheCRevent, andthe selectioncriteriaof Sec- tion3areapplied.Themisidentificationprobabilityfora

τ

hjetto be erroneouslyidentifiedasab jetistakenintoaccount.Correc- tions are applied to account forthe trigger efficiency,the accep- tanceandefficiencyofthe

μ

selection,andtheratioofbranching fractions B F(W→

τ

h

ν

)/B F(W→

μν

)=⁰.65 [67]. The resulting event yield provides the

τ

h background estimate. The method is validatedwithaclosuretest,whoseresultsareshowninthelower plot ofFig. 3.Systematicuncertainties are assignedbasedon the levelofclosure,asdescribedforthelost-leptonbackground.Other systematicuncertaintiesareassociatedwiththemuonacceptance, theresponsefunctions,andthemisidentificationrateof

τ

hjetsas b jets.Thedominantuncertainty,asforthelost-leptonbackground, arisesfromthelimitednumberofeventsinthe CR.

5.2. BackgroundfromZ→

νν

events

A straightforward method to evaluate the background from Z+jets events with Z→

νν

consistsof selecting Z+jets events with Z→ ⁺⁻ (=^e,

μ

), removing the ⁺ and ⁻ to emu- late the Z→

νν

process, and applying the event selection cri- teria of Section 3. The resulting efficiency-corrected eventyields can be directlytranslated intoa predictionforthe Z→

νν

back- ground through multiplication by the known ratio of branching fractions[67].A limitationofthisprocedureisthesmallZ→ ⁺⁻ branchingfractioninrelationtothatfor Z→

νν

.

An alternative approachis toexploit thesimilarity betweenZ bosonradiationandthemorecopiousradiationofphotonsbyse- lecting

γ

₊jets events, removingthephoton fromtheevent,and applying the selection criteria ofSection 3. The

γ

+jets process differsfromtheZ+jets processbecauseofthresholdeffectsassoci- atedwiththeZ bosonmassandbecauseofthedifferentcouplings ofZ bosonsandphotonstoup- anddown-typequarks.Thesedif- ferences are generally well understood and described adequately withsimulation.

Our evaluation of the Z→

νν

background utilizes both ap- proaches. A

γ

+^{jets CR is selected using a trigger that requires}

Fig. 3. (Upper plot): Thelost-leptonbackgroundinthe72searchregionsoftheanalysisasdetermineddirectlyfromtt,singletopquark,W+^{jets,diboson,andrare-event} simulation(points,withstatisticaluncertainties)andaspredictedbyapplyingthelost-leptonbackgrounddeterminationproceduretosimulatedelectronandmuoncontrol samples(histograms,withstatisticaluncertainties).Thelowerpanelshowsthesameresultsfollowingdivisionbythepredictedvalue,wherebinswithoutmarkershaveratio valuesoutsidethescaleoftheplot.(Lower plot): Thecorrespondingsimulatedresultsforthebackgroundfromhadronicallydecayingτleptons.Forbothplots,thesixresults withineachregiondelineatedbydashedlinescorrespondsequentiallytothesixregionsofHTandH_T^missindicatedinFig. 2.

HT>500 GeV andphoton pT>90 GeV. A Z+jets CRwith Z→ ⁺⁻ is selectedusing atrigger that requires H_T>350 GeV and atleastoneelectronormuonwith p_T>15 GeV.Fitsasdescribed inRefs.[23] and[22] areused toextract theprompt-photon and Z bosonyields, respectively. Becauseofcurrent limitationsinthe simulationsforthetheoreticalmodelingof

γ

+jets versusZ+^jets productionwithheavy flavor jets,we restrict the useof

γ

+^jets events to the 18 search regions with Nb-jet=^{0. The Z}→ ⁺⁻ sample,integratedover HT and H_T^miss becauseofthelimitedsta- tisticalprecision,isusedtoextrapolatetheNb-jet=^{0 resultstothe} Nb-jet>0 searchregions.

The

γ

+jets analysisissimilartothatpresentedinRef.[23].We predictthenumber N^pred_Z→νν ofZ(→

νν

)+jets eventscontributing toeach N_b-jet=^{0 searchregionfromthenumber Ndata}_γ ^ofevents inthecorresponding Njet,HT,andH^miss_T binofthe

γ

+^{jets CR:}

N^pred_Z→νν

 

N_b-jet=⁰

= ρ

R^sim_Z→νν/γ

β

_γ^dataN_γ^data

,

(1)

whereβ_γ^data isthe purityoftheCR, determined fromthefit[23]

to data, and R^sim_{Z→νν/γ the} ^{ratio from simulation (“sim”) of the} numbers of Z(→

νν

)+jets events to

γ

+jets events, with the

γ

₊jets termobtainedfromaleading-order MadGraph5_amc@nlo calculation.Correctionsareappliedtoaccountforefficiencydiffer- encesbetweenthedata andsimulation andforan angularcutoff inthesimulationthatcontrolsthesingularityassociatedwithsoft collinearradiativecorrections.Thefactor

ρ

[23]inEq.(1),defined as

ρ =

^R

data Z→⁺⁻/γ R^sim_Z→+⁻/γ

=

^N

data Z→⁺⁻ N^data_γ

N^sim_γ

N^sim_Z→+−

,

(2) uses theZ→ ⁺⁻ CRtoaccount forpotential differencesin the RZ→νν/γ factorbetween simulation anddata, such as those ex- pectedduetomissinghigher-ordertermsinthe

γ

+jets calcula- tion,andisfound tohavea value of0.92(takento beconstant), with uncertainties, deduced from linear fits to projections onto

158 CMS Collaboration / Physics Letters B 758 (2016) 152–180

Fig. 4. TheZ→ννbackgroundinthe72searchregionsoftheanalysisasdetermineddirectlyfromZ(→νν)+^{jets and}ttZ simulation(points),andaspredictedbyapplying theZ→ννbackgrounddeterminationproceduretostatisticallyindependentZ(→ ⁺⁻)+jets simulatedeventsamples(histogram).ForbinscorrespondingtoNb-jet=^0, theagreementisexactbyconstruction.Thelowerpanelshowstheratiobetweenthetrueandpredictedyields.Forboththeupperandlowerpanels,theshadedregions indicatethequadraturesumofthesystematicuncertaintyassociatedwiththedependenceofFonthekinematicparameters(HTandH^miss_T )andthestatisticaluncertainty ofthesimulatedsample.ThelabelingofthesearchregionsisthesameasinFig. 3.

eachdimension,thatvarywithN_jet,HT,andH^miss_T between8and 60%.

Forsearchregions withN_b-jet>0,theZ→

νν

backgroundes- timateis



N^pred_Z→νν



j,b,k

= 

N_Z^pred_→νν



j,0,kFj,b

;

⁽³⁾

Fj,b

= 

N^data_Z→+−

β

^data



0,b

/



N_Z^data_→+−

β

^data



0,0



Jj,b

;

⁽⁴⁾

Jj,b

=

^Nmodel_j,b

/

N^model_0,b

,

(5)

where j, b, and k are bin indices (numbered from zero) for the Njet, Nb-jet, and kinematic (i.e., HT and H^miss_T ) variables, re- spectively. For example, j=^{0 (b}=³⁾ corresponds to N_jet=^4–6 (N_b-jet≥^{3), while k}=^{0 denotes “Bin 1” ofFig. 2.The first term} on the right-hand side of Eq. (3) is obtained from Eq. (1). The N_b-jet extrapolationfactor F ^{[Eq.(4)] is obtainedfromthe fitted} Z→ ⁺⁻ yields, with data-derived corrections β^data to account for the Nb-jet-dependent purity. Other efficiencies cancel in the ratio. The dependence of the N_b-jet shape of F ^{on N}jet is de- scribed with the factor J ^{[Eq. (5)], which is determined using} a model estimate N^model_j,b because of the limited statistical pre- cision of the Z→ ⁺⁻ data. The model uses the resultsof the Z→ ⁺⁻simulationforthecentralvalueofJ^{.Basedonsimula-} tionstudies,wedeterminecorrespondingupperandlowerbounds todefineasystematicuncertainty.AsalowerboundonJ^,weset N^model_j,b =^N₀^model_,b ^,i.e.,Jj,b=^{1 inEq.(4).Inthislimit}F ^isindepen- dentofNjet,correspondingtoafactorizationofthemechanismsto producebottomquarkjetsandadditionaljets.Asanupperbound, wetake N^model_j,b =

N_jet∈^j,N_b-jet∈^bB(^Nb-jet|^Njet;^p),whereB^isabi- nomialdistribution,withp theprobabilityforajettobetaggedas ab jet.Inbothsimulationanddatawefindp tobeindependentof Njet.Thisbinomialbehaviorwouldbeexpectedshouldalltaggedb jetsbeerroneous,i.e.,notinitiatedbybquarks,orshouldthepro- ductionofquarksinthehadronshower notdependonflavor ex- ceptviaascalefactorthatisabsorbedintotheempiricalfactor p.

Withrespecttoasystematicuncertainty,thefactorizationandbi- nomial extrapolations represent opposite extremes. The binomial assumptionisvalidatedinsimulation;theresultp=⁰.062±⁰.007

is obtainedfromafitto thedata,of which⁰.02 is attributable tolight-partonorcharmquarkjetserroneouslyidentifiedasb jets.

TheresultingsystematicuncertaintiesinJ ^{rangefromafewper-} centto≈^{60%,dependingonN}jet andN_b-jet.

AclosuretestofthemethodispresentedinFig. 4.Theshaded bandsrepresentthesystematicuncertainty(10–20%,dependingon N_b-jet)arisingfromourtreatmentofF^asindependentofthekine- maticparameters,combinedwiththestatisticaluncertaintyofthe Z(→ ⁺⁻)+jets simulation.

Rare processes such as ttZ and V(V)Z (V=^{W or Z) produc-} tion can contribute to the background. We add the expectations for theseprocesses,obtainedfromsimulation, tothe background predictedfromtheproceduredescribedabove.Notethatprocesses with a Z boson and a Z→

γ

counterpart are alreadyaccounted for in Nγ^data andlargely cancel in the RZ→νν/γ ratio. For search regions withNb-jet≥^{2, the}contributionofttZ eventsisfound to be comparableto that from Z+jets events, with an uncertainty of ≈^{50%,consistent with the rateand}uncertainty forttZ events foundinRef.[68].

Besidestheuncertaintyrelatedtothe Nb-jetextrapolation,dis- cussed above, systematicuncertainties associatedwiththe statis- tical precision of the simulation, the photon reconstruction effi- ciency, thephotonanddileptonpurities, andthe

ρ

R^sim_{Z→νν/γ term} are evaluated. Ofthese, the

ρ

R^sim_{Z→νν/γ term} ^{(10–60%)dominates} the overall uncertainty except in the highest(Njet, Nb-jet) search regions wherethe overalluncertaintyis dominatedbythe statis- ticalprecision ofthesimulation(70–110%)andbytheuncertainty intheZ→ ⁺⁻ purity(40%).Theunderlyingsourceofthelead- ingsystematicuncertaintiesisthelimitednumberofeventsinthe CR.

5.3. BackgroundfromQCDmultijetevents

Toevaluate thebackgroundassociated withQCD multijetpro- duction,weselectaQCDdominatedCRbyinvertingtheφ_Hmiss

T ,j_i requirements,i.e.,by requiringatleastoneofthefourhighest pT jetsinaneventtofailtherespective φ_Hmiss

T ,j_i selection criterion listed in Section 3. The resulting sample is called the “low-φ”

Fig. 5. TheQCDmultijetbackgroundinthe72searchregionsoftheanalysisasdetermineddirectlyfromQCDmultijetsimulation(points,withstatisticaluncertainties)and aspredictedbyapplyingtheQCDmultijetbackgrounddeterminationproceduretosimulatedeventsamples(histograms,withstatisticalandsystematicuncertaintiesadded inquadrature).Thelowerpanelshowsthesameresultsfollowingdivisionbythepredictedvalue.ThelabelingofthesearchregionsisthesameasinFig. 3.Binswithout markershavenoeventsinthecontrolregions.Noresultisgiveninthelowerpanelifthevalueofthepredictioniszero.

CR. The QCD background in each search region is given by the product ofthe observed event yield in the corresponding region ofthelow-φ CRmultipliedbya factor R^QCD expressingthera- tio of the expected QCD multijet background in the respective signalandlow-φ regions, takinginto accountthe contributions fromnon-QCDSMprocesses.Thenon-QCDSMcontributionstothe low-φ CR,whichcorrespondtoaround14%oftheeventsinthis CR,areevaluatedusingthetechniquesdescribedaboveforthetop quark,W+^jets,andZ+jets backgrounds,exceptwiththeinverted

φ_Hmiss

T ,ji requirements.The R^QCD termsaredeterminedprimarily fromdata,asdescribedbelow.Theprocedureisanalogoustothat usedinRefs.[22,69]toevaluatetheQCDmultijetbackground.

TheR^QCD factorincreaseswithN_jetbutisfoundempiricallyto havea negligibledependenceonN_b-jet foragiven N_jet value.We thereforedividethe4≤^Njet≤^{6 searchregionintothreeexclusive} bins:Njet=⁴, 5, and 6.Oncethisisdone,thereisnodependence ofR^QCDon Nb-jet.Similarly,wedividethe200≤^HmissT ≤^{500 GeV} search region into two bins: 200<H^miss_T <300 GeV and 300<

H^miss_T <500 GeV; thefirst ofthesetwo binsis enhanced inQCD backgroundevents, both in the low-φ and signal samples. The H_T,H^miss_T ,andN_jetdependenceof R^QCDismodeledas:

R^QCD_i,j,k

=

K^data_H

T,iS^sim

H_T^miss,jS^data_N

jet,k

,

(6)

where i, j,and k arebin indices.The K_H^data

T,i termis the ratioof the expected number of QCD multijet events in the search re- giontothat inthe low-φ regionfor H_T bini in thefirst H^miss_T andN_jet bins.The S^sim

H^miss_T ,j termrepresentsa correctionfor H^miss_T bin j with respect to the first H^miss_T bin, and the S^data_N

jet,k term a correction for Njet bin k with respect to the first Njet bin. The K^data_H

T,i and S^data_N

jet,k terms are determined froma fit to data in the 200< H_T^miss<300 GeV bin, with the non-QCD SM background taken into account. The S^sim

H_T^miss,j terms are taken from the QCD multijetsimulation.Basedonstudiesofthedifferingcontributions of events in which the jet with the largest pT mismeasurement isorisnot amongstthe fourhighestpT jets, uncertaintiesof50, 100, and100% are assignedto the H^miss_T 300–500, 500–750,and

≥750 GeV bins, respectively, to account for potential differences betweendataandsimulationinthe S_Hmiss

T ,j factors.Weighted re- sultsforR^QCDarecalculatedwhenrecombiningtheH^miss_T andN_jet resultstocorrespondtothenominalsearchregions.Fig. 5presents closuretestresultsforthemethod.

Forthelowest H^miss_T searchregion,theuncertaintyinthepre- diction of theQCD multijet backgroundis dominatedby the un- certaintiesinK^data_H

T,iandS^data_N

jet,k,whichthemselvesaremostlydueto uncertaintiesinthenon-QCDSMbackgroundinthesearchregions.

ForthetwohigherH^miss_T searchregions,theuncertaintyinS^sim H^miss_T ,j and the limited statisticalprecision of the low-φ CR dominate the uncertainty.The uncertainties related to potential nonclosure (Fig. 5) areeithersmallincomparisonorstatisticalinnatureand arenotconsidered.

6. Resultsandinterpretation

The observed numbersof eventsin the72 search regions are showninFig. 6incomparisontothesummedpredictionsforthe SMbackgrounds,withnumericalvaluestabulatedinTables B.1–B.3 ofAppendix B.Thepredictedbackgroundisobservedtobestatis- tically compatiblewith thedata forall 72regions. Therefore,we donotobserveevidencefornewphysics.

Fig. 7 presents one-dimensional projections of the results in H_T^missorHTaftercriteriaareimposed,asindicatedinthelegends, toselectintervalsofthesearchregionparameterspaceparticularly sensitive totheT1bbbb,T1tttt, T1qqqq, orT5qqqqVVscenario.In eachcase, exampledistributions areshownfortwosignal scenar- ios not excluded by our Run 1 studies [22,23]. These scenarios, one withm_g^m_χ⁰

1 andone withmχ_1⁰∼^mg,lie well within the parameterspaceexcludedbythepresentanalysis(seebelow).

Alikelihoodfitto dataisusedtoset limitson theproduction crosssectionsofthesignalscenarios.Thefittedparametersarethe SUSYsignalstrength,theyieldsofthefourbackgroundclassesin- dicated inFig. 6,andvariousnuisance parameters.The limitsare determinedasafunctionofmχ_1⁰ andm_g.Thelikelihoodfunctionis theproduct ofPoissonprobability densityfunctions,oneforeach search region,andconstrainttermsthat accountforuncertainties inthe backgroundpredictionsandsignal yields. Theseuncertain-