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Physics
Letters
B
www.elsevier.com/locate/physletb
Search
for
non-resonant
Higgs
boson
pair
production
in
the
bb
ν
ν
final
state
with
the
ATLAS
detector
in
pp collisions
at
√
s
=
13 TeV
.TheATLASCollaboration
a r t i c l e i n f o a b s t ra c t
Articlehistory:
Received19August2019
Receivedinrevisedform4December2019
Accepted5December2019
Availableonline13December2019
Editor:M.Doser
Asearchfornon-resonantHiggsbosonpairproduction,aspredictedbytheStandardModel,ispresented, where one ofthe Higgs bosonsdecays via the H→bb channel and the othervia one of the H→ W W∗/Z Z∗/τ τ channels.Theanalysisselection requireseventstohaveatleasttwob-taggedjetsand exactlytwoleptons(electronsormuons)withoppositeelectricchargeinthefinalstate.Candidateevents consistentwithHiggsbosonpairproductionareselectedusingamulti-classneuralnetworkdiscriminant. Theanalysis uses139 fb−1 ofpp collisiondata recordedatacentre-of-massenergyof13 TeVbythe ATLASdetectorattheLargeHadronCollider.Anobserved(expected)upperlimitof1.2(0.9+−00..43) pbis set on thenon-resonant Higgsboson pairproductioncross-section at95% confidence level,which is equivalentto40(29+−149)timesthevaluepredictedintheStandardModel.
©2019TheAuthor(s).PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense (http://creativecommons.org/licenses/by/4.0/).FundedbySCOAP3.
1. Introduction
In2012,theATLASandCMSCollaborationsreportedthe obser-vationofanewparticleinthesearchfortheStandardModel(SM) Higgsboson (H )[1,2]. Sofar,measurementsofthespin and cou-plingsofthe newparticleare consistentwiththose predictedby theBrout–Englert–Higgs(BEH)mechanismofthe SM[3–12]. The SM predicts non-resonant productionof Higgs boson pairs (H H ) in proton–proton(pp) collisions, referred to as non-resonantH H production,withthedominantproductionmodesattheLHC pro-ceedingviathegluon–gluonfusion(ggF)process.TheggFprocess hastwo leading order contributions: thefirst corresponds to the so-called‘trianglediagram’,which includesthe Higgsboson self-coupling,andthesecond istheso-called‘boxdiagram’,which in-cludesaheavy-quarkloopwithtwofermion–fermion–Higgs( f f H ) vertices.Thesetwoamplitudesinterferedestructively,resultingin alow cross-section of only31.05±1.90 fb forthe ggF H H pro-ductionmode,computedatnext-to-next-to-leading order(NNLO) andincludingfinitetop-quarkmasseffects[13–20].Feynman dia-gramsillustratingthesetwocontributionsareshowninFig.1.The measurementofnon-resonant H H productionattheLHCstandsas animportanttestoftheBEHmechanism.Inmanybeyond-the-SM (BSM)theories,H H productioncanbeenhancedbymodifyingthe Higgs boson self-coupling, λH H H, or the top-quark Yukawa cou-pling, yt,and/orbyintroducingnewcontactinteractions between
E-mailaddress:atlas.publications@cern.ch.
Fig. 1. FeynmandiagramsforleadingorderggFproductionofHiggsbosonpairs:the ‘trianglediagram’sensitivetotheHiggsbosonself-couplingontheleftandthe‘box diagram’ontheright.
two top-quarks or gluons and two Higgs bosons or introducing productionmechanismsviaintermediateBSMparticles[21–23].
The ATLAS and CMS Collaborations have performed searches for non-resonant H H production in a variety of final states at 13 TeV [24–33]. No significant excess of events beyond SM ex-pectationsisobservedinthesesearches,withtheATLAS andCMS data-analyses setting observed(expected) limitson non-resonant H H production to be no larger than 6.9 (10.0) and 22.2 (12.8) timesthepredictedrateintheSM,respectively[34,35].
This Letter describes a search for non-resonant H H produc-tion inthe bbνν final state, where refers to a lepton(either an electron ora muon), using13 TeV pp collision datacollected with the ATLAS detector during 2015–2018 and corresponding to a total integrated luminosity of 139 fb−1. The analysis uses machine-learningtechniquesbasedonfeedforwardneuralnetwork architectures[36] toconstruct an event-level classifier trainedto distinguish between the H H signal and SM backgrounds. Analy-ses searching for non-resonant H H production via similar decay channelswereperformedpreviouslyinthesingle-leptonfinalstate
https://doi.org/10.1016/j.physletb.2019.135145
0370-2693/©2019TheAuthor(s).PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense(http://creativecommons.org/licenses/by/4.0/).Fundedby SCOAP3.
byATLASinsearchesforH H→bbW W∗ [28] andinthedilepton channelbyCMSinsearchesforH H→bbW W∗/bb Z Z∗ [31].
2. ATLASdetector
The ATLAS detector [37–39] is a general-purpose particle de-tectorwithforward–backwardsymmetriccylindricalgeometry.1 It includesaninnertrackingdetector(ID),immersedinanaxial mag-netic field,which providesprecision tracking ofchargedparticles over the rangeof |η|<2.5.Calorimeter systems with either liq-uidargonorscintillatortilesastheactivemediumprovideenergy measurements overthe rangeof|η|<4.9.The muon spectrome-ter(MS)ispositioned outsidethecalorimetersandincludesthree air-coretoroidalmagnets.TheMSiscomposedofseveraltypesof muondetectorswhichprovidetriggerandhigh-precisiontracking capabilitiesfor |η|<2.4 and |η|<2.7,respectively. A hardware-based trigger followed by a software-based trigger reduce the recordedeventratetoanaverageof1 kHz[40].
3. Datasetandsimulatedevents
Thedatausedforthissearchwerecollectedin pp collisionsat theLHCwithacentre-of-massenergyof13 TeV.Onlythose data collected during stableLHC beam conditions andwith all ATLAS detectorsubsystems fullyoperationalare used,andcorrespondto an integrated luminosity of 139 fb−1. The selection of candidate
eventswithoppositelychargedleptons isbasedonacombination of single-lepton and dilepton triggers.2 The use of a given
trig-gerdepends on the flavour and the transverse momenta (pT) of
thetwo(pT-ordered)leptonsintheevent,andonthedata-taking
period.Single-leptontriggerswith pT thresholds between22 and
28 GeVaregivenpriorityoverdileptontriggers.Thecriteriaofthe dileptontriggersarecheckedonlyifnosingle-leptontrigger crite-riaare metandhavepT thresholdsaslowas19(10) GeVforthe
leading (subleading)lepton.At leastone reconstructed lepton(or leptonpair)hastomatchacorrespondingtriggerobject,inwhich casetheir offline pT mustbehigherthanthetriggerthresholdby
atleast2 GeV,inordertobeontheefficiencyplateauofthe cor-respondingtrigger.
MonteCarlo(MC) simulation[41] isused tomodel thesignal processes and in the estimation of SM background processes. A GEANT4 [42] simulation ofthe ATLAS detectorwas used forthe backgroundprocesses.ThesignalMCsampleswereprocessedwith afastsimulationthatreliesonaparameterisationofthe calorime-terresponse[41] andon GEANT4 forthetrackingdetectors. Simu-latedeventsare reconstructedusingthesamealgorithms asused fordataandincludetheeffectsofmultiple pp interactionsinthe sameor neighbouringbunch crossings, collectively referred to as pile-up.The simulation of pile-up collisions was performed with Pythia 8.186 [43] using the ATLAS A3 set of tuned parameters [44] and the NNPDF2.3LO parton distribution function (PDF) set [45].Simulatedeventswere reweightedtomatchthedistribution ofpile-up interactions indata. Theaverage amount ofpile-up in thedatacollectedduring2015–2018was33.7.
Thesignal processes withggF-initiated non-resonant H H pro-ductioninthebbννfinalstateweregeneratedwithaneffective
1 ATLASusesaright-handed coordinatesystemwith itsoriginat thenominal
interactionpoint(IP)inthecentreofthedetectorandthez-axisalongthebeam pipe.Thex-axispointsfromtheIPtothecentreoftheLHCring,andthe y-axis pointsupwards.Cylindricalcoordinates(r,φ)areusedinthetransverseplane,φ beingtheazimuthalanglearoundthez-axis.Thepseudorapidityisdefinedinterms ofthepolarangleθasη= −ln tan(θ/2).Theangulardistanceismeasuredinunits ofR≡(η)2+ (φ)2.
2 Distinctsetsofsingle-leptontriggersareusedforelectronsandmuons.Dilepton
triggersrequireeithertwoelectrons,twomuons,oroneelectronandonemuon.
Lagrangianintheinfinitetop-quarkmassapproximation.The gen-erated signal eventswerereweighted withformfactors thattake into account the finite mass of the top-quark [46,47]. SM back-groundprocessesweresimulatedusingdifferentMCevent gener-ators.TheMCmatrixelement(ME)eventgeneratorsandPDFsets, the parton showering (PS) and the underlying event (UE) mod-elling, UE tuned parameters (tune), andthe accuracy ofthe the-oretical cross-sections usedto normalise thesimulated processes are summarised in Table 1.Each SM backgroundprocess is nor-malised to the best available respective theoretical cross-section. ThemassoftheHiggsbosonwassetto125 GeVforallsignaland backgroundprocesses.The H H branchingfractions(BF)predicted bytheSM [13] areusedforallHiggsbosondecays. MadSpin [48] was used to model top-quark spin correlations and EvtGen [49] was usedtomodelpropertiesofb- andc-hadrondecays for pro-cessesusing Pythia andforthesignalprocesses.
SM top-quarkpair production (t¯t) andthe production of sin-gletop-quarksinassociationwithW bosons(W t)contributewith significantbackgroundcontaminationinthebbνν finalstate.At next-to-leading-order (NLO) accuracy, there exists non-trivial in-terferencebetweenthesetwoprocessesthatmaybe enhancedin phase-spaceregionswhereintherearehighfractionsofW t events [50]. Twoschemes are typically used to remove the overlap be-tween these two processes: the so-called diagram removal (DR) and diagram subtraction (DS) schemes [51]; the former is used inthe presentanalysisto removetheoverlapping eventsandthe latterisusedtoevaluatethesystematicuncertaintyin correspond-ing background event yields. Because of these effects, the sum of the simulated t¯t and W t processes is considered as a single background process and referred to asthe ‘Top’ process in what follows.
4. Eventselectionandobjectdefinitions
Selectedeventsarerequiredtohaveatleastone pp interaction vertexreconstructedfromatleasttwoIDtrackswithpT>0.4 GeV.
Theprimaryvertexforeacheventisdefinedasthevertexwiththe highest(pT)2 ofassociatedID tracks[102].Eventsthat contain
atleastonejetarisingfromnon-collisionsourcesordetectornoise arerejectedbyasetofqualitycriteria[103].
Loose and signal criteria are defined in orderto select recon-structed lepton and jet candidates, where the latter is a subset of the former. Compared to the loose objects, the signal objects arerequiredtosatisfytighteridentificationorqualitycriteriathat are designedtosuppressbackgroundcontributions.Reconstructed loose(signal) electrons arerequiredto satisfy the‘Loose’(‘Tight’) likelihoodidentificationcriteria[104].Looseelectronsarerequired tohave pT>10 GeV andtobewithin|η|<2.47.Inaddition,
sig-nal electrons are required to be outside the range 1.37<|η|< 1.52,whichcorrespondstothetransitionregionsbetweenthe bar-rel and endcaps of the electromagnetic calorimeters. In order to reduce background contributions fromjets misidentified as elec-trons,signal electronsarerequiredtobeisolated accordingtothe ‘Gradient’ selection criteria [104]. Reconstructed loose andsignal muon candidatesare requiredtohave pT>10 GeV,to be within
|η|<2.4,andtosatisfy the‘Medium’identificationcriteria[105]. Additionally,signalmuonsarerequiredtobeisolatedaccordingto the‘FixedCutLoose’selectioncriteria[105].Signalelectron(muon) candidates are required to originate from the primary vertex by demanding that the significanceof thetransverse impact param-eter, definedasthe absolutevalue ofthetracktransverse impact parameter,d0,measuredrelativetotheprimaryvertex,dividedby
its uncertainty, σd0, satisfy |d0|/σd0 <5 (3). The difference z0 betweenthevalueofthez coordinateofthepointonthetrackat which d0 is definedandthe longitudinalpositionof theprimary
Table 1
ListoftheMEgeneratorsandPS/UEmodellingalgorithmsusedinthesimulation.AlternativegeneratorsandPS/UEmodels,usedtoestimatesystematicuncertainties,are showninparentheses.ThePDFsets,tunes,andtheperturbativeQCDhighest-orderaccuracy(leading-order,LO;next-to-leading-order,NLO;next-to-next-to-leading-order, NNLO;next-to-next-to-leading-logarithm,NNLL)usedforthenormalisationofthesamplesarealsoincluded.Thetop-quarkmassissetto172.5 GeV.
Process MEgenerator
(alternative)
ME PDF PS/UEmodel
(alternative)
UE tune Predictionorderfor
totalcross-section
tt [¯ 52,53] Powheg-Box v2[54,55] NNPDF3.0NLO [56] Pythia8.230 [57] A14 [58] NNLO + NNLL [59–65]
(MadGraph 5_aMC@NLO) (Herwig 7.0.4) (H7-MMHT14)
Single-tops-channel,W t [52,66,67]
Powheg-Box NNPDF3.0NLO Pythia8.230 A14 NLO + NNLL [68,69]
(MadGraph 5_aMC@NLO) (Herwig 7.0.4) (H7-MMHT14)
Single-topt-channel[52,66] Powheg-Box, MadSpin [48] NNPDF3.04fNLO Pythia8.230 A14 NLO + NNLL [70]
(MadGraph 5_aMC@NLO) (Herwig 7.0.4) (H7-MMHT14)
W,Z/γ∗+jets [71] Sherpa2.2.1 [72,73] NNPDF3.0NNLO Sherpa2.2.1 Sherpadefault NLO(LO)≤2(4) partons [74–78]
(Z/γ∗+jets) (MadGraph 5_aMC@NLO) (Pythia 8.230) (A14)
Diboson(W W,W Z,Z Z ) [79]
Sherpa2.2.2 NNPDF3.0NNLO Sherpa2.2.2 Sherpadefault NLO(LO)≤1(3) partons [75–78]
tt W ,¯ t¯t Z [80] MadGraph5_aMC@NLO [81] NNPDF3.0NLO Pythia8.210 A14 NLO [82,83]
tt H [¯ 80] MadGraph5_aMC@NLO NNPDF3.0NLO Pythia8.210 A14 NLO [84,85]
W H,Z H [86] Pythia8.186 [43] NNPDF2.3LO [45] Pythia8.186 A14 NNLO QCD + NLO EW [87–93]
ggFH [94] Powheg-Box v2NNLOPS [95] CT10 [96] Pythia8.212 AZNLO [97] NNNLO QCD + NLO EW [98]
SMH H→bbνν[99] MadGraph5_aMC@NLO 2.6.2 CT10 Herwig7.0.4 [100] H7-MMHT14 [101] NNLO [14–20]
vertexisrequiredtosatisfy|z0×sinθ|<0.5 mm,whereθ isthe
polarangleofthetrackwithrespecttothez-axis.
Jetsare reconstructed fromtopological clusters of energy de-positsinthe calorimeters[106] usingthe anti-kt algorithm[107, 108] with a radius parameter of R=0.4 and calibrated as de-scribed in Ref. [109]. Candidate loose jets are required to have pT>20 GeV. Signaljetsare requiredto have|η|<2.8 andmust
satisfypile-upsuppressionrequirementsbasedontheoutputofa multivariate classifier [110], which identifies jetsconsistent with a primary vertex in the region |η|<2.4 and pT <120 GeV.
The MV2c10multivariate algorithm [111] isused to identify jets containing b-hadrons (b-tagged jets). An MV2c10 working point with a b-tagging efficiency of 70%, estimated from simulated tt¯ events[112], is used. The b-tagged jetsmust have pT>20 GeV
and |η|<2.5. The momentum of b-tagged jets is adjusted us-ing the muon-in-jet correction, as described in Ref. [6], by ac-countingformomentumlossesduetomuonsoriginatingfrom in-flightsemileptonicb-hadrondecaysoccurringwithintheb-tagged jet.
The missing transverse momentum pmissT , the magnitude of whichis denotedby EmissT ,isconstructed fromthe negative vec-torial sumofthe transverse momenta ofcalibrated looseobjects intheevent.Anadditionaltermisincludedtoaccountforthe en-ergy ofID tracks that are matched to the primary vertexin the eventbutnottoanyoftheselectedlooseobjects[113].
Toavoiddouble-counting,looseobjectsaresubjecttothe over-lapremovalprocedure definedasfollows.Ifareconstructed elec-tron andmuon share a trackin theID, the electron is removed. However, if the muon sharing the track with the electron is calorimeter-tagged,3thenthemuonisremovedinsteadofthe
elec-tron.IfajetandanelectronarereconstructedwithinR=0.2 of eachother,thenthejetisremoved.Ifajetandamuonarewithin R=0.2 of eachother,andthe jethaslessthan threetracksor carrieslessthan50% ofthemuonpT,thenthejetisremoved;
oth-erwise,themuon isremoved.Electronsormuonsseparatedfrom theremainingjetsbyR<0.4 areremoved.
The analysis selects candidate events with exactly two oppo-sitelychargedsignalleptons,electronsormuons,andatleasttwo signal b-tagged jets. To enhance sensitivity to the signal process
3 Acalorimeter-taggedmuonhasonlyareconstructedtrackintheIDmatched
toenergydepositsinthecalorimetercompatiblewithaminimumionisingparticle, butnocorrespondingtracksegmentintheMS.
and to maximise rejection of the expected SM backgrounds, the analysisusesamultivariateapproachtoselectsignalevents.
5. Analysisstrategy
Theanalysisreliesontheuseofamultivariatediscriminant de-signedtoselectcandidateeventsconsistentwithnon-resonantH H production.Section 5.1describesthearchitectureandthetraining ofthe deep neural network(DNN) classifier fromwhich the dis-criminant is constructed. Section 5.2 describes the signal region selection criteria. Section 5.3describesthe final background esti-mationprocedure.
5.1. DeeplearningapproachtotargetH H
The discriminant uses the outputs of a DNN classifier that is builtusingthe Keras librarywith Tensorflow asabackend[114, 115] andusesthe lwtnn library[116] tointerfacewiththe analy-sissoftwareinfrastructureoftheATLASexperiment.Thesampleof eventsused fortraining iscomposedof equalnumbersof events fromthe signalandeach ofthe dominantbackgroundprocesses: Top(asdefinedinSection 3), Z/γ∗→ (Z-),and Z/γ∗→τ τ
(Z-τ τ) production.The signal sample used inthe training ofthe classifier containsonly the H H→bbW W∗ componentduetoits larger BF relative to the H H→bbτ τ and H H→bb Z Z∗ compo-nents. However,the sumofall threesignal componentsis evalu-ated asthesignal when performing thestatisticalanalysis. Addi-tionally, all processes that make up the training sample (H H→ bbW W∗, Top,Z-,and Z-τ τ) havethe same weightduring the trainingoftheclassifier.Thetrainingsampleiscomposedof simu-latedcandidateeventswithm>20 GeV andhavingoneormore
b-taggedjets, whereeventswithexactly oneb-tagged jetare in-cludedtoincreasethenumberofeventsavailablefortraining.For thetrainingeventswithexactlyoneb-taggedjet,eachobservable thatrequiresatleasttwob-taggedjetsissettoitsmeanvalueas computedwiththefullsetoftraining eventsthatcontainatleast two b-taggedjets. Observablesthatrequiretwo b-taggedjetsare definedusingtheleadingtwob-taggedjets.Theclassifiercontains two fullyconnectedhiddenlayers each with250nodes.Rectified linearunit(ReLU)activations areusedforeachlayer[117].In or-dertoimprovetherobustnessofthetrainingandtoreduceeffects duetoovertraining, thereisa dropoutlayer thatrandomly drops 50% ofthe nodesbetween thetwo fullyconnected layers during training[118].Theclassifierproducesfouroutputsthatarepassed through asoftmaxactivation, constraining their sumto one[36].
Table 2
DescriptionofthevariablesusedasinputstotheDNNclassifier.
(pT,η,φ) pT,η, andφof the leptons, leading two jets (not necessarily b-tagged), and leading two b-tagged jets
Dilepton flavour Whether the event is composed of two electrons, two muons, or one of each (encoded as 3 booleans)
R,|φ| R and magnitude of theφbetween the two leptons
m, pT Invariant mass and the transverse momentum of the dilepton system
Emiss T , E
miss
T -φ Magnitude of the missing transverse momentum vector and itsφcomponent
|φ(pmiss
T ,pT)| Magnitude of theφbetween the pmissT and the transverse momentum of the dilepton system
|pmiss T +p
T| Magnitude of the vector sum of the p
miss
T and the transverse momentum of the dilepton system
Jet multiplicities Numbers of b-tagged and non-b-tagged jets
|φbb| Magnitude of theφbetween the leading two b-tagged jets
mbbT2 mT2[120] using the leading two b-tagged jets as the visible inputs and pmissT as invisible input
HT2 Scalar sum of the magnitudes of the momenta of the H→ ννand H→bb systems,
HT2= |pmissT +p ,0 T +p ,1 T | + |p b,0 T +p b,1 T | HR
T2 Ratio of HT2and scalar sum of the transverse momenta of the H decay products,
HR T2=HT2/(EmissT + |p ,0 T | + |p ,1 T | + |p b,0 T | + |p b,1 T |),
where p(Tb) ,0{1}are the transverse momenta of the leading {subleading} lepton (b-tagged jet)
Theresulting fouroutputs, each constrainedtovaluesbetween0 and1,arereferredtoaspi(i∈ {H H,Top,Z-,Z-τ τ}).Valuesofpi nearerto1indicatethattheeventlikelybelongstoclassi and val-uesnearerto 0indicate otherwise.The maindiscriminant inthe analysis, dH H, is constructed from the four pi and is defined as dH H=ln
pH H/
pTop+pZ-+pZ-τ τ.
The H H →bbνν signal events are characterised by two distinct ‘Higgs hemispheres’. One hemisphere contains the two b-taggedjetsfromthe H→bb decayandit istypically opposite inthetransverseplanetothesecondhemispherethatcontainsthe two leptons and EmissT from the H→W W∗/Z Z∗/τ τ decay. The final-stateobjectsintheSM backgrounds,theTop processin par-ticular,aredistributedmore uniformlywithin theeventandthey typically donot exhibit the same opposite hemispherestopology asthe H H signal. TheseHiggshemispheres thusprovide a topo-logicalcriterionthatdistinguishesthesignalfromthebackground and motivatesthe choice of input observables that are provided to theclassifier. Thirty-five such variables are provided asinputs totheclassifier, rangingfrommomentumcomponentsofthe visi-blefinal-stateobjectstoobservablesusingevent-wideinformation, andare constructed using only calibratedfinal state objects that havewell-understood uncertainties (Section6).A completelistis providedinTable2.Theevent-wideinputobservablesaresensitive tothepresenceofHiggshemispheresinthesignalandarelargely angularinnatureortakeadvantageofthefactthatthefinalstate objects from each of the Higgs bosons in the signal tend to be neartoeachother.TheobservablesHRT2 andmbbT2arenon-standard high-levelobservablesthatarenotstraightforwardfunctionsofthe momentaofthefinal-stateobjects.Byconstruction, HRT2 cantake valuesbetweenzeroandone;it peaksnearone forsignal andis more broadly distributed for background. The mbb
T2 observable is
definedsimilarlytotheMbb
T2 observableinRef. [119] butdoesnot
includethe final-stateleptons. As discussedin Ref. [119],forthe Top backgroundsmbbT2 generallyhasvaluesbelowthemassofthe top-quark dueto kinematic constraints while forthe Z/γ∗ pro-cesses, which have little-to-no ETmiss, mbbT2 is typically below 45 GeV. Theuseof dropoutregularisationduring thetraining ofthe classifier allows it to more effectively use the information con-tained inthe full set of inputspresented inTable 2 by reducing itssusceptibilitytoovertrainingeffectsthatmayotherwiseappear asa resultof usingsuch an extended input featurespace inthe casewherenosuchregularisationisperformed.Toverifythis, the performance of the classifier was checked using an independent sampleofeventsnotusedinthetrainingoftheclassifierandwas
found to be compatible to its performance when presentedwith thoseofthetrainingsample.
5.2. Signalselectioncriteria
To define signal selection criteria, the analysis relies on the invariant mass of the two leptons, m, and the invariant mass
of the two leading (pT-ordered)b-tagged jets, mbb. Due to spin-correlationeffectspresentintheH→W W∗→ ννdecaywithin the dominant H H →bbW W∗ signal process, the signal events exhibit values of m that are typically below 60 GeV. By
se-lecting low valuesof m,the signal purity can thereforebe
en-hanced while rejecting a large component of the SM Z boson and Top backgrounds. Additionally, mbb has a peak at the mass of the Higgsboson forthe signal process andthereforeprovides an effectivemeans to define selections inwhich the H H contri-bution isenhanced. The signalselection criteriathereforerequire m∈ (20,60)GeV andmbb∈ (110,140) GeV. The m>20 GeV
requirement is enforced in order to remove contamination from low-massresonancesandZ/γ∗processes.Thesignalselection cri-teria are further broken down into same-flavour (SF), i.e. ee or
μμ,ordifferent-flavour(DF),i.e.eμ,regions.Separatingby dilep-tonflavourenhancestheseparationpowerbetweenthesignaland Z/γ∗ background; theformer hasroughly equal probabilitiesfor theSFandDFfinalstatesandthelatterleadspredominantlytoSF finalstates.
Inadditiontothem andmbb requirements,thesame-flavour anddifferent-flavoursignalregions, SR-SFandSR-DF,respectively, are defined by requiring high values of dH H and are presented in Table3. Thechosen threshold valuesofdH H>5.45 (5.55) for SR-SF (SR-DF) are found to maximise the expected sensitivity to thenon-resonant H H process.ThepredictedH H→bbνν signal yieldsinSR-SFandSR-DFareshowninTable3,andarecomposed of 90% H H→bbW W∗, 9% H H→bbτ τ, and1% H H→bb Z Z∗. The predominanceof the H H→bbW W∗ process over theother two is a result ofboth its larger overall BF andof the classifier havingbeentrainedonlyonthiscomponentofthesignal. 5.3. Backgroundestimation
As mentioned in Section 5.1, the dominant backgrounds ex-pected to contaminate the signal regions are the Top and Z/γ∗
Table 3
Analysisregionandbackgroundestimationsummary.Shownarethedefinitionsofthecontrol,validation,andsignalregionsusedintheanalysisaswellasthepredicted andobservedeventyieldsineachoftheseregions.Thepredictedyieldsareshownafterbackground-onlyfitstodatainthecontrol regions.The Top and Z/γ∗+ HF post-fitnormalisationfactors,obtainedfrombackground-onlyfitsinthecorrespondingcontrolregions,areshownatthebottomofthetable.Alsoshownisthepredicted H H→bbννsignalyieldineachoftheregions,multipliedbyafactorof20.OftheH H yieldinthesignalregions,90%comesfromtheH H→bbW W∗process,9%from theH H→bbτ τprocess,and1%fromtheH H→bb Z Z∗process.Theuncertaintiesineachyieldandinthenormalisationcorrectionfactorsaccountforthestatisticaland systematicuncertaintiesdescribedinSection6,withthoseonthenormalisationcorrectionsdueonlytoexperimentalsources.
Region definitions Observable CR-Top VR-1 CR-Z+HF VR-2 SR-SF SR-DF Dilepton flavour DF SF DF or SF SF SF DF m[GeV] (20,60) (20,60) (81.2,101.2) (71.2,81.2)or(101.2,115) (20,60) (20,60) mbb[GeV] ∈ (/ 100,140) >140 (100,140) (100,140) (110,140) (110,140) dH H >4.5 >4.5 >0 >0 >5.45 >5.55 Event yields Data 108 171 852 157 16 9 Total Bkg. 108±10 162±10 852±29 147±11 14.9±2.1 4.9±1.2 Top 92±11 77±10 55±7 71±10 4.8±1.4 3.8±1.1 Z/γ∗+ HF 3.2±0.5 70±4 686±33 60±4 7.8±1.4 0.21±0.05 Other 13.1±3.4 14.2±1.9 110±13 15.8±1.2 2.3±0.5 0.9±0.4 H H (×20) 2.70±0.25 1.03±0.22 1.97±0.11 1.22±0.05 5.0±0.6 4.8±0.8 Post-fit normalisation μTop=0.79±0.10 μZ/γ∗+ HF=1.36±0.07 originating from heavy-flavour hadrons (bb, bc, or cc),
subse-quentlyreferredtoas Z/γ∗+ HF.SubdominantSM processes con-tributevia tt production¯ inassociation withan electroweak vec-torboson, single Higgsboson production (predominantly via the t¯t H mode), Z/γ∗ productioninassociationwithlight-flavourjets, andelectroweakdibosonprocesses.There is additionallya minor contributionofbackgroundevents fromnon-promptleptons pro-ducedin semileptonicdecays ofheavy-flavour hadronsandfrom misidentifiedelectroncandidatesarising fromphoton conversions andjets. Thisbackgroundisestimatedusingeventswitha same-charge lepton pair, following procedures described in Ref. [121], aftersubtracting the prompt-lepton contribution.The restof the SM background processes detailed in Table 1 are estimated pri-marilyusingsimulation.
Dedicatedcontrolregionsaredefinedtoderivedata-driven nor-malisationcorrectionsforthedominantbackgroundprocesses: CR-TopforTop andCR-Z+HFfor Z/γ∗+ HF.Thesenormalisation cor-rections havea uniform prior and are checkedin two validation regions, VR-1 and VR-2,enriched withevents from the Top and Z/γ∗+ HF processes. The control and validation regions are de-finedinTable3andarekinematically closetothesignal regions. CR-Top(CR-Z+HF)andVR-1(VR-2)aredefinedbyinvertingthembb (m)requirementsrelativetothoseofthesignalregionsbutretain
aselectionofthehighdH H regionsimilartothesignalregions.The dH H selectionswererelaxedtoincreasestatisticalpower, indepen-dentchecksshowedthatthisdidnothaveasignificantimpacton thepost-fitnormalisationcorrectionsinTable3.
VR-1keeps onlythose events withmbb>140 GeV, excluding the region mbb<100 GeV which is included in CR-Top, due to significantcontaminationofZ/γ∗+ HF events.Thecorrelations be-tweenthemandmbbobservablesanddH H afterthepreselection areobservedtobesmallanddonotpreventtheuseoftheformer twointheconstructionoftheanalysisregionsdefinedinTable3, asdH H is found to rely mainly on the information provided by theadditionalinputobservableslistedinTable2.Thisabsenceof strongcorrelationensuresthatthemeasurementsmadeinthetails ofdH H inthecontrol regionscan beextrapolatedtothoseinthe signalregions.
The Top background in the signal regions is expected to be composed of approximately equal contributions from the t¯t and single-top-quark W t process andthereforesusceptible to the
in-terferenceeffectsasdescribedinSection3.Forthisreason,CR-Top andthevalidationregions aredefinedsothattheyhavepredicted tt and¯ W t compositionssimilartothatofthesignalregions. This ensuresthatthenormalisationcorrectiondeterminedinthefitfor the Top background results in an accurate estimate of the com-bined tt and¯ W t process in the signal regions, accounting for potential interference effects present in data but not necessar-ily modelled in MC simulation. Table 3 compares the observed and predicted event yields, where the background event yields obtained after background-only fits in the corresponding control regions arealso shown.The post-fit normalisationcorrection fac-torsfortheTop and Z/γ∗+ HF backgroundprocesses,respectively
μTop=0.79±0.10 and μZ/γ∗+ HF=1.36±0.07,arealsoshownin
Table3.Theuncertaintiesin μTop and μZ/γ∗+ HFtakeintoaccount
thestatisticalandsystematicuncertaintiesduetotheexperimental sources,asdescribedinSection6.
Distributions of dH H in the control regions after performing background-only fits to data in the control regions and applying the Top and Z/γ∗+ HF normalisation corrections are shown in Fig. 2.In thecontrol andvalidation regions, good agreement be-tween the data and SM prediction provided by the post-fit MC simulation is observedfor theobservables relevant tothe analy-sis.
6. Systematicuncertainties
Theanalysisevaluatesseveralsourcesofsystematicuncertainty for the signal and background processes,which are classified as either experimental (detectororluminosity related) ortheoretical modelling uncertainties. Statistical uncertainties of the simulated eventsamples are alsotaken intoaccount. The main uncertainty componentsare summarisedinTable4.MC modelling uncertain-tiesintheTop andZ/γ∗+ HF backgroundestimatesaredominant, followedbystatisticalanddetectoruncertainties.
The normalisationcorrectionsofthe Top and Z/γ∗+ HF back-groundprocesses aredetermined primarily by thedata eventsin thecontrolregionswhenperformingthestatisticalanalysis.These correctionstakeintoaccount thestatisticalandsystematic uncer-taintiesduetotheexperimentalsources,asdescribedlaterinthis section. In addition, the systematic uncertainties in the theoret-ical modelling of these processes are applied as uncertainties in
Fig. 2. DistributionsofdH HinCR-Top(left)andCR-Z+HF(right).Distributionsareshownafterthefittodataunderthebackground-onlyhypothesisintheshowncontrol
regions.Theratioofthedatatothesumofthebackgroundsisshowninthelowerpanel.Thehatchedbandsindicatethecombinedstatisticalandsystematicuncertainty.
the corrected predictions in the signal regions using the follow-ingprocedures.TheuncertaintiesintheestimatedTop background eventyields dueto partonshower modellingare assessedasthe differencebetweenthepredictionsof Powheg-Box showeredwith Pythiaor Herwig,andthoseduetothechoiceofeventgenerator areassessedbycomparingthepredictionsof Powheg-Box or Mad-Graph5_aMC@NLO [122],bothshoweredwith Pythia.The uncer-tainties duetomissing higher-ordercorrectionsare estimatedby changingtherenormalisationandfactorisationscales(μr and μf,
respectively)upanddownbyafactoroftwo(8-pointsvariation). Theuncertaintiesduetothemodellingofinitial- andfinal-state ra-diation(ISRandFSR,respectively)inthegeneratorsusedto simu-latetheTop backgroundprocessesareevaluatedusingthemethod described in Ref. [122]. The Top background composition is var-iedwithin the uncertaintiesin thetheoretical predictionsforthe tt and¯ single-top-quark W t cross-sections [65,68,123].The uncer-tainty arising fromtheinterference betweentheNLO predictions fort¯t andW t processesisestimatedbytakingthedifference be-tweenthepredictedTop backgroundyields obtainedwiththeDR andDSschemes usedforthe NLO W t calculation [122].The un-certaintiesduetoPDFvariationsarecomputedastheenvelopeof thecentralvaluesofthenominalNNPDF3.0PDFsetandtheCT14, MMHT14,andPDF4LHC15_30PDFPDFsets[124].Alluncertainties exceptthoseinthescalevariations,cross-section,andinterference are considered as fully correlated between the tt and¯ W t pro-cesses.The Z/γ∗+ HF modellinguncertaintiesareestimatedusing thenominal Sherpa 2.2.1samplesbyconsideringdifferentmerging (CKKW-L)[125] andresummationscales.Theuncertaintiesdueto PDFvariationsandchangesin μr and μf arecalculatedusingthe
sameproceduresasfortheTop backgrounds.Anadditional uncer-tainty in the Z/γ∗ process is computedby takingthe difference betweenthenominal Sherpa 2.2.1sampleswithsamplesgenerated using MadGraph 5_aMC@NLO+Pythia8. The dominant uncertain-tiesinthetotalbackgroundestimatesinSR-SFarethe Z/γ∗+ HF modellinguncertainties(8%), primarilythat duetocomparisonof Sherpa2.2.1 and MadGraph 5_aMC@NLO,andthe partonshower uncertainty affecting the Top background process (5%). The un-certainties in the background estimates in SR-DF are dominated by the uncertainty due to the parton shower affecting the Top backgroundprocess (12%), theuncertainty in the Top normalisa-tioncorrection μTop (10%),theuncertaintyduetothecomparison
betweenthe generators usedforthe Top process (7.5%),andthe
uncertainty duetothe modellingofISR andFSR inthe Top pro-cess(5%).
Systematicuncertainties in thesignal acceptancedue to vary-ing μrand μf,aswellasPDF-induceduncertainties,areevaluated
usingthesameprocedureasfortheTop backgroundprocess.The resulting scale (PDF) uncertainties are <3% (<1%) in both sig-nal regions. Theuncertainty dueto thepartonshower modelling is computed by comparing Herwig7 with Pythia8, and is found to be 8% (9%)in SR-SF (SR-DF). The uncertainty inthe H H pro-ductioncross-section,evaluatedtobe5%,isincludedasan uncer-taintyin σSM(gg→H H)whencomputingtheupperlimitsonthe cross-sectionratioinTable5.Thisvalue isthequadraturesumof the scale,PDF+αs,andtop masscontributionsasreportedby the LHCXSWG[20].
The uncertainties dueto experimental sources arise primarily from the mismeasurement of reconstructed objectmomenta and from the mismodelling of reconstruction efficiencies. These un-certainties includeuncertaintiesfromthemismodellingofthe jet energyscale(JES)[109] andjetenergyresolution(JER)[126]. Addi-tionaluncertainties forb-taggedjetsarisefromthemismodelling of the b-tagging efficiency [111] and from the mismodelling of the rates at which charm- and light-flavoured jets are selected asb-taggedjets [127,128].Lepton-relateduncertaintiesarisefrom themismodellingoftheelectron[104] (muon[105])reconstructed energy (momentum) measurements, as well as in the mismod-elling of their reconstruction and identification efficiencies [104, 105].TheEmissT scaleandresolution[113] uncertainties,aswellas uncertainties fromthe mismodellingof pile-up,trigger efficiency and luminosity, are also taken into account. The uncertainty in thecombined2015–2018integratedluminosity is1.7% [129], ob-tainedusingtheLUCID-2detector[130] fortheprimaryluminosity measurements.Thecombinedeffectoftheexperimentalsourcesof systematicuncertaintyinthepredictedbackgroundyields is sum-marised in Table 4 and is dominated by the JER, with all other contributionsfoundtobenegligible.
7. Results
Inordertoextractinformationaboutthe H H→bbνν signal cross-section, acountingexperimentis performedwitha profile-likelihood fit [131] simultaneously across the CR-Top, CR-Z+HF, SR-SF,andSR-DF regionsusing thepredictedandobservedevent counts ineach region asinputs. The Top and Z/γ∗+ HF
normal-Table 4
BreakdownofthemainuncertaintycomponentsinthebackgroundestimatesinthetwosignalregionsfortheTop,Z/γ∗+ HF,and allother(“Other”)backgrounds.Theuncertaintycomponentsassociatedwiththetotalbackgroundestimateinthesignalregions (thesumofTop, Z/γ∗+ HF,andOther)islistedunder“TotalBkg.”.AsintheupperhalfofTable3,alluncertaintiesareshown “post-fit”.Thepercentagesshowthesizeoftheuncertaintyrelativetotheexpectedbackgroundineachcolumnanduncertainties canbecorrelated,notnecessarilyaddinginquadraturetothetotaluncertaintyineachcolumnoracrosseachrow.Uncertaintiesin thepost-fitnormalisationfactors,μTopandμZ/γ∗+ HF,areonlyapplicablefortheTop andZ/γ∗+ HF processes.
Uncertainty [%] SR-SF SR-DF
Top Z/γ∗+ HF Other Total Bkg. Top Z/γ∗+ HF Other Total Bkg.
Total uncertainty 28 18 20 14 30 26 41 25
Theoretical 21 15 17 11 20 15 40 17
Experimental 12 <5 8 <5 15 17 8 12
MC statistics 8 8 6 8 13 13 7 11
μTop,μZ/γ∗+ HF 13 5 n/a 5 13 5 n/a 10
Fig. 3. Distributionsofmbb(left),m(middle),andthediscriminantdH H(right).Thedistributionsareshownafterthefittodatainthecontrolregionsunderthe
background-onlyhypothesis.EachdistributionincludesboththeSFandDFeventsandimposessignalselectionrequirementsonallquantitiesexcepttheonebeingplotted,butthe requirementondH HhasbeenrelaxedtodH H>5 forthedistributionsofmbb andm.TheH H→bbνν signal(“H H ”)isoverlaidandhasitscross-sectionscaledbya
factorof20relativetotheSMpredictionforvisualisationpurposes.Theratioofthedatatothesumofthebackgroundsisshowninthelowerpanelofeachfigure.The hatchedbandsindicatethecombinedstatisticalandsystematicuncertainty.
Table 5
ObservedandexpectedupperlimitsontheggF-initiatednon-resonantH H productioncross-sectionat95% CLand theirratiostotheSMprediction(σSM(gg→H H)=31.05±1.90 fb[13–20]).The±1σ and±2σ variationsabout theexpectedlimitarealsoshown.UncertaintiesintheSMcross-sectionaretakenintoaccountwhencomputing theupperlimitsonthecross-sectionratio.
−2σ −1σ Expected +1σ +2σ Observed
σ(gg→H H)[pb] 0.5 0.6 0.9 1.3 1.9 1.2
σ(gg→H H) /σSM(gg→H H) 14 20 29 43 62 40
isation correctionsare also extractedfromthis fit andare found to differ negligibly from those presented in Table 3. All sources of systematic and statistical uncertainty in the signal and back-groundmodels are implemented asdeviations fromthe nominal model,scaledby nuisanceparameters thatare profiled inthefit. Thep-valuecorrespondingtothebackground-onlyhypothesis, giv-ingthe probability thatthe datainthe signal regionsbe atleast asincompatiblewiththe background-onlyhypothesis asthat ob-servedinSR-SFandSR-DF,isp0=0.15 andcorrespondsto1.05σ
significance.Distributions ofmbb,m,and dH H after performing background-only fits to data in the control regions and apply-ing the Top and Z/γ∗+ HF normalisation corrections are shown inFig. 3.The signal selection criteriaare imposed on all observ-ablesshowninFig.3apartfromtheonebeingplotted,exceptthat thedH H requirementforthembb andm distributions isrelaxed
todH H>5.No significantexcessofeventsover theexpectedSM backgroundisobservedandupperlimitsareseton non-resonant Higgsbosonpairproductionat95% confidencelevel(CL)usingthe CLs method [132]. Table 5 presentsthese upperlimitsand
com-parisonswiththeSM prediction.Theobserved(expected)limitat
95% CLis1.2 (0.9)pb,correspondingto40 (29)timestheSM pre-diction.
8. Conclusions
Asearchfornon-resonantHiggsbosonpairproduction,as pre-dictedbytheSM, ispresentedinthefinalstatewithatleasttwo b-taggedjetsandexactlytwoleptonswithoppositeelectriccharge, where one of the Higgs bosons decays to bb and the other de-cays to either W W∗, Z Z∗,or τ τ. The analysisuses pp collision datarecorded at√s=13 TeVby theATLAS detectoratthe LHC, corresponding to an integratedluminosity of139 fb−1. The data
areinagreementwiththepredictionsfortheSMbackground pro-cesses. An observed (expected) 95% CLupper limit is set on the cross-sectionfortheproductionofHiggsbosonpairs, correspond-ing to 40 (29) times the SM prediction. These limits are com-parable to the previous leading searches for non-resonant Higgs boson pairproduction performedby the ATLAS and CMS experi-ments.
Acknowledgements
We thankCERN for the very successfuloperation of theLHC, aswell asthe support stafffrom ourinstitutions without whom ATLAScouldnotbeoperatedefficiently.
WeacknowledgethesupportofANPCyT,Argentina;YerPhI, Ar-menia; ARC, Australia; BMWFW and FWF, Austria; ANAS, Azer-baijan; SSTC, Belarus; CNPq andFAPESP, Brazil; NSERC, NRC and CFI,Canada; CERN; CONICYT,Chile; CAS, MOSTandNSFC, China; COLCIENCIAS, Colombia; MSMT CR, MPO CR and VSC CR, Czech Republic;DNRFandDNSRC,Denmark;IN2P3-CNRS,CEA-DRF/IRFU, France; SRNSFG, Georgia; BMBF, HGF, and MPG, Germany; GSRT, Greece;RGC,Hong KongSAR,China;ISF andBenoziyo Center, Is-rael; INFN, Italy; MEXT and JSPS, Japan; CNRST, Morocco; NWO, Netherlands;RCN, Norway;MNiSW andNCN, Poland;FCT, Portu-gal; MNE/IFA, Romania; MES of Russia andNRC KI, Russian Fed-eration; JINR; MESTD, Serbia; MSSR, Slovakia; ARRS and MIZŠ, Slovenia;DST/NRF,SouthAfrica;MINECO,Spain;SRCand Wallen-berg Foundation, Sweden; SERI, SNSF and Cantons of Bern and Geneva, Switzerland; MOST, Taiwan; TAEK, Turkey; STFC, United Kingdom;DOEandNSF,UnitedStatesofAmerica. Inaddition, in-dividualgroupsandmembershavereceivedsupport fromBCKDF, Canarie,CRCandComputeCanada,Canada;COST,ERC,ERDF, Hori-zon 2020, andMarie Skłodowska-Curie Actions, European Union; Investissements d’Avenir Labex and Idex, ANR, France; DFG and AvH Foundation, Germany; Herakleitos, Thales and Aristeia pro-grammesco-financedbyEU-ESFandtheGreekNSRF,Greece; BSF-NSF and GIF, Israel; CERCA Programme Generalitat de Catalunya, Spain;TheRoyalSocietyandLeverhulmeTrust,UnitedKingdom.
The crucial computingsupport fromall WLCG partners is ac-knowledged gratefully, in particular from CERN, the ATLAS Tier-1 facilities at TRIUMF (Canada), NDGF (Denmark, Norway, Swe-den),CC-IN2P3(France),KIT/GridKA(Germany),INFN-CNAF(Italy), NL-T1(Netherlands),PIC(Spain),ASGC(Taiwan),RAL(UK)andBNL (USA),theTier-2facilitiesworldwideandlargenon-WLCGresource providers.Majorcontributorsofcomputingresourcesarelisted in Ref. [133].
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