Contents lists available atScienceDirect
Physics
Letters
B
www.elsevier.com/locate/physletb
Measurement
of
the
associated
production
of
a
Higgs
boson
decaying
into
b-quarks
with
a
vector
boson
at
high
transverse
momentum
in
pp
collisions
at
√
s
=
13 TeV with
the
ATLAS
detector
.
The
ATLAS
Collaboration
a
r
t
i
c
l
e
i
n
f
o
a
b
s
t
r
a
c
t
Article history: Received6August2020
Receivedinrevisedform3February2021 Accepted5March2021
Availableonline17March2021 Editor: M.Doser
TheassociatedproductionofaHiggsbosonwithaW or Z bosondecayingintoleptonsandwherethe Higgsbosondecaystoabb pair¯ ismeasured inthehighvector-boson transversemomentumregime, above250 GeV,withtheATLASdetector.Theanalyseddata,corresponding toanintegratedluminosity of139 fb−1,werecollectedinproton–protoncollisionsattheLargeHadronColliderbetween2015and 2018atacentre-of-massenergyof√s=13 TeV.Themeasuredsignalstrength,definedastheratioofthe measuredsignalyieldtothatpredictedbytheStandardModel,is0.72+0.39
−0.36correspondingtoanobserved
(expected)significanceof2.1(2.7)standarddeviations.Cross-sectionsofassociatedproductionofaHiggs bosondecaying intob quarkpairs witha W or Z gauge boson,decaying intoleptons,are measured intwo exclusive vectorboson transverse momentumregions,250–400 GeV and above 400 GeV, and interpretedasconstraintsonanomalouscouplingsintheframeworkofaStandardModeleffectivefield theory.
©2021TheAuthor.PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense (http://creativecommons.org/licenses/by/4.0/).FundedbySCOAP3.
1. Introduction
SincethediscoveryoftheHiggsboson(H ) [1–4] withamassof around125 GeV [5] bytheATLASandCMSCollaborations [6,7] in 2012, theanalysis ofproton–proton(pp)collision dataat centre-of-massenergiesof7 TeV,8 TeVand13 TeVdeliveredbytheLarge HadronCollider(LHC) [8] hasledtoprecise measurementsofthe main production cross-sectionsand decayrates of theHiggs bo-son, aswell asmeasurements ofits massanditsspin andparity properties.Inparticular,theobservationofthedecayoftheHiggs bosonintob-quarkpairs provideddirectevidencefortheYukawa coupling of the Higgsboson to down-type quarks [9,10]. Finally, a combination of 13 TeV results searching for the Higgs boson produced inassociationwitha leptonicallydecaying W or Z
bo-son established the observation ofthis productionprocess [9]. A firstcross-section measurementasafunctionofthevector-boson transversemomentumwasalsocarriedoutbytheATLAS Collabo-ration [11].
ThepreviousATLASanalyses [9,11] inthischannelweremainly sensitivetovector bosonswithtransversemomentum(pT)inthe
rangeofapproximately100–300 GeV.Theseanalysesconsidereda pairofjetswithradiusparameterof R
=
0.
4,referredtoas small-radius (small-R)jets, to reconstruct the Higgs boson. For higher Higgsbosontransversemomenta,thedecayproductscanbecomeE-mail address:atlas.publications@cern.ch.
closeenoughthatthey cannotbereconstructedwithtwosmall-R jets. To explore this ‘boosted’ regime, the Higgs boson is recon-structed as a single large-R jet with R
=
1.
0 [12]. This high-pTregime is particularlyinteresting dueto its sensitivity to physics beyondtheStandardModel [13].
ThisLetterpresentsameasurementofcross-sectionsforthe as-sociatedproduction ofahightransversemomentum Higgsboson that decays into a bb pair
¯
with a leptonically decaying W or Zboson.Theanalysisuses pp collisiondatarecordedbetween2015 and 2018 by the ATLAS detector [14] during Run 2 at the LHC. Thisdatasetcorrespondstoan integratedluminosityof139 fb−1. Eventsare selectedin0-,1- and2-leptonchannels, basedonthe numberofreconstructed chargedleptons,
(electronsormuons), in the final state to explore the Z H
→
ννb
b,¯
W H→
νb
b and¯
Z H
→
bb signatures,¯
respectively. The Higgs boson isrecon-structed as a single large-R jet and the b-quarksfrom its decay asapairofjets,reconstructedwitha pT-dependentradius
param-eter,associatedwiththelarge-R jetandidentifiedascontaininga
b-hadron.
Theanalysisusing small-R jetsandfocusingon slightlylower Higgsbosontransverse momentum regions wasrecently updated withthecompleteRun 2dataset [15].Thelarge-R jetanalysis sig-nificantlyoverlapswiththesmall-R jets analysis.The tworesults canthereforenotbestraightforwardlycombined.
The dominant background processes after the event selection correspondtotheproductionofV
+
jets,whereV referstoeither aW or Z boson,t¯
t,single-topanddibosons.Thesignalisextractedhttps://doi.org/10.1016/j.physletb.2021.136204
0370-2693/©2021TheAuthor.PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense(http://creativecommons.org/licenses/by/4.0/).Fundedby SCOAP3.
from a combined profile likelihood fit to the large-R jet mass, usingseveralsignalandcontrolregions.Theyieldofdiboson pro-duction V Z with Z
→
bb is¯
alsomeasured usingthesamefitand provides a validation of the analysis. The cross-section measure-ments areperformedwithinthesimplifiedtemplatecross-section (STXS) framework [16,17].These measurements are then used to constrainanomalous couplingsina StandardModeleffectivefield theory(SMEFT) [18].2. ATLASdetector
The ATLAS detector [14] at the LHC is a multipurpose parti-cle detector with a forward–backward symmetric cylindrical ge-ometry anda near4
π
coverage in solid angle.1 It consistsofaninnerdetector(ID)fortrackingsurroundedbyathin superconduct-ing solenoidprovidinga2 Taxialmagnetic field,electromagnetic andhadroniccalorimeters,andamuonspectrometer. TheID cov-ersthepseudorapidity range
|
η
|
<
2.
5.Itconsistsofsiliconpixel, silicon microstrip, and transition radiation tracking detectors.An inner pixel layer, the insertable B-layer [19,20], was added at a meanradiusof3.3 cmduring thelongshutdownperiodbetween Run 1 and Run 2 of the LHC. Lead/liquid-argon (LAr) sampling calorimeters provide electromagnetic (EM) energy measurements with high granularity (|
η
|
<
3.
2). The hadronic calorimeter uses a steel/scintillator-tile samplingdetectorinthe central pseudora-pidity range (|
η
|
<
1.
7) and a copper/LAr detector in the region 1.
5<
|
η
|
<
3.
2. The forward regions (3.
2<
|
η
|
<
4.
9) are instru-mented with copper/LAr and tungsten/LAr calorimeter modules optimisedforelectromagneticandhadronicmeasurements, respec-tively.Amuonspectrometerwithanair-coretoroidmagnetsystem surroundsthecalorimeters.Threelayersofhigh-precisiontracking chambersprovidecoverageintherange|
η
|
<
2.
7,whilededicated fastchambers allowmuon triggering intheregion|
η
|
<
2.
4. The ATLAS triggersystemconsistsofahardware-based first-level trig-gerfollowedbyasoftware-basedhigh-leveltrigger [21].3. DataandMonteCarlosimulation
Thedatawerecollected inpp collisionsat
√
s=
13 TeV during Run 2 ofthe LHC. Thedata sample corresponds to an integrated luminosityof139 fb−1 afterrequiringthatalldetectorsubsystems wereoperatingnormallyandrecordinghigh-qualitydata [22].The uncertainty in the combined 2015–2018 integratedluminosity is 1.7% [23], obtained using the LUCID-2 detector [24] for the pri-mary luminosity measurements. Collision events considered for this analysis were recorded with a combination of triggers se-lecting events with high missing transverse momentum or with ahigh-pT lepton,depending ontheanalysischannel.MoredetailsofthetriggerselectionaregiveninSection5.
MonteCarlo(MC)simulatedeventsamplesprocessedwiththe ATLAS detector simulation [25] based on Geant 4 [26] are used to modelthesignal andbackgroundcontributions, exceptforthe multijet production, whose contribution is estimated with data-driven techniques asdetailedinSection 6. Asummary of all the signal and backgroundprocesses with thecorresponding genera-tors usedforthenominalsamplesisshowninTable1.All simu-latedprocessesare normalised usingthemostprecise theoretical
1 ATLAS usesaright-handedcoordinatesystemwithitsoriginatthenominal interactionpointinthecentreofthedetector.Thepositive
x-axis
isdefinedbythe directionfromtheinteractionpointtothecentreoftheLHCring,withthepositive y-axis pointingupwards,whilethebeamdirectiondefinesthez-axis.
Cylindrical coordinates(r,φ)areusedinthetransverseplane,φbeing theazimuthalangle aroundthez-axis.
Thepseudorapidityηisdefinedintermsofthepolarangleθbyη= −ln tan(θ/2).Theangular distanceisdefined as R ≡( η)2+ ( φ)2. Rapidityisdefinedas y = 0.5ln[(E+pz)/(E−pz)]where
E denotes
theenergyand
p
zisthecomponentofthemomentumalongthebeamdirection.predictions currentlyavailable of their cross-sections. In addition to the hard scatter, each event was overlaid with additional pp
collisions(pile-up)generatedwith Pythia 8.1 [27] usingtheATLAS A3setoftuned parameters [28] andtheNNPDF23LO [29] parton distributionfunction(PDF)set.Simulatedeventswerethen recon-structedwiththesamealgorithmsasthoseappliedtodataandare weightedtomatchthepile-updistributionobservedinthedata.
Forthe signal events,the AZNLO [30] modelof parton show-ers and the underlying event (UE) was used. For the top-quark pairandsingle-top-quarkproductionprocesses,theUEmodelwas takenfromtheATLASA14 [31] setoftuned Pythia 8.1 [27] param-eters and for the other backgrounds the default Sherpa [32–35] tunesetwasused.Forallsamplesofsimulatedevents,exceptfor thosegeneratedusing Sherpa,the EvtGenv1.2.0program [36] was used to describe the decays of bottom and charm hadrons. The nominal PDF set used for W
/
Z +jets and diboson processes was NNPDF3.0NNLO [37] while for the top-quark pair and single-top productiontheNNPDF3.0NLO [37] setwasused.Samplesproduced withalternativegeneratorswhich areusedto estimatemodelling systematicuncertaintiesaredescribedinSection7.Allqq-initiatedsignalprocessesweresimulatedwithuptoone
additionalpartonatnext-to-leading-order (NLO)accuracy inQCD usingthe Powheg-Box v2 [41] andthe GoSam [43] generatorwith theMiNLO (Multiscale Improved NLO) [44,45] procedureapplied, interfacedto Pythia 8.212forthesimulationofthepartonshower (PS), UE and multiple parton interactions. The gg
→
Z Hcontri-butionwassimulatedatleadingorder(LO) inQCDwith Powheg-Box v2.The gg
→
Z H cross-sectionprocesswascalculatedatNLO in QCD including soft gluon resummation up to next-to-leading logarithms (NLL) [53–57]. Signal MC events were generated us-ingtheNNPDF3.0NLOPDFsetandsubsequentlyreweightedtothe PDF4LHC15NLOPDF set [38].Thetotalinclusivecross-sectionsfor allsignalprocesses(W H andZ H )werecalculatedat next-to-next-to-leading-order(NNLO) QCD andNLOelectroweak (EW) [46–52] accuracy, including photon-inducedcontributions calculated with Hawk[39,40].Thenominaltop-quarkpairproductiongeneratorwas Powheg-Box v2withreal andvirtual correctionsatNLO accuracy inQCD and interfaced to Pythia 8.230 for the parton showering. The nominal top-quark pair production cross-section is from a re-summedNNLOandnext-to-next-to-leadinglogarithm(NNLL) pre-diction [59].
Singletop-quarkproductionwasalsogeneratedwith Powheg-Boxv2interfacedto Pythia 8.230.Thenominalcross-section nor-malisationsforthesingletop-quarkproductions- andt-processes
wereestimatedfromresummedcalculationsatNLO,whileforthe
W t processapproximateNNLOwasused [61,62,64].Athigher or-dersinQCD, the definitionofthe W t process can correspondto leading-ordertop-quarkpairproductionprocesses.Toaccount for theseambiguities and relatedinterference effects when generat-ingtheprocessesseparately,thediagramremoval(DR)subtraction schemewasused [68].
The nominal W
/
Z +jets backgroundsamples used Sherpa2.2.1 [33–35] forthematrixelement(ME)andpartonshowerwith vir-tualcorrectionsatNLOaccuracyforup totwo additionaljetsand at LO forup to four additional jets using OpenLoops [32,34,35]. Inthesesamples,the simulationof theemission ofhard partons matchedwithapartonshowerwasbasedontheCatani–Seymour subtractionterm [32,34,35] andthemulti-parton MEwasmerged withthe parton shower using an improved ckkw matching pro-cedure extendedto NLO accuracyusing the MEPS@NLO prescrip-tion [66]. The nominalnormalisation ofthisbackgroundwas ob-tainedfromanNNLOfixed-orderestimate [67].Thedibosonnominalsamplesweregeneratedusing Sherpa2.2.1 forthedominantqq-initiatedprocessesforwhichzeroorone ad-ditional parton was calculated at NLO in the ME, while two or
Table 1
Signalandbackgroundprocesseswiththecorrespondinggeneratorsusedforthenominalsamples.Ifnotspecified,theorderofthecross-sectioncalculationreferstothe expansioninthestrongcouplingconstant(αS).()TheeventsweregeneratedusingthefirstPDFintheNNPDF3.0NLOsetandsubsequentlyreweightedtothePDF4LHC15NLO set [38] usingtheinternalalgorithmin Powheg-Boxv2.(†)TheNNLO(QCD)+NLO(EW)cross-sectioncalculationforthe
pp
→Z H process alreadyincludesthe gg→Z H contribution.Thepp
→Z H process, aftersubtractingthegg
→Z H contribution. Anadditionalscalefactor isappliedtotheV H differential
cross-sectioncomputedwith Hawk [39,40].Process ME generator ME PDF PS and hadronisation UE model tune Cross-section order
Signal (mH=125 GeV and bb branching fraction set to 58%)¯
qq→W H→ νbb¯ Powheg-Box v2[41] + NNPDF3.0NLO()[37] Pythia8.212 [42] AZNLO [30] NNLO(QCD)+
GoSam[43] + MiNLO [44,45] NLO(EW) [46–52]
qq→Z H→ννbb¯/bb¯ Powheg-Box v2+ NNPDF3.0NLO() Pythia8.212 AZNLO NNLO(QCD)(†)+
GoSam+ MiNLO NLO(EW)
gg→Z H→ννbb¯/bb¯ Powheg-Box v2 NNPDF3.0NLO() Pythia8.212 AZNLO NLO+
NLL [53–57] Top quark (mt=172.5 GeV)
t¯t Powheg-Box v2[41,58] NNPDF3.0NLO Pythia8.230 A14 [31] NNLO+NNLL [59]
s-channel Powheg-Box v2[41,60] NNPDF3.0NLO Pythia8.230 A14 NLO [61]
t-channel Powheg-Box v2[41,60] NNPDF3.0NLO Pythia8.230 A14 NLO [62]
W t Powheg-Box v2[41,63] NNPDF3.0NLO Pythia8.230 A14 Approximate NNLO [64]
Vector boson + jets
W→ ν Sherpa 2.2.1[32–35] NNPDF3.0NNLO Sherpa 2.2.1[65,66] Default NNLO [67]
Z/γ∗→ Sherpa 2.2.1 NNPDF3.0NNLO Sherpa 2.2.1 Default NNLO
Z→νν Sherpa 2.2.1 NNPDF3.0NNLO Sherpa 2.2.1 Default NNLO
Diboson
qq→W W Sherpa 2.2.1 NNPDF3.0NNLO Sherpa 2.2.1 Default NLO
qq→W Z Sherpa 2.2.1 NNPDF3.0NNLO Sherpa 2.2.1 Default NLO
qq→Z Z Sherpa 2.2.1 NNPDF3.0NNLO Sherpa 2.2.1 Default NLO
gg→V V Sherpa 2.2.2 NNPDF3.0NNLO Sherpa 2.2.2 Default NLO
threeadditionalpartonswereincludedatLOinQCD.The subdom-inant gg-initiatedprocessesweregeneratedwith Sherpa2.2.2.For thesesamples,zerooroneadditionalpartonwas calculatedatLO intheME.Thesegeneratorsalsoprovidedthenominal normalisa-tionforthisprocess.
4. Objectreconstruction
Ofallthereconstructed pp collisionverticeswithatleasttwo reconstructed trajectories of charged particles in the ID (tracks) with pT
>
0.
5 GeV,thehard-scatteringprimary vertexisselectedasthe onewiththe highestsumofsquaredtransverse momenta ofassociatedtracks [69].
Leptons areused foreventcategorisationasdescribed in Sec-tion5.ElectronsarereconstructedfromtracksintheIDassociated with topological clusters of energy depositions in the calorime-ter [70,71]. The identification criteria closely follow those de-scribed in Ref. [9]. Baseline electrons are required to have pT
>
7 GeVand
|
η
|
<
2.
47,tobeisolatedfromothertracksandenergy deposit clusters, to meet looselikelihood selection criteria based on shower shapes and to satisfy|
d0/
σ
(
d0)
|
<
5 and|
z0sinθ
|
<
0
.
5 mm,whered0 andz0 arethetransverseandlongitudinalim-pact parameters defined relative to the primary vertex position2 and
σ
(
d0)
is the d0 uncertainty. Signal electrons are a subset ofthe baseline electron set and are selected using a tighter likeli-hood requirement,which alsoincludes trackingandtrack–cluster matchingvariables,andusingatightercalorimeter-basedisolation criterion.
Muon candidates are identified by matching ID tracks to full tracks or track segments reconstructed in the muon spectrome-ter within the inner detector coverage and using only informa-tionfromthemuonspectrometeroutsideofthatcoverage.Muons are required to have pT
>
7 GeV and|
η
|
<
2.
7 and to have|
d0/
σ
(
d0)
|
<
3 and|
z0sinθ
|
<
0.
5 mm.Twomuoncategoriesare 2 Forthecomputationoftheimpactparameters,thebeamlineisusedto approx-imatetheprimaryvertexpositioninthetransverseplane.usedintheanalysis:baseline muonsareselectedusingthe‘loose’ identificationcriterionofRef. [72] andaloosetrackisolation; sig-nal muonsare requiredtohave
|
η
|
<
2.
5,tosatisfy the‘medium’ identificationcriterion [72] andatightertrack-basedisolation cri-terion.Thelow-threshold (7 GeV) baseline leptonsare usedto define thethreemain channelsrequiringexactly zero,one andtwo lep-tons. The latter1- and 2-lepton channelsfurther requireat least
one signal lepton, with identification and isolation requirements
chosen to optimise the suppression of the multijet background. Signal leptons must have a pT
>
27 GeV (except inthe 1-leptonmuonsub-channelwherea pT
>
25 GeVisused).Calorimeterjetsarereconstructedfromnoise-suppressed topo-logical clusters (topoclusters) of calorimeter energy depositions [73], usingthe anti-kt algorithm [74] with radius parameter R
=
1
.
0 (large-R jets) or R=
0.
4 (small-R jets) implementedin Fast-Jet [75]. Small-R jets are built from topoclusters calibrated at the electromagnetic scale [76], while large-R jets are built from topoclusterscalibratedatthelocalhadronicscale [73].Large-R jets aregroomedusingtrimming [77,78] toimprovethejetmass res-olutionanditsstability withrespectto pile-upby discardingthe softer components of jets that originate from initial-state radia-tion,pile-upinteractions,ortheunderlyingevent.Thisisdoneby reclusteringtheconstituentsoftheinitiallarge-R jet,usingthektalgorithm [79,80], into subjets with radius parameter Rsub
=
0.
2andremoving anysubjet that hasa pT lessthan 5% ofthe
par-ent jet pT. The large-R jet mass mJ is computed using tracking
andcalorimeter information [81]. A dedicated MC-based calibra-tion,similartotheprocedureusedinRef. [81],isappliedtocorrect thepTandmassofthetrimmedjetstotheparticlelevel.Large-R
jetsarerequiredtohavepT
>
250 GeV,mJ>
50 GeVand|
η
|
<
2.
0,thelastduetotrackingacceptance.
Small-R jets are used in building the missingtransverse mo-mentumandeventcategorisation.Theyarecalibratedwithaseries ofsimulation-based correctionsand in situ techniques, including correctionsto accountforpile-upenergyentering thejetarea, as describedinRef. [76].Theyarerequiredtohave pT
>
30 GeVandpile-upinteractions,small-R jetsarerequiredtopassthejetvertex tagger(JVT) [82] requirementiftheyareintherangepT
<
120 GeVand
|
η
|
<
2.
5 duetotrackingacceptance.Track-jets formedfromcharged-particle tracks are usedto re-constructacandidatetwo-bodyH
→
bb decay¯
withinthelarge-R jet. Track-jetsarebuiltwiththeanti-kt algorithm witha variableradius(VR) pT-dependentparameter,fromtracksreconstructedin
the inner detector with pT
>
0.
5 GeVand|
η
|
<
2.
5 [83–85]. VRtrack-jets havean effectivejet radius Reff proportional to the
in-verse ofthejet pT inthe jetfinding procedure: Reff
(
pT)
=
ρ
/
pT,wherethe
ρ
-parameterissetto30 GeV.Therearetwoadditional parameters, Rmin and Rmax,used toset theminimumandmaxi-mumcut-offs onthejetradius,andtheseare setto0.02 and0.4, respectively. Only VR track-jets with pT
>
10 GeV,|
η
|
<
2.
5 andwithatleasttwoconstituentsareconsidered [86].VRtrack-jetsare matchedtothelarge-R calorimeterjetsviaghost-association [87]. Track-jets not associated with large-R jets are also used in the analysisforeventcategorisationasdescribedinSection5.
The ‘truth’flavour labelling oftrack-jets insimulation isdone by geometricallymatchingthe jetto ‘truth’hadrons, using‘truth’ informationfromthegenerator’seventrecord.Ifab-hadronwith
pT above 5 GeVisfoundwithin
R
=
0.
3 ofthedirectionofthetrack-jet, the track-jet is labelled as a b-jet. If the b-hadron is matched to more than one track-jet,only the closest track-jet is labelled asa b-jet. Ifno b-hadron is found, the procedure is re-peatedfirstforc-hadronstolabelc-jetsandthenfor
τ
-leptonsto labelτ
-jets.Asisthecasefordefiningab-jet,thelabellingisalso exclusiveforc- andτ
-jets. Ajetforwhichnosuch matchingcan bemadeislabelledasalight-flavourjet.To identify track-jets containing b-hadron decay products, track-jets are tagged using the multivariate algorithm MV2c10, whichexploitsthepresenceoflarge-impact-parametertracks,the topological decaychain reconstruction andthe displaced vertices fromb-hadrondecays [88,89].TheMV2c10algorithmisconfigured toachieveanaverageefficiencyof70%fortaggingjetslabelledas
b-jets inan MC sample oft
¯
t events. Thisrequirementhas corre-sponding rejectionfactorsof9 and304forjetslabelledasc-jetsandlight-flavourjets,respectively,insimulatedtt events.
¯
The tag-gingefficiencies perjet flavour arecorrectedinthe simulationto matchthosemeasuredindata [86,90,91].Two additional corrections are applied to the large-R jets to improve the scale and the resolution of their energy and mass measurements. First, to account for semileptonic decays of
the b-hadrons, the four-momentum of the closest reconstructed
non-isolated muon candidate within
R
=
min(
0.
4,
0.
04+
10 GeV/
pmuonT
)
of a track-jet matched to the large-R jet by ghostassociation is added to the calorimeter-based component of the large-R jet four-momentum while its expected calorimeter en-ergydepositsareremoved [85].Thisisknownasthemuon-in-jet correction.Non-isolatedmuonssatisfythe‘medium’identification criterion [72],butnoisolationorimpactparametercriteriaare ap-plied.Second,inthe2-leptonchannelonly,aper-eventlikelihood usesthefullreconstructionoftheeventkinematicstoimprovethe estimate ofthe energy of the b-jets [92]. The kinematic fit con-strainsthe
+
−bb systemandtheadditional small-R jetsinthe eventtobebalancedinthetransverseplaneandthedilepton
sys-tem tothe Z boson mass, byscaling the four-momentumof the
objects inthe eventincluding thelarge-R jet, additionalsmall-R jets and leptons within their detector response resolutions. The large-R jet mass is then scaled by the ratio of the energies af-terand before thecorrection. For theevent selection detailedin Section 5,thelarge-R jetmassresolution improvesby5% to10% afterthefirstcorrection(dependingontheleptonchannel),while thesecond correctionbringsan additionalimprovementinthe 2-leptonchannelofupto40%.
ThepresenceofneutrinosintheW H
→
νb
b and¯
Z H→
ννb
b¯
signatures can be inferred from a momentum imbalance in the transverse plane. The missingtransverse momentum Emiss
T is
re-constructedasthenegativevectorsumofthemomentaofleptons and small-R jets in the event plus a ‘soft term’ built from ad-ditional tracks associated with the primary vertex [93]. Small-R jetsused forthe EmissT reconstruction are required to have pT
>
20 GeV.ThemagnitudeofEmiss
T isreferredtoasEmissT .Tosuppress
non-collision and multijet backgrounds in the 0-lepton channel, an additional track-based missing transverse momentum estima-tor,Emiss
T, trk,isbuiltindependentlyasthenegativevectorsumofthe
transversemomentaofalltracksfromtheprimaryvertex. An overlap removal procedure is applied to avoid double-countingbetweenreconstructedleptons [9],includinghadronically decaying
τ
-leptons [94],andsmall-R jets [92].5. Eventselection
Eventsarecategorisedintothe0-,1- and2-leptonchannels de-pendingonthenumberofselectedelectronsandmuonstotarget the Z H
→
v vbb,¯
W H→
νb
b and¯
Z H→
bb signatures,¯
respec-tively.The 0-lepton selection is applied to events selected with an
EmissT trigger with thresholds varying from 70 to 110 GeV de-pendingonthedata-takingperiodtocopewithincreasingtrigger rates athigher instantaneous luminosities. In the 1-lepton chan-nel,single-electroneventsarerequiredtobetriggered byatleast oneofseveralunprescaledsingle-electrontriggers.The lowest ET
thresholdoftheseunprescaledtriggers varied withtimefrom24 to26 GeV.Eventsinthesingle-muonchannelweretriggeredusing thesame EmissT triggerasusedinthe0-leptonchannel.Giventhat muonsdonotenterintheonlineEmissT calculationandthat unin-strumentedregionsaffectthecoverageofthemuonspectrometer, the EmissT triggers translate into a requirementon the transverse momentum of the lepton and neutrino pair, pTν, which is more efficient in the analysis phase space than the single-muon trig-gers.Inthe 2-leptonchannel, thesame triggerstrategy asinthe 1-leptonchannel isadopted.Thedielectronselectionisappliedto eventstriggeredbyatleastoneoftheun-prescaledsingle-electron triggers.Thedimuonselectionisappliedtoeventstriggeredbyan
EmissT trigger.Alltriggersusedinthisanalysisarefullyefficientfor theeventsselectedusingtherequirementsdescribedbelow.
In all three channels, events are required to contain at least one large-R jet with pT
>
250 GeV and|
η
|
<
2.
0. To select theHiggs boson candidate, the leading pT large-R jet is chosen, at
leasttwoVR track-jetsare requiredtobematchedtoitby ghost-association,andthetwoleadingonesarerequiredtobeb-tagged.
This jet is referred to as the ‘Higgs-jet candidate’in the follow-ing.Toavoidtheambiguouscasesofconcentricjets,eventswhere theb-taggedVRtrack-jetsoverlapwithother VRtrack-jets, satis-fying
R
/
Rs<
1 (whereR corresponds to the distanceamong
anypairofVRtrack-jetsand Rs correspondstothesmallerradius
oftheconsideredpair),areremoved.Thereconstructedtransverse momentumpVT ofthevectorbosoncorrespondstoEmissT inthe 0-leptonchannel, tothemagnitudeofthe vectorsumof EmissT and the charged-lepton transverse momentum in the 1-lepton chan-nel, andto the transverse momentum of the 2-lepton systemin the2-leptonchannel.The pV
T isrequiredtobeabove 250 GeVin
allthreechannels.TheeventselectionisdetailedinTable2,with further explanations provided below for the non-straightforward selectioncriteria.
The multijet background in the 0-lepton channel originates mainly from jet energy mismeasurements. To reduce this back-groundtoa negligiblelevel,threededicated selectioncriteriaare applied. Events are removed if the missing transverse momen-tumis pointing towards the direction ofthe Higgs-jet candidate
Table 2
Eventselectionrequirementsfortheboosted
V H
,H→bb analysis ¯ channelsandsub-channels.Selection 0leptonchannel 1 lepton channel 2 leptons channel
e sub-channel μsub-channel e sub-channel μsub-channel
Trigger Emiss
T Single electron EmissT Single electron EmissT
Leptons 0 baseline leptons 1 signal lepton 2 baseline leptons among which
pT>27 GeV pT>25 GeV ≥1 signal lepton, pT>27 GeV
no second baseline lepton both leptons of the same flavour
- opposite sign muons
EmissT >250 GeV >50 GeV -
-pV
T pVT>250 GeV
Large-R jets at least one large-R jet, pT>250 GeV ,|η| <2.0
Track-jets at least two track-jets, pT>10 GeV ,|η| <2.5, matched to the leading large-R jet b-tagged jets leading two track-jets matched to the leading large-R must be b-tagged (MV2c10, 70%)
mJ >50 GeV min[ φ(Emiss T , small-R jets)] >30◦ - φ(Emiss T , Hcand) >120◦ - φ(Emiss T , EmissT, trk) <90◦ - y(V,Hcand) - | y(V,Hcand)| <1.4 m - 66 GeV<m<116 GeV Lepton pTimbalance - (pT1−p 2 T)/p Z T<0.8
(
φ (
EmissT , Hcand) >
120◦).Events are alsoremovedifthecalori-metric EmissT andthetrack EmissT, trkarefarapart(
φ (
EmissT,
EmissT, trk)
<
90◦). The EmissT is required to be isolated from any calorime-ter small-R jet with transverse momentum in excess of 70 GeV (min
[ φ(
EmissT , small-R jets)
]
>
30◦). In this case, only small-R jetsnotoverlappingwiththeHiggs-jetcandidatewithinR
=
1.
0 areconsidered.In the 1-lepton channel, the isolation requirements remove most of the non-prompt lepton background. An additional Emiss
T
requirementisapplied intheelectronsub-channeltoreduce this backgroundfurther.Inordertoreduceother backgrounds,suchas topandW
+
jetsproduction,afurtherselectionontherapidity dif-ference between the Higgs-jetcandidate andthe vector boson is applied(|
y(
V,
Hcand)
|
<
1.4).TheW -bosonrapidityisestimatedassumingthat EmissT isthepT oftheneutrinoandthelongitudinal
momentumoftheneutrinoisestimatedusingtheW -bosonmass constraint. Thismethodleads toaquadraticequationforthe lon-gitudinalmomentumoftheneutrino.Incaseoftworealsolutions: theretainedsolutionistheonethatminimisesthedifference be-tweenthelongitudinalboostoftheW bosonandtheHiggsboson. Incaseofnorealsolution,theimaginarypartissetto0.3
In the 2-lepton channel, where two same-flavour leptons are required (in the dimuon sub-channelthe two muons are further requiredtobeofoppositesign,inthedielectroncasethisselection is not applied dueto thecomparatively highercharge misidenti-fication),the rapiditydifference (
|
y(
V,
Hcand)
|
<
1.4)effectivelyreducesthemainZ
+
jetsbackground.Arequirementisimposedon theleptonpTimbalance((
pT1−
p2
T
)/
pTZ<
0.8),whichissensitiveto the Z boson polarisation [95].Since the Z bosonhasdifferent statesofpolarisationinthe Z H signalandtheZ
+
jetsbackground, thisselectionfurtherreducesthisbackground.Since the signal-to-background ratio increases for large Higgs boson transverse momenta [12,96], events are further split into two pV
T binswith250
<
pVT<
400 GeV andwithpVT≥
400 GeV. 3 ThisprocedureisequivalenttosettingthereconstructedW transverse
massto theW mass.
Theselectionefficiencyinthe0-,1- and2-leptonchannelsand two pTV bins ranges between approximately 6% and 16% for the
W H and Z H processes where the W and Z bosons decay
lep-tonicallyandtheHiggsbosondecaysinto apairofb-quarks.The analysisdoesnotexplicitlyselect
τ
-leptonsbuttheyareaccounted for in the case of leptonically decayingτ
-leptons in the 1- and 2-lepton channels andhadronically decayingτ
-leptons in the 0-leptonchanneliftheyaremisidentifiedasjets.As discussedin Section 1 the overlapsbetween theevent se-lectionspresentedhereinandthoseofRef. [15] arenonnegligible. In the 250 GeV
<
pTV<
400 GeV region, approximately 40% of thesignal events are selectedby both sets ofselections, andthe fractionofsignaleventsuniquelyselectedbythelarge-R jet anal-ysisvariesbetween5%and30%withincreasing pVT.Inthe pVT>
400 GeVregion, the overlapdecreases progressively toreach ap-proximately15%andtheuniquelarge-R jetanalysissignalevents increaseto75%ata pV
T ofaround700 GeV.
The tt process
¯
is a major background in the 0- and1-leptonchannels.Fortt events,
¯
theb-taggedtrack-jetsassociatedwiththe Higgs-jetcandidatearemainlyab- andac-jet(theformerfroma top-quarkdecayandthelatterfromthehadronicW bosondecay) andthereforethe second b-jet fromthe other top-quarkisoften expectedto be identified as an additional b-tagged track-jet not associatedwiththe Higgs-jetcandidate. Takingthisinto account, signalregions(SR)inthe0- and1-leptonchannelsaredefinedby vetoingonb-taggedtrack-jetsoutsidetheHiggs-jetcandidateand control regions (CR), enriched in tt events,¯
are builtfromevents whichfailthisveto.TheSRsandCRsareaccountedforinthesame wayinthefit,butCRsaredominatedbybackgroundsandareused toconstrainspecificbackgroundcomponents.Eventsinthe0- and 1-leptonchannelsarefurthercategorised depending on the number of small-R jets not matched to the Higgs-jetcandidate,i.e.with
R(Hcand,small-R jet)>1.0.Two
cat-egories are defined: a high-purity signal region (HP SR) with 0 small-R jets not matched to the Higgs-jet candidate and a
low-purity signalregion(LP SR)with
≥
1 small-R jets notmatchedtotheHiggs-jetcandidate.
Table 3
Summaryofthedefinitionoftheanalysisregions. SignalenrichedregionsaremarkedwiththelabelSR.Thereare regionswithrelativelylargesignalpurity(HPSR)andwithlowpurity(LPSR).Backgroundenrichedregionsaremarked withthelabelCR.Theshorthand“add”standsforadditionalsmall-R jets,i.e.numberofsmall-R jetsnotmatchedto theHiggs-jetcandidate.
Channel Categories
250<pV
T <400 GeV pVT≥400 GeV
0 add. b-track-jets ≥1 add.
b-track-jets
0 add. b-track-jets ≥1 add.
b-track-jets 0add. small-R jets ≥1 add. small-R jets 0add. small-R jets ≥1 add. small-R jets 0-lepton HP SR LP SR CR HP SR LP SR CR 1-lepton HP SR LP SR CR HP SR LP SR CR 2-lepton SR SR
6. Backgroundcompositionandestimation
ThebackgroundcontributionintheSRsisdifferentforeachof the three channels. In the 0-lepton channel, the dominant back-groundsources are Z
+
jets andtt events¯
withasignificant con-tribution from W+
jets and dibosonproduction.In the 1-lepton channel, the largest backgrounds are tt and¯
W+
jets produc-tionfollowedbythesingle-topbackground.Inthe2-lepton chan-nel, Z+
jets production isthe dominantbackgroundfollowedby the Z Z background. Contributionsfromt¯
t V andt¯
t H are negligi-ble. The multijet background,due to semileptonic heavy-flavour-hadron decays or misidentified jets, is found to be negligible in the0- and2-leptonchannelsaswellasinthe1-leptonmuon sub-channelafterapplyingtheeventselectionsdescribedinSection5, asconfirmedusingdata-driventechniques.Inthe1-leptonelectron sub-channelitscontributionisnotneglected.Allinitialbackground distributionshapespriortothefit(describedinSection8),except those for multijet, are estimated from the samples of simulated events.Themultijetshapeandnormalisationaredeterminedusing data.The W
/
Z+
jets simulated event samples are split into 6 cat-egories depending on the ‘truth’ labels of the track-jets ghost-associated to the Higgs-jet candidate: W/
Z+
bb, W/
Z+
bc, W/
Z+
bl, W/
Z+
cc, W/
Z+
cl and W/
Z+
ll; in this notationl referstoalight-flavourjet.4 The W
/
Z+
bb fractioncorrespondstoapproximately80%ofthetotalW
/
Z+
jetsbackground.This cat-egorisation is used in the uncertainties variations of the ratiosV
+
bc/
V+
bb, V+
bl/
V+
bb and V+
cc/
V+
bb to coverun-certainties on the flavour composition in V +jets production, see Section7.
In the statistical analysis described in Section 8, the compo-nentsW
/
Z+
bb,W/
Z+
bc,W/
Z+
bl andW/
Z+
cc aretreatedas a singlebackgroundcomponentdenoted by W/
Z +HF. The W +HFand Z +HF contributions,whichtogether constitute90%of V
+
jetsbackground,areestimatedseparately,each withitsown normali-sationfactordeterminedfromthefittodata.
The tt productionbackground arisesfromtopologieswith
de-cays of W bosons into
τ
-leptons which then decayhadronicallyinthe0-leptonchannel andfromW bosonsdecayingintoe
/
μ
in the 1-leptonchannel. Inthe 2-leptonchannel the tt contributionis muchsmaller. Forthe 0- and1-lepton channels, two indepen-dent normalisationfactors are considered andleft floatingin the fit,wheretheyareconstrainedbytheCRs.
Single-topproductioncontributestothe0- and1-lepton
chan-nelsandW t productionisthedominantprocess(s- andt-channel
processesamounttolessthan1%globally andlessthan5%ofthe single-topcontribution).
4 Whenlabellingjetsinthe V+jets backgroundsmodelling,the labellingof τ-jetsisomittedandthenegligibleτ-leptoncontributionisincludedwith light-flavourjets.
Thedibosonbackgroundprocessconsistsoffinal statesarising mostlyfrom W Z and Z Z events,wherea Z boson decaysintoa pairofb-quarks.Thisprocesshasatopologyverysimilartothatof thesignal,exhibitingapeakinmJatthemassofthehadronically
decayingvectorboson.Althoughitisasubdominantcontribution, itprovidesanimportantreferenceforvalidation.Itsnormalisation ismeasuredsimultaneouslywiththe V H signal.
In the 1-lepton channel, the multijet background originating from jets misidentified as leptons and/or due to semileptonic heavy-flavour-hadrondecayscannotbeneglected.SinceMC simu-lationsamplesarestatisticallylimitedandarenotexpectedto re-producethemultijetproductioninthiscornerofthephasespace, itisestimatedfromatemplatefitusingthedata.ThemJtemplates
intheelectron andmuonsub-channels aretakenfromdedicated CRsenrichedin multijetbackground,obtainedfromtheinversion ofthetight leptonisolation requirementsandtheremovalofthe
EmissT requirement,andaftersubtractionoftheotherbackgrounds. ThemultijetnormalisationsareestimatedintheSRsfromafitto the transversemass5 distribution separately for the electron and
muon sub-channels. The contribution of the multijetbackground is found to be negligible in the muon sub-channel. In the elec-tron sub-channelit is approximately 2% of the total background, withan uncertainty of55% estimated mainlyfrom thestatistical uncertaintyofthetransversemassfit.Thiscontributionandits as-sociateduncertaintyaretakenintoaccountinthesignalextraction fit.
7. Systematicuncertainties
Systematicuncertaintiescanhaveanimpactontheoverall sig-nal andbackground yields, on the shapesof thejet mass distri-butions, on the CRto SR extrapolations, andon the relative ac-ceptancesbetweenthe HPandLPSRsandbetweenthe pTV bins. Systematicuncertaintiesarediscussedherein forthreemain cate-gories:experimental,signalmodelling,andbackgroundmodelling.
7.1. Experimentalsystematicuncertainties
The uncertainties in the small-R jet energy scale and resolu-tionhave contributionsfrom in situ calibrationstudies,fromthe dependency on the pile-up activity and on the flavour compo-sition of the jets [76]. For large-R jets, the uncertainties in the energyandmassscales arebasedonacomparisonoftheratioof calorimeter-based totrack-based measurements in dijetdataand simulation,asdescribedinRef. [81]. Theimpactofthejet energy scaleandresolutionuncertaintiesonthe large-R jetmassare as-sessed by applying different calibration scales and smearings to
5 The transverse mass m
T of the W boson candidate in the event
is calculated using the lepton candidate and EmissT according to mT =
2p
the jet observablesin the simulation,accordingto the estimated uncertainties.Anabsoluteuncertaintyof2%isusedforthejet en-ergyresolutionwhilearelativeuncertaintyof20% isusedforthe jet massresolution,consistent withprevious studiesfortrimmed jets [97,98].
The b-tagging uncertainties are assessed from the calibration
data in various kinematic regions and separately for b-, c-, and light-flavourjets. The uncertainties are then decomposedineach of the flavour categories intoindependent components. An addi-tional uncertaintyis includedto account forthe extrapolation to jets with pT beyond the kinematic reach of the data calibration
(the thresholdsare 250 GeV,140 GeVand300 GeVforb-,c- and
light-flavourjets,respectively) [86,90,91].
Other experimental systematic uncertainties with a smaller impact are those in the lepton energy and momentum scales, in lepton reconstruction and identification efficiency, and in the efficiency of the triggers. An uncertainty associated with the modelling of pile-up in the simulation is included to cover the difference between the predicted and measured inelastic cross-sections [99].Theuncertaintiesintheenergyscaleandresolution ofthe small-R jetsandleptons are propagatedto thecalculation of EmissT , which also has additional uncertainties from the scale, resolutionandreconstructionefficiencyofthetracksusedto com-pute the soft term, along with the modelling of the underlying event [93].
7.2. Signalmodellingsystematicuncertainties
The systematic uncertainties that affect the modelling of the signal are derived closely following the procedure outlined in Refs. [11,16,92] andinRefs. [100,101] foruncertaintiesspecific to STXS. The systematicuncertainties in thecalculations ofthe V H
production cross-sectionsandthe H
→
bb branching¯
fraction are assigned following the recommendations ofthe LHC Higgs Cross Section Working Group [56,57,102–104]. Acceptance and shape systematicuncertaintiesarederivedtoaccountformissing higher-order QCDandEW corrections, forPDF+α
S uncertainties, andforvariations of thePS andUE models. Factorisationand renormali-sation scales are varied by factors of 0.5 and2. PDF-related un-certainties are derived following Ref. [38]. The effects of the un-certaintiesfrommissinghigher-orderEWcorrections,PDF+
α
SandQCD scalevariations onthejetmass shapearenegligible.The PS andUEuncertaintyisevaluated bycomparingthenominalsignal Powheg-Boxsamplesshoweredby Pythia8withalternative sam-plesshoweredby Herwig 7 [105].
7.3. Backgroundmodellingsystematicuncertainties
The principal additional modelling uncertainties for the back-grounds that were considered are the following: renormalisation andfactorisationscalevariationsbyfactorsof0.5and2forhigher order in QCD corrections of the matrix element of the process; mergingscalevariationsfrommulti-legsimulations; resummation scale orparton shower uncertainties;PDF uncertainties; and dif-ferenceswithalternativeMCgenerators. Theimpactofthese sys-tematicuncertaintiesintermsofnormalisation,shape,acceptance andextrapolationbetweenanalysisregions isthenestimatedand includedinthe fitmodel(describedinSection 8).Giventhat the analysisis basedonthe fitofthemJ variableonly, all shape
un-certaintiesareestimatedwithrespecttothisobservable.
The normalisations of the W
/
Z +HF backgrounds are free pa-rameters in the fit. They are determined thanks to the use of the jet mass distributions in SRs once tt is¯
constrained fromC R enriched in t
¯
t events. In addition to scale variations within Sherpa2.2.1, alternative samples foracceptance andshape varia-tions generatedwith MadGraph interfacedto Pythia8werecon-sidered.Finally,variationsintheV
+
bc/
V+
bb,V+
bl/
V+
bb andV
+
cc/
V+
bb ratiosareaccountedforindependentlyfortheW-andZ -bosonbackgrounds.
Fortop-quarkpair productionmodellinguncertainties, specific initial-state radiation (ISR) and final-state radiation (FSR) Pythia parametersareusedtoassesstherelatedsystematicuncertainties. In addition to the typical scale variations, alternative NLO sam-ples using the MadGraph5_aMC@NLO and Herwig7 generators wereconsidered.Thett normalisationisfreeinthefitandmainly constrained in the CRs for the 0- and 1-lepton channel. For the 2-lepton channel it isconstrained to its nominalpredicted value withanuncertaintyof20%.Duetotopdecaysnotfullycontained withinthelarge-R jet,therelativenumberofeventswhereexactly two andwhere three or more VR track-jets are ghost-associated tothelarge-R jetcan modifythelarge-R jetmasstemplate.This isaccountedforby an additional uncertaintyestimatedfromthe impact onthe tt background template of a 20% variation in this relativeratio.
The normalisations, acceptances and shapes of all single-top production processes are constrained to their predictions within the corresponding uncertainties. For the dominant W t channel,
ISR/FSR uncertainties as well as alternative generator samples, Herwig7 and Madgraph5_aMC@NLO, are considered. Since the
W t channelhasthesameflavourcompositionandasimilarshape
inthe0- and1-leptonchannels,themodellinguncertainties were studied in the 1-lepton channel and then propagated to the 0-lepton channel. An associated extrapolation uncertainty is taken intoaccount.
Toaccount forthe ambiguitiesin the interferencebetweentt
¯
and single-top production,an alternative sample generated with Powheg-Boxinterfacedto Pythia 8,usingthediagramsubtraction (DS)scheme,isused [68]. ThedifferencebetweentheDSandDR schemesforthe W t single-topproduction isaccountedforasan additionalsystematicuncertainty.
Fordibosonproduction,in additionto the scalevariations for acceptance, extrapolation and shape systematic uncertainties, al-ternative dibosonsampleswere generated using Powheg-Box in-terfacedto Pythia8andthedifferencewithrespecttothe Sherpa nominalsampleswasusedasanadditionaluncertainty.
8. Results
The results are obtained from a binned maximum-profile-likelihoodfittothedataofthemJdistribution,usingallthesignal
andcontrolregionsdefinedinSection5.Thefitisperformedusing the RooStats framework [106,107].SignalandbackgroundmJ
tem-platesaredeterminedfromMCsimulation(describedinSection3) in all cases except for the multijet background in the 1-lepton channel, which is extracted from the data as discussed in Sec-tion6.
Thelikelihoodfunction isconstructedfromtheproductofthe Poissonprobabilitiesofeachbinofthemassdistributionsand aux-iliarytermsusedtomodelsystematicuncertainties.Thelikelihood function isdescribed inmore detail in Ref. [92]. The parameters ofinterest(POI) arethe signalstrengths
μ
, multiplicationfactors thatscaletheexpectedSMHiggsbosonsignal,inoneormore sub-channels, or the V Z process.The signal strength parameters are extractedsimultaneouslywiththeoverall dibosonsignal strengthμ
bbV Z bymaximisingthelikelihood.
Systematicuncertaintiesaremodelledinthelikelihoodfunction by parameterised variations of the number of signal and back-ground events, and of the templates through nuisance parame-ters(NP). Systematic variations ofthe templates that are subject to large statisticalfluctuationsare smoothed, andsystematic un-certainties that have a negligible impact on the final results are pruned away region-by-region [108]. NPs corresponding to most
Fig. 1. The
m
Jpost-fitdistributionsin(a,b)the0-lepton,(c,d)1-leptonand(e,f)2-leptonsignalregionsfor2-b-taggedeventsfor(a,c,e)250 GeV<pVT<400 GeV and (b,d,f)p
VT≥400 GeV.Thelow-purityandhigh-puritycategoriesinthecaseofthe0-leptonand1-leptonchannelsaremergedinthisfigure.Thebackgroundcontributions afterthelikelihoodfitareshownasfilledhistograms.TheHiggsbosonsignal(mH=125 GeV)isshownasafilledhistogramontopofthefittedbackgroundsnormalised
tothesignalyieldextractedfromdata(μbb
V H=0.72),andunstackedasanunfilledhistogram,scaledbytheSMpredictiontimesafactoroftwo.Thesizeofthecombined
statisticalandsystematicuncertaintyforthesumofthefittedsignalandbackgroundisindicatedbythehatchedband.Thehighestbininthedistributionscontainsthe overflow.Theratioofthedatatothesumofthefittedsignalandbackgroundisshowninthelowerpanel.
Table 4
Factorsappliedtothenominalnormalisationsofthe
tt,
W+HF andZ
+HF backgrounds,asobtainedfromthe likelihoodfit.Theerrorsrepresentthecombined statisti-calandsystematicuncertainties.Process and category Normalisation factor tt 0-lepton 0.88±0.10 tt 1-lepton 0.83±0.09
W+HF 1.12±0.14
Z+HF 1.32±0.16
uncertainties discussed in Section 7 are constrained using Gaus-sianorlog-normalprobability densityfunctionsasauxiliaryterms inthelikelihood.Thenormalisationsofthelargestbackgrounds,t
¯
t(in the 0- and 1-lepton channels), W +HFand Z +HF, are left un-constrainedinthefit.Thebackgroundnormalisationfactorvalues fromthe fitcorrespond to 0
.
88±
0.
10 and0.
83±
0.
09 for tt,¯
in the0- and 1-leptonchannels,respectively; 1.
12±
0.
14 forW +HFand1
.
32±
0.
16 for Z +HFandarealsosummarisedinTable4.The fitmodelusesasinglenormalisationfactorforZ +HFand compat-ibleresultswerefoundwhenusingtwodifferentfactorsforthe 0-and2-lepton channels. Toaccountfor theuncertaintydueto the limitedsizeoftheMCsimulationsamples,anNPisusedforeach binofthetemplates [109].ThemJ distributionswithsignalstrengths,background
normal-isationsandallNPssetattheirbest-fitvalues,areshowninFig.1
forallthreechannels’SRsandinFig.2fortheCRs.Thelow-purity andhigh-puritycategoriesinthecaseofthe0-leptonand1-lepton channelsaremergedinFig.1.InallSRsandCRsagoodagreement betweenthedataandthepredictionisobserved.
ForaHiggs bosonmassof125 GeV,whenall leptonchannels arecombined,theobservedexcesswithrespecttothe background-only hypothesis has a significance of 2.1 standard deviations, to be compared withanexpectationof 2.7standarddeviations.The fitted
μ
bbV H valueis:
μ
bbV H=
0.
72−+00..3936=
0.
72−+00..2928(
stat.)
+−00..2622(
syst.).
In this result, the largest uncertainties are statistical and in-cludetheimpactfromthefloatingbackgroundnormalisations un-constrainedin the fit.The lattercomponentis subdominant.The impact of systematic uncertainties is almost asimportant as the totalstatisticaluncertainty.Thedominantsourceofsystematic un-certaintyisexperimentalandrelatedtothelarge-R jetcalibration, inparticular inthemJ resolution,amounting toan impactof
ap-proximately0.13on
μ
bbV H.Thesecondlargestsourceofsystematic
uncertaintyisthebackgroundmodelling,whichoverallhasan im-pact ofapproximately 0.10on the result. The limitedsize of the MC simulation sampleshas a non-negligible impactof 0.09. Sys-tematic uncertainties in the signal modelling have an impact of approximately 0.04, on par withuncertainties relatedto small-R jets. The breakdown of the systematic uncertainties in the mea-surementofthesignalstrengthisdisplayed inTable5.
ThemJdistributionisshowninFig.3(a)summedoverall
chan-nelsandsignalregions,weightedbytheirrespectivevaluesofthe ratio of the fitted Higgs boson signal to background yields and after subtraction of all backgrounds except for the W Z and Z Z
dibosonprocesses.
Fig.3(b)showstheresultsof:afitwithsixV H POIsmeasuring the individual signal strengths ineach of thethree channelsand
pV
T bins separately; a three V H POI fit measuring the combined
signal strengthsin eachchannel;atwo V H POIfit combiningall channelsinthetwo pVT binsseparately;andtheoverallsingle V H
POIcombination.
ForV Z productionthefittedsignalstrength
μ
bb V Z isμ
V Zbb=
0.
91+−00..2923=
0.
91±
0.
15(
stat.)
+−00..2417(
syst.),
Table 5
Breakdownofthe absolutecontributionstothe uncer-taintyinμbb
V H inclusivein
p
VT.Thesuminquadratureof the systematicuncertaintiesattachedtothecategories differsfromthetotalsystematicuncertaintydueto cor-relations.Thereportedvaluesrepresenttheaverage be-tweenthepositiveandnegativeuncertaintiesonμbbV H.
Source of uncertainty Avg. impact
Total 0.372 Statistical 0.283 Systematic 0.240 Experimental uncertainties Small-R jets 0.038 Large-R jets 0.133 Emiss T 0.007 Leptons 0.010 b-tagging b-jets 0.016 c-jets 0.011 light-flavour jets 0.008 extrapolation 0.004 Pile-up 0.001 Luminosity 0.013
Theoretical and modelling uncertainties
Signal 0.038
Backgrounds 0.100
→Z + jets 0.048
→W + jets 0.058
→t¯t 0.035
→Single top quark 0.027
→Diboson 0.032
→Multijet 0.009
MC statistical 0.092
in agreement with the SM prediction and the W±Z differential
cross-sectionmeasurementperformedbyATLASathightransverse momentum ofthe Z boson(pTZ
>
220 GeV)in thefully leptonic channel (W±Z→
ν
+
−) [110]. The simultaneous fit teststhe performance of the analysis on an irreducible background, the known V Z production, with a topology similar to the V H
sig-nal.Withallthreeleptonchannelscombined,asignificanceof5.4 standarddeviations isobserved forthe V Z process, comparedto anexpectationof5.7standarddeviations.Thecorrelationwiththe
μ
bbV H signal strength is approximately11%. The statistical
uncer-taintiesamounttoapproximately60%ofthetotaluncertainty.The dominantsourceofsystematicuncertaintyisthebackground mod-elling,which has an impact of approximately0.16 on the result. Thesourceofsystematicuncertaintyrelatedtothelarge-R jet re-constructionfollowsclosely,withanimpactofapproximately0.09 on
μ
bbV Z.
Thecross-sectionsinthe STXSframework are measured sepa-ratelyfor Z H and W H productionintwo pV
T regions,250 GeV
<
pV
T
<
400 GeV and pTV≥
400 GeV.TheanalysiscloselyfollowsthestrategyusedinRef. [11].Theexpectedsignaldistributionsand ac-ceptancetimesefficienciesforeachSTXSregionareestimatedfrom thesimulatedsignal samplesby selectingeventsusingthe gener-ator’s‘truth’ information,inparticular the‘truth’ pV
T,denoted by
pVT,t. Thelikelihood function usedis differentfromtheone used toextractthe
μ
bbV H and
μ
bbV Z resultspresentedbefore.Ithas
mul-tiplePOIs corresponding tothe cross-sectionsinthefour regions usedintheanalysis, multipliedbythe H
→
bb and¯
V→
leptons branching fractions. These four regions, i.e. Z H and W Hpro-duction and the two pVT,t bins, are known as reduced stage-1.2 regions in the STXS framework [111]. The sources of systematic uncertaintyareidenticalto thosedefinedinSection 7,exceptfor thetheoretical cross-section andbranching fractionuncertainties, which are not included in the likelihood function because they affect the signal strength measurements but not the STXS mea-surements.
Fig. 2. The
m
J post-fitdistributions inthet
t control ¯ regionfor (a,b)the 0-leptonchanneland the1-leptonchannelfor250 GeV<pTV<400 GeV and(c, d)the 0-leptonchannelandthe1-leptonchannelforp
VT>400 GeV.Thebackgroundcontributionsafterthelikelihoodfitareshownasfilledhistograms.TheHiggsbosonsignal (mH=125 GeV)isshownasafilledhistogramontopofthefittedbackgroundsnormalisedtothesignalyieldextractedfromdata(μbbV H=0.72),andunstackedasanunfilledhistogram,scaledbytheSMpredictiontimesafactorof2.Thesizeofthecombinedstatisticalandsystematicuncertaintyforthesumofthefittedsignaland backgroundisindicatedbythehatchedband.Thehighestbininthedistributionscontainstheoverflow.Theratioofthedatatothesumofthefittedsignalandbackground isshowninthelowerpanel.
Thecross-sectionsarenotconstrainedtobepositiveinthefit. Themeasuredreducedstage-1.2V H cross-sectiontimesbranching fraction
σ
×
B ineachSTXSbin,togetherwiththeSMpredictions are summarised in Fig. 4 where the red error bands correspond to thetheoretical uncertaintyofthefiducialcross-section predic-tion ineach bin.The measurements are alsoreported inTable 6andareinagreementwiththeSMpredictionsfromthesignalMC sample.Theprincipalsourcesofsystematicuncertaintiesare simi-lartothoseaffecting
μ
bbV H.
These results complement and extend those obtained by the small-R jetsanalysis [15] usingthesamedataset.The latter pro-videsa moreprecisemeasurementofthecross-section inthe in-clusive pVT
>
250 GeVregion.Thiscanbe attributedtothelarger acceptance atlower pVT value, the usage ofmore precisephysics
objects calibration and to the use of multivariate analysis tech-niques.Theresultsobtainedbythetwoanalysesinthisregionare compatiblewithinonestandarddeviation.
9. ConstraintsonanomalousHiggsbosoninteractions
The STXSresults presented inSection 8are interpreted in an effectivefield theoryapproach wherethe scaleofnew physicsis significantly largerthan the SM electroweak scale soas toaffect themeasuredobservablesattheLHConlythrougheffective inter-actionsamongSMparticles.
In thisSMEFT approach, the SM Lagrangian is extended with higher-dimensionaloperatorsthatcapturethelow-energylimit ef-fectsofafundamental ultraviolettheory,withouta priori knowl-edgeofthistheory [18]
L
SMEFT=
L
SM+
d 1d−4 i c(id)
O
(d) i,
where
O
(id)aredimension-d operatorsandc(id)arethe correspond-ing numerical coefficients called Wilson coefficients. All Wilson coefficients are assumed real. In the SM, all Wilson coefficientsFig. 3. (a)
m
JdistributionindataaftersubtractionofallbackgroundsexceptfortheW Z and Z Z diboson
processes.Thecontributionsfromallleptonchannelsandsignal regionsaresummedandweightedbytheirrespectivevaluesoftheratiooffittedHiggsbosonsignalandbackgroundyields.Theexpectedcontributionoftheassociated W H and Z H production ofaSMHiggsbosonwithm
H=125 GeVisshownscaledbythemeasuredcombinedsignalstrength(μbbV H=0.72).Thedibosoncontributionisnormalisedtoitsbest-fitvalueofμbb
V Z=0.91.Thesizeofthecombinedstatisticalandsystematicuncertaintyisindicatedbythehatchedband.Thiserrorbandiscomputed
fromafullsignal-plus-backgroundfitincludingallthesystematicuncertaintiesdefinedinSection7,exceptforthe V H/V Z experimental andtheoryuncertainties.(b) FittedvaluesoftheHiggsbosonsignalstrengthparameter,μbb
V H,for
m
H=125 GeVforthe0-,1- and2-leptonchannelsindifferentp
VT regionsseparatelyandforvarious combinations.Table 6
Measuredandpredicted
V H
,V→leptons reducedstage-1.2simplifiedtemplatecrosssectionstimestheH
→bb¯ andV
→leptonsbranchingfractionswithcorrespondinguncertainties.AllpossibleZ decays
intoneutraland chargedleptonsareconsidered.STXS region(|yH| <2.5,H→bb¯) SM prediction [fb] Result (Tot.) (Stat.) (Syst.) [fb]
W→ ν;pWT,t∈ [250,400]GeV 5.83±0.26 3.3 +4 .8 −4.6 +3 .6 −3.4 +3 .2 −3.0 W→ ν;pWT,t∈ [400,∞]GeV 1.25±0.06 2.1 +1 .2 −1.1 +1 .0 −0.9 +0 .6 −0.5 Z→ ,νν; pZT,t∈ [250,400]GeV 4.12±0.45 1.4 +3 .1 −2.9 +2 .4 −2.3 +1 .9 −1.7 Z→ ,νν; pZT,t∈ [400,∞]GeV 0.72±0.05 0.2 +0 .7 −0.6 +0 .6 −0.5 +0 .3 −0.3
Fig. 4. Measured
V H reduced
stage-1.2simplifiedtemplatecross-sectionstimesthe H→bb and V¯ →leptonsbranchingfractions.are zero.The scale of newphysics
is a free parameter set to 1 TeV.Inthisanalysis,theWarsawbasis [112] ofdimensiond
=
6 operatorsisused,takingintoaccountonlythelepton- and baryon-number-conserving ones. Furthermore, it only considers the CP-eventermsrespectingaU(
3)
5 flavoursymmetry,whichaffectthepp
→
V(
→
leptons)
H(
→
bb)
process [113].The operators affect-ingthesignalprocessesarelistedinTable7[114].The Wilson coefficients are used to parameterise the STXS andtheHiggsbosondecayrates [114] fromleading-order predic-tions [113] andcanbeconstrainedusingtheSTXSmeasurements presented in Section 8. The parameterisation of the STXS takes
Table 7
Wilsoncoefficientsandtheircorrespondingdimension-6 operatorsintheWarsawformulationconsideredinthis analysis [112,114]. Coefficient Operator cH (H†H)(H†H) cH D D (H†DμH)∗(H†DμH) cdH (H†H)(qpdrH) cH W H†H WμνI WIμν cH B H†H BμνBμν cH W B H†τIH WμνI Bμν c(Hl1) H†i ←→ DμH(lpγμlr) c(Hl3) H†i←→DI μH(lpτIγμlr) c(He1) H†i ←→ DμH(epγμer) c(Hq1) H†i←→DμH(qpγμqr) c(Hq3) H†i←→DI μH(qpτIγμqr) cHu H†i←→DμH(upγμur) cHd H†i←→DμH(dpγμdr) cll (lpγμlr)(lsγμlt)
intoaccountthelineartermsoriginatingfromtheinterference be-tween SM andnon-SMamplitudes aswell asthe quadraticones from the squared non-SM amplitudes. The former are of order 1