Measurement of the Higgs boson mass in the H -> ZZ* -> 4l and H -> gamma gamma channels with root s=13 TeV pp collisions using the ATLAS detector

(1)

Contents lists available atScienceDirect

Physics

Letters

B

www.elsevier.com/locate/physletb

Measurement

of

the

Higgs

boson

mass

in

the

H

→

Z Z

∗

→

4 and

H

→

γ γ

channels

with

√

s

=

13 TeV

pp collisions

using

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

Articlehistory: Received4June2018

Receivedinrevisedform20July2018 Accepted27July2018

Availableonline2August2018 Editor: M. Doser

The mass of the Higgs boson is measured in the H→Z Z∗→4and in the H→

γ γ

decay channels with 36.1 fb−1 _of_{proton–proton}_collision_data_from_the_Large_Hadron_Collider_at_a_{centre-of-mass}

energy of 13 TeV recorded by the ATLAS detector in 2015 and 2016. The measured value in the H→Z Z∗→4channel is mZ Z∗

H =124.79 ±0.37 GeV, while the measured value in the H→

γ γ

channel is mγ γ_H =124.93 ±0.40 GeV. Combining these results with the ATLAS measurement based on 7 and 8 TeV proton–proton collision data yields a Higgs boson mass of mH=124.97 ±0.24 GeV.

1. Introduction

The observationof a Higgs boson, H ,by the ATLAS andCMS experiments [1,2] with the Large Hadron Collider (LHC) Run 1 proton–proton (pp) collision data at centre-of-mass energies of

√

s

=

7 and 8 TeV was a major step towards understanding the mechanism of electroweak (EW) symmetry breaking [3–5]. The massoftheHiggsbosonwasmeasuredtobe125

.

09

±

0

.

24 GeV [6] basedonthecombinedRun 1datasamplesoftheATLASandCMS Collaborations, who also reportedindividual mass measurements inRefs. [7,8].Recently,theCMSCollaborationmeasuredtheHiggs boson mass in the H

→

Z Z∗

→

4

channel using 35.9 fb−1 _of

13 TeV pp collisiondata [9]. The measured value of themass is 125

.

26

±

0

.

21 GeV.

ThisLetter presentsa measurement ofthe Higgs bosonmass,

mH,with36.1 fb−1 of

√

s

=

13 TeV pp collisiondatarecordedwith

theATLASdetector.Themeasurementisderivedfromacombined ﬁtto the four-leptonand diphotoninvariant mass spectra inthe decaychannelsH

→

Z Z∗

→

4

(

=

e

,

μ

)andH

→

γ γ

.A combi-nationwiththeATLASRun 1dataisalsopresented.

2. ATLASdetector

TheATLASexperiment [10] attheLHCisamulti-purpose par-ticledetectorwithnearly 4

π

coverage insolid angle.1 It consists

_E-mail_address:_atlas_{.publications}_@cern_.ch_.

1 _ATLAS_uses_a_right-handed_coordinate_system_with_its_origin_at_the _nominal

interactionpoint(IP)inthecentreofthedetectorandthez-axisalongthebeam pipe.Thex-axispointsfromtheIPtothecentreoftheLHCring,andthe y-axis

ofan inner trackingdetector(ID)surrounded bya 2 T supercon-ductingsolenoid,electromagnetic(EM)andhadroniccalorimeters, and a muon spectrometer (MS) incorporating three large super-conductingtoroidalmagnets.TheIDprovidestrackingforcharged particlesfor

|

η

|

<

2

.

5.Thecalorimetersystemcovers the pseudo-rapidityrange

|

η

|

<

4

.

9.Itselectromagneticpartissegmentedinto threeshower-depthlayersfor

|

η

|

<

2

.

5 andincludesapresampler for

|

η

|

<

1

.

8. The MS includes high-precision tracking chambers (

|

η

|

<

2

.

7) andfasttriggerchambers(

|

η

|

<

2

.

4). Onlineevent se-lectionisperformedbya ﬁrst-leveltriggerwithamaximumrate of 100 kHz, implemented in custom electronics, followed by a software-basedhigh-leveltriggerwithamaximumrateof1kHz. 3. Dataandsimulatedsamples

Thismeasurementuses datafrom pp collisionswitha centre-of-massenergy of 13 TeV collected during 2015 and2016 using single-lepton,dilepton,trileptonanddiphotontriggers,withlooser identiﬁcation, isolation and transverse momentum (pT)

require-ments than those applied oﬄine.The combined eﬃciencyof the lepton triggers is about 98% for the H

→

Z Z∗

→

4

events (as-sumingmH

=

125 GeV)passingtheoﬄineselection.Thediphoton

triggereﬃciencyis higherthan99% forselected H

→

γ γ

events (assumingmH

=

125 GeV).Aftertriggeranddata-quality

require-ments, theintegratedluminosity ofthedatasample is 36.1 fb−1_.

pointsupwards.Cylindricalcoordinates(r,φ)areusedinthetransverseplane,φ

beingtheazimuthalanglearoundthez-axis.Thepseudorapidityisdeﬁnedinterms ofthepolarangleθasη= − ln tan(θ/2).Angulardistanceismeasuredinunitsof

R≡( η)2_{+ ( φ)}2_. https://doi.org/10.1016/j.physletb.2018.07.050

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Themeannumberofproton–protoninteractionsperbunch cross-ing (integrated luminosity) is14 (3.2 fb−1) inthe 2015 dataset and25(32.9 fb−1)inthe2016dataset.

MonteCarlo(MC) simulationis usedinthe analysisto model thedetectorresponseforsignalandbackgroundprocesses.Forthe

H

→

Z Z∗

→

4

measurement,adetailedlistanddescriptionofthe MC-simulatedsamplesused canbe foundinRef. [11] and onlya few differencesspeciﬁcto themass analysisarementioned here. Forthegluon–gluonfusion (ggF)signal,theNNLOPS sample gen-erated atnext-to-next-to-leading order(NNLO) in QCD [12] with

mH

=

123

,

125

,

126GeV and thePDF4LHC NLO parton

distribu-tion function (PDF) set [13] wasused.Additional samples gener-atedatdifferentmH values(120,122,124,125,126,128,130 GeV)

atnext-to-leadingorder(NLO)were alsoused.TheNLO ggF sim-ulation was performed with Powheg-Box v2 [14] interfaced to Pythia_{8 [}₁₅_{] for}_parton_showering_and_{hadronisation,}_and_to Evt-Gen[16] forthesimulationofb-hadrondecays.TheCT10NLO [17] PDF setwas usedfor thehard process andthe CTEQ6L1 [18] set forthepartonshower.Thenon-perturbativeeffectsweremodelled usingtheAZNLOsetoftunedparameters [19].

The Z Z∗ continuum backgroundfromquark–antiquark annihi-lation was modelled at NLO in QCD using Powheg-Box v2 and interfacedto Pythia 8forpartonshoweringandhadronisation,and to EvtGen for b-hadrondecays.The PDF set usedis thesame as for the NLO ggF signal. NNLO QCD [20,21] and NLO EW correc-tions [22,23] wereapplied asa functionof theinvariant mass of the Z Z∗ system(mZ Z∗).

FortheH

→

γ γ

measurement,thesameH

→

γ γ

signal (gen-eratedformH

=

125 GeV)andbackgroundsimulatedeventsused

for the measurements of the Higgs boson couplings andﬁducial cross-sections inthe diphoton ﬁnal state [24] were used. In ad-dition,signal sampleswithalternative mH values(110, 122,123,

124,126,127, 130,140 GeV) wereproduced,withthesame gen-eratorsand settings asthe mH

=

125 GeV samples, but only for

thefourHiggsbosonproductionmodeswithlargestcross-section: gluon–gluonfusion,vector–bosonfusion(VBF),andassociated pro-ductionwith avector boson V

=

W

,

Z

(

V H

)

, forqq

¯

→

V H and gg

→

Z H . For rarer processes, such as associated production of theHiggsbosonwithatop-quarkpair(tt H )

¯

orasingletop-quark (t H ), contributingto lessthan 2% ofthe total cross-section,only samplesatmH

=

125 GeV wereused.

Except for the

γ γ

background sample, whose modelling re-quiresalargeMCsample obtainedthroughafastparametric sim-ulationofthecalorimeterresponse [25], thegeneratedeventsfor allprocesseswerepassedthrougha Geant4 [26] simulationofthe responseof theATLAS detector [25].Forboth detectoremulation methods,eventswere reconstructed withthe samealgorithms as thedata.Additional proton–protoninteractions (pile-up)were in-cludedinboththeparametricandthe Geant4simulations, match-ingtheaveragenumberofinteractionsperLHCbunchcrossingto thespectrumobservedinthedata.

TheStandardModel(SM)expectationsfortheHiggsboson pro-ductioncross-sectiontimesbranchingratio,inthevarious produc-tionmodesandﬁnalstatesunderstudyandateachvalue ofmH,

were taken from Refs. [27–30] and used to normalise the simu-latedsamples,asdescribedinRefs. [11,24].

4. Muonreconstruction,identiﬁcationandcalibration

Muon trackreconstructionis ﬁrstperformedindependentlyin the ID and the MS. Hit information from the individual subde-tectors is then used in a combined muon reconstruction, which includesinformationfromthecalorimeters.

Correctionstothereconstructedmomentumare appliedin or-der to matchthe simulation to data precisely. These corrections

to thesimulatedmomentumresolutionandmomentumscaleare parameterisedasapowerexpansioninthemuonpT,witheach

co-eﬃcientmeasuredseparatelyfortheIDandMS,asafunctionof

η

and

φ

,fromlargedatasamplesof J

/ψ

→

μ

+

μ

−and Z

→

μ

+

μ

−

decays. Thescale correctionsrange from0

.

1% to 0

.

5% forthe pT

ofmuonsoriginatingfrom J

/ψ

→

μ

+

μ

− and Z

→

μ

+

μ

− decays andaccountforinaccuratemeasurementoftheenergylostinthe traversedmaterial,localmagneticﬁeldinaccuraciesand geometri-caldistortions.Thecorrectionstothemuonmomentumresolution formuonsfrom J

/ψ

→

μ

+

μ

−andZ

→

μ

+

μ

−areatthepercent level. After detectoralignment, there are residual local misalign-ments that bias the muon tracksagitta, leaving thetrack

χ

2

in-variant [31,32],andintroduceasmallcharge-dependentresolution degradation. Thebias inthemeasured momentum ofeachmuon is corrected by an iterative procedure derived from Z

→

μ

+

μ

−

decaysandcheckedagainstthe E

/

p ratiomeasuredin Z

→

e+e−

decays. The residual effectafter correction is reduced to theper mille levelat thescale ofthe Z boson mass.Thiscorrection im-proves the resolution of the dimuon invariant mass in Z boson

decaysby1%to5%,depending on

η

and

φ

ofthemuon.The sys-tematicuncertaintyassociatedwiththiscorrectionisestimatedfor each muonusingsimulationandisfoundtobe about0

.

4

×

10−3 fortheaveragemomentumofmuonsfrom Z

→

μ

+

μ

− decays.

For muons from Z

→

μ

+

μ

− decays, with momenta ofabout 45 GeV,themomentumscaleisdeterminedtoaprecisionof0

.

05% for muonswith

|

η

|

<

2,and about0

.

2% formuonswith

|

η

|

≥

2. Similarly, the resolutionis known with a precision ranging from 1% to2%formuonswith

|

η

|

<

2 andaround10%formuonswith

|

η

|

≥

2 [33].Boththemomentumscaleandmomentumresolution uncertaintiesinthecorrectionstosimulationaretakenasfully cor-relatedbetweentheRun1andRun2measurements.

5. Photonandelectronreconstruction,identiﬁcationand calibration

Photon and electron candidates are reconstructed from clus-ters of electromagnetic calorimeter cells [34]. Clusters without a matchingtrackorreconstructedconversionvertexintheinner de-tector areclassiﬁedasunconvertedphotons.Those witha match-ingreconstructedconversionvertexoramatchingtrack,consistent with originatingfroma photon conversion, are classiﬁedas con-verted photons [35]. Clusters matched to a trackconsistent with originatingfroman electron(based on transitionradiation inthe ID)produced inthe beaminteractionregion areconsidered elec-troncandidates.

The energymeasurement forreconstructed electronsand pho-tonsis performedby summingthe energiesmeasured inthe EM calorimetercellsbelongingtothecandidatecluster.Theenergyis measured fromaclustersize of

η

× φ =

0

.

075

×

0

.

175 inthe barrel region of the calorimeter and

η

× φ =

0

.

125

×

0

.

125 in the calorimeter endcaps. The procedure for the energy mea-surement of electrons and photons closely follows that used in Run 1 [36],withupdatestoreﬂectthe2015and2016data-taking conditions:

•

Thedifferentlayersoftheelectromagneticcalorimeterare in-tercalibrated by applying methods similar tothose described in Ref. [36]. The ﬁrst and second calorimeter layers are in-tercalibratedusingtheenergydepositedbymuonsfrom Z

→

μ

+

μ

−decays,withatypicaluncertaintyof0.7%to1.5%(1.5% to 2.5%) as a function of

η

in the barrel (endcap) calorime-ter, for

|

η

|

<

2

.

4. This uncertaintyis added in quadrature to the uncertainty in the modelling of the muon ionisation in thesimulation(1%to1.5%depending on

η

).Theenergyscale ofthe presamplerisestimatedusingelectrons from Z boson

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decays,aftercorrectingthesimulationonthebasisofthe cor-relations between the amount of detector material and the ratio ofthe energies depositedin theﬁrst andsecond layers of thecalorimeter. The uncertaintyin thepresamplerenergy scalevariesbetween1.5%and3%dependingon

η

.

•

The clusterenergyiscorrectedforenergylossintheinactive materialsinfrontofthecalorimeter,thefractionofenergy de-posited outsidethearea ofthe clusterin the

η

–

φ

plane, the amountofenergylostbehindtheelectromagneticcalorimeter, and toaccount forthe variation ofthe energyresponse asa functionoftheimpactpointinthecalorimeter.Thecalibration coeﬃcientsusedtoapplythesecorrectionsareobtainedfrom adetailedsimulationofthedetectorresponsetoelectronsand photons,andareoptimisedwithaboosteddecisiontree(BDT). Thealgorithm,describedinRef. [37],hasbeentrainedon sim-ulatedsamplescorrespondingtothedata-takingconditionsof 2015and2016.Theresponseiscalibratedseparatelyfor elec-troncandidates,convertedphotoncandidatesandunconverted photon candidates. In data,small corrections are applied for the

φ

-dependent energy loss in the gaps between the bar-rel calorimeter modules (corrections up to 2%, in about 5% ofthecalorimeteracceptance)andforinhomogeneitiesdueto sectorsoperatedatnon-nominalhighvoltage(corrections be-tween1%and7%,inabout2%ofthecalorimeteracceptance).

•

Theglobalcalorimeterenergyscaleisdeterminedinsituwith a largesample of Z

→

e+e−eventsselected inthe2015and 2016datasets.The energyresponseindataandsimulationis equalisedbyapplying

η

-dependentcorrectionfactorstomatch theinvariant massdistributions ofZ

→

e+e−events.The un-certainty intheseenergyscalecorrection factorsranges from 0.02%to0.1%asafunctionof

η

,exceptforthebarrel–endcap transition region (1

.

37

<

|

η

|

<

1

.

52), where it reaches a few permille.Inthisprocedure,thesimulatedwidthofthe recon-structed Z boson mass distribution ismatched to the width observed indata by adding in the simulation a contribution totheconstanttermc oftheelectronenergyresolution, σE

E

=

a

√

E

⊕

b

E

⊕

c.This constant termvariesbetween 0.7%and 2%

for

|

η

|

<

2

.

4 withanuncertaintyof0.03%–0.3%,exceptforthe barrel–endcap transition region, where the constant term is slightlyhigher(2.5%–2.9%)withanuncertaintyreaching0.6%. Themainsourcesofsystematicuncertaintiesinthecalibration procedurediscussedinRef. [36] havebeenrevisited.Thesesources include uncertainties in the method used to extract the energy scalecorrectionfactors,aswellasuncertaintiesduetothe extrap-olationoftheenergyscalefromZ

→

e+e−eventstophotons,and alsoto electrons withenergies differentfrom those produced in

Z

→

e+e− decays. The latter arise from the uncertainties in the linearityoftheresponseduetotherelativecalibrationofthe dif-ferent gains used in the calorimeter readout, in the knowledge ofthe materialin front ofthecalorimeter (insideandoutsideof theID,referredtoasIDandnon-IDmaterialinthefollowing),in theintercalibrationofthedifferentcalorimeterlayers,inthe mod-elling of the lateral shower shapes and in the reconstruction of photon conversions. The total calibrationuncertainty forphotons withtransverseenergy(ET)around60 GeV is0.2%–0.3%inthe

bar-reland0.45%–0.8%intheendcap. Theseuncertaintiesarecloseto thosequotedinRef. [36],buttypicallyabout10%larger.Thesmall increaseintheuncertaintyarisesmostlyfromalargeruncertainty intherelative calibrationoftheﬁrst andsecondcalorimeter lay-erswithmuonsbecauseofaworseratioofsignaltopile-upnoise inRun 2 data. In the caseof electrons with ET around 40 GeV,

the total uncertainty ranges between 0.03% and0.2% inmost of thedetectoracceptance.Forelectrons withET around10 GeV the

uncertaintyrangesbetween0.3%and0.8%.

The accuracy of the energy calibration for low-energy elec-trons (5–20 GeV) is checked by computingresidual energy cali-bration corrections(after applyingthe correctionsextractedfrom theZ

→

e+e−sample)foranindependentsampleof J

/ψ

→

e+e−

events.Theseresidualcorrectionfactorsarefoundtobe compati-blewithonewithinuncertainties.Asimilarcheckisperformedby computingresidualcorrectionsforphotonsinasampleofradiative

Z bosondecays.Theyarefoundtobecompatiblewithonewithin uncertainties which are givenby the combinationof the statisti-caluncertaintyoftheradiative Z bosondecayssample andofthe systematicuncertaintyfromtheextrapolationofthe energyscale fromelectronstophotons.

Systematic uncertainties in the calorimeter energy resolution arise from uncertainties in the modelling of the sampling term

a

/

√

E andin the measurementof the constant termin Z boson

decays,intheamountofmaterialinfrontofthecalorimeter,which affectselectrons andphotonsdifferently, andinthe modellingof thecontributiontotheresolutionfromﬂuctuationsinthepile-up fromadditionalproton–protoninteractions inthesame or neigh-bouringbunchcrossings.The uncertaintyoftheenergyresolution forelectrons andphotonswithtransverseenergybetween30and 60 GeV variesbetween5%and10%.

The identiﬁcationof photonsand the rejectionof background fromhadronsisbasedprimarilyonshowershapesinthe calorime-ter. The two levels ofselection, looseand tight, are described in Ref. [35].Tofurtherreducethebackgroundfromjets,two comple-mentaryisolationselection criteriaare used,basedontopological clustersofenergydepositsinthecalorimeterandonreconstructed tracksinadirectionclosetothat ofthe photoncandidate,as de-scribedinRef. [24].

Electronsare identiﬁed usingalikelihood-based method com-bining informationfrom theelectromagnetic calorimeterandthe ID. As in the case of photons, electrons are required to be iso-lated using both the calorimeter-based and track-based isolation variablesasdescribedinRef. [38].

6. Statisticalmethods

The mass measurement is based on the maximisation of the proﬁlelikelihoodratio [39,40]

(

mH

)

=

L

mH

, ˆˆ

θ (

mH

)

L

mH

ˆ

, ˆ

θ

,

wherethe vectors

ˆθ

andm

ˆ

H denotetheunconditional-maximum

likelihood estimates ofthe parameters ofthe likelihood function

L,while

ˆˆθ

istheconditionalmaximum-likelihoodestimate ofthe parameters

θ

for a ﬁxed value of the parameter mH. Systematic

uncertainties and their correlations are modelled by introducing nuisanceparameters

θ

describedbylikelihoodfunctionsassociated withtheestimateofthecorrespondingeffect [6].

ThestatisticaluncertaintyofmH isestimatedbyﬁxing all

nui-sanceparameterstotheirbest-ﬁtvalues,allremainingparameters are thus left unconstrained. This approach yields a lower bound onthestatisticaluncertainty,whenthecombinationofthe differ-ent event categoriesdiscussed in the next sections is performed neglecting the differentimpact ofthesystematic uncertainties in eachcategory.Theupperboundonthetotalsystematicuncertainty isestimatedbysubtractinginquadraturethestatisticaluncertainty fromthetotaluncertainty.

Alternatively, the decomposition of the uncertainty into sta-tistical and systematiccomponents is performed using the BLUE method [41–43].Thetwoapproachesmayleadtodifferentresults from the decomposition of the uncertainty for a combination of

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measurementswithsigniﬁcantanduncorrelatedsystematic uncer-tainties.

7. MassmeasurementintheH

→

Z Z∗

→

4

channel

7.1. Eventselection

Events are required to contain at least four isolated leptons (

=

e

,

μ

) that emergefroma commonvertex,formtwo pairs of oppositelychargedsame-ﬂavourleptons.Electronsarerequiredto be within thefull pseudorapidity rangeofthe inner tracking de-tector (

|

η

|

<

2

.

47) andhavetransverseenergy ET

>

7 GeV, while

muonsarerequiredto be withinthe pseudorapidityrangeofthe muon spectrometer (

|

η

|

<

2

.

7) and have transverse momentum

pT

>

5 GeV.The threehigher-pT (ET) leptons ineach quadruplet

are required to pass thresholds of 20, 15, and 10 GeV, respec-tively.A detaileddescriptionof theeventselection can be found inRefs. [11,44].

Theleptonpairwithan invariantmassclosest tothe Z boson

massineachquadrupletisreferredtoastheleadingdileptonpair, while the remaining pair is referred to as the subleading dilep-ton pair.The selectedeventsare split accordingtothe ﬂavour of the leading and subleading pairs; ordered according to the ex-pected selection eﬃciency, they are 4

μ

,2e2

μ

,2

μ

2e, 4e. Recon-structedphoton candidatespassing ﬁnal-stateradiationselections aresearchedforinall theevents [45].Suchphotonsarefound in 4% of the eventsand their energy is includedin the mass com-putation.Inaddition,akinematicﬁtisperformedtoconstrainthe invariant mass of the leading lepton pair to the Z boson mass, improvingthem4 resolutionbyabout15% [7]. Theimprovement brought by the correction of the local tracker misalignments, as discussedinSection 4,isatthepercent levelforthem4 resolu-tionofsignal events.Aftereventselection,them4 resolutionfor thesignal(atmH

=

125 GeV),estimatedwithaGaussianﬁtaround

the peak, is expected to be about 1.6, 1.8, 2.2 and 2

.

4 GeV for the4

μ

,2e2

μ

,2

μ

2e and 4e channelsrespectively.Intheﬁtrange of 110

<

m4

<

135 GeV,123 candidateevents are observed.The yieldisinagreementwithanexpectationof107

±

6 events,53%of whichareexpectedtobefromthesignal,assumingmH

=

125 GeV.

The dominantcontributionto thebackground isnon-resonant

Z Z∗ production(about84% ofthetotalbackgroundyield).Events withhadrons, orhadron decayproducts, misidentiﬁedasprompt leptonsalsocontribute (about15%).Eventsoriginatingfromt

¯

t+ Z , Z Z Z , W Z Z , and W W Z production are estimated to contribute lessthan 1% of the total background.The residual combinatorial background,originating fromevents with additionalprompt lep-tons,wasfoundtobenegligiblysmall [44].

Theprecisionofthemassmeasurementisfurtherimprovedby categorisingeventswithamultivariatediscriminantwhich distin-guishesthesignalfromtheZ Z∗background.TheBDTdescribedin Ref. [7],basedonthesameinputvariables,istrainedonsimulated signaleventswithdifferentmassvaluessimultaneously (124,125 and126 GeV)and Z Z∗ backgroundeventsthat passtheevent se-lection. For each ﬁnal state, four equal-size exclusive bins inthe BDT response are used. This improves the precision of the mH

measurementinthe4

decaychannelbyabout6%.

7.2. Signalandbackgroundmodel

Theinvariantmassineachcategoryisdescribedbythesumof asignalandabackgrounddistribution.

Non-resonant Z Z∗ production is estimated using simulation normalisedto themostaccurate predictions andvalidatedinthe sidebands of the selected 4

mass range. Smaller contributions tothebackgroundfromtt+ Z ,

¯

Z Z Z , W Z Z and W W Z production

are alsoestimated usingsimulationwhile thecontributions from

Z +jets, W Z , and t

¯

t production where one or more hadrons, or hadron decay products, are misidentiﬁed as a prompt lepton are estimatedfromdatausingminimalinput fromsimulation follow-ing the methodologydescribed in Ref. [11]. Foreach contribution to the background, the probability density function (pdf) is esti-matedwiththekerneldensityestimation.

For the determination of the signal distribution, an approach based on the event-by-event response of the detector is em-ployed. The measured m4 signal distribution is modelledas the convolution of arelativistic Breit–Wignerdistribution, of4

.

1MeV width [27–30] and a peak at mH, with a four-lepton invariant

mass response distributionwhich isderived event-by-eventfrom the expectedresponse distributionsoftheindividual leptons. The lepton energy responsedistributions are derived fromsimulation asafunctionoftheleptonenergyanddetectorregion.Thelepton energy response is modelled as a weighted sum of three Gaus-sian distributions. Foran observed event, them4 pdf isderived from the convolution of the response distributions of the four measured leptons. Thedirect convolutionofthe fourleptons dis-tributions, leading to34

=

81 Gaussiandistributions,is simplified to a weighted sum of four Gaussian pdfs following an iterative mergingprocedureasperformedwiththeGaussian-sumfilter pro-cedure [46,47]. Anadditional correctionis appliedto remove the residualdifferenceswhicharise fromthe correlationbetweenthe lepton energy measurements introduced by the kinematic con-strainedfitontheleadingdileptonpairandtheBDTcategorisation ofevents.These arecorrected bya fitofscaling modifiersofthe reducedresponseparameters tothesimulatedfour-lepton resolu-tion.Thesemodifiersareabout0

.

1% forthemeansandupto10% forthewidthsoftheGaussiansofthereducedresponse.

Finally, the mass of the Higgs boson mH is determined by a

simultaneous unbinnedﬁtofsignal-plus-backgrounddistributions to dataover thesixteencategories.2 _The _per-event_component_of

thesignalpdfisaddedtothebackgrounddistributionwhichis in-tegrated over all kinematic configurations of the four final state leptons.IneachofthefourBDTcategories, thesignalyieldis fac-torised bya floatingnormalisationmodifier independentforeach BDT category. The measured Higgs boson mass depends on the lepton energy resolution and thelepton energyscale. Uncertain-ties inthese quantities are accountedforin the fitby Gaussian-distributed penalty termswhosewidths are obtainedfrom auxil-iarydataorsimulationcontrolsamples.Theexpecteduncertainty, withmH

=

125GeV andproductionratespredictedbytheSM,for

adatasampleofthesizeoftheexperimentalset,evaluatedusing simulation-basedpseudo-experiments,is

±

0

.

35 GeV.

AvalidationwithdataisperformedwithZ

→

4

eventstotest theperformanceofthemethodonaknownresonancewithsimilar topology.Inthistest,thepeakandwidthoftherelativisticBreit– Wigner function are set to those of the Z boson. The measured

Z bosonmass was found to be 91

.

62

±

0

.

35 GeV including sta-tisticalandsystematicuncertainty. Theobserveduncertaintyisin agreement withthe expectationof

±

0

.

34 GeV,asevaluatedfrom simulation. The measured value is in agreement with the world averageof91

.

1876

±

0

.

0021 GeV [48].

Asanindependentcheck,thetemplatemethod [7] isalsoused to measure mH. The simulated distributions ofthe samples

gen-erated for mH values between 110 and 130 GeV are smoothed

with akernel densityestimate technique, and thenparametrised as a function ofmH by means of aB-spline interpolationto

ob-tainthesignalmodelforanyvalueofmH.Theexpectedstatistical

uncertainty of mH obtained with the per-event method from a

(5)

Fig. 1. (a)Invariantmassdistributionforthedata(pointswitherrorbars)showntogetherwiththesimultaneousfitresulttoH→Z Z∗→4candidates(continuousline). Thebackgroundcomponentofthefitisalsoshown(filledarea).Thesignalprobabilitydensityfunctionisevaluatedper-eventandaveragedovertheobserveddata.(b)Value of

−

2ln asafunctionofmH forthecombinedﬁttoallH→Z Z∗→4categories.Theintersectionofthe

−

2ln curvewiththehorizontallineslabelled1σ and2σ

providethe68.3%and95.5%conﬁdenceintervals.

sampleequalinsizetotheexperimentaldatasetis,onaverage,3% smallerthanthestatisticaluncertaintyobtainedwiththetemplate method.Bothmethodsarefoundtobeunbiasedwithinthe statis-ticaluncertaintyofthesimulatedsamplesusedofabout8 MeV on

mH.

7.3.Results

The estimate of mH for the per-event and template methods

isextracted witha simultaneous profile likelihoodfit to the six-teen categories. The free parameters of the fit are mH, the

nor-malisationmodiﬁers ofeach BDT category, andthe nuisance pa-rameters associated withsystematic uncertainties. The measured value of mH from the per-event method is found to be m_HZ Z∗

=

124

.

79

±

0

.

36

(

stat

)

±

0

.

05

(

syst

)

GeV

=

124

.

79

±

0

.

37 GeV. The total uncertainty is in agreement with the expectation and is dominated by the statistical component. The root-mean-square of the expecteduncertainty due to statisticalﬂuctuations intheeventyieldsofeachcategorywasestimatedtobe40 MeV. The p-valueof theuncertainty beingas highor higherthan the observed value, estimated with pseudo-experiments, is found to be 0

.

47. The total systematic uncertainty is 50 MeV, the lead-ing sources beingthe muon momentum scale (40 MeV) andthe electron energy scale (26 MeV), with other sources (background modellingandsimulationstatistics)beingsmallerthan10 MeV.

Forthetemplate method,the totaluncertainty isfound to be

+0.41

−0.39 GeV,larger by 35 MeV thanforthe per-event method.The

observeddifference forthe mH estimates ofthe two methods is

foundtobe0

.

16 GeV,whichiscompatiblewiththeexpected vari-anceestimatedwithpseudo-experimentsandcorrespondstoaone sided p-valueof0.19. Fig.1(a)showsthe m4 distribution ofthe data together with the result of the ﬁt to the H

→

Z Z∗

→

4

candidateswhen usingtheper-event method.Thefit isalso per-formedindependentlyforeachdecaychannel,fittingallBDT cate-goriessimultaneously;theresultinglikelihoodprofileiscompared withthe combinedfitin Fig.1(b).Thecombinedmeasured value ofmH is foundto be compatible withthe value measured

inde-pendentlyforeachchannel, withthelargestdeviationbeing1.4

σ

forthe2

μ

2e channelandtheothersbeingwithin1

σ

.

The Higgsbosonmassinthe four-leptonchannel isalso mea-suredby usinga proﬁlelikelihood ratioto combinethe informa-tionfromtheRun 1analysis [6],wheremH

=

124

.

51

±

0

.

52 GeV,

andtheRun 2analysis,keepingeach individualsignal normalisa-tionparameterindependent.Thesystematicuncertaintiestakento becorrelatedbetweenthetworunsarethemuonmomentumand electronenergyscales,whileallothersystematicuncertaintiesare considereduncorrelated. ThecombinedRun1andRun2resultis

mZ Z∗

H

=

124

.

71

±

0

.

30

(

stat

)

±

0

.

05

(

syst

)

GeV

=

124

.

71

±

0

.

30 GeV.

The difference betweenthe measured values ofmH in the

four-leptonchannelinthetworunsis

mZ Z∗

H

=

0

.

28

±

0

.

63 GeV,with

thetworesultsbeingcompatible,withap-valueof0.84.

8. MassmeasurementintheH

→

γ γ

channel

In the diphoton channel, the Higgs boson mass is measured fromthepositionofthenarrow resonantpeakinthemγ γ

distri-butionduetotheHiggsbosondecaytotwophotons.Suchapeak isobserved overa large,monotonicallydecreasing,mγ γ

distribu-tion from continuum background events. The diphoton invariant mass is computedfromthe measured photon energies andfrom their directions relative to the diphoton production vertex, cho-sen among all reconstructed primary vertex candidates using a neural-network algorithm based on trackand primary vertex in-formation,aswell asthedirectionsofthetwo photonsmeasured inthecalorimeterandinnerdetector [49].

Events are selected and divided into categories with differ-ent mass resolutions and signal-to-background ratios, optimised forthemeasurementofsimpliﬁedtemplatecross-sections [30,50] and of production mode signal strengths of the Higgs boson in the diphoton decay channel. The event selection and classiﬁca-tion are described in Ref. [24]. Apotential reduction of the total expected uncertainty by 4% could have been obtainedusing the sameeventcategorieschosenforthemassmeasurementwiththe Run 1 data [7]. Giventhe small expectedimprovement,a choice wasmadetousethesamecategorisationforthemeasurementof themassandoftheproductionmodesignalstrengths.

(6)

Fig. 2. (a)Invariantmassdistributions(circles)ofsimulatedH→γ γeventsreconstructedintwocategorieswithoneofthebest(“ggH0JCen”:opencircles)andoneofthe worst(“ggH0JFwd”:solidcircles)experimentalresolutions.Thesignalmodelderivedfromafitofthesimulatedeventsissuperimposed(solidlines).(b)Diphotoninvariant massdistributionofallselecteddataevents,overlaidwiththeresultofthefit(solidredline).Bothfordataandforthefit,eachcategoryisweightedbyafactorln(1+S/B), whereS andB arethefittedsignalandbackgroundyieldsinamγ γ intervalcontaining90%oftheexpectedsignal.Thedottedlinedescribesthebackgroundcomponentof

themodel.Thebottominsetshowsthedifferencebetweenthesumofweightsandthebackgroundcomponentoftheﬁttedmodel(dots),comparedwiththesignalmodel (blackline).(Forinterpretationofthecoloursintheﬁgure(s),thereaderisreferredtothewebversionofthisarticle.)

8.1. Eventselectionandcategorisation

Afteraninitialpreselection,describedinRef. [24],requiringthe presenceofatleasttwolooselyidentiﬁedphotoncandidateswith

|

η

|

<

1

.

37 or1

.

52

<

|

η

|

<

2

.

37, eventsareselected iftheleading and the subleading photon candidates have ET

/

mγ γ

>

0

.

35 and

0.25 respectively, and satisfy the tight identiﬁcation criteria and isolation criteria based on calorimeter and tracking information. Only events with invariant mass of the leading and subleading photonintherange105 GeV

<

mγ γ

<

160 GeV arekept.

The events passing the previous selection are then classiﬁed, accordingtothepropertiesofthetwoselectedphotonsandofjets, electrons,muonsandmissingtransversemomentum,into31 mu-tuallyexclusivecategories [24].Themostpopulatedclass,targeting gluon–gluon fusionproductionwithoutreconstructedjets, issplit intotwocategoriesofeventswithverydifferentenergyresolution: theﬁrst(“ggH 0JCen”) requiresbothphotonsto have

|

η

|

<

0

.

95, whilethesecond(“ggH0JFwd”)retainstheremainingevents.

8.2. Signalandbackgroundmodels

For each category, the shape of the diphoton invariant mass distribution of the signal is modelled with a double-sided Crys-tal Ballfunction [51], i.e.a Gaussian function in thepeak region withpower-lawfunctionsinbothtails.Thedependenceofthe pa-rametersontheHiggsboson massmH isdescribed by ﬁrst-order

polynomials,whoseparametersareﬁxedbyﬁttingsimultaneously all thesimulatedsignal samples generatedfordifferentvalues of

mH.

Thequantity

σ

68,deﬁnedashalfofthesmallestrange

contain-ing68%oftheexpectedsignalevents,isanestimate ofthesignal

mγ γ resolutionandformH

=

125 GeV itrangesbetween1

.

41 GeV

and2

.

10 GeV dependingon the category, whileforthe inclusive caseitsvalueis1

.

84 GeV.Fig.2(a)showsanexampleofthesignal modelfora categorywithone ofthebest invariantmass resolu-tionsandforacategorywithoneoftheworstresolutions.

The expected signal yield is expressed as the product of in-tegrated luminosity,productioncross-section, diphoton branching ratio,acceptanceandeﬃciency.Thecross-sectionisparameterised asafunctionofmH separatelyforeachproductionmode.Similarly,

thebranchingratioisparameterisedasafunctionofmH.The

prod-uct of acceptanceand eﬃciency is evaluated separately for each productionmode usingonlythe sampleswithmH

=

125 GeV.Its

dependenceonthemassisweak(relativevariationbelow1%when varying theHiggsbosonmassby

±

1 GeV)andisthus neglected. The cross-sectionsareﬁxed totheSMvaluesmultipliedbya sig-nalmodiﬁerforeachproductionmode:

μ

ggF,

μ

VBF,

μ

V H and

μ

tt H¯ .

The expected yield formH

=

125 GeV varies betweenabout one

eventincategoriessensitivetorareproductionmodes(t

¯

t H ,t H )to almost 500eventsinthemostpopulatedeventcategory (“ggH0J Fwd”).

Thebackgroundinvariantmassdistributionofeachcategoryis parameterisedwithanempiricalcontinuousfunctionofthe dipho-tonsysteminvariantmassvalue.Theparametersofthesefunctions areﬁtteddirectlytodata.Thefunctionalformusedtodescribethe backgroundineachcategory ischosen amongseveralalternatives accordingtothethreecriteriadescribedinRef. [24]:(i)theﬁtted signalyieldinatestsamplerepresentativeofthedatabackground, built by combining simulation and control regions in data, must beminimised;(ii)the

χ

2 _probability_for_the_ﬁt_of_this_background

control sample must be larger than a certain threshold; (iii) the qualityoftheﬁttodatasidebandsmustnotimprovesigniﬁcantly whenaddinganextradegreeoffreedomtothemodel.Themodels selectedbythisprocedureareexponentialorpower-lawfunctions with one degree of freedom for the categories with few events, whileexponentialfunctionsofasecond-orderpolynomialareused fortheothers.

From the extrapolation of a background-only ﬁt to the side-bands of the mγ γ distribution in data, excluding events with 121 GeV

<

mγ γ

<

129 GeV,theexpectedsignal-to-background ra-tioinamγ γ windowcontaining90%ofthesignaldistributionfor

mH

=

125 GeV varies between2% in the “ggH 0JFwd” category

(7)

targetingH +2jet, VBF-likeeventswithlow transversemomentum oftheH +2jetsystem.

8.3.Systematicuncertainties

The main sources of systematic uncertainty in the measured Higgsboson mass in the diphoton channel are the uncertainties in the photon energy scale (PES), the uncertainty arising from the background model, and the uncertainty in the selection of the diphoton production vertex. They are described in detail in Ref. [24].

ForeachsourceofuncertaintyinthePESdescribedinSection5, thediphoton invariant massdistribution for each category is re-computedaftervaryingthephotonenergybyitsuncertaintyandis thencomparedwiththenominaldistribution.Thesumin quadra-tureofthepositiveornegativeshiftsofthemγ γ peakpositiondue tosuchvariationsrangesfrom

±

260 MeV inthe“ggH0JCen” cat-egoryto

±

470 MeV in the“jet BSM” category, whichrequiresat leastonejetwithpT

>

200 GeV.AllthePESeffectsareconsidered

asfullycorrelatedacrosscategories.

Theuncertaintyduetothebackgroundmodellingis evaluated following the procedure described in Ref. [7]. The expected sig-nalcontributionaspredictedbythesignal modelisaddedtothe backgroundcontrolsample.ThebiasintheestimatedHiggsboson massfromasignal-plus-backgroundﬁttothetestsample relative totheinjectedmassisconsideredasasystematicuncertaintydue tothebackgroundmodelling.Itsvalueisaround

±

60 MeV forthe mostrelevantcategoriesforthe massmeasurement. Inthe other categoriesitcanassumelarger values,whicharecompatiblewith statisticalﬂuctuationsofthe backgroundcontrol sample. Forthis reasonthis systematic uncertainty is ignored in the poorly pop-ulatedtt H categories,

¯

which givea negligiblecontribution tothe massmeasurement.Thissystematicuncertaintyisassumedto be uncorrelatedbetweendifferentcategories.

The systematic uncertainty related to the selection of the diphotonproduction vertexis evaluated using Z

→

ee events, as describedinRef. [7].Anexpecteduncertaintyof

±

40 MeV inmH

isused for all the categoriesand assumedto be fully correlated acrossdifferentcategories.

Systematicuncertaintiesinthediphotonmassresolutiondueto uncertainties inthe photon energy resolutionvary between

±

6% (forthe “ggH0J Cen”category)and11% (for the“jet BSM” cate-gory),andare expectedto have anegligible impact onthe mass measurement.

Systematicuncertainties in the yield and in the migration of eventsbetweencategoriesdescribed inRef. [24] haveanegligible impactonthemassmeasurement.

Theuncertainty duetothe signal modellingisevaluated sim-ilarlyto thatdueto thebackground modelling. Asample isbuilt usingtheexpectedbackgrounddistributionandthesimulated sig-nal events atmH

=

125 GeV. The bias in the ﬁtted Higgs boson

massisconsidered asasystematicuncertaintyandisassumedto becorrelatedbetweendifferentcategories.Therelativebiasis be-low10−4 _in_most_of_the_categories,_and_at_most_a_few_times₁₀−4

intheothercategories.

8.4.Results

The Higgs boson mass in the diphoton channel is estimated witha simultaneous binned maximum-likelihood ﬁt to the mγ γ

distributionsoftheselectedeventcategories.Ineachcategory,the distribution is modelled witha sumof the background and sig-nalmodels.The freeparametersoftheﬁtaremH,thefoursignal

strengths, the number ofbackground events and the parameters

describing the shape of the background invariant mass distribu-tion ineach category,andall the nuisanceparameters associated with systematicuncertainties. Fig. 2(b) showsthe distribution of thedataoverlaidwiththeresultofthesimultaneousﬁt.Allevent categories are included. For illustration purposes, events in each categoryareweightedbyafactorln

(

1

+

S

/

B

)

,whereS and B are

theﬁttedsignalandbackgroundyieldsinamγ γ interval contain-ing90%ofthesignal.

The measuredmassof theHiggsbosonin thediphoton chan-nel ismγ γ_H

=

124

.

93

±

0

.

21

(

stat

)

±

0

.

34

(

syst

)

GeV

=

124

.

93

±

0

.

40 GeV wheretheﬁrsterroristhestatisticaluncertaintywhile the second is the total systematicuncertainty, dominatedby the photonenergyscaleuncertainty.

Assuming signal strengths asin theSM andthesignal model determined from the simulation, the expected statistical uncer-taintyis0

.

25GeV andtheexpectedtotaluncertaintyis0

.

41GeV, witha root-mean-square, estimatedfrom pseudo-experiments, of about 40 MeV. Compared to the expectation, the slightly larger systematicuncertaintyandsmallerstatisticaluncertaintyobserved indataareduetoalowerthanexpectedsignalyieldinsome cat-egories with large expected yield andsmall photon energyscale uncertainty, andtothe ﬁttedresolution indatabeinga few per-centbetterthaninthesimulation(butstillagreeingwithitwithin onestandarddeviation).

To check if the measurement is sensitive to the assumption aboutthe splittingofthe productionmodes, themeasurement is repeatedusingone commonsignalstrength forallthe processes. A small shift of the measured mH by 20 MeV is observed. The

massmeasurement isalsoperformedby allowing theoverall sig-nalyieldineachanalysiscategorytoﬂoatindependentlyintheﬁt. ThemeasuredvalueofmH changesbylessthan30 MeV.

Other checks targetingpossiblemiscalibration dueto detector effectsforsomespeciﬁccategoryofphotonsareperformedby par-titioning theentire datasample intodetector-oriented categories, different from those used for the nominalresult, and determin-ingtheprobabilitythatmH measuredinoneofthesecategoriesis

compatiblewiththeaveragemH fromtheother categories.Aﬁrst

categorisationisbasedonwhetherthephotonsarereconstructed as converted or not, a second is based on the photons’ impact pointsinthecalorimeter(eitherinthebarrelregion,

|

η

|

<

1

.

37,or intheendcapregion,

|

η

|

>

1

.

52),andathirdisbasedonthe num-berofinteractionsperbunchcrossing.Foreachofthesecategories anewbackgroundmodel,anewsignalmodelandnewsystematic uncertaintyvalues are computed. Foreach categorythe compati-bility of its mH value withthe combined mH value is testedby

consideringasanadditionallikelihoodparameterthequantity

i

equaltothedifferencebetweenthatcategory’smH valueandthe

combinedvalue.Novalueof

isigniﬁcantlydifferentfromzerois

found.Asimilartestisperformedtoassesstheglobal compatibil-ityofallthe differentcategorieswitha commonvalueofmH.In

thethreecategorisationsconsideredthesmallestglobalp-valueis 12%.The sameprocedureisapplied tothecategoriesused inthe analysis:thesmallestp-valuecomputedonsinglecategoriesis7% whiletheglobalp-valueis94%.

AcombinationoftheHiggsbosonmassmeasuredinthe dipho-ton channel by ATLAS in Run 1, 126

.

02

±

0

.

51 GeV [6], and in Run 2 is performed using a proﬁle likelihood ratio. The signal strengths are treated asindependent parameters. The systematic uncertainties consideredcorrelatedbetweenthetwoLHC run pe-riods are mostof the photon energy scale andresolution uncer-tainties and those in the pile-up modelling, while all the other systematicuncertainties are considered uncorrelated. The photon energy calibration uncertainties that are treated as uncorrelated between the two LHC data-taking periods are a few uncertain-ties included only in the Run 2 measurement, the uncertainty

(8)

Fig. 3. Thevalueof

−

2ln asafunctionofmHfor(a)H→γ γ,H→Z Z∗→4channelsandtheircombination(red,blueandblack,respectively)usingRun 2dataonlyand

for(b)Run 1,Run 2andtheircombination(red,blueandblack,respectively).Thedashedlinesshowthemassmeasurementuncertaintiesassumingstatisticaluncertainties only.

in the photon energy leakage outside the reconstructed clus-ter, whose measurement is limited by the statisticalaccuracy of

Z

→

γ

,andthe uncertaintyinthe electromagneticcalorimeter response non-linearity, which is estimated with different proce-duresinthe two LHCrun periods. Theresult ismγ γ_H

=

125

.

32

±

0

.

19

(

stat

)

±

0

.

29

(

syst

)

GeV

=

125

.

32

±

0

.

35 GeV. The differ-encebetweenthe measured valuesofmH in the diphoton

chan-nel in the two LHC run periods is

mγ γ_H

=

1

.

09

±

0

.

46 (stat)

±

0

.

34 (syst) GeV

=

1

.

09

±

0

.

57 GeV.The probabilitythat thetwo resultsarecompatibleis5.1%.

9. Combinedmassmeasurement

The Higgsboson mass ismeasured by combining information fromboththeH

→

Z Z∗

→

4

andH

→

γ γ

channels.The correla-tionsbetweenthesystematicuncertaintiesinthetwochannelsare accountedforintheproﬁlelikelihoodfunction.The mainsources of correlated systematic uncertainty include the calibrations of electronsandphotons, thepile-upmodelling, andthe luminosity. Signalyieldnormalisationsaretreatedasindependentfree param-etersin theﬁtto minimisemodel-dependentassumptions inthe measurementoftheHiggsbosonmass.

ThecombinedvalueofthemassmeasuredusingRun 2datais

mH

=

124

.

86

±

0

.

27 GeV. Assuming statistical uncertainties only,

the uncertainty in the combined value is

±

0

.

18 GeV. The cor-responding proﬁle likelihood, for the two channels andfor their combination, is shownin Fig. 3(a). This result is in good agree-mentwiththeATLAS+CMSRun 1measurement [6],mH

=

125

.

09

±

0

.

24 GeV.

ThecombinedmassmeasurementfromtheATLASRun 1(mH

=

125

.

36

±

0

.

41 GeV)andRun 2resultsismH

=

124

.

97

±

0

.

24 GeV.

Assuming statistical uncertainties only, the measurement uncer-tainty amountsto0

.

16 GeV.Fig.3(b)showsthevalue of

−

2ln

asafunctionofmH forthetwochannelscombined,separatelyfor

theATLASRun 1andRun 2datasets,aswell asfortheir combi-nation.

Thecontributionsofthemainsourcesofsystematicuncertainty tothecombinedmassmeasurement,usingbothATLASRun 1and Run 2data,aresummarisedinTable1.Theimpactofeachsource ofsystematicuncertaintyisevaluated startingfromthe contribu-tionofeachindividualnuisanceparametertothetotaluncertainty. Thiscontributionisdeﬁnedasthemassshift

δ

mH observedwhen

Table 1

MainsourcesofsystematicuncertaintyintheHiggsbosonmassmHmeasuredwith

the 4andγ γ ﬁnalstatesusingRun 1and Run 2data.Thesuminquadrature oftheindividualcontributionsisnotexpectedtoreproducethetotalsystematic uncertaintyduetothedifferentmethodologiesemployedtoderivethem.

Source Systematic uncertainty in mH[MeV]

EM calorimeter response linearity 60

Non-ID material 55

EM calorimeter layer intercalibration 55

Z→ee calibration 45

ID material 45

Lateral shower shape 40

Muon momentum scale 20

Conversion reconstruction 20

H→γ γbackground modelling 20

H→γ γvertex reconstruction 15

e/γenergy resolution 15

All other systematic uncertainties 10

re-evaluating the profilelikelihood ratioafterfixing the nuisance parameter inquestion toits best-fitvalue increasedordecreased by one standard deviation, while all remainder nuisance param-eters remain free to float. The sum in quadrature of groups of nuisance parameter variations gives the impact of each category of systematic uncertainties. The nuisance parameter values from theunconditionalmaximum-likelihoodfitare consistentwiththe pre-fitvalueswithinonestandarddeviation.

The probability that the mH results from the four

measure-ments(inthe4

and

γ γ

ﬁnalstates,usingRun 1orRun 2ATLAS data) are compatible is 12.3%. Due to the impact of the corre-latedsystematicuncertainties,thecorrelation betweenmH inthe

H

→

γ γ

channelover thetwo runsis23%. Theresidual correla-tion between H

→

Z Z∗

→

4

and H

→

γ γ

is typically 1%. The resultsfromeachofthefourindividualmeasurements,aswellas various combinations,along withtheLHC Run 1result, are sum-marisedinFig.4.

The combination of the four ATLAS measurements using the BLUE approach as an alternative method, assuming two uncor-related channels,3 is found to be mH

=

124

.

97

±

0

.

23GeV

=

3 _The _combination_of_the_two _LHC_run _periods_for _each_channel_was_used_as

(9)

Fig. 4. SummaryoftheHiggsbosonmassmeasurementsfromtheindividualand combinedanalysesperformedhere,comparedwiththecombinedRun 1 measure-mentbyATLASandCMS [6].Thestatistical-only(horizontalyellow-shadedbands) andtotal(blackerrorbars)uncertaintiesareindicated.The(red)verticallineand corresponding(grey)shadedcolumnindicatethecentralvalueandthetotal uncer-taintyofthecombinedATLASRun 1+2measurement,respectively.

124

.

97

±

0

.

19

(

stat

)

±

0

.

13

(

syst

)

GeV. The splitting of the errors takesintoaccountthe relativeweightofthe twochannelsinthe combinedmeasurement.

10. Conclusion

ThemassoftheHiggsbosonhasbeenmeasuredfroma com-bined ﬁt to the invariant mass spectra of the decay channels

H

→

Z Z∗

→

4

and H

→

γ γ

. The results are obtained from a Run 2pp collisiondatasamplerecordedbytheATLASexperiment attheCERN LargeHadron Colliderata centre-of-mass energyof 13 TeV, corresponding to an integrated luminosity of 36.1 fb−1_.

Themeasurements arebased onthelatest calibrationsofmuons, electrons,andphotons,andonimprovementstotheanalysis tech-niquesusedtoobtainthepreviousresultsfromATLASRun 1data. The measured values of the Higgs boson mass for the H

→

Z Z∗

→

4

andH

→

γ γ

channelsare

mH

=

124

.

79

±

0

.

37 GeV

,

mH

=

124

.

93

±

0

.

40 GeV

.

Fromthecombinationofthesetwochannels,themassismeasured tobe

mH

=

124

.

86

±

0

.

27 GeV

.

ThisresultisingoodagreementwiththeaverageoftheATLASand CMSRun 1 measurements. The combinationof the ATLAS Run 1 andRun 2measurementsyields

mH

=

124

.

97

±

0

.

24 GeV

.

Acknowledgements

We thankCERN for thevery successful operation ofthe LHC, aswell asthe support stafffromour institutions without whom ATLAScouldnotbeoperatedeﬃciently.

WeacknowledgethesupportofANPCyT,Argentina;YerPhI, Ar-menia; ARC, Australia; BMWFW and FWF, Austria; ANAS, Azer-baijan;SSTC, Belarus; CNPq and FAPESP, 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,HongKongSAR,China;ISF,I-COREandBenoziyo Cen-ter, Israel; INFN, Italy; MEXT and JSPS, Japan; CNRST, Morocco; NWO, Netherlands; RCN, Norway;MNiSW andNCN, Poland; FCT, Portugal; MNE/IFA, Romania; MES ofRussia andNRC KI, Russian Federation;JINR;MESTD, Serbia;MSSR,Slovakia; ARRSandMIZŠ, 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-dividualgroupsandmembershavereceived supportfromBCKDF, theCanadaCouncil,Canarie,CRC,ComputeCanada,FQRNT,andthe OntarioInnovation Trust,Canada; EPLANET,ERC,ERDF, FP7, Hori-zon 2020 and Marie Skłodowska-Curie Actions, European Union; Investissements d’Avenir Labex and Idex, ANR, Région Auvergne andFondationPartagerleSavoir,France;DFGandAvHFoundation, Germany;Herakleitos,ThalesandAristeiaprogrammesco-ﬁnanced byEU-ESF andtheGreekNSRF;BSF,GIFandMinerva, Israel;BRF, Norway; CERCA Programme Generalitat de Catalunya, Generalitat Valenciana,Spain;theRoyalSocietyandLeverhulmeTrust,United Kingdom.

The crucial computingsupport from all WLCG partnersis 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.Majorcontributorsofcomputingresourcesare listedin Ref. [52].

References

[1]ATLAS Collaboration, Observation of a new particle in the search for the

Stan-dard Model Higgs boson with the ATLAS detector at the LHC, Phys. Lett. B 716 (2012) 1, arXiv:1207.7214 [hep -ex].

[2]CMS Collaboration, Observation of a new boson at a mass of 125 GeV with

the CMS experiment at the LHC, Phys. Lett. B 716 (2012) 30, arXiv:1207.7235 [hep -ex].

[3]F. Englert, R. Brout, Broken symmetry and the mass of gauge vector mesons,

Phys. Rev. Lett. 13 (1964) 321.

[4]P.W. Higgs, Broken symmetries and the masses of gauge bosons, Phys. Rev. Lett.

13 (1964) 508.

[5]G. Guralnik, C. Hagen, T. Kibble, Global conservation laws and massless

parti-cles, Phys. Rev. Lett. 13 (1964) 585.

[6]ATLAS, CMS Collaborations, Combined measurement of the Higgs boson mass

in pp collisions at √s=7 and 8 TeV with the ATLAS and CMS experiments,

Phys. Rev. Lett. 114 (2015) 191803, arXiv:1503 .07589 [hep -ex].

[7]ATLAS Collaboration, Measurement of the Higgs boson mass from the H→γ γ

and H→Z Z∗→4channels in pp collisions at center-of-mass energies of 7 and 8 TeV with the ATLAS detector, Phys. Rev. D 90 (2014) 052004, arXiv: 1406 .3827 [hep -ex].

[8]CMS Collaboration, Precise determination of the mass of the Higgs boson

and tests of compatibility of its couplings with the standard model predic-tions using proton collisions at 7 and 8 TeV, Eur. Phys. J. C 75 (2015) 212, arXiv:1412 .8662 [hep -ex].

[9]CMS Collaboration, Measurements of properties of the Higgs boson decaying

into the four-lepton ﬁnal state in pp collisions at √s=13 TeV, J. High Energy

Phys. 11 (2017) 047, arXiv:1706 .09936 [hep -ex].

[10]ATLAS Collaboration, The ATLAS experiment at the CERN Large Hadron Collider,

J. Instrum. 3 (2008) S08003.

[11]ATLAS Collaboration, Measurement of inclusive and differential cross sections

in the H→Z Z∗→4decay channel in pp collisions at √s=13 TeV with the

ATLAS detector, J. High Energy Phys. 10 (2017) 132, arXiv:1708 .02810 [hep -ex].

[12]K. Hamilton, P. Nason, E. Re, G. Zanderighi, NNLOPS simulation of Higgs boson

production, J. High Energy Phys. 10 (2013) 222, arXiv:1309 .0017 [hep -ph].

[13]J. Butterworth, et al., PDF4LHC recommendations for LHC Run II, J. Phys. G 43

(2016) 023001, arXiv:1510 .03865 [hep -ph].

[14]S. Alioli, P. Nason, C. Oleari, E. Re, NLO Higgs boson production via gluon fusion

matched with shower in POWHEG, J. High Energy Phys. 04 (2009) 002, arXiv: 0812 .0578 [hep -ph].

(10)

[15]T. Sjöstrand, S. Mrenna, P.Z. Skands, A brief introduction to PYTHIA 8.1, Comput.

Phys. Commun. 178 (2008) 852, arXiv:0710 .3820 [hep -ph].

[16]D.J. Lange, The EvtGen particle decay simulation package, Nucl. Instrum.

Meth-ods A 462 (2001) 152.

[17]H.-L. Lai, et al., New parton distributions for collider physics, Phys. Rev. D 82

(2010) 074024, arXiv:1007.2241 [hep -ph].

[18]J. Pumplin, et al., New generation of parton distributions with uncertainties

from global QCD analysis, J. High Energy Phys. 07 (2002) 012, arXiv:hep -ph / 0201195 [hep -ph].

[19]ATLAS Collaboration, Measurement of the Z/γ∗boson transverse momentum

distribution in pp collisions at √s=7 TeV with the ATLAS detector, J. High Energy Phys. 09 (2014) 145, arXiv:1406 .3660 [hep -ex].

[20]F. Cascioli, et al., ZZ production at hadron colliders in NNLO QCD, Phys. Lett. B

735 (2014) 311, arXiv:1405 .2219 [hep -ph].

[21]M. Grazzini, S. Kallweit, D. Rathlev, ZZ production at the LHC: ﬁducial cross

sections and distributions in NNLO QCD, Phys. Lett. B 750 (2015) 407, arXiv: 1507.06257 [hep -ph].

[22]B. Biedermann, A. Denner, S. Dittmaier, L. Hofer, B. Jäger, Electroweak

correc-tions to pp→μ+μ−e+e−+X at

the LHC: a Higgs boson background study,

Phys. Rev. Lett. 116 (2016) 161803, arXiv:1601.07787 [hep -ph].

[23]B. Biedermann, A. Denner, S. Dittmaier, L. Hofer, B. Jager, Next-to-leading-order

electroweak corrections to the production of four charged leptons at the LHC, J. High Energy Phys. 01 (2017) 033, arXiv:1611.05338 [hep -ph].

[24]ATLAS Collaboration, Measurements of Higgs boson properties in the diphoton

decay channel with 36 fb−1_{of pp collision data at}√_s₌_{13 TeV with the ATLAS}

detector, arXiv:1802 .04146 [hep -ex], 2018.

[25]ATLAS Collaboration, The ATLAS simulation infrastructure, Eur. Phys. J. C 70

(2010) 823, arXiv:1005 .4568 [physics .ins -det].

[26]S. Agostinelli, et al., GEANT4 – a simulation toolkit, Nucl. Instrum. Methods A

506 (2003) 250.

[27]LHC Higgs Cross Section Working Group, S. Dittmaier, C. Mariotti, G. Passarino,

R. Tanaka (Eds.), Handbook of LHC Higgs Cross Sections: 1. Inclusive Observ-ables, CERN, Geneva, 2011, CERN-2011-002, arXiv:1101.0593 [hep -ph].

[28]LHC Higgs Cross Section Working Group, S. Dittmaier, C. Mariotti, G. Passarino,

R. Tanaka (Eds.), Handbook of LHC Higgs Cross Sections: 2. Differential Distri-butions, CERN, Geneva, 2012, CERN-2012-002, arXiv:1201.3084 [hep -ph].

[29]LHC Higgs Cross Section Working Group, S. Heinemeyer, C. Mariotti, G.

Pas-sarino, R. Tanaka (Eds.), Handbook of LHC Higgs Cross Sections: 3. Higgs Prop-erties, CERN, Geneva, 2013, CERN-2013-004, arXiv:1307.1347 [hep -ph].

[30]LHC Higgs Cross Section Working Group, D. de Florian, C. Grojean, F. Maltoni,

C. Mariotti, A. Nikitenko, M. Pieri, P. Savard, M. Schumacher, R. Tanaka (Eds.), Handbook of LHC Higgs Cross Sections: 4. Deciphering the Nature of the Higgs Sector, CERN, Geneva, 2017, CERN-2017-002, arXiv:1610 .07922 [hep -ph].

[31] ATLASCollaboration,Early innerdetector trackingperformanceinthe 2015 dataat√s=13 TeV,ATL-PHYS-PUB-2015-051,URL:https://cds .cern .ch /record / 2110140,2015.

[32] ATLASCollaboration,Studyofalignment-relatedsystematiceffectsonthe AT-LASInnerDetectortrackreconstruction,ATLAS-CONF-2012-141,URL:https:// cds .cern .ch /record /1483518,2012.

[33]ATLAS Collaboration, Muon reconstruction performance of the ATLAS detector

in proton–proton collision data at √s=13 TeV, Eur. Phys. J. C 76 (2016) 292,

arXiv:1603 .05598 [hep -ex].

[34]ATLAS Collaboration, Topological cell clustering in the ATLAS calorimeters and

its performance in LHC Run 1, Eur. Phys. J. C 77 (2017) 490, arXiv:1603 .02934 [hep -ex].

[35]ATLAS Collaboration, Measurement of the photon identiﬁcation eﬃciencies

with the ATLAS detector using LHC Run-1 data, Eur. Phys. J. C 76 (2016) 666, arXiv:1606 .01813 [hep -ex].

[36]ATLAS Collaboration, Electron and photon energy calibration with the ATLAS

detector using LHC Run 1 data, Eur. Phys. J. C 74 (2014) 3071, arXiv:1407.5063 [hep -ex].

[37] ATLAS Collaboration, Electron and photon energy calibration with the AT-LASdetector usingdata collectedin2015at √s=13 TeV, ATL-PHYS-PUB-2016-015,URL:https://cds .cern .ch /record /2203514,2016.

[38]ATLAS Collaboration, Electron eﬃciency measurements with the ATLAS

detec-tor using 2012 LHC proton–proton collision data, Eur. Phys. J. C 77 (2017) 195, arXiv:1612 .01456 [hep -ex].

[39]ATLAS Collaboration, Combined search for the Standard Model Higgs boson in

pp collisions at √s=7 TeV with the ATLAS detector, Phys. Rev. D 86 (2012) 032003, arXiv:1207.0319 [hep -ex].

[40]G. Cowan, K. Cranmer, E. Gross, O. Vitells, Asymptotic formulae for

likelihood-based tests of new physics, Eur. Phys. J. C 71 (2011) 1554, arXiv:1007.1727.

[41] R.Nisius,Onthecombinationofcorrelatedestimatesofaphysicsobservable, Eur.Phys.J.C(ISSN 1434-6052)74(2014)3004,https://doi .org /10 .1140 /epjc / s10052 -014 -3004 -2.

[42]L. Lyons, D. Gibaut, P. Clifford, How to combine correlated estimates of a single

physical quantity, Nucl. Instrum. Methods A 270 (1988) 110.

[43]A. Valassi, Combining correlated measurements of several different physical

quantities, Nucl. Instrum. Methods A 500 (2003) 391.

[44]M. Aaboud, et al., Measurement of the Higgs boson coupling properties in the

H→Z Z∗→4decay channel at √s=13 TeV with the ATLAS detector, J. High Energy Phys. 03 (2018) 095, arXiv:1712 .02304 [hep -ex].

[45]ATLAS Collaboration, Measurements of Higgs boson production and couplings

in the four-lepton channel in pp collisions at center-of-mass energies of 7 and 8 TeV with the ATLAS detector, Phys. Rev. D 91 (2015) 012006, arXiv:1408 .5191 [hep -ex].

[46]R. Frühwirth, Track ﬁtting with non-Gaussian noise, Comput. Phys. Commun.

100 (1997) 1.

[47] ATLAS Collaboration, Improved electron reconstruction in ATLAS using the GaussianSumFilter-basedmodelforbremsstrahlung, ATLAS-CONF-2012-047, URL:https://cds .cern .ch /record /1449796,2012.

[48]M. Tanabashi, et al., Particle Data Group, Review of particle physics, Phys. Rev.

D 98 (2018) 010001.

[49]ATLAS Collaboration, Measurement of Higgs boson production in the diphoton

decay channel in pp collisions at center-of-mass energies of 7 and 8 TeV with the ATLAS detector, Phys. Rev. D 90 (2014) 112015, arXiv:1408 .7084 [hep -ex].

[50]J.R. Andersen, et al., Les Houches 2015: physics at TeV colliders standard model

working group report, arXiv:1605 .04692 [hep -ph].

[51]ATLAS Collaboration, Search for resonances in diphoton events at √s=13 TeV with the ATLAS detector, J. High Energy Phys. 09 (2016) 001, arXiv:1606 .03833 [hep -ex].

[52] ATLAS Collaboration, ATLAS computing acknowledgements, ATL-GEN-PUB-2016-002,URL:https://cds.cern.ch/record/2202407.