Higgs boson production cross-section measurements and ...

Eur. Phys. J. C (2020) 80:957 https://doi.org/10.1140/epjc/s10052-020-8227-9

Regular Article - Experimental Physics

Higgs boson production cross-section measurements and theirEFT interpretation in the 4� decay channel at

√s =13 TeV with

the ATLAS detector

ATLAS Collaboration�

CERN, 1211 Geneva 23, Switzerland

Received: 8 April 2020 / Accepted: 9 July 2020© CERN for the benefit of the ATLAS collaboration 2020

Abstract Higgs boson properties are studied in the four-lepton decay channel (where lepton = e, μ) using 139 fb−1

of proton–proton collision data recorded at√s =13 TeV by

the ATLAS experiment at the Large Hadron Collider. Theinclusive cross-section times branching ratio for H → Z Z∗decay is measured to be 1.34 ± 0.12 pb for a Higgs bosonwith absolute rapidity below 2.5, in good agreement withthe Standard Model prediction of 1.33 ± 0.08 pb. Cross-sections times branching ratio are measured for the mainHiggs boson production modes in several exclusive phase-space regions. The measurements are interpreted in termsof coupling modifiers and of the tensor structure of Higgsboson interactions using an effective field theory approach.Exclusion limits are set on the CP-even and CP-odd ‘beyondthe Standard Model’ couplings of the Higgs boson to vectorbosons, gluons and top quarks.

Contents

1 Introduction . . . . . . . . . . . . . . . . . . . . . .1.1 Simplified template cross-sections . . . . . . .1.2 Higgs boson couplings in the κ-framework . . .1.3 Tensor structure of Higgs boson couplings in

the effective field theory approach . . . . . . .2 ATLAS detector . . . . . . . . . . . . . . . . . . . .3 Data set and event simulation . . . . . . . . . . . . .4 Event selection . . . . . . . . . . . . . . . . . . . .

4.1 Event reconstruction . . . . . . . . . . . . . .4.2 Selection of the Higgs boson candidates . . . .

5 Event categorisation and production mode discrim-ination . . . . . . . . . . . . . . . . . . . . . . . . .5.1 Event categorisation . . . . . . . . . . . . . . .5.2 Multivariate production mode discriminants . .

6 Background contributions . . . . . . . . . . . . . . .6.1 Background processes with prompt leptons . .

� e-mail: [email protected]

6.2 Background processes with non-prompt leptons7 Systematic uncertainties . . . . . . . . . . . . . . .

7.1 Experimental uncertainties . . . . . . . . . . .7.2 Theoretical uncertainties . . . . . . . . . . . .

8 Measurement of the Higgs boson production modecross-sections . . . . . . . . . . . . . . . . . . . . .8.1 Observed data . . . . . . . . . . . . . . . . . .8.2 Measurement of simplified template cross-sections

9 Constraints on the Higgs boson couplings in the κ-framework . . . . . . . . . . . . . . . . . . . . . . .

10 Constraints on the tensor coupling structure in theEFT approach . . . . . . . . . . . . . . . . . . . . .10.1 EFT signal model . . . . . . . . . . . . . . . .10.2 EFT interpretation results . . . . . . . . . . . .

11 Conclusion . . . . . . . . . . . . . . . . . . . . . .References . . . . . . . . . . . . . . . . . . . . . . . . .

1 Introduction

The observation of the Higgs boson by the ATLAS and CMSexperiments [1,2] with the Large Hadron Collider (LHC)Run 1 data set at centre-of-mass energies of

√s = 7 TeV and

8 TeV was a major step towards an understanding of the elec-troweak (EW) symmetry breaking mechanism [3–5]. Testsof its spin and CP quantum numbers strongly indicate thatthe observed particle is of scalar nature and that the domi-nant coupling structure is CP-even, consistent with the Stan-dard Model (SM) expectation [6–8]. The measurements ofthe Higgs boson production and differential cross-sections,branching ratios, and the derived constraints on coupling-strength modifiers, assuming the SM coupling structure, havealso shown no significant deviation from the predictions forthe SM Higgs boson with a mass of 125 GeV [9–12]. Further-more, constraints have been set on various coupling param-eters beyond the SM (BSM) that modify the tensor structureof the Higgs boson couplings to SM particles [8,13–20].

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957 of 54 Eur. Phys. J. C (2020) 80:957

Motivated by a clear Higgs boson signature and a highsignal-to-background ratio in the H → Z Z∗ → 4� decaychannel (where � = e or μ), the updated measurements ofthe Higgs boson coupling properties in this channel are pre-sented using the entire Run 2 data set with 139 fb−1of proton–proton (pp) collision data collected at

√s = 13 TeV by the

ATLAS detector between 2015 and 2018. Three types ofresults are presented in this paper: (i) measurements of theHiggs boson production cross-sections times branching ratio,hereafter referred to as cross-sections, for the main produc-tion modes in several exclusive phase-space bins in dedicatedfiducial regions; (ii) interpretation of the measurements interms of constraints on the Higgs boson coupling-strengthmodifiers within the κ-framework [21]; and (iii) interpreta-tion of the measurements in terms of modifications to thetensor structure of Higgs boson couplings using an effectivefield theory (EFT) approach.

In addition to a nearly four times higher integrated lumi-nosity, there are several other important differences com-pared to the previous results in this analysis channel [17]:

• an improved lepton isolation to mitigate the impact ofadditional pp interactions in the same or neighbouringbunch crossings (pile-up),

• an improved jet reconstruction using a particle flow algo-rithm [22],

• additional event categories for the classification of Higgsboson candidates,

• new discriminants to enhance the sensitivity to distin-guish the various production modes of the SM Higgsboson,

• the use of data sidebands to constrain the dominant Z Z∗background process,

• a dedicated control region to constrain the background inthe reconstructed event categories probing t t H produc-tion,

• improved estimates of Z+jets, t t , and WZ backgrounds,and

• an EFT interpretation, based on a parameterisation of thecross-sections rather than a direct parameterisation of thereconstructed event yields.

1.1 Simplified template cross-sections

In the framework of Simplified Template Cross Sections(STXS) [23–25], exclusive regions of phase space are definedfor each Higgs boson production mechanism. These phase-space regions, referred to as production bins, are definedto reduce the dependence on theoretical uncertainties thatdirectly fold into the measurements and at the same timemaximise the experimental sensitivity to measure the bins,enhance the contribution from possible BSM effects, andallow measurements from different Higgs boson decay

modes to be combined. The number of production bins islimited to avoid loss of measurement sensitivity for a givenamount of integrated luminosity.

The definitions of the production bins used for this mea-surement are shown in the left panel of Fig. 1 (shaded area).All production bins are defined for Higgs bosons with rapid-ity |yH | < 2.5 and no requirement is placed on the particle-level leptons. Two sets of production bins with different gran-ularity are considered, as a trade-off between statistical andtheoretical uncertainties.

The first set of production bins (Production Mode Stage)[24] is defined according to the Higgs boson produc-tion modes: gluon–gluon fusion (ggF), vector-boson fusion(VBF) and associated production with vector bosons (VH,where V = W or Z ) or top quark pairs (t t H ). Since b-jetsfrom bbH associated production are emitted at small anglesrelative to the beam axis and usually outside of the detectoracceptance, the bbH and ggF Higgs boson production modeshave similar signatures and acceptances. Their contributionsare considered together with their relative ratio fixed to theSM prediction. In the following, the sum of their contribu-tions is referred to as ggF. Similarly, single top production(tH) is considered together with t t H , with their relative ratiofixed to the SM prediction. In contrast to the Stage-0 produc-tion bins described in Ref. [24], the VH events with hadronicdecays of the vector boson V are included in the VH pro-duction bin rather than in the ggF or VBF bins. In this way,each of the four main Higgs boson production modes can bemeasured separately.

The second set of production bins (Reduced Stage 1.1)is more exclusive than the first one. Starting from the pro-duction bins of a more granular Stage 1.1 set [25], severalproduction bins are merged as the full set of bins cannotbe measured separately in the H → Z Z∗ → 4� chan-nel with the current data sample. The definitions of thebins are based on the multiplicity of particle-level jets, theHiggs boson transverse momentum pHT and the invariantmass m j j of the two jets with the highest transverse momen-tum. Particle-level jets are built from all stable particles (par-ticles with lifetime cτ>10 mm) including neutrinos, pho-tons, and leptons from hadron decays or those produced inthe parton shower. The anti-kt jet reconstruction algorithm[26,27] with a radius parameter R = 0.4 is used. All Higgsboson decay products, as well as the leptons and neutrinosfrom the decays of the associated V bosons are excludedfrom the jet building, while the decay products from hadron-ically decaying associated V bosons, are included. The jetsare required to have pT > 30 GeV, with no restrictions onrapidity.

Events from ggF production and gg → ZH productionwith a hadronically decaying Z boson are split into sevencommon production bins. Six bins have a Higgs boson trans-verse momentum below 200 GeV, while the seventh bin with

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ATLAS √s = 13 TeV, 139 fb-1

ProductionMode

VH

VBF

ttH

ggF

VH-Lep

pTH < 60 GeV

pTH > 120 GeV

60 < pTH < 120 GeV

≥ 2-jets

= 0-jet

= 1-jet

mjj < 60 GeV or 120 < mjj < 350 GeV or mjj > 350 GeV, pT

H < 200 GeV

60 < mjj < 120 GeV

Leptonic V decay

STXS ReducedStage 1.1

ttH

gg2H-0j-pTH-Low

gg2H-1j-pTH-High

gg2H-1j-pTH-Low

gg2H-1j-pTH-Med

gg2H-0j-pTH-High

qq2Hqq-BSM

qq2Hqq-VH

qq2Hqq-VBF

gg2H-2j

gg2H-pTH-High

pTH < 200 GeV

pTH > 200 GeV

pTH < 10 GeV

pTH > 10 GeV

Particle-level Production Bins

gg →

Z(2

j) +

H

qq’ →

V(2

j) +

H

mjj > 350 GeV, pTH > 200 GeV

ttH Hadronic

m4l = [115, 130] GeV

ttH Leptonic

Nlep ≥ 5

pT4l < 10 GeV

Njet = 0, pT4l > 100 GeV

10 < pT4l < 100 GeV

60 < pT4l < 120 GeV

pT4l < 60 GeV

120 < pT4l < 200 GeV Njet = 1

Njet = 0

mjj > 120 GeV, pT4l > 200 GeV

mjj < 120 GeV or pT4l < 200 GeV

pT4l > 200 GeV

Njets ≥ 2

SB - 0j

Njet = 1

Njet = 0

SB - 1j

m4l = [105, 115] U [130, 350] GeV

Nlep ≥ 5

Njets ≥ 2

tXX-like

SB - VH-Lep-enriched

SB - 2j

SB - tXX-enriched

m4l = [105, 115] U [130, 160] GeV

Reconstructed event categoriesSideband Region

Reconstructed event categoriesSignal Region

ttH-Had-enriched

0j-pT4l-Low

1j-pT4l-Medium

1j-pT4l-High

ttH-Lep-enriched

2j

2j-BSM-like

0j-pT4l-Medium

0j-pT4l-High

VH-Lep-enriched

1j-pT4l-BSM-like

1j-pT4l-Low

Fig. 1 Two sets (Production Mode Stage and Reduced Stage 1.1) ofexclusive phase-space regions (production bins) defined at particle-levelfor the measurement of the Higgs boson production cross-sections (leftand middle-left shaded panels), and the corresponding reconstructedevent categories for signal (middle-right panel) and sidebands (rightpanel). The description of the production bins is given in Sect. 1.1,

while the reconstructed signal region and sideband event categories aredescribed in Sects. 5 and 6, respectively. The bbH (t H ) contribution isincluded in the ggF (t t H ) production bins. The colours of each recon-structed event category box indicates the contributions from the relevantproduction processes

Higgs boson transverse momentum above 200 GeV (gg2H-pHT -High) is sensitive to contributions from BSM physics.For pHT below 200 GeV, further splits are made accordingto the jet multiplicity and pHT . Events with no jets are splitinto two bins with pHT below and above 10 GeV. Eventswith one jet are split into three bins with pHT below 60 GeV,between 60 and 120 GeV, and above 120 GeV. Finally, Higgsboson events with two or more jets are combined into onebin. The bins are respectively denoted by gg2H-0 j-pHT -Low,gg2H-0 j-pHT -High, gg2H-1 j-pHT -Low, gg2H-1 j-pHT -Med,gg2H-1 j-pHT -High and gg2H-2 j .

As described in Ref. [25], VBF and VH production withhadronically decaying associated V bosons represent thet-channel and s-channel contributions to the same elec-troweak qqH production process and are therefore consid-ered together for further splitting. Three bins are defined: onebin, sensitive to BSM contributions (qq2Hqq-BSM), with pHTabove 200 GeV and m j j above 350 GeV; one bin (qq2Hqq-VH) with m j j between 60 and 120 GeV to target the VH pro-duction mode; and one bin (qq2Hqq-VBF) with the Higgsboson not satisfying these criteria to ensure sensitivity to the

VBF process. qqH events in which one or both jets havetransverse momenta below the 30 GeV threshold are treatedas a part of the qq2Hqq-VBF bin.

The VH process with the associated V boson decayingleptonically is considered separately (VH-Lep). The leptonicdecay includes the decays into τ -leptons and neutrino pairs.The t t H production bin remains the same as in the ProductionMode Stage.

The middle-right and right panels of Fig. 1 summarise thecorresponding categories of reconstructed events in whichthe cross-section measurements and background estimationsare performed. These are described in detail in Sect. 5.

1.2 Higgs boson couplings in the κ-framework

To probe physics beyond the SM, the measured produc-tion cross-sections are interpreted within a leading-order-motivated κ-framework [21], in which a set of coupling mod-ifiers �κ is introduced to parameterise deviations from theSM predictions of the Higgs boson couplings to SM bosonsand fermions. The framework assumes that the data origi-

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nate from a single CP-even Higgs boson state with a massof 125 GeV and the tensor coupling structure of the SM forits interactions. Only the coupling strengths are allowed tobe modified by the BSM processes. The Higgs boson widthis assumed to be small enough such that the narrow-widthapproximation is valid, allowing the Higgs boson productionand decay to be factorised:

σ · B (i → H → f ) = σi (�κ) · � f (�κ)

�H (�κ),

where σi is the production cross-section via the initial state i ,B and � f are the branching ratio and partial decay width forthe decay into the final state f , respectively, and �H is thetotal width of the Higgs boson. For a Higgs boson produc-tion and decay process via couplings i and f , respectively,coupling-strength modifiers are defined as

κ2i = σi

σ SMi

and κ2f = � f

�SMf

,

so that

σ · B (i → H → f ) = κ2i · κ2

f · σ SMi · �SM

f

�H (κ2i , κ2

f ).

1.3 Tensor structure of Higgs boson couplings in theeffective field theory approach

The κ-framework assumes that the tensor structure of theHiggs boson couplings is the same as in the SM. In orderto probe for possible non-SM contributions to the tensorstructure of the Higgs boson couplings, the measured sim-plified template cross-sections are interpreted using an EFTapproach. In this approach, which exploits exclusive kine-matical regions of the Higgs boson production and decayphase space, the BSM interactions are introduced via addi-tional higher-dimensional operators O(d)

i of dimension d,supplementing the SM Lagrangian LSM,

LEFT = LSM +∑

i

C (d)i

�(d−4)O(d)

i for d > 4.

The parameters C (d)i specify the strength of new interactions

and are known as the Wilson coefficients, and � is the scaleof new physics. Only dimension-six operators are consideredfor this paper, since the dimension-five and dimension-sevenoperators violate lepton and baryon number conservation andthe impact of higher-dimensional operators is expected to besuppressed by more powers of the cutoff scale � [28]. Forenergies less than the scale of new physics, only the ratioci = C (d=6)

i /�2 can be constrained by the data.Constraints are set on the Wilson coefficients defined

within the Standard Model Effective Field Theory (SMEFT)formalism [29] in the Warsaw basis [30]. The measurementsin the H → Z Z∗ → 4� channel do not provide sensitivity

for simultaneous constraints on the full set of these coeffi-cients. To reduce the number of relevant parameters, a mini-mal flavour-violating scenario is assumed and only operatorsaffecting the Higgs boson cross-section at tree level are con-sidered. Operators affecting only double Higgs boson pro-duction and those affecting the Higgs boson couplings todown-type quarks and leptons are neglected due to limitedsensitivity. The impact of these operators on the total Higgsboson decay width is also neglected.

The remaining ten operators (see Table 1) comprise fiveCP-even and five CP-odd ones. The CP-even operatorsdescribing interactions between the Higgs boson and gluonsand the top-Yukawa interactions are associated with the Wil-son coefficients cHG and cuH from Ref. [29], respectively.Similarly, the CP-even Higgs boson interactions with vectorbosons are related to cHW , cHB , and cHW B that impact theVBF and VH production and the Higgs boson decay into Zbosons. The Wilson coefficients for the corresponding CP-odd operators are cuH , cHG , cHW , cH B and cHW B .

The constraints on the Wilson coefficients can be derivedby comparing the expected with the measured simplifiedtemplate cross-sections. For that purpose, the correspond-ing expected signal production cross-sections, the branchingratio and the signal acceptances are parameterised in termsof the Wilson coefficients. The dependence of signal produc-tion cross-sections on the EFT parameters can be obtainedfrom its separation into three components:

σ ∝ |MSMEFT|2 =∣∣∣∣∣MSM +

∑

i

Ci

�2 Mi

∣∣∣∣∣

2

= |MSM|2 +∑

i

2Re(M∗

SMMi) Ci

�2

+∑

i j

2Re(M∗

i M j) CiC j

�4 ,

where the first term on the right-hand side is the squaredmatrix element for the SM, the second term represents theinterference between the SM and dimension-six EFT ampli-tudes and the third term comprises the pure BSM contribu-tion from dimension-six EFT operators alone. Following thisexpression, the dependence of the Higgs boson cross-sectionσ p(�c) in a given production bin p on a set of Wilson coef-ficients �c is parameterised relative to the SM prediction σ

pSM

as

σ p(�c)σp

SM

= 1 +∑

i

Api ci +

∑

i j

B pi j ci c j , (1)

where the coefficients Api and B p

i j are independent of �cand are determined from simulation. A similar procedure isapplied to obtain from simulation the EFT parameterisationof the branching ratio B4� for the H → Z Z∗ → 4� decayfrom the partial (�4�) and total decay width (�tot) parame-

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Table 1 Summary of EFT operators in the SMEFT formalism that areprobed in the H → Z Z∗ → 4� channel. The corresponding tensorstructure in terms of the SM fields from Ref. [29] is shown togetherwith the associated Wilson coefficients, the affected production ver-tices and the impact on the H → Z Z∗ decay vertex. The Higgs doubletfield and its complex conjugate are denoted as H and H , respectively.The left-handed quark doublets of flavour p (the right-handed up-type

quarks) are denoted qp (ur ). Vμν (Vμν = εμνρσVρσ ) is the (dual) fieldstrength tensor for a given gauge field V = G,W, B. The bosonic oper-ators with (without) a dual field strength tensor are CP-odd (CP-even).For the remaining operator with fermions (OuH ), the CP-odd contri-bution is introduced through the non-vanishing imaginary part of thecorresponding Wilson coefficient, denoted as cuH

CP-even CP-odd Impact on

Operator Structure Coeff. Operator Structure Coeff. production decay

OuH HH†qpur H cuH OuH HH†qpur H cuH tt H -

OHG HH†GAμνG

μνA cHG OHG HH†G AμνG

μνA cHG ggF Yes

OHW HH†WlμνW

μνl cHW OHW HH†W lμνW

μνl cHW VBF, VH Yes

OHB HH†BμνBμν cHB OH B HH† BμνBμν cH B VBF, VH Yes

OHWB HH†τ lW lμνB

μν cHW B OHW B HH†τ l W lμνB

μν cHW B VBF, VH Yes

terisations,

B4�(�c) = �4�(�c)�tot(�c)

= B4�SM · 1 + ∑

i A4�i ci + ∑

i j B4�i j ci c j

1 + ∑f

(∑i A

fi ci + ∑

i j Bfi j ci c j

) , (2)

where the total decay width is the sum of all partial decaywidths � f related to the decay mode f . The procedure forthe parameterisation of the cross-sections and the branchingratios is described in more detail in Ref. [31]. The criteriaemployed in the selection of four-lepton candidates introducean additional dependence of the signal acceptance on the EFTparameters. This is taken into account in the interpretation,as discussed in Sect. 10.

2 ATLAS detector

The ATLAS detector [32–34] at the LHC is a multipurposeparticle detector with a forward–backward symmetric cylin-drical geometry1 and a nearly 4π coverage in solid angle.It consists of an inner tracking detector (ID) surrounded bya thin superconducting solenoid, which provides a 2 T axialmagnetic field, electromagnetic (EM) and hadron calorime-ters, and a muon spectrometer (MS). The inner trackingdetector covers the pseudorapidity range |η| < 2.5. It con-sists of silicon pixel, silicon microstrip, and transition radia-tion tracking detectors. A lead/liquid-argon (LAr) sampling

1 ATLAS uses a right-handed coordinate system with its origin at thenominal interaction point (IP) in the centre of the detector and the z-axis along the beam pipe. The x-axis points from the IP to the centre ofthe LHC ring, and the y-axis points upwards. Cylindrical coordinates(r, φ) are used in the transverse plane, φ being the azimuthal anglearound the z-axis. The pseudorapidity is defined in terms of the polarangle θ as η = − ln tan(θ/2). Angular distance is measured in units of�R ≡ √

(�η)2 + (�φ)2.

calorimeter provides electromagnetic energy measurementsin the pseudorapidity range |η| < 3.2 with high granularity.A steel/scintillator-tile hadron calorimeter covers the centralpseudorapidity range (|η| < 1.7). The endcap and forwardregions are instrumented up to |η| = 4.9 with LAr calorime-ters for both the EM and hadronic energy measurements. Thecalorimeters are surrounded by the MS and three large air-core toroidal superconducting magnets with eight coils each.The field integral of the toroid magnets ranges between 2.0and 6.0 Tm across most of the detector. The MS includes asystem of precision tracking chambers and fast detectors fortriggering, covering the region |η| < 2.7. Events are selectedusing a first-level trigger implemented in custom electronics,which reduces the event rate to a maximum of 100 kHz usinga subset of detector information. Software algorithms withaccess to the full detector information are then used in thehigh-level trigger to yield a recorded event rate of about 1 kHz[35].

3 Data set and event simulation

The full ATLAS Run 2 data set, consisting of pp collisiondata at

√s = 13 TeV taken between 2015 and 2018, is used for

this analysis. The total integrated luminosity after imposingdata quality requirements [36] is 139 fb−1.

The production of the SM Higgs boson via gluon–gluonfusion, via vector-boson fusion, with an associated vectorboson and with a top quark pair was modelled with thePowheg-Box v2 Monte Carlo (MC) event generator [37–39]. For ggF, the PDF4LHC next-to-next-to-leading-order(NNLO) set of parton distribution functions (PDF) was used,while for all other production modes, the PDF4LHC next-to-leading-order (NLO) set was used [40].

The simulation of ggF Higgs boson production used thePowheg method for merging the NLO Higgs boson + jet

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cross-section with the parton shower and the multi-scaleimproved NLO (MINLO) method [41–44] to simultaneouslyachieve NLO accuracy for the inclusive Higgs boson produc-tion. In a second step, a reweighting procedure (NNLOPS)[45,46], exploiting the Higgs boson rapidity distribution,was applied using the HNNLO program [47,48] to achieveNNLO accuracy in the strong coupling constant αS. Thetransverse momentum spectrum of the Higgs boson obtainedwith this sample is compatible with the fixed-order calcula-tion from HNNLO and the resummed calculation at next-to-next-to-leading-logarithm accuracy matched to NNLO fixed-order with Hres2.3 [49,50].

The matrix elements of the VBF, qq → V H , and t t Hproduction mechanisms were calculated up to NLO in QCD.For VH production, the MINLO method was used to merge0-jet and 1-jet events [41,43,51–54]. The gg → ZH contri-bution was modelled at leading order (LO) in QCD.

The production of a Higgs boson in association with abottom quark pair (bbH ) was simulated at NLO with Mad-

Graph5_aMC@NLO v2.3.3 [55,56], using the CT10 NLOPDF [57]. The production in association with a single topquark (t H+X where X is either jb or W , defined in thefollowing as t H ) [58,59] was simulated at NLO with Mad-

Graph5_aMC@NLO v2.6.0 using the NNPDF3.0nlo PDFset [60].

For all production mechanisms, the Pythia 8 [61] genera-tor was used for the H → Z Z∗ → 4� decay with � = (e, μ)

as well as for parton showering, hadronisation and the under-lying event. The contribution of the Z → ττ decays is shownto have a negligible impact on the final result. The event gen-erator was interfaced to EvtGen v1.2.0 [62] for simulationof the bottom and charm hadron decays. For the ggF, VBFand VH processes, the AZNLO [63] set of tuned parameterswas used, while the A14 [64] set was used for t t H , bbH andt H processes. All signal samples were simulated for a Higgsboson mass mH = 125 GeV.

For additional cross-checks, the ggF sample was alsogenerated with MadGraph5_aMC@NLO. This simulationis accurate at NLO QCD accuracy for zero, one and twoadditional partons merged with the FxFx merging scheme[55,65]. The events were showered using the Pythia 8 gen-erator with the A14 set of tuned parameters.

The Higgs boson production cross-sections and decaybranching ratios, as well as their uncertainties, are taken fromRefs. [21,24,60,66–71]. The ggF production is calculatedwith next-to-next-to-next-to-leading order (N3LO) accuracyin QCD and has NLO electroweak (EW) corrections applied[72–82]. For VBF production, full NLO QCD and EW cal-culations are used with approximate NNLO QCD correc-tions [83–85]. The qq- and qg-initiated VH production iscalculated at NNLO in QCD and NLO EW corrections areapplied [86–94], while gg-initiated VH production is cal-culated at NLO in QCD. The t t H [95–98], bbH [99–101]

Table 2 The predicted SM Higgs boson production cross-sections (σ )for ggF, VBF and five associated production modes in pp collisions formH = 125 GeV at

√s = 13 TeV [21,24,58–60,66–105]. The quoted

uncertainties correspond to the total theoretical systematic uncertaintiescalculated by adding in quadrature the uncertainties due to missinghigher-order corrections and PDF+αS. The decay branching ratios (B)with the associated uncertainty for H → Z Z∗ and H → Z Z∗ → 4�,with � = e, μ, are also given

Production process σ [pb]

ggF (gg → H) 48.6 ± 2.4

VBF(qq ′ → Hqq ′) 3.78 ± 0.08

WH(qq ′ → WH

)1.373 ± 0.028

ZH (qq/gg → ZH) 0.88 ± 0.04

t t H (qq/gg → t t H) 0.51 ± 0.05

bbH (qq/gg → bbH) 0.49 ± 0.12

t H (qq/gg → t H) 0.09 ± 0.01

Decay process B [· 10−4]

H → Z Z∗ 262 ± 6

H → Z Z∗ → 4� 1.240 ± 0.027

and tH [58,59] processes are calculated to NLO accuracy inQCD. The total branching ratio is calculated in the SM forthe H → Z Z∗ → 4� decay with mH = 125 GeV and � =(e, μ) using PROPHECY4F [102,103], which includes thecomplete NLO EW corrections, and the interference effectsbetween identical final-state fermions. Due to the latter, theexpected branching ratios of the 4e and 4μ final states areabout 10% higher than the branching ratios to 2e2μ and 2μ2efinal states. Table 2 summarises the predicted SM productioncross-sections and branching ratios for the H → Z Z∗ → 4�

decay for mH = 125 GeV.For the study of the tensor structure of Higgs boson

couplings within an effective field theory approach, sev-eral samples with different values of EFT parameters weresimulated at LO in QCD separately for the ggF + bbH ,VBF + V (→ qq)H , qq → Z(→ ��)H , qq → W (→�ν)H , t t H , t HW and t H jb production modes usingMadGraph5_aMC@NLO and the NNPDF23lo PDF. TheBSM signal is defined by the flavour symmetric SMEFT-

sim_A_U35_MwScheme_UFO_v2.1model [29,106], whichincorporates the SMEFT dimension-six operators in the stan-dard Universal FeynRules Output format created using theFeynRules framework [107,108]. The light quarks (u, d, sand c) and leptons are assumed to be massless in the model.The generated events were showered with Pythia 8, usingthe CKKW-L matching scheme to match matrix element andparton shower computations with different jet multiplicities[61]. The A14 set of tuned parameters was used. All pro-cesses were simulated in the four-flavour scheme, apart fromthe t HW production, for which the five-flavour scheme wasused [55].

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The Z Z∗ continuum background from quark–antiquarkannihilation was modelled using Sherpa v2.2.2 [109–112],which provides a matrix element calculation accurate to NLOin αS for 0-jet and 1-jet final states and LO accuracy for2-jets and 3-jets final states. The merging with the Sherpa

parton shower [113] was performed using the ME+PS@NLOprescription [114]. The NLO EW corrections were appliedas a function of the invariant mass mZZ∗ of the Z Z∗ system[115,116].

The gluon-induced Z Z∗ production was modelled bySherpa v2.2.2 [109–111] at LO in QCD for 0-jet and1-jet final states. The higher-order QCD effects for thegg → Z Z∗ continuum production cross-section were cal-culated for massless quark loops [117–119] in the heavy top-quark approximation [120], including the interference withgg → H∗ → Z Z processes [121,122]. The gg → Z Zsimulation was scaled by a K -factor of 1.7 ± 1.0, which isdefined as the ratio of the higher-order to the leading-ordercross-section predictions.

Production of Z Z∗ via vector-boson scattering was sim-ulated with the Sherpa v2.2.2 [112] generator. The LO-accurate matrix elements were matched to a parton showerusing the MEPS@LO prescription.

For all Z Z∗ processes modelled using Sherpa, theNNPDF3.0nnlo PDF set [60] was used, along with a ded-icated set of tuned parton-shower parameters.

For additional checks, the qq-initiated Z Z∗ continuumbackground was also modelled using Powheg-Box v2 andMadGraph5_aMC@NLO, using the CT10 [57] and thePDF4LHC NLO PDF set, respectively. For the former, thematrix element was generated at NLO accuracy in QCD andeffects of singly resonant amplitudes and interference effectsdue to Z/γ ∗ were included. For the latter, the simulationsare accurate to NLO in QCD for zero and one additionalparton merged with the FxFx merging scheme. For both,the Pythia 8 generator was used for the modelling of par-ton showering, hadronisation, and the underlying event. TheAZNLO and A14 sets of tuned parameters were used forthe simulations performed with Powheg-Box v2 and Mad-

Graph5_aMC@NLO generators, respectively.The WZ background [123] was modelled at NLO accu-

racy in QCD using Powheg-Box v2 with the CT10 PDFset and was interfaced to Pythia 8, using the AZNLO set oftuned parameters for modelling of parton showering, hadro-nisation, and the underlying event and to EvtGen v1.2.0 forthe simulation of bottom and charm hadron decays. The tri-boson backgrounds ZZZ, WZZ, and WWZ with four or moreprompt leptons (VVV ) were modelled at NLO accuracy forthe inclusive process and at LO for up to two additional par-ton emissions using Sherpa v2.2.2.

The simulation of t t Z events with both top quarks decay-ing semileptonically and the Z boson decaying leptoni-cally was performed with MadGraph5_aMC@NLO using

the NNPDF3.0nlo [60] PDF set interfaced to Pythia 8using the A14 set of tuned parameters, and the total cross-section was normalised to a prediction computed at NLOin the QCD and EW couplings [98]. For modelling com-parisons, Sherpa v2.2.1 was used to simulate t t Z eventsat LO. The tW Z , t tWW , t tW Z , t t Zγ , t t Z Z , t t t , t t t tand t Z background processes were simulated with Mad-

Graph5_aMC@NLO interfaced to Pythia 8, using the A14set of tuned parameters. These processes are collectivelyreferred to as the tXX process.

The modelling of events containing Z bosons with asso-ciated jets (Z+ jets) was performed using the Sherpa v2.2.1generator. Matrix elements were calculated for up to twopartons at NLO and four partons at LO using Comix [110]and OpenLoops [111], and merged with the Sherpa partonshower [113] using the ME+PS@NLO prescription [114].The NNPDF3.0nnlo PDF set is used in conjunction with ded-icated set of tuned parton-shower parameters.

The t t background was modelled using Powheg-Box v2with the NNPDF3.0nlo PDF set. This simulation was inter-faced to Pythia 8, using the A14 set of tuned parameters, forparton showering, hadronisation, and the underlying event,and toEvtGen v1.2.0 for heavy-flavour hadron decays. Sim-ulated Z+ jets and t t background samples were normalisedto the data-driven estimates described in Sect. 6.

Generated events were processed through the ATLASdetector simulation [124] within the Geant4 framework[125] and reconstructed in the same way as collision data.Additional pp interactions in the same and nearby bunchcrossings were included in the simulation. Pile-up eventswere generated using Pythia 8 with the A2 set of tunedparameters [126] and the MSTW2008LO PDF set [127].The simulation samples were weighted to reproduce the dis-tribution of the number of interactions per bunch crossingobserved in data.

4 Event selection

4.1 Event reconstruction

The selection and categorisation of the Higgs boson candi-date events rely on the reconstruction and identification ofelectrons, muons, and jets, closely following the analysesreported in Refs. [17,128].

Proton–proton collision vertices are constructed fromreconstructed trajectories of charged particles in the ID withtransverse momentum pT > 500 MeV. Events are required tohave at least one collision vertex with at least two associatedtracks. The vertex with the highest

∑p2

T of reconstructedtracks is selected as the primary vertex of the hard interac-tion. The data are subjected to quality requirements to reject

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events in which detector components were not operating cor-rectly.

Electron candidates are reconstructed from energy clus-ters in the electromagnetic calorimeter that are matched toID tracks [129]. A Gaussian-sum filter algorithm [130] isused to compensate for radiative energy losses in the ID forthe track reconstruction, while a dynamical, topological cell-based approach for cluster building is used to improve theenergy resolution relative to the previous measurements inRefs. [17,128], in particular for the case of bremsstrahlungphotons. Electron identification is based on a likelihood dis-criminant combining the measured track properties, transi-tion radiation response, electromagnetic shower shapes andthe quality of the track–cluster matching. The ‘loose’ likeli-hood criteria, applied in combination with track hit require-ments, provide an electron reconstruction and identifica-tion efficiency of at least 90% for isolated electrons withpT > 30 GeV and 85%–90% below [129]. Electrons arerequired to have ET > 7 GeV and pseudorapidity |η| < 2.47,with their energy calibrated as described in Ref. [129].

Muon candidate reconstruction [131] within the range|η| < 2.5 is primarily performed by a global fit to fully recon-structed tracks in the ID and the MS, with a ‘loose’ [131]identification criterion applied. This criterion has an effi-ciency of at least 98% for isolated muons with pT = 5 GeVand rises to 99.5% at higher pT. At the centre of the detec-tor (|η| < 0.1), which has a reduced MS geometrical cov-erage, muons are also identified by matching a fully recon-structed ID track to either an MS track segment or a calorime-ter energy deposit consistent with a minimum-ionising par-ticle (calorimeter-tagged muons). For these two cases, themuon momentum is measured from the ID track alone. Inthe forward MS region (2.5 < |η| < 2.7), outside the fullID coverage, MS tracks with hits in the three MS layers areaccepted and combined with forward ID tracklets, if theyexist (stand-alone muons). Calorimeter-tagged muons arerequired to have pT > 15 GeV. For all other muon can-didates, the transverse momentum is required to be greaterthan 5 GeV. The muon momentum is calibrated using theprocedure described in Ref. [131]. Muons with transverseimpact parameter greater than 1 mm are rejected.2 Addition-ally, muons and electrons are required to have a longitudinalimpact parameter (|z0 sin θ |) less than 0.5 mm.

Jets are reconstructed using a particle flow algorithm [22]from noise-suppressed positive-energy topological clusters[132] in the calorimeter using the anti-kt algorithm [26,27]with a radius parameter R = 0.4. Energy deposited in the

2 The transverse impact parameter d0 of a charged-particle track isdefined in the transverse plane as the distance from the primary vertex tothe track’s point of closest approach. The longitudinal impact parameterz0 is the distance in the z direction between this track point and theprimary vertex.

calorimeter by charged particles is subtracted and replacedby the momenta of tracks that are matched to those topolog-ical clusters. Compared to only using topological clusters,jets reconstructed with the particle flow algorithm with pT >

30 GeV have approximately 10% better transverse momen-tum resolution. The two different algorithms have similarresolution for pT above 100 GeV. The jet four-momentum iscorrected for the calorimeter’s non-compensating response,signal losses due to noise threshold effects, energy lostin non-instrumented regions, and contributions from pile-up [22,133,134]. Jets are required to have pT > 30 GeVand |η| < 4.5. Jets from pile-up with |η| < 2.5 are sup-pressed using a jet-vertex-tagger multivariate discriminant[135,136]. Jets with |η| < 2.5 containing b-hadrons are iden-tified using the MV2c10 b-tagging algorithm [137,138], andits 60%, 70%, 77% and 85% efficiency working points arecombined into a pseudo-continuous b-tagging weight [139]that is assigned to each jet.

Ambiguities are resolved if electron, muon, or jet candi-dates overlap in geometry or share the same detector infor-mation. If the two calorimeter energy clusters from the twoelectron candidates overlap, the electron with the higher ET

is retained. If a reconstructed electron and muon share thesame ID track, the muon is rejected if it is calorimeter-tagged;otherwise the electron is rejected. Reconstructed jets geomet-rically overlapping in a cone of radial size �R = 0.1 (0.2)with a muon (an electron) are also removed.

The missing transverse momentum vector, ⇀EmissT , is defined

as the negative vector sum of the transverse momenta of allthe identified and calibrated leptons, photons and jets and theremaining unclustered energy, where the latter is estimatedfrom low-pT tracks associated with the primary vertex butnot assigned to any lepton, photon, hadronically decayingτ -lepton or jet candidate [140,141]. The missing transversemomentum (Emiss

T ) is defined as the magnitude of ⇀EmissT .

4.2 Selection of the Higgs boson candidates

A summary of the event selection criteria is given in Table 3.Events were triggered by a combination of single-lepton,dilepton and trilepton triggers with different transversemomentum thresholds. Single-lepton triggers with the low-est thresholds had strict identification and isolation require-ments. Both the high-threshold single-lepton triggers andthe multilepton triggers had looser selection criteria. Dueto an increasing peak luminosity, these thresholds increasedslightly during the data-taking periods [142,143]. For single-muon triggers, the pT threshold ranged from between 20 and26 GeV, while for single-electron triggers, the pT thresholdranged from 24 to 26 GeV. The global trigger efficiency forsignal events passing the final selection is about 98%.

In the analysis, at least two same-flavour and opposite-charge lepton pairs (hereafter referred to as lepton pairs) are

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Table 3 Summary of the criteria applied to the selected Higgs boson candidate in each event. The mass threshold mmin is defined in Sect. 4.1

Trigger

Combination of single-lepton, dilepton and trilepton triggers

Leptons and jets

Electrons ET > 7 GeV and |η| < 2.47

Muons pT > 5 GeV and |η| < 2.7, calorimeter-tagged: pT > 15 GeV

Jets pT > 30 GeV and |η| < 4.5

Quadruplets

All combinations of two same-flavour and opposite-charge lepton pairs

– Leading lepton pair: lepton pair with invariant mass m12 closest to the Z boson mass mZ

– Subleading lepton pair: lepton pair with invariant mass m34 second closest to the Z boson mass mZ

Classification according to the decay final state: 4μ, 2e2μ, 2μ2e, 4e

Requirements on each quadruplet

Lepton – Three highest-pT leptons must have pT greater than 20, 15 and 10 GeV

reconstruction – At most one calorimeter-tagged or stand-alone muon

Lepton pairs – Leading lepton pair: 50 < m12 < 106 GeV

– Subleading lepton pair: mmin < m34 < 115 GeV

– Alternative same-flavour opposite-charge lepton pair: m�� > 5 GeV

– �R(�, �′) > 0.10 for all lepton pairs

Lepton isolation – The amount of isolation ET after summing the track-based and 40% of the

calorimeter-based contribution must be smaller than 16% of the lepton pT

Impact parameter - Electrons: |d0|/σ(d0) < 5

significance – Muons: |d0|/σ(d0) < 3

Common vertex – χ2-requirement on the fit of the four lepton tracks to their common vertex

Selection of the best quadruplet

– Select quadruplet with m12 closest to mZ from one decay final state in decreasing order of priority: 4μ, 2e2μ, 2μ2e and 4e

– If at least one additional (fifth) lepton with pT > 12 GeV meets the isolation, impact parameter and angular separation criteria, select

the quadruplet with the highest matrix-element value

Higgs boson mass window

– Correction of the four-lepton invariant mass due to the FSR photons in Z boson decays

– Four-lepton invariant mass window in the signal region: 115 < m4� < 130 GeV

– Four-lepton invariant mass window in the sideband region: 105 < m4� < 115 GeV or 130 < m4� < 160 (350) GeV

required in the final state, resulting in one or more possi-ble lepton quadruplets in each event. The three highest-pT

leptons in each quadruplet are required to have transversemomenta above 20 GeV, 15 GeV and 10 GeV, respectively.To minimise the background contribution from non-promptmuons, at most one calorimeter-tagged or stand-alone muonis allowed per quadruplet.

The lepton pair with the invariant mass m12 (m34) closest(second closest) to the Z boson mass [144] in each quadrupletis referred to as the leading (subleading) lepton pair. Basedon the lepton flavour, each quadruplet is classified into one ofthe following decay final states: 4μ, 2e2μ, 2μ2e and 4e, withthe first two leptons always representing the leading lepton

pair. In each of these final states, the quadruplet with m12

closest to the Z boson mass has priority to be consideredfor the selection of the final Higgs boson candidate. In caseadditional prompt leptons are present in the event, the prior-ity may change due to the matrix-element based pairing asdescribed later on. All quadruplets are therefore required topass the following selection criteria.

To ensure that the leading lepton pair from the signal origi-nates from a Z boson decay, the leading lepton pair is requiredto satisfy 50 GeV < m12 < 106 GeV. The subleading leptonpair is required to have a mass mmin < m34 < 115 GeV,where mmin is 12 GeV for the four-lepton invariant mass m4�

below 140 GeV, rising linearly to 50 GeV at m4� = 190 GeV

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and then remaining at 50 GeV for all higher m4� values.This criterion suppresses the contributions from processes inwhich an on-shell Z boson is produced in association with aleptonically decaying meson or virtual photon. In the 4e and4μ final states, the two alternative opposite-charge leptonpairings within a quadruplet are required to have a dilep-ton mass above 5 GeV to suppress the J/ψ background. Allleptons in the quadruplet are required to have an angular sep-aration of �R > 0.1.

Each electron (muon) track is required to have a transverseimpact parameter significance |d0/σ(d0)| < 5 (3), to sup-press the background from heavy-flavour hadrons. Reduciblebackground from the Z+jets and t t processes is further sup-pressed by imposing track-based and calorimeter-based iso-lation criteria on each lepton [131,145]. A scalar pT sum(track isolation) is made from the tracks with pT > 500 MeVwhich either originate from the primary vertex or have|z0 sin θ | < 3 mm if not associated with any vertex and liewithin a cone of �R = 0.3 around the muon or electron.Above a lepton pT of 33 GeV, this cone size falls linearlywith pT to a minimum cone size of 0.2 at 50 GeV. Similarly,the scalar ET sum (calorimeter isolation) is calculated fromthe positive-energy topological clusters that are not associ-ated with a lepton track in a cone of �R = 0.2 around themuon or electron. The sum of the track isolation and 40% ofthe calorimeter isolation is required to be less than 16% of thelepton pT. The calorimeter isolation is corrected for electronshower leakage, pile-up and underlying-event contributions.Both isolations are corrected for track and topological clus-ter contributions from the remaining three leptons. The pile-up dependence of this isolation selection is improved com-pared with that of the previous measurements [17,128,146]by optimising the criteria used for exclusion of tracks asso-ciated with a vertex other than the primary vertex and bythe removal of topological clusters associated with tracks.The signal efficiency of the isolation criteria is greater than80%, improving the efficiency by about 5% compared withthe previous analysis for the same background rejection.

The four quadruplet leptons are required to originate froma common vertex point. A requirement corresponding to asignal efficiency of better than 99.5% is imposed on the χ2

value from the fit of the four lepton tracks to their commonvertex.

If there is more than one decay final state per event withthe priority quadruplet (m12 closest to mZ ) satisfying theselection criteria, the quadruplet from the final state withhighest selection efficiency, i.e. ordered 4μ, 2e2μ, 2μ2e and4e, is chosen as the Higgs boson candidate.

In the case of VH or t t H production, there may be addi-tional prompt leptons present in the event, together with theselected quadruplet. Therefore, there is a possibility thatone or more of the leptons selected in the quadruplet donot originate from a Higgs boson decay, but rather from

the V boson leptonic decay or the top quark semileptonicdecay. To improve the lepton pairing in such cases, a matrix-element-based pairing method assuming the SM tensor struc-ture is used for all events containing at least one additionallepton with pT > 12 GeV and satisfying the same iden-tification, isolation and angular separation criteria as thefour quadruplet leptons [17,128]. For all possible quadru-plet combinations that satisfy the selection, a matrix elementfor the Higgs boson decay is computed at LO using theMadGraph5_aMC@NLO [55] generator, with the recon-structed lepton momentum vectors as inputs to the calcula-tion. The quadruplet with the largest matrix-element valueis selected as the Higgs boson candidate. This method leadsto a 50% improvement in correctly identifying the leptons inthe quadruplet as those originating from a Higgs boson decayif an extra lepton is identified. The impact of the matrix ele-ment on the expected invariant mass distribution is shown inFig. 2a.

To improve the four-lepton invariant mass reconstruction,the reconstructed final-state radiation (FSR) photons in Zboson decays are accounted for using the same strategy as theprevious publications [17,128]. Collinear FSR candidates aredefined as candidates with �R < 0.15 to the nearest lepton inthe quadruplet. Collinear FSR candidates are considered onlyfor muons from the leading lepton pair, while non-collinearFSR candidates are considered for both muons and electronsfrom leading and subleading Z bosons.

Collinear FSR candidates are selected from reconstructedphoton candidates and from electron candidates that sharean ID track with the muon. Further criteria are appliedto each candidate, based on the following discriminants:the fraction, f1, of cluster energy in the front segmentof the EM calorimeter divided by the total cluster energyto reduce backgrounds from muon ionisation; the angu-lar distance, �Rcluster,μ, between the candidate EM clus-ter and the muon; and the candidate pT, which must beat least 1 GeV. For all selected electron candidates andfor photon candidates with pT < 3.5 GeV, a requirement off1 > 0.2 and �Rcluster,μ < 0.08 is imposed. The collinearphoton candidates with pT > 3.5 GeV are selected if f1 > 0.1and �Rcluster,μ < 0.15. Non-collinear FSR candidates areselected only from reconstructed isolated photons meetingthe ‘tight’ criteria [129,147] and satisfying pT > 10 GeV and�Rcluster,� > 0.15.

Only one FSR candidate is included in the quadruplet, withpreference given to collinear FSR and to the candidate withthe highest pT. An FSR candidate is added to the lepton pair ifthe invariant mass of the lepton pair is between 66 and 89 GeVand if the invariant mass of the lepton pair and the photon isbelow 100 GeV. Approximately 3% of reconstructed Higgsboson candidates have an FSR candidate and its impact onthe expected invariant mass distribution is shown in Fig. 2b.

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The Higgs boson candidates within a mass window of115 GeV < m4� < 130 GeV are selected as the signal region.Events failing this requirement but that are within a mass win-dow of 105 GeV < m4�< 115 GeV or 130 GeV < m4�< 160(350) GeV are assigned to the sideband regions used to esti-mate the leading backgrounds as described in Sect. 6.

The selection efficiencies of the simulated signal in thefiducial region |yH | < 2.5, where yH is the Higgs bosonrapidity, are about 33%, 25%, 19% and 16%, in the 4μ, 2e2μ,2μ2e and 4e final states, respectively.

5 Event categorisation and production modediscrimination

In order to be sensitive to different production bins in theframework of simplified template cross-sections, the selectedHiggs boson candidates in the mass window 115 GeV <

m4� < 130 GeV are classified into several dedicated recon-structed event categories. In addition, the events in the masssidebands are also categorised for purposes of backgroundestimation described in Sect. 6. In general, more than oneproduction mode contributes to each reconstructed event cat-egory, as well as various background processes. For this rea-son, multivariate discriminants are introduced in most of themutually exclusive reconstructed event categories to distin-guish between these contributions.

5.1 Event categorisation

For signal events, the classification is performed in the ordershown in the middle-right panel of Fig. 1 (from bottom totop) and as described below. First, those events classified asenriched in the t t H process are split according to the decaymode of the two W bosons from the top quark decays. Forsemileptonic and dileptonic decays (ttH-Lep-enriched), atleast one additional lepton with pT > 12 GeV3 together withat least two b-tagged jets (with 85% b-tagging efficiency),or at least five jets among which at least one b-tagged jet(with 85% b-tagging efficiency) or at least two jets amongwhich at least one b-tagged jet (with 60% b-tagging effi-ciency) is required. For the fully hadronic decay (ttH-Had-enriched), there must be either at least five jets among whichat least two b-tagged jets (with 85% b-tagging efficiency) orat least four jets among which at least one b-tagged jet (with60% b-tagging efficiency). Events with additional leptons butnot satisfying the jet requirements define the next categoryenriched inVH production events with leptonic vector-bosondecay (VH-Lep-enriched).

3 The additional lepton is a lepton candidate as defined in Sect. 4.1.It is also required to satisfy the same isolation, impact parameter andangular separation requirements as the leptons in the quadruplet.

The remaining events are classified according to theirreconstructed jet multiplicity into events with no jets, exactlyone jet or at least two jets. Events with at least two recon-structed jets are divided into two categories: one is a ‘BSM-like’ category (2 j-BSM-like) and the other (2 j) contains thebulk of events with significant contributions from the VBFand VH production modes in addition to ggF. The 2 j-BSM-like category requires the invariant mass m j j of the twoleading jets to be larger than 120 GeV and the four-leptontransverse momentum, p4�

T , to be larger than 200 GeV; theremaining events are placed in the 2 j category.

Events with zero or one jet in the final state are expected tobe mostly from the ggF process. Following the particle-leveldefinition of production bins in Sect. 1.1, the 1-jet categoryis further split into four categories with p4�

T smaller than60 GeV (1 j-p4�

T -Low), between 60 and 120 GeV (1 j-p4�T -

Med), between 120 and 200 GeV (1 j-p4�T -High), and larger

than 200 GeV (1 j-p4�T -BSM-like).

The largest number of ggF events and the highest ggFpurity are expected in the zero-jet category. The zero-jet cat-egory is split into three categories with p4�

T smaller than10 GeV (0 j-p4�

T -Low), between 10 and 100 GeV (0 j-p4�T -

Med) and above 100 GeV (0 j-p4�T -High). The first two cat-

egories follow the production bin splitting, and the last cate-gory improves the discrimination betweenVH (V → �ν/νν)and ggF.

As illustrated in Fig. 1, there is a dedicated reconstructedevent category for each production bin except for gg2H-2 j ,qq2Hqq-VH and qq2Hqq-VBF. These production bins arelargely measured from the 2-jet reconstruction category, andto a lesser extent from the 1-jet categories, using multivariatediscriminants (see Sect. 5.2). The gg2H-pHT -High productionbin is measured simultaneously in all reconstructed eventcategories with high transverse momentum of the four-leptonsystem, independent of the reconstructed jet multiplicity.

The rightmost panel of Fig. 1 shows the backgroundevent classification. For estimating the tXX process fromthe mass sideband, a tXX-enriched sideband category (SB-t X X -enriched) is defined, which includes events with atleast two jets including at least one tagged as a b-jet with60% efficiency and Emiss

T > 100 GeV in the m4� mass range105–115 GeV or 130–350 GeV. This region is dominated byt t Z (87%) and has small contributions from t t , t t t t , tW Z ,t tW , t tWW , t tW Z , t t Zγ , t t Z Z and t Z . The tXX processis expected to give the largest contribution in ‘t t H -like’ cat-egories. The large mass range for this category, larger thanfor the non-resonant Z Z as discussed next, allows better sta-tistical precision for the estimate of this background.

For the estimation of non-resonant Z Z∗ production,events not meeting the criteria for the SB-t X X -enrichedcategory and in the m4� mass range 105–115 GeV or 130–160 GeV are split according to the number of reconstructedjets: exactly zero jets (SB-0 j), exactly one jet (SB-1 j) or at

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[GeV]4lm

3−10

2−10

1−10

1E

vent

s/2

GeV

Before matrix element pairing

After matrix element pairing 4l→ ZZ* →H

-1 = 13 TeV, 139 fbs 1 extra lepton≥Events with

ATLAS Simulation

(a)

100 120 140 160 180 200 220 90 100 110 120 130 140

[GeV]4lm

0

0.2

0.4

0.6

0.8

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1.2

Eve

nts/

1 G

eV

Before FSR correction

After FSR correction

4l→ ZZ* →H -1 = 13 TeV, 139 fbs

Events with a FSR candidate

ATLAS Simulation

(b)

Fig. 2 Impact on the expected invariant mass distribution of theselected Higgs boson candidates due to (a) matrix-element-based pair-ing for candidates with at least one extra lepton and (b) accounting for

final-state radiation for candidates with an FSR candidate. For (a), theoverflow events are included in the last bin

least two jets (SB-2 j). This mass range limits the contribu-tion from the single-resonance process, Z → 4�, and fromthe on-shell Z Z process. Similarly, events in the same massrange with an extra reconstructed lepton separately form theSB-VH-Lep-enriched category, which is enriched with sig-nal events containing leptons from the associated V leptonicdecay or the top quark semileptonic decay. This categoryis mainly designed to improve the expected sensitivity forVH-Lep by about 5%, having a VH purity of about 19%.

The expected number of signal events is shown in Table 4for each reconstructed event category separately for each pro-duction mode. The ggF and bbH contributions are shownseparately to compare their relative contributions, but bothbelong in the same (ggF) production bin. The highest bbHevent yield is expected in the 0 j categories since the jetstend to be more forward than in the t t H process, thus escap-ing the acceptance of the t t H selection criteria. The sourcesof uncertainty in these expectations are detailed in Sect. 7.The signal composition in terms of the Reduced Stage-1.1production bins is shown in Fig. 3.

The separation of the contributions from different pro-duction bins, such as the gg2H-2 j , qq2Hqq-VH and qq2Hqq-VBF components contributing in categories with two or morejets, is improved by means of discriminants obtained usingmultivariate data analysis, as described in the following sec-tion.

5.2 Multivariate production mode discriminants

To further increase the sensitivity of the cross-section mea-surements in the production bins (Sect. 1.1), multivariate

discriminants using neural networks (NNs) [148] are intro-duced in many of the reconstructed signal event categories asobservables used in the statistical fit, described in Sect. 8.2.The NN architecture and training procedure are definedusing Keras with TensorFlow [149,150]. These networks aretrained using several discriminating observables, as definedin Table 5, on simulated SM Higgs boson signals withmH = 125 GeV or non-Higgs-boson background. Due tothe low number of signal events expected in the 0 j-p4�

T -High,1 j-p4�

T -BSM-like and ttH-Lep-enriched categories, only theobserved yield is used as the discriminant in these categories.

Two types of NNs are used: feed-forward multilayer per-ceptron (MLP) and recurrent (RNN) [148–152]. Each NNdiscriminant combines two RNNs, one for the pT-orderedvariables related to the four leptons in the quadruplet andone for variables related to jets, and an MLP with additionalvariables related to the full event. The jet RNN accepts inputsfrom up to three jets. The outputs of the MLP and the twoRNNs are chained into another MLP to complete an NNdiscriminant, which is trained to approximate the posteriorprobability for an event to originate from a given process.This is used in each reconstructed event category to discrim-inate between two or three processes, e.g. ggF, VBF and Z Zbackground in the 1 j-p4�

T -Low category. The variables usedto train the MLP and RNNs for each category along with theprocesses being separated are summarised in Table 5.

The NN training variables not previously defined are listedas follows. The kinematic discriminant DZZ∗[153], definedas the difference between the logarithms of the squaredmatrix elements for the signal decay (same as in Sect. 4) andsquared matrix elements for the background process, is used

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Eur. Phys. J. C (2020) 80:957 of 54 957

Table4

The

expe

cted

num

bero

fSM

Hig

gsbo

son

even

tsw

ithm

H=

125

GeV

fora

nin

tegr

ated

lum

inos

ityof

139

fb−1

at√ s

=13

TeV

inea

chre

cons

truc

ted

even

tsig

nal(

115

<m

4�<

130

GeV

)an

dsi

deba

nd(m

4�in

105–

115

GeV

or13

0–16

0G

eVfo

rZZ

∗ ,13

0–35

0G

eVfo

rtXX

)cat

egor

y,sh

own

sepa

rate

lyfo

reac

hpr

oduc

tion

bin

ofth

ePr

oduc

tion

Mod

eSt

age.

The

ggF

andbb

Hyi

elds

are

show

nse

para

tely

butb

oth

cont

ribu

teto

the

sam

e(g

gF)p

rodu

ctio

nbi

n,an

dZH

andW

Har

ere

port

edse

para

tely

buta

rem

erge

dto

geth

erfo

rthe

final

resu

lt.St

atis

tical

and

syst

emat

icun

cert

aint

ies,

incl

udin

gth

ose

for

tota

lSM

cros

s-se

ctio

npr

edic

tions

,are

adde

din

quad

ratu

re.C

ontr

ibut

ions

that

are

belo

w0.

2%of

the

tota

lsi

gnal

inea

chre

cons

truc

ted

even

tca

tego

ryar

eno

tsh

own

and

are

repl

aced

by‘−

’

Rec

onst

ruct

edev

entc

ateg

ory

SMH

iggs

boso

npr

oduc

tion

mod

e

ggF

VB

FWH

ZH

ttH

+tH

bbH

Sign

al11

5<

m4�

<13

0G

eV

0j-p4� T

-Low

23.9

±3.

50.

073

±0.

006

0.01

73±

0.00

310.

0131

±0.

0023

−0.

17±

0.09

0j-p4� T

-Med

74±

81.

03±

0.15

0.37

±0.

050.

40±

0.05

−0.

8±

0.4

0j-p4� T

-Hig

h0.

109

±0.

026

0.01

57±

0.00

240.

056

±0.

005

0.17

3±

0.01

60.

0006

5±

0.00

023

−1j-p4� T

-Low

31±

41.

99±

0.11

0.52

±0.

050.

35±

0.04

−0.

41±

0.21

1j-p4� T

-Med

17.3

±2.

82.

50±

0.18

0.52

±0.

060.

40±

0.04

0.00

78±

0.00

130.

09±

0.04

1j-p4� T

-Hig

h3.

6±

0.8

0.84

±0.

070.

158

±0.

015

0.16

6±

0.01

60.

0044

±0.

0006

0.01

1±

0.00

6

1j-p4� T

-BSM

-lik

e0.

87±

0.23

0.24

6±

0.02

00.

060

±0.

007

0.05

4±

0.00

60.

0015

6±

0.00

032

0.00

09±

0.00

05

2j

25±

58.

5±

0.6

1.94

±0.

151.

69±

0.13

0.46

±0.

040.

30±

0.15

2j-

BSM

-lik

e1.

9±

0.6

1.08

±0.

050.

120

±0.

016

0.12

2±

0.01

60.

075

±0.

007

0.00

21±

0.00

10

VH

-Lep

-enr

iche

d0.

050

±0.

011

0.01

9±

0.00

40.

80±

0.07

0.24

5±

0.02

10.

166

±0.

013

0.00

27±

0.00

14

ttH

-Had

-enr

iche

d0.

15±

0.16

0.02

1±

0.00

40.

020

±0.

005

0.05

5±

0.01

30.

75±

0.07

0.02

0±

0.01

1

ttH

-Lep

-enr

iche

d0.

0019

±0.

0022

0.00

019

±0.

0000

80.

0046

±0.

0026

0.00

32±

0.00

180.

41±

0.04

−Si

deba

nd10

5<

m4�

<11

5G

eVor

130

<m

4�<

160

GeV

SB-0

j4.

2±

0.5

0.05

0±

0.01

00.

096

±0.

011

0.04

2±

0.00

5−

0.04

4±

0.02

2

SB-1j

2.37

±0.

290.

241

±0.

024

0.10

0±

0.01

30.

063

±0.

008

0.00

49±

0.00

090.

023

±0.

012

SB-2

j1.

25±

0.26

0.43

±0.

050.

119

±0.

014

0.10

3±

0.01

20.

109

±0.

010

0.01

6±

0.00

8

SB-VH

-Lep

-enr

iche

d0.

015

±0.

005

0.00

29±

0.00

110.

084

±0.

008

0.10

4±

0.01

00.

065

±0.

006

0.00

13±

0.00

07

105

<m

4�<

115

GeV

or13

0<

m4�

<35

0G

eV

SB-tXX

-enr

iche

d0.

001

±0.

010

0.00

012

±0.

0000

90.

0006

±0.

0004

0.00

08±

0.00

040.

068

±0.

008

−To

tal

186

±14

17.0

±0.

85.

0±

0.4

3.97

±0.

292.

13±

0.18

1.9

±1.

0

123

957 of 54 Eur. Phys. J. C (2020) 80:957

Expected Composition

-Lep-enrichedttH-Had-enrichedttH

-High4lT

p-j0-Lep-enrichedVH

-BSM-likej2j2

-BSM-like4lT

p-j1-High4l

Tp-j1

-Med4lT

p-j1-Low4l

Tp-j1

-Med4lT

p-j0-Low4l

Tp-j0

Rec

onst

ruct

ed E

vent

Cat

egor

y

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

-LowHT

p-jgg2H-0

-HighHT

p-jgg2H-0

-LowHT

p-jgg2H-1

-MedHT

p-jgg2H-1-HighH

Tp-jgg2H-1

jgg2H-2

-HighHT

pgg2H-

qq2Hqq-VBF

VHqq2Hqq-

qq2Hqq-BSM-LepVH

tH+ttH

ATLAS Simulation 4l→ ZZ* →H

-1 = 13 TeV, 139 fbs

Fig. 3 Standard Model signal composition in terms of the Reduced Stage-1.1 production bins in each reconstructed event category. The bbHcontributions are included in the ggF production bins

Table 5 The input variables used to train the MLP, and the two RNNsfor the four leptons and the jets (up to three). For each category, theprocesses which are classified by an NN, their corresponding inputvariables and the observable used are shown. For example, there are

eight input variables for the Lepton RNN being trained if p�T and η� are

listed. Leptons and jets are denoted by ‘�’ and ‘ j’. See the text for thedefinitions of the variables

Category Processes MLP Lepton RNN Jet RNN Discriminant

0 j-p4�T -Low ggF, Z Z∗ p4�

T , DZZ∗ , m12, m34, p�T, η� – NNggF

0 j-p4�T -Med |cos θ∗|, cos θ1, φZ Z

1 j-p4�T -Low ggF, VBF, Z Z∗ p4�

T , p jT, η j , p�

T, η� – NNVBF for NNZ Z < 0.25

�R4�j , DZZ∗ NNZ Z for NNZ Z > 0.25

1 j-p4�T -Med ggF, VBF, Z Z∗ p4�

T , p jT, η j , Emiss

T , p�T, η� – NNVBF for NNZ Z < 0.25

�R4�j , DZZ∗ , η4� NNZ Z for NNZ Z > 0.25

1 j-p4�T -High ggF, VBF p4�

T , p jT, η j , p�

T, η� – NNVBF

EmissT , �R4�j , η4�

2 j ggF, VBF, VH m j j , p4�j jT p�

T, η� p jT, η j NNVBF for NNV H < 0.2

NNV H for NNV H > 0.2

2 j-BSM-like ggF, VBF ηZeppZ Z , p4�j j

T p�T, η� p j

T, η j NNVBF

VH-Lep-enriched VH , t t H Njets, Nb-jets,70%, p�T – NNt t H

EmissT , HT

ttH-Had-enriched ggF, t t H , tXX p4�T , m j j , p�

T, η� p jT, η j NNt t H for NNt X X < 0.4

�R4�j , Nb-jets,70%, NNt X X for NNt X X > 0.4

to distinguish ggF from the non-resonant Z Z background.Three angles [7] are used to further distinguish these pro-cesses: the cosine of the leading Z boson’s production angleθ∗ in the four-lepton rest frame; the cosine of θ1 defined as the

angle between the negatively charged lepton of the leadingZ in the leading Z rest frame and the direction of flight of theleading Z in the four-lepton rest frame; and the angle φZ Z ,between the two Z decay planes in the four-lepton rest frame.

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Eur. Phys. J. C (2020) 80:957 of 54 957

The angular separation of the leading jet from the 4� system,�R4�j , is used to distinguish VBF or t t H from ggF. For cat-egories with two or more jets, kinematic variables that alsoinclude the information from the two leading jets are used:the invariant mass, m j j ; the transverse momentum of the

4� and the 2-jet system, p4�j jT ; and the Zeppenfeld variable,

ηZeppZ Z =

∣∣∣η4� − η j1+η j22

∣∣∣ [154]. The number of reconstructed

jets, Njets, the number of b-tagged jets at 70% tagging effi-ciency, Nb-jets,70%, and the scalar sum of the pT of all recon-structed jets, HT, are used to identify the t t H process.

Depending on the category and the number of processesbeing targeted, the NN has two or three output nodes. Thevalue computed at each node represents the probability, withan integral of one, for the event to originate from the givenprocess. For example, for the 0-jet category, two probabilitiesare evaluated, NNggF and NNZ Z . As these two values are alinear transformation of each other, only one output, NNggF,is used as a discriminant in the fit model. In categories withthree targeted processes, only two of the three correspondingoutput probabilities are independent. In a given category, aselection is applied on one of the three output probabilitiesto split the events in two subcategories. This output prob-ability is then used as the discriminant for the subcategoryof events passing the selection, while for the other subcate-gory one of the two remaining output probabilities is used.The selection criterion is chosen so as to provide the largestpurity of the targeted process for events passing the selec-tion. For example, in the 1-jet category, NNVBF and NNZ Z

are used. The subcategory of events with NNZ Z larger than0.25 uses NNZ Z as the discriminant in the fit model, whileNNVBF is used in the remaining subcategory. The subcat-egory definitions and observables used in all reconstructedevent categories are summarised in Table 5.

6 Background contributions

6.1 Background processes with prompt leptons

Non-resonant SM Z Z∗ production via qq annihilation,gluon–gluon fusion and vector-boson scattering can resultin four prompt leptons in the final state and constitutes thelargest background for the analysis. While for the previousanalyses [17,128], simulation was exclusively used to esti-mate both the shape and normalisation, in this analysis thenormalisation is constrained by a data-driven technique. Thisallows the systematic uncertainty to be reduced by removingboth the theoretical and luminosity uncertainties contributingto the normalisation uncertainty.

As outlined in Sect. 5.1, to estimate the normalisation,sideband categories in them4� mass region 105–115 GeV and130–160 GeV are defined according to the jet multiplicity

(SB-0 j , SB-1 j , SB-2 j). The normalisation of the Z Z∗ back-ground is simultaneously fitted with a common normalisa-tion factor for signal region and sideband categories with thesame jet multiplicity. For example, the Z Z∗ background isscaled by a common factor for 2 j , 2 j-BSM-like and SB-2 jcategories. The background shape templates for NN discrim-inants and the expected fraction of events in relevant recon-structed signal-region event categories are obtained fromsimulation. As shown in Fig. 4a, good agreement is foundbetween data and simulation for the shape of the NN observ-able. All expected distributions are shown after the final fit tothe data for the Production Mode measurement (see Sect. 8)and are referred to as post-fit distributions in the following.The simulated distributions of the observables p4�

T and m j j

employed for the prediction of event fractions in each eventcategory also agree with data, as seen in Figs. 4b, c respec-tively. The estimation of the Z Z∗ process in the jet multiplic-ity bins removes one of the leading theoretical uncertainties[155]. Due to the limited sensitivity and the low expectedyield, the normalisation of Z Z∗ in t t H -like categories isestimated from simulation.

Similarly, backgrounds affecting the t t H -like categoriesare estimated simultaneously from an enriched sampleselected in a dedicated sideband region (SB-t X X -enriched),with the mass cut extended up to 350 GeV to improve thestatistical precision of the estimate. The normalisation ofthe t X X process is simultaneously fitted across the ttH-Lep-enriched, ttH-Had-enriched and SB-t X X -enriched cat-egories. The Njets observable distribution, which is used topredict the event fractions in each category, is shown inFig. 4d and agrees with data. In all other categories, the sen-sitivity of the t X X measurement is limited due to a smallnumber of expected t X X events and its normalisation is esti-mated from simulation.

The contribution from VVV processes is estimated for allcategories using the simulated samples presented in Sect. 3.

6.2 Background processes with non-prompt leptons

Other processes, such as Z + jets, t t , and WZ , containingat least one jet, photon or lepton from a hadron decay thatis misidentified as a prompt lepton, also contribute to thebackground. These ‘reducible’ backgrounds are significantlysmaller than the non-resonant Z Z∗ background and are esti-mated from data using different approaches for the �� + μμ

and �� + ee final states [17,128].In the �� + μμ final states, the normalisation of the Z +

jets and t t backgrounds are determined by performing fitsto the invariant mass of the leading lepton pair in dedicatedindependent control regions. The shape of the invariant massdistribution for each region is parameterised using simulatedsamples. In contrast to the previous analyses [17,128], thisfit is performed independently for each reconstructed event

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957 of 54 Eur. Phys. J. C (2020) 80:957

0 0.2 0.4 0.6 0.8 1

ggFNN

0

20

40

60

80

100

120

140

Eve

nts

Data

ggF+bbH ZZ*VBF tXX, VVV

VH tZ+jets, t

ttH+tH Uncertainty

ATLAS 4l→ ZZ* →H

-1 = 13 TeV, 139 fbs

< 160 GeV4lm130 < < 115 GeV, 4lm105 <

jSB-0

(a)

0 20 40 60 80 100 120 140 160 180 200

[GeV]4lT

p

0

20

40

60

80

100

120

Eve

nts/

10 G

eV Data


VH tZ+jets, t

ttH+tH Uncertainty


-1 = 13 TeV, 139 fbs

< 160 GeV4lm130 < < 115 GeV, 4lm105 <

(b)

0 100 200 300 400 500 600

[GeV]jjm

0

5

10

15

20

25

Eve

nts/

40 G

eV Data


VH tZ+jets, t

ttH+tH Uncertainty


-1 = 13 TeV, 139 fbs

< 160 GeV4lm130 < < 115 GeV, 4lm105 <

2≥ jetsN

(c)

= 2 = 3 4≥

jetsN

0

2

4

6

8

10

12

14

16

18E

vent

sData


VH tZ+jets, t

ttH+tH Uncertainty


-1 = 13 TeV, 139 fbs

< 350 GeV4lm130 < < 115 GeV, 4lm105 <

-enrichedtXXSB-

(d)

Fig. 4 The observed and expected (post-fit) distributions for an inte-grated luminosity of 139 fb−1 at

√s = 13 TeV in the different back-

ground enriched regions: (a) NNggF in the SB-0 j sideband region, (b)p4�

T in the sideband region combining the SB-0 j , SB-1 j and SB-2 jcategories, (c) m j j in the SB-2 j category, and (d) Njets in the SB-t X X -

enriched region. The SM Higgs boson signal is assumed to have a massof mH = 125 GeV. The uncertainty in the prediction is shown by thehatched band, calculated as described in Sect. 7. For comparison only,the hatched band includes the theoretical uncertainties in the SM cross-section for the signal and the background processes

category, which removes the use of simulation to estimatethe event fractions in these categories.

The control regions used to estimate this background aredefined by closely following the requirements outlined inSect. 4.2. The definition and modified requirements for eachof the four control regions are:

1. an enhanced heavy-flavour control region with invertedimpact-parameter and relaxed isolation requirements onthe subleading lepton pair and relaxed vertex χ2 require-ments,

2. an enhanced t t eμ+μμ control region with an opposite-flavour leading lepton pair eμ and relaxed impact-parameter, isolation, and opposite-sign charge require-ments on the subleading lepton pair μμ, as well as relaxedvertex χ2 requirements,

3. an enhanced light-flavour control region with invertedisolation requirements for at least one lepton in the sub-leading lepton pair, and

4. a same-sign �� + μ±μ± control region with relaxedimpact-parameter and isolation requirements.

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Eur. Phys. J. C (2020) 80:957 of 54 957

The first two are the primary control regions used to estimateZ + jets and t t , and the latter two improve the estimate byreducing the statistical error of the fitted normalisation.

The background normalisations are obtained separatelyfor the Z+ jets and t t background processes using the simul-taneous fit in the four control regions. The normalisation nCR

iin each control region CR for the background process i isexpressed as a fraction, nCR

i = tCRi × NV R

i , of the normal-isation NV R

i in a dedicated relaxed validation region (VR).NV Ri is used as the common parameter when fitting the nor-

malisations in the different CRs. The transfer factor tCRi is the

ratio of the background contribution in the relaxed validationregion and the given control regions. The relaxed validationregion is defined by following the requirements outlined inSect. 4.2 but by relaxing the impact-parameter and isola-tion requirements on the subleading lepton pair. This regioncontains a substantially larger number of events comparedwith the other four control regions, allowing a more reli-able prediction of the shapes of the NN distributions. Theshapes of the background NN distribution are then extrapo-lated together with the corresponding background normalisa-tion from the relaxed validation to the signal region by meansof additional transfer factors Ti . Transfer factors tCR

i and Tito extrapolate the background contributions from the controlregions to the relaxed validation region and from there to thesignal region are estimated from simulation and validated inseveral additional data control regions

The �� + ee control-region selection requires the elec-trons in the subleading lepton pair to have the same charge,and relaxes the identification, impact parameter and isola-tion requirements on the electron candidate with the lowesttransverse energy. This fake electron candidate, denoted byX , can be a light-flavour jet, an electron from photon conver-sion or an electron from heavy-flavour hadron decay. Theheavy-flavour background is determined from simulation.Good agreement is observed between simulation and datain a heavy-flavour enriched control region.

The remaining background is separated into light-flavourand photon conversion background components using thesPlot method [156] which is performed on electron candi-dates X , separately for each reconstructed category in binsof the jet multiplicity and the transverse momentum of theelectron candidate. The size of the two background compo-nents is obtained from a fit to the number of hits from theelectron candidate X in the innermost ID layer in the ��+ eedata control region, where a hit indicates either a hadrontrack or an early conversion. A hit in the next-to-innermostpixel layer is used when the electron falls in a region that waseither not instrumented with an innermost pixel layer moduleor where the module was not operating. The templates of thefinal discriminants for the mentioned fit of the light-flavourand photon conversion background components are obtainedfrom simulated Z+X events with an on-shell Z boson decay

candidate accompanied by an electron X selected using thesame criteria as in the �� + ee control region. The simu-lated Z + X events are also used to obtain the transfer factorfor the X candidate for the extrapolation of the light-flavourand photon conversion background contributions from the�� + ee control region to the signal region, after correctingthe simulation to match the data in dedicated control samplesof Z+X events. The extrapolation to the signal region is alsoperformed in bins of the electron transverse momentum andthe jet multiplicity, separately for each reconstructed eventcategory. A method similar to that for the �� + μμ finalstate is used to extract the NN shape, where the fractionsof events from light-flavour jets and photon conversions areestimated from simulation and corrected transfer factors areused.

7 Systematic uncertainties

The systematic uncertainties are categorised into experimen-tal and theoretical uncertainties. The first category includesuncertainties in lepton and jet reconstruction, identification,isolation and trigger efficiencies, energy resolution and scale,and uncertainty in the total integrated luminosity. Uncertain-ties from the procedure used to derive the data-driven back-ground estimates are also included in this category. The sec-ond category includes uncertainties in theoretical modellingof the signal and background processes.

The uncertainties can affect the signal acceptance, selec-tion efficiency and discriminant distributions as well as thebackground estimates. The dominant sources of uncertaintyand their effect are described in the following subsections.The impact of these uncertainties on the measurements issummarised in Table 6.

7.1 Experimental uncertainties

The uncertainty in the combined 2015–2018 integrated lumi-nosity is 1.7% [157], obtained using the LUCID-2 detector[158] for the primary luminosity measurements. This uncer-tainty affects the signal and the normalisation of the simu-lated background estimates when not constrained by the datasidebands.

The uncertainty in the predicted yields due to pile-up mod-elling ranges between 1% and 2% and is derived by varyingthe average number of pile-up events in the simulation tocover the uncertainty in the ratio of the predicted to mea-sured inelastic cross-sections [159].

The electron (muon) reconstruction, isolation and identi-fication efficiencies, and the energy (momentum) scale andresolution are derived from data using large samples ofJ/ψ → �� and Z → �� decays [129,131]. Typical uncer-tainties in the predicted yields for the relevant decay channels

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957 of 54 Eur. Phys. J. C (2020) 80:957

Table 6 The impact of the dominant systematic uncertainties (in per-cent) on the cross-sections in production bins of the Production ModeStage and the Reduced Stage 1.1. Similar sources of systematic uncer-tainties are grouped together: luminosity (Lumi.), electron/muon recon-struction and identification efficiencies and pile-up modelling (e, μ,pile-up), jet energy scale/resolution and b-tagging efficiencies (Jets,flav. tag), uncertainties in reducible background (reducible bkg), theo-

retical uncertainties in Z Z∗ background and tXX background, and the-oretical uncertainties in the signal due to parton distribution function(PDF), QCD scale (QCD) and parton showering algorithm (Shower).The uncertainties are rounded to the nearest 0.5%, except for the lumi-nosity uncertainty, which is measured to be 1.7% and increases for theVH signal processes due to the simulation-based normalisation of theVVV background

Measurement Experimental uncertainties [%] Theory uncertainties [%]

Lumi. e, μ, Jets, Reducible Background Signal

pile-up flav. tag bkg Z Z∗ tXX PDF QCD Shower

Inclusive cross-section

1.7 2.5 0.5 < 0.5 1 < 0.5 < 0.5 1 2

Production mode cross-sections

ggF 1.7 2.5 1 < 0.5 1.5 < 0.5 0.5 1 2

VBF 1.7 2 4 < 0.5 1.5 < 0.5 1 5 7

VH 1.9 2 4 1 6 < 0.5 2 13.5 7.5

t t H 1.7 2 6 < 0.5 1 0.5 0.5 12.5 4

Reduced Stage-1.1 production bin cross-sections

gg2H-0 j-pHT -Low 1.7 3 1.5 0.5 6.5 < 0.5 < 0.5 1 1.5

gg2H-0 j-pHT -High 1.7 3 5 < 0.5 3 < 0.5 < 0.5 0.5 5.5

gg2H-1 j-pHT -Low 1.7 2.5 12 0.5 7 < 0.5 < 0.5 1 6

gg2H-1 j-pHT -Med 1.7 3 7.5 < 0.5 1 < 0.5 < 0.5 1.5 5.5

gg2H-1 j-pHT -High 1.7 3 11 0.5 2 < 0.5 < 0.5 2 7.5

gg2H-2 j 1.7 2.5 16.5 1 12.5 0.5 < 0.5 2.5 10.5

gg2H-pHT -High 1.7 1.5 3 0.5 3.5 < 0.5 < 0.5 2 3.5

qq2Hqq-VH 1.8 4 17 1 4 1 0.5 5.5 8

qq2Hqq-VBF 1.7 2 3.5 < 0.5 5 < 0.5 < 0.5 6 10.5

qq2Hqq-BSM 1.7 2 4 < 0.5 2.5 < 0.5 < 0.5 3 8

VH-Lep 1.8 2.5 2 1 2 0.5 < 0.5 1.5 3

t t H 1.7 2.5 5 0.5 1 0.5 < 0.5 11 3

due to the identification and reconstruction efficiency uncer-tainties are below 1% for muons and 1%–2% for electrons.The uncertainty in the expected yields due to the muon andelectron isolation efficiency is also taken into account, withthe typical size being 1%. The uncertainties in the triggerefficiencies have a negligible impact. The uncertainties inthe electron and muon energy and momentum scale and res-olution are small and also have a negligible impact on themeasurements.

The uncertainties in the jet energy scale and resolution arein the range 1%–3% [133]. The impact of these uncertaintiesis more relevant for the VH, VBF and t t H production modecross-sections (3%–5%) and for all the Reduced Stage-1.1cross-section measurements, including the ggF process splitinto the different Njets exclusive production bins (5%–20%).

The uncertainty in the calibration of the b-tagging algo-rithm, which is derived from dileptonic t t events, amounts toa few percent over most of the jet pT range [138]. This uncer-tainty is only relevant in the ttH category, with its expected

impact being approximately 1% in the t t H cross-sectionmeasurement. The uncertainties associated with the Emiss

Treconstruction have a negligible impact.

A shift in the simulated Higgs boson mass correspond-ing to the precision of the Higgs boson measurement, mH =125.09±0.24 GeV [160], is shown to have a negligible impacton the signal acceptance. A small dependency of the NNggF

discriminant shape in the 0 j-p4�T -Low and 0 j-p4�

T -Med cat-egories on mH is observed for the signal (below 2% in thehighest NN score bins) and is included in the signal model.This uncertainty affects the measurement of ggF production,as well as the measurements in other production bins withlarge ggF contamination.

For the data-driven measurement of the reducible back-ground, three sources of uncertainty are considered: statis-tical uncertainty, overall systematic uncertainty for each of�� + μμ and �� + ee, and a shape systematic uncertaintythat varies with the reconstructed event category. Since theyields are estimated by using a statistical fit to a control data

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region with large statistics, the inclusive background esti-mate has a relatively small (3%) statistical uncertainty. Thesystematic uncertainty for �� + μμ and the heavy-flavourcomponent of �� + ee is estimated by comparing the leptonidentification, isolation and impact parameter significanceefficiency between data and simulated events in a separateregion, enriched with on-shell Z boson decays accompaniedby an electron or a muon. For both the �� + μμ and �� + eeestimates, the difference in efficiency is assigned as the uncer-tainty in the extrapolation of the yield estimate from the con-trol region to the signal region. For the �� + ee light-flavourcomponent, the efficiency is derived from an enriched controlregion with a systematic uncertainty estimated by varying theassumed light- and heavy-flavour components. These inclu-sive uncertainties (6%) are treated as correlated across thereconstructed event categories. Finally, there are additionaluncorrelated uncertainties (8%–70%) in the fraction of thereducible background in each event category due to the sta-tistical precision of the simulated samples.

7.2 Theoretical uncertainties

The theoretical modelling of the signal and background pro-cesses is affected by uncertainties due to missing higher-order corrections, modelling of parton showers and the under-lying event, and PDF+αS uncertainties.

The impact of the theory systematic uncertainties on thesignal depends on the kind of measurement that is performed.For signal-strength measurements, defined as the measuredcross-section divided by the SM prediction, or interpretationof cross-section using the EFT approach, each source of the-ory uncertainty affects both the acceptance and the predictedSM cross-section. For the cross-section measurements, onlyeffects on the acceptance need to be considered.

The impact of the theory systematic uncertainties on thebackground depends on the method of estimating the normal-isation. If simulation is used, the uncertainties in the accep-tance and the predicted SM cross-section are included. If thenormalisation is estimated from a data-driven method, onlythe impact on the relative event fractions between categoriesis considered.

One of the dominant sources of theoretical uncertainty isthe prediction of the ggF process in the different Njets cat-egories. The ggF process gives a large contribution in cate-gories with at least two jets. To estimate the variations dueto the impact of higher-order contributions not included inthe calculations and migration effects on the Njets ggF cross-sections, the approach described in Refs. [24,161] is used,which exploits the latest predictions for the inclusive jetcross-sections. In particular, the uncertainty from the choiceof factorisation and renormalisation scales, the choice ofresummation scales, and the migrations between the 0-jetand 1-jet phase-space bins or between the 1-jet and ≥ 2-

jet bins are considered [24,162–164]. The impact of QCDscale variations on the Higgs boson pT distribution is takeninto account as an additional uncertainty. The uncertainty inhigher-order corrections to the Higgs boson pT originatingfrom the assumption of infinite top quark mass in the heavy-quark loop is also taken into account by comparing the pT

distribution predictions to finite-mass calculations. An addi-tional uncertainty in the acceptance of the ggF process inVBF topologies [165] due to missing higher orders in QCDin the calculation is estimated by variations of the renormali-sation and factorisation scales using fixed-order calculationswith MCFM [166]. An additional uncertainty in the Higgsboson pT distribution, derived by varying the renormalisa-tion, factorisation and NNLOPS scale in the simulation, inthe 0-jet topology is considered. This is particularly relevantwhen measuring the inclusive ggF cross-section using thep4�

T categories for events with no jet activity. To account for

higher-order corrections to pH j jT , which is used as an NN

input variable, the uncertainty is derived by comparing thepredicted distribution obtained usingPowheg NNLOPS andMadGraph5_aMC@NLO with the FxFx merging scheme.

For the VBF production mode, the uncertainty due tomissing higher orders in QCD is parameterised using thescheme outlined in Ref. [23]. The migration effects due tothe selection criteria imposed on the number of jets, trans-verse momentum of the Higgs boson, transverse momen-tum of the Higgs boson and the leading dijet system andthe invariant mass of the two leading jets, used to define thefull Stage 1.1 STXS production bins, are computed by vary-ing the renormalisation and factorisation scales by a factorof two. The uncertainties are cross-checked with fixed-ordercalculations. Similarly, for the VH production mode withthe associated V decaying leptonically, the scale variationsare parameterised as migration effects due to the selectioncriteria imposed on the number of jets and the transversemomentum of the associated boson [167].

For theVH production mode with the associated V decay-ing hadronically and the t t H production mode, the uncer-tainty due to missing higher orders in QCD is obtained byvarying the renormalisation and factorisation scales by a fac-tor of two. The configuration with the largest impact, asquantified by the relative difference between the varied andthe nominal configuration, is chosen to define the uncer-tainty in each experimental category. These uncertaintiesare treated as uncorrelated among the different productionmodes. Due to the limited accuracy of the simulated samples,the uncertainties evaluated using this method for the totalcross-sections are larger than those described in Ref. [24].

The uncertainties in the acceptance due to the modellingof parton showers and the underlying event are estimatedwith AZNLO tune eigenvector variations and by comparingthe acceptance using the parton showering algorithm from

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Pythia 8 with that from Herwig 7 [168] for all signal pro-cesses. The uncertainty due to each AZNLO tune variationis taken as correlated among the different production modeswhile the difference between the parton showering algo-rithms is treated as an uncorrelated uncertainty. The uncer-tainties due to higher-order corrections to the Higgs bosondecay are modelled using the PROPHECY4F [102,105] andHto4L [104,169] generators. These corrections are below2% and have a negligible impact on the results. A 100%uncertainty is assigned to heavy-flavour quark productionmodelling for the ggF contribution entering in the ttH cate-gory. This has a negligible impact on the results.

The impact of the PDF uncertainty is estimated with thethirty eigenvector variations of the PDF4LHC_nlo_30 Hes-sian PDF set following the PDF4LHC recommendations[40]. The modification of the predictions originating fromeach eigenvector variation is added as a separate source ofuncertainty in the model. The same procedure is applied forthe ggF, VBF, VH and t t H processes, enabling correlationsto be taken into account in the fit model.

The impacts of the theoretical uncertainties, as describedabove, on the shape of NN discriminants are also con-sidered. For ggF production, a further cross-check is per-formed by comparing the NN shapes in the correspondingcategories as predicted by Powheg NNLOPS and Mad-

Graph5_aMC@NLO with the FxFx merging scheme. Allthe NN shapes from the two generators agree within the scalevariations and, therefore, no additional shape uncertainty isincluded.

For signal-strength measurements, an additional uncer-tainty related to the H → Z Z∗ branching ratio prediction[102,105] is included in the measurement.

Since the normalisation of the Z Z∗ process in most recon-structed event categories is constrained by performing asimultaneous fit to sideband regions enriched in this con-tribution together with the signal regions, most of the theo-retical uncertainty in the normalisation for this backgroundvanishes. Nevertheless, uncertainties in the shapes of the dis-criminants for the Z Z∗ background and in the relative con-tribution of this background between the sidebands and thesignal regions are taken into account. The uncertainties due tomissing higher-order effects in QCD are estimated by vary-ing the factorisation and renormalisation QCD scales by afactor of two; the impact of the PDF uncertainty is estimatedby using the MC replicas of the NNPDF3.0 PDF set. Uncer-tainties due to parton shower modelling for the Z Z∗ processare considered as well. The impact of these uncertainties isbelow 2% for all production mode cross-sections measured.In addition, a comparison between Sherpa and Powheg isalso taken as an additional source of systematic uncertainty.This model uncertainty is treated as uncorrelated among thedifferent sideband-to-signal region extrapolations (in 0-jet,1-jet and 2-jet categories).

The uncertainty in the gluon-initiated and the vector-boson-initiated Z Z∗ process is taken into account by chang-ing the relative composition of the quark-initiated, the gluon-initiated and the vector-boson-scattered Z Z∗ componentsaccording to the theoretical uncertainty in the predicted cross-sections and the respective K -factors. In addition, the eventyield and NN discriminant shapes in each event categoryare compared with the data in an m4� sideband around thesignal region (105 GeV< m4� < 115 GeV or 130 GeV<

m4� < 160 GeV). Good agreement between the Sherpa pre-dictions and the data is found.

For the tXX process, uncertainties due to PDF andQCD scale variations are considered in the relative frac-tion of events present in the t t H -like categories, in the SB-t X X -enriched control region and in the NN discriminantshape. Differences between MadGraph5_aMC@NLO andSherpa are considered as an additional systematic uncer-tainty. For all other categories where this process is estimatedfrom simulation, the impact of these uncertainties on the SMcross-section and acceptance are also considered.

Uncertainties in the PDF and in missing higher-order cor-rections in QCD are applied to theVVV background estimate,which is fully taken from MC simulation.

To probe the tensor structure of the Higgs boson couplingin the EFT approach, theoretical uncertainties due to PDFand QCD scale variations are assigned to the signal predic-tions based on the simulated highest-order SM signal sam-ples. The same uncertainties are assigned to all correspondingBSM signal predictions, since it is shown using the MC sig-nal samples simulated at LO accuracy that the uncertaintieschange negligibly as a function of the Wilson coefficients.

8 Measurement of the Higgs boson production modecross-sections

8.1 Observed data

The expected and observed four-lepton invariant mass (post-fit) distributions of the selected Higgs boson candidates afterthe event selection are shown in Fig. 5.

The observed and expected (post-fit) distributions of thejet multiplicity, the dijet invariant mass, and the four-leptontransverse momenta in different Njets bins, which are usedfor the categorisation of reconstructed events, are shown inFig. 6 for different steps of the event categorisation.

The expected numbers of signal and background eventsin each reconstructed event category are shown in Table 7together with the corresponding observed number of events.The expected event yields are in good agreement with theobserved ones. The observed and expected (post-fit) distri-butions of the NN discriminants are shown in Fig. 7 andin Figure 8. In addition, Fig. 8g, h show the observed andexpected yields in the categories where no NN discriminant

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√s = 13 TeV. The SM Higgs boson

signal is assumed to have a mass mH = 125 GeV. The uncertainty inthe prediction is shown by the hatched band, calculated as described inSect. 7. For comparison only, the hatched band includes the theoreticaluncertainties in the SM cross-section for the signal and the backgroundprocesses

is used and in the mass sidebands used to constrain the Z Z∗and t X X background, respectively. All distributions are ingood agreement with the data.

The statistical interpretation of the results and compatibil-ity with the SM are discussed in the following.

8.2 Measurement of simplified template cross-sections

To measure the product �σ ·B of the Higgs boson produc-tion cross-section and the branching ratio for H → Z Z∗decay for the production bins of the Production Mode Stageor the Reduced Stage 1.1, a fit to the discriminant observ-ables introduced in Sect. 5.2 is performed using the like-lihood function L(�σ , �θ) that depends on the Higgs bosonproduction cross-section �σ = {σ1, σ2, . . . , σN } where σp isthe cross-section in each production bin p and the nuisanceparameters �θ accounting for the systematic uncertainties. Thelikelihood function is defined as a product of conditionalprobabilities over binned distributions of the discriminatingobservables in each reconstructed signal and sideband eventcategory j ,

L(�σ , �θ) =Ncategories∏

j

Nbins∏

i

P(Ni, j | L · �σ · B · �Ai, j (�θ) + Bi, j (�θ)

)

×Nnuisance∏

mCm(�θ) ,

(3)

with Poisson distributions P corresponding to the observa-tion of Ni, j events in each histogram bin i of the discriminat-ing observable given the expectations for each backgroundprocess, Bi, j (�θ), and for the signal, Si, j (�θ) = L · �σ · B ·�Ai, j (�θ), where L is the integrated luminosity and �Ai, j ={A1

i, j , A2i, j , . . . , A

Ni, j } is the set of signal acceptances from

each production bin. The signal acceptance Api, j is defined as

the fraction of generated signal events in the production binp that satisfy the event reconstruction and selection criteriain the histogram bin i of the reconstructed event categoryj . For a given production bin p, the acceptance consists ofApi, j = a p · ε

pi, j , where a p is the particle-level acceptance

in the fiducial region defined from requirements listed inSects. 4 and 5 and ε

pi, j is the reconstruction efficiency of these

particle-level events. Constraints on the nuisance parameterscorresponding to systematic uncertainties described in Sect. 7are represented by the functions Cm(�θ). The cross-sectionsare treated as independent parameters for each production binand correlated among the different reconstructed event cat-egories. The test statistic used to perform the measurementsis the ratio of profile likelihoods [170],

q(�σ) = −2 lnL(�σ ,

ˆ�θ(�σ))

L( �σ , �θ)

= −2 ln λ(�σ) ,

where �σ represents only the cross-section(s) considered asparameter(s) of interest in a given fit. The likelihood in thenumerator is the estimator of a conditional fit, i.e. with param-eter(s) of interest σi fixed to a given value, while the remain-ing cross-sections and nuisance parameters are free-floatingparameters in the fit. The values of the nuisance parame-

tersˆ�θ(�σ)) maximise the likelihood on the condition that the

parameters of interest are held fixed to a given value. Thelikelihood in the denominator is the estimator of an uncondi-tional fit in which all �σ and �θ parameters are free parametersof the fit. The parameter of interest σ in each production binis alternatively replaced by μ ·σSM(�θ), allowing an interpre-tation in terms of the signal strength μ relative to the SMprediction σSM(�θ).

Assuming that the relative signal fractions in each pro-duction bin are given by the predictions for the SM Higgsboson, the inclusive H → Z Z∗ production cross-section for|yH | < 2.5 is measured to be:

σ · B ≡ σ · B(H → Z Z∗)= 1.34 ± 0.11(stat.) ± 0.04(exp.) ± 0.04(th.) pb

= 1.34 ± 0.12 pb,

where the uncertainties are either statistical (stat.) or of exper-imental (exp.) or theoretical (th.) systematic nature.

The SM prediction is (σ ·B)SM ≡ (σ ·B(H → Z Z∗))SM

= 1.33 ± 0.08 pb. The data are also interpreted in terms ofthe global signal strength, yielding

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Fig. 6 The observed and expected distributions (post-fit) of (a) thejet multiplicity Njets after the inclusive event selection, the four-leptontransverse momenta p4�

T for events with (b) exactly zero jets, (c) withexactly one jet and (d) with at least two jets and (e) the dijet invari-ant mass m j j for events with at least two jets. The SM Higgs boson

signal is assumed to have a mass mH = 125 GeV. The uncertainty inthe prediction is shown by the hatched band, calculated as described inSect. 7. For comparison only, the hatched band includes the theoreticaluncertainties in the SM cross-section for the signal and the backgroundprocesses

μ = 1.01 ± 0.08(stat.) ± 0.04(exp.) ± 0.05(th.)

= 1.01 ± 0.11.

The measured cross-section and signal strength are in anexcellent agreement with the SM prediction, with a p-valueof 98.6% for both compatibility tests.

The corresponding likelihood functions are shown inFig. 9. The dominant systematic uncertainty in the cross-section measurement is the experimental uncertainty in thelepton efficiency and integrated luminosity measurementsand theoretical uncertainties related to parton shower mod-

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Table 7 The expected (pre-fit) and observed numbers of events for anintegrated luminosity of 139 fb−1 at

√s = 13 TeV in the signal region

115 < m4� < 130 GeV and sideband region 105 < m4� < 115 GeVor 130 < m4� < 160 GeV (350 GeV for tXX-enriched) in each recon-structed event category assuming the SM Higgs boson signal with amass mH = 125 GeV. The sum of the expected number of SM Higgs

boson events and the estimated background yields is compared with thedata. Combined statistical and systematic uncertainties are included forthe predictions. Expected contributions that are below 0.2% of the totalyield in each reconstructed event category are not shown and replacedby ‘-’

Reconstructedevent category

Signal Z Z∗ t X X Other Total Observedbackground background backgrounds expected

Signal 115 < m4� < 130 GeV

0 j-p4�T -Low 24.2 ± 3.5 30 ± 4 − 0.93 ± 0.13 55 ± 5 56

0 j-p4�T -Med 76 ± 8 37 ± 4 − 6.5 ± 0.6 120 ± 9 117

0 j-p4�T -High 0.355 ± 0.031 0.020 ± 0.012 0.0094 ± 0.0027 0.30 ± 0.05 0.69 ± 0.06 1

1 j-p4�T -Low 34 ± 4 15.5 ± 2.7 − 1.91 ± 0.29 52 ± 5 41

1 j-p4�T -Med 20.8 ± 2.8 4.0 ± 0.7 0.114 ± 0.013 1.02 ± 0.19 26.0 ± 2.9 31

1 j-p4�T -High 4.7 ± 0.8 0.48 ± 0.10 0.043 ± 0.008 0.27 ± 0.04 5.5 ± 0.8 4

1 j-p4�T -BSM-like 1.23 ± 0.23 0.069 ± 0.031 0.0067 ± 0.0031 0.062 ± 0.012 1.37 ± 0.23 2

2 j 38 ± 5 9.1 ± 2.7 0.95 ± 0.08 2.13 ± 0.31 50 ± 6 48

2 j-BSM-like 3.3 ± 0.6 0.18 ± 0.06 0.032 ± 0.005 0.091 ± 0.017 3.6 ± 0.6 6

VH-Lep-enriched 1.29 ± 0.07 0.156 ± 0.025 0.039 ± 0.009 0.0194 ± 0.0032 1.50 ± 0.08 1

ttH-Had-enriched 1.02 ± 0.18 0.058 ± 0.025 0.252 ± 0.032 0.119 ± 0.033 1.45 ± 0.18 2

ttH-Lep-enriched 0.42 ± 0.04 0.002 ± 0.005 0.0157 ± 0.0023 0.0028 ± 0.0029 0.44 ± 0.04 1

Sideband 105 < m4� < 115 GeV or 130 < m4� < 160 GeV

SB-0 j 4.5 ± 0.5 150 ± 13 − 16.2 ± 2.2 171 ± 13 183

SB-1 j 2.80 ± 0.30 51 ± 7 1.29 ± 0.16 8.4 ± 1.2 63 ± 7 64

SB-2 j 2.02 ± 0.27 25 ± 7 4.4 ± 0.5 6.0 ± 0.9 38 ± 7 41

SB-VH-Lep-enriched 0.273 ± 0.015 0.48 ± 0.06 0.125 ± 0.018 0.126 ± 0.019 1.00 ± 0.07 3

105 < m4� < 115 GeV or 130 < m4� < 350 GeV

SB-tXX-enriched 0.071 ± 0.012 0.32 ± 0.12 12.1 ± 1.3 0.84 ± 0.33 13.3 ± 1.4 19

elling affecting the acceptance. The signal-strength measure-ment is also affected by the theoretical uncertainty in theggF cross-section due to missing higher-order corrections inQCD.

The expected SM cross-section, the observed values ofσ ·B(H → Z Z∗) and their ratio for the inclusive productionand in each production bin of the Production Mode Stage andthe Reduced Stage 1.1 are shown in Table 8.

The corresponding values are summarised in Fig. 10. Inthe ratio calculation, uncertainties in the SM expectationare not taken into account. The Production Mode Stage andReduced Stage-1.1 measurements agree with the predictionsfor the SM Higgs boson. The p-values of the correspondingcompatibility tests are 91% and 77%, respectively.

For the qq2Hqq-VBF bin, most of the sensitivity to theVBF production mode comes from the phase space withm j j > 350 GeV and pHT < 200 GeV. To probe the VBFcontribution more directly, the cross-sections in this andin the remaining phase space region of the qq2Hqq-VBF

bin are fitted separately to the data, simultaneously withthe other Reduced Stage 1.1 bins, using the reconstruc-tion categories described in Sect. 5. The cross-section inthe m j j > 350 GeV and pHT < 200 GeV phase space ismeasured to be 0.060+0.025

−0.020 pb compared with the predicted

cross-section of 0.0335+0.0007−0.0011 pb. This measurement has a

correlation of 20% with the measurement in the gg2H-2 jbin, while correlations with other bins are up to 50%.

The dominant contribution to the measurement uncer-tainty in the ggF Production Mode Stage bin originates fromthe same sources as in the inclusive measurement. For theVBF production bin, the dominant systematic uncertaintiesare related to parton showering modelling and jet energy scaleand resolution uncertainties. The VBF, VH and t t H produc-tion bins are also affected by the theoretical uncertaintiesrelated to the modelling of the ggF process. For the ReducedStage-1.1 bins, the dominant cross-section uncertainties arethe jet energy scale and resolution, and parton shower uncer-tainties.

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√s = 13 TeV in the different

zero- and one-jet categories: (a) NNggF in 0 j-p4�T -Low, (b) NNggF in

0 j-p4�T -Med, (c) NNVBF 1 j-p4�

T -Low with NNZ Z < 0.25, (d) NNZ Z

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T -Med withNNZ Z < 0.25, (f) NNZ Z in 1 j-p4�

T -Med with NNZ Z > 0.25 and (g)

NNVBF in 1 j-p4�T -High. The SM Higgs boson signal is assumed to have

a massmH = 125 GeV. The uncertainty in the prediction is shown by thehatched band, calculated as described in Sect. 7. For comparison only,the hatched band includes the theoretical uncertainties in the SM cross-section for the signal and the background processes. The bin boundariesare chosen to maximise the significance of the targeted signal in eachcategory

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> 0.2VH with NNj2

(b)

0 0.2 0.4 0.6 0.8 1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.2 0.4 0.6 0.8 1

VBF-BSMj2

NN

0

2

4

6

8

10

12

Eve

nts

Data


VH tZ+jets, t

ttH+tH Uncertainty


-1 = 13 TeV, 139 fbs < 130 GeV4lm115 <

-BSM-likej2

(c)

ttH-HadttHNN

0

1

2

3

4

5

6

7

Eve

nts

Data


VH tZ+jets, t

ttH+tH Uncertainty


-1 = 13 TeV, 139 fbs < 130 GeV4lm115 <

< 0.4tXX-Had-enriched with NNttH

(d)tXX

-HadttHNN

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2E

vent

s

Data


VH tZ+jets, t

ttH+tH Uncertainty


-1 = 13 TeV, 139 fbs < 130 GeV4lm115 <

> 0.4tXX-Had-enriched with NNttH

(e)

0 0.2 0.4 0.6 0.8 1 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.2 0.4 0.6 0.8 1

ttH-LepVH

NN

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

Eve

nts

Data

ttH+tH ZZ*VH tXX, VVV

ggF+bbH tZ+jets, t

VBF Uncertainty


-1 = 13 TeV, 139 fbs < 130 GeV4lm115 <

-Lep-enrichedVH

(f)

-High4lT

p-j0 -BSM-like4lT

p-j1 -Lep-enrichedttH

Category

0

1

2

3

4

5

6

7

Eve

nts

Data


VH tZ+jets, t

ttH+tH Uncertainty


-1 = 13 TeV, 139 fbsSignal Region

(g)

j0 j1 j2 tXX -LepVH

Category

0

50

100

150

200

250

Eve

nts

Data


VH tZ+jets, t

ttH+tH Uncertainty


-1 = 13 TeV, 139 fbsSideband Region

(h)

Fig. 8 The observed and expected NN output (post-fit) distributionsfor an integrated luminosity of 139 fb−1 at

√s = 13 TeV in the dif-

ferent categories: (a) NNVBF in 2 j with NNV H < 0.2, (b) NNV H in2 j with NNV H > 0.2, (c) NNVBF in 2 j-BSM-like, (d) NNt t H in ttH-Had-enriched with NNt X X < 0.4, (e) NNt X X in ttH-Had-enriched withNNt X X > 0.4 and (f) NNt t H in VH-Lep-enriched. g Shows the cate-gories where no NN discriminant is used while (h) shows the sidebands

used to constrain the Z Z∗ and t X X backgrounds. The SM Higgs bosonsignal is assumed to have a mass mH = 125 GeV. The uncertainty inthe prediction is shown by the hatched band, calculated as described inSect. 7. For comparison only, the hatched band includes the theoreticaluncertainties in the SM cross-section for the signal and the backgroundprocesses. The bin boundaries are chosen to maximise the significanceof the targeted signal in each category

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0

2

4

6

8

10

12

14

)λ-2

ln(

Observed-Stat. only

Observed


-1 = 13 TeV, 139 fbs| < 2.5

H|y

σ1

σ2

(a)

0.7 0.8 0.9 1 1.1 1.2 1.3 0.7 0.8 0.9 1 1.1 1.2 1.3μ

0

2

4

6

8

10

12

14

)λ-2

ln(

Observed-Stat. only

Observed


-1 = 13 TeV, 139 fbs| < 2.5

H|y

σ1

σ2

(b)

Fig. 9 Observed profile likelihood as a function of (a) σ · B(H → Z Z∗) normalised by the SM expectation and (b) the inclusive signal strengthμ; the scans are shown both with (solid line) and without (dashed line) systematic uncertainties

Table 8 The expected SM cross-section (σ ·B)SM, the observed valueof σ · B, and their ratio (σ · B)/(σ · B)SM for the inclusive productionand for each Production Mode Stage and Reduced Stage-1.1 productionbin for the H → Z Z∗ decay for an integrated luminosity of 139 fb−1

at√

s = 13 TeV. The bbH (t H ) contribution is included in the ggF(t t H ) production bins. The uncertainties are given as (stat.)+(exp.)+(th.)

for the inclusive cross-section and the Production Mode Stage, and as(stat.)+(syst.) for the Reduced Stage 1.1. The Reduced Stage-1.1 resultsare dominated by the statistical uncertainty and the impact of theoryuncertainties is smaller than for the Production Mode Stage. The impactof the theory uncertainties for the Reduced Stage 1.1 is smaller than theleast significant digit

Production binCross-section (σ · B) [pb] (σ · B)/(σ · B)SM

SM expected Observed Observed

Inclusive production, |yH | < 2.5

1.33 ± 0.08 1.34 ± 0.11 ± 0.04 ± 0.03 1.01 ± 0.08 ± 0.03 ± 0.02

Production Mode Stage bins, |yH | < 2.5

ggF 1.17 ± 0.08 1.12 ± 0.12 ± 0.04 ± 0.03 0.96 ± 0.10 ± 0.03 ± 0.03

VBF 0.0920 ± 0.0020 0.11 ± 0.04 ± 0.01 ± 0.01 1.21 ± 0.44 +0.13−0.08

+0.07−0.05

VH 0.0524+0.0027−0.0049 0.075+0.059

−0.047+0.011−0.007

+0.013−0.009 1.44+1.13

−0.90+0.21−0.14

+0.24−0.17

t t H 0.0154+0.0010−0.0013 0.026+0.026

−0.017 ± 0.002 ± 0.002 1.7+1.7−1.2 ± 0.2 ± 0.2

Reduced Stage-1.1 bins, |yH | < 2.5

gg2H-0 j-pHT -Low 0.176 ± 0.025 0.17 ± 0.05 ± 0.02 0.96 ± 0.30 ± 0.09

gg2H-0 j-pHT -High 0.55 ± 0.04 0.63 ± 0.09 ± 0.06 1.15 ± 0.17 ± 0.11

gg2H-1 j-pHT -Low 0.172 ± 0.025 0.05 ± 0.07 +0.04−0.06 0.3 ± 0.4 +0.2

−0.3

gg2H-1 j-pHT -Med 0.119 ± 0.018 0.17 ± 0.05 +0.02−0.01 1.4 ± 0.4 ± 0.1

gg2H-1 j-pHT -High 0.020 ± 0.004 0.009+0.016−0.011 ± 0.002 0.5+0.8

−0.6 ± 0.1

gg2H-2 j 0.127 ± 0.027 0.04 ± 0.07 ± 0.04 0.3 ± 0.5 ± 0.3

gg2H-pHT -High 0.015 ± 0.004 0.038+0.021−0.016

+0.003−0.002 2.5+1.3

−1.0+0.2−0.1

qq2Hqq-VH 0.0138+0.0004−0.0006 0.021+0.037

−0.029+0.009−0.006 1.5+2.7

−2.1+0.6−0.4

qq2Hqq-VBF 0.1076+0.0024−0.0035 0.15 ± 0.05 +0.02

−0.01 1.4 ± 0.5 +0.2−0.1

qq2Hqq-BSM 0.00420 ± 0.00018 0.0005+0.0079−0.0047 ± 0.008 0.1+1.9

−1.1 ± 0.2

VH-Lep 0.0164 ± 0.0004 0.022+0.028−0.018

+0.003−0.001 1.3+1.7

−1.1+0.2−0.1

t t H 0.0154+0.0010−0.0013 0.025+0.026

−0.017+0.005−0.003 1.6+1.7

−1.1+0.3−0.2

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1 2 3 4 5

Inclusive

ttH

VH

VBF

ggF


-1 = 13 TeV, 139 fbs| < 2.5

HProduction Mode - |y

-value = 91%p

120±1340

17− 26+26

49− 61+75

40±110

130±1120

80±1330

1.3− 1.0+15.4

4.9− 2.7+52.4

2.0±92.0

80±1170

1 1.2 1.4 1.6 1.8

SMN/N

tXX

ZZ-2j

ZZ-1j

ZZ-0j

Observed: Stat+Sys SM Prediction

Observed: Stat-Only -value = 91%p

120±1340

17− 26+26

49− 61+75

40±110

130±1120

80±1330

1.3− 1.0+15.4

4.9− 2.7+52.4

2.0±92.0

80 ±1170

(a)

1−

0.8−

0.6−

0.4−

0.2−

0

0.2

0.4

0.6

0.8

1

ggF

VB

F

VH

ttH

ZZ

-0j

ZZ

-1j

ZZ

-2j

tXX

tXX

ZZ-2j

ZZ-1j

ZZ-0j

ttH

VH

VBF

ggF

-0.00 0.00 0.01 -0.04 0.01 0.01 0.01 1.00

-0.07 -0.05 -0.10 -0.01 0.06 0.07 1.00

-0.13 -0.00 -0.02 0.01 0.10 1.00

-0.18 0.03 0.01 -0.00 1.00

0.01 0.00 -0.18 1.00

-0.27 -0.02 1.00

-0.22 1.00

1.00 ATLAS 4l→ ZZ* →H

-1 = 13 TeV, 139 fbs

(b)

1− 0 1 2 3 4 5 6 7

ttH

-LepVH

qq2Hqq-BSM

qq2Hqq-VBF

VHqq2Hqq-

-HighH

Tpgg2H-

jgg2H-2

-HighH

Tp-jgg2H-1

-MedH

Tp-jgg2H-1

-LowH

Tp-jgg2H-1

-HighH

Tp-jgg2H-0

-LowH

Tp-jgg2H-0


-1 = 13 TeV, 139 fbs| < 2.5

HReduced Stage 1.1 - |y

-value = 77%p

17− 26+25

18− 28+22

4.8− 7.9+0.5 52− 64+150

35±21

16− 21+38

75±40

12− 16+9

50±170

80±50

110±630

55±170

1.3− 1.0+15.4

0.4±16.4

0.18±4.20

3.5− 2.4+107.6

0.6− 0.4+13.8

4±15

27±127

4±20

18±119

25±172

40±550

25±176

1 1.2 1.4 1.6 1.8

SMN/N

tXX

ZZ-2j

ZZ-1j

ZZ-0j

Observed: Stat+Sys SM Prediction

Observed: Stat-Only -value = 77%p

17− 26+25

18− 28+22

4.8− 7.9+0.5 52− 64+150

35±21

16− 21+38

75±40

12− 16+9

50±170

80±50

110±630

55±170

1.3− 1.0+15.4

0.4±16.4

0.18±4.20

3.5− 2.4+107.6

0.6− 0.4+13.8

4±15

27±127

4±20

18±119

25±172

40±550

25±176

(c)

1−0.8−0.6−0.4−0.2−

0

0.2

0.4

0.6

0.8

1

-Low

H Tp-j

gg2H

-0

-Hig

hH T

p-jgg

2H-0

-Low

H Tp-j

gg2H

-1

-Med

H Tp-j

gg2H

-1

-Hig

hH T

p-jgg

2H-1

jgg

2H-2

-Hig

hH T

pgg

2H-

VH

qq2H

qq-

qq2H

qq-V

BF

qq2H

qq-B

SM

-Lep

VH

ttH

ZZ

-0j

ZZ

-1j

ZZ

-2j

tXX

tXX

ZZ-2j

ZZ-1j

ZZ-0j

ttH

-LepVH

qq2Hqq-BSM

qq2Hqq-VBF

VHqq2Hqq-

-HighHT

pgg2H-

jgg2H-2

-HighHT

p-jgg2H-1

-MedHT

p-jgg2H-1

-LowHT

p-jgg2H-1

-HighHT

p-jgg2H-0

-LowHT

p-jgg2H-0

-0.00 -0.00 0.01 -0.00 -0.00 0.00 0.00 0.00 0.00 0.00 0.01 -0.05 0.01 0.01 0.01 1.00

-0.00 -0.01 0.03 0.02 0.02 -0.28 -0.02 -0.01 0.02 -0.00 -0.00 0.01 0.05 0.05 1.00

-0.03 -0.01 -0.16 -0.12 -0.05 0.08 -0.01 -0.03 -0.00 0.01 -0.00 0.00 0.08 1.00

-0.20 -0.13 0.04 0.01 0.00 -0.01 0.00 0.00 -0.00 -0.00 -0.03 -0.01 1.00

0.00 0.00 0.02 0.02 0.02 -0.04 -0.10 -0.11 0.01 0.03 -0.08 1.00

0.01 -0.03 -0.01 -0.04 -0.08 -0.01 -0.04 -0.03 -0.00 0.01 1.00

-0.00 -0.02 0.03 -0.02 0.00 0.04 -0.42 0.03 -0.02 1.00

0.00 -0.01 -0.13 -0.18 -0.20 -0.28 -0.06 0.06 1.00

0.01 0.05 -0.05 0.07 0.02 -0.45 -0.13 1.00

0.00 0.04 -0.01 0.05 0.01 -0.03 1.00

-0.01 -0.15 0.09 -0.26 -0.12 1.00

0.00 0.07 -0.02 0.09 1.00

0.02 0.13 -0.10 1.00

-0.03 -0.52 1.00

-0.06 1.00

1.00


-1 = 13 TeV, 139 fbs

(d)

Fig. 10 The observed and expected SM values of the cross-sectionsσ · B normalised by the SM expectation (σ · B)SM for (a) the inclu-sive production and in the Production Mode Stage and (c) the ReducedStage-1.1 production bins for an integrated luminosity of 139 fb−1 at√

s = 13 TeV. The fitted normalisation factors for the Z Z and t X Xbackground are shown in the inserts. Different colours indicate dif-

ferent Higgs boson production modes (or background sources). Thevertical band represents the theory uncertainty in the signal prediction.The correlation matrices between the measured cross-sections and theZ Z and t X X normalisation factors are shown for (b) the ProductionMode Stage and (d) the Reduced Stage 1.1

Figure 11 shows the likelihood contours in the (ggF,VBF), (ggF, VH), (VBF, VH) and (gg2H-0 j-pHT -Low,gg2H-0 j-pHT -High) planes. The other cross-section parame-ters are left free in the fit, i.e. they are not treated as parametersof interest. The compatibility with the SM expectation is atthe level of 0.22, 0.25, 0.19 and 0.33 standard deviations,respectively.

9 Constraints on the Higgs boson couplings in theκ-framework

The cross-sections measured at the Production Mode Stageare interpreted in the κ-framework described in Sect. 1.2. Therelevant cross-sections and the branching ratio of Eq. (3) areparameterised in terms of the coupling-strength modifiers�κ . One interesting benchmark allows two different Higgsboson coupling-strength modifiers to fermions and bosons,reflecting the different structure of the interactions of theSM Higgs sector with gauge bosons and fermions. The uni-versal coupling-strength modifiers κF for fermions and κV

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0

1

2

3

4

5 ATLAS 4l→ ZZ* →H

-1 = 13 TeV, 139 fbs| < 2.5

H|y

Obs Best Fit

Obs 68% CL.

Obs 95% CL.

SM

(a)

0.6 0.8 1 1.2 1.4 0.6 0.8 1 1.2 1.40

2

4

6

8

10ATLAS

4l→ ZZ* →H -1 = 13 TeV, 139 fbs

| < 2.5H

|y

Obs Best Fit

Obs 68% CL.

Obs 95% CL.

SM

(b)

0

2

4

6

8

10ATLAS

4l→ ZZ* →H -1 = 13 TeV, 139 fbs

| < 2.5H

|y

Obs Best Fit

Obs 68% CL.

Obs 95% CL.

SM

(c)

0 1 2 3 0 0.5 1 1.5 2

0.5

1

1.5

2

2.5 ATLAS 4l→ ZZ* →H

-1 = 13 TeV, 139 fbs| < 2.5

H|y

Obs Best Fit

Obs 68% CL.

Obs 95% CL.

SM

(d)

Fig. 11 Likelihood contours at 68% CL (dashed line) and 95% CL(solid line) in the (a) (ggF, VBF), (b) (ggF, VH), (c) (VBF, VH) and(d) (gg2H-0 j-pHT -Low, gg2H-0 j-pHT -High) plane. The SM prediction

is shown together with its theory uncertainty (filled ellipse). The VHparameter of interest is constrained to positive values

for vector bosons are defined as κV = κW = κZ andκF = κt = κb = κc = κτ = κμ. It is assumed that there areno undetected or invisible Higgs boson decays. The observedlikelihood contours in the κV –κF plane are shown in Fig. 12(only the quadrant κF > 0 and κV > 0 is shown since thischannel is not sensitive to the relative sign of the two cou-pling modifiers). The best-fit value is κV = 1.02 ± 0.06 andκF = 0.88±0.16, with the correlation of −0.17. The proba-bility of compatibility with the Standard Model expectationis at the level of 75%.

10 Constraints on the tensor coupling structure in theEFT approach

To interpret the observed data in the framework of an effec-tive field theory, an EFT signal model is built by parame-terising the production cross-sections in each production binof the Reduced Stage 1.1, as well as the branching ratio andthe signal acceptances, as a function of the SMEFT Wilsoncoefficients introduced in Sect. 1.3. The constraints on theWilson coefficients are then obtained from the simultane-ous fit to the data in all reconstructed signal and sideband

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Eur. Phys. J. C (2020) 80:957 of 54 957

event categories. Due to the statistical precision of the datasample, the constraints are always set on one or at most twoof the Wilson coefficients at a time, while the values of theremaining coefficients are assumed to be equal to zero.

10.1 EFT signal model

The EFT parameterisation of the production cross-sectionsin each production bin of the Reduced Stage 1.1 is obtainedfrom Eq. (1) using simulated BSM samples introduced inSect. 3. The contribution from the gg → Z(→ ��)H processis taken from the SM simulation and assumed to scale withBSM parameters in the same way as the qq → Z(→ ��)Hprocesses. As in the case of simplified template cross-sectionmeasurements, t t H and t H processes are combined intoa single t t H production bin. The cut-off scale is set to� = 1 TeV. Only LO computation of QCD and SM elec-troweak processes is provided, with LO effective couplingsfor the SM Higgs boson to gluon and to photon vertices. Anassumption is made that higher-order corrections, applied in amultiplicative way, are the same for both the SM and the BSMLO predictions and therefore no changes in the parameteri-sation are expected due to higher-order effects [171]. Withthe current amount of data, the constraints from the VBF,VH and t t H production modes on the relevant Wilson coef-ficients still allow a rather large range of parameter values inwhich the quadratic term (the last term in Eq. (1)) cannot beneglected even though its contribution is suppressed by �4.Such dimension-six quadratic terms are therefore includedin the EFT parameterisation. Since the linear terms fromdimension-eight operators are suppressed by the same factor,they could in general also give similar non-negligible con-tributions. Dimension-eight terms are currently not availablein the SMEFT model and are thus not taken into account.

The branching ratio for the H→Z Z∗→4� decay is param-eterised in terms of Wilson coefficients following Eq. (2).The partial and total decay widths are calculated in Mad-

Graph5_aMC@NLO. The total decay width is calculated bytaking into account the dominant Higgs boson decay modes:γ γ , Zγ , bb, gg, WW and Z Z . Other decay modes are notaffected by the probed Wilson coefficients. Their contributionto the total decay width is therefore given by the correspond-ing SM predictions.

The selection criteria for the four-lepton Higgs bosoncandidates, in particular the requirements on the minimuminvariant massm34 of the subleading lepton pair, introduce anadditional dependence of the signal acceptance on the BSMcoupling parameters. The particle-level signal acceptance A,defined as the fraction of signal events satisfying the Higgsboson candidate selection criteria applied at particle-level,has therefore been simultaneously parameterised in terms ofthe three Wilson coefficients cHW , cHB and cHW B (cHW ,cH B and cHW B) assuming that the values of CP-odd (CP-

0.7 0.8 0.9 1 1.1 1.2 1.3

Vκ

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

2.2

2.4Fκ

Best Fit

Observed 68% CL

Observed 95% CL

SM value


-1 = 13 TeV, 139 fbs

Best fit p-value = 0.75

Fig. 12 Likelihood contours at 68% CL (dashed line) and 95% CL(solid line) in the κV –κF plane. The best fit to the data (solid cross) andthe SM prediction (star) are also indicated

even) parameters vanish. The dependence of the acceptanceon other EFT coupling parameters is shown to be negli-gible as these parameters have negligible or no impact onthe H → Z Z∗ decay. The acceptance correction relativeto the SM prediction is described by a three-dimensionalLorentzian function with free acceptance parameters α0, α1,α2, βi , δi , δ(i, j) and δ(i, j,k),

A(�c)ASM

= α0 + (α1)2 ·

[α2 +

∑

i

δi · (ci + βi )2

+∑

i ji = j

δ(i, j) · ci c j + δ(i, j,k)i = j =k

· ci c j ck

⎤

⎥⎥⎦

−1

, (4)

where indices i , j and k run over (HW,HB,HWB) in case ofthe acceptance correction for the set of CP-even parametersand over (HW , HB, HWB) in case of the CP-odd parameters.A common parameterisation is used for all production binssince the differences between production bins are shown tobe negligible. In addition, the reconstructed event categorisa-tion criteria imposed on the selected Higgs boson candidatesand the classification in bins of multivariate NN discrimi-nant values do not impact the acceptance parameterisation.The impact of reconstruction efficiencies on the parameteri-sation is also negligible, such that Eq. (4) also holds for theratio A(�c)/ASM of reconstruction-level acceptances definedin Sect. 8. The resulting acceptance parameterisation curvesare shown in Fig. 13 for the cases in which all but one of theWilson coefficients are set to zero. For all cases, the accep-tance correction is equal to one at the SM point. In the case

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of the cHW and cHW B Wilson coefficients, the acceptancecorrections reach a maximum value slightly larger than one,leading to the shift of the maximum position from the SMpoint. This shift is compatible with the statistical accuracyof the fit and the impact of linear EFT terms which are notsymmetric around the SM point.

The final parameterisation of signal yields relative to theSM prediction in each production bin of the Reduced Stage 1.1is obtained as the product of the corresponding cross-section, branching ratio and acceptance parameterisations.The expected event yields normalised to the SM predictionare shown in Fig. 14 for each of the CP-even Wilson coef-ficients after setting all other coefficients to zero. Only pro-duction bins with the highest sensitivity to a given Wilsoncoefficient are shown. The impact of the quadratic terms inthe EFT parameterisation can clearly be seen as a non-lineardependence on all but the cHG Wilson coefficient. For com-parison, the predictions without the acceptance corrections(σ ·B), and without both the acceptance and branching ratiocorrections (σ ) are also shown. Both the acceptance and thebranching ratio parameterisations have a strong impact onthe sensitivity to different Wilson coefficients, especially forthe cHW , cHB and cHW B parameterisations in gg2H produc-tion bins (Fig. 14a, b, c). Since these coefficients do not enterthe ggF production vertex, the corresponding sensitivity isentirely driven by their impact on the decay and the accep-tance of selected signal events. The acceptance correctionssignificantly degrade the sensitivity to the cHW coefficient(see Fig. 14a). Additional sensitivity to this coefficient canbe gained from the qq2Hqq production bins as shown inFig. 14d. The Wilson coefficients cHG and cuH , on the otherhand, do not affect the acceptance since they are not presentin the decay vertex (Fig. 14e, f). The coefficient cHG stillhas a non-vanishing impact on the branching ratio throughits contributions to the total decay width. Similar effects arealso seen for the Wilson coefficients of CP-odd operators.

10.2 EFT interpretation results

The ratios of the expected signal yield for a chosen EFTparameter value to its SM prediction are shown in Fig. 15 ineach production bin of the Reduced Stage 1.1, together withthe corresponding measurement.

The EFT parameterisation of signal yields is imple-mented in the likelihood function of Eq. (3) using the BSM-dependent signal-strength parameters μp(�c) for each givenproduction bin p,

μp(�c) = σ p(�c)σSM

· B4�(�c)B4�

SM

· A(�c)ASM

.

This is then fitted to the observed event yields. Default SMpredictions at the highest available order are employed for

the cross-sections and branching ratios multiplying the signalstrengths in the likelihood function. Modifications of back-ground contributions due to EFT effects are not taken intoaccount.

The fit results with only one Wilson coefficient fitted at atime are summarised in Fig. 16 and in Table 9. The resultsare in good agreement with the SM predictions. The mea-surements are dominated by the statistical uncertainty. In thecase of the CP-odd coupling parameters, each fit gives twodegenerate minima since the corresponding EFT parameter-isation contains only quadratic terms which are not sensitiveto the sign of the fitted parameter. The fit of the CP-evencoupling parameter cuH also results in two minima sincethe corresponding EFT parameterisation curve in the onlysensitive t t H production bin crosses the expected SM cross-section value at two different values of the cuH parameter(see Fig. 14f). The same is true also for the observed t t Hcross-section. The small degeneracies for other CP-even cou-pling parameters are removed by the combination of severalsensitive production bins.

The strongest constraint, driven mostly by the ggF recon-structed event categories, is obtained on the cHG coefficientrelated to the CP-even Higgs boson interactions with gluons.The highest sensitivity to this parameter is reached by themeasurements in the gg2H-0 j-pHT -Low and gg2H-0 j-pHT -High production bins due to the highest statistical precision.The sensitivity in the gg2H-pHT -High production bin, whichis designed to target the BSM physics effects, is limited dueto the small number of events observed in the correspondingreconstructed event category. Additional sensitivity in thisbin may be provided by the two-loop interactions which arenot implemented in the current simulation of the ggH ver-tex. The constrained range is stringent enough for the linearapproximation to hold, i.e. the quadratic terms in the sig-nal parameterisation are small compared with the linear ones(see Fig. 14e). The constraint on the cHG parameter of therelated CP-odd operator is worse by about a factor of threesince the linear terms from CP-odd operators do not con-tribute to the total production cross-section. The constraintson the remaining EFT parameters are weaker, such that boththe CP-even and CP-odd signals become dominated by thequadratic terms and are therefore comparable in size. Thenext-strongest constraints are obtained on the cHB , cHW B ,cHW , cH B , cHW B and cHW coefficients that mostly affectthe H → Z Z∗ decays. Due to the larger number of eventsin the 0-jet reconstructed event categories, the correspond-ing gg2H production bins provide the highest sensitivityto these decays. Additional smaller sensitivity is obtainedfrom the production vertex of the VBF and VH productionmodes, with the dominant contribution from qq2Hqq-VBFand qq2Hqq-BSM bins. The latter one is designed to enhancethe sensitivity to BSM physics. Theqq2Hqq production binsimprove in particular the sensitivity to the cHW and cHW

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4− 3− 2− 1− 0HWc

0

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SM=1.0

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Fig. 13 The dependence of the signal acceptance normalised to the SM acceptance on the Wilson coefficients (a) cHW and cHW , (b) cHB andcH B , (c) cHW B and cHW B after setting all other coefficients to zero

4− 3− 2− 1− 0HWc

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SM B)⋅ σ B)/(⋅ σ(

SM A)⋅ B ⋅ σ A)/(⋅ B ⋅ σ(


s VeT 31 = -High

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SM=1.0

6− 4− 2− 0HWc

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s VeT 31 = qq2Hqq-VBF

SM=1.0

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0.02 0.01− 0HGc

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SM B)⋅ σ B)/(⋅ σ(


s VeT 31 = -High

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20− 10− 02 4 6 0.01 0.02 10 20 30 40uHc

0

1

2

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ised

to S

M p

redi

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s VeT 31 = ttH+tH

SM=1.0

(f)

(a) (b) (c)

Fig. 14 The expected event yields (σ · B · A) relative to the SM pre-diction as a function of the Wilson coefficient (a) cHW , (b) cHB and(c) cHW B in the gg2H-0 j-pHT -High production bin, (d) cHW in theqq2Hqq-VBF production bin, (e) cHG in the gg2H-0 j-pHT -High pro-duction bin and (f) cuH in the t t H production bin. The dependenceon only one Wilson coefficient is shown on each plot while setting allothers to zero. For comparison, the predictions are also shown for theparameterisation without the acceptance corrections (σ · B) and forthe production cross-section only (σ ) without the acceptance and the

branching ratio corrections. The σ parameterisations in (a), (b) and (c)coincide with the SM expectation at 1 as the coefficients cHW , cHB andcHW B are not present in the ggF production vertex. Since the accep-tance does not depend on the cHG and cuH parameters, no corresponding(σ · B · A) expectation is shown in (e) and (f). Similarly, no (σ · B)expectation is shown in (f), since the cuH parameter has a negligibleimpact on the branching ratio. The bands indicate the expected preci-sion of the cross-section measurement in a given production bin at theone standard deviation level

parameters that is otherwise significantly degraded by theacceptance corrections. Finally, looser constraints are set on

the top-Yukawa coupling parameters cuH and cuH , driven bythe measurements in the t t H production bin.

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Particle-level production bin

1−

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5S

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)⋅ σ

B)/

(⋅ σ(

-LowT,H

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ed

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T,H

gg2H-1j-p

gg2H-2j-High

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gg2H-p

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qq2Hqq-VH-Like

qq2Hqq-BSM

qq/gg2HLep

ttH

ATLAS4l→ZZ*→H

-1 = 13 TeV, 139 fbs

Data = 0.004HGc

= -7.5uHc = 0.85HWc = 0.4HBc = 1.0HWBc

Particle-level production bin

1−

0

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SM

B)

⋅ σ B

)/(

⋅ σ(

-LowT,H

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ed

T,H

gg2H-1j-p-High

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gg2H-1j-p

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T,H

gg2H-p

qq2Hqq-VBF

qq2Hqq-VH-Like

qq2Hqq-BSM

qq/gg2HLep

ttH

ATLAS4l→ZZ*→H

-1 = 13 TeV, 139 fbs

Data = 0.02G~

Hc

= 26Hu~c = 1.3W~

Hc

= 0.4B~

Hc = 0.7

BW~

Hc

(a) (b)

Fig. 15 The expected signal yield ratio for chosen (a) CP-even and (b)CP-odd EFT parameter values together with the corresponding cross-section measurement in each production bin of Reduced Stage 1.1. The

parameter values correspond approximately to the expected confidenceintervals at the 68% CL obtained from the statistical interpretation ofdata

(a) (b)

Fig. 16 The observed and expected values of SMEFT Wilson coef-ficients from (a) CP-even and (b) CP-odd operators obtained for anintegrated luminosity of 139 fb−1 at

√s = 13 TeV. Only one Wilson

coefficient is fitted at a time while all others are set to zero. The values

for the cHG and cHG coefficients are scaled by a factor of 100, and forthe cuH and cuH coefficients by a factor of 0.05. The horizontal bandsrepresent the expected measurement uncertainty

To explore possible correlations between different Wilsoncoefficients, the simultaneous fits are also performed on twoWilson coefficients at a time. The corresponding results areshown in Fig. 17 for several combinations of two CP-evenEFT parameters and in Fig. 18 for the corresponding CP-oddoperators. The best-fit values as well as the deviation fromthe SM prediction are shown in Table 10. Good agreementwith the SM predictions is observed for all such possiblecombinations.

The anti-correlation between the cHW and cHB coef-ficients, as well as between cHW and cH B , is driven bytheir impact on the signal acceptance. The non-ellipsoidalshape is caused by the acceptance correction, which degrades

the original branching ratio-driven sensitivity for increasingparameter values, in particular in the case of the cHW (cHW )coefficient. The sensitivity is, however, partially recouped bythe VBF production vertex.

The ‘V’-shaped correlation between the cHG and cHB

parameters is due to the interplay between the EFT param-eterisation in the ggF production vertex and the parameteri-sation of the branching ratios and acceptances. The ggF pro-duction vertex provides the constraint on the cHG parameteralone, independently of cHB . Due to the decay vertex withits acceptance corrections, this constrained range is shiftedupward with increasing values of cHB . Close to the SM point,the constrained cHG range remains approximately the same

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Table 9 The expected and observed confidence intervals at 68% and 95% CL on the SMEFT Wilson coefficients for an integrated luminosity of139 fb−1 at

√s = 13 TeV. Only one Wilson coefficient is fitted at a time while all others are set to zero

EFT couplingparameter

Expected Observed Best-fit Best-fit

68% CL 95% CL 68% CL 95% CL value p-value

cHG [−0.004, 0.004] [−0.007, 0.008] [−0.005, 0.003] [−0.008, 0.007] −0.001 0.79

cuH [−8, 20] [−14, 26] [−12, 6] [−18, 30] −6, 18 0.50

cHW [−1.6, 0.9] [−2.9, 1.6] [−1.5, 1.3] [−3.4, 2.1] 0.5 0.66

cHB [−0.43, 0.38] [−0.62, 0.60] [−0.42, 0.37] [−0.62, 0.59] −0.03 0.98

cHW B [−0.75, 0.63] [−1.09, 0.99] [−0.71, 0.63] [−1.06, 0.99] 0.1 0.93

cHG [−0.022, 0.022] [−0.031, 0.031] [−0.019, 0.019] [−0.029, 0.029] 0.000 1.00

cuH [−26, 26] [−40, 40] [−37, 37] [−50, 50] ±21 0.48

cHW [−1.3, 1.3] [−2.1, 2.1] [−1.5, 1.5] [−2.4, 2.4] ±0.6 0.84

cH B [−0.39, 0.39] [−0.57, 0.57] [−0.37, 0.37] [−0.56, 0.56] 0.00 1.00

cHW B [−0.71, 0.71] [−1.05, 1.05] [−0.69, 0.69] [−1.03, 1.03] 0.0 1.00

(a) (b) (c)

Fig. 17 Expected (dashed line) and observed (full line) 2D-fit like-lihood curves at the 95% CL for the SMEFT Wilson coefficientsof CP-even operators at an integrated luminosity of 139 fb−1 and

√s = 13 TeV. The best fit to the data (solid cross) and the SM prediction

(star) are also indicated. Except for the two fitted Wilson coefficients,all others are set to zero

as without the decay constraints. An additional constrainton cHB is provided by the VBF production mode. Aroundthe SM point, the cHB constraints correspond approximatelyto those from the one-dimensional parameter fit. Additionalsensitivity to intermediate values of the cHB parameter is pro-vided by the acceptance corrections, resulting in two addi-tional allowed parameter regions that are disjoint from theregion around the SM point. Similar arguments hold alsofor the CP-odd case with the cHG and cH B parameters. Asopposed to the CP-even case, however, the likelihood con-tours are symmetric around the cHG = 0 axis, since thereare no linear terms contributing to the ggF production cross-section.

The correlation between the cHG and cuH (cHG and cuH )parameters is introduced through the interference term in thet t H vertex. However, the impact of this term on the finalresult is negligible since the cHG (cHG) parameter is alreadyconstrained to very small values compared with cuH (cuH ).

Therefore, the t t H production vertex mainly constrains thecuH and cuH parameters, while the ggF vertex constrains onlythe other two. The acceptance correction has no impact onthese results. The CP-odd parameter range is less constrainedthan the CP-even one due to the missing linear cuH terms inthe cross-section parameterisation.

11 Conclusion

Higgs boson properties are studied in the four-lepton decaychannel using 139 fb−1 of LHC proton–proton collisiondata at

√s = 13 TeV collected by the ATLAS experiment.

The Higgs boson candidate events are categorised into sev-eral topologies, providing sensitivity to different productionmodes in various regions of phase space. Additional mul-tivariate discriminants are used to further improve the sen-sitivity in reconstructed event categories with a sufficiently

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(a) (b) (c)

Fig. 18 Expected (dashed line) and observed (full line) 2D-fit likeli-hood curves at the 95% CL for the SMEFT Wilson coefficients of CP-odd operators at an integrated luminosity of 139 fb−1 and

√s = 13 TeV.

The best fit to the data (solid cross) and the SM prediction (star) arealso indicated. Except for the two fitted Wilson coefficients, all othersare set to zero

Table 10 The best-fit values and the corresponding deviation from theSM prediction obtained from the two-dimensional likelihood scans ofthe CP-odd BSM coupling parameters performed with 139 fb−1 of data

at a centre-of-mass energy of√s = 13 TeV. The limits are computed

using the confidence-level interval method. Except for the two fittedBSM coupling parameters, all others are set to zero

BSM couplingparameter

Observed best fit Best-fitp-value

cHW , cHB cHW = 0.57 cH B = 0.05 0.88

cHG , cHB cHG = −0.001 cH B = −0.04 0.78

cHG , cuH cHG = −0.001 cuH = −5.7, 17.7 0.80

cHW , cH B cHW = ±1.12 cH B = ∓0.21 0.91

cHG , cH B cHG = 0.00 cH B = 0.00 1.00

cHG , cuH cHG = 0.000 cuH = ±21 0.78

large number of events. The cross-section times branchingratio for H → Z Z∗ decay measured in dedicated produc-tion bins are in good agreement with the SM predictions. Theinclusive cross-section times branching ratio for H → Z Z∗decay in the Higgs boson rapidity range of |yH | < 2.5 is mea-sured to be 1.34 ± 0.12 pb compared with the SM predictionof 1.33 ± 0.08 pb. Results are also interpreted within theκ-framework with coupling-strength modifiers κV and κF ,showing compatibility with the SM. Based on the productof cross-section, branching ratio and acceptance measuredin Reduced Stage-1.1 production bins of simplified templatecross-sections, constraints are placed on possible CP-evenand CP-odd BSM interactions of the Higgs boson to vectorbosons, gluons and top quarks within an effective field theoryframework in the H → Z Z∗ decay. The data are found tobe consistent with the SM hypothesis.

Acknowledgements We thank CERN for the very successful operationof the LHC, as well as the support staff from our institutions withoutwhom ATLAS could not be operated efficiently.

We acknowledge the support of ANPCyT, Argentina; YerPhI, Arme-nia; ARC, Australia; BMWFW and FWF, Austria; ANAS, Azerbai-jan; SSTC, Belarus; CNPq and FAPESP, Brazil; NSERC, NRC andCFI, Canada; CERN; CONICYT, Chile; CAS, MOST and NSFC,China; COLCIENCIAS, Colombia; MSMT CR, MPO CR and VSCCR, Czech Republic; DNRF and DNSRC, Denmark; IN2P3-CNRSand CEA-DRF/IRFU, France; SRNSFG, Georgia; BMBF, HGF andMPG, Germany; GSRT, Greece; RGC and Hong Kong SAR, China;ISF and Benoziyo Center, Israel; INFN, Italy; MEXT and JSPS, Japan;CNRST, Morocco; NWO, Netherlands; RCN, Norway; MNiSW andNCN, Poland; FCT, Portugal; MNE/IFA, Romania; MES of Russia andNRC KI, Russia Federation; JINR; MESTD, Serbia; MSSR, Slovakia;ARRS and MIZŠ, Slovenia; DST/NRF, South Africa; MINECO, Spain;SRC and Wallenberg Foundation, Sweden; SERI, SNSF and Cantonsof Bern and Geneva, Switzerland; MOST, Taiwan; TAEK, Turkey;STFC, United Kingdom; DOE and NSF, United States of America. Inaddition, individual groups and members have received support fromBCKDF, CANARIE, Compute Canada and CRC, Canada; ERC, ERDF,Horizon 2020, Marie Skłodowska-Curie Actions and COST, EuropeanUnion; Investissements d’Avenir Labex, Investissements d’Avenir Idexand ANR, France; DFG and AvH Foundation, Germany; Herakleitos,Thales and Aristeia programmes co-financed by EU-ESF and the GreekNSRF, Greece; BSF-NSF and GIF, Israel; CERCA Programme Gener-alitat de Catalunya and PROMETEO Programme Generalitat Valen-

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ciana, Spain; Göran Gustafssons Stiftelse, Sweden; The Royal Societyand Leverhulme Trust, United Kingdom.The crucial computing support from all WLCG partners is acknowl-edged gratefully, in particular from CERN, the ATLAS Tier-1 facili-ties at TRIUMF (Canada), NDGF (Denmark, Norway, Sweden), CC-IN2P3 (France), KIT/GridKA (Germany), INFN-CNAF (Italy), NL-T1 (Netherlands), PIC (Spain), ASGC (Taiwan), RAL (UK) and BNL(USA), the Tier-2 facilities worldwide and large non-WLCG resourceproviders. Major contributors of computing resources are listed in Ref.[172].

Data Availability Statement This manuscript has no associated dataor the data will not be deposited. [Authors’ comment: All ATLAS sci-entific output is published in journals, and preliminary results are madeavailable in Conference Notes. All are openly available, without restric-tion on use by external parties beyond copyright law and the standardconditions agreed by CERN. Data associated with journal publicationsare also made available: tables and data from plots (e.g. cross sectionvalues, likelihood profiles, selection efficiencies, cross section limits,...) are stored in appropriate repositories such as HEPDATA (http://hepdata.cedar.ac.uk/). ATLAS also strives to make additional materialrelated to the paper available that allows a reinterpretation of the datain the context of new theoretical models. For example, an extendedencapsulation of the analysis is often provided for measurements in theframework of RIVET (http://rivet.hepforge.org/)”. This information istaken from the ATLAS Data Access Policy, which is a public docu-ment that can be downloaded from http://opendata.cern.ch/record/413[opendata.cern.ch].]

Open Access This article is licensed under a Creative Commons Attri-bution 4.0 International License, which permits use, sharing, adaptation,distribution and reproduction in any medium or format, as long as yougive appropriate credit to the original author(s) and the source, pro-vide a link to the Creative Commons licence, and indicate if changeswere made. The images or other third party material in this articleare included in the article’s Creative Commons licence, unless indi-cated otherwise in a credit line to the material. If material is notincluded in the article’s Creative Commons licence and your intendeduse is not permitted by statutory regulation or exceeds the permit-ted use, you will need to obtain permission directly from the copy-right holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.Funded by SCOAP3.

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http://orcid.org/0000-0002-4961-8368

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http://orcid.org/0000-0002-4963-8836

http://orcid.org/0000-0002-4499-2545

http://orcid.org/0000-0002-1222-7937

http://orcid.org/0000-0001-6056-7947

http://orcid.org/0000-0002-9037-2152

http://orcid.org/0000-0003-2280-8636

http://orcid.org/0000-0001-6331-3272

http://orcid.org/0000-0002-2029-2659

http://orcid.org/0000-0002-5447-1989

http://orcid.org/0000-0001-8265-6916

http://orcid.org/0000-0002-4198-3029

http://orcid.org/0000-0002-5110-5959

http://orcid.org/0000-0001-7335-4983

http://orcid.org/0000-0002-5706-7180

http://orcid.org/0000-0002-9907-838X

http://orcid.org/0000-0002-9778-9209

http://orcid.org/0000-0002-9336-9338

http://orcid.org/0000-0001-5241-6559

http://orcid.org/0000-0001-8659-5727

http://orcid.org/0000-0002-8265-474X

http://orcid.org/0000-0003-4731-0754

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X. Zhang60b , Y. Zhang15a,15d , Z. Zhang63a, Z. Zhang65 , P. Zhao49 , Z. Zhao60a, A. Zhemchugov80 , Z. Zheng106,D. Zhong172 , B. Zhou106, C. Zhou180 , H. Zhou7 , M. S. Zhou15a,15d , M. Zhou154 , N. Zhou60c , Y. Zhou7,C. G. Zhu60b , C. Zhu15a,15d , H. L. Zhu60a , H. Zhu15a , J. Zhu106 , Y. Zhu60a , X. Zhuang15a , K. Zhukov111 ,V. Zhulanov122a,122b , D. Zieminska66 , N. I. Zimine80 , S. Zimmermann52 , Z. Zinonos115, M. Ziolkowski150,L. Živkovic16 , G. Zobernig180 , A. Zoccoli23a,23b , K. Zoch53 , T. G. Zorbas148 , R. Zou37 , L. Zwalinski36

1 Department of Physics, University of Adelaide, Adelaide, Australia2 Physics Department, SUNY Albany, Albany, NY, USA3 Department of Physics, University of Alberta, Edmonton, AB, Canada4 (a)Department of Physics, Ankara University, Ankara, Turkey; (b)Application and Research Center for Advanced

Studies, Istanbul Aydin University, Istanbul, Turkey; (c)Division of Physics, TOBB University of Economics andTechnology, Ankara, Turkey

5 LAPP, Université Grenoble Alpes, Université Savoie Mont Blanc, CNRS/IN2P3, Annecy, France6 High Energy Physics Division, Argonne National Laboratory, Argonne, IL, USA7 Department of Physics, University of Arizona, Tucson, AZ, USA8 Department of Physics, University of Texas at Arlington, Arlington, TX, USA9 Physics Department, National and Kapodistrian University of Athens, Athens, Greece

10 Physics Department, National Technical University of Athens, Zografou, Greece11 Department of Physics, University of Texas at Austin, Austin, TX, USA12 (a)Faculty of Engineering and Natural Sciences, Bahcesehir University, Istanbul, Turkey; (b)Faculty of Engineering and

Natural Sciences, Istanbul Bilgi University, Istanbul, Turkey; (c)Department of Physics, Bogazici University, Istanbul,Turkey; (d)Department of Physics Engineering, Gaziantep University, Gaziantep, Turkey

13 Institute of Physics, Azerbaijan Academy of Sciences, Baku, Azerbaijan14 Institut de Física d’Altes Energies (IFAE), Barcelona Institute of Science and Technology, Barcelona, Spain15 (a)Institute of High Energy Physics, Chinese Academy of Sciences, Beijing, China; (b)Physics Department, Tsinghua

University, Beijing, China; (c)Department of Physics, Nanjing University, Nanjing, China; (d)University of ChineseAcademy of Science (UCAS), Beijing, China

16 Institute of Physics, University of Belgrade, Belgrade, Serbia17 Department for Physics and Technology, University of Bergen, Bergen, Norway18 Physics Division, Lawrence Berkeley National Laboratory and University of California, Berkeley, CA, USA19 Institut für Physik, Humboldt Universität zu Berlin, Berlin, Germany20 Albert Einstein Center for Fundamental Physics and Laboratory for High Energy Physics, University of Bern, Bern,

Switzerland21 School of Physics and Astronomy, University of Birmingham, Birmingham, UK22 (a)Facultad de Ciencias y Centro de Investigaciónes, Universidad Antonio Nariño, Bogotá, Colombia; (b)Departamento

de Física, Universidad Nacional de Colombia, Bogotá, Colombia, Colombia23 (a)Dipartimento di Fisica, INFN Bologna and Universita’ di Bologna, Bologna, Italy; (b)INFN Sezione di Bologna,

Bologna, Italy24 Physikalisches Institut, Universität Bonn, Bonn, Germany25 Department of Physics, Boston University, Boston, MA, USA26 Department of Physics, Brandeis University, Waltham, MA, USA27 (a)Transilvania University of Brasov, Brasov, Romania; (b)Horia Hulubei National Institute of Physics and Nuclear

Engineering, Bucharest, Romania; (c)Department of Physics, Alexandru Ioan Cuza University of Iasi, Iasi,Romania; (d)Physics Department , National Institute for Research and Development of Isotopic and MolecularTechnologies, Cluj-Napoca, Romania; (e)University Politehnica Bucharest, Bucharest, Romania; (f)West University inTimisoara, Timisoara, Romania

28 (a)Faculty of Mathematics, Physics and Informatics, Comenius University, Bratislava, Slovak Republic; (b)Department ofSubnuclear Physics, Institute of Experimental Physics of the Slovak Academy of Sciences, Kosice, Slovak Republic

29 Physics Department, Brookhaven National Laboratory, Upton, NY, USA30 Departamento de Física, Universidad de Buenos Aires, Buenos Aires, Argentina31 California State University, CA, USA32 Cavendish Laboratory, University of Cambridge, Cambridge, UK

123

http://orcid.org/0000-0003-4341-1603

http://orcid.org/0000-0002-4554-2554

http://orcid.org/0000-0002-7853-9079

http://orcid.org/0000-0003-0054-8749

http://orcid.org/0000-0002-3360-4965

http://orcid.org/0000-0001-9377-650X

http://orcid.org/0000-0001-5904-7258

http://orcid.org/0000-0002-7986-9045

http://orcid.org/0000-0002-8554-9216

http://orcid.org/0000-0001-7223-8403

http://orcid.org/0000-0002-1775-2511

http://orcid.org/0000-0001-8015-3901

http://orcid.org/0000-0002-5918-9050

http://orcid.org/0000-0001-8479-1345

http://orcid.org/0000-0001-8066-7048

http://orcid.org/0000-0002-5278-2855

http://orcid.org/0000-0002-7306-1053

http://orcid.org/0000-0003-0996-3279

http://orcid.org/0000-0003-2468-9634

http://orcid.org/0000-0002-0306-9199

http://orcid.org/0000-0002-6311-7420

http://orcid.org/0000-0003-0277-4870

http://orcid.org/0000-0002-1529-8925

http://orcid.org/0000-0003-4236-8930

http://orcid.org/0000-0001-8113-1499

http://orcid.org/0000-0002-0993-6185

http://orcid.org/0000-0003-2138-6187

http://orcid.org/0000-0003-2073-4901

http://orcid.org/0000-0002-0542-1264

http://orcid.org/0000-0002-9397-2313

957 of 54 Eur. Phys. J. C (2020) 80:957

33 (a)Department of Physics, University of Cape Town, Cape Town, South Africa; (b)iThemba Labs, Western Cape, SouthAfrica; (c)Department of Mechanical Engineering Science, University of Johannesburg, Johannesburg,South Africa; (d)Department of Physics, University of South Africa, Pretoria, South Africa; (e)School of Physics,University of the Witwatersrand, Johannesburg, South Africa

34 Department of Physics, Carleton University, Ottawa, ON, Canada35 (a)Faculté des Sciences Ain Chock, Réseau Universitaire de Physique des Hautes Energies - Université Hassan II,

Casablanca, Morocco; (b)Faculté des Sciences, Université Ibn-Tofail, Kénitra, Morocco; (c)Faculté des SciencesSemlalia, Université Cadi Ayyad, LPHEA, Marrakech, Morocco; (d)Faculté des Sciences, Université Mohamed Premierand LPTPM, Oujda, Morocco; (e)Faculté des sciences, Université Mohammed V, Rabat, Morocco

36 CERN, Geneva, Switzerland37 Enrico Fermi Institute, University of Chicago, Chicago, IL, USA38 LPC, Université Clermont Auvergne, CNRS/IN2P3, Clermont-Ferrand, France39 Nevis Laboratory, Columbia University, Irvington, NY, USA40 Niels Bohr Institute, University of Copenhagen, Copenhagen, Denmark41 (a)Dipartimento di Fisica, Università della Calabria, Rende, Italy; (b)INFN Gruppo Collegato di Cosenza, Laboratori

Nazionali di Frascati, Italy42 Physics Department, Southern Methodist University, Dallas, TX, USA43 Physics Department, University of Texas at Dallas, Richardson, TX, USA44 National Centre for Scientific Research “Demokritos”, Agia Paraskevi, Greece45 (a)Department of Physics, Stockholm University, Stockholm, Sweden; (b)Oskar Klein Centre, Stockholm, Sweden46 Deutsches Elektronen-Synchrotron DESY, Hamburg and Zeuthen, Germany47 Lehrstuhl für Experimentelle Physik IV, Technische Universität Dortmund, Dortmund, Germany48 Institut für Kern- und Teilchenphysik, Technische Universität Dresden, Dresden, Germany49 Department of Physics, Duke University, Durham, NC, USA50 SUPA - School of Physics and Astronomy, University of Edinburgh, Edinburgh, UK51 INFN e Laboratori Nazionali di Frascati, Frascati, Italy52 Physikalisches Institut, Albert-Ludwigs-Universität Freiburg, Freiburg, Germany53 II. Physikalisches Institut, Georg-August-Universität Göttingen, Göttingen, Germany54 Département de Physique Nucléaire et Corpusculaire, Université de Genève, Genève, Switzerland55 (a)Dipartimento di Fisica, Università di Genova, Genova, Italy; (b)INFN Sezione di Genova, Genova, Italy56 II. Physikalisches Institut, Justus-Liebig-Universität Giessen, Giessen, Germany57 SUPA - School of Physics and Astronomy, University of Glasgow, Glasgow, UK58 LPSC, Université Grenoble Alpes, CNRS/IN2P3, Grenoble INP, Grenoble, France59 Laboratory for Particle Physics and Cosmology, Harvard University, Cambridge, MA, USA60 (a)Department of Modern Physics and State Key Laboratory of Particle Detection and Electronics, University of Science

and Technology of China, Hefei, China; (b)Institute of Frontier and Interdisciplinary Science and Key Laboratory ofParticle Physics and Particle Irradiation (MOE), Shandong University, Qingdao, China; (c)School of Physics andAstronomy, Shanghai Jiao Tong University, KLPPAC-MoE, SKLPPC, Shanghai, China; (d)Tsung-Dao Lee Institute,Shanghai, China

61 (a)Kirchhoff-Institut für Physik, Ruprecht-Karls-Universität Heidelberg, Heidelberg, Germany; (b)Physikalisches Institut,Ruprecht-Karls-Universität Heidelberg, Heidelberg, Germany

62 Faculty of Applied Information Science, Hiroshima Institute of Technology, Hiroshima, Japan63 (a)Department of Physics, Chinese University of Hong Kong, Shatin, N.T., Hong Kong, China; (b)Department of Physics,

University of Hong Kong, Hong Kong, China; (c)Department of Physics and Institute for Advanced Study, Hong KongUniversity of Science and Technology, Clear Water Bay, Kowloon, Hong Kong, China

64 Department of Physics, National Tsing Hua University, Hsinchu, Taiwan65 IJCLab, Université Paris-Saclay, CNRS/IN2P3, 91405, Orsay, France66 Department of Physics, Indiana University, Bloomington, IN, USA67 (a)INFN Gruppo Collegato di Udine, Sezione di Trieste, Udine, Italy; (b)ICTP, Trieste, Italy; (c)Dipartimento Politecnico

di Ingegneria e Architettura, Università di Udine, Udine, Italy68 (a)INFN Sezione di Lecce, Lecce, Italy; (b)Dipartimento di Matematica e Fisica, Università del Salento, Lecce, Italy69 (a)INFN Sezione di Milano, Milano, Italy; (b)Dipartimento di Fisica, Università di Milano, Milano, Italy70 (a)INFN Sezione di Napoli, Napoli, Italy; (b)Dipartimento di Fisica, Università di Napoli, Napoli, Italy

123

Eur. Phys. J. C (2020) 80:957 of 54 957

71 (a)INFN Sezione di Pavia, Pavia, Italy; (b)Dipartimento di Fisica, Università di Pavia, Pavia, Italy72 (a)INFN Sezione di Pisa, Pisa, Italy; (b)Dipartimento di Fisica E. Fermi, Università di Pisa, Pisa, Italy73 (a)INFN Sezione di Roma, Roma, Italy; (b)Dipartimento di Fisica, Sapienza Università di Roma, Roma, Italy74 (a)INFN Sezione di Roma Tor Vergata, Roma, Italy; (b)Dipartimento di Fisica, Università di Roma Tor Vergata, Roma,

Italy75 (a)INFN Sezione di Roma Tre, Roma, Italy; (b)Dipartimento di Matematica e Fisica, Università Roma Tre, Roma, Italy76 (a)INFN-TIFPA, Trento, Italy; (b)Università degli Studi di Trento, Trento, Italy77 Institut für Astro- und Teilchenphysik, Leopold-Franzens-Universität, Innsbruck, Austria78 University of Iowa, Iowa City, IA, USA79 Department of Physics and Astronomy, Iowa State University, Ames, IA, USA80 Joint Institute for Nuclear Research, Dubna, Russia81 (a)Departamento de Engenharia Elétrica, Universidade Federal de Juiz de Fora (UFJF), Juiz de Fora, São Paulo,

Brazil; (b)Universidade Federal do Rio De Janeiro COPPE/EE/IF, Rio de Janeiro, São Paulo, Brazil; (c)UniversidadeFederal de São João del Rei (UFSJ), São João del Rei, São Paulo, Brazil; (d)Instituto de Física, Universidade de SãoPaulo, São Paulo, Brazil

82 KEK, High Energy Accelerator Research Organization, Tsukuba, Japan83 Graduate School of Science, Kobe University, Kobe, Japan84 (a)Faculty of Physics and Applied Computer Science, AGH University of Science and Technology, Krakow,

Poland; (b)Marian Smoluchowski Institute of Physics, Jagiellonian University, Krakow, Poland85 Institute of Nuclear Physics Polish Academy of Sciences, Krakow, Poland86 Faculty of Science, Kyoto University, Kyoto, Japan87 Kyoto University of Education, Kyoto, Japan88 Research Center for Advanced Particle Physics and Department of Physics, Kyushu University, Fukuoka , Japan89 Instituto de Física La Plata, Universidad Nacional de La Plata and CONICET, La Plata, Argentina90 Physics Department, Lancaster University, Lancaster, UK91 Oliver Lodge Laboratory, University of Liverpool, Liverpool, UK92 Department of Experimental Particle Physics, Jožef Stefan Institute and Department of Physics, University of Ljubljana,

Ljubljana, Slovenia93 School of Physics and Astronomy, Queen Mary University of London, London, UK94 Department of Physics, Royal Holloway University of London, Egham, UK95 Department of Physics and Astronomy, University College London, London, UK96 Louisiana Tech University, Ruston, LA, USA97 Fysiska institutionen, Lunds universitet, Lund, Sweden98 Centre de Calcul de l’Institut National de Physique Nucléaire et de Physique des Particules (IN2P3), Villeurbanne,

France99 Departamento de Física Teorica C-15 and CIAFF, Universidad Autónoma de Madrid, Madrid, Spain

100 Institut für Physik, Universität Mainz, Mainz, Germany101 School of Physics and Astronomy, University of Manchester, Manchester, UK102 CPPM, Aix-Marseille Université, CNRS/IN2P3, Marseille, France103 Department of Physics, University of Massachusetts, Amherst, MA, USA104 Department of Physics, McGill University, Montreal, QC, Canada105 School of Physics, University of Melbourne, Victoria, Australia106 Department of Physics, University of Michigan, Ann Arbor, MI, USA107 Department of Physics and Astronomy, Michigan State University, East Lansing, MI, USA108 B.I. Stepanov Institute of Physics, National Academy of Sciences of Belarus, Minsk, Belarus109 Research Institute for Nuclear Problems of Byelorussian State University, Minsk, Belarus110 Group of Particle Physics, University of Montreal, Montreal, QC, Canada111 P.N. Lebedev Physical Institute of the Russian Academy of Sciences, Moscow, Russia112 National Research Nuclear University MEPhI, Moscow, Russia113 D.V. Skobeltsyn Institute of Nuclear Physics, M.V. Lomonosov Moscow State University, Moscow, Russia114 Fakultät für Physik, Ludwig-Maximilians-Universität München, München, Germany115 Max-Planck-Institut für Physik (Werner-Heisenberg-Institut), München, Germany116 Nagasaki Institute of Applied Science, Nagasaki, Japan

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117 Graduate School of Science and Kobayashi-Maskawa Institute, Nagoya University, Nagoya, Japan118 Department of Physics and Astronomy, University of New Mexico, Albuquerque, NM, USA119 Institute for Mathematics, Astrophysics and Particle Physics, Radboud University Nijmegen/Nikhef, Nijmegen, The

Netherlands120 Nikhef National Institute for Subatomic Physics and University of Amsterdam, Amsterdam, The Netherlands121 Department of Physics, Northern Illinois University, DeKalb, IL, USA122 (a)Budker Institute of Nuclear Physics and NSU, SB RAS, Novosibirsk, Russia; (b)Novosibirsk State University,

Novosibirsk, Russia123 Institute for High Energy Physics of the National Research Centre Kurchatov Institute, Protvino, Russia124 Institute for Theoretical and Experimental Physics named by A.I. Alikhanov of National Research Centre “Kurchatov

Institute”, Moscow, Russia125 Department of Physics, New York University, New York, NY, USA126 Ochanomizu University, Otsuka, Bunkyo-ku, Tokyo, Japan127 Ohio State University, Columbus, OH, USA128 Homer L. Dodge Department of Physics and Astronomy, University of Oklahoma, Norman, OK, USA129 Department of Physics, Oklahoma State University, Stillwater, OK, USA130 Palacký University, RCPTM, Joint Laboratory of Optics, Olomouc, Czech Republic131 Institute for Fundamental Science, University of Oregon, Eugene, OR, USA132 Graduate School of Science, Osaka University, Osaka, Japan133 Department of Physics, University of Oslo, Oslo, Norway134 Department of Physics, Oxford University, Oxford, UK135 LPNHE, Sorbonne Université, Université de Paris, CNRS/IN2P3, Paris, France136 Department of Physics, University of Pennsylvania, Philadelphia, PA, USA137 Konstantinov Nuclear Physics Institute of National Research Centre “Kurchatov Institute”, PNPI, St. Petersburg, Russia138 Department of Physics and Astronomy, University of Pittsburgh, Pittsburgh, PA, USA139 (a)Laboratório de Instrumentação e Física Experimental de Partículas - LIP, Lisboa, Portugal; (b)Departamento de Física,

Faculdade de Ciências, Universidade de Lisboa, Lisboa, Portugal; (c)Departamento de Física, Universidade de Coimbra,Coimbra, Portugal; (d)Centro de Física Nuclear da Universidade de Lisboa, Lisboa, Portugal; (e)Departamento de Física,Universidade do Minho, Braga, Portugal; (f)Departamento de Física Teórica y del Cosmos, Universidad de Granada,Granada, Spain; (g)Dep Física and CEFITEC of Faculdade de Ciências e Tecnologia, Universidade Nova de Lisboa,Caparica, Portugal; (h)Instituto Superior Técnico, Universidade de Lisboa, Lisboa, Portugal

140 Institute of Physics of the Czech Academy of Sciences, Prague, Czech Republic141 Czech Technical University in Prague, Prague, Czech Republic142 Charles University, Faculty of Mathematics and Physics, Prague, Czech Republic143 Particle Physics Department, Rutherford Appleton Laboratory, Didcot, UK144 IRFU, CEA, Université Paris-Saclay, Gif-sur-Yvette, France145 Santa Cruz Institute for Particle Physics, University of California Santa Cruz, Santa Cruz, CA, USA146 (a)Departamento de Física, Pontificia Universidad Católica de Chile, Santiago, Chile; (b)Department of Physics,

Universidad Andres Bello, Santiago, Chile; (c)Instituto de Alta Investigación, Universidad de Tarapacá, Santiago,Chile; (d)Departamento de Física, Universidad Técnica Federico Santa María, Valparaíso, Chile

147 Department of Physics, University of Washington, Seattle, WA, USA148 Department of Physics and Astronomy, University of Sheffield, Sheffield, UK149 Department of Physics, Shinshu University, Nagano, Japan150 Department Physik, Universität Siegen, Siegen, Germany151 Department of Physics, Simon Fraser University, Burnaby, BC, Canada152 SLAC National Accelerator Laboratory, Stanford, CA, USA153 Physics Department, Royal Institute of Technology, Stockholm, Sweden154 Departments of Physics and Astronomy, Stony Brook University, Stony Brook, NY, USA155 Department of Physics and Astronomy, University of Sussex, Brighton, UK156 School of Physics, University of Sydney, Sydney, Australia157 Institute of Physics, Academia Sinica, Taipei, Taiwan158 (a)E. Andronikashvili Institute of Physics, Iv. Javakhishvili Tbilisi State University, Tbilisi, Georgia; (b)High Energy

Physics Institute, Tbilisi State University, Tbilisi, Georgia

123

Eur. Phys. J. C (2020) 80:957 of 54 957

159 Department of Physics, Technion, Israel Institute of Technology, Haifa, Israel160 Raymond and Beverly Sackler School of Physics and Astronomy, Tel Aviv University, Tel Aviv, Israel161 Department of Physics, Aristotle University of Thessaloniki, Thessaloniki, Greece162 International Center for Elementary Particle Physics and Department of Physics, University of Tokyo, Tokyo, Japan163 Graduate School of Science and Technology, Tokyo Metropolitan University, Tokyo, Japan164 Department of Physics, Tokyo Institute of Technology, Tokyo, Japan165 Tomsk State University, Tomsk, Russia166 Department of Physics, University of Toronto, Toronto, ON, Canada167 (a)TRIUMF, Vancouver, BC, Canada; (b)Department of Physics and Astronomy, York University, Toronto, ON, Canada168 Division of Physics and Tomonaga Center for the History of the Universe, Faculty of Pure and Applied Sciences,

University of Tsukuba, Tsukuba, Japan169 Department of Physics and Astronomy, Tufts University, Medford, MA, USA170 Department of Physics and Astronomy, University of California Irvine, Irvine, CA, USA171 Department of Physics and Astronomy, University of Uppsala, Uppsala, Sweden172 Department of Physics, University of Illinois, Urbana, IL, USA173 Instituto de Física Corpuscular (IFIC), Centro Mixto Universidad de Valencia - CSIC, Valencia, Spain174 Department of Physics, University of British Columbia, Vancouver, BC, Canada175 Department of Physics and Astronomy, University of Victoria, Victoria, BC, Canada176 Fakultät für Physik und Astronomie, Julius-Maximilians-Universität Würzburg, Würzburg, Germany177 Department of Physics, University of Warwick, Coventry, UK178 Waseda University, Tokyo, Japan179 Department of Particle Physics, Weizmann Institute of Science, Rehovot, Israel180 Department of Physics, University of Wisconsin, Madison, WI, USA181 Fakultät für Mathematik und Naturwissenschaften, Fachgruppe Physik, Bergische Universität Wuppertal, Wuppertal,

Germany182 Department of Physics, Yale University, New Haven, CT, USA

a Also at Borough of Manhattan Community College, City University of New York, New York NY, USAb Also at Centro Studi e Ricerche Enrico Fermi, Italyc Also at CERN, Geneva, Switzerlandd Also at CPPM, Aix-Marseille Université, CNRS/IN2P3, Marseille, Francee Also at Département de Physique Nucléaire et Corpusculaire, Université de Genève, Genève, Switzerlandf Also at Departament de Fisica de la Universitat Autonoma de Barcelona, Barcelona, Spaing Also at Department of Financial and Management Engineering, University of the Aegean, Chios, Greeceh Also at Department of Physics and Astronomy, Michigan State University, East Lansing MI, USAi Also at Department of Physics and Astronomy, University of Louisville, Louisville, KY, USAj Also at Department of Physics, Ben Gurion University of the Negev, Beer Sheva, Israel

k Also at Department of Physics, California State University, East Bay, USAl Also at Department of Physics, California State University, Fresno, USA

m Also at Department of Physics, California State University, Sacramento, USAn Also at Department of Physics, King’s College London, London, UKo Also at Department of Physics, St. Petersburg State Polytechnical University, St. Petersburg, Russiap Also at Department of Physics, University of Fribourg, Fribourg, Switzerlandq Also at Dipartimento di Matematica, Informatica e Fisica, Università di Udine, Udine, Italyr Also at Faculty of Physics, M.V. Lomonosov Moscow State University, Moscow, Russias Also at Giresun University, Faculty of Engineering, Giresun, Turkeyt Also at Graduate School of Science, Osaka University, Osaka, Japanu Also at Hellenic Open University, Patras, Greecev Also at IJCLab, Université Paris-Saclay, CNRS/IN2P3, 91405, Orsay, Francew Also at Institucio Catalana de Recerca i Estudis Avancats, ICREA, Barcelona, Spainx Also at Institut für Experimentalphysik, Universität Hamburg, Hamburg, Germanyy Also at Institute for Mathematics, Astrophysics and Particle Physics, Radboud University Nijmegen/Nikhef, Nijmegen,

Netherlands

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aa Also at Institute for Nuclear Research and Nuclear Energy (INRNE) of the Bulgarian Academy of Sciences, Sofia,Bulgaria

ab Also at Institute for Particle and Nuclear Physics, Wigner Research Centre for Physics, Budapest, Hungary.ac Also at Institute of Particle Physics (IPP), Vancouver, Canadaad Also at Institute of Physics, Azerbaijan Academy of Sciences, Baku, Azerbaijanae Also at Instituto de Fisica Teorica, IFT-UAM/CSIC, Madrid, Spainaf Also at Joint Institute for Nuclear Research, Dubna, Russiaag Also at Louisiana Tech University, Ruston LA, USAah Also at Moscow Institute of Physics and Technology State University, Dolgoprudny, Russiaai Also at National Research Nuclear University MEPhI, Moscow, Russiaaj Also at Physics Department, An-Najah National University, Nablus, Palestine

ak Also at Physikalisches Institut, Albert-Ludwigs-Universität Freiburg, Freiburg, Germanyal Also at The City College of New York, New York NY, USA

am Also at TRIUMF, Vancouver BC, Canada.an Also at Universita di Napoli Parthenope, Napoli, Italyao Also at University of Chinese Academy of Sciences (UCAS), Beijing, China.

∗Deceased

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