Search for Higgs boson pair production in the $WW^{(*)}WW^{(*)}$ decay channel using ATLAS data recorded at $\sqrt{s}=13$ TeV

A search for a pair of neutral, scalar bosons with each decaying into two $W$ bosons is presented using 36.1 fb$^{-1}$ of proton-proton collision data at a centre-of-mass energy of 13 TeV recorded with the ATLAS detector at the Large Hadron Collider. This search uses three production models: non-resonant and resonant Higgs boson pair production and resonant production of a pair of heavy scalar particles. Three final states, classified by the number of leptons, are analysed: two same-sign leptons, three leptons, and four leptons. No significant excess over the expected Standard Model backgrounds is observed. An observed (expected) 95% confidence-level upper limit of 160 (120) times the Standard Model prediction of non-resonant Higgs pair production cross-section is set from a combined analysis of the three final states. Upper limits are set on the production cross-section times branching ratio of a heavy scalar $X$ decaying into a Higgs boson pair in the mass range of 260 GeV $\le m_X \le$ 500 GeV and the observed (expected) limits range from 9.3 (10) pb to 2.8 (2.6) pb. Upper limits are set on the production cross-section times branching ratio of a heavy scalar $X$ decaying into a pair of heavy scalars $S$ for mass ranges of 280 GeV $\le m_X \le$ 340 GeV and 135 GeV $\le m_S \le$ 165 GeV and the observed (expected) limits range from 2.5 (2.5) pb to 0.16 (0.17) pb.


Introduction
A scalar boson was discovered by the ATLAS and CMS collaborations [1,2] in 2012.It has been shown to have properties consistent with those predicted for the Standard Model (SM) Higgs boson, H, through spin and coupling measurements [3][4][5][6][7][8][9][10].These measurements are based on production of the Higgs boson via gluon-gluon fusion, vector-boson fusion and in association with a W or Z boson or a top quark pair.The SM predicts non-resonant Higgs boson pair production via top quark loops as well as through self-coupling.The SM HH production cross-section is computed to be 33.4 fb [11,12] at next-to-next-to-leading order (NNLO) in QCD, including resummation of soft-gluon emission at next-tonext-to-leading-logarithmic (NNLL) accuracy for m H = 125.09GeV.The actual production rate could be larger than that predicted in the SM due to a variety of Beyond the Standard Model (BSM) physics effects.One such extension includes a modification to the SM Higgs self-coupling, λ H H H , and another the existence of a new heavy resonance which decays into a pair of Higgs bosons.An important Higgs boson decay channel is H → VV ( * ) in which V can be either a W or Z boson, on or off-shell, and this paper focuses on the 4W final state [13] in both SM and BSM HH production scenarios.This work investigates HH production through three different processes.The first is (1) the SM HH production (non-resonant HH).The second and third are both BSM processes inspired by an extended Higgs sector, such as a two-Higgs-doublet model [14], in which a neutral heavy Higgs boson, X [15] is produced and decays either (2) directly into two SM Higgs bosons (resonant HH) or (3) into a pair of new scalar bosons, S (X → SS), each of which in turn decays to other SM particles with the same mass-dependent branching ratios of the SM H.The reactions considered in this work are: pp → HH → WW ( * ) WW ( * ) (non-resonant, SM), (1) pp → X → HH → WW ( * ) WW ( * ) (resonant, BSM), and (2) pp → X → SS → WW ( * ) WW ( * ) (X → SS, BSM). (3) The measured final states encompass multiple combinations of leptons and hadrons: WW ( * ) WW ( * ) → ν + ν + 4q, WW ( * ) WW ( * ) → ν + ν + ν + 2q, or where is either an electron or a muon, q refers to quark and anti-quark decay products from the hadronically decaying W boson(s), and ν represents a neutrino, which results in missing transverse momentum.Therefore, three final states are searched for with two, three, or four leptons (plus missing energy and multiple jets), which allow any of the mentioned production modes to be probed.
The production of a new X scalar (2) would be seen as a local excess in the reconstructed di-Higgs mass spectrum.It is assumed in this work that m X > 2m H such that both H are produced on their mass shell.In the other extended Higgs sector model (3) X → SS is assumed to be the dominant X decay mode.In this scenario, the WW ( * ) WW ( * ) channel is the dominant decay mode for the mass ranges 270 GeV < m X < 2m t and 135 GeV < m S < m X /2, where m t , m X and m S are the mass of the top quark, X, and S scalars, respectively.The mass range m X > 2m t , where X → t t is expected to dominate, is not considered.It is assumed that m S > 135 GeV such that S → WW ( * ) is the dominant decay mode.It is also assumed that m S < m X /2 such that both S bosons are produced on their mass shell.
Previous searches were performed for resonant and non-resonant HH production using various channels, such as bbγγ [16,17], bbbb [18][19][20], bbVV [21], bbττ [22,23] and WW γγ [24], with data from the ATLAS and CMS experiments.Additionally, a combination of channels has been performed using data from the CMS experiment [25].This paper describes a search for resonant and non-resonant Higgs boson pair production in the HH → WW * WW * decay channel and for an extended Higgs sector with the decay of X → SS → WW ( * ) WW ( * ) .The analysis is divided into three independent channels depending on the number of light leptons (e or µ) from leptonic decays of W bosons, and then statistically combined to give the final result.
This paper is organised as follows.Data and simulation samples are described in Section 2. The object reconstruction and selection are outlined in Section 3. Section 4 details the event selection for each of the three final states analysed.The background estimation and the systematic uncertainties are described in Section 5 and Section 6, respectively.The results of this analysis are presented in Section 7 and summarised in Section 8. Finally, the Appendix lists the lepton pairing strategy used in each channel, the final event selection criteria and the corresponding acceptance and selection efficiencies.

Data and simulation samples
The data were collected with the ATLAS detector in 2015 and 2016 using pp collisions produced at √ s = 13 TeV at the Large Hadron Collider (LHC), corresponding to an integrated luminosity of 36.1 fb −1 [26].The ATLAS detector is described in detail in Ref. [27].Only data-taking periods in which all relevant detector systems are operational are used.
Samples simulated using Monte Carlo (MC) techniques are used to estimate the signal acceptance and selection efficiency.Simulated samples are also used to estimate the acceptance and selection efficiency for various background processes which contribute prompt leptons from W or Z boson decay and leptons originating from photon conversion.Backgrounds due to electrons with misidentified charge and jets misidentified as leptons are estimated using data-driven techniques, as described in Section 5.
The non-resonant gg → HH and resonant gg → X → HH signal samples in which H is constrained to decay into WW * are generated using M G 5_aMC@NLO [28,29] with the CT10 parton distribution function (PDF) set [30] and the parton shower is modelled by Herwig++ [31] with the UEEE5 set of tuned parameters (tune) for the underlying event [32] and the CTEQ6L1 PDF set [33].In resonant production, X decays into a pair of SM Higgs bosons with a negligible width compared to the experimental mass resolution.Various resonance mass hypotheses, m X , are considered: 260, 300, 400, and 500 GeV.The branching ratio B(X → HH) is assumed to be one.Samples of X → SS → WW ( * ) WW ( * ) events produced by gluon-gluon fusion are generated at leading order (LO) using P 8 with the NNPDF2.3LOPDF set [34] such that both the X and S scalars are assumed to have narrow decay widths.The mass hypotheses are selected to scan a range of both m X and m S .In the first scan, m S is fixed to 135 GeV for samples with m X = 280, 300, 320, and 340 GeV.In the second scan, m X is fixed to 340 GeV for samples with m S = 135, 145, 155, and 165 GeV.The branching ratio B(X → SS) is assumed to be one and the branching ratio B(S → WW ( * ) ) is assumed to be the mass-dependent expected branching ratios of the SM Higgs boson.
Multi-boson (VV/VVV) and V γ background samples are generated at next-to-leading-order (NLO) using S 2.1 [35].The V+jets samples are generated at NLO with S 2.2.The CT10 PDF set is used for these samples.The V H background sample is generated at leading-order (LO) using P 8 with the NNPDF2.3LOPDF set.The t t background sample is generated at NLO using P -B 2.0 [36] interfaced with P 8 with the NNPDF2.3LOPDF set.Single-top background samples are generated at NLO using P -B 2.0 interfaced with P 6.4 [37] with the CT10 PDF set.The t tV background sample is generated at NLO using M G 5_aMC@NLO interfaced with P 8 with the NNPDF2.3LOPDF set.The t tH background sample is generated at NLO using M G 5_aMC@NLO interfaced with Herwig++ with the NNPDF3.0[38] PDF set.The simulated samples of t t, t tH, t tV, and VV are described in more detail in Refs.[39][40][41].
The standard ATLAS detector simulation [42] based on G 4 [43] is used for background simulated samples.For signal events, the calorimeter simulation is replaced with the fast ATLAS calorimeter simulation [44] that uses a parameterised detector response.Soft collisions generated using P 8 [45] with the CTEQ6L1 PDF set and the A2 tune [46] are overlaid on the hard-scatter processes.The number of in-time and out-of-time collisions per bunch crossing (pileup) is adjusted to that observed in data.

Object selection
Electron candidates are reconstructed from energy clusters in the electromagnetic calorimeter that are associated with tracks reconstructed in the inner detector (ID).Electrons are identified using medium (tight) criteria [47] for the four lepton channel (two and three lepton channels).Electrons are required to have a transverse energy E T > 10 GeV and be within the detector fiducial volume of |η| < 2.47 excluding the transition region between the barrel and end-cap calorimeter, 1.37 < |η| < 1.52.1 Muon candidates are reconstructed by combining tracks reconstructed in the ID with tracks reconstructed in the muon spectrometer.Muons are identified using medium (tight) criteria [48] for the four lepton channel (two and three lepton channels).Muons are required to have a transverse momentum p T > 10 GeV and |η| < 2.5.Electrons are required to satisfy calorimeter and track isolation criteria and muons are required to satisfy a track isolation criterion.The calorimeter (track) isolation requires that the total sum of cluster transverse energies (transverse momenta of tracks with p T > 1 GeV) in a surrounding cone of size ∆R = 0.2 around the lepton, excluding the cluster E T (track p T ) of the lepton from the sum, is less than 30% (15%) of the p T of the lepton for the four lepton selection and 6% for the two and three lepton selections.
Jets are reconstructed from calibrated topological clusters in the calorimeters [49] using the anti-k t algorithm [50] with a radius parameter R = 0.4.Jet energies are corrected for effects from the detector and from pileup [51] using simulated and in situ techniques [51].Jets are required to have p T > 25 GeV and |η| < 2.5.Jets with p T < 60 GeV and |η| < 2.4 are required to satisfy additional pileup rejection criteria [52].Jets containing b-hadrons are identified (b-tagged) using the MV2c10 multivariate discriminant [53].The b-tagging requirement results in an efficiency of 70% for jets containing b-hadrons, as determined in a simulated sample of t t events [54].An overlap removal procedure is applied in order to resolve ambiguities between reconstructed physics objects.Jets within ∆R = 0.2 of a reconstructed electron are removed.If the nearest remaining jet is within ∆R = 0.4 of an electron, the electron is removed.Selected muons with an angular separation of ∆R < min(0.4,0.04 + 10 GeV/p µ T ) from the nearest jet are removed if the jet has at least three tracks originating from the primary vertex; otherwise the jet is removed and the muon is kept.The missing transverse momentum, E miss T , vector is the negative of the vector sum of the transverse momenta of all electrons, muons, and jets.Tracks from the primary vertex2 that are not associated with any objects are also taken into account in the E miss T reconstruction [55].

Event selection
Events are required to pass single-lepton or dilepton triggers [56] with minimum p T thresholds in the range 20-26 GeV, depending on the data collection period, and to have at least two leptons (e or µ).Events are also required to have at least one lepton (two leptons) to be matched to the single-lepton (dilepton) trigger signatures.A higher p T requirement than the online trigger p T threshold is applied to the trigger-matched lepton.Three channels are defined according to the number of reconstructed leptons (two leptons, three leptons and four leptons), and events are further classified according to the charge and flavour of the 1 ATLAS uses a right-handed coordinate system with its origin at the nominal 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 of the LHC ring, and the y-axis points upwards.Cylindrical coordinates (r, φ) are used in the transverse plane, φ being the azimuthal angle around the z-axis.
The pseudorapidity is defined in terms of the polar angle θ as η = − ln tan(θ/2).Angular distance is measured in units of ∆R ≡ (∆η) 2 + (∆φ) 2 . 2 Proton-proton collision vertices are reconstructed by requiring that at least two tracks with p T > 0.4 GeV are associated with a given vertex.The primary vertex is defined as the vertex with the largest p 2 T,track .
leptons.In order to suppress top quark backgrounds and to be orthogonal to other Higgs boson pair production searches (bbγγ [16], bbbb [18], and bbττ [22]) at ATLAS, events containing b-tagged jets are rejected.
Events in the two lepton channel are required to have exactly two leptons with the same electric charge, while the three lepton channel events are required to have exactly three leptons with a summed electric charge i ∈ q i = ±1.Events are required to have N jets ≥ 2 and E miss T > 10 (30) GeV for the two (three) lepton channel.In order to suppress backgrounds containing a Z boson in the same-sign ee channel (due to the misidentification of an electron's charge) and in the three lepton channel, events are removed if they contained a same-flavour lepton pair with an invariant mass, m , near the Z boson mass: |m − m Z | < 10 GeV.In order to reduce the backgrounds from non-prompt leptons, the leading (subleading) lepton is required to have p T > 30 (20) GeV in the two lepton channel.The two leptons with the same charge are both required to have p T > 20 GeV in the three lepton channel.For nonresonant production and resonant production with m X > 300 GeV, signal events tend to have jets with larger p T compared to low m X resonant production scenarios and thus N jets ≥ 3 is required in the two lepton channel to account for more jets passing the p T requirement.Additionally, events containing a same-flavour opposite-sign (SFOS) lepton pair with an invariant mass m < 15 GeV are also removed in order to suppress backgrounds from hadron resonances or virtual photons.Following this preselection, a number of observables are considered and four variables are chosen based on the ranking of the generic algorithm [57] and the correlations betweeen variables.These four variables that consist of the angular separation between each lepton and the nearest jet as well as invariant masses among different combinations of the leptons and jets are used for further selection.The final selections on these variables are optimised in order to maximise signal significance.One of these variables is the invariant mass of two (three) leptons in the two (three) lepton channel and is shown in Figure 1(a) (1(b)) to illustrate its discriminating power.The optimisation procedure using all four variables is performed separately for each analysis channel, each signal mass point, each lepton flavour category (for the two lepton channel), and each number of same-flavour opposite-sign (N SFOS ) lepton pairs (for the three lepton channel).The optimised selection criteria are listed in Tables 3-9 in the Appendix.
Events in the four lepton channel are required to have exactly four leptons with i ∈ q i = 0.At least one of the leptons is required to have p T > 22 GeV.Events that contain a SFOS lepton pair with m < 4 GeV are removed.Following this preselection, selections on the invariant masses and angular separation of lepton pairs are implemented to reject backgrounds containing a Z boson or non-prompt leptons or other objects incorrectly identified as leptons, known as fake leptons.A summary of the selection criteria used in the four lepton channel is shown in Tables 10-11 in the Appendix.Figure 1(c) shows the kinematic distribution of the four lepton invariant mass.

Background estimation
The backgrounds in this search all have final states that contain leptons that can be classified according to their origin into prompt leptons3, leptons with misidentified charges, and fake leptons (including nonprompt and misidentified jets).The backgrounds in the two and three lepton channels are dominated by irreducible prompt-lepton processes, including VV (W Z and Z Z), t t Z and VVV, with a significant contribution from fake leptons.The background in the four lepton channel is almost exclusively due to Z Z production (including both on-shell and off-shell production).Prompt-lepton backgrounds are modelled using simulated samples described in Section 2. Control regions containing one pair (two pairs) of SFOS leptons with invariant mass |m − m Z | < 10 GeV in the three (four) lepton channel are used to check the modelling of W Z (Z Z) background.A data-driven method [7,58] is used to estimate the charge misidentification rate for electrons from a sample of Z → ee events with m ee in a narrow window around m Z .The corresponding same-sign charge misidentification (QmisID) background is evaluated by scaling the opposite-sign events by this rate.The probability of misidentifying the charge of a muon is checked in both data and simulation, and found to be negligible in the kinematic ranges relevant to this analysis.
In the two and three lepton channels non-prompt-lepton contributions from the conversion of prompt photons are estimated using V γ simulated samples.Fake-lepton and non-prompt-lepton contributions from misidentification of hadronic jets as leptons, semileptonic decay of heavy-flavour hadrons and photon conversions from neutral pion decays are estimated using data with a fake-factor method [59].The method defines "tight" leptons as leptons passing all requirements described in Section 3 and "anti-tight" leptons as leptons failing the isolation or identification requirements.The fake factor is calculated as the ratio of events with tight leptons to events with one tight lepton replaced by an anti-tight lepton in the data control samples.The control samples of the two and three lepton channels are ensured to be largely orthogonal to corresponding preselection samples by requiring a lower jet multiplicity.A control sample containing three leptons with enriched Z+jets processes is used in the four lepton channel to extract the fake factors.All simulated prompt-lepton contributions are subtracted from the data before measuring the fake factor.The fake-lepton background contributions are estimated by applying the fake factors to events with the same selection as for the signal regions but with at least one anti-tight lepton replacing one of the prompt leptons.The fake factors in the four lepton channel are applied to events in two control samples, one with three tight leptons and one anti-tight lepton and the other with two tight leptons and two anti-tight leptons.

Systematic uncertainties
Experimental systematic uncertainties are evaluated.They include uncertainties related to the electron and jet energy measurements [51], muon momentum measurement, E miss T modelling [55], and lepton reconstruction, identification, and isolation efficiencies.The dominant systematic uncertainty in the fake-lepton background estimations arises from a closure test of the fake-factor method and the relative contributions from heavy-flavour hadron decays and photon conversions.Pileup modelling, b-tagging efficiencies, and jet pileup rejection modelling are also included.Theoretical uncertainties are evaluated for all simulated samples.These include uncertainties in PDF, QCD scale, and parton shower modelling that impact efficiency times acceptance for signal samples and uncertainties in the production crosssections for simulated background samples.The statistical uncertainties in MC signal and background samples as well as in data control regions are included as systematic uncertainties.
The systematic uncertainties with the largest impact on the HH production cross-section (times branching ratio) limits come from the jet energy scale and resolution with a relative impact compared to the total systematic plus statistical uncertainty of 45% (29%-55%) and fake-lepton background estimations with a relative impact of 42% (31%-54%) for the non-resonant (resonant) production searches.Theoretical uncertainties are found to have a relative impact of 23% (24%-36%) for the non-resonant (resonant) production searches.The relative impact of jet energy measurements, fake-lepton background estimations, and theoretical uncertainties in the X → SS analysis are 38%-51%, 37%-52% and 25%-32%, respectively.Other experimental uncertainties due to lepton, pileup, b-tagging, pileup jet rejection, prompt-lepton background estimations, and E miss T modelling are found to have a small impact on the results.The uncertainty in the combined 2015+2016 integrated luminosity is 2.1%.It is derived, following a methodology similar to that detailed in Ref. [26], and using the LUCID-2 detector for the baseline luminosity measurements [60], from calibration of the luminosity scale using x-y beam-separation scans.It has a 5%-10% relative impact due to its simultaneous effect on the signal and background estimates.All simulated processes except Z Z are affected by the uncertainty in the luminosity measurement.The relative impact of all systematic uncertainties is found to be 71% (60%-79%) for the non-resonant (resonant) production searches.In addition to the systematic effects, the statistical uncertainties are found to have a relative impact of 71% (61%-80%) for the non-resonant (resonant) production searches.

Results
The expected and observed yields in each channel after all selection criteria for the non-resonant HH production searches are shown in Figure 2 and Table 1.
A statistical analysis using a profile-likelihood-ratio test statistic [61] for the two, three, and four lepton channels, separately, as well as the combination of the three channels is performed.The expected and observed yields in each of the nine signal regions shown in Figure 2 as well as the Z Z control region in the four lepton channel are used as the input parameters to the likelihood.No significant excess over the estimated backgrounds is observed in data.Upper limits at 95% confidence level (CL) are set on the production cross-section for non-resonant SM HH production and on the production cross-section times branching ratio for resonant HH production as well as X → SS production.The expected and observed limits on the signal strength of non-resonant SM HH production, defined as the ratio of the signal crosssection to the Standard Model prediction (σ/σ SM ), are calculated using the modified frequentist CL s method [62] using the asymptotic approximation and are shown in Table 2.All systematic uncertainties −   are included in the profile-likelihood fit as Gaussian nuisance parameters and are treated as correlated across all signal regions.The combined observed (expected) upper limit on the non-resonant SM HH production cross-section is found to be 5.3 (3.8) pb, which corresponds to a limit on the signal strength of 160 (120).

Observed
Expected limit on σ/σ SM limit on σ/σ SM Median +2σ +1σ −1σ −2σ    Upper limits at 95% CL on the production cross-section times branching ratio are set for a scalar resonance decaying into either a pair of SM Higgs bosons (shown in Figure 3) or into a pair of heavy scalars (shown in Figure 4).The observed (expected) upper limits on resonant HH production vary with the resonance mass m X and range from 9.3 (10) pb to 2.8 (2.6) pb, with the smallest limit set for m X = 500 GeV.Upper limits on resonant SS production vary with the resonance mass m X and the scalar mass m S .The observed (expected) limits range from 2.5 (2.5) pb to 0.16 (0.17) pb, with the smallest limit set for m X = 340 GeV and m S = 165 GeV.

Conclusions
A search for resonant and non-resonant Higgs boson pair production as well as for a heavy scalar pair production has been performed in the WW ( * ) WW ( * ) decay channel using 36.1 fb −1 of √ s = 13 TeV proton-proton collision data collected by the ATLAS experiment at the LHC in 2015 and 2016.The analysis is performed separately in three channels based on the number of leptons in the final state: two same-sign leptons, three leptons, and four leptons.No significant excesses over the expected backgrounds are observed in data and the results from the three channels are statistically combined.An observed (expected) 95% CL upper limit of 160 ( 120) is set on the signal strength for the non-resonant Higgs boson pair production.Upper limits are set on the production cross-section times branching ratio of a heavy scalar X that decays into two Higgs bosons for a mass range of 260 GeV ≤ m X ≤ 500 GeV and the observed (expected) limits range from 9.3 (10) pb to 2.8 (2.6) pb.Upper limits are also set on the production cross-section times branching ratio of a heavy scalar X that decays into two heavy scalars S for mass ranges of 280 GeV ≤ m X ≤ 340 GeV and 135 GeV ≤ m S ≤ 165 GeV and the observed (expected) limits range from 2.5 (2.5) pb to 0.16 (0.17) pb.
CERCA Programme Generalitat de Catalunya, Spain; The Royal Society and Leverhulme Trust, United Kingdom.

Appendix Signal selection criteria after preselection
Tables 3-6 list the final selection criteria in the two lepton channel.Tables 7-9 present the final selection criteria in the three lepton channel.Table 10 defines the variables and Table 11 lists the selection criteria in the four lepton channel.
The lepton pairing strategy in the four leptons channel is designed to identify the decay of a Z boson in order to efficiently reject the dominant Z Z background in events with at least one SFOS lepton pair.Events are classified based on the number of SFOS lepton pairs they contain in order to account for the different background composition in each signal region.
Table 12 shows the final acceptance and selection efficiencies for the signal samples.Table 5: Optimised selection criteria used in the two lepton channel in the non-resonant HH search and the X → HH search with m X = 400 GeV and m X = 500 GeV.

Mass
Channel ∆R       The final acceptance times selection efficiencies in the 4W channel for non-resonant, resonant, and SS signal samples after all selection criteria are applied.Acceptance times selection efficiency is defined as the ratio of reconstructed signal events passing all selection criteria to the number of generated signal events that are filtered for the corresponding channel.The generator filter efficiencies are 4.4 × 10 −3 for the two same-sign lepton channel, 4.2 × 10 −3 for the three lepton channel, and 5.1 × 10 −4 for the four lepton channel.All numbers are given as percentages.

Figure 1 :
Figure1: Distributions of the invariant mass of (a) two, (b) three, and (c) four leptons for the two, three, and four lepton channels after preselection.The charge misidentification background in the two lepton channel and the non-Z Z backgrounds in the four lepton channel are non-zero but are too small to be seen in the distributions.The shaded band in the ratio plot shows the systematic uncertainty in the background estimate.Resonant HH signal samples are denoted by m X .The integral of each signal sample distribution is scaled to that of the expected background.

Figure 2 :
Figure 2: Expected and observed yields in each channel after all selection criteria for the non-resonant HH production searches.The label N SFOS indicates the number of same-flavour, opposite-sign lepton pairs in the channel.Low and high m 4 indicates m 4 < 180 GeV and m 4 > 180 GeV, respectively.The shaded band in the ratio plot shows the systematic uncertainty in the background estimate.The signal is scaled by a factor of 20.

√ s = 13
TeV of 33.4 fb.The label N SFOS indicates the number of same-flavour, opposite-sign lepton pairs in the channel.Systematic uncertainties on the signal and background estimates are shown.

Figure 3 :
Figure 3: Expected and observed 95% CL exclusion limits set on the cross-section times branching ratio of resonant HH production as a function of m X .Limits are shown for each channel individually as well as for the combination of the channels.Statistical and systematic uncertainties are included.

Figure 4 :
Figure 4: Expected and observed 95% CL exclusion limits set on the cross-section times branching ratio of resonant X → SS production as a function of (a) m S and (b) m X .Limits are shown for each channel individually as well as for the combination of the channels.Statistical and systematic uncertainties are included.
Angular distance between N and the nearest jet m Invariant mass of the two leptons m N j j Invariant mass of N and the two nearest jets m all Invariant mass of all objects that pass the selection criteria

Table 6 :
Optimised selection criteria used in the two lepton channel in the X → SS search.The selection criteria in the first row are used for m S = 135 GeV and m X = 280, 300, and 320 GeV.The selection criteria in the second row are used for m X = 340 GeV and m S = 135, 145, 155, and 165 GeV.Variable Description N SFOS Number of same-flavour opposite-sign lepton pairs 1 Lepton with charge opposite to that of the same-sign pair 2 Lepton from the same-sign pair that is closest to 1 in η-φ space 3 Remaining lepton m Invariant mass of the three leptons m N j Invariant mass of N and the nearest jet m N j j Invariant mass of N and the two nearest jets m + j j The minimum sum of the invariant mass of two opposite-sign leptons and the invariant mass of the remaining lepton and the two leading jets ∆R Angular distance between two leptons

Table 9 :> 22 , 4
Optimised selection criteria for the X → SS searches in the three lepton channel.The selection criteria are chosen to ensure constant signal selection efficiency between the N SFOS = 0 and N SFOS = 1,2 categories.Variable Description p i T p T of lepton i 2 and 3 (N SFOS > 0) SFOS lepton pair with invariant mass closest to Z boson (p T,2 > p T,3 ) 2 and 3 (N SFOS = 0) Different-flavour OS lepton pair with invariant mass closest to Z boson (p T,2 > p T,3 ) 0 and 1 Remaining lepton pair (p T,0 > p T,1 ) Table 10: Description of the notation used in the four lepton analysis.Event selection in the four lepton channel 4 leptons with p T > 10 GeV and q i = 25, 27 GeV (depending on data period trigger) m > 4 GeV (for all SFOS pairs) N b-tag = 0 m 0 1 > 10 GeV N SFOS = 0,1 selection |m 2 3 − m Z | > 5 GeV m 4 < 180 GeV m

Table 1 :
Expected and observed yields in each channel after all selection criteria and the profile-likelihood fit for the non-resonant HH production searches.The expected signal refers to the SM non-resonant HH production, corresponding to its calculated cross-section at

Table 2 :
Expected and observed 95% CL exclusion limits set on the non-resonant HH signal strength.The SM non-resonant HH cross-section at √ s = 13 TeV is calculated to be 33.4 fb.Limits are shown for each channel individually as well as for the combination of the channels.Statistical and systematic uncertainties are included.

Table 3 :
Description of the notation used in the two lepton analysis.

Table 4 :
Optimised selection criteria used in the two lepton channel in the X → HH search with m X = 260 GeV and m X = 300 GeV.

Table 7 :
Description of the notation used in the three lepton analysis.

Table 8 :
Optimised selection criteria for non-resonant and resonant HH searches in the three lepton channel.The selection criteria are chosen to ensure constant signal selection efficiency between the N SFOS = 0 and N SFOS = 1,2 categories.

Table 11 :
Summary of the selection criteria used in the four lepton channel.All events are required to pass the common selection and then category-dependent selection criteria are applied according to the number of sameflavour opposite-sign lepton pairs in the event.

Table 12 :
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[57] A. Hoecker et al., TMVA: Toolkit for Multivariate Data Analysis, PoS ACAT (2007) 040, arXiv: physics/0703039.[58] ATLAS Collaboration, Search for the standard model Higgs boson produced in association with top quarks and decaying into a b b pair in pp collisions at √ s = 13 TeV with the ATLAS detector, b c Also at CERN, Geneva; Switzerland.d Also at CPPM, Aix-Marseille Université, CNRS/IN2P3, Marseille; France.e Also at Département de Physique Nucléaire et Corpusculaire, Université de Genève, Genève; Switzerland.f Also at Departament de Fisica de la Universitat Autonoma de Barcelona, Barcelona; Spain.g Also at Departamento de Física Teorica y del Cosmos, Universidad de Granada, Granada (Spain); Spain.h Also at Department of Applied Physics and Astronomy, University of Sharjah, Sharjah; United Arab Emirates.i Also at Department of Financial and Management Engineering, University of the Aegean, Chios; Greece.j Also at Department of Physics and Astronomy, University of Louisville, Louisville, KY; United States of America.k Also at Department of Physics and Astronomy, University of Sheffield, Sheffield; United Kingdom.l Also at Department of Physics, California State University, Fresno CA; United States of America.m x Also at II.Physikalisches Institut, Georg-August-Universität Göttingen, Göttingen; Germany.y Also at Institucio Catalana de Recerca i Estudis Avancats, ICREA, Barcelona; Spain.z aq Also at Tomsk State University, Tomsk, and Moscow Institute of Physics and Technology State University, Dolgoprudny; Russia.ar Also at TRIUMF, Vancouver BC; Canada.as Also at Universita di Napoli Parthenope, Napoli; Italy.* Deceased