Combination of searches for Higgs boson pairs in p p collisions at 13 TeV with the ATLAS experiment

ATLAS-CONF-2018-043 13September2018

ATLAS CONF Note

ATLAS-CONF-2018-043

11th September 2018

Combination of searches for Higgs boson pairs in p p collisions at 13 TeV with the ATLAS experiment

The ATLAS Collaboration

This note presents a combination of searches for Higgs boson pairs using up to 36.1 fb

of proton–proton collision data at a centre-of-mass energy

√s =

13 TeV recorded with the ATLAS detector at the LHC. The combination is performed using three analyses searching for the

¯

¯ ,

¯

and

¯ decay channels. Results are presented for both non-resonant and resonant Higgs boson pair production modes. The combined observed (expected) limit on the non-resonant Higgs boson pair cross-section is 0.22 pb (0.35 pb) at 95% confidence level, which corresponds to 6.7 (10.4) times the predicted Standard Model cross-section. The ratio of the Higgs boson self-coupling to its Standard Model expectation

κ_λ=λ_{H H H}/λ^SM_{H H H}

is observed (expected) to be constrained at 95% confidence level to

−

5

0

12

1

5

8

12

0

. Exclusion limits are also set on resonant Higgs boson pair production, probing a model with an extended Higgs sector based on two doublets, as well as a Randall–Sundrum bulk graviton model.

© 2018 CERN for the benefit of the ATLAS Collaboration.

Reproduction of this article or parts of it is allowed as specified in the CC-BY-4.0 license.

1 Introduction

The discovery of the Higgs boson (

) at the Large Hadron Collider (LHC) [1] in 2012 [2, 3], with a measured mass

125 GeV [4] and properties in agreement with Standard Model (SM) predictions within the uncertainties of the measurements [5], has experimentally confirmed the Brout-Englert-Higgs (BEH) mechanism of electroweak symmetry breaking and mass generation [6, 7]. The BEH mechanism not only predicts the existence of a massive scalar particle, but also requires the scalar field to couple to itself. Therefore, observing the production of Higgs boson pairs and measuring the Higgs boson self-coupling

would be another crucial validation of the BEH mechanism, and any deviation from the SM predictions would open a window on new physics.

In the SM, gluon–gluon fusion (ggF) accounts for more than 90% of the Higgs boson pair production cross-section, and only this production mode is considered here. It can proceed via loops of heavy- quarks as illustrated in Figure 1. Two of these loop diagrams, namely those depicted in Figure 1(a) and Figure 1(b), are proportional to the square of the heavy-quark Yukawa coupling, while the third one, illustrated in Figure 1(c), is proportional to the product of the heavy-quark Yukawa coupling and the Higgs boson self-coupling. The interference between these three diagrams is destructive and yields an overall cross-section of 33.4 fb at

√s =

13 TeV, calculated at next-to-leading-order (NLO) in QCD, fully accounting for finite top-quark mass effects [8], and corrected at next-to-next-to-leading-order (NNLO) in QCD matched with next-to-next-to-leading logarithmic (NNLL) resummation in the heavy top-quark limit [9]. Hence, the production of a Higgs boson pair in a single proton–proton (

) interaction is not expected to be observed with the current dataset, unless its cross-section is enhanced in Beyond-the- Standard-Model (BSM) scenarios. Such enhancements can come from anomalous couplings, e.g. arising from new contact interactions between two top-quarks and two Higgs bosons (which are not considered in this report), or deviations from the SM couplings of the Higgs boson with other particles or itself. In this note, the top-quark Yukawa coupling is set to its SM value, while the effective Higgs boson self-coupling is parameterised by a scale factor

. The theoretical and phenomenological implications of such couplings for complete models are discussed in Refs. [10] and [11].

Several BSM theories also predict the existence of heavy particles decaying into a pair of Higgs bosons.

Figure 1(d) shows the production of such a resonance in the ggF mode. Models with two Higgs doublets (2HDMs) [12, 13] result in the prediction of a second CP-even, heavier, Higgs boson that can decay into two SM-like lighter Higgs bosons. Alternatively, an

pair can be produced resonantly through the decay of a spin-2 graviton, as predicted in the Randall–Sundrum model of warped dimensions [14].

This note presents a statistical combination of results from searches for both non-resonant and resonant Higgs boson pair production in

collisions at

√s=

13 TeV. The dataset was collected with the ATLAS experiment [15–17], which is a multi-purpose particle detector with a forward-backward symmetric cylindrical geometry and nearly 4

coverage in solid angle.1 It consists of an inner tracking detector surrounded by a thin superconducting solenoid providing a 2 T axial magnetic field, electromagnetic and hadron calorimeters, and a muon spectrometer. A two-level trigger [18, 19] reduces the event rate to a maximum of 1 kHz for offline data storage. The data used in the searches were collected during stable beam conditions and with all ATLAS subsystems fully operational, corresponding to an integrated luminosity

1ATLAS uses a right-handed coordinate system with its origin at the nominal interaction point (IP) in the centre of the detector and thez-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 thez-axis.

The pseudorapidity is defined in terms of the polar angleθasη=−ln tan(θ/2). Angular distance is measured in units of

∆R≡p

(∆η)2+(∆φ)2.

g

g

κt

κt

H

H t/b

(a)

g

g

κt

κt

H

H t/b

(b)

g

g

κt κ_λ H

H t/b

H

(c)

g

g

H

H t/b

X

(d)

Figure 1: Examples of leading-order Feynman diagrams for Higgs boson pair production proportional to (a)-(b) the square of the heavy-quark Yukawa coupling, and to (c) the product of the latter with the Higgs boson self-coupling.

Here,κ_tandκ_λare the SM coupling multipliers of, respectively, the heavy-quark Yukawa coupling and the Higgs boson self-coupling. The diagram (d) illustrates the production of a Higgs boson pair via the decay of an intermediate resonance (X) produced through a heavy-quark loop.

of up to 36.1 fb

(with one exception discussed below), derived following a methodology similar to that detailed in Ref. [20]. The three most sensitive search channels are used:

¯

¯ ,

¯

and

¯ , with analysis strategies detailed in Refs. [21–23] and summarised below.

• In the search for

¯

, two different analyses are performed, referred to as “resolved analysis” and “boosted analysis”. The resolved analysis is based on jets reconstructed using the anti-

algorithm [24] with a radius parameter value of

0

4. Two Higgs boson candidates are formed from the four jets for which the probabilities of containing a

-hadron (

-tagging) are highest. During the 2016 data-taking, an inefficiency in the vertex reconstruction affected the trigger-level

-tagging algorithm, preventing the acquisition of a fraction of the data. Therefore, the resolved analysis is performed with a reduced amount of data, corresponding to an integrated luminosity of 27.5 fb

, and the datasets collected in 2015 and 2016 are treated independently. The boosted analysis is based on jets reconstructed using the anti-

algorithm with

1

0, each jet fully contains the decay products of one Higgs boson and is required to have a

-tagged track-jet associated to it and a jet mass compatible with

. The boosted analysis is performed on the full 2015+2016 dataset, corresponding to an integrated luminosity of 36.1 fb

. In both analyses, the predominant multi-jet background is estimated with a data-driven method. A data sample containing fewer

-tagged jets than in the nominal selection is used to estimate the shape of the multi-jet background. This data sample is re-weighted with a set of correction factors, which are derived in dedicated sideband regions and take into account the kinematic differences between events containing the nominal number of

-tagged jets and those with fewer

-tagged jets. The normalisations of the multi-jet and

backgrounds are determined simultaneously from fits to sensitive variables in the sideband region and used in a profile-likelihood fit of the invariant mass of the two Higgs boson candidates to extract the signal.

• In the search for

¯

, the selected final states consist of either one electron/muon and

a narrow jet coming from a hadronically decaying

-lepton (referred to as

) or two

candidates, together with two

-tagged jets and missing transverse energy (E

) coming from the neutrinos produced in the decays of the two

-leptons. In the two search channels (referred to as

and

), several kinematic variables providing good separation between signal and SM backgrounds are used as inputs to Boosted Decision Trees (BDTs). In the

channel, two complementary trigger configurations are employed. Events triggered by a single electron or muon are assigned to the category Single Lepton Trigger (SLT in the following). Events not assigned to the SLT category and with one electron or muon together with one

object at trigger level are assigned to the category Lepton Tau Trigger (LTT). A profile-likelihood fit is applied to the BDT score distributions in three signal regions (SLT

, LTT

and

) and to the event yields in relevant background-enriched control regions to extract the signal and constrain the normalisation factors of two dominant backgrounds:

and

production with heavy-flavor quarks.

• In the search for

¯ , events are required to have two isolated photons and two jets with an invariant mass

compatible with

, of which at least one jet is

-tagged. Events are separated into different signal categories depending on whether one or two

-tagged jets are found, then two kinematic selections are applied. A first selection is optimised to search for the SM non-resonant

production and for resonances with masses in the range 500–1000 GeV, while a second, looser, selection is used to search for resonances with masses in the range 260–500 GeV and to probe non-SM values of

. In the search for non-resonant Higgs boson pair production, the signal is extracted using a fit to the

distribution of the selected events. When searching for resonant production of

pairs,

is required to be compatible with the Higgs boson mass and the signal is extracted from a fit to the

distribution.

A combination of the results of the same three search channels and the less sensitive

channel was performed using data collected in the Run-1 of LHC at

√s =

8 TeV [25]. For the non-resonant Higgs boson pair production mode, the observed (expected) 95% confidence-level (CL) exclusion limits set by ATLAS on the cross-section for

at 8 TeV were 70 (48) times the SM prediction. For the production of Higgs boson pairs via narrow resonances, the Run-1 observed (expected) exclusion limits for a heavy Higgs boson decay range from 2.1 (1.1) pb for a Higgs boson mass of 260 GeV to 0.011 (0.018) pb at 1000 GeV. The CMS Collaboration combined the results of the

¯ and

¯

searches using data collected in the Run-1 of LHC [26, 27] and, more recently, combined the results of Higgs boson pair searches at 13 TeV based on 35.9 fb

of data, using the decay channels into

¯

,

¯ where

is a vector boson,

¯

and

¯ [28]. The corresponding observed (expected) 95%

CL upper limit on the

production cross-section was found to be 22.2 (12.8) times the SM value, and resonances with masses in the range 250–3000 GeV were probed, with no evidence of BSM physics.

2 Combination of results on non-resonant Higgs boson pair production

The statistical interpretation of the combined search results is based on a simultaneous fit of the signal cross-section and the nuisance parameters

that encode statistical and systematic uncertainties, by means of a negative log-likelihood minimisation. The branching fractions of the Higgs boson are assumed to be equal to the SM predictions [9]. The test statistic ˜

[29] used to test the compatibility of the data with the background-only and signal plus background hypotheses is computed from the profile likelihood ratio. The asymptotic approximation is used for the statistical analysis of all decay channels, and their combination.

The same approach is used in the individual published results of the

¯

and

¯ search

channels, while pseudo-experiments are used in the published results of

¯ . The asymptotic

approximation is found to be in agreement with pseudo-experiments at a level of 10% for all results on the individual

¯ channel presented here, while an agreement at the level of 5% is obtained for the results on the combination of the three channels.

All the signal regions considered in the simultaneous fit either are orthogonal by construction or have negligible overlap. The instrumental systematic uncertainties, as well as the 2.1% uncertainty on the integrated luminosity [20], are correlated across all search channels. On the other hand, given the different final states, the uncertainties in the modelling of the SM backgrounds and the acceptance of the

signals are treated as uncorrelated across the search channels.

The 95% CL upper limits on the signal strength in units of the SM non-resonant

cross-sections are shown in Figure 2, for the individual search channels, as well as their combination. In order to show the impact of the systematic uncertainties, combined expected limits with only statistical uncertainties are also reported. The observed (expected) combined limit with all statistical and systematic uncertainties is, respectively, 0.22 pb (0.35 pb), corresponding to 6.7 (10.4) times the SM prediction, taking into account all correlations between the three individual channels. With respect to the published results of the searches for

¯ and

¯

, theoretical uncertainties on the total signal cross-section are not considered and, in the case of

¯ only, the asymptotic approximation is used instead of pseudo- experiments. The combined observed upper limit on the non-resonant

production is stronger than expected, but within the 2

uncertainty band. All three search channels have a deficit of data with respect to the background-only prediction. In particular, in the

¯

search, the non-resonant signal shape has its maximum around 400 GeV, with a slowly-falling reconstructed

spectrum towards high mass and, in several bins, the number of observed events is below the prediction, see Ref. [21] for details.

0 10 20 30 40 50 60 70 80

ggF

σSM

HH) normalized to

→ (pp σggF

95% CL upper limit on Combined

γ γ b

→ b HH

τ-

τ+

b

→ b HH

b b b

→ b

HH ^{12.9 20.7 18.5}

12.6 14.6 11.9

20.4 26.3 25.1

6.7 10.4 9.2

Obs. Exp. Exp. stat.

Observed Expected

σ

± 1 Expected

σ

± 2 Expected

ATLAS Preliminary

= 13 TeV, 27.5 - 36.1 fb-1

s

HH) = 33.4 fb

→ (pp

ggF

σSM

Figure 2: Upper limits at 95% CL on the cross-section of the ggF non-resonant Higgs boson pair production from theHH→bbb¯ b¯,HH→bbτ¯ ⁺τ⁻andHH→bbγγ¯ searches, and their statistical combination. The column "obs."

represents the observed limits, "exp." the expected limits with all statistical and systematic uncertainties, and "exp.

stat." the expected limits obtained with statistical uncertainties only.

After setting all couplings except the Higgs boson self-coupling

to their SM values, a

-scan is

performed. This scale factor affects both the production cross-section and the kinematic distributions of

the Higgs boson pairs, by modifying the amplitude of the interference among the three

production

diagrams.

For each value of

, kinematic distributions, and in particular the

spectrum, are computed at the generator-level, using the leading-order (LO) version of MadGraph5_aMC@NLO [30] with the NNPDF 2.3 LO [31] parton distribution function (PDF) set, together with Pythia8 [32] for the showering model.

As the amplitude for Higgs boson pair production depends on

, linear combinations of three LO samples are used to make predictions for any value of

. This procedure is illustrated in Figure 3, which shows variations of the

spectrum with

. Binned ratios of

distributions for any given

and the SM case (

1) are computed and then used to re-weight the kinematic distributions of the nominal sample.

The nominal sample of non-resonant

production was generated using MadGraph5_aMC@NLO at NLO in QCD, with the CT10 NLO [33] PDF set, interfaced to Herwig++ [34] for the parton shower model.

The re-weighting procedure is applied after having corrected the NLO

spectrum to reproduce the spectrum calculated in Refs. [8, 35], which fully accounts for top-quark mass effects. For that purpose, it is assumed that NLO QCD corrections are independent of

. In turn, the re-weighted NLO sample can be used to compute the signal acceptance for varied values of

, separately for each search channel, as shown in Figure 4.

300 400 500 600 700 800

[GeV]

mHH

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14

Arbitrary units

ATLAS Simulation Preliminary

= 13 TeV s

λ = 0 κ

λ = 2 κ

λ = 5 κ

300 400 500 600 700 800

[GeV]

mHH

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14

Arbitrary units

ATLAS Simulation Preliminary

= 13 TeV s

−5

λ = κ

λ = 1 κ

λ= 10 κ

Figure 3: Generator-levelmH H distributions computed for various values of κ_λ by linearly combining three LO samples produced with MadGraph5_aMC@NLO.

• In the

¯

search channel, the reconstructed

distribution is used as a fit template in the statistical analysis, as in the corresponding search for SM non-resonant

production. Its shape has a strong dependence on the chosen value of the Higgs boson self-coupling (see Figure 5), and so does the signal acceptance, as shown in Figure 4(a): it varies by a factor 2.5 over the probed range of

-values. Both effects together determine how the exclusion limits on the cross-section of

¯

¯ vary as a function of

.

• In the

¯

search channel, only the SLT

and

signal regions are used.

Also, the BDTs are trained using the re-weighted NLO signal sample corresponding to

20, which shows good sensitivity over the whole range of probed

-values. The fit template is the BDT score distribution, which has a dependence on

(see Figure 6) through the shape variations of some BDT input variables, in particular

, with the Higgs boson self-coupling. In addition, the sensitivity of this analysis is also affected by the fact that the signal acceptance varies by a factor of about 3 over the probed range of

-values, as shown in Figure 4(b).

• In the

¯ search channel, the kinematic selection used for the

-scan is less stringent

than when setting limits on the SM

cross-section, as the average transverse momentum of the Higgs bosons is lower at large values of

. The statistical analysis is performed using the

distribution as the fit template, as in the corresponding search for SM non-resonant

production.

While the shape of the discriminant remains independent of

, the signal acceptance varies by about 30% over the probed range of

-values, as illustrated in Figure 4(c). This is the main cause of the variations of the exclusion limits on the cross-section of

¯ with

.

−20 −15 −10 −5 0 5 10 15 20

κλ

0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2

Efficiency [%]× Acceptance

2015 2016

ATLAS Simulation Preliminary

b b b

→ b

=13 TeV, HH s

(a)

−20 −15 −10 −5 0 5 10 15 20

κλ

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5

Efficiency [%]× Acceptance

had SLT

lepτ τ

τhad

τhad

ATLAS Simulation Preliminary

τ-

τ+

b

→ b

=13 TeV, HH s

(b)

−20 −15 −10 −5 0 5 10 15 20

κλ

5 6 7 8 9 10 11

Efficiency [%]× Acceptance

1 b-tag 2 b-tags

ATLAS Simulation Preliminary

γ γ b

→ b

=13 TeV, HH s

(c)

Figure 4: Signal acceptance times efficiency as a function ofκ_λ for (a) HH → bbb¯ b¯, (b) HH → bbτ¯ ⁺τ⁻ and (c) HH → bbγγ¯ . The acceptances are split by years for the HH → bbb¯ b¯ analysis, due to different trigger configurations, and by event categories for theHH→bbτ¯ ⁺τ⁻andHH→bbγγ¯ analyses.

The exclusion limits resulting from the

-scan are shown in Figure 7. They follow the features of

the product of the cross-section and the signal acceptance, with e.g. a minimum at

2

5 where

the destructive interference is the largest, and a maximum at

5 where the

spectrum is the

softest. The variations of the exclusion limits with

are less pronounced in the

¯ search

channel, as the final discriminant (

) is not dependent on the shape of the

spectrum. The

values that are allowed at 95% CL are reported in Table 1. In order to show the impact of the systematic

uncertainties on this analysis, Table 1 and Figure 7(b) show also results computed without including

systematic uncertainties.

[GeV]

Reconstructed mHH

200 400 600 800 1000 1200 1400

Events / 100 GeV

1 10 102 103 104 105 106 107

Data Multijet

t Hadronic t

t Semi-leptonic t Stat+Syst Uncertainty

=-5 (x 95) κλ NR HH

=1 (x 1291) κλ NR HH

=10 (x 98) κλ NR HH

Preliminary ATLAS

= 13 TeV, 27.5 fb-1 s

b b b

→ b HH

Resolved Signal Region, 2015+2016

[GeV]

Reconstructed mHH

200 400 600 800 1000 1200 1400

S / B

0 0.01

0.02 NR HH normalized to σxBR

[GeV]

Reconstructed mHH

200 400 600 800 1000 1200 1400

Events / 100 GeV

1 10 102 103 104 105 106 107

Data Multijet

t Hadronic t

t Semi-leptonic t Stat+Syst Uncertainty

=0 (x 663) κλ NR HH

=2 (x 2519) κλ NR HH

=5 (x 712) κλ NR HH

Preliminary ATLAS

= 13 TeV, 27.5 fb-1 s

b b b

→ b HH

Resolved Signal Region, 2015+2016

[GeV]

Reconstructed mHH

200 400 600 800 1000 1200 1400

S / B

0 0.002 0.004

0.006 NR HH normalized to σxBR

Figure 5: Reconstructedm_{H H} distribution in the non-resonant (NR)HH→bbb¯ b¯analysis, with overlaid signal for severalκ_λ-values. In the upper panel, the signal normalisation is scaled to 50% of the overall data yield by the factors shown in the legend, while it is normalised to the expected cross-section for the indicatedκ_λ-value in the lower panel. The background distributions are shown: the data-driven multi-jet background (Multijet), thett¯→W⁺W⁻bb¯ background with bothW bosons decaying hadronically (Hadronictt¯) and the same process with at least one of the W bosons decaying leptonically (Semi-leptonictt¯).

Search channel Allowed

interval at 95% CL

obs. exp. exp. stat.

HH→bbb¯

¯

−10.9 – 20.1 −11.6 – 18.7 −9.9 – 16.4

¯

−7.3 – 15.7 −8.8 – 16.7 −7.8 – 15.4

¯ −8.1 – 13.2 −8.2 – 13.2 −7.7 – 12.7 Combination −5.0 – 12.1 −5.8 – 12.0 −5.2 – 11.4

Table 1: Allowed κ_λ intervals at 95% CL for each search channel and their combination. The column “obs.”

represents the observedκ_λintervals, “exp.” the expectedκ_λintervals with all statistical and systematic uncertainties, and “exp. stat.” the expectedκ_λintervals obtained with statistical uncertainties only.

3 Combination of results on resonant Higgs boson pair production

Following a similar methodology, a statistical combination of the searches for resonant

production is performed in the mass range 260–1000 GeV. The resonance decaying to a pair of Higgs bosons is assumed to be either a heavy scalar particle

with a narrow width or a spin-2 Kaluza–Klein graviton,

, with

¯

set to either 1 or 2, where

is the curvature of the warped extra dimension in the bulk Randall–

Sundrum model and ¯

2

4

10

GeV is the effective four-dimensional Planck scale. Relative to the graviton mass, the width ranges from 3% (6%) at low mass to 13% (25%) at the highest mass for

¯

1

2

. The search for gravitons is performed only in the

¯

and the

¯

channels. All spin-2 signal samples were generated at LO in QCD using MadGraph5_aMC@NLO with the NNPDF 2.3 LO PDF set, interfaced to Pythia8 for the parton shower model, while different choices were made for the spin-0 signal samples, as described in Refs. [21–23].

No statistically significant excess is observed across the probed mass range of the resonance. For a scalar

resonance, the observed (expected) combined 95% CL upper limits on the

production are

0.83 pb at 260 GeV and 0.02 pb at 1 TeV (0.73 pb and 0.03 pb). For a spin-2

, the observed (expected)

−1 −0.8−0.6−0.4−0.2 0 0.2 0.4 0.6 0.8 1 BDT 1

10 102

103

104

105

106

107

Events / Bin

Data

λ=-5 κ NR HH

λ=1 κ NR HH

λ=10 κ NR HH Top-quark

fakes τhad

→ jet

+(bb,bc,cc) τ τ

→ Z Other SM Higgs Uncertainty Pre-fit background ATLAS Preliminary

= 13 TeV, 36.1 fb-1

s τ-

τ+

b

→ b HH

SLT 2 b-tags τhad

τlep

−1 −0.8−0.6−0.4−0.2 0 0.2 0.4 0.6 0.8 1 BDT 0.8

1 1.2

Data/Pred.

−1 −0.8−0.6−0.4−0.2 0 0.2 0.4 0.6 0.8 1 BDT 1

10 102

103

104

105

106

107

Events / Bin

Data

λ=0 κ NR HH

λ=2 κ NR HH

λ=5 κ NR HH Top-quark

fakes τhad

→ jet

+(bb,bc,cc) τ τ

→ Z Other SM Higgs Uncertainty Pre-fit background ATLAS Preliminary

= 13 TeV, 36.1 fb-1

s τ-

τ+

b

→ b HH

SLT 2 b-tags τhad

τlep

−1 −0.8−0.6−0.4−0.2 0 0.2 0.4 0.6 0.8 1 BDT 0.8

1 1.2

Data/Pred.

−1 −0.8−0.6−0.4−0.2 0 0.2 0.4 0.6 0.8 1 BDT 1

10 102

103

104

105

106

107

Events / Bin

Data

λ=-5 κ NR HH

λ=1 κ NR HH

λ=10 κ NR HH Top-quark

fakes (Multi-jets) τhad

→ jet

+(bb,bc,cc) τ τ

→ Z

) t fakes (t τhad

→ jet Other SM Higgs Uncertainty Pre-fit background ATLAS Preliminary

= 13 TeV, 36.1 fb-1

s τ-

τ+

b

→ b HH

2 b-tags τhad

τhad

−1 −0.8−0.6−0.4−0.2 0 0.2 0.4 0.6 0.8 1 BDT 0.81

1.2

Data/Pred.

−1 −0.8−0.6−0.4−0.2 0 0.2 0.4 0.6 0.8 1 BDT 1

10 102

103

104

105

106

107

Events / Bin

Data

λ=0 κ NR HH

λ=2 κ NR HH

λ=5 κ NR HH Top-quark

fakes (Multi-jets) τhad

→ jet

+(bb,bc,cc) τ τ

→ Z

) t fakes (t τhad

→ jet Other SM Higgs Uncertainty Pre-fit background ATLAS Preliminary

= 13 TeV, 36.1 fb-1

s τ-

τ+

b

→ b HH

2 b-tags τhad

τhad

−1 −0.8−0.6−0.4−0.2 0 0.2 0.4 0.6 0.8 1 BDT 0.81

1.2

Data/Pred.

Figure 6: BDT distribution in the non-resonant (NR)HH→bbτ¯ ⁺τ⁻analysis for theτ_lepτ_had(top) and theτ_hadτ_had (bottom) channels. Signal is overlaid for severalκ_λ-values and it is normalised to the total expected background.

The main backgrounds arett¯and single-top-quark production (Top-quark), the background arising from jets faking hadronic taus (jet→ τ_hadfakes),Z → τ⁺τ⁻plus two heavy-flavor jets [Z →ττ+(bb,bc,cc)], SM single Higgs boson production (SM Higgs) and other minor backgrounds (Other).

−20 −15 −10 −5 0 5 10 15 20 λSM HHH / λ

λ = κ

−2

10

−1

10 1 10 102

HH) [pb]→ (pp ggFσ95% CL upper limit on

SM

(exp.) b b b b

(obs.) b b b b

(exp.) τ- τ+ b b

(obs.) τ- τ+ b b

(exp.) γ γ b b

(obs.) γ γ b b

Combined (exp.) Combined (obs.)

(Combined) σ

±1 Expected

(Combined) σ

±2 Expected Theory prediction

ATLAS Preliminary 27.5 - 36.1 fb-1

= 13 TeV, s

(a)

−20 −15 −10 −5 0 5 10 15 20 λSM HHH / λ

λ = κ

−2

10

−1

10 1 10 102

HH) [pb]→ (pp ggFσ95% CL upper limit on

SM

(exp.) b b b b

(exp.) τ- τ+ b b

(exp.) γ γ b b

Combined (exp.) Combined (exp.) full syst.

(Combined) σ

±1 Expected

(Combined) σ

±2 Expected Theory prediction

ATLAS Preliminary 27.5 - 36.1 fb-1

= 13 TeV, s

Stat. only

(b)

Figure 7: Upper limits at 95% CL on the cross-section of the ggF non-resonant Higgs boson pair production as a function ofκ_λ, (a) with all systematic and statistical uncertainties and (b) with only statistical uncertainties, except for the combined limits (long-dashed line) that also include the systematic uncertainties. In (a), observed (expected) limits are shown in solid (dashed) lines. In theHH→ bbγγ¯ channel, the observed and expected limits coincide.

In both figures, the±1σand±2σbands are only shown for the combined expected limit. The theory prediction is obtained scaling the NNLO + NNLL SM cross section by theκ_λdependent factorσ^κλ(pp→HH)/σ^κλ=1(pp→HH) computed at LO.

combined 95% CL limits are 1.89 pb at 260 GeV and 0.02 pb at 1 TeV (1.50 pb and 0.02 pb) for

¯

1, and they become 0.13 pb and 0.04 pb (0.19 pb and 0.03 pb) for

¯

2. The upper limits are shown as a function of the resonance mass in Figure 8 for the spin-0 hypothesis, and in Figures 9(a) and 9(b) for the spin-2 hypotheses and

¯

equal to 1 and 2, respectively.

In a simplified minimal supersymmetric model, known as the hMSSM [36–38], the scalar resonance is the heavier

-even Higgs boson, while the lighter

-even Higgs boson has its mass fixed to 125 GeV.

In such a scenario, 260 GeV

462 GeV is excluded at 95% CL for tan

= 2, where tan

is

the ratio of the vacuum expectation values of the two scalar doublets. In the case of

¯

1, the

bulk Randall–Sundrum model is excluded by the combination of

¯

and

¯

at

95% CL for graviton masses above 307 GeV. Beyond 1 TeV, where no combination is performed, only

¯

¯ provides significant sensitivity, bringing the exclusion range to 1362 GeV [21]. Within the

probed mass range, the exclusion expands to

values below 1744 GeV if

¯

2, again set by the

¯

search channel.

300 400 500 600 700 800 900 1000 [GeV]

mS

−3

10

−2

10

−1

10 1 10 102

103

HH) [pb]→ S →(pp σ95% CL upper limit on

SM

(exp.) b b b b

(obs.) b b b b

(exp.) τ-

τ+

b b

(obs.) τ-

τ+

b b

(exp.) γ γ b b

(obs.) γ γ b b

Combined (exp.) Combined (obs.)

(Combined) σ

±1 Expected

(Combined) σ

±2 Expected

= 2) β hMSSM (tan

ATLAS Preliminary = 13 TeV, 27.5 - 36.1 fb-1

s spin-0

Figure 8: Upper limits at 95% CL on the cross-section of the spin-0 resonant Higgs boson pair production. The observed (expected) limits are shown in solid (dashed) lines. The±1σ and±2σ bands are only shown for the expected limits of the combination.

300 400 500 600 700 800 900 1000

[GeV]

KK G*

m

−2

10

−1

10 1 10 102

HH) [pb]→KK

* G→(pp σ95% CL upper limit on SM

(exp.) b b b b

(obs.) b b b b

(exp.) τ- τ+ b b

(obs.) τ- τ+ b b

Combined (exp.) Combined (obs.)

(Combined) σ

±1 Expected

(Combined) σ

±2 Expected

= 1.0 MPl Bulk RS, k/

ATLAS Preliminary = 13 TeV, 27.5 - 36.1 fb-1

s spin-2, k/M_Pl = 1.0

(a)

300 400 500 600 700 800 900 1000

[GeV]

KK G*

m

−3

10

−2

10

−1

10 1 10 102 HH) [pb]→KK

* G→(pp σ95% CL upper limit on SM

(exp.) b b b b

(obs.) b b b b

(exp.) τ- τ+ b b

(obs.) τ- τ+ b b

Combined (exp.) Combined (obs.)

(Combined) σ

±1 Expected

(Combined) σ

±2 Expected

= 2.0 MPl Bulk RS, k/

ATLAS Preliminary = 13 TeV, 27.5 - 36.1 fb-1

s spin-2, k/M_Pl = 2.0

(b)

Figure 9: Upper limits at 95% CL on the cross-section of the spin-2 resonant Higgs boson pair production, for (a) k/M¯_Pl=1 and (b)k/M¯_Pl=2. The observed (expected) limits are shown in solid (dashed) lines. The±1σand±2σ bands are only shown for the expected limits of the combination. Only theHH→bbb¯ b¯andHH→bbτ¯ ⁺τ⁻search results are used in this combination.

4 Conclusion

Using 36.1 fb

of

collision data recorded at 13 TeV with the ATLAS experiment at the LHC, a statistical combination of three channels,

¯

¯ ,

¯

and

¯ , for the search of non-resonant and resonant production of Higgs boson pairs is presented. For the non-resonant

production mode, the observed (expected) 95% CL upper limit on the

cross-section is 6.7 (10.4) times the SM prediction corresponding to 0.22 pb (0.35 pb). Exclusion limits are also computed as a function of the Higgs boson self-coupling scale factor

with the allowed range being

−

5

0

12

1 (

5

8

12

0) at 95% CL. In the resonant

production mode no statistically

significant excess of events above the SM predictions is found, and upper limits are set on the production

cross-section of heavy spin-0 and spin-2 resonances decaying into a pair of Higgs bosons in the mass

range 260–1000 GeV.

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