Search for nonresonant pair production of Higgs bosons in the b¯bb¯b final state in pp collisions at √s=13 TeV with the ATLAS detector

Search for nonresonant pair production of Higgs bosons in the b¯ bb¯ bfinal state in pp collisions at ffiffis p=13 TeV with the ATLAS detector G. Aad et al.* (ATLAS Collaboration) (Received 10 January 2023; accepted 30 June 2023; published 5 September 2023) A search for nonresonant Higgs boson pair production in the b¯ bb¯ bfinal state is presented. The analysis uses 126 fb−1of pp collision data at ffiffiffis p¼13 TeV collected with the ATLAS detector at the Large Hadron Collider, and targets both the gluon-gluon fusion and vector-boson fusion production modes. No evidence of the signal is found and the observed (expected) upper limit on the cross section for nonresonant Higgs boson pair production is determined to be 5.4 (8.1) times the Standard Model predicted cross section at 95% confidence level. Constraints are placed on modifiers to the HHH and HHVV couplings. The observed (expected) 2σconstraints on the HHH coupling modifier, κλ, are determined to be ½−3.5;11.3 (½−5.4;11.4), while the corresponding constraints for the HHVV coupling modifier, κ2V, are ½−0.0;2.1 (½−0.1;2.1). In addition, constraints on relevant coefficients are derived in the context of the Standard Model effective field theory and Higgs effective field theory, and upper limits on the HH production cross section are placed in seven Higgs effective field theory benchmark scenarios. DOI: 10.1103/PhysRevD.108.052003 I. INTRODUCTION The discovery of the 125 GeV Higgs boson (H)[1–4] at the Large Hadron Collider (LHC) has prompted a broad research program to investigate its properties and compare the measurements with the Standard Model (SM) predictions. Of particular interest is the search for nonresonant Higgs boson pair production, also known as di-Higgs ðHHÞ production. This process has a strong dependence on the Higgs self-coupling, which is a key ingredient of the electroweak symmetry breaking mechanism and a sensitive probe for physics beyond the SM (BSM physics) in various scenarios, such as two-Higgs-doublet models [5], composite Higgs models [6], twin Higgs models [7], and the minimal supersymmetric extension of the SM [8,9]. The Higgs selfcoupling also plays a fundamental role in understanding the stability of the universe [10]. The dominant SM HH production process is gluon–gluon fusion (ggF). Its cross section, for a Higgs boson mass mH¼125 GeV, calculated at next-to-next-to-leading order (NNLO) including finite top-quark-mass effects [11],is 31.05 fb at a center-of-mass energy ffiffiffis p¼13 TeV. The two dominant leading-order Feynman diagrams contributing to this process are shown in Fig. 1, where Fig. 1(a) is commonly referred to as the box diagram and Fig. 1(b) as the triangle diagram. The triangle diagram introduces the dependence on the trilinear Higgs self-coupling, λ,shownby the redvertex inFig.1(b),whichcanbe expressedin terms of its modifier, κλ.1In the SM, these two diagrams interfere destructively. As a result, the HH production cross section and kinematic properties depend critically on thevalue of κλ. The HH production process with the second-highest cross section in the SM is vector-boson fusion (VBF), with a calculated value of 1.73 fb at next-to-next-to-nextto-leading order (N3LO) [12],formH¼125 GeV at ffiffiffis p¼13 TeV. Figure 2illustrates the Feynman diagrams involved in di-Higgs production via vector-boson fusion at leading order (LO). The coupling modifiers κλ,κV,andκ2V are respectively shown at the HHH,HVV,andHHVV interaction vertices, where Vstands for the gauge vector bosons Wor Z. In the SM, the divergences in the Figs. 2(b) and 2(c) diagrams exactly cancel out due to perturbative unitarity. As κVand κ2Vdepart from their SM value of one, this canceling out no longer occurs, introducing a linear dependence of the cross section on the effective center-ofmass energy of the incoming vector bosons [13]. Therefore, the Higgs bosons produced in non-SM κV=κ2Vscenarios are expected to be more energetic and more central in the detector on average. This increase in the energy of Higgs bosons with increasing deviation from the SM continues up *Full author list given at the end of the article. Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3. 1A coupling modifier, κ, is defined as the ratio of the modified coupling to its SM value, κ¼c=cSM. By definition, κ¼1 denotes the value of the coupling predicted by the SM. PHYSICAL REVIEW D 108, 052003 (2023) 2470-0010=2023=108(5)=052003(38) 052003-1 © 2023 CERN, for the ATLAS Collaboration to the scale of some new physics, which is required to unitarize the total amplitude. The analysis described in this paper targets the HH process in the b¯ bb¯ bfinal state, in both the ggF and VBF production modes, using the data collected by ATLAS between 2016 and 2018, during Run 2 of the LHC. Assuming the SM branching ratio of 58.2% for H→b¯ b [14,15], about one third of di-Higgs events decay into b¯ bb¯ b, making it the most abundant di-Higgs final state. However, as this is a fully hadronic final state, the analysis faces the challenge of large backgrounds, which originate mostly from nonresonant QCD production of multiple heavy (b=t) quarks, as well as from light-quark-initiated jets misidentified as originating from heavy quarks. The results are interpreted in terms of constraints on the κλand κ2Vcoupling modifiers, assuming κV¼1. The analysis also provides oneand two-dimensional constraints on relevant couplings in the SM effective field theory (SMEFT) [16–18] and Higgs effective field theory (HEFT) [19,20] frameworks. In the SMEFT framework, the effects of new physics may be described with an effective Lagrangian: LSMEFT ¼LSM þ1 Λ2X k cð6Þ kOð6Þ k;ð1Þ where LSM represents the SM Lagrangian, Okare higherdimensional local operators, ckare the Wilson coefficients, and Λis the mass scale of the new physics phenomena (set to 1 TeV for this result). The analysis considers operators Okin the Warsaw basis, which provides a complete set of operators allowed by SM gauge symmetries at dimension six [21] (dimension-five operators introduce lepton and baryon number violation, and are therefore ignored in this result). The five operators relevant to the HH process and their coefficients, cH,cH□,ctH,ctG, and cHG, are listed in Table I [22]. The computation of amplitudes from the above Lagrangian includes three terms: a pure SM term, a “quadratic”term of order ð1=Λ4Þincluding purely new physics, and a “linear”term of order ð1=Λ2Þaccounting for the interference between the SM and new physics. The SMEFT constraints calculated in this analysis include both the linear and quadratic new physics terms. In the HEFT framework, new physics in the electroweak sector is described through anomalous couplings of the Higgs boson. The organization of the HEFT Lagrangian is guided by chiral perturbation theory [23], with the lowenergy dynamics of electroweak symmetry breaking described using a nonlinear realization of the gauge (a) (b) FIG. 1. Thetwoleading-ordergluon-gluonfusiondi-HiggsproductionFeynmandiagrams:(a)theboxdiagram; (b) thetriangle diagram. (a) (b) (c) FIG. 2. The three tree-level vector-boson fusion di-Higgs production Feynman diagrams. TABLE I. The five relevant SMEFT coefficients and their corresponding dimension-6 operators, as defined in the Warsaw basis [21,22]. Wilson coefficient Operator cHðH†HÞ3 cH□ðH†HÞ□ðH†HÞ ctH ðH†HÞð¯ Q ˜ HtÞ cHG H†HGA μνGμν A ctG ð¯ QσμνTAtÞ˜ HGA μν G. AAD et al. PHYS. REV. D 108, 052003 (2023) 052003-2 symmetry group SUð2ÞL×Uð1ÞY. One advantage of the HEFT framework is that the anomalous single-Higgsboson and HH couplings are defined separately, allowing simplified HH interpretations. In the HEFT Lagrangian, ggF HH production is described at LO by five relevant operators and their associated Wilson coefficients: cHHH, ct¯ tH,cggH,cggHH, and ct¯ tHH. In this formalism, cHHH is equivalent to κλand ct¯ tH is equivalent to the modifier for the coupling between the Higgs boson and top quark, κt, shown by the light blue vertex in Fig. 1. Fixing ct¯ tH ¼cHHH ¼1 and cggH ¼cggHH ¼ct¯ tHH ¼0restores the SM. At next-toleading order (NLO), seven HEFT benchmark models (BM) [24] have been defined using cluster analysis [25] to probe a wide variety of characteristic shapes of the mHH spectrum resulting from different BSM scenarios. The values of the coefficients used to define these scenarios are given in Table II. The ATLAS Collaboration has previously published search results for nonresonant HH →b¯ bb¯ bproduction using 27 fb−1of early Run 2 data [26], and a dedicated search for VBF HH production in 126 fb−1of data collected between 2016 and 2018 [27]. The present analysis benefits from the use of the 2016–2018 data for both production channels and also takes advantage of improvements in jet reconstruction and in the identification of jets arising from the hadronization of b-quarks (“b-tagging”) achieved by the ATLAS Collaboration since the publication of Ref. [26].In addition, the analysis employs a fully data-driven technique for the background estimation, which uses an artificial neural network to perform a kinematic reweighting of data from an alternative control region of the data to model the background in the region of interest. The CMS Collaboration has also published results of a search for nonresonant HH →b¯ bb¯ bwith its full Run 2 dataset [28], setting the observed (expected) upper limit on the HH cross section at 3.9 (7.8) times the SM predicted cross section, and restricting the allowed interval for κλto ½−2.3;9.4 (½−5.0;12.0), both at 95% confidence level (CL). A more recent CMS HH →b¯ bb¯ bpublication [29], in which the analysis exploits topologies arising from highly energetic Higgs boson decays into b¯ b, sets the observed (expected) upper limit at 9.9 (5.1) times the SM cross section expectation, and restricts the allowed interval for κ2Vto [0.62, 1.41] ([0.66, 1.37]), at 95% CL. Other searches for nonresonant HH production were performed by ATLAS and CMS in the b¯ bτþτ−[30,31],b¯ bγγ [32,33],b¯ blþνl−ν[34,35] decay channels, as well as by ATLAS in the b¯ bqqlν[36],WWγγ [37] and WWWW[38] decay channels. Among them, the most sensitive results to date from ATLAS come from the b¯ bγγ analysis, which sets the observed (expected) 95% CL upper limit on the SM nonresonant HH cross section at 4.2 (5.7) times the SM expectation and restricts the corresponding κλinterval to ½−1.5;6.7(½−2.4;7.7). The most sensitive results to date from CMS come from the combination of the b¯ bZZ, multilepton, b¯ bγγ,b¯ bττ,andb¯ bb¯ banalyses, which set the observed (expected) 95% CL upper limit on the SM nonresonant HH cross section at 3.4 (2.5) times the SM expectation and restricts the corresponding observed κλ interval to ½−1.24;6.49[39]. This document is structured as follows. The ATLAS detector and the data and simulated events used in the analysis are described in Secs. II and III, respectively. Section IV presents the reconstruction and identification of physics objects in this analysis and Sec. Vdetails the event selection and categorization. The background modeling method is described in Sec. VI, the systematic uncertainties are detailed in Sec. VII and, finally, the results are reported in Sec. VIII and the conclusion is given in Sec. IX. II. ATLAS DETECTOR The ATLAS detector [40] at the LHC covers nearly the entire solid angle around the collision point.2It consists of an inner tracking detector surrounded by a thin superconducting solenoid, electromagnetic and hadron calorimeters, and a muon spectrometer incorporating three large superconducting air-core toroidal magnets. The inner-detector (ID) system is immersed in a 2 Taxial magnetic field and provides charged-particle tracking in the range jηj<2.5. The high-granularity silicon pixel detector covers the vertex region and typically provides four spacepoint measurements per track, the first hit normally being in the insertable B-layer installed before Run 2 [41,42]. Following the pixel detector is the silicon microstrip tracker, which usually provides eight measurements per track. These silicon detectors are surrounded by the TABLE II. The values of the HEFT Wilson coefficients in the SM and in seven BSM benchmark models, as defined in Ref. [24]. Benchmark model cHHH cttH cggH cggHH cttHH SM 11 000 BM1 3.94 0.94 1=21=3−1=3 BM2 6.84 0.61 0 −1=31=3 BM3 2.21 1.05 1=21=2−1=3 BM4 2.79 0.61 −1=21=61=3 BM5 3.95 1.17 1=6−1=2−1=3 BM6 5.68 0.83 −1=21=31=3 BM7 −0.10 0.94 1=6−1=61 2ATLAS uses a right-handed coordinate system with its origin at the nominal interaction point (IP) in the center of the detector and the z-axis along the beam pipe. The x-axis points from the IP to the center of the LHC ring, and the y-axis points upwards. Cylindrical coordinates ðr; ϕÞare used in the transverse plane, ϕ being the azimuthal angle around the z-axis. The pseudorapidity is defined in terms of the polar angle θas η¼−lntanðθ=2Þ. Angular distance is measured in units of ΔR≡ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ðΔηÞ2þðΔϕÞ2 p. SEARCH FOR NONRESONANT PAIR PRODUCTION OF HIGGS …PHYS. REV. D 108, 052003 (2023) 052003-3 transition radiation tracker, which enables radially extended track reconstruction up to jηj¼2.0. The calorimeter system covers the pseudorapidity range jηj<4.9. Within jηj<3.2, electromagnetic calorimetry is provided by barrel and endcap high-granularity lead/ liquid-argon (LAr) calorimeters, with an additional thin LAr presampler covering jηj<1.8to correct for energy loss in material upstream of the calorimeters. Hadron calorimetry is provided by the steel/scintillator-tile calorimeter, segmented into three barrel structures within jηj<1.7, and two copper/LAr hadron endcap calorimeters. The solid angle coverage is completed with forward copper/LAr and tungsten/LAr calorimeter modules optimized for electromagnetic and hadronic energy measurements respectively. The muon spectrometer (MS) comprises separate trigger and high-precision tracking chambers measuring the deflection of muons in a magnetic field generated by the superconducting air-core toroidal magnets. The field integral of the toroids ranges between 2.0 and 6.0T · m across most of the detector. A set of precision chambers covers the region jηj<2.7with three layers of monitored drift tubes, complemented by cathode-strip chambers in the forward region, where the background is highest. The muon trigger system covers the range jηj<2.4with resistive-plate chambers in the barrel, and thin-gap chambers in the endcap regions. Interesting events are selected by the first-level trigger system implemented in custom hardware, followed by selections made by algorithms implemented in software in the high-level trigger [43]. The first-level trigger accepts events from the 40 MHz bunch crossings at a rate below 100 kHz, which the high-level trigger reduces in order to record events to disk at about 1 kHz. An extensive software suite [44] is used in data simulation, in the reconstruction and analysis of real and simulated data, in detector operations, and in the trigger and data acquisition systems of the experiment. III. DATA AND SIMULATED SAMPLES A. Data sample This analysis is performed in LHC proton–proton ðppÞ collision data at ffiffiffis p¼13 TeV collected between 2016 and 2018. Only data collected during stable beam conditions are used, with all relevant detector systems functional [45], corresponding to an integrated luminosity of 126 fb−1. During 2016 data taking, a fraction of the data (8.3fb−1) was affected by an inefficiency in the online primary vertex reconstruction, which reduced the efficiency of the btagging algorithms in the trigger; those events were not retained for further analysis, resulting in an integrated luminosity of 24.6fb−1for the 2016 dataset. The integrated luminosities of the 2017 and 2018 datasets are 43.7fb−1 and 57.7fb−1, respectively. The analysis uses events that satisfy either of two types of trigger signatures, each with different requirements on the number of jets and their b-tagging status [46]. The jets used are reconstructed with the anti-ktalgorithm [47,48], with a radius parameter of R¼0.4. The b-tagging is performed at the trigger level with the MV2c20 algorithm in 2016 and the MV2c10 algorithm in 2017 and 2018 [46], with a range of b-jet identification efficiency operating points from 40% to 70% (as calculated from simulated t¯ t samples.) The first of the two trigger signatures used for selecting b¯ bb¯ bevents requires two b-jets plus one additional jet (“2b1j”), while the second requires two b-jets plus two additional jets (“2b2j”). The minimum transverse energy (ET) requirement on the jets is 35 GeV for all jets used in the 2b2j trigger. In the 2b1j trigger, the b-tagged jets must have ET>55 GeV, while the requirement on the minimum ETof the additional jet is between 100 and 150 GeV, depending on the year of data taking. B. Simulated samples Monte Carlo (MC) simulation is used for the modeling of signal events, as well as to produce event samples of background processes for cross-checks and validation studies. The Higgs boson mass is set to 125 GeV in the simulation. All samples were processed by the ATLAS simulation framework [49] and the detector response was simulated with G eant4 [50]. The ggF signal process was simulated using the POWHEG BOX v2 generator [51–53] at NLO, including finite topquark-mass effects, using the PDF 4 LHC 15 [54] parton distribution function (PDF) set. Parton showers and hadronization were simulated with PYTHIA 8.244 [55] with the A14 set of tuned parameters [56] and the NNPDF 2.3 LO PDF set [57]. The SM ggF HH cross section was taken as σggF ¼ 31.05 fb, calculated at NNLO including finite top-quarkmass effects [11]. Signal samples for the ggF process were generated explicitly for coupling modifier values of κλ¼1 and 10. A reweighting method is used to obtain a ggF signal sample at each κλvalue, as described in Ref. [58]:scale factors are derived as a function of κλin bins of the generator-level invariant mass of the HH system by performing a linear combination of generator-level samples at three different κλvalues (κλ¼0, 1, and 20). The κλ¼10 ggF signal sample is used to validate the derived scale factors; this generated sample and the signal sample obtained from the reweighting method are found to agree within the statistical precision of the simulated sample. Additional generator-level ggF HH signal samples without parton showering were produced with POWHEG BOX v2 for the κλ¼0and 20 coupling modifier configurations to provide a basis for the κλreweighting, along with the SM ggF sample. For the reweighted ggF signal, the NNLO cross section as a function of κλis taken from Ref. [11]. In order to assess parton showering uncertainties, alternative ggF samples were generated using the POWHEG BOX v2 generator at G. AAD et al. PHYS. REV. D 108, 052003 (2023) 052003-4 NLO with the PDF 4 LHC 15 PDF set, interfaced to H erwig 7.1.6 [59] for parton showering and hadronization using the H erwig 7.1-default set of tuned parameters [60] and MMHT 2014 LO PDF set [61]. To extract SMEFT coefficient constraints, parton-level ggF HH samples were generated with M ad G raph5_a MC @ NLO [62–64] with the SMEFT@NLO model [65] for a variety of SMEFT coefficients. A finely spaced multidimensional grid of signal samples was obtained using a LO-derived reweighting procedure in the generator-level invariant mass of the HH system; this procedure is similar to that used to obtain κλvariations for the ggF signal, as described above. To extract HEFT coefficient constraints, a similar NLOderived reweighting procedure was applied to the simulated reconstruction-level ggF signal sample to produce a variety of HEFT signal scenarios, including the seven benchmark scenarios defined in Sec. I, following the prescription outlined in Refs. [66,67]. Additional K-factors were applied to the SMEFT samples; these K-factors were derived using the ratio of the NLO cross section to the LO cross section at the equivalent HEFT point, as obtained using the HEFT to SMEFT translation from Ref. [24].3 The VBF signal process was simulated using M ad G raph 2.7.3 [63] at LO with the NNPDF 3.0 NLO PDF set [68], interfaced with PYTHIA 8.244 for parton showering and hadronization using the A14 set of tuned parameters and NNPDF 2.3 LO PDF set. Signal samples for the VBF process were generated explicitly for coupling modifier values of ðκλ;κ2V;κVÞ¼ð1;1;1Þ;ð1;1.5;1Þ;ð2;1;1Þ;ð10;1;1Þ; ð1;1;0.5Þ;ð−5;1;0.5Þ;ð0;1;1Þ;ð1;0;1Þ, and (1,3,1). A linear combination of the first six of the listed samples is used to derive distributions for a finer granularity of κ2V values, following a technique used previously to generate κλdistributions [69]. The specific basis of six samples utilized is chosen to avoid large statistical uncertainties in the reweighted signal samples resulting from sparsely populated areas of kinematic phase space. The generated VBF signal samples not included in the linear combination basis—ðκλ;κ2V;κVÞ¼ð0;1;1Þ;ð1;0;1Þ,and(1,3,1)— were used to validate the performance of the combination method. These generated samples and the corresponding signal samples obtained from the combination method were found to agree within the statistical precision of the simulated samples. The cross section for the VBF HH process, evaluated at N3LO in QCD, is 1.73 fb in the SM [12,70–72]. For the reweighted VBF signal points, the N3LO to LO cross section ratio at the SM value is calculated, and this factor is applied to the cross sections at each κλ,κ2V,andκVpoint. In order to assess parton showering uncertainties, alternative LO samples were generated using M ad G raph 2.7.3 with the NNPDF 3.0 NLO PDF set, interfaced to H erwig 7.0.4 with the H erwig 7.1-default set of tuned parameters and MMHT 2014 LO PDF set for parton showering and hadronization. Top-quark pair production (t¯ t) and multijet background processes were simulated in order to validate the background modeling procedure. The t¯ tsample was simulated at NLO in αsusing POWHEG BOX v2 [73]. Parton showering, hadronization, and the underlying event were modeled using PYTHIA 8.230. The matrix element calculation uses NNPDF 3.0 NLO as the PDF set, while the parton shower and underlying-event modeling uses NNPDF 2.3 LO and the A14 set of tuned parameters. The damping parameter hdamp, which effectively regulates radiation at high pT, was set to 1.5 times the top quark’s mass. The t¯ tsimulation is normalized using the value of the inclusive cross section calculated with T op++ 2.0 [74,75]. This accounts for NNLO corrections in αs, including next-to-next-to-leading logarithmic (NNLL) resummation of soft gluon terms. The multijet background samples were modeled using PYTHIA 8.235. This simulates pure QCD 2-to-2 interactions at LO in αs. Events were showered using the parton shower native to PYTHIA , which includes radiation and splitting that can result in additional jets. The A14 set of tuned parameters and the NNPDF 2.3 LO PDF set were used. Other background processes, such as SM Higgs boson, HH (in other final states) and electroweak diboson production, have been estimated to give negligible contributions to the selected event yields and are therefore not included. The effect of multiple interactions in the same and neighboring bunch crossings (pile-up) was modeled by overlaying each simulated hard-scattering event with inelastic pp events generated with PYTHIA 8.186 using the NNPDF 2.3 LO PDF set and the A3 set of tuned parameters [76]. Additionally, for all HH signal samples, heavy-flavor decays were modeled using E vt G en 1.7.0 [77]. IV. OBJECT RECONSTRUCTION Primary vertices from pp interactions are reconstructed [78] using at least two charged-particle tracks with transverse momentum (pT) above 500 MeV measured with the ID. The vertex with the largest sum of squared track momenta (Pp2 T) is taken as the hard-scatter primary vertex. Hadronic jets are reconstructed using the anti-ktalgorithm with radius parameter R¼0.4. The jet clustering uses particle-flow objects as inputs [79]. Particle-flow objects are charged-particle tracks matched to the hard-scatter vertex and calorimeter energy clusters after applying an energy subtraction algorithm that removes the calorimeter deposits associated with good-quality tracks from any vertex. The tracking information helps to improve the energy resolution of the calorimeter clusters and reduce the impact from pile-up. The momenta of reconstructed jets are calibrated in a multistep procedure [80].JetswithpT<60 GeV and 3Variations in the ctG Wilson coefficient were neglected when calculating K-factors because the corresponding chromomagnetic operator does not appear at LO within HEFT. SEARCH FOR NONRESONANT PAIR PRODUCTION OF HIGGS …PHYS. REV. D 108, 052003 (2023) 052003-5 jηj<2.4must also satisfy a requirement based on the output of the multivariate “jet vertex tagger”(JVT) algorithm [81], which is used to identify and reject jets in which much of the energy originates from pile-up interactions. Correction factors are applied to the simulated events to compensate for differences between the JVT efficiencies in data and simulation. In the HH →b¯ bb¯ banalysis, jets are discarded if they fail the “Tight”JVTworking point, corresponding to an average efficiency of 96% for jets from the hard-scatter vertex. Jets with radius parameter R¼0.4are also reconstructed from topological clusters of energy deposits in the calorimeter [82] and calibrated in the same way as the jets reconstructed from particle-flow objects. These jets are used exclusively for the purpose of applying quality criteria to identify events which are consistent with noise in the calorimeter or noncollision background [83]. Events containing at least one such jet with pT>20 GeV, satisfying the JVT requirement, but not these quality criteria, are rejected. The identification of jets originating from b-quarks is performed by the DL1r algorithm [84], which is applied to all jets with jηj<2.5. DL1r is based on a multivariate classification technique combining information from the impact parameters of ID tracks, the presence of displaced secondary vertices, and the reconstructed flight paths of b-andc-hadrons inside the jet. The DL1r working point used in the HH →b¯ bb¯ banalysis is the one that gives 77% efficiency for jets associated with true b-hadrons in simulated t¯ tevents. At this working point, the light-jet (charmjet) rejection measured in t¯ tsimulation is about a factor of 130 (4.9). The calibration of the DL1r algorithm is performed separately for each jet type [85,86] and correction factors are derived and applied to the simulated samples to compensate for differences between the b-tagging efficiencies in data and simulation. Muons are reconstructed by matching ID tracks with either MS tracks or aligned individual hits in the MS and performing a combined track fit [87]. They are required to have pT>4GeV and jηj<2.5, and to satisfy “Medium” identification criteria based on track-quality variables. Muons are used only to apply energy corrections to jets. A momentum correction is applied to b-tagged jets to account for energy lost to soft out-of-cone radiation and to muons and neutrinos in semileptonic b-hadron decays. This correction follows the procedure used in Ref. [88] and consists of two steps. First, a search is performed for muons located near the jet which fall within a cone of variable size ΔRðμ;jetÞ<minð0.4;0.04 þ10=pμ TGeVÞaround the jet axis. If a muon is found, its four-momentum is added to that of the jet, and the energy deposited in the calorimeter by the muon is subtracted from the jet to avoid double counting; this is computed according to the description in Ref. [89]. In the second step, a global scale factor is applied to each b-tagged jet according to its pTand whether or not it has a muon associated with it. These scale factors are derived from simulation. V. ANALYSIS SELECTION AND CATEGORIZATION The analysis utilizes a set of criteria to select HH → b¯ bb¯ bcandidate events, including dedicated requirements to separate events into orthogonal ggF and VBF signal regions. “Forward”and “central”jets are used with the following selection criteria: (i) central jets: jηj<2.5and pT>40 GeV; and (ii) forward jets: 2.5<jηj<4.5and pT>30 GeV. An initial “preselection”is applied to all events, which requires at least four central jets with pT>40 GeV, at least two of which are b-tagged. As described in Sec. III,the events considered in this analysis are selected online through the 2b2jor2b1j trigger signatures. In order to simplify the modeling of trigger efficiencies, a further selection is applied using offline kinematic quantities. Events are selected if they have a leading4jet with pT>170 GeV, a third leading jet with pT>70 GeV, and pass the 2b1j trigger, or if they fail either of the two jet-pTrequirements and pass the 2b2j trigger. This selection step retains about 90% of signal efficiency, and it enables the reliable calculation of simulation-to-data correction factors for estimating the trigger efficiency in the remaining HH →b¯ bb¯ bsignal events, depending on which of the above two trigger classes they belong to. Events passing the above preselection are required to contain at least four central jets passing the b-tagging requirement outlined in Sec. IV. The four highest-pT b-tagged jets are chosen to reconstruct the decays of the two Higgs bosons. In about 75% of simulated signal events reaching this selection stage, these four jets can be matched one-to-one (within ΔR<0.3) to the four b-quarks from the decays of the Higgs bosons. In signal events where this matching fails, one of the b-quarks from the Higgs boson decays typically produces a jet that is outside the analysis acceptance. From the four selected b-tagged jets, there are three possible combinatorial pairings to form the two Higgs boson candidates. Of those three configurations, the analysis selects the one in which the higher-pTjet pair has the smallest ΔRseparation. In the simulated samples with SM coupling values, for which the analysis was mainly optimized, this method gives the correct pairing in around 90% of those signal events in which the four b-tagged jets are correctly matched to the b-quarks from the decays of the Higgs bosons. While the pairing accuracy drops for values of the coupling modifiers κλand κ2Vthat result in softer pT spectra for the produced Higgs bosons, this pairing method 4In this document, terms like “leading,”“subleading”etc for physics objects refer to the ordering of these objects in decreasing pT. G. AAD et al. PHYS. REV. D 108, 052003 (2023) 052003-6 leads to a smoothly varying distribution of the expected background in the plane of the invariant masses of the two Higgs boson candidates, which facilitates the data-driven background estimation described in Sec. VI. Events are then subjected to additional selections designed to separate out those consistent with the VBF production mode. For this, events must contain at least two additional jets, central or forward; b-tagged jets are excluded. The two jets forming the pair with the largest invariant mass (mjj) are chosen as the “VBF jets.”The VBF jet pair is required to satisfy mjj >1TeV, and the pseudorapidity separation between the two jets, jΔηjjj, must satisfy jΔηjjj>3. Lastly, the transverse component of the momentum vector sum of the two VBF jets and the four jets forming the Higgs boson candidates is required to be less than 65 GeV. Events satisfying the above criteria enter the VBF signal region, while those failing to satisfy any of these criteria are considered further in the ggF signal region. Events satisfying either the ggF or VBF selections are required to satisfy additional selection criteria designed to reduce the background and improve the analysis sensitivity. In order to suppress the t¯ tbackground, a top-veto discriminant xWt is defined as: xWt ¼min2 4ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi mjj −mW 0.1mjj 2 þmjjb−mt 0.1mjjb2 s3 5;ð2Þ where mW¼80.4GeV and mt¼172.5GeV are the nominal W boson and top quark masses, and mjj and mjjbare the invariant masses of W boson and top quark candidates formed from jet combinations in each event. The “minimum”refers to the minimum value from all possible jet combinations (of one b-tagged jet and two additional untagged jets) that would give a Wboson candidate and a corresponding top candidate. The factor of 0.1 in the denominators is chosen to approximate the experimental dijet mass resolution. The Wboson candidates are formed from any pair of central jets in the event and the top quark candidates are then reconstructed by pairing the Wboson candidates with any remaining b-tagged Higgs boson candidate jets. The xWt discriminant is designed to quantify the likelihood that an event contains a hadronic top quark decay. Events with xWt <1.5are rejected. This reduces the t¯ tbackground by a factor of about 2 in simulated events, for a small loss of signal efficiency, of around 15%, and a similar reduction in the non-t¯ t, multijet background. In order to further reduce the overall background contamination, events in the ggF signal region are also required to have reconstructed Higgs bosons that satisfy a pseudorapidity separation jΔηHHj<1.5. No such requirement is imposed in the VBF signal region, since SM VBF HH signal events tend to have a larger jΔηHHj. A final analysis selection criterion to test the compatibility of events with the HH decay is applied in both the ggF and VBF selections. A discriminant XHH is defined as: XHH ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi mH1−124 GeV 0.1mH12 þmH2−117 GeV 0.1mH22 s;ð3Þ where mH1and mH2are the masses of the leading and subleading reconstructed Higgs boson candidates respectively. The values of 124 GeV and 117 GeV in the XHH definition are chosen in accord with the centers of the mH1 and mH2distributions for correctly paired signal events from simulation. Events are required to have XHH <1.6to be included in the signal region (SR) of the analysis. Both the ggF and VBF signal regions are subdivided into a number of orthogonal categories in order to better isolate the HH signal and improve the analysis sensitivity. The XHH and jΔηHHjquantities are used to define six orthogonal ggF categories. The categories are defined by two intervals in XHH, with boundaries at 0, 0.95, and 1.6, and three in jΔηHHj, with boundaries at 0, 0.5, 1, and 1.5. In the VBF signal region, two categories are defined using the jΔηHHj quantity, with the dividing boundary at jΔηHHj¼1.5.The jΔηHHj<1.5category is more sensitive to VBF signals with non-SM couplings, while the jΔηHHj>1.5category is more sensitive to SM VBF production. The reconstructed invariant mass of the Higgs boson candidate pair, mHH, is used as the discriminating variable for all analysis regions and categories when extracting results, as detailed in Sec. VIII. The mHH distribution is found to have significant separation power between background and signal, for all the different values of coupling modifiers. The binning of the mHH distributions may vary between categories and is chosen in order to both maintain discrimination power and limit the expected statistical uncertainty in each bin to less than approximately 30%. This 30% limit ensures that the assumptions used in the statistical procedure, outlined in Sec. VIII, are satisfied. In the VBF signal region, only events with mHH >400 GeV are considered, as the background in the lower mHH region was found to be inadequately modeled by the data-driven method described in Sec. VI in validation studies with control data samples. For the ggF signal region, no requirements on mHH are applied. All the selection steps of the analysis are summarized in Fig. 3. The yields in the data and the simulated signal samples for some typical coupling values are shown in Table III. This sample of data events is referred to as 4b events hereafter. VI. BACKGROUND MODELING After the selection described above, about 90% of the background events come from multijet processes SEARCH FOR NONRESONANT PAIR PRODUCTION OF HIGGS …PHYS. REV. D 108, 052003 (2023) 052003-7 (excluding top quark production), with the approximately 10% remainder almost entirely composed of t¯ tevents. This background composition was determined by applying the full event selection to simulated samples of the various processes and comparing the yields with the total background estimate in the SR; it is purely meant to be indicative and is not used for deriving any results. The background is modeled using the fully data-driven technique described below. The background estimation makes use of an alternative set of events, which pass the same b-jet triggers and satisfy all the same selection criteria as the 4bevents, with one difference: they are required to contain exactly two b-tagged jets. This sample, referred to hereafter as “2b,”has about two orders of magnitude more events than the 4b sample, hence the presence of any HH →b¯ bb¯ bsignal in it is negligible, making it suitable for the background estimation. The jets selected to form the two Higgs boson TABLE III. The yields of data and various example ggF and VBF HH signal models at each step of the analysis selection. The “Preselection”entry denotes an initial selection requiring at least four jets with pT>40 GeV, at least two of which are b-tagged. Events which satisfy the “VBF selection”requirements are considered as part of the VBF signal region of the analysis, while the rest are considered for the ggF signal region. The signal yields are taken from simulation and are normalized by their theoretical cross sections and the integrated luminosity of 126 fb−1. Corrections for differences in the b-tagging efficiency and trigger acceptance between data and simulation are applied starting from the “Trigger class”requirement. Data ggF signal VBF signal SM κλ¼10 SM κ2V¼0 Common preselection Preselection 5.70 ×108530 7300 22 630 Trigger class 2.49 ×108380 5300 16 410 ggF selection Fail VBF selection 2.46 ×108380 5200 14 330 At least 4 b-tagged central jets 1.89 ×10686 1000 1.9 65 jΔηHHj<1.51.03 ×10672 850 0.94 46 xWt >1.57.51 ×10560 570 0.74 43 XHH <1.6(ggF signal region) 1.62 ×10429 180 0.24 23 VBF selection Pass VBF selection 3.30 ×1065.2 81 2.2 71 At least 4 b-tagged central jets 2.71 ×1041.1 15 0.74 28 xWt >1.52.18 ×1041.0 11 0.67 26 XHH <1.65.02 ×1020.48 3.1 0.33 17 mHH >400 GeV (VBF signal region) 3.57 ×1020.43 1.8 0.30 16 FIG. 3. A flowchart summarizing the nine selection criteria used for the VBF and ggF analysis selections. Events must satisfy selection criteria 1–3 in order to be considered for either analysis signal region. Events failing to satisfy any of the selection criteria 4–6 are considered for inclusion in the ggF signal region, while those satisfying selection criteria 4–6 are considered for the VBF signal region. G. AAD et al. PHYS. REV. D 108, 052003 (2023) 052003-8 candidates in the 2bevents are the two b-tagged jets and the two untagged central jets with the highest pT(excluding the VBF jets in the VBF categories). The kinematic properties of the 2band 4bevents are not expected to be identical, partly due to different processes contributing to the two samples, but also due to differences in the trigger acceptance and because the probability of tagging a b-jet varies as a function of jet pTand η. Therefore, a reweighting function is required, which, when applied to the 2bevents, maps their kinematic distributions onto the corresponding 4bdistributions. This function is derived using the 2band 4bevents in a control region (CR) surrounding the SR in the reconstructed (mH1,mH2) plane and then applied to the 2bevents in the SR to produce the background estimate. The “inner edge”of the CR is defined by XHH ¼1.6and the “outer edge”by the circle: RCR ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ðmH1−1.05 ·124 GeVÞ2þðmH2−1.05 ·117 GeVÞ2 q¼45 GeV:ð4Þ The shift of the center of the above circle by a factor of 1.05, relative to XHH ¼0, is found to be the optimal tradeoff between having a good number of events outside of the SR and avoiding the low mH1=mH2regions, where the differences between 2band 4bkinematic distributions are larger. The CR is split into four roughly equal directional quadrants, defined by 45° and 135° lines passing through the SR center, (124, 117) GeV. The four quadrants are given labels based on compass directions: the upper quadrant QN, the lower QS, the left QW, and the right QE. The above lines also define four quadrants, with the same names as above, in the SR. Events in CR QNand QS, hereafter referred to as CR1, are used to derive the reweighting function for the nominal background estimate, while an alternative reweighting function, derived from the CR events in QEand QW(referred to hereafter as CR2) is used to define a systematic uncertainty related to the reweighting function interpolation into the SR, as detailed in Sec. VII. The boundaries of the SR, CR1, and CR2 in the reconstructed (mH1,mH2) plane are shown in Fig. 4. The horizontal and vertical bands of lower event density around 80 GeV visible in these plots are caused by the xWt selection criterion. For comparison, the distributions of the simulated ggF and VBF HH signals in the reconstructed (mH1,mH2) plane are presented in Fig. 5. The reweighting function has the form: wð xÞ¼p4bð xÞ p2bð xÞ;ð5Þ where p4bð xÞand p2bð xÞare the probability density functions for 4band 2bdata, respectively, over a set of kinematic variables  x. The computation of wð xÞis a density ratio estimation problem, for which a variety of approaches exist. The method employed in this analysis is modified from Refs. [90,91] and makes use of an artificial neural network (NN). This NN is trained on 2band 4bCR1 data (or CR2 data, for determining systematic uncertainties, as described Sec. VII). The training minimizes the following loss function: (a) (b) FIG. 4. The mass planes of the reconstructed Higgs boson candidates for the (a) ggF and (b) VBF signal regions of the analysis, shown for the 4bdata events. In (a), the analysis selection up to step 8 (as outlined in Fig. 3) of the ggF selection has been applied, while in (b), the analysis selection up to step 7 of the VBF selection has been applied. The continuous red line describes the signal region (SR), the dashed line describes control region 1 (CR1) and the dotted line describes control region 2 (CR2). SEARCH FOR NONRESONANT PAIR PRODUCTION OF HIGGS …PHYS. REV. D 108, 052003 (2023) 052003-9 collected between 2016 and 2018 [27], the upper limit on the VBF HH cross section is over 75% lower, with this improvement arising entirely from advances in analysis technique and object reconstruction. The total uncertainty in the upper limit of the cross section is dominated by the uncertainty sources related to the background modeling procedure and theoretical predictions. With only the statistical uncertainties of the reweighted 2bdata, observed 4bdata, and simulated signal samples included in the fit, the expected upper limit on μggFþVBF is found to be 6.0 times the SM prediction. Including the uncertainty sources resulting from the background estimation (the bootstrap uncertainty, the uncertainty from the kinematic differences between the SR and CR1, and, in the ggF signal region, the 3b1f nonclosure uncertainty), the expected upper limit on μggFþVBF is relaxed to 7.1 times the SM prediction. The further reduction of sensitivity to the value of 8.1, as quoted in Table VII,is driven primarily by the uncertainties arising from theoretical predictions. The relative impact of the various sources of systematic uncertainty on the expected upper limit on μggFþVBF is summarized in Table VIII. Constraints are placed on the κλand κ2Vmodifiers using two different interpretations, the first named the “95% CL” method and the second named the “profile likelihood ratio” method. The former uses the signal strength μas the POI, while the latter uses the vector of coupling modifiers κ¼ðκλ;κ2VÞ. The 95% CL method allows for interpretation as a traditional search for an arbitrarily normalized set of signals with different shapes against an estimated background, while the profile likelihood ratio method allows for interpretation as to whether the data are compatible with the specific cross section and shape predictions of the κ framework. The 95% CL results presented here offer a consistent comparison with previous ATLAS HH measurements. The constraints obtained from the two interpretations TABLE VI. The yields in each analysis category of the data, expected background, and expected SM ggF and VBF signals. The expected background yields are obtained using a fit to the data with the background-only hypothesis; the quoted uncertainties are the sum in quadrature of all the per-bin systematic uncertainties. The expected signal yields are obtained from simulation. Category Data Expected ggF signal VBF signal Background SM SM ggF signal region jΔηHHj<0.5,XHH <0.95 1940 1935 25 7.0 0.038 jΔηHHj<0.5,XHH >0.95 3602 3618 37 6.5 0.036 0.5<jΔηHHj<1.0,XHH <0.95 1924 1874 21 5.1 0.037 0.5<jΔηHHj<1.0,XHH >0.95 3540 3492 35 4.7 0.040 jΔηHHj>1.0,XHH <0.95 1880 1739 22 2.9 0.043 jΔηHHj>1.0,XHH >0.95 3285 3212 37 2.8 0.041 VBF signal region jΔηHHj<1.5116 125.34.40.37 0.090 jΔηHHj>1.5241 230.65.30.06 0.21 TABLE VII. The observed and expected upper limits on the SM ggF HH production cross section σggF, SM VBF HH production cross section σVBF, and combined SM ggF and VBF HH production cross section σggFþVBF at the 95% CL, expressed as multiples of the corresponding SM cross sections. The expected values are shown with corresponding oneand two-standarddeviation error bounds, and they are obtained using a background-only fit to the data. When extracting the limits on σggFþVBF, the relative contributions of ggF and VBF production to the total cross section are fixed to the SM prediction. Observed limit −2σ−1σ Expected limit þ1σþ2σ μggF 5.5 4.4 5.9 8.2 12.4 19.6 μVBF 130 70 100 130 190 280 μggFþVBF 5.4 4.3 5.8 8.1 12.2 19.1 TABLE VIII. Breakdown of the dominant systematic uncertainties. The impact of the uncertainties on the expected upper limit on μggFþVBF when re-evaluating the profile likelihood ratio after fixing the nuisance parameter(s) in question to its (their) best-fit value(s), while all remaining nuisance parameters remain free to float. The impact is shown in %. Only (groups of) systematic uncertainties that have an impact of at least 1% are shown. The impact of each experimental source of systematic uncertainty described in the text, as well as of all of them together, is less than 1%. Source of uncertainty Δμ=μ Theory uncertainties Theory uncertainty in signal cross section −9.0% All other theory uncertainties −1.4% Background modeling uncertainties Bootstrap uncertainty −7.1% CR to SR extrapolation uncertainty −7.5% 3b1f nonclosure uncertainty −2.0% G. AAD et al. PHYS. REV. D 108, 052003 (2023) 052003-16 are not expected to be identical, as the two strategies employ slightly different physical assumptions. In the profile likelihood ratio interpretation, the signal strength is fixed to the prediction obtained for a specific coupling modifier configuration, while for the 95% CL interpretation, the signal strength is allowed to float. The profile likelihood ratio method utilizes a hypothesis consisting of the predicted background plus the SM HH signal, while the 95% CL results utilize a hypothesis containing only the predicted background and no HH signal. Given the relatively small size of the SM HH signal compared to the predicted background, the use of different hypotheses is not expected to have a significant effect. Additionally, 2σ-level constraints are quoted from the profile likelihood ratio interpretation, as opposed to 95% CL constraints. The 95% CL constraints on κλand κ2Vare obtained by determining the 95% CL upper limits on the cross section as a function of these coupling modifiers, μggFþVBFðκλ;κ2VÞ. Values of the coupling modifiers ðκλ;κ2VÞare excluded if the predicted cross section of the signal model obtained with that configuration is excluded at the 95% CL. The H→b¯ b branching ratio is fixed to the SM prediction in the likelihood fit and any dependence on κλis ignored. Upper limits on the HH signal strength as a function of κλand κ2Vare shown in Fig. 10, and the exclusion boundaries are summarized in Table IX. With the values of the other modifiers (κVand either κ2Vor κλ, respectively) fixed to their SM value of 1, values of κλbeyond ½−3.9;11.1and values of κ2Vbeyond ½−0.03;2.11are excluded. Figure 11 shows the 95% CL exclusion limits in the twodimensional plane of the κλ–κ2Vmodifier space. (a) (b) FIG. 10. The observed 95% CL exclusion limits as a function of (a) κλ(obtained using the signal strength μggFþVBF as the POI) and (b) κ2V(obtained using the signal strength μVBF as the POI) from the combined ggF and VBF signal regions, as shown by the solid black line. In each case, the value of the other modifier is fixed to 1. The blue and yellow bands show respectively the 1σand 2σbands around the expected exclusion limits, which are shown by the dashed black line. The expected exclusion limits are obtained using a fit to the data with the background-only hypothesis. The dark red line shows in (a) the predicted combined ggF and VBF HH cross section as a function of κλand in (b) the predicted VBF HH cross section as a function of κ2V. The dark pink bands surrounding the predicted crosssection lines indicate the theoretical uncertainty of the cross section, as taken from Ref. [99]. The band in (b) is smaller than the width of the plotted line. TABLE IX. The observed and expected constraints on the κλ and κ2Vcoupling modifiers at 95% CL. For each modifier, the constraints were extracted with all other modifiers fixed to the SM prediction. Expected constraint Observed constraint Parameter Lower Upper Lower Upper κλ−4.610.8 −3.911.1 κ2V−0.05 2.12 −0.03 2.11 FIG. 11. The observed 95% CL exclusion limit obtained using the signal strength μggFþVBF as the POI in the two-dimensional κλ vs κ2Vspace, obtained from the combined ggF and VBF signal model, as shown by the solid black line. The blue and yellow bands show respectively the 1σand 2σbands around the expected exclusion limits, which are shown by the dashed black line. The star denotes the SM prediction (κλ¼κ2V¼1). SEARCH FOR NONRESONANT PAIR PRODUCTION OF HIGGS …PHYS. REV. D 108, 052003 (2023) 052003-17 The alternative coupling modifier constraints are obtained using the profile likelihood ratio interpretation, with the coupling modifiers κ¼ðκλ;κ2VÞas the POIs, rather than the signal strength μ: −2ΔlnLðκÞ¼−2lnLðκ; ˆ ˆ θÞ Lðˆ κ; ˆ θÞ:ð8Þ A scan of the profile likelihood ratio is performed as a function of the coupling modifiers at discrete points to produce the curves shown in Fig. 12. The best-fit value of κλis found to be 6.2 from the profile likelihood scan. The observed pull of the best-fit κλvalue away from the SM value is due to a slight excess in the observed data in the ggF signal region, specifically in the low-mHH range. The particular signal model in which κλis close to 6 is favored due to a balance between two competing effects: the mHH spectrum becomes softer as κλincreases away from the SM, but the cross section also grows beyond the magnitude of the excess as κλincreases much further. This slight excess also results in the deviation of the observed limits in Fig. 12 from the expected limits by about 1σ. No such excess is observed in the VBF signal region, and the best-fit value of κ2Vfrom the likelihood scan is found to be 1.0. With the values of the other modifiers (κVand either κ2Vor κλ, respectively) fixed to their SM value of 1, the observed (a) (b) FIG. 12. The observed profile likelihood ratio scans for the (a) κλand (b) κ2Vcoupling modifiers, shown by the solid black line, using the coupling modifiers κas the POIs. In each case, the value of the other parameter is fixed to 1. The dashed blue line shows the expected profile likelihood ratio, as obtained using a fit to the data with the background-only hypothesis. The pink line indicates the 2σexclusion boundary. (a) (b) FIG. 13. (a) The observed profile likelihood ratio exclusion limits for the two-dimensional κλvs. κ2Vmodifier space, shown by the solid dark purple line at the 1σlevel and the dashed turquoise line at the 2σlevel. The black cross denotes the best-fit values of ðκλ;κ2VÞ. The expected exclusion limits are presented in (b), where the solid pink line denotes the 1σ-level exclusion and the dashed orange line denotes the 2σ-level exclusion. For both the expected and observed limit plots, the black star indicates the SM prediction (κλ¼κ2V¼1). G. AAD et al. PHYS. REV. D 108, 052003 (2023) 052003-18 (expected) 2σallowed range for κλis found to be ½−3.5;11.3(½−5.4;11.4) and the corresponding range for κ2Vis ½−0.0;2.1(½−0.1;2.1). The exclusion constraints obtained using the profile likelihood ratio method are also presented in the twodimensional κλ–κ2Vcoupling modifier space, similarly to the 95% CL constraints described above. The excluded regions are presented in Fig. 13. With both modifiers able to float in the two-dimensional fit that combines both the ggF and VBF signal regions, the fit converges to κλand κ2V values slightly different from the ones where the minimum is found in the fits with a single parameter free. In addition to constraints on the ggF and VBF HH cross sections and the κλand κ2Vcoupling modifiers, constraints for relevant coefficients can be derived from the ggF selection of the analysis in the SMEFT and HEFT frameworks, as outlined in Sec. I. The VBF HH process was ignored for both the SMEFT and HEFT results; including the VBF HH process as a background was found to have a negligible effect on the extracted parameter limits. The slight dependence of the H→b¯ bbranching fraction on the SMEFT and HEFT coefficients is also ignored, as the (a) (b) (c) (d) FIG. 14. The observed 95% CL exclusion limits on the SMEFT coefficients in the two-dimensional spaces (a) cHG vs cH, (b) ctG vs cH, (c) ctH vs cH, and (d) cH□vs cH, shown by the solid black lines. The dashed black line indicates the expected 95% CL exclusion limits. The shaded blue band indicates the 1σuncertainty of the exclusion limits, while the yellow band indicates the 2σuncertainty. The values of the other three coefficients for each plot are fixed to 0. The VBF HH process is ignored for this result. TABLE X. The extracted upper and lower limits on the SMEFT parameters to which the analysis is sensitive. For each parameter, the constraints are provided assuming the other parameters are fixed to 0. The VBF HH process is ignored for this result. Expected constraint Observed constraint Parameter Lower Upper Lower Upper cH−20 11 −22 11 cHG −0.056 0.049 −0.067 0.060 cH□−9.313.9 −8.914.5 ctH −10.06.4 −10.76.2 ctG −0.97 0.94 −1.12 1.15 SEARCH FOR NONRESONANT PAIR PRODUCTION OF HIGGS …PHYS. REV. D 108, 052003 (2023) 052003-19 impact on the analysis sensitivity is small. Constraints on the SMEFT coefficients are extracted by considering the 95% CL exclusion of the cross section as a function of SMEFT parameter, as was done for the κλand κ2V constraints discussed previously. The extracted constraints on individual parameters in the scenario where the other parameters are fixed to 0 are summarized in Table X. Limits approaching or exceeding 4πshould be interpreted with caution because of the potential impact from effects such as missing higher-order model contributions. The exclusion limits are also presented in two-dimensional SMEFT coefficient subspaces. The exclusion limits for each coefficient versus the cHcoefficient (with the remaining three coefficients fixed to 0) are shown in Fig. 14. The upper limits on the HEFT ggF HH production cross section in the seven benchmark models are presented in Fig. 15.The spread of sensitivity between the seven benchmark models reflects the different signal kinematics and, hence, shapes of the signal mHH distributions. The different variation between observed and expected limits is linked to the slight excess observed in the low mHH region, as discussed earlier. The red crosses in Fig. 15 indicate the predicted HH cross sections from the respective benchmark models. As can be seen, BM3, BM5, and BM7 are observed to be excluded with more than 95% confidence. Constraints are placed on the values of cggHH and ct¯ tHH, with all other HEFT coefficients fixed to SM values. The observed (expected) constraints on cggHH are found to be ½−0.36;0.78 (½−0.42;0.75), while the observed (expected) constraints on ct¯ tHH are found to be ½−0.55;0.51(½−0.46;0.40). IX. CONCLUSION A search for nonresonant pair production of Higgs bosons in the b¯ bb¯ bfinal state was carried out, with dedicated analyses for the ggF and VBF production modes, using 126 fb−1of ffiffiffis p¼13 TeV pp collision data collected by the ATLAS detector at the LHC. The sensitivity of the analyses is improved relative to previous iterations by using more sophisticated background modeling techniques, event categorization and improved jet reconstruction and flavor identification algorithms, in addition to the increased integrated luminosity of the analyzed data. No evidence of signal is found and the observed (expected) upper limit on the cross section for nonresonant Higgs boson pair production is determined to be 5.4 (8.1) times the Standard Model predicted cross section at 95% confidence level. Constraints are placed upon modifiers to the HHH and HHVV couplings. The observed (expected) 2σconstraints on the HHH coupling modifier, κλ, are determined to be ½−3.5;11.3(½−5.4;11.4), while the corresponding constraints for the HHVV coupling modifier, κ2V, are ½−0.0;2.1(½−0.1;2.1). The results are also used to derive constraints on relevant coefficients in the SM effective field theory and the Higgs effective field theory frameworks. ACKNOWLEDGMENTS We thank CERN for the very successful operation of the LHC, as well as the support staff from our institutions without whom ATLAS could not be operated efficiently. We acknowledge the support of ANPCyT, Argentina; YerPhI, Armenia; ARC, Australia; BMWFW and FWF, Austria; ANAS, Azerbaijan; CNPq and FAPESP, Brazil; NSERC, NRC and CFI, Canada; CERN; ANID, Chile; CAS, MOST and NSFC, China; Minciencias, Colombia; MEYS CR, Czech Republic; DNRF and DNSRC, Denmark; IN2P3CNRS and CEA-DRF/IRFU, France; SRNSFG, Georgia; BMBF, HGF and MPG, Germany; GSRI, Greece; RGC and Hong Kong SAR, China; ISF and Benoziyo Center, Israel; INFN, Italy; MEXT and JSPS, Japan; CNRST, Morocco; NWO, Netherlands; RCN, Norway; MEiN, Poland; FCT, Portugal; MNE/IFA, Romania; MESTD, Serbia; MSSR, Slovakia; ARRS and MIZŠ, Slovenia; DSI/NRF, South Africa; MICINN, Spain; SRC and Wallenberg Foundation, Sweden; SERI, SNSF and Cantons of Bern and Geneva, Switzerland; MOST, Taiwan; TENMAK, Türkiye; STFC, United Kingdom; DOE and NSF, United States of America. In addition, individual groups and members have received support from BCKDF, CANARIE, Compute Canada and CRC, Canada; PRIMUS 21/SCI/017 and UNCE SCI/013, Czech Republic; COST, ERC, ERDF, Horizon 2020 and Marie Skłodowska-Curie Actions, European Union; FIG. 15. The observed 95% CL exclusion limits on the ggF HH production cross section in the SM and each of the seven HEFT benchmark models, given by the solid black points. The blue and yellow bands show respectively the 1σand 2σbands around the expected upper limits, which are shown by the open circles. The predicted ggF HH production cross section from each benchmark is indicated by a pink cross. Benchmarks where the theory cross section is higher than the exclusion limit (i.e. to the right) are excluded. The VBF HH process is ignored for this result. G. AAD et al. PHYS. REV. D 108, 052003 (2023) 052003-20 Investissements d’Avenir Labex, Investissements d’Avenir Idex and ANR, France; DFG and AvH Foundation, Germany; Herakleitos, Thales and Aristeia programmes co-financed by EU-ESF and the Greek NSRF, Greece; BSFNSF and MINERVA, Israel; Norwegian Financial Mechanism 2014-2021, Norway; NCN and NAWA, Poland; La Caixa Banking Foundation, CERCA Programme Generalitat de Catalunya and PROMETEO and GenT Programmes Generalitat Valenciana, Spain; Göran Gustafssons Stiftelse, Sweden; The Royal Society and Leverhulme Trust, United Kingdom. The crucial computing support from all WLCG partners is acknowledged gratefully, in particular from CERN, the ATLAS Tier1 facilities 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 nonWLCG resource providers. Major contributors of computing resources are listed in Ref. [103]. [1] ATLAS Collaboration, Observation of a new particle in the search for the Standard Model Higgs boson with the ATLAS detector at the LHC, Phys. Lett. B 716, 1 (2012). [2] CMS Collaboration, Observation of a new boson at a mass of 125 GeV with the CMS experiment at the LHC, Phys. Lett. B 716, 30 (2012). [3] ATLAS Collaboration, Observation of H→b¯ bdecays and VH production with the ATLAS detector, Phys. Lett. B 786, 59 (2018). [4] CMS Collaboration, Observation of Higgs Boson Decay to Bottom Quarks, Phys. Rev. Lett. 121, 121801 (2018). [5] G. C. Branco, P. M. Ferreira, L. Lavoura, M. N. Rebelo, M. Sher, and J. P. Silva, Theory and phenomenology of twoHiggs-doublet models, Phys. Rep. 516, 1 (2012). [6] R. Gröber and M. Mühlleitner, Composite Higgs boson pair production at the LHC, J. High Energy Phys. 06 (2011) 020. [7] Z. Chacko, Y. Nomura, M. Papucci, and G. Perez, Natural little hierarchy from a partially Goldstone twin Higgs, J. High Energy Phys. 01 (2006) 126. [8] P. Fayet, Supersymmetry and weak, electromagnetic and strong interactions, Phys. Lett. 64B, 159 (1976). [9] P. Fayet, Spontaneously broken supersymmetric theories of weak, electromagnetic and strong interactions, Phys. Lett. B 69, 489 (1977). [10] G. Degrassi, S. Di Vita, J. Elias-Miró, J. R. Espinosa, G. F. Giudice, G. Isidori, and A. Strumia, Higgs mass and vacuum stability in the standard model at NNLO, J. High Energy Phys. 08 (2012) 098. [11] M. Grazzini, G. Heinrich, S. Jones, S. Kallweit, M. Kerner, J. M. Lindert, and J. Mazzitelli, Higgs boson pair production at NNLO with top quark mass effects, J. High Energy Phys. 05 (2018) 059. [12] F. A. Dreyer and A. Karlberg, Vector-boson fusion Higgs pair production at N3LO, Phys. Rev. D 98, 114016 (2018). [13] F. Bishara, R. Contino, and J. Rojo, Higgs pair production in vector-boson fusion at the LHC and beyond, Eur. Phys. J. C 77, 481 (2017). [14] D. de Florian et al., Handbook of LHC Higgs cross sections: 4. Deciphering the nature of the Higgs sector, arXiv:1610.07922. [15] A. Djouadi, J. Kalinowski, and M. Spira, HDECAY :A program for Higgs boson decays in the standard model and its supersymmetric extension, Comput. Phys. Commun. 108, 56 (1998). [16] W. Buchmuller and D. Wyler, Effective Lagrangian analysis of new interactions and flavour conservation, Nucl. Phys. B268, 621 (1986). [17] C. N. Leung, S. T. Love, and S. Rao, Low-energy manifestations of a new interactions scale: Operator analysis, Z. Phys. C 31, 433 (1986). [18] I. Brivio and M. Trott, The standard model as an effective field theory, Phys. Rep. 793, 1 (2019). [19] R. Alonso, M. Gavela, L. Merlo, S. Rigolin, and J. Yepes, The effective chiral Lagrangian for a light dynamical “Higgs particle”,Phys. Lett. B 722, 330 (2012). [20] G. Buchalla, O. Cat`a, and C. Krause, Complete electroweak chiral Lagrangian with a light Higgs at NLO, Nucl. Phys. B880, 552 (2014);B913, 475(E) (2016). [21] B. Grzadkowski, M. Iskrzynski, M. Misiak, and J. Rosiek, Dimension-six terms in the standard model Lagrangian, J. High Energy Phys. 10 (2010) 085. [22] ATLAS Collaboration, Combined effective field theory interpretation of Higgs boson and weak boson production and decay with ATLAS data and electroweak precision observables, Report No. ATL-PHYS-PUB-2022-037, 2022, https://cds.cern.ch/record/2816369. [23] G. Buchalla, O. Catá, and C. Krause, On the power counting in effective field theories, Phys. Lett. B 731, 80 (2014). [24] M. Capozi and G. Heinrich, Exploring anomalous couplings in Higgs boson pair production through shape analysis, J. High Energy Phys. 03 (2020) 091. [25] A. Carvalho et al., Higgs pair production: Choosing benchmarks with cluster analysis, J. High Energy Phys. 04 (2016) 126. [26] ATLAS Collaboration, Search for pair production of Higgs bosons in the b¯ bb¯ bfinal state using proton–proton collisions at ffiffiffis p¼13 TeV with the ATLAS detector, J. High Energy Phys. 01 (2019) 030. [27] ATLAS Collaboration, Search for the HH →b¯ bb¯ bprocess via vector-boson fusion production using proton–proton collisions at ffiffiffis p¼13 TeV with the ATLAS detector, J. High Energy Phys. 07 (2020) 108; 01 (2021) 145(E). [28] CMS Collaboration, Search for Higgs Boson Pair Production in the Four b Quark Final State in Proton-Proton SEARCH FOR NONRESONANT PAIR PRODUCTION OF HIGGS …PHYS. REV. D 108, 052003 (2023) 052003-21 Collisions at ffiffiffis p¼13 TeV, Phys. Rev. Lett. 129, 081802 (2022). [29] CMS Collaboration, Search for nonresonant pair production of highly energetic Higgs bosons decaying to bottom quarks, arXiv:2205.06667. [30] ATLAS Collaboration, Search for resonant and nonresonant Higgs boson pair production in the b¯ bτþτ−decay channel using 13 TeV pp collision data from the ATLAS detector, J. High Energy Phys. 07 (2023) 040. [31] CMS Collaboration, Search for Higgs boson pair production in events with two bottom quarks and two tau leptons in proton–proton collisions at ffiffiffis p¼13 TeV, Phys. Lett. B 778, 101 (2018). [32] ATLAS Collaboration, Search for Higgs boson pair production in the two bottom quarks plus two photons final state in pp collisions at ffiffiffis p¼13 TeV with the ATLAS detector, Phys. Rev. D 106, 052001 (2021). [33] CMS Collaboration, Search for nonresonant Higgs boson pair production in final states with two bottom quarks and two photons in proton–proton collisions at ffiffiffis p¼13 TeV, J. High Energy Phys. 03 (2021) 257. [34] ATLAS Collaboration, Search for non-resonant Higgs boson pair production in the bblνlνfinal state with the ATLAS detector in pp collisions at ffiffiffis p¼13 TeV, Phys. Lett. B 801, 135145 (2020). [35] CMS Collaboration, Search for resonant and nonresonant Higgs boson pair production in the b¯ blνlνfinal state in proton–proton collisions at ffiffiffis p¼13 TeV, J. High Energy Phys. 01 (2018) 054. [36] ATLAS Collaboration, Search for Higgs boson pair production in the b¯ bWWdecay mode at ffiffiffis p¼13 TeV with the ATLAS detector, J. High Energy Phys. 04 (2019) 092. [37] ATLAS Collaboration, Search for Higgs boson pair production in the γγWWchannel using pp collision data recorded at ffiffiffis p¼13 TeV with the ATLAS detector, Eur. Phys. J. C 78, 1007 (2018). [38] ATLAS Collaboration, Search for Higgs boson pair production in the WWðÞWWðÞ decay channel using ATLAS data recorded at ffiffiffis p¼13 TeV, J. High Energy Phys. 05 (2019) 124. [39] CMS Collaboration, A portrait of the Higgs boson by the CMS experiment ten years after the discovery, Nature (London) 607, 60 (2022). [40] ATLAS Collaboration, The ATLAS experiment at the CERN Large Hadron Collider, J. Instrum. 3, S08003 (2008). [41] ATLAS Collaboration, ATLAS insertable B-layer: Technical design report, Reports No. ATLAS-TDR-19, No. CERN-LHCC-2010-013, 2010, https://cds.cern.ch/ record/1291633; Addendum: Reports No. ATLAS-TDR19-ADD-1, No. CERN-LHCC-2012-009, 2012, https:// cds.cern.ch/record/1451888. [42] B. Abbott et al., Production and integration of the ATLAS insertable B-layer, J. Instrum. 13, T05008 (2018). [43] ATLAS Collaboration, Performance of the ATLAS trigger system in 2015, Eur. Phys. J. C 77, 317 (2017). [44] ATLAS Collaboration, The ATLAS Collaboration software and firmware, Report No. ATL-SOFT-PUB-2021001, 2021, https://cds.cern.ch/record/2767187. [45] ATLAS Collaboration, ATLAS data quality operations and performance for 2015–2018 data-taking, J. Instrum. 15, P04003 (2020). [46] ATLAS Collaboration, Configuration and performance of the ATLAS b-jet triggers in Run 2, Eur. Phys. J. C 81, 1087 (2021). [47] M. Cacciari, G. P. Salam, and G. Soyez, The anti-ktjet clustering algorithm, J. High Energy Phys. 04 (2008) 063. [48] M. Cacciari, G. P. Salam, and G. Soyez, F ast J et user manual, Eur. Phys. J. C 72, 1896 (2012). [49] ATLAS Collaboration, The ATLAS simulation infrastructure, Eur. Phys. J. C 70, 823 (2010). [50] S. Agostinelli et al., G eant4—A simulation toolkit, Nucl. Instrum. Methods Phys. Res., Sect. A 506, 250 (2003). [51] P. Nason, A new method for combining NLO QCD with shower Monte Carlo algorithms, J. High Energy Phys. 11 (2004) 040. [52] S. Frixione, P. Nason, and C. Oleari, Matching NLO QCD computations with parton shower simulations: The POWHEG method, J. High Energy Phys. 11 (2007) 070. [53] S. Alioli, P. Nason, C. Oleari, and E. Re, A general framework for implementing NLO calculations in shower Monte Carlo programs: The POWHEG BOX ,J. High Energy Phys. 06 (2010) 043. [54] J. Butterworth et al., PDF 4 LHC recommendations for LHC Run II, J. Phys. G 43, 023001 (2016). [55] T. Sjöstrand, S. Ask, J. R. Christiansen, R. Corke, N. Desai, P. Ilten, S. Mrenna, S. Prestel, C. O. Rasmussen, and P, Z. Skands, An introduction to PYTHIA 8.2,Comput. Phys. Commun. 191, 159 (2015). [56] ATLAS Collaboration, ATLAS PYTHIA 8tunes to 7 TeV data, Report No. ATL-PHYS-PUB-2014-021, 2014, https://cds.cern.ch/record/1966419. [57] R. D. Ball et al. (NNPDF Collaboration), Parton distributions with LHC data, Nucl. Phys. B867, 244 (2013). [58] ATLAS Collaboration, Validation of signal Monte Carlo event generation in searches for Higgs boson pairs with the ATLAS detector, Report No. ATL-PHYS-PUB-2019-007, 2019, https://cds.cern.ch/record/2665057. [59] M. Bähr et al., H erwig++ physics and manual, Eur. Phys. J. C58, 639 (2008). [60] S. Gieseke, C. Röhr, and A. Siodmok, Colour reconnections in H erwig++,Eur. Phys. J. C 72, 2225 (2012). [61] L. A. Harland-Lang, A. D. Martin, P. Motylinski, and R. S. Thorne, Parton distributions in the LHC era: MMHT 2014 PDFs, Eur. Phys. J. C 75, 204 (2015). [62] ATLAS Collaboration, A study of optimal parameter setting for M ad G raph5_ AMC @ NLO + PYTHIA 8matched setup, Report No. ATL-PHYS-PUB-2015-048, 2015, https://cds.cern.ch/record/2103221. [63] J. Alwall, R. Frederix, S. Frixione, V. Hirschi, F. Maltoni, O. Mattelaer, H.-S. Shao, T. Stelzer, P. Torrielli, and M. Zaro, The automated computation of tree-level and nextto-leading order differential cross sections, and their G. AAD et al. PHYS. REV. D 108, 052003 (2023) 052003-22 matching to parton shower simulations, J. High Energy Phys. 07 (2014) 079. [64] J. Alwall, M. Herquet, F. Maltoni, O. Mattelaer, and T. Stelzer, M ad G raph 5: Going beyond, J. High Energy Phys. 06 (2011) 128. [65] C. Degrande, G. Durieux, F. Maltoni, K. Mimasu, E. Vryonidou, and C. Zhang, Automated one-loop computations in the standard model effective field theory, Phys. Rev. D 103, 096024 (2021). [66] G. Buchalla, M. Capozi, A. Celis, G. Heinrich, and L. Scyboz, Higgs boson pair production in non-linear effective field theory with full mt-dependence at NLO QCD, J. High Energy Phys. 09 (2018) 057. [67] ATLAS Collaboration, HEFT interpretations of Higgs boson pair searches in b¯ bγγ and b¯ bτþτ−final states and of their combination in ATLAS, Report No. ATL-PHYSPUB-2022-019, 2022, https://cds.cern.ch/record/2806411. [68] R. D. Ball et al. (The NNPDF Collaboration), Parton distributions for the LHC run II, J. High Energy Phys. 04 (2015) 040. [69] ATLAS Collaboration, Combination of searches for Higgs boson pairs in pp collisions at ffiffiffis p¼13 TeV with the ATLAS detector, Phys. Lett. B 800, 135103 (2020). [70] J. Baglio, A. Djouadi, R. Gröber, M. M. Mühlleitner, J. Quevillon, and M. Spira, The measurement of the Higgs self-coupling at the LHC: Theoretical status, J. High Energy Phys. 04 (2013) 151. [71] L.-S. Ling, R.-Y. Zhang, W.-G. Ma, L. Guo, W.-H. Li, and X.-Z. Li, NNLO QCD corrections to Higgs pair production via vector boson fusion at hadron colliders, Phys. Rev. D 89, 073001 (2014). [72] F. A. Dreyer and A. Karlberg, Fully differential vectorboson fusion Higgs pair production at next-to-next-toleading order, Phys. Rev. D 99, 074028 (2019). [73] J. M. Campbell, R. K. Ellis, P. Nason, and E. Re, Top-pair production and decay at NLO matched with parton showers, J. High Energy Phys. 04 (2015) 114. [74] M. Czakon and A. Mitov, T op++: A program for the calculation of the top-pair cross section at hadron colliders, Comput. Phys. Commun. 185, 2930 (2014). [75] ATLAS Collaboration, Improvements in t¯ tmodelling using NLO þPS Monte Carlo generators for run 2, Report No. ATL-PHYS-PUB-2018-009, 2018, https://cds.cern.ch/ record/2630327. [76] ATLAS Collaboration, The PYTHIA 8A3 tune description of ATLAS minimum bias and inelastic measurements incorporating the Donnachie–Landshoff diffractive model, Report No. ATL-PHYS-PUB-2016-017, 2016, https://cds .cern.ch/record/2206965. [77] D. J. Lange, The E vt G en particle decay simulation package, Nucl. Instrum. Methods Phys. Res., Sect. A 462, 152 (2001). [78] ATLAS Collaboration, Vertex reconstruction performance of the ATLAS detector at ffiffiffis p¼13 TeV, Report No. ATLPHYS-PUB-2015-026, 2015, https://cds.cern.ch/record/ 2037717. [79] ATLAS Collaboration, Jet reconstruction and performance using particle flow with the ATLAS detector, Eur. Phys. J. C77, 466 (2017). [80] ATLAS Collaboration, Jet energy scale and resolution measured in proton–proton collisions at ffiffiffis p¼13 TeV with the ATLAS detector, Eur.Phys.J.C81,689 (2020). [81] ATLAS Collaboration, Performance of pile-up mitigation techniques for jets in pp collisions at ffiffiffis p¼8TeV using the ATLAS detector, Eur. Phys. J. C 76,581 (2016). [82] ATLAS Collaboration, Topological cell clustering in the ATLAS calorimeters and its performance in LHC Run 1, Eur. Phys. J. C 77, 490 (2017). [83] ATLAS Collaboration, Selection of jets produced in 13 TeV proton–proton collisions with the ATLAS detector, Report No. ATLAS-CONF-2015-029, 2015, https://cds .cern.ch/record/2037702. [84] ATLAS Collaboration, ATLAS flavour-tagging algorithms for the LHC Run 2 pp collision dataset, arXiv:2211 .16345. [85] ATLAS Collaboration, Calibration of light-flavour b-jet mistagging rates using ATLAS proton–proton collision data at ffiffiffis p¼13 TeV, Report No. ATLAS-CONF-2018006, 2018, https://cds.cern.ch/record/2314418. [86] ATLAS Collaboration, Measurement of the c-jet mistagging efficiency in t¯ tevents using pp collision data at ffiffiffis p¼ 13 TeV collected with the ATLAS detector, Eur. Phys. J. C 82, 95 (2022). [87] ATLAS Collaboration, Muon reconstruction and identification efficiency in ATLAS using the full Run 2 pp collision data set at ffiffiffis p¼13 TeV, Eur. Phys. J. C 81, 578 (2021). [88] ATLAS Collaboration, Evidence for the H→b¯ bdecay with the ATLAS detector, J. High Energy Phys. 12 (2017) 024. [89] ATLAS Collaboration, Muon reconstruction performance of the ATLAS detector in proton–proton collision data at ffiffiffis p¼13 TeV, Eur. Phys. J. C 76, 292 (2016). [90] G. V. Moustakides and K. Basioti, Training neural networks for likelihood/density ratio estimation, arXiv:1911 .00405. [91] T. Kanamori, S. Hido, and M. Sugiyama, A least-squares approach to direct importance estimation, J. Mach. Learn. Res. 10, 1391 (2009), https://jmlr.csail.mit.edu/papers/ volume10/kanamori09a/kanamori09a.pdf. [92] V. Nair and G. E. Hinton, Rectified linear units improve restricted Boltzmann machines, in Proceedings of the 27th International Conference on International Conference on Machine Learning, ICML’10 (Omnipress, Haifa, Israel, 2010), p. 807, ISBN: 9781605589077, https://dl.acm.org/ doi/10.5555/3104322.3104425. [93] B. Lakshminarayanan, A. Pritzel, and C. Blundell, Simple and scalable predictive uncertainty estimation using deep ensembles, Proceedings of the 31st International Conference on Neural Information Processing Systems, NIPS’17 (2017), pp. 6405–6416, https://dl.acm.org/doi/10 .5555/3295222.3295387. [94] B. Efron, Bootstrap methods: Another look at the jackknife, Ann. Stat. 7, 1 (1979). [95] ATLAS Collaboration, Measurement of the Inelastic Proton–Proton Cross Section at ffiffiffis p¼13 TeV with the SEARCH FOR NONRESONANT PAIR PRODUCTION OF HIGGS …PHYS. REV. D 108, 052003 (2023) 052003-23 ATLAS Detector at the LHC, Phys. Rev. Lett. 117, 182002 (2016). [96] ATLAS Collaboration, ATLAS b-jet identification performance and efficiency measurement with t¯ tevents in pp collisions at ffiffiffis p¼13 TeV, Eur. Phys. J. C 79, 970 (2019). [97] ATLAS Collaboration, Luminosity determination in pp collisions at ffiffiffis p¼13 TeV using the ATLAS detector at the LHC, Report No. ATLAS-CONF-2019-021, 2019, https://cds.cern.ch/record/2677054. [98] G. Avoni et al., The new LUCID-2 detector for luminosity measurement and monitoring in ATLAS, J. Instrum. 13, P07017 (2018). [99] J. Baglio, F. Campanario, S. Glaus, M. Mühlleitner, J. Ronca, and M. Spira, gg →HH: Combined uncertainties, Phys. Rev. D 103, 056002 (2021). [100] W. Verkerke and D. Kirkby, The R oo F it toolkit for data modeling, arXiv:physics/0306116. [101] G. Cowan, K. Cranmer, E. Gross, and O. Vitells, Asymptotic formulae for likelihood-based tests of new physics, Eur. Phys. J. C 71, 1554 (2011);73, 2501(E) (2013). [102] A. L. Read, Presentation of search results: The CLS technique, J. Phys. G 28, 2693 (2002). [103] ATLAS Collaboration, ATLAS computing acknowledgements, Report No. ATL-SOFT-PUB-2021-003, 2021, https://cds.cern.ch/record/2776662. G. Aad ,102 B. Abbott ,120 K. Abeling ,55 S. H. Abidi ,29 A. Aboulhorma ,35e H. Abramowicz ,151 H. Abreu ,150 Y. Abulaiti ,117 A. C. Abusleme Hoffman ,137a B. S. Acharya ,69a,69b,b C. Adam Bourdarios ,4L. Adamczyk ,85a L. Adamek ,155 S. V. Addepalli ,26 J. Adelman ,115 A. Adiguzel ,21c S. Adorni ,56 T. Adye ,134 A. A. Affolder ,136 Y. Afik ,36 M. N. Agaras ,13 J. Agarwala ,73a,73b A. Aggarwal ,100 C. Agheorghiesei ,27c J. A. Aguilar-Saavedra ,130f A. Ahmad ,36 F. Ahmadov ,38,c W. S. Ahmed ,104 S. Ahuja ,95 X. Ai ,48 G. Aielli ,76a,76b M. Ait Tamlihat ,35e B. Aitbenchikh ,35a I. Aizenberg ,169 M. Akbiyik ,100 T. P. A. Åkesson ,98 A. V. Akimov ,37 K. Al Khoury ,41 G. L. Alberghi ,23b J. Albert ,165 P. Albicocco ,53 S. Alderweireldt ,52 M. Aleksa ,36 I. N. Aleksandrov ,38 C. Alexa ,27b T. Alexopoulos ,10 A. Alfonsi ,114 F. Alfonsi ,23b M. Alhroob ,120 B. Ali ,132 S. Ali ,148 M. Aliev ,37 G. Alimonti ,71a W. Alkakhi ,55 C. Allaire ,66 B. M. M. Allbrooke ,146 C. A. Allendes Flores ,137f P. P. Allport ,20 A. Aloisio ,72a,72b F. Alonso ,90 C. Alpigiani ,138 M. Alvarez Estevez ,99 A. Alvarez Fernandez ,100 M. G. Alviggi ,72a,72b M. Aly ,101 Y. Amaral Coutinho ,82b A. Ambler ,104 C. Amelung,36 M. Amerl ,1C. G. Ames ,109 D. Amidei ,106 S. P. Amor Dos Santos ,130a K. R. Amos ,163 V. Ananiev ,125 C. Anastopoulos ,139 T. Andeen ,11 J. K. Anders ,36 S. Y. Andrean ,47a,47b A. Andreazza ,71a,71b S. Angelidakis ,9A. Angerami ,41,d A. V. Anisenkov ,37 A. Annovi ,74a C. Antel ,56 M. T. Anthony ,139 E. Antipov ,145 M. Antonelli ,53 D. J. A. Antrim ,17a F. Anulli ,75a M. Aoki ,83 T. Aoki ,153 J. A. Aparisi Pozo ,163 M. A. Aparo ,146 L. Aperio Bella ,48 C. Appelt ,18 N. Aranzabal ,36 V. Araujo Ferraz ,82a C. Arcangeletti ,53 A. T. H. Arce ,51 E. Arena ,92 J-F. Arguin ,108 S. Argyropoulos ,54 J.-H. Arling ,48 A. J. Armbruster ,36 O. Arnaez ,4H. Arnold ,114 Z. P. Arrubarrena Tame,109 G. Artoni ,75a,75b H. Asada ,111 K. Asai ,118 S. Asai ,153 N. A. Asbah ,61 J. Assahsah ,35d K. Assamagan ,29 R. Astalos ,28a R. J. Atkin ,33a M. Atkinson,162 N. B. Atlay ,18 H. Atmani,62b P. A. Atmasiddha ,106 K. Augsten ,132 S. Auricchio ,72a,72b A. D. Auriol ,20 V. A. Austrup ,171 G. Avner ,150 G. Avolio ,36 K. Axiotis ,56 G. Azuelos ,108,e D. Babal ,28a H. Bachacou ,135 K. Bachas ,152,f A. Bachiu ,34 F. Backman ,47a,47b A. Badea ,61 P. Bagnaia ,75a,75b M. Bahmani ,18 A. J. Bailey ,163 V. R. Bailey ,162 J. T. Baines ,134 C. Bakalis ,10 O. K. Baker ,172 P. J. Bakker ,114 E. Bakos ,15 D. Bakshi Gupta ,8R. Balasubramanian ,114 E. M. Baldin ,37 P. Balek ,133 E. Ballabene ,71a,71b F. Balli ,135 L. M. Baltes ,63a W. K. Balunas ,32 J. Balz ,100 E. Banas ,86 M. Bandieramonte ,129 A. Bandyopadhyay ,24 S. Bansal ,24 L. Barak ,151 E. L. Barberio ,105 D. Barberis ,57b,57a M. Barbero ,102 G. Barbour,96 K. N. Barends ,33a T. Barillari ,110 M-S. Barisits ,36 T. Barklow ,143 P. Baron ,122 D. A. Baron Moreno ,101 A. Baroncelli ,62a G. Barone ,29 A. J. Barr ,126 L. Barranco Navarro ,47a,47b F. Barreiro ,99 J. Barreiro Guimarães da Costa ,14a U. Barron ,151 M. G. Barros Teixeira ,130a S. Barsov ,37 F. Bartels ,63a R. Bartoldus ,143 A. E. Barton ,91 P. Bartos ,28a A. Basan ,100 M. Baselga ,49 I. Bashta ,77a,77b A. Bassalat ,66,g M. J. Basso ,155 C. R. Basson ,101 R. L. Bates ,59 S. Batlamous,35e J. R. Batley ,32 B. Batool ,141 M. Battaglia ,136 D. Battulga ,18 M. Bauce ,75a,75b P. Bauer ,24 J. B. Beacham ,51 T. Beau ,127 P. H. Beauchemin ,158 F. Becherer ,54 P. Bechtle ,24 H. P. Beck ,19,h K. Becker ,167 A. J. Beddall ,21d V. A. Bednyakov ,38 C. P. Bee ,145 L. J. Beemster,15 T. A. Beermann ,36 M. Begalli ,82d M. Begel ,29 A. Behera ,145 J. K. Behr ,48 C. Beirao Da Cruz E Silva ,36 J. F. Beirer ,55,36 F. Beisiegel ,24 M. Belfkir ,159 G. Bella ,151 L. Bellagamba ,23b A. Bellerive ,34 P. Bellos ,20 K. Beloborodov ,37 N. L. Belyaev ,37 D. Benchekroun ,35a F. Bendebba ,35a Y. Benhammou ,151 D. P. Benjamin ,29 G. AAD et al. PHYS. REV. D 108, 052003 (2023) 052003-24 M. Benoit ,29 J. R. Bensinger ,26 S. Bentvelsen ,114 L. Beresford ,36 M. Beretta ,53 E. Bergeaas Kuutmann ,161 N. Berger ,4B. Bergmann ,132 J. Beringer ,17a S. Berlendis ,7G. Bernardi ,5C. Bernius ,143 F. U. Bernlochner ,24 T. Berry ,95 P. Berta ,133 A. Berthold ,50 I. A. Bertram ,91 S. Bethke ,110 A. Betti ,75a,75b A. J. Bevan ,94 M. Bhamjee ,33c S. Bhatta ,145 D. S. Bhattacharya ,166 P. Bhattarai ,26 V. S. Bhopatkar ,121 R. Bi,29,i R. M. Bianchi ,129 O. Biebel ,109 R. Bielski ,123 M. Biglietti ,77a T. R. V. Billoud ,132 M. Bindi ,55 A. Bingul ,21b C. Bini ,75a,75b A. Biondini ,92 C. J. Birch-sykes ,101 G. A. Bird ,20,134 M. Birman ,169 M. Biros ,133 T. Bisanz ,36 E. Bisceglie ,43b,43a D. Biswas ,170 A. Bitadze ,101 K. Bjørke ,125 I. Bloch ,48 C. Blocker ,26 A. Blue ,59 U. Blumenschein ,94 J. Blumenthal ,100 G. J. Bobbink ,114 V. S. Bobrovnikov ,37 M. Boehler ,54 D. Bogavac ,36 A. G. Bogdanchikov ,37 C. Bohm ,47a V. Boisvert ,95 P. Bokan ,48 T. Bold ,85a M. Bomben ,5M. Bona ,94 M. Boonekamp ,135 C. D. Booth ,95 A. G. Borb´ely ,59 H. M. Borecka-Bielska ,108 L. S. Borgna ,96 G. Borissov ,91 D. Bortoletto ,126 D. Boscherini ,23b M. Bosman ,13 J. D. Bossio Sola ,36 K. Bouaouda ,35a N. Bouchhar ,163 J. Boudreau ,129 E. V. Bouhova-Thacker ,91 D. Boumediene ,40 R. Bouquet ,5A. Boveia ,119 J. Boyd ,36 D. Boye ,29 I. R. Boyko ,38 J. Bracinik ,20 N. Brahimi ,62d G. Brandt ,171 O. Brandt ,32 F. Braren ,48 B. Brau ,103 J. E. Brau ,123 K. Brendlinger ,48 R. Brener ,169 L. Brenner ,114 R. Brenner ,161 S. Bressler ,169 D. Britton ,59 D. Britzger ,110 I. Brock ,24 G. Brooijmans ,41 W. K. Brooks ,137f E. Brost ,29 L. M. Brown ,165 T. L. Bruckler ,126 P. A. Bruckman de Renstrom ,86 B. Brüers ,48 D. Bruncko ,28b,a A. Bruni ,23b G. Bruni ,23b M. Bruschi ,23b N. Bruscino ,75a,75b T. Buanes ,16 Q. Buat ,138 A. G. Buckley ,59 I. A. Budagov ,38,a M. K. Bugge ,125 O. Bulekov ,37 B. A. Bullard ,143 S. Burdin ,92 C. D. Burgard ,49 A. M. Burger ,40 B. Burghgrave ,8J. T. P. Burr ,32 C. D. Burton ,11 J. C. Burzynski ,142 E. L. Busch ,41 V. Büscher ,100 P. J. Bussey ,59 J. M. Butler ,25 C. M. Buttar ,59 J. M. Butterworth ,96 W. Buttinger ,134 C. J. Buxo Vazquez,107 A. R. Buzykaev ,37 G. Cabras ,23b S. Cabrera Urbán ,163 D. Caforio ,58 H. Cai ,129 Y. Cai ,14a,14d V. M. M. Cairo ,36 O. Cakir ,3a N. Calace ,36 P. Calafiura ,17a G. Calderini ,127 P. Calfayan ,68 G. Callea ,59 L. P. Caloba,82b D. Calvet ,40 S. Calvet ,40 T. P. Calvet ,102 M. Calvetti ,74a,74b R. Camacho Toro ,127 S. Camarda ,36 D. Camarero Munoz ,26 P. Camarri ,76a,76b M. T. Camerlingo ,72a,72b D. Cameron ,125 C. Camincher ,165 M. Campanelli ,96 A. Camplani ,42 V. Canale ,72a,72b A. Canesse ,104 M. Cano Bret ,80 J. Cantero ,163 Y. Cao ,162 F. Capocasa ,26 M. Capua ,43b,43a A. Carbone ,71a,71b R. Cardarelli ,76a J. C. J. Cardenas ,8F. Cardillo ,163 T. Carli ,36 G. Carlino ,72a J. I. Carlotto ,13 B. T. Carlson ,129,j E. M. Carlson ,165,156a L. Carminati ,71a,71b M. Carnesale ,75a,75b S. Caron ,113 E. Carquin ,137f S. Carrá ,71a,71b G. Carratta ,23b,23a F. Carrio Argos ,33g J. W. S. Carter ,155 T. M. Carter ,52 M. P. Casado ,13,k A. F. Casha,155 M. Caspar ,48 E. G. Castiglia ,172 F. L. Castillo ,63a L. Castillo Garcia ,13 V. Castillo Gimenez ,163 N. F. Castro ,130a,130e A. Catinaccio ,36 J. R. Catmore ,125 V. Cavaliere ,29 N. Cavalli ,23b,23a V. Cavasinni ,74a,74b E. Celebi ,21a F. Celli ,126 M. S. Centonze ,70a,70b K. Cerny ,122 A. S. Cerqueira ,82a A. Cerri ,146 L. Cerrito ,76a,76b F. Cerutti ,17a A. Cervelli ,23b G. Cesarini ,53 S. A. Cetin ,21d Z. Chadi ,35a D. Chakraborty ,115 M. Chala ,130f J. Chan ,170 W. Y. Chan ,153 J. D. Chapman ,32 B. Chargeishvili ,149b D. G. Charlton ,20 T. P. Charman ,94 M. Chatterjee ,19 S. Chekanov ,6 S. V. Chekulaev ,156a G. A. Chelkov ,38,l A. Chen ,106 B. Chen ,151 B. Chen ,165 H. Chen ,14c H. Chen ,29 J. Chen ,62c J. Chen ,142 S. Chen ,153 S. J. Chen ,14c X. Chen ,62c X. Chen ,14b,m Y. Chen ,62a C. L. Cheng ,170 H. C. Cheng ,64a S. Cheong ,143 A. Cheplakov ,38 E. Cheremushkina ,48 E. Cherepanova ,114 R. Cherkaoui El Moursli ,35e E. Cheu ,7 K. Cheung ,65 L. Chevalier ,135 V. Chiarella ,53 G. Chiarelli ,74a N. Chiedde ,102 G. Chiodini ,70a A. S. Chisholm ,20 A. Chitan ,27b M. Chitishvili ,163 M. V. Chizhov ,38 K. Choi ,11 A. R. Chomont ,75a,75b Y. Chou ,103 E. Y. S. Chow ,114 T. Chowdhury ,33g L. D. Christopher ,33g K. L. Chu,64a M. C. Chu ,64a X. Chu ,14a,14d J. Chudoba ,131 J. J. Chwastowski ,86 D. Cieri ,110 K. M. Ciesla ,85a V. Cindro ,93 A. Ciocio ,17a F. Cirotto ,72a,72b Z. H. Citron ,169,n M. Citterio ,71a D. A. Ciubotaru,27b B. M. Ciungu ,155 A. Clark ,56 P. J. Clark ,52 J. M. Clavijo Columbie ,48 S. E. Clawson ,101 C. Clement ,47a,47b J. Clercx ,48 L. Clissa ,23b,23a Y. Coadou ,102 M. Cobal ,69a,69c A. Coccaro ,57b R. F. Coelho Barrue ,130a R. Coelho Lopes De Sa ,103 S. Coelli ,71a H. Cohen ,151 A. E. C. Coimbra ,71a,71b B. Cole ,41 J. Collot ,60 P. Conde Muiño ,130a,130g M. P. Connell ,33c S. H. Connell ,33c I. A. Connelly ,59 E. I. Conroy ,126 F. Conventi ,72a,o H. G. Cooke ,20 A. M. Cooper-Sarkar ,126 F. Cormier ,164 L. D. Corpe ,36 M. Corradi ,75a,75b F. Corriveau ,104,p A. Cortes-Gonzalez ,18 M. J. Costa ,163 F. Costanza ,4D. Costanzo ,139 B. M. Cote ,119 G. Cowan ,95 J. W. Cowley ,32 K. Cranmer ,117 S. Cr´ep´e-Renaudin ,60 F. Crescioli ,127 M. Cristinziani ,141 M. Cristoforetti ,78a,78b,q V. Croft ,114 G. Crosetti ,43b,43a A. Cueto ,36 T. Cuhadar Donszelmann ,160 H. Cui ,14a,14d Z. Cui ,7W. R. Cunningham ,59 F. Curcio ,43b,43a P. Czodrowski ,36 M. M. Czurylo ,63b SEARCH FOR NONRESONANT PAIR PRODUCTION OF HIGGS …PHYS. REV. D 108, 052003 (2023) 052003-25 S. Terzo ,13 M. Testa ,53 R. J. Teuscher ,155,p A. Thaler ,79 O. Theiner ,56 N. Themistokleous ,52 T. Theveneaux-Pelzer ,102 O. Thielmann ,171 D. W. Thomas,95 J. P. Thomas ,20 E. A. Thompson ,17a P. D. Thompson ,20 E. Thomson ,128 E. J. Thorpe ,94 Y. Tian ,55 V. Tikhomirov ,37,l Yu. A. Tikhonov ,37 S. Timoshenko,37 E. X. L. Ting ,1P. Tipton ,172 S. H. Tlou ,33g A. Tnourji ,40 K. Todome ,23b,23a S. Todorova-Nova ,133 S. Todt,50 M. Togawa ,83 J. Tojo ,89 S. Tokár ,28a K. Tokushuku ,83 O. Toldaiev ,68 R. Tombs ,32 M. Tomoto ,83,111 L. Tompkins ,143,v K. W. Topolnicki ,85b P. Tornambe ,103 E. Torrence ,123 H. Torres ,50 E. Torró Pastor ,163 M. Toscani ,30 C. Tosciri ,39 M. Tost ,11 D. R. Tovey ,139 A. Traeet,16 I. S. Trandafir ,27b T. Trefzger ,166 A. Tricoli ,29 I. M. Trigger ,156a S. Trincaz-Duvoid ,127 D. A. Trischuk ,26 B. Trocm´e, 60 C. Troncon ,71a L. Truong ,33c M. Trzebinski ,86 A. Trzupek ,86 F. Tsai ,145 M. Tsai ,106 A. Tsiamis ,152,ee P. V. Tsiareshka,37 S. Tsigaridas ,156a A. Tsirigotis ,152,ff V. Tsiskaridze ,145 E. G. Tskhadadze,149a M. Tsopoulou ,152,ee Y. Tsujikawa ,87 I. I. Tsukerman ,37 V. Tsulaia ,17a S. Tsuno ,83 O. Tsur,150 D. Tsybychev ,145 Y. Tu ,64b A. Tudorache ,27b V. Tudorache ,27b A. N. Tuna ,36 S. Turchikhin ,38 I. Turk Cakir ,3a R. Turra ,71a T. Turtuvshin ,38,oo P. M. Tuts ,41 S. Tzamarias ,152,ee P. Tzanis ,10 E. Tzovara ,100 K. Uchida,153 F. Ukegawa ,157 P. A. Ulloa Poblete ,137c E. N. Umaka ,29 G. Unal ,36 M. Unal ,11 A. Undrus ,29 G. Unel ,160 J. Urban ,28b P. Urquijo ,105 G. Usai ,8R. Ushioda ,154 M. Usman ,108 Z. Uysal ,21b L. Vacavant ,102 V. Vacek ,132 B. Vachon ,104 K. O. H. Vadla ,125 T. Vafeiadis ,36 A. Vaitkus ,96 C. Valderanis ,109 E. Valdes Santurio ,47a,47b M. Valente ,156a S. Valentinetti ,23b,23a A. Valero ,163 A. Vallier ,102,hh J. A. Valls Ferrer ,163 D. R. Van Arneman ,114 T. R. Van Daalen ,138 P. Van Gemmeren ,6M. Van Rijnbach ,125,36 S. Van Stroud ,96 I. Van Vulpen ,114 M. Vanadia ,76a,76b W. Vandelli ,36 M. Vandenbroucke ,135 E. R. Vandewall ,121 D. Vannicola ,151 L. Vannoli ,57b,57a R. Vari ,75a E. W. Varnes ,7C. Varni ,17a T. Varol ,148 D. Varouchas ,66 L. Varriale ,163 K. E. Varvell ,147 M. E. Vasile ,27b L. Vaslin,40 G. A. Vasquez ,165 F. Vazeille ,40 T. Vazquez Schroeder ,36 J. Veatch ,31 V. Vecchio ,101 M. J. Veen ,103 I. Veliscek ,126 L. M. Veloce ,155 F. Veloso ,130a,130c S. Veneziano ,75a A. Ventura ,70a,70b A. Verbytskyi ,110 M. Verducci ,74a,74b C. Vergis ,24 M. Verissimo De Araujo ,82b W. Verkerke ,114 J. C. Vermeulen ,114 C. Vernieri ,143 P. J. Verschuuren ,95 M. Vessella ,103 M. C. Vetterli ,142,e A. Vgenopoulos ,152,ee N. Viaux Maira ,137f T. Vickey ,139 O. E. Vickey Boeriu ,139 G. H. A. Viehhauser ,126 L. Vigani ,63b M. Villa ,23b,23a M. Villaplana Perez ,163 E. M. Villhauer,52 E. Vilucchi ,53 M. G. Vincter ,34 G. S. Virdee ,20 A. Vishwakarma ,52 C. Vittori ,36 I. Vivarelli ,146 V. Vladimirov,167 E. Voevodina ,110 F. Vogel ,109 P. Vokac ,132 J. Von Ahnen ,48 E. Von Toerne ,24 B. Vormwald ,36 V. Vorobel ,133 K. Vorobev ,37 M. Vos ,163 K. Voss ,141 J. H. Vossebeld ,92 M. Vozak ,114 L. Vozdecky ,94 N. Vranjes ,15 M. Vranjes Milosavljevic ,15 M. Vreeswijk ,114 R. Vuillermet ,36 O. Vujinovic ,100 I. Vukotic ,39 S. Wada ,157 C. Wagner,103 J. M. Wagner ,17a W. Wagner ,171 S. Wahdan ,171 H. Wahlberg ,90 R. Wakasa ,157 M. Wakida ,111 J. Walder ,134 R. Walker ,109 W. Walkowiak ,141 A. M. Wang ,61 A. Z. Wang ,170 C. Wang ,100 C. Wang ,62c H. Wang ,17a J. Wang ,64a R.-J. Wang ,100 R. Wang ,61 R. Wang ,6S. M. Wang ,148 S. Wang ,62b T. Wang ,62a W. T. Wang ,80 X. Wang ,14c X. Wang ,162 X. Wang ,62c Y. Wang ,62d Y. Wang ,14c Z. Wang ,106 Z. Wang ,62d,51,62c Z. Wang ,106 A. Warburton ,104 R. J. Ward ,20 N. Warrack ,59 A. T. Watson ,20 H. Watson ,59 M. F. Watson ,20 G. Watts ,138 B. M. Waugh ,96 A. F. Webb ,11 C. Weber ,29 H. A. Weber ,18 M. S. Weber ,19 S. M. Weber ,63a C. Wei,62a Y. Wei ,126 A. R. Weidberg ,126 E. J. Weik ,117 J. Weingarten ,49 M. Weirich ,100 C. Weiser ,54 C. J. Wells ,48 T. Wenaus ,29 B. Wendland ,49 T. Wengler ,36 N. S. Wenke,110 N. Wermes ,24 M. Wessels ,63a K. Whalen ,123 A. M. Wharton ,91 A. S. White ,61 A. White ,8M. J. White ,1D. Whiteson ,160 L. Wickremasinghe ,124 W. Wiedenmann ,170 C. Wiel ,50 M. Wielers ,134 C. Wiglesworth ,42 L. A. M. Wiik-Fuchs ,54 D. J. Wilbern,120 H. G. Wilkens ,36 D. M. Williams ,41 H. H. Williams,128 S. Williams ,32 S. Willocq ,103 P. J. Windischhofer ,39 F. Winklmeier ,123 B. T. Winter ,54 J. K. Winter ,101 M. Wittgen,143 M. Wobisch ,97 R. Wölker ,126 J. Wollrath,160 M. W. Wolter ,86 H. Wolters ,130a,130c V. W. S. Wong ,164 A. F. Wongel ,48 S. D. Worm ,48 B. K. Wosiek ,86 K. W. Woźniak ,86 K. Wraight ,59 J. Wu ,14a,14d M. Wu ,64a M. Wu ,113 S. L. Wu ,170 X. Wu ,56 Y. Wu ,62a Z. Wu ,135,62a J. Wuerzinger ,110 T. R. Wyatt ,101 B. M. Wynne ,52 S. Xella ,42 L. Xia ,14c M. Xia ,14b J. Xiang ,64c X. Xiao ,106 M. Xie ,62a X. Xie ,62a S. Xin ,14a,14d J. Xiong ,17a I. Xiotidis,146 D. Xu ,14a H. Xu,62a H. Xu ,62a L. Xu ,62a R. Xu ,128 T. Xu ,106 Y. Xu ,14b Z. Xu ,62b Z. Xu ,14a B. Yabsley ,147 S. Yacoob ,33a N. Yamaguchi ,89 Y. Yamaguchi ,154 H. Yamauchi ,157 T. Yamazaki ,17a Y. Yamazaki ,84 J. Yan,62c S. Yan ,126 Z. Yan ,25 H. J. Yang ,62c,62d H. T. Yang ,62a S. Yang ,62a T. Yang ,64c X. Yang ,62a X. Yang ,14a Y. Yang ,44 Y. Yang ,62a Z. Yang ,62a,106 W-M. Yao ,17a Y. C. Yap ,48 H. Ye ,14c H. Ye ,55 J. Ye ,44 S. Ye ,29 X. Ye ,62a Y. Yeh ,96 G. AAD et al. PHYS. REV. D 108, 052003 (2023) 052003-32 I. Yeletskikh ,38 B. K. Yeo ,17a M. R. Yexley ,91 P. Yin ,41 K. Yorita ,168 S. Younas ,27b C. J. S. Young ,54 C. Young ,143 Y. Yu ,62a M. Yuan ,106 R. Yuan ,62b,pp L. Yue ,96 M. Zaazoua ,35e B. Zabinski ,86 E. Zaid,52 T. Zakareishvili ,149b N. Zakharchuk ,34 S. Zambito ,56 J. A. Zamora Saa ,137d,137b J. Zang ,153 D. Zanzi ,54 O. Zaplatilek ,132 C. Zeitnitz ,171 J. C. Zeng ,162 D. T. Zenger Jr. ,26 O. Zenin ,37 T. Ženiš,28a S. Zenz ,94 S. Zerradi ,35a D. Zerwas ,66 M. Zhai ,14a,14d B. Zhang ,14c D. F. Zhang ,139 J. Zhang ,62b J. Zhang ,6K. Zhang ,14a,14d L. Zhang ,14c P. Zhang,14a,14d R. Zhang ,170 S. Zhang ,106 T. Zhang ,153 X. Zhang ,62c X. Zhang ,62b Y. Zhang ,62c,5 Y. Zhang ,96 Z. Zhang ,17a Z. Zhang ,66 H. Zhao ,138 P. Zhao ,51 T. Zhao ,62b Y. Zhao ,136 Z. Zhao ,62a A. Zhemchugov ,38 X. Zheng ,62a Z. Zheng ,143 D. Zhong ,162 B. Zhou,106 C. Zhou ,170 H. Zhou ,7N. Zhou ,62c Y. Zhou,7C. G. Zhu ,62b H. L. Zhu ,62a J. Zhu ,106 Y. Zhu ,62c Y. Zhu ,62a X. Zhuang ,14a K. Zhukov ,37 V. Zhulanov ,37 N. I. Zimine ,38 J. Zinsser ,63b M. Ziolkowski ,141 L. Živković,15 A. Zoccoli ,23b,23a K. Zoch ,56 T. G. Zorbas ,139 O. Zormpa ,46 W. Zou ,41 and L. Zwalinski 36 (ATLAS Collaboration) 1Department of Physics, University of Adelaide, Adelaide, Australia 2Department of Physics, University of Alberta, Edmonton, Alberta, Canada 3aDepartment of Physics, Ankara University, Ankara, Türkiye 3bDivision of Physics, TOBB University of Economics and Technology, Ankara, Türkiye 4LAPP, Universit´e Savoie Mont Blanc, CNRS/IN2P3, Annecy, France 5APC, Universit´e Paris Cit´e, CNRS/IN2P3, Paris, France 6High Energy Physics Division, Argonne National Laboratory, Argonne, Illinois, USA 7Department of Physics, University of Arizona, Tucson, Arizona, USA 8Department of Physics, University of Texas at Arlington, Arlington, Texas, USA 9Physics Department, National and Kapodistrian University of Athens, Athens, Greece 10Physics Department, National Technical University of Athens, Zografou, Greece 11Department of Physics, University of Texas at Austin, Austin, Texas, USA 12Institute of Physics, Azerbaijan Academy of Sciences, Baku, Azerbaijan 13Institut de Física d’Altes Energies (IFAE), Barcelona Institute of Science and Technology, Barcelona, Spain 14aInstitute of High Energy Physics, Chinese Academy of Sciences, Beijing, China 14bPhysics Department, Tsinghua University, Beijing, China 14cDepartment of Physics, Nanjing University, Nanjing, China 14dUniversity of Chinese Academy of Science (UCAS), Beijing, China 15Institute of Physics, University of Belgrade, Belgrade, Serbia 16Department for Physics and Technology, University of Bergen, Bergen, Norway 17aPhysics Division, Lawrence Berkeley National Laboratory, Berkeley, California, USA 17bUniversity of California, Berkeley, California, USA 18Institut für Physik, Humboldt Universität zu Berlin, Berlin, Germany 19Albert Einstein Center for Fundamental Physics and Laboratory for High Energy Physics, University of Bern, Bern, Switzerland 20School of Physics and Astronomy, University of Birmingham, Birmingham, United Kingdom 21aDepartment of Physics, Bogazici University, Istanbul, Türkiye 21bDepartment of Physics Engineering, Gaziantep University, Gaziantep, Türkiye 21cDepartment of Physics, Istanbul University, Istanbul, Türkiye 21dIstinye University, Sariyer, Istanbul, Türkiye 22aFacultad de Ciencias y Centro de Investigaciónes, Universidad Antonio Nariño, Bogotá, Colombia 22bDepartamento de Física, Universidad Nacional de Colombia, Bogotá, Colombia 23aDipartimento di Fisica e Astronomia A. Righi, Universit`a di Bologna, Bologna, Italy 23bINFN Sezione di Bologna, Bologna, Italy 24Physikalisches Institut, Universität Bonn, Bonn, Germany 25Department of Physics, Boston University, Boston, Massachusetts, USA 26Department of Physics, Brandeis University, Waltham, Massachusetts, USA 27aTransilvania University of Brasov, Brasov, Romania 27bHoria Hulubei National Institute of Physics and Nuclear Engineering, Bucharest, Romania 27cDepartment of Physics, Alexandru Ioan Cuza University of Iasi, Iasi, Romania 27dNational Institute for Research and Development of Isotopic and Molecular Technologies, Physics Department, Cluj-Napoca, Romania SEARCH FOR NONRESONANT PAIR PRODUCTION OF HIGGS …PHYS. REV. D 108, 052003 (2023) 052003-33 27eUniversity Politehnica Bucharest, Bucharest, Romania 27fWest University in Timisoara, Timisoara, Romania 27gFaculty of Physics, University of Bucharest, Bucharest, Romania 28aFaculty of Mathematics, Physics and Informatics, Comenius University, Bratislava, Slovak Republic 28bDepartment of Subnuclear Physics, Institute of Experimental Physics of the Slovak Academy of Sciences, Kosice, Slovak Republic 29Physics Department, Brookhaven National Laboratory, Upton, New York, USA 30Universidad de Buenos Aires, Facultad de Ciencias Exactas y Naturales, Departamento de Física, y CONICET, Instituto de Física de Buenos Aires (IFIBA), Buenos Aires, Argentina 31California State University, Fresno, California, USA 32Cavendish Laboratory, University of Cambridge, Cambridge, United Kingdom 33aDepartment of Physics, University of Cape Town, Cape Town, South Africa 33biThemba Labs, Western Cape, South Africa 33cDepartment of Mechanical Engineering Science, University of Johannesburg, Johannesburg, South Africa 33dNational Institute of Physics, University of the Philippines Diliman (Philippines), Quezon, Philippines 33eUniversity of South Africa, Department of Physics, Pretoria, South Africa 33fUniversity of Zululand, KwaDlangezwa, South Africa 33gSchool of Physics, University of the Witwatersrand, Johannesburg, South Africa 34Department of Physics, Carleton University, Ottawa, Ontario, Canada 35aFacult´e des Sciences Ain Chock, R´eseau Universitaire de Physique des Hautes Energies—Universit´e Hassan II, Casablanca, Morocco 35bFacult´e des Sciences, Universit´e Ibn-Tofail, K´enitra, Morocco 35cFacult´e des Sciences Semlalia, Universit´e Cadi Ayyad, LPHEA-Marrakech, Morocco 35dLPMR, Facult´e des Sciences, Universit´e Mohamed Premier, Oujda, Morocco 35eFacult´e des sciences, Universit´e Mohammed V, Rabat, Morocco 35fInstitute of Applied Physics, Mohammed VI Polytechnic University, Ben Guerir, Morocco 36CERN, Geneva, Switzerland 37Affiliated with an institute covered by a cooperation agreement with CERN 38Affiliated with an international laboratory covered by a cooperation agreement with CERN 39Enrico Fermi Institute, University of Chicago, Chicago, Illinois, USA 40LPC, Universit´e Clermont Auvergne, CNRS/IN2P3, Clermont-Ferrand, France 41Nevis Laboratory, Columbia University, Irvington, New York, USA 42Niels Bohr Institute, University of Copenhagen, Copenhagen, Denmark 43aDipartimento di Fisica, Universit`a della Calabria, Rende, Italy 43bINFN Gruppo Collegato di Cosenza, Laboratori Nazionali di Frascati, Italy 44Physics Department, Southern Methodist University, Dallas, Texas, USA 45Physics Department, University of Texas at Dallas, Richardson, Texas, USA 46National Centre for Scientific Research “Demokritos,”Agia Paraskevi, Greece 47aDepartment of Physics, Stockholm University, Stockholm, Sweden 47bOskar Klein Centre, Stockholm, Sweden 48Deutsches Elektronen-Synchrotron DESY, Hamburg and Zeuthen, Germany 49Fakultät Physik, Technische Universität Dortmund, Dortmund, Germany 50Institut für Kernund Teilchenphysik, Technische Universität Dresden, Dresden, Germany 51Department of Physics, Duke University, Durham, North Carolina, USA 52SUPA—School of Physics and Astronomy, University of Edinburgh, Edinburgh, United Kingdom 53INFN e Laboratori Nazionali di Frascati, Frascati, Italy 54Physikalisches Institut, Albert-Ludwigs-Universität Freiburg, Freiburg, Germany 55II. Physikalisches Institut, Georg-August-Universität Göttingen, Göttingen, Germany 56D´epartement de Physique Nucl´eaire et Corpusculaire, Universit´e de Gen`eve, Gen`eve, Switzerland 57aDipartimento di Fisica, Universit`a di Genova, Genova, Italy 57bINFN Sezione di Genova, Genova, Italy 58II. Physikalisches Institut, Justus-Liebig-Universität Giessen, Giessen, Germany 59SUPA—School of Physics and Astronomy, University of Glasgow, Glasgow, United Kingdom 60LPSC, Universit´e Grenoble Alpes, CNRS/IN2P3, Grenoble INP, Grenoble, France 61Laboratory for Particle Physics and Cosmology, Harvard University, Cambridge, Illinois, USA 62aDepartment of Modern Physics and State Key Laboratory of Particle Detection and Electronics, University of Science and Technology of China, Hefei, China 62bInstitute of Frontier and Interdisciplinary Science and Key Laboratory of Particle Physics and Particle Irradiation (MOE), Shandong University, Qingdao, China G. AAD et al. PHYS. REV. D 108, 052003 (2023) 052003-34 62cSchool of Physics and Astronomy, Shanghai Jiao Tong University, Key Laboratory for Particle Astrophysics and Cosmology (MOE), SKLPPC, Shanghai, China 62dTsung-Dao Lee Institute, Shanghai, China 63aKirchhoff-Institut für Physik, Ruprecht-Karls-Universität Heidelberg, Heidelberg, Germany 63bPhysikalisches Institut, Ruprecht-Karls-Universität Heidelberg, Heidelberg, Germany 64aDepartment of Physics, Chinese University of Hong Kong, Shatin, N.T., Hong Kong, China 64bDepartment of Physics, University of Hong Kong, Hong Kong, China 64cDepartment of Physics and Institute for Advanced Study, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong, China 65Department of Physics, National Tsing Hua University, Hsinchu, Taiwan 66IJCLab, Universit´e Paris-Saclay, CNRS/IN2P3, 91405, Orsay, France 67Centro Nacional de Microelectrónica (IMB-CNM-CSIC), Barcelona, Spain 68Department of Physics, Indiana University, Bloomington, Indiana, USA 69aINFN Gruppo Collegato di Udine, Sezione di Trieste, Udine, Italy 69bICTP, Trieste, Italy 69cDipartimento Politecnico di Ingegneria e Architettura, Universit`a di Udine, Udine, Italy 70aINFN Sezione di Lecce, Lecce, Italy 70bDipartimento di Matematica e Fisica, Universit`a del Salento, Lecce, Italy 71aINFN Sezione di Milano, Milano, Italy 71bDipartimento di Fisica, Universit`a di Milano, Milano, Italy 72aINFN Sezione di Napoli, Napoli, Italy 72bDipartimento di Fisica, Universit`a di Napoli, Napoli, Italy 73aINFN Sezione di Pavia, Pavia, Italy 73bDipartimento di Fisica, Universit`a di Pavia, Pavia, Italy 74aINFN Sezione di Pisa, Pisa, Italy 74bDipartimento di Fisica E. Fermi, Universit`a di Pisa, Pisa, Italy 75aINFN Sezione di Roma, Roma, Italy 75bDipartimento di Fisica, Sapienza Universit`a di Roma, Roma, Italy 76aINFN Sezione di Roma Tor Vergata, Roma, Italy 76bDipartimento di Fisica, Universit`a di Roma Tor Vergata, Roma, Italy 77aINFN Sezione di Roma Tre, Roma, Italy 77bDipartimento di Matematica e Fisica, Universit`a Roma Tre, Roma, Italy 78aINFN-TIFPA, Trento, Italy 78bUniversit`a degli Studi di Trento, Trento, Italy 79Universität Innsbruck, Department of Astro and Particle Physics, Innsbruck, Austria 80University of Iowa, Iowa City, Iowa, USA 81Department of Physics and Astronomy, Iowa State University, Ames, Iowa, USA 82aDepartamento de Engenharia El´etrica, Universidade Federal de Juiz de Fora (UFJF), Juiz de Fora, Brazil 82bUniversidade Federal do Rio De Janeiro COPPE/EE/IF, Rio de Janeiro, Brazil 82cInstituto de Física, Universidade de São Paulo, São Paulo, Brazil 82dRio de Janeiro State University, Rio de Janeiro, Brazil 83KEK, High Energy Accelerator Research Organization, Tsukuba, Japan 84Graduate School of Science, Kobe University, Kobe, Japan 85aAGH University of Science and Technology, Faculty of Physics and Applied Computer Science, Krakow, Poland 85bMarian Smoluchowski Institute of Physics, Jagiellonian University, Krakow, Poland 86Institute of Nuclear Physics Polish Academy of Sciences, Krakow, Poland 87Faculty of Science, Kyoto University, Kyoto, Japan 88Kyoto University of Education, Kyoto, Japan 89Research Center for Advanced Particle Physics and Department of Physics, Kyushu University, Fukuoka, Japan 90Instituto de Física La Plata, Universidad Nacional de La Plata and CONICET, La Plata, Argentina 91Physics Department, Lancaster University, Lancaster, United Kingdom 92Oliver Lodge Laboratory, University of Liverpool, Liverpool, United Kingdom 93Department of Experimental Particle Physics, Jožef Stefan Institute and Department of Physics, University of Ljubljana, Ljubljana, Slovenia 94School of Physics and Astronomy, Queen Mary University of London, London, United Kingdom 95Department of Physics, Royal Holloway University of London, Egham, United Kingdom 96Department of Physics and Astronomy, University College London, London, United Kingdom SEARCH FOR NONRESONANT PAIR PRODUCTION OF HIGGS …PHYS. REV. D 108, 052003 (2023) 052003-35 97Louisiana Tech University, Ruston, Louisiana, USA 98Fysiska institutionen, Lunds universitet, Lund, Sweden 99Departamento de Física Teorica C-15 and CIAFF, Universidad Autónoma de Madrid, Madrid, Spain 100Institut für Physik, Universität Mainz, Mainz, Germany 101School of Physics and Astronomy, University of Manchester, Manchester, United Kingdom 102CPPM, Aix-Marseille Universit´e, CNRS/IN2P3, Marseille, France 103Department of Physics, University of Massachusetts, Amherst, Massachusetts, USA 104Department of Physics, McGill University, Montreal, Quebec, Canada 105School of Physics, University of Melbourne, Victoria, Australia 106Department of Physics, University of Michigan, Ann Arbor, Michigan, USA 107Department of Physics and Astronomy, Michigan State University, East Lansing, Michigan, USA 108Group of Particle Physics, University of Montreal, Montreal, Quebec, Canada 109Fakultät für Physik, Ludwig-Maximilians-Universität München, München, Germany 110Max-Planck-Institut für Physik (Werner-Heisenberg-Institut), München, Germany 111Graduate School of Science and Kobayashi-Maskawa Institute, Nagoya University, Nagoya, Japan 112Department of Physics and Astronomy, University of New Mexico, Albuquerque, New Mexico, USA 113Institute for Mathematics, Astrophysics and Particle Physics, Radboud University/Nikhef, Nijmegen, Netherlands 114Nikhef National Institute for Subatomic Physics and University of Amsterdam, Amsterdam, Netherlands 115Department of Physics, Northern Illinois University, DeKalb, Illinois, USA 116aNew York University Abu Dhabi, Abu Dhabi, United Arab Emirates 116bUniversity of Sharjah, Sharjah, United Arab Emirates 117Department of Physics, New York University, New York, New York, USA 118Ochanomizu University, Otsuka, Bunkyo-ku, Tokyo, Japan 119The Ohio State University, Columbus, Ohio, USA 120Homer L. Dodge Department of Physics and Astronomy, University of Oklahoma, Norman, Oklahoma, USA 121Department of Physics, Oklahoma State University, Stillwater, Oklahoma, USA 122Palacký University, Joint Laboratory of Optics, Olomouc, Czech Republic 123Institute for Fundamental Science, University of Oregon, Eugene, Oregon, USA 124Graduate School of Science, Osaka University, Osaka, Japan 125Department of Physics, University of Oslo, Oslo, Norway 126Department of Physics, Oxford University, Oxford, United Kingdom 127LPNHE, Sorbonne Universit´e, Universit´e Paris Cit´e, CNRS/IN2P3, Paris, France 128Department of Physics, University of Pennsylvania, Philadelphia, Pennsylvania, USA 129Department of Physics and Astronomy, University of Pittsburgh, Pittsburgh, Pennsylvania, USA 130aLaboratório de Instrumentação e Física Experimental de Partículas—LIP, Lisboa, Portugal 130bDepartamento de Física, Faculdade de Ciências, Universidade de Lisboa, Lisboa, Portugal 130cDepartamento de Física, Universidade de Coimbra, Coimbra, Portugal 130dCentro de Física Nuclear da Universidade de Lisboa, Lisboa, Portugal 130eDepartamento de Física, Universidade do Minho, Braga, Portugal 130fDepartamento de Física Teórica y del Cosmos, Universidad de Granada, Granada, Spain 130gDepartamento de Física, Instituto Superior T´ecnico, Universidade de Lisboa, Lisboa, Portugal 131Institute of Physics of the Czech Academy of Sciences, Prague, Czech Republic 132Czech Technical University in Prague, Prague, Czech Republic 133Charles University, Faculty of Mathematics and Physics, Prague, Czech Republic 134Particle Physics Department, Rutherford Appleton Laboratory, Didcot, United Kingdom 135IRFU, CEA, Universit´e Paris-Saclay, Gif-sur-Yvette, France 136Santa Cruz Institute for Particle Physics, University of California Santa Cruz, Santa Cruz, California, USA 137aDepartamento de Física, Pontificia Universidad Católica de Chile, Santiago, Chile 137bMillennium Institute for Subatomic physics at high energy frontier (SAPHIR), Santiago, Chile 137cInstituto de Investigación Multidisciplinario en Ciencia y Tecnología, y Departamento de Física, Universidad de La Serena, La Serena, Chile 137dUniversidad Andres Bello, Department of Physics, Santiago, Chile 137eInstituto de Alta Investigación, Universidad de Tarapacá, Arica, Chile 137fDepartamento de Física, Universidad T´ecnica Federico Santa María, Valparaíso, Chile 138Department of Physics, University of Washington, Seattle, Washington, USA 139Department of Physics and Astronomy, University of Sheffield, Sheffield, United Kingdom 140Department of Physics, Shinshu University, Nagano, Japan G. AAD et al. PHYS. REV. D 108, 052003 (2023) 052003-36 141Department Physik, Universität Siegen, Siegen, Germany 142Department of Physics, Simon Fraser University, Burnaby, British Columbia, Canada 143SLAC National Accelerator Laboratory, Stanford, California, USA 144Department of Physics, Royal Institute of Technology, Stockholm, Sweden 145Departments of Physics and Astronomy, Stony Brook University, Stony Brook, New York, USA 146Department of Physics and Astronomy, University of Sussex, Brighton, United Kingdom 147School of Physics, University of Sydney, Sydney, Australia 148Institute of Physics, Academia Sinica, Taipei, Taiwan 149aE. Andronikashvili Institute of Physics, Iv. Javakhishvili Tbilisi State University, Tbilisi, Georgia 149bHigh Energy Physics Institute, Tbilisi State University, Tbilisi, Georgia 149cUniversity of Georgia, Tbilisi, Georgia 150Department of Physics, Technion, Israel Institute of Technology, Haifa, Israel 151Raymond and Beverly Sackler School of Physics and Astronomy, Tel Aviv University, Tel Aviv, Israel 152Department of Physics, Aristotle University of Thessaloniki, Thessaloniki, Greece 153International Center for Elementary Particle Physics and Department of Physics, University of Tokyo, Tokyo, Japan 154Department of Physics, Tokyo Institute of Technology, Tokyo, Japan 155Department of Physics, University of Toronto, Toronto, Ontario, Canada 156aTRIUMF, Vancouver, British Columbia, Canada 156bDepartment of Physics and Astronomy, York University, Toronto, Ontario, Canada 157Division of Physics and Tomonaga Center for the History of the Universe, Faculty of Pure and Applied Sciences, University of Tsukuba, Tsukuba, Japan 158Department of Physics and Astronomy, Tufts University, Medford, Massachusetts, USA 159United Arab Emirates University, Al Ain, United Arab Emirates 160Department of Physics and Astronomy, University of California Irvine, Irvine, California, USA 161Department of Physics and Astronomy, University of Uppsala, Uppsala, Sweden 162Department of Physics, University of Illinois, Urbana, Illinois, USA 163Instituto de Física Corpuscular (IFIC), Centro Mixto Universidad de Valencia—CSIC, Valencia, Spain 164Department of Physics, University of British Columbia, Vancouver, British Columbia, Canada 165Department of Physics and Astronomy, University of Victoria, Victoria, British Columbia, Canada 166Fakultät für Physik und Astronomie, Julius-Maximilians-Universität Würzburg, Würzburg, Germany 167Department of Physics, University of Warwick, Coventry, United Kingdom 168Waseda University, Tokyo, Japan 169Department of Particle Physics and Astrophysics, Weizmann Institute of Science, Rehovot, Israel 170Department of Physics, University of Wisconsin, Madison, Wisconsin, USA 171Fakultät für Mathematik und Naturwissenschaften, Fachgruppe Physik, Bergische Universität Wuppertal, Wuppertal, Germany 172Department of Physics, Yale University, New Haven, Connecticut, USA aDeceased. bAlso at Department of Physics, King’s College London, London, United Kingdom. cAlso at Institute of Physics, Azerbaijan Academy of Sciences, Baku, Azerbaijan. dAlso at Lawrence Livermore National Laboratory, Livermore, California, USA. eAlso at TRIUMF, Vancouver, British Columbia, Canada. fAlso at Department of Physics, University of Thessaly, Greece. gAlso at An-Najah National University, Nablus, Palestine. hAlso at Department of Physics, University of Fribourg, Fribourg, Switzerland. iAlso at University of Colorado Boulder, Department of Physics, Boulder, Colorado, USA. jAlso at Department of Physics, Westmont College, Santa Barbara, California, USA. kAlso at Departament de Fisica de la Universitat Autonoma de Barcelona, Barcelona, Spain. lAlso at Affiliated with an institute covered by a cooperation agreement with CERN. mAlso at The Collaborative Innovation Center of Quantum Matter (CICQM), Beijing, China. nAlso at Department of Physics, Ben Gurion University of the Negev, Beer Sheva, Israel. oAlso at Universit`a di Napoli Parthenope, Napoli, Italy. pAlso at Institute of Particle Physics (IPP), Canada. qAlso at Bruno Kessler Foundation, Trento, Italy. rAssociated at SUPA—School of Physics and Astronomy, University of Glasgow, Glasgow, United Kingdom. sAlso at Borough of Manhattan Community College, City University of New York, New York, New York, USA. tAlso at National Institute of Physics, University of the Philippines Diliman (Philippines), Philippines. uAlso at Department of Financial and Management Engineering, University of the Aegean, Chios, Greece. SEARCH FOR NONRESONANT PAIR PRODUCTION OF HIGGS …PHYS. REV. D 108, 052003 (2023) 052003-37 vAlso at Department of Physics, Stanford University, Stanford, California, USA. wAlso at Centro Studi e Ricerche Enrico Fermi, Italy. xAlso at Department of Physics, California State University, East Bay, Hayward, California, USA. yAlso at Institucio Catalana de Recerca i Estudis Avancats, ICREA, Barcelona, Spain. zAlso at Technical University of Munich, Munich, Germany. aaAlso at University of Chinese Academy of Sciences (UCAS), Beijing, China. bbAlso at Yeditepe University, Physics Department, Istanbul, Türkiye. ccAlso at Institute of Theoretical Physics, Ilia State University, Tbilisi, Georgia. ddAlso at CERN, Geneva, Switzerland. eeAlso at Center for Interdisciplinary Research and Innovation (CIRI-AUTH), Thessaloniki, Greece. ffAlso at Hellenic Open University, Patras, Greece. ggAlso at Center for High Energy Physics, Peking University, China. hhAlso at L2IT, Universit´e de Toulouse, CNRS/IN2P3, UPS, Toulouse, France. iiAlso at Department of Physics, California State University, Sacramento, California, USA. jjAlso at D´epartement de Physique Nucl´eaire et Corpusculaire, Universit´e de Gen`eve, Gen`eve, Switzerland. kkAlso at Washington College, Chestertown, Maryland, USA. llAssociated at Durham University, IPPP, Durham, United Kingdom. mmAlso at Institut für Experimentalphysik, Universität Hamburg, Hamburg, Germany. nnAlso at Institute of Applied Physics, Mohammed VI Polytechnic University, Ben Guerir, Morocco. ooAlso at Institute of Physics and Technology, Ulaanbaatar, Mongolia. ppAlso at Department of Physics and Astronomy, Michigan State University, East Lansing, Michigan, USA. qqAlso at Institute for Nuclear Research and Nuclear Energy (INRNE) of the Bulgarian Academy of Sciences, Sofia, Bulgaria. G. AAD et al. PHYS. REV. D 108, 052003 (2023) 052003-38