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Journal of High Energy Physics. 2024 Nov 15;2024(11):97
The Author(s)
ATLAS Collaboration
Measurements of the Higgs boson production times decay rates and differential cross-sections have recently been performed by the ATLAS experiment in several decay channels using up to 139 fb−1 of proton-proton collision data at s = 13 TeV recorded at the Large Hadron Collider. This paper presents multiple interpretations of these Higgs boson measurements. Measurements of production-mode cross-sections, simplified template cross-sections and fiducial differential cross-sections in different decay channels are reparameterised in terms of the impact of Standard Model effective field theory operators, and constraints are reported on the corresponding Wilson coefficients. Production and decay rate measurements are interpreted in UV-complete extensions of the Standard Model, namely the two-Higgs-doublet model (2HDM) near the alignment limit and the Minimal Supersymmetric Standard Model (MSSM) for various MSSM benchmark scenarios. The constraints on the 2HDM parameters (cos(β − α), tanβ) and the MSSM parameters (mA, tanβ) are complementary to those obtained from direct searches for additional Higgs bosons.
JHEP11(2024)097PuAlished for SISS Ay SpringerReceived: February 9, 2024Revised: September 13, 2024Accepted: October 13, 2024Published: November 15, 2024Interpretations of the ATLAS measurements of Higgsboson production and decay rates and differentialcross-sections in pp collisions at √s = 13TeVThe ATLAS collaborationE-mail: atlas.publications@cern.chAbstract: Measurements of the Higgs boson production times decay rates and differentialcross-sections have recently been performed by the ATLAS experiment in several decaychannels using up to 139 fb−1 of proton-proton collision data at√s = 13TeV recorded at theLarge Hadron Collider. This paper presents multiple interpretations of these Higgs bosonmeasurements. Measurements of production-mode cross-sections, simplified template cross-sections and fiducial differential cross-sections in different decay channels are reparameterisedin terms of the impact of Standard Model effective field theory operators, and constraints arereported on the corresponding Wilson coefficients. Production and decay rate measurementsare interpreted in UV-complete extensions of the Standard Model, namely the two-Higgs-doublet model (2HDM) near the alignment limit and the Minimal Supersymmetric StandardModel (MSSM) for various MSSM benchmark scenarios. The constraints on the 2HDMparameters (cos(β − α), tanβ) and the MSSM parameters (mA, tanβ) are complementary tothose obtained from direct searches for additional Higgs bosons.Keywords: Hadron-Hadron Scattering , Higgs PhysicsArXiv ePrint: 2402.05742Open Access, Copyright CERN,for the benefit of the ATLAS Collaboration.Article funded by SCOAP3.https://doi.org/10.1007/JHEP11(2024)097JHEP11(2024)097Contents1 Introduction 12 Measurements of Higgs boson cross-sections 32.1 Data samples 32.2 Simulation of the Standard Model signal 32.3 Signal yield parameterisation 53 Interpretations based on SM effective field theory 123.1 Methodology of effective field theory interpretations 123.2 Constraints from STXS measurements 203.3 Constraints from fiducial differential measurements 384 Interpretations based on UV-complete BSM models 414.1 Constraints on two-Higgs-doublet models 414.2 Constraints on the MSSM 485 Conclusions 56A Validity of Gaussian approximation of STXS measurements in the SMEFTinterpretation 58The ATLAS collaboration 701 IntroductionSince a particle (H) with attributes consistent with those of the Higgs boson [1–6] ofthe Standard Model (SM) of particle physics was discovered [7, 8] by the ATLAS andCMS experiments, its properties have been measured with proton-proton (pp) collisiondata produced by the Large Hadron Collider (LHC) at CERN. The ATLAS and CMSCollaborations recently presented their first results on the combination of Higgs bosonproduction and decay rate measurements with up to 139 fb−1 of 13TeV pp collision data [9, 10],collected during the full LHC Run 2 in the years 2015 through 2018. Two interpretationsof the ATLAS measurements are presented here. The first one is based on an effectivefield theory (EFT) framework of the Standard Model. The second interpretation relies onspecific theories that provide ultraviolet (UV) completions of the SM, specifically severalbenchmark scenarios within the two-Higgs doublet model (2HDM) [11–14] or within a minimalsupersymmetric extension of the Standard Model (MSSM) [15–19].In addition to the production and decay rates mentioned above, the fiducial differentialcross-sections for Higgs boson production as a function of selected event kinematics have beenmeasured by the ATLAS Collaboration with the same data sample in the H→ZZ∗→ 4ℓ (ℓ =e,µ) [20] and H → γγ [21] decay channels, among others [22, 23]. The fiducial differential– 1 –JHEP11(2024)097cross-sections measured as a function of the total transverse momentum1 of the Higgs bosondecay products in the two decay channels, p4ℓT and pγγT , are used in this paper to constrainanomalous Higgs boson couplings to gluons and top quarks, and an anomalous Higgs-gluon-top-antitop quark coupling, within the same EFT framework. These couplings are also probedusing the EFT interpretation of Higgs boson production and decay rate measurements; thesensitivities obtained with the two approaches are compared.Effective field theories provide a model-independent approach to describe new physics athigh mass scales, systematically improvable with higher-order perturbative calculations, toparametrise the effects of candidate theories beyond the Standard Model (BSM) that reduceto the Standard Model at low energies. In the SM Effective Field Theory (SMEFT), the effectsof BSM dynamics at energy scales Λ that are large in comparison to the vacuum-expectation-value (vev) v of the SM Higgs field (Λ≫ v) can be parameterised at low energies, E ≪ Λ,in terms of higher-dimensional operators that are built up from the Standard Model fieldsand respect its symmetries. Measurements of (fiducial) cross-sections can be used to placeconstraints on the Wilson coefficients associated with the SMEFT operators, correspondingto limits on BSM physics at some fixed scale Λ.The methodology employed here for the EFT interpretation of the combined measurementsof Higgs boson production and decay rates is similar to the one used by the individual analyses.The interpretation is applied to the combined measurements of the Higgs boson productioncross-sections times branching ratios in the following decay channels: H → ZZ∗(→ 4ℓ),H → γγ, H → bb, H → ττ , H → WW ∗(→ eνµν), H → Zγ, and H → µµ [24–34].A similar approach is used for the interpretation of the fiducial pT-differential cross-sections in the H→ZZ∗→ 4ℓ and H → γγ channels. For this study the pT distributionwas chosen as it was previously measured in both channels and is sensitive to anoma-lous Higgs boson couplings to top-quarks and gluons. The method resembles closely thatdescribed in ref. [21] for the joint interpretation of five differential cross-sections in theH → γγ decay channel in terms of a few dimension-6 SMEFT operators, but only thecross-section measurements as a function of p4ℓT and pγγT are used, and a smaller num-ber of operators is probed. On the other hand, the joint interpretation with a seconddecay channel with similar statistical precision increases the sensitivity to the probedBSM operators.In the interpretations presented in the second part of this paper, performed in the contextof UV-complete BSM theories, two additional measurements of production and decay rates,based on a partial Run 2 data sample collected in the years 2015 and 2016, are considered:H → WW ∗ in the WH and ZH production modes [35], and H → multileptons in thett¯H production mode [36]. In the latter, the selection requirement of two prompt leptonsprimarily selects H → WW ∗ and H → ττ decays, with a small additional contributionof H → ZZ∗ decays.1ATLAS uses a right-handed coordinate system with its origin at the nominal interaction point (IP) in thecentre of the detector and the z-axis along the beam pipe. The x-axis points from the IP to the centre ofthe LHC ring, and the y-axis points upwards. Cylindrical coordinates (r,ϕ) are used in the transverse plane,ϕ being the azimuthal angle around the z-axis. The pseudorapidity is defined in terms of the polar angleθ as η = − ln tan(θ/2). Angular distance is measured in units of ∆R ≡√(∆η)2 + (∆ϕ)2. The transversemomentum pT is the momentum component in the transverse plane.– 2 –JHEP11(2024)097In a previous publication [37], measurements were interpreted within the hMSSMmodel [38]. In this paper, in addition to the hMSSM model, seven more recent bench-mark MSSM scenarios [39, 40] are tested. In addition, an interpretation within the 2HDMnear the alignment limit, in which the light neutral Higgs boson of the 2HDM is SM-like,2is also reported. These constraints are compared with those inferred from the limits on theSMEFT Wilson coefficients after matching the 2HDM parameters to the SMEFT operators.The paper is structured as follows. Section 2 gives an overview of the Higgs bosonproduction-mode cross-sections and decay rate measurements and of the fiducial differentialcross-section measurements that are used to derive the results presented. Section 3, devotedto the EFT interpretation of the measurements, starts with a description of the generalapproach of deriving limits on Wilson coefficients (section 3.1). This is followed by the detailsof the specific choices of Wilson coefficients probed in the interpretations of the combinedmeasurements of Higgs boson production-mode cross-sections and decay rates (section 3.2) orof the measurements of the fiducial differential cross-sections as a function of pHT (section 3.3),together with the corresponding constraints. The interpretations in UV-complete extensionsof the SM are detailed in section 4. The approach taken to interpret the Higgs bosonproduction-mode cross-sections and decay rate measurements in terms of constraints on theparameters of the 2HDM or the MSSM, and the derived results, are described in sections 4.1and 4.2, respectively. Finally, section 5 presents the conclusions.2 Measurements of Higgs boson cross-sections2.1 Data samplesThe results presented in this article are based on up to 139 fb−1 of pp collision data collectedby the ATLAS detector [41–43] in the years 2015 to 2018, with the LHC operating at a centre-of-mass energy of 13TeV. The decay channels, targeted production modes and integratedluminosity of the data sample used in each input analysis are summarised in table 1, wherethe simplified template cross-section measurements labelled ‘STXS’ are identical to those usedin ref. [9]. The analyses used for this interpretation were published while the uncertainty inthe combined 2015–2018 integrated luminosity was 1.7%. It was derived from the calibrationof the luminosity scale using x–y beam-separation scans, following a methodology similar tothat detailed in ref. [44], and using the LUCID-2 detector [45] for the baseline luminositymeasurements. Subsequently an improved estimate of the integrated luminosity was made [46],with a slightly higher central value (+0.8%) and half the uncertainty (0.8%). The resultsdescribed in the following sections assume the older, less precise luminosity calibration; theywould not be significantly affected if recomputed using the latest one.2.2 Simulation of the Standard Model signalMonte Carlo (MC) simulated event samples of SM Higgs bosons produced in pp collisions anddecaying into the final states considered in this study were generated and normalised to SMpredictions calculated for a Higgs boson mass mH = 125.09 GeV [48]. For each Higgs boson2The terms SM-like and analogous ones are used throughout this paper to denote particles with similarproperties to those of the named particle.– 3 –JHEP11(2024)097Analysis L Reference Binning SMEFT 2HDM andDecay channel Production mode [fb−1] (h)MSSMH → γγ (ggF, VBF, WH, ZH, ttH, tH) 139 [25] STXS-1.2 ✓ ✓[21] differential ✓(subset)H → ZZ∗ (ZZ∗ → 4ℓ: ggF, VBF, WH + ZH, ttH + tH) 139 [24] STXS-1.2 ✓ ✓[20] differential ✓(subset)(ZZ∗ → ℓℓνν¯/ℓℓqq¯: ttH multileptons) 36.1 [36] STXS-0∗ ✓H → ττ (ggF, VBF, WH + ZH, ttH + tH) 139 [31] STXS-1.2 ✓ ✓(ttH multileptons) 36.1 [36] STXS-0∗ ✓H →WW ∗ (ggF, VBF) 139 [32] STXS-1.2 ✓ ✓(WH, ZH) 36.1 [47] STXS-0∗ ✓(ttH multileptons) 36.1 [36] STXS-0∗ ✓H → bb (WH, ZH) 139 [26, 27] STXS-1.2 ✓ ✓(VBF) 126 [28] STXS-1.2 ✓ ✓(ttH + tH) 139 [30] STXS-1.2 ✓ ✓(boosted Higgs bosons: inclusive production) 139 [29] STXS-1.2 ✓ ✓H → Zγ (inclusive production) 139 [33] STXS-0∗ ✓ ✓H → µµ (ggF+ ttH + tH, VBF+WH + ZH) 139 [34] STXS-0∗ ✓ ✓Table 1. The decay channels (1st column), targeted production modes (2nd column) and integratedluminosity L (3rd column) of the data sample used for each analysis included in the combinedmeasurements of Higgs boson production and decay rates, couplings and simplified template cross-sections (labelled as ‘STXS’ in the ‘Binning’ column), or in the measurements of fiducial pT-differentialcross-sections (labelled as ‘differential’ in the ‘Binning’ column). The references for the input analyses(5th column) and information about which input analyses are considered for the SMEFT-basedinterpretation (6th column) and the interpretations in terms of UV-complete models (7th column) arealso provided. The STXS-0∗ binning only distinguishes inclusive production processes, whereas theSTXS-1.2 and differential binnings partition production processes in kinematic regions at a varyinglevel of granularity. The full definitions of these binning schemes for the measurements and thecorresponding signal yield parameterisations are detailed in section 2.3. In all the analyses, the tinyexpected contribution from associated bb¯H production is applied as a correction to ggF as describedin the text.decay mode, the branching ratio that was used corresponds to the theoretical calculationat the highest available order of accuracy in perturbation theory [49].Higgs boson production via gluon-gluon fusion was simulated using the PowhegBox v2 [50–53] NNLOPS implementation [54, 55]. The event generator uses HNNLO [56] toreweight the inclusive Higgs boson rapidity distribution produced by the next-to-leading-order(NLO) generation of pp→ H + parton events, with the scale of each parton emission deter-mined using the MiNLO procedure [57]. The PDF4LHC15 [58] next-to-next-to-leading-order(NNLO) parton distribution functions (PDFs) were used for the central prediction and uncer-tainty, except for the H → bb¯ and H → Zγ measurements, which used the NNPDF3.0 [59]NNLO PDFs. The sample is normalised such that it reproduces the total cross-section pre-dicted by a next-to-next-to-next-to-leading-order (N3LO) quantum chromodynamics (QCD)calculation with NLO electroweak (EW) corrections applied [49, 60–63]. The NNLOPSgenerator reproduces the Higgs boson pT distribution predicted by the NNLO plus next-to-– 4 –JHEP11(2024)097next-to-leading logarithm (NNLL) calculation of Hres2.3 [64], which includes the effects oftop- and bottom-quark masses and uses dynamical renormalisation and factorisation scales.The VBF and qq¯ → V H (gg → ZH) production processes were simulated at NLO(LO) accuracy in QCD using the Powheg Box v2 [65] generator where the simulation ofqq¯ → V H relies on improved NLO calculations [66]. The PDF4LHC15 NLO set of PDFswas used, except for the H → bb¯ and H → Zγ measurements, which used the NNPDF3.0NLO PDFs. In the vector-boson fusion (VBF) H → bb¯ analysis, NLO EW corrections werecalculated using MadGraph5_aMC@NLO 3.0 and applied as a function of the generatedHiggs boson transverse momentum. The VBF sample is normalised to an approximate-NNLOQCD cross-section with NLO EW corrections applied [49, 67–69]. The V H samples arenormalised to cross-sections calculated at NNLO in QCD with NLO EW corrections [70, 71]and additional NLO QCD corrections [72] for the gg → ZH subprocess [49].Higgs boson production in association with a top-antitop quark pair (ttH) was sim-ulated at NLO accuracy in QCD using the Powheg Box v2 generator, except for theH → µµ analysis and the measurements based on 36.1 fb−1 of data, which used the Mad-Graph5_aMC@NLO 2.6 [73] generator. The PDF4LHC15 NLO set of PDFs was used in theH → γγ and H→ZZ∗→ 4ℓ analyses, while the NNPDF3.0 (N)NLO set of PDFs was usedin the other ones. In all cases, the sample is normalised to a calculation with NLO QCD andEW corrections [49, 74–78]. Higgs boson production in association with a single top quark inthe t-channel (tHq) or with an additional W boson (tHW ) were simulated at NLO accuracyusing MadGraph5_aMC@NLO 2.6 and either the NNPDF3.0(N)NLO PDF set or theCT10 NLO PDF set. The two tH samples are normalised to NLO QCD calculations [49, 79].All parton-level events were input to Pythia 8.2 [80] to model the Higgs boson decay,parton showering, hadronisation, and multiple parton interactions. The generators wereinterfaced to Pythia 8.2 using the AZNLO [81] or A14 [82] sets of tuned parameters (tunes).Particle-level events were passed through a Geant 4 [83] simulation of the ATLASdetector [84] and reconstructed using the same analysis software as used for the data.Event pile-up was included in the simulation by overlaying inelastic pp collisions, such thatthe distribution of the average number of interactions per bunch crossing reproduces thatobserved in the data. The inelastic pp collisions were simulated with Pythia 8.1 using theMSTW2008LO [85] set of PDFs with the A2 tune [86], or using the NNPDF2.3LO [87]set of PDFs with the A3 tune [88].2.3 Signal yield parameterisationIn all analyses listed in table 1, the likelihood function for each signal region k, with oneor more bins r, is modelled asL(Nk|µ,θ) =∏rPoisson(Nk,r|sk(µ,θ) · fk,rs (θ) + bk,r(θ)), (2.1)where Nk,r is the observed event count of bin r in region k, sk is the expected signal countin region k, fk,rs is the expected fraction of the signal in region k that is contained in bin r,and bk,r represents the expected event count from background processes. The ensemble ofparameters of interest µ describes the Higgs boson signal normalisation, while θ representsthe set of nuisance parameters taking into account the systematic uncertainties that originate– 5 –JHEP11(2024)097from theoretical and experimental sources, as well as additional degrees of freedom withoutprior constraints such as background yields or normalisations in some of the input channels.The full likelihood function is then the product of the likelihood functions for each signalregion k and of Gaussian or log-normal probability density functions that constrain thenuisance parameters.Depending on the level of detail implemented in each analysis, the signal yield parametersµ can be indexed by Higgs boson production process (i), decay mode (X), and fiducialphase space region defined at the particle level (k′). Analysis region k, defined at thereconstruction level, is typically chosen to match the particle-level region k′ as closely aspossible, to reduce the extrapolation uncertainty. As reconstruction-level selections do notgenerally correspond exactly to particle-level regions, multiple particle-level regions willcontribute to the signal yield sk.For the measurements listed in table 1, two distinct signal parameterisation strategiesare followed as defined in eq. (2.2) and eq. (2.3). For analyses labelled as ‘STXS-0∗’ or‘STXS-1.2’, the signal yield for region k is modelled as a scale factor µi,k′,Xk applied to the SMHiggs boson production cross-section times branching ratio, for each Higgs boson productionprocess i and decay X, in a fiducial region k′ defined at the particle level. Alternatively,for analyses labelled as ‘differential’, the signal yield is modelled as a cross-section σk′,Xfid.describing the sum of all production processes, separately for each Higgs boson decay modeX and fiducial region k′ defined at the particle level. The corresponding parameterisationsof the signal yield sk in terms of the parameters of interest µk = {µi,k′,Xk } or {µk′,Xk } andof the nuisance parameters θ are:sSTXSk (µk,θ) = L ×∑i,k′,Xµi,k′,Xk × (σ × B)i,k′,XSM,(N(N))NLO(θ)× ϵi,k′,XSTXS,k(θ), (2.2)sdiff.k (µk,θ) = L ×∑k′,Xµk′,Xk × σk′,XSM,fid.(θ)× ϵk′,Xdiff.,k(θ), (2.3)where L is the integrated luminosity, (σ × B)i,k′,XSM,(N(N))NLO is the calculation, at the highestavailable order, of the SM Higgs boson cross-section for the production process i in particle-level region k′ multiplied by the SM Higgs boson branching ratio to the final state X, andσSM,fid. is the SM Higgs boson production cross-section for the fiducial region k′, summed overall production modes. The factors ϵi,k′,XSTXS,k and ϵk′,Xdiff.,k represent the products of acceptancetimes efficiency of the reconstruction-level region k for the particle-level fiducial phase spaceregion k′ and Higgs boson decay X (in production mode i for the STXS interpretation).For each interpretation based on a particular model (SMEFT, 2HDM, or MSSM) with avector of model parameters α, the original signal parameters µ are replaced with expressionsthat parameterise the model predictions, i.e., µ→ µ(α), so that the likelihood of eq. (2.1)is directly expressed in terms of the parameters α. Then, constraints on these parameterscan be directly inferred from the modified likelihood expression. The model-specific re-parameterisations of the signal parameters are detailed in sections 3 and 4.The acceptance factors ϵi,k′,XSTXS,k and ϵk′,Xdiff.,k, as well as the signal bin fractions fk,rs , arederived assuming SM Higgs boson kinematics. For interpretations of the measurements inphysics models that significantly alter kinematic distributions, additional correction factors– 6 –JHEP11(2024)097may be needed to account for changes in the acceptance and signal shape as a function ofBSM model parameters. These are discussed when applicable in sections 3 and 4.2.3.1 Fiducial differential cross-section measurementsFor the interpretation of fiducial differential cross-section measurements in the H→ γγ andH→ZZ∗→ 4ℓ analyses, the differential distributions in the transverse momentum of theHiggs boson decay products are considered. The H→ZZ∗→ 4ℓ analysis defines nine analysisregions with boundaries in p4ℓT at{0, 10, 20, 30, 45, 60, 80, 120, 200, 300} GeV,whereas theH→ γγ analysis defines a finer granularity with 20 analysis regions with boundariesin pγγT at{0, 5, 10, 15, 20, 25, 30, 35, 45, 60, 80, 100, 120, 140, 170, 200, 250, 300, 450, 650, 13000} GeV,resulting in a total of 29 fiducial cross-section measurements that are interpreted in section 3.3.Further details of these analyses, including the full definitions of the fiducial regions, canbe found in refs. [20, 21].2.3.2 Production and decay rate and simplified template cross-sectionmeasurementsFor the interpretations based on the SMEFT framework presented in section 3, measurementsof ‘simplified template cross-sections’ of various Higgs boson production processes in theregions of phase space defined within the STXS framework [49, 89–91] are used. The inclusiveproduction process classes defined at ‘Stage-0’ in the STXS scheme are bbH production, ttHand tH processes, qq → Hqq processes (with contributions from both VBF production andquark-initiated V H production with a hadronic decay of the gauge boson), WH and ZHproduction (including gg → ZH , followed by any leptonic decay of the vector boson V (lep)H)and finally the gg → H process, consisting of ggF and gg → ZH, Z → qq¯ production.Since the acceptances for gg → H and bbH production are similar for all input analyses,the bbH production mode is modelled as a 1% increase of the gg → H yield in each regionof production phase space [49]. Theory uncertainties for the gg → H, qq → Hqq, andttH processes are defined as in refs. [24, 25], while those of the V (lep)H process follow thescheme described in ref. [92].The analyses listed in table 1 as using the ‘STXS-0∗’ binning provide measurements ofthe scale factors µi,X for the product of the inclusive cross-section of one or more productionmodes i, with i = ggF, VBF, WH, ZH, ttH, tH,3 and branching ratio of the Higgs bosondecay mode X. Analyses of the most sensitive production modes performed with the fullRun 2 data sample, labelled ‘STXS-1.2’ in table 1, report measurements of signal yield scalefactors in the more fine-grained ‘Stage-1.2’ definition of Higgs boson production cross-sections.3The classification of production modes used here differs in one respect from the Stage-0 STXS definition: inthe STXS definition qq → V H(qq) production and VBF production are both labelled as a common qq → Hqqproduction mode, whereas these production modes are labelled separately here, based on the correspondingdefinition/settings of the MC event generators.– 7 –JHEP11(2024)097At Stage-1.2, the Stage-0 regions are partitioned in particle-level kinematic volumes, forinstance in a few coarse intervals of Higgs boson transverse momentum (pHT ), which are helpfulfor distinguishing momentum-dependent and momentum-independent SMEFT operators.The ensemble of parameters µi,k′,XSTXS−1.2 describes deviations in differential distributions, withthe level of detail controlled by the number of particle-level regions that are defined. Theprecision with which the more fine-grained set of scale factors µi,k′,XSTXS−1.2 can be measureddepends on the design of the analysis and the amount of available data. As individualanalyses provide only limited sensitivity to some of the Stage-1.2 categories with the currentdata sample, some of these categories are merged compared to the Stage-1.2 definitionsgiven in ref. [49]. Details of the merged category definitions in each analysis are providedin refs. [24–32]. The grouping of the production modes for STXS-0∗ and STXS-1.2 regionsis also shown in the second column of table 1.After merging, a total of 78 signal yield parameters are extracted from the STXSmeasurements listed in table 1. The kinematic definitions of these 78 STXS signal yieldparameters, along with their measured signal strengths (i.e., their ratios to the correspondingSM predictions) and uncertainties, are shown in figures 1–3. While the data underlying themeasurements in these figures is the same as that used for the interpretation of the combinedHiggs boson measurements shown in ref. [9], the granularity of the STXS model used hereis substantially larger, providing additional constraining power for the parameters of theSMEFT interpretation of the data. The χ2 for the compatibility between the observed valuesand the SM hypothesis is 50 for 78 degrees of freedom, corresponding to a p-value of 99.4%.For the MSSM and tree-level 2HDM interpretations of section 4, no predictions areavailable for all production modes for the full STXS Stage-1.2 phase space partitioning.In this case, the interpretation is performed based on the STXS-0∗ production mode scalefactors measured by each input analysis.– 8 –JHEP11(2024)09710− 8− 6− 4− 2− 0 2 4 6 8 x B normalized to SM valueσTotal Stat.Syst. SMATLAS-1 = 13 TeV, 139 fbs| < 2.5Hy = 125.09 GeV, |Hm (WW*)H→gg (WW*)Hqq→qq (ZZ*)H→gg (ZZ*)Hqq→qq (ZZ*)VH-lep (ZZ*)Htt Total Stat. Syst. < 200 GeVHTp0-jet, 0.15−0.16+ 0.08± 0.17−0.18+ 1.27 ( ) , < 60 GeVHTp1-jet, 0.50−0.51+ 0.29−0.30+ 0.58−0.59+ 0.66 ( ) , < 120 GeVHTp ≤1-jet, 60 0.33−0.37+ 0.32± 0.46−0.49+ 0.68 ( ) , < 200 GeVHTp ≤1-jet, 120 0.44−0.62+ 0.62−0.63+ 0.76−0.89+ 1.43 ( ) , < 200 GeVHTp 2-jet, ≥ 0.72−0.85+ 0.42−0.43+ 0.84−0.95+ 1.54 ( ), 200 GeV≥ HTp 0.44−0.65+ 0.62−0.63+ 0.76−0.91+ 1.37 ( ) , < 200 GeVHTp < 700 GeV, jjm ≤ 2-jet, 350 ≥ 0.41± 0.41−0.45+ 0.58−0.60+ 0.12 )( , < 200 GeVHTp < 1000 GeV, jjm ≤ 2-jet, 700 ≥ 0.33−0.37+ 0.51−0.57+ 0.61−0.68+ 0.57 )( , < 200 GeVHTp < 1500 GeV, jjm ≤ 2-jet, 1000 ≥ 0.24−0.40+ 0.45−0.50+ 0.51−0.64+ 1.32 )( , < 200 GeVHTp 1500 GeV, ≥ jjm 2-jet, ≥ 0.17−0.23+ 0.38−0.42+ 0.42−0.48+ 1.19 )( , 200 GeV≥ HTp 350 GeV, ≥ jjm 2-jet, ≥ 0.22−0.34+ 0.46−0.51+ 0.51−0.61+ 1.54 )( , < 10 GeVHTp0-jet, 0.13−0.19+ 0.27−0.30+ 0.30−0.36+ 0.93 )( , < 200 GeVHTp ≤0-jet, 10 0.11−0.14+ 0.17−0.18+ 0.20−0.23+ 1.15 )( , < 60 GeVHTp1-jet, 0.13−0.16+ 0.36−0.40+ 0.38−0.43+ 0.31 )( , < 120 GeVHTp ≤1-jet, 60 0.18−0.30+ 0.38−0.42+ 0.42−0.52+ 1.42 )( , < 200 GeVHTp ≤1-jet, 120 0.08−0.23+ 0.58−0.80+ 0.59−0.84+ 0.41 )( , < 200 GeVHTp 2-jet, ≥0.14−0.23+ 0.51−0.55+ 0.53−0.60+ 0.35 )( , 200 GeV≥ HTp0.31−0.75+ 1.04−1.32+ 1.09−1.52+ 2.41 )( , VBF 0.09−0.17+ 0.50−0.61+ 0.50−0.63+ 1.49 ( ) , < 120 GeVjjm 2-jet, 60 < ≥ 0.29−0.45+ 2.22−2.79+ 2.24−2.83+ 1.51 ( ) , 200 GeV≥ HTp 350 GeV, ≥ jjm 2-jet, ≥  0.18+  2.08+  2.09+ 0.18 ( ) , ( 0.01−0.15+ 1.05−1.67+ 1.05−1.67+ 1.29 ) , 0.18−0.39+ 1.13−1.72+ 1.14−1.77+ 1.73 ( ),Figure 1. Measured signal strength for each of the H → WW ∗ and H → ZZ∗ STXS categoriesincluded in the combination. In the H → ZZ∗ analysis, V H production events with the vector bosonV decaying into leptons are assigned to the V H-lep category. In one category the negative uncertaintyis truncated, as indicated by the hatched region, which corresponds to cross-section values for whichthe total yield prediction in an analysis region is negative. In that case, the negative uncertainty andits breakdown in terms of statistical and systematic components are not reported, and replaced witha long dash (–).– 9 –JHEP11(2024)0978− 6− 4− 2− 0 2 4 6 8 10 x B normalized to SM valueσTotal Stat.Syst. SMATLAS-1 = 13 TeV, 139 fbs| < 2.5Hy = 125.09 GeV, |Hm)γγ (H→gg)γγ (Hqq→qq)γγ (νHl→qq)γγ (ννHll/→gg/qq)γγ (Htt)γγ (tH)γ(Z H Total Stat. Syst. < 10 GeVHTp0-jet, 0.09−0.12+ 0.24± 0.26−0.27+ 0.66 ( ), < 200 GeVHTp ≤0-jet, 10 0.08−0.10+ 0.15± 0.17−0.18+ 1.24 ( ) , < 60 GeVHTp1-jet, 0.11−0.13+ 0.36± 0.38−0.39+ 1.16 ( ), < 120 GeVHTp ≤1-jet, 60 0.15−0.22+ 0.33± 0.36−0.40+ 1.14 ( ), < 200 GeVHTp ≤1-jet, 120 0.10−0.20+ 0.52−0.53+ 0.53−0.57+ 0.93 ( ), < 120 GeVHTp < 350 GeV, jjm 2-jet, ≥ 0.14−0.19+ 0.52−0.53+ 0.54−0.56+ 0.58 ( ), < 200 GeVHTp ≤ < 350 GeV, 120 jjm 2-jet, ≥ 0.09−0.15+ 0.47−0.48+ 0.48−0.50+ 1.31 ( ), < 200 GeVHTp 350 GeV, ≥ jjm 2-jet, ≥ 0.34−0.30+ 0.89−0.91+ 0.95± 1.09 ( ) , < 300 GeVHTp ≤200 0.13−0.18+ 0.39−0.41+ 0.41−0.45+ 1.56 ( ) , < 450 GeVHTp ≤300 0.15−0.14+ 0.47−0.54+ 0.49−0.56+ 0.17 ( ) , 450 GeV≥ HTp0.23−0.41+ 1.15−1.42+ 1.18−1.47+ 2.11 ( ) , -vetoVH 1-jet and ≤0.18−0.32+ 0.84−0.90+ 0.86−0.96+ 1.05 ( ),-hadVH 2-jet, ≥0.12−0.14+ 0.62−0.72+ 0.63−0.74+ 0.21 ( ), < 200 GeVHTp < 700 GeV, jjm ≤ 2-jet, 350 ≥ 0.23−0.51+ 0.56−0.61+ 0.60−0.80+ 1.28 ( ) , < 200 GeVHTp < 1000 GeV, jjm ≤ 2-jet, 700 ≥ 0.23−0.43+ 0.64−0.72+ 0.68−0.84+ 1.47 ( ), < 200 GeVHTp 1000 GeV, ≥ jjm 2-jet, ≥ 0.20−0.29+ 0.33−0.36+ 0.38−0.46+ 1.31 ( ), 200 GeV≥ HTp < 1000 GeV, jjm ≤ 2-jet, 350 ≥ 0.11−0.13+ 0.59−0.73+ 0.61−0.74+ 0.31 ( ), 200 GeV≥ HTp 1000 GeV, ≥ jjm 2-jet, ≥ 0.23−0.28+ 0.52−0.61+ 0.57−0.67+ 1.69 ( ), < 150 GeVVTp ( ) , 0.09−0.16+ 0.72−0.80+ 0.73−0.82+ 1.75 150 GeV≥ VTp ( ) , 0.10−0.13+ 0.89−1.11+ 0.90−1.12+ 1.65 < 150 GeVVTp , ( ) 0.13+  0.87+  0.88+ -0.64 150 GeV≥ VTp , ( )0.18−0.21+ 0.91−1.08+ 0.92−1.10+ 0.39 < 60 GeVHTp , ( )0.05−0.11+ 0.68−0.81+ 0.69−0.82+ 0.83 < 120 GeVHTp ≤60 , ( )0.04−0.08+ 0.50−0.59+ 0.51−0.60+ 0.81 < 200 GeVHTp ≤120 , ( )0.08−0.13+ 0.53−0.63+ 0.54−0.64+ 0.65 < 300 GeVHTp ≤200 , ( )0.06−0.11+ 0.65−0.80+ 0.65−0.81+ 1.23 300 GeV≥ HTp , ( )0.12−0.16+ 0.74−0.95+ 0.75−0.96+ 1.17 , ( )0.90−1.22+ 3.14−3.94+ 3.27−4.13+ 2.06 0.33−0.41+ 0.87−0.88+ 0.93−0.97+ 2.05 ( ),Figure 2. Measured signal strength for each of the H → γγ and H → Zγ STXS categories includedin the combination. In the H → γγ analysis, events with two or more particle-level jets are assigned tothe V H-veto (V H-had) categories if the leading dijet invariant mass mjj is in the range mjj < 60 GeVor 120 ≤ mjj < 350 GeV (60 ≤ mjj < 120 GeV). In one category the uncertainty is truncated, asindicated by the hatched region, which corresponds to cross-section values for which the total yieldprediction in an analysis region is negative. In that case, the negative uncertainty and its breakdownin terms of statistical and systematic components are not reported, and replaced with a long dash (–).– 10 –JHEP11(2024)0978− 6− 4− 2− 0 2 4 6 8Total Stat.Syst. SMATLAS-1 = 13 TeV, 139 fbs| < 2.5Hy = 125.09 GeV, |Hm)ττ (H→gg)ττ (Hqq→qq)ττ (Htt (bb)Hqq→qq (bb)νHl→qq (bb)ννHll/→gg/qq (bb)Htt)µµ (Htt, H→gg)µµ, VH (Hqq→qq Total Stat. Syst. < 200 GeVHTp ≤1-jet, 120 0.54−0.55+ 0.40−0.41+ 0.67−0.68+ 0.19 ( ) , < 60 GeVHTp ≤ < 350 GeV, 0 jjm 1-jet, ≥ 0.76−0.75+ 0.56± 0.94± 0.31 ( ) , < 200 GeVHTp ≤ < 350 GeV, 120 jjm 2-jet, ≥ 0.57−0.68+ 0.54± 0.78−0.87+ 0.60 ( ), < 200 GeVHTp 350 GeV, ≥ jjm 2-jet, ≥ 1.36−1.92+ 1.30−1.31+ 1.88−2.33+ 3.55 ( ), < 300 GeVHTp ≤200 0.28−0.46+ 0.30−0.31+ 0.41−0.55+ 1.02 ( ), 300 GeV≥ HTp0.31−0.61+ 0.45−0.46+ 0.54−0.77+ 1.27 ( ) , 120 GeV≤ jjm ≤ 2-jet, 60 ≥ 0.34−0.36+ 0.53−0.55+ 0.63−0.66+ 0.97 ( ), 350 GeV≥ jjm 2-jet, ≥ 0.12−0.15+ 0.16−0.17+ 0.20−0.23+ 0.80 ( ) , 0.55−0.77+ 0.98−1.11+ 1.12−1.35+ 1.24 ( ),0.18−0.20+ 0.33± 0.38−0.39+ 0.98 ( ) , < 250 GeVVTp ≤150 0.36−0.37+ 0.33−0.34+ 0.49−0.50+ 0.79 ( ) , < 400 GeVVTp ≤250 0.18−0.20+ 0.34−0.35+ 0.38−0.41+ 1.10 ( ) , 400 GeV≥ VTp0.41−0.51+ 0.72−0.78+ 0.83−0.93+ 1.50 ( ), < 150 GeVVTp ≤75 0.49−0.52+ 0.47± 0.68−0.71+ 0.90 ( ) , < 250 GeVVTp ≤150 0.20−0.25+ 0.27± 0.34−0.37+ 1.13 ( ) , < 400 GeVVTp ≤250 0.17± 0.33−0.35+ 0.37−0.39+ 1.01 ( ) , 400 GeV≥ VTp0.51−0.53+ 0.69−0.76+ 0.85−0.92+ 0.29 ( ), < 120 GeVHTp0.87−0.94+ 0.48± 0.99−1.05+ 1.10 ( ) , < 200 GeVHTp ≤120 0.75−0.73+ 0.70−0.72+ 1.03−1.02+ -0.22 ( ), < 300 GeVHTp ≤200 0.53−0.57+ 0.68−0.71+ 0.86−0.91+ 0.98 ( ) , < 450 GeVHTp ≤300 0.47−0.45+ 0.54−0.58+ 0.72−0.73+ -0.23 ( ) , > 450 GeVHTp1.06−1.03+ 0.91−1.06+ 1.40−1.48+ -0.19 ( ) , 0.19−0.22+ 0.83± 0.85± 0.54 ( ) , 0.25−0.31+ 1.22−1.28+ 1.24−1.32+ 2.23 ( ),40− 30− 20− 10− 0 10 20 30 40 x B normalized to SM valueσ (bb)H→gg < 650 GeVHTp ≤450 7.9−3.9+ 5.0−5.0+ 9.4−6.4+ -4.2 ( ) , 650 GeV≥ HTp7.4−10.4+ 10.2−10.3+ 12.6−14.7+ 8.6 ( ) , Figure 3. Measured signal strength for each of the H → ττ , bb¯, and µµ STXS categories implemented.– 11 –JHEP11(2024)0973 Interpretations based on SM effective field theory3.1 Methodology of effective field theory interpretationsThe SM effective field theory provides an elegant language to encode the modifications of theHiggs boson properties induced by a wide class of BSM theories. Within the mathematicallanguage of the SMEFT, the effects of BSM dynamics at high energies Λ, well above theelectroweak scale v = 246GeV ((Λ/v)2 ≫ 1), can be parameterised at low energies, E ≪ Λ,in terms of higher-dimensional operators built up from the SM fields and respecting itssymmetries such as gauge invariance. This yields an effective Lagrangian:LSMEFT = LSM +Nd=6∑iciΛ2O(6)i +Nd=8∑jbjΛ4O(8)j + . . . , (3.1)where LSM is the SM Lagrangian, O(6)i and O(8)j represent a complete set of operators of mass-dimensions d = 6 and d = 8, and ci, bj are the corresponding dimensionless Wilson coefficients.Operators with d = 5 and d = 7 violate lepton and/or baryon number conservation andare not considered in this study. The effective theory expansion in eq. (3.1) is robust, fullygeneral, and can be systematically matched to explicit UV-complete BSM scenarios.The goal of the analysis is to constrain the d = 6 Wilson coefficients that correspond tooperators that either directly or indirectly impact Higgs boson couplings to SM particles [93,94]. Contributions of operators of mass-dimension d = 8, which are suppressed by 1/Λ2relative to the leading effects from d = 6 operators and whose impact on Higgs bosonproduction and decay in the kinematic regions of interest are not fully calculated, are notconsidered. The ‘Warsaw’ basis [95] is used, which forms a complete set of all O(6)i operatorsin eq. (3.1) allowed for by the SM gauge symmetries. This basis is widely used in EFTconstraints in various fields of particle physics.The ‘top’ flavour symmetry scheme for EFT operators is assumed, following the recom-mendation of ref. [96]. In this scheme, quarks of the first two generations and quarks of the3rd generation are described by independent fields, a U(2)3 symmetry is imposed on the lightquarks, and the quark sector of the EFT is assumed to have no mixing; all lepton generationsare modelled independently. Table 2 lists the operators considered in the analysis of STXSdata, and their corresponding Wilson coefficients ci. Only CP-even d = 6 operators for whichthe Λ−2-suppressed contribution to any of the STXS measurements shown in figures 1–3exceeds 0.1% relative to the SM prediction at ci/Λ2 = 1/TeV2 are listed. The EFT analysisof the differential data only considers a subset of the coefficients listed, cHG, ctH and ctG, dueto the more restricted sensitivity of the differential analyses.A value of Λ = 1TeV is assumed, coefficients for alternative values of Λ = X can beobtained through a scaling of the results presented in this article by a factor (X/1TeV)2.All Wilson coefficients are assumed to be real.3.1.1 Simulation of the impact of SMEFT operatorsThe impact of the d = 6 SMEFT operators listed in table 2 are computed with two universalFeynRules output (UFO) models of MadGraph [73] normalised to theoretical calculationsof production cross-sections and decay branching ratios as follows.– 12 –JHEP11(2024)097Wilson coefficient OperatorcH (H†H)3cH (H†H) (H†H)cG fabcGaνµ Gbρν GcµρcW ϵIJKW Iνµ W Jρν WKµρcHDD(H†DµH)∗ (H†DµH)cHG H†H GAµνGAµνcHB H†H BµνBµνcHW H†HW IµνW IµνcHWB H†τ IHW IµνBµνc(1)Hl,11 (H†i←→D µH)(l¯1γµl1)c(1)Hl,22 (H†i←→D µH)(l¯2γµl2)c(1)Hl,33 (H†i←→D µH)(l¯3γµl3)c(3)Hl,11 (H†i←→D IµH)(l¯1τ Iγµl1)c(3)Hl,22 (H†i←→D IµH)(l¯2τ Iγµl2)c(3)Hl,33 (H†i←→D IµH)(l¯3τ Iγµl3)cHe,11 (H†i←→D µH)(e¯1γµe1)cHe,22 (H†i←→D µH)(e¯2γµe2)cHe,33 (H†i←→D µH)(e¯3γµe3)c(1)Hq (H†i←→D µH)(q¯γµq)c(3)Hq (H†i←→D IµH)(q¯τ Iγµq)cHu (H†i←→D µH)(u¯pγµur)cHd (H†i←→D µH)(d¯pγµdr)c(1)HQ (H†i←→D µH)(Q¯γµQ)c(3)HQ (H†i←→D IµH)(Q¯τ IγµQ)cHt (H†i←→D µH)(t¯γµt)cHb (H†i←→D µH)(b¯γµb)Wilson coefficient Operatorc(1,1)Qq (Q¯γµQ)(q¯γµq)c(1,8)Qq (Q¯TaγµQ)(q¯T aγµq)c(3,1)Qq (Q¯σiγµQ)(q¯σiγµq)c(3,8)Qq (Q¯σiT aγµQ)(q¯σiT aγµq)c(3,1)qq (q¯σiγµq)(q¯σiγµq)c(1)tu (t¯γµt)(u¯γµu)c(8)tu (t¯T aγµt)(u¯T aγµu)c(1)td (t¯γµt)(d¯γµd)c(8)td (t¯Taγµt)(d¯T aγµd)c(1)Qu (Q¯γµQ)(u¯γµu)c(8)Qu (Q¯TaγµQ)(u¯T aγµu)c(1)Qd (Q¯γµQ)(d¯γµd)c(8)Qd (Q¯TaγµQ)(d¯T aγµd)c(1)tq (q¯γµq)(t¯γµt)c(8)tq (q¯T aγµq)(t¯T aγµt)ceH,22 (H†H)(l¯2e2H)ceH,33 (H†H)(l¯3e3H)cuH (H†H)(q¯Y †uuH˜)ctH (H†H)(Q¯H˜t)cbH (H†H)(Q¯Hb)ctG (Q¯σµνTAt)H˜ GAµνctW (Q¯σµνt)τ IH˜ W IµνctB (Q¯σµνt)H˜ Bµνcll,1221 (l¯1γµl2)(l¯2γµl1)Table 2. Wilson coefficients c and corresponding d = 6 SMEFT operators Oj used in this analysis.The operator and coefficient notation follows the convention of ref. [97].Calculations for Higgs boson production modes with tree-level diagrams are performedwith SMEFTsim [97] assuming the ‘top’ flavour symmetry scheme, following the recommen-dation of ref. [96] and providing as input GF = 1.1663787× 10−5 GeV−2, mZ = 91.1876 GeV,and mW = 80.387 GeV, where GF is the Fermi constant and mZ and mW are the Z and Wboson masses respectively. Cross-sections are calculated at NLO accuracy in QCD for ggF,gg→ZH and H → gg with SMEFTatNLO [98] and at NLO EW accuracy for SMEFT-SMinterference terms in H→ γγ [99] and H → Zγ [100]. Lowest-order calculations in QCD formH = 125.09 GeV are used for all other production and decay modes. SMEFT modificationsto the background processes in the included analyses are not considered, but their impact– 13 –JHEP11(2024)097on the SMEFT measurements of the signal is expected to be small as most backgrounddistributions are constrained by control regions.In the simulation, the following requirements are applied at particle level: the minimaljet transverse momentum is pT > 20 GeV and an angular separation ∆R > 0.05 betweentwo jets or two leptons is required, to avoid divergences in the matrix element calculation.For all events, Pythia8 was used for the simulation of parton showering, where the Higgsboson decay is based on the width calculated by MadGraph for the EFT parameters inquestion. In ggF events a matching was performed with the MLM algorithm [101, 102] toremove phase space overlap between the jets from the matrix element and the shower.For analyses based on the STXS methodology, the Rivet program [103] is usedto analyse the simulated events, where the computation of high-level kinematic quanti-ties and classification of the events according to their STXS region is performed by theHiggsTemplateCrossSections in accordance with definitions in [49].4The cross-section predictions for a specific process, calculated as described above, areestimated as the sum of three terms:σSMEFT = σSM + σint + σBSM, (3.2)where σSM is the SM cross-section, σint describes the interference between the SMEFToperators (BSM processes) and SM operators, and σBSM is the cross-section involvingexclusively SMEFT operators. When considering only d = 6 SMEFT operators, it followsfrom eq. (3.1) that σint consists of terms involving a single d = 6 SMEFT operator, suppressingeach term by a factor Λ−2, and that σBSM contains terms involving products of two d = 6SMEFT operators, suppressing each term by a factor Λ−4. For this reason, the impact of theσBSM term is generally expected to be small, though its impact may still be non-negligible incertain regions of phase space, e.g., when energy scales are of order Λ.Additional terms suppressed by a factor Λ−4 occur in the general SMEFT expansion ofeq. (3.1), i.e., the lowest-order cross-section terms generated by d = 8 operators that involveinterference between SM and these operators. As only a subset of Higgs boson processeshave been calculated with d = 8 operators [104–106], the list of terms suppressed by a factorΛ−4 considered is incomplete and the effect of the missing d = 8 terms relative to σBSM isnot known. However, their effect may be of a magnitude comparable to that of products oftwo d = 6 SMEFT operators, as the suppression factor is at the same order. For this reason,SMEFT interpretations are presented both with and without the σBSM contribution to givea general indication of the sensitivity of the analysis to Λ−4 terms.To reduce the perturbative QCD uncertainty in the extraction of the SMEFT Wilsoncoefficients, the parameterisation of the predicted cross-section of eq. (3.2) is computedas a relative correction to the SM prediction computed at the highest available order for4The Rivet algorithm has been modified to classify events in which a Higgs boson and two leptons arisefrom the same production vertex as VH production events. This change ensures the proper classificationof events with leptons from off-shell V decays, since MadGraph only saves on-shell intermediate particles.Contributions from off-shell V bosons are small in the SM, but can be enhanced by SMEFT operators.– 14 –JHEP11(2024)097each process:σiSMEFT = σi,((N)N)NLOSM ×(1 + σi,(N)LOintσi,(N)LOSM+ σi,(N)LOBSMσi,(N)LOSM). (3.3)This calculation strategy assumes that higher-order terms have the same relative effect onσint and σBSM as on σSM [107] and that the SMEFT operator predominantly modifies theproduction process i under consideration.The predictions are further modified by the impact of SMEFT operators on Higgs bosondecay branching ratios. Since the Higgs boson is a narrow, scalar particle, and only on-shellproduction is considered in this analysis, its production cross-section and decay width factorise.The impact of SMEFT operators on production and decay therefore also factorises and canbe derived independently. Thus, the cross-section for a given Higgs boson production processi in particle-level region k′ and for a given decay mode H → X is(σ×B)i,k′,H→XSMEFT = σi,k′SMEFT×BH→XSMEFT =(σi,k′SM + σi,k′int + σi,k′BSM)×(ΓH→XSM + ΓH→Xint + ΓH→XBSMΓHSM + ΓHint + ΓHBSM).The factorised SMEFT prediction is calculated with ratios as in eq. (3.3) to utilise the SMprediction at the highest available order:(σ×B)i,k′,H→XSMEFT =(σ×B)i,k′,H→XSM,(N(N))NLO1+ σi,k′int,(N)LOσi,k′SM,(N)LO+σi,k′BSM,(N)LOσi,k′SM,(N)LO1+ ΓH→XintΓH→XSM+ ΓH→XBSMΓH→XSM1+ ΓHintΓHSM+ ΓHBSMΓHSM ,(3.4)where the ratios σint/σSM and Γint/ΓSM have a linear dependence on SMEFT operators andare suppressed by a factor Λ−2, and the ratios σBSM/σSM and ΓBSM/ΓSM have a quadraticdependence on SMEFT operators and are suppressed by a factor Λ−4. In the analysis, theseratios are parameterised asσi,k′intσi,k′SM=∑jAσi,k′j cjσi,k′BSMσi,k′SM=∑j,l≥jBσi,k′jl cjcl (3.5)ΓH→XintΓH→XSM=∑jAΓH→Xj cjΓH→XBSMΓH→XSM=∑j,l≥jBΓH→Xjl cjcl (3.6)ΓHintΓHSM=∑jAΓHj cjΓHBSMΓHSM=∑j,l≥jBΓHjl cjcl, (3.7)withAΓHj =∑XΓH→XSM AΓH→Xj∑XΓH→XSMBΓHjl =∑XΓH→XSM BΓH→Xjl∑XΓH→XSM. (3.8)In eq. (3.8), the sum includes all possible final states X with up to four elementary particlesproduced by one of the following Higgs boson decays: H → ff¯ (f = c, b,µ, τ), H → γγ,H → Zγ, and H → V V ∗ (V =W ,Z). All Aσi,k′j , AΓH→Xj , Bσi,k′jl and BΓH→Xjl coefficients areconstant factors obtained from simulation that express the sensitivity of the process to the– 15 –JHEP11(2024)097operators Oj and Ol that correspond to the Wilson coefficients cj and cl, where the indicesj, l run over all non-negligible operators. The coefficients Aj and Bjl are proportional toΛ−2 and Λ−4 respectively. The values of all SM Higgs boson branching ratios that entereq. (3.8) are taken from ref. [49].For the interpretation of the differential analyses, where the measured parameters µk′,Xdo not label individual production processes, the relative fractions of the different processesare predicted according to the SMEFT calculations as in eq. (3.3).Using eqs. (3.4)–(3.7), two statistical models are constructed for the interpretation ofthe data: a linearised variant that only considers terms suppressed by up to a factor Λ−2,and a variant including quadratic terms with suppression factor Λ−4.3.1.2 Cross-section calculation with linear termsIn a scenario where Λ−4-suppressed contributions are ignored, the predicted deviation ofthe cross-section, partial width and total width from their SM values can each be explicitlylinearised as a function of the Wilson coefficients c. Ignoring all Λ−4-suppressed BSMterms in eq. (3.4), and using the parameterisation of eqs. (3.5)–(3.7), the expression for thecross-section times branching ratio reduces to(σ×B)i,k′,H→XSMEFT = (σ×B)i,k′,H→XSM,((N)N)NLO ×1 + σi,k′int,(N)LOσi,k′SM,(N)LO×1 + ΓH→XintΓH→XSM1 + ΓHintΓHSM= (σ×B)i,k′,H→XSM,((N)N)NLO ×1 +∑jAσi,k′j cj×1 +∑jAΓH→Xj cj1 +∑jAΓHj cj ,= (σ×B)i,k′,H→XSM,((N)N)NLO ×1 +∑j(Aσi,k′j +AΓH→Xj)cj +O(Λ−4)1 +∑jAΓHj cj +O (Λ−4) , (3.9)where all higher order terms in the expansion are suppressed by power Λ−4 or beyond.A subsequent Taylor expansion of the width ratio expression of eq. (3.9) and truncationof terms beyond Λ−2 would result in a completely linearised expression for σ×B. However,as the parametric dependence of a Wilson coefficient in a branching fraction f is effectivelyof the form c/(1 + f · c), the linearity in c of this expression assumed for small values ofc does not hold for large values of c. This effect is particularly pronounced for operatorsaffecting Higgs boson decays with a large branching fraction, e.g., cbH , and operators thathave a large measured uncertainty that allows large values of c in the error propagation. Forthis reason, a full Taylor expansion of the ratio is not performed.– 16 –JHEP11(2024)0973.1.3 Cross-section calculation including quadratic termsThe SMEFT prediction including the available terms proportional to Λ−4 is:(σ×B)i,k′,H→XSMEFT (3.10)=(σ×B)i,k′,H→XSM,((N)N)NLO1+∑jAσi,k′j cj+∑j,l≥jBσi,k′jl cjcl1+∑jAΓH→Xj cj+∑j,l≥jBΓH→Xjl cjcl1+∑jAΓHj cj+∑j,l≥jBΓHjl cjcl,=(σ×B)i,k′,H→XSM,((N)N)NLO·1+∑j(Aσi,k′j +AΓH→Xj)cj+∑j,l(Aσi,k′j AΓH→Xl)cjcl+∑j,l≥j(Bσi,k′jl +BΓH→Xjl)cjcl+O(Λ−6)1+∑j(AΓHj)cj+∑j,l≥j(BΓHjl)cjcl+O(Λ−6)where both the numerator and denominator are a second-order Taylor expansion resultingin a linearised expression for terms of order Λ−2 and a quadratic expression for terms oforder Λ−4. Similarly to eq. (3.9), and for the same reason, the width ratio expressionin eq. (3.10) is not subjected to a further Taylor expansion. While the set of operatorsproportional to Λ−4 considered in eq. (3.10) is not complete due to missing d = 8 operators,as noted earlier a comparison of results obtained with the linear statistical model and themodel including quadratic terms is indicative of the sensitivity of the measurements toterms suppressed by Λ−4.Figure 4 illustrates the impact of the linear terms Aj for the three SMEFT operatorsconsidered in the interpretation of the fiducial differential cross-section measurements, whereasfigure 5 shows the impact of linear terms and the impact including quadratic terms onproduction (Aσi,k′j ) and decay(1+AΓH→Xj1+AΓHj− 1)rates.The relative importance of the quadratic term increases linearly with the consideredvariation of the corresponding Wilson coefficient. Figure 5 shows that the quadratic termshave the highest impact in the high-pT regions of V H production for the coefficients c(3)Hq,c(1)Hq, cHd, and cHu, on high-pT (inclusive) tt¯H production for the coefficients ctG, c(1,8)Qq , c(3,1)Qq ,c(8)tq, c(8)Qu, c(8)tu, (cG) and in the tH channel for the coefficients c(3)HQ and c(3,1)Qq .3.1.4 Assumptions on SM Higgs boson kinematicsWith the insertion of the SMEFT cross-section predictions of eqs. (3.9) or (3.10) in eqs. (2.2)and (2.3) describing the expected signal yield sk for each analysis region k, i.e.,µi,k′,X → (σ×B)i,k′,H→XSM+Λ−2,−4(σ×B)i,k′,H→XSM,((N(N))NLOin eq. (2.2),µk′,X →σk′,H→XSM+Λ−2,−4,fid.σk′,H→XSM,fid.in eq. (2.3),the effect of SMEFT cross-section modifications on the inclusive Higgs boson signal yield foreach particle-level region k′ is fully taken into account for every reconstruction-level region k.However, the SMEFT operators may also affect other terms of the likelihood, notably theefficiency times acceptance factors ϵi,X,k′k occurring in eqs. (2.2) and (2.3), as well as the signalyield distribution inside each region k represented by the factor f r,ks occurring in eq. (2.1).– 17 –JHEP11(2024)0970.51unc.0.2−0.1−00.10.20.30.40.5 B)(c)/SM× σ(∆=0.01HG c=-0.2tG c=-2.0tH cATLAS-1 = 13 TeV, 139 fbs0-5 5-10 10-15 15-20 20-25 25-30 30-35 35-45 45-60 60-80 80-100 100-120 120-140 140-170 170-200 200-250 250-300 300-450 450-650 650≥ 0-1010-2020-3030-4545-6060-8080-120120-200200-300 [GeV]γγTp [GeV]4lTpFigure 4. Expected impact of the SMEFT operators on the fiducial differential distributions of thetransverse momentum of the Higgs boson decay products in H→ γγ and H → ZZ∗ decays, relativeto the SM cross-section, assuming the linearised SMEFT model. The values of the Wilson coefficients,specified in the legend, are chosen to show the distribution of the operator impact in the same rangeas the typical uncertainty of the measurement. To judge the experimental sensitivity to constrainthe operators from the data in the listed fiducial regions, the total uncertainty in the measurementin each region is shown in the top panel. For presentational clarity, the uncertainty of low precisionregions is clipped off in the plot. The impact of these three operators in the STXS analysis is shownin matching colours in the bottom panel of figure 5 for coefficient variations of identical magnitude.In both the linear SMEFT model and the model including quadratic terms, it is assumedthat the theoretical systematic uncertainties assigned to the acceptance factors ϵi,X,k′k , whichare fully taken into account in the SM cross-section prediction, are large compared to the effectof the possible acceptance changes induced by SMEFT operators in Higgs boson productionthrough the full validity range of the SMEFT model, and that this additional SMEFT relatedtheory uncertainty can therefore be neglected.This assumption is motivated by the similarity of reconstruction-level analysis regionsto STXS and differential fiducial regions, which are designed to be relatively insensitive toacceptance changes induced by SMEFT operators. In addition, the rather fine binning ofthe Stage-1.2 STXS regions reduces further the possibility of significant variations of theacceptance factors inside each region. The effect of SMEFT operators on other observablesused in the definition of the analysis regions, e.g., through multivariate discriminants, isassumed to be negligible.Conversely, the effect of SMEFT operators on Higgs boson decays can strongly affectthe acceptance factors ϵi,Xk , since decays are not limited to a restricted fiducial phasespace in the STXS framework. For 2-body decays, such acceptance effects are generallysmall [25]. However, the four-body H→ZZ∗→ 4ℓ and H → WW ∗ → ℓνℓν decays aresignificantly impacted by acceptance effects, hence for these decays the impact factors AH→Xjand BH→Xjl are recalculated including an approximate implementation of the reconstruction-level requirements at the particle level. The impact of acceptance effects is evaluated for alloperators in table 2 that can affect ΓH→ZZ∗ or ΓH→WW ∗ , i.e., cH , cHDD, cHW , cHB , cHWB ,c(1)Hl,11, c(1)Hl,22, c(3)Hl,11, c(3)Hl,22, cHe,11, cHe,22 and cll,1221, and is observed to be non-negligible for– 18 –JHEP11(2024)0970.51unc.0.2−00.20.40.60.811.2 B)(c)/SM× σ(∆=-0.002eH,22 c=-0.02eH,33 c=0.04(3)Hq c=-0.04bH c0.2−00.20.40.60.811.2 B)(c)/SM× σ(∆=0.01HG c=-0.2tG c=-2.0tH c0.2−00.20.40.60.811.2 B)(c)/SM× σ(∆=-0.01HB c=0.02HWB c=-0.02HW c=0.2tB c=0.2tW c0.2−00.20.40.60.811.2 B)(c)/SM× σ(∆=0.08Hu c=-0.08(1)Hq c=-0.1Hd c=4.0(3)Hl,33 c=-4.0Ht c=-4.0He,33 c0.2−00.20.40.60.811.2 B)(c)/SM× σ(∆=0.4(1,8)Qq c=0.4(3,1)Qq c=0.4(8)tq c=0.4(8)Qu c=0.4(8)tu c=0.1G c0.2−00.20.40.60.811.2 B)(c)/SM× σ(∆=4.0H c=-4.0(3)Hl,11 c=-4.0(3)Hl,22 c=4.0ll,1221 c0.2−00.20.40.60.811.2 B)(c)/SM× σ(∆=4.0(1)Hl,11 c=4.0(1)Hl,22 c=-4.0He,22 c=-4.0He,11 c=-2.0HDD c=2.0(3)HQ cATLAS-1 = 13 TeV, 139 fbsggFσ VBFσ WHσ ZHσ ttHσ tHσ B < 10 GeVHTp 0-jet, H→gg < 200 GeVHTp ≤ 0-jet, 10 H→gg < 60 GeVHTp 1-jet, H→gg < 120 GeVHTp ≤ 1-jet, 60 H→gg < 200 GeVHTp ≤ 1-jet, 120 H→gg < 120 GeVHTp < 350 GeV, jjm 2-jet, ≥ H→gg < 200 GeVHTp ≤ < 350 GeV, 120 jjm 2-jet, ≥ H→gg < 200 GeVHTp, jjm ≥ 2-jet, 350 ≥ H→gg < 300 GeVHTp ≤ 200 H→gg < 450 GeVHTp ≤ 300 H→gg 450 GeV≥ HTp H→ggjet1-≤ Hqq→qq-topoVH 2-jet, ≥ Hqq→qq-vetoVH 1-jet and ≤ Hqq→qq < 200 GeVHTp < 700 GeV, jjm ≤ 2-jet, 350 ≥ Hqq→qq < 200 GeVHTp < 1000 GeV, jjm ≤ 2-jet, 700 ≥ Hqq→qq < 200 GeVHTp < 1500 GeV, jjm ≤ 2-jet, 1000 ≥ Hqq→qq < 200 GeVHTp 1500 GeV, ≥ jjm 2-jet, ≥ Hqq→qq 200 GeV≥ HTp < 1000 GeV, jjm ≤ 2-jet, 350 ≥ Hqq→qq 200 GeV≥ HTp 1000 GeV, ≥ jjm 2-jet, ≥ Hqq→qq < 75 GeVVTp νHl→qq < 150 GeVVTp ≤ 75 νHl→qq < 250 GeVVTp ≤ 150 νHl→qq < 400 GeVVTp ≤ 250 νHl→qq 400 GeV≥ VTp νHl→qq < 150 GeVVTp Hll→gg/qq < 250 GeVVTp ≤ 150 Hll→gg/qq < 400 GeVVTp ≤ 250 Hll→gg/qq 400 GeV≥ VTp Hll→gg/qq < 60 GeVHTp Htt < 120 GeVHTp ≤ 60 Htt < 200 GeVHTp ≤ 120 Htt < 300 GeVHTp ≤ 200 Htt < 450 GeVHTp ≤ 300 Htt > 450 GeVHTp Htt tHb b→Hµµ →Hττ →Hν lν l→ WW* →H 4l→ ZZ* →Hγ Z→Hγγ →HFigure 5. Expected impact of the most relevant SMEFT operators on the observables O (cross-sections in STXS-1.2 regions or decay branching ratios), relative to the SM predictions, for thelinearised SMEFT model (shaded histogram) and the SMEFT model including quadratic terms (openhistogram). The values of the Wilson coefficients, specified in the legend, are chosen to show thedistribution of the operator impact in the same range as the typical uncertainty of the measurement.To judge the experimental sensitivity to constrain the operators from the data, the total uncertaintyin the measurement of each observable is shown in the top panel. For presentational clarity, theuncertainty of low precision measurements is clipped off in the plot.four of these, cHW , cHB, cHWB, and c(3)Hl. For these, the corresponding recalculated factorsAH→Xj ,BH→Xjl (X = WW ∗,ZZ∗) with approximate acceptance modelling are used in theSTXS SMEFT analysis. Figure 6 illustrates the effect of the cHW operator on the acceptancein the H → WW ∗ and H → ZZ∗ decay modes. The acceptance correction is not usedin the differential analysis of H → ZZ∗, as none of the three operators analyzed for thatmeasurement are affected. For all other Higgs boson decays, the acceptance effects fromSMEFT operators are neglected.– 19 –JHEP11(2024)09700.0050.010.0150.020.0250.03Normalized to SM [a.u.]0 10 20 30 40 50 60 70 80 90 100 [GeV]llm0.911.1SMEFT / SMSM-2Λ = 1, up to HWc-4Λ = 1, up to HWc ATLASνµνe→*WW→H-1 = 13 TeV, 139 fbs(a)00.010.020.030.040.050.060.07Normalized to SM [a.u.]0 10 20 30 40 50 60 [GeV]2Zm0.511.52SMEFT / SMSM-2Λ = 1, up to HWc-4Λ = 1, up to HWc ATLAS4l→*ZZ→H-1 = 13 TeV, 139 fbs(b)Figure 6. Illustration of the effect of a variation of the SMEFT coefficient cHW on kinematicobservables used in the event selection: (a) impact on the dilepton invariant mass in the H →WW ∗ → eνµν analysis, and (b) impact on the invariant mass of the 3rd and 4th pT-ranked leptonin the H → ZZ∗ → 4ℓ analysis. The vertical dotted lines indicate the selection criteria applied tothe corresponding variables by the H →WW ∗ analysis (10 < mℓℓ < 55 GeV) and by the H → ZZ∗analysis (mZ2 > 12 GeV). The shaded bands show the statistical uncertainty of the SMEFT simulation.The value of the Wilson coefficient (cHW = 1) is significantly larger than the sensitivity of this study,and is chosen for illustration purposes.Finally, if the signal yield distribution inside an analysis region k deviates from the SMdistribution encoded in f r,ks in eq. (2.1), the measured yield sk may be biased. This effect isexpected to be negligible for all regions where the discriminant observable inside the region isthe reconstructed invariant mass of the Higgs boson, which is largely unaffected by SMEFToperators. Regions that feature a multivariate discriminant as the observable can potentiallybe more affected by SMEFT induced shape differences, but are only used in regions with lowsignal yields where it is assumed that any effect induced by signal shape deviations is smallcompared to the statistical uncertainties. For the high-yield H →WW ∗ channel, where thetransverse mass mT is used as discriminant observable, which is sensitive to SMEFT operators,it is verified that the effect of shape variations induced by the SMEFT operators is negligiblefor the range of coefficient values that are consistent with the observed measurement.3.2 Constraints from STXS measurementsThe aim of the EFT analysis is to obtain constraints on the Wilson coefficients cj through amaximum likelihood analysis of the Higgs boson STXS measurements shown in figures 1–3. Allsignal strength modifiers µi,k′,X of eq. (2.2) are directly expressed in terms of the coefficients cj :sk(c,θ) =∑i,k′,Xµi,k′,X ≡ (σ×B)i,k′,H→XSMEFT (c)(σ×B)i,k′,H→XSM,(N(N))NLO× L× (σ×B)i,k′,H→XSM,(N(N))NLO(θ)× ϵi,k′,Xk (θ),– 20 –JHEP11(2024)097with L, ϵi,k′,Xk (θ) and θ as defined in eq. (2.2), and where the signal cross-section(σ×B)i,k′,H→XSMEFT (c) is either taken from the linear model of eq. (3.9) or the model includ-ing quadratic terms of eq. (3.10).The available data samples contain insufficient information to constrain all coefficients clisted in table 2 simultaneously. A standard numerical joint maximum likelihood estimationof this set of parameters c will not converge due to the presence of flat directions in theparameter space, corresponding to the unconstrained degrees of freedom.As degrees of freedom left unconstrained by the data do not necessarily correspond toindividual coefficients cj , but may also be linear combinations∑j ajcj , a modified basis isdefined and used in the following, to ensure the convergence of the numerical likelihoodmaximisation procedure for the largest number of degrees of freedom that can be probedby the current set of measurements.3.2.1 Sensitivity estimate and choice of parametersTo determine a modified basis c′ that can be estimated from the data, the SM expectedcovariance matrix VSTXS of the measurement, expressed in the STXS basis {µi,k′,X}, isanalysed. From VSTXS, the Hessian matrix V −1STXS is obtained, and then rotated to theSMEFT basis {cj}:V −1SMEFT = PT(i,k′,X)→(j) V−1STXS P(i,k′,X)→(j). (3.11)The expected Jacobian matrix P(i,k′,X)→(j) is based on the linearised SMEFT model ofeq. (3.9) assuming small ci:P(i,k′,X)→(j) = Aσi,k′j +AΓH→Xj −AΓHj , (3.12)where Aσi,k′j ,AΓH→Xj and AΓHj are the constant factors obtained from the simulation.In the limit of Gaussian STXS measurements, the matrix V −1SMEFT represents the Fisherinformation matrix of its linearised SMEFT model re-parameterisation, with the additionalcaveat that for large coefficient variations the representation of V −1SMEFT may be suboptimal,as a consequence of the fully linearized form of eq. (3.12) that is only valid in the limit ofsmall coefficient values. An eigenvalue decomposition of the Fisher information matrix yieldsthe eigenvectors ev[i] and their corresponding eigenvalues λi and variances 1/λi.Figure 7 lists the eigenvectors obtained from the expected measurements accounting forthe observed values of nuisance parameters, ranked by eigenvalue and truncated to eigenvaluesλi ≥ 0.01, corresponding to a truncation at an estimated uncertainty of σ(ev[i]) ≤ 10, wellbeyond the validity range of the Wilson coefficients of O(1).From the ranking shown in figure 7 and a survey of the sensitivity of the STXS regions tothe Wilson coefficients in the linearised model, as shown in figure 5, the following observationsare made:• The coefficients ceH,33, ceH,22, and cbH , representing the Yukawa coupling modifiers ofthe H → ττ , H → µµ, and H → bb decays respectively, can be individually measuredfrom the corresponding Higgs boson channels that enter the combination. There areweak correlations of these operators with other SMEFT operators, primarily for cbH ,through their contribution to the total Higgs boson width.– 21 –JHEP11(2024)0970.010.96−0.280.01−0.010.010.090.1−0.070.99−0.02−0.03−0.020.01−0.01−0.06−0.02−0.090.080.230.960.04−0.01−0.010.010.05−0.020.030.620.73−0.22−0.150.010.06−0.050.010.03−0.01−0.04−0.050.020.030.250.84−0.470.03−0.160.03−0.02−0.02−0.04−0.010.29−0.10.89−0.28−0.02−0.02−0.01−0.030.020.10.75−0.210.030.130.12−0.010.08−0.020.010.12−0.01−0.010.01−0.01−0.010.010.090.180.020.04−0.370.32−0.030.020.110.390.74−0.040.020.02−0.05−0.030.020.260.580.060.120.56−0.440.110.030.110.22−0.040.030.020.01−0.05−0.020.030.30.640.070.13−0.390.310.01−0.01−0.06−0.21−0.41−0.03−0.010.010.01−0.01−0.01−0.010.010.01−0.01−0.02−0.21−0.16−0.520.040.05−0.010.01−0.030.010.020.02−0.01−0.020.01−0.01−0.010.010.010.02−0.110.050.37−0.010.22−0.040.02−0.01−0.180.250.83−0.010.010.07−0.01−0.210.090.25−0.020.85−0.120.15−0.09−0.32−0.030.160.03−0.010.88−0.350.04−0.010.02−0.08−0.26−0.020.520.03−0.06−0.070.020.010.030.020.010.01−0.21−0.080.04−0.04−0.02−0.18−0.030.020.05−0.040.02−0.01−0.01−0.11−0.020.010.04−0.030.020.070.01−0.01−0.010.020.05−0.130.1−0.010.8−0.02−0.030.54−0.050.01−0.170.04−0.030.01−0.13−0.33−0.020.44−0.040.01−0.140.030.160.180.65−0.03−0.23−0.02−0.010.17−0.01−0.050.01−0.04−0.12−0.28−0.020.42−0.03−0.140.03−0.02−0.01−0.07−0.16−0.010.25−0.02−0.080.02−0.02−0.02−0.07−0.14−0.010.25−0.02−0.080.02−0.02−0.03−0.05−0.010.14−0.01−0.050.01−0.02−0.01−0.03−0.06−0.010.15−0.01−0.050.010.01−0.03−0.13−0.190.01−0.010.17−0.01−0.040.010.01−0.04−0.10.07−0.01−0.02−0.01−0.030.05−0.01−0.01−0.01−0.020.03−0.01−0.010.02−0.01−0.010.42−0.4−0.03−0.1−0.07−0.14−0.09−0.1−0.370.22−0.080.070.020.020.010.24−0.14−0.03−0.02−0.02−0.020.010.040.55−0.21−0.05−0.02−0.03−0.010.010.18−0.16−0.02−0.06−0.02−0.020.010.040.54−0.21−0.05−0.02−0.03−0.010.010.20.05−0.02−0.02−0.02−0.03−0.290.140.040.010.02−0.17−0.090.060.02−0.01−0.020.520.02−0.030.03−0.010.010.01−0.14−0.080.060.02−0.01−0.020.520.02−0.030.04−0.010.010.01−0.140.03−0.010.030.01−0.05−0.37−0.010.02−0.03−0.01−0.01−0.150.02−0.010.040.01−0.05−0.37−0.010.02−0.04−0.01−0.010.150.18−0.030.010.030.230.370.030.010.030.020.01−0.30.410.03−0.01−0.1−0.120.010.01−0.02−0.01−0.030.040.07−0.020.040.01−0.01−0.13−0.01−0.01ATLAS√ s=13TeV,139fb−1−1−0.9−0.8−0.7−0.6−0.5−0.4−0.3−0.2−0.100.10.20.30.40.50.60.70.80.9110−310−210−1100101ev[19]ev[18]ev[17]ev[16]ev[15]ev[14]ev[13]ev[12]ev[11]ev[10]ev[9]ev[8]ev[7]ev[6]ev[5]ev[4]ev[3]ev[2]ev[1]σexp.c eH,22c eH,33c(3)Hqc bHc HGc tGc tHc HBc HWc HWBc tBc tWcWc Huc(1)Hqc Hdc(3)Hl,33c Htc He,33c(1)Hl,33c Hbc Gc(1,8)Qqc(3,8)Qqc(8)tqc(8)Quc(8)tuc(8)tdc(8)Qdc(3,8)Qqc(1,1)Qqc(1)tuc(1)tqc(1)Quc(1)Qdc H✷c(3)Hl,11c(3)Hl,22c ll ,1221c(1)Hl,11c(1)Hl,22c He,11c He,22c HDDc(3)HQc(1)HQFigure7.Eigenvectorsev[i]oftheinverseEFTcovariancematrixobtainedbypropagatingtheSMEFTparameterisationtothecovariancematrixVSTXSandrequiringasignificant(≥0.01)eigenvalueλ.Theeigenvectorsarelinearcombinations∑ Aijc joftheWilsoncoefficientsc jshownatthebottomoftherightpanel.TheelementsofthematrixshowninthispanelcorrespondtothevaluesoftheAijcoefficients.Valuesof|Aij|<0.01arenotshown.Thecorrespondingexpecteduncertaintyσexp.=1/√ λforeacheigenvectorisshownintheleftpanel.– 22 –JHEP11(2024)097• The coefficient c(3)Hq affects both the WH and ZH production modes with an increasingimpact as a function of the transverse momentum pVT of the W and Z bosons, and isconstrained almost exclusively by the V H, H → bb¯ analysis.• The coefficients cHG, ctG and ctH are constrained by ggF and tt¯H production. As theuncertainties of the constrained directions span more than two orders of magnitude, itis beneficial to represent them by decorrelated parameters, even though the rotationmatrix required to decorrelate them is close to an identity matrix.• The coefficients cHB , cHW , cHWB , ctB and ctW are constrained in two directions throughtheir impacts on the branching ratios of the H → γγ and H → Zγ decays. Thereis an additional small impact of these operators on VBF and V H production, mildlyconstraining a third direction in this parameter group.• The coefficients cHu, cHd, cHt, cHb and c(1)Hq mainly affect the neutral current interactionswith quarks, while cHe,33, c(1)Hl,33, c(3)Hl,33 mainly affect the W and Z vertices with thirdgeneration leptons. Both sets of coefficients are primarily constrained by the V H,H → bb¯ analysis. The small sensitivity to cHt and cHb arises from the pT-dependentcorrections that they induce in the subleading production mode gg → ZH.• The coefficients of the four-fermion operators involving the top-quark, i.e., c(1,8)Qq , c(3,1)Qq ,c(8)tq , c(8)Qu, c(8)tu , c(8)td , c(8)Qd, c(3,8)Qq , c(1,1)Qq , c(1)tu , c(1)tq , c(1)Qu, and c(1)Qd, as well as the trilineargluon coupling cG, affect the ttH and tH production modes and are largely degenerate.The pHT spectrum measured in the H → γγ and H → bb channels constrains two linearcombinations of these 14 coefficients. The separate constraint on tH production in theH → γγ analysis weakly constrains a third direction in this group.• The coefficients cll,1221, c(3)Hl,11, and c(3)Hl,22 primarily cause a shift in the Fermi constant,resulting in an overall normalisation factor across different production modes. The coef-ficient cH only affects the measurements through a Higgs boson propagator correctionand thus acts similarly as an overall scale factor in the observed cross-sections. Only asingle linear combination of these four operators can be constrained from the data.• The coefficients c(1)Hl,11, c(1)Hl,22, cHe,11 and cHe,22 introduce anomalous HZee and HZµµvertices and are mainly constrained by the branching ratio of the Higgs boson decay intofour leptons (electrons or muons), together with cHDD (responsible for an anomalousHZZ vertex) and c(3)HQ, c(1)HQ (leading to HZtt and HZbb couplings that modify theZ boson propagator, but to which the Higgs boson measurements included here arenot sensitive). The ZH, H → bb¯ analysis also constrains the couplings to first- andsecond-generation leptons such as cHe,11, c(1)Hl,11, cHe,22, c(1)Hl,22, but the constraints aresignificantly looser than those from the H → ZZ∗ → 4ℓ decay.Based on these observations, a new fit basis c′ is defined that achieves both fit stabilityand fit-parameter interpretability. This basis c′ is expressed in terms of single Warsawbasis coefficients cj whenever possible, and in terms of linear combinations (denoted by e)– 23 –JHEP11(2024)097of coefficients when necessary:c ={ceH,22} ∪ c′ ={ceH,22} ∪{ceH,33} ∪ {ceH,33} ∪{c(3)Hq} ∪ {c(3)Hq} ∪{cbH} ∪ {cbH} ∪{cHG, ctG, ctH} ∪ → {e[1]ggF, e[2]ggF, e[3]ggF} ∪{cHB, cHW , cHWB, ctB, ctW } ∪ → {e[1]Hγγ,Zγ , e[2]Hγγ,Zγ , e[3]Hγγ,Zγ} ∪{cHu, c(1)Hq, cHd, c(3)Hl,33,cHt, cHe,33, c(1)Hl,33, cHb} ∪ → {e[1]ZH , e[2]ZH , e[3]ZH , e[4]ZH} ∪{cG, c(1,8)Qq , c(3,1)Qq , c(8)tq , c(8)Qu, c(8)tu , c(8)td ,c(8)Qd, c(3,8)Qq , c(1,1)Qq , c(1)tu , c(1)tq , c(1)Qu, c(1)Qd} ∪ → {e[1]ttH, e[2]ttH, e[3]ttH} ∪{cH , c(3)Hl,11, c(3)Hl,22, cll,1221} ∪ → {e[1]glob} ∪{c(1)Hl,11, c(1)Hl,22, cHe,11, cHe,22, cHDD, c(3)HQ, c(1)HQ} → {e[1]Hllll}.Only subgroup eigenvectors with an expected uncertainty ≤ 10 are retained as modelparameters. The remaining coefficients, to which the data are not really sensitive, are fixedto zero in the analysis. The subgroup eigenvector directions relative to the Warsaw basisare shown in figure 8. The names of the eigenvectors are chosen to reflect the productionor decay process that dominates the experimental sensitivity of the parameter group, asshown in figure 5, although single parameters within some of the groups sometimes havea dominant sensitivity to another process.No separate optimisation of the parameter basis c′ is performed for the SMEFT modelincluding quadratic terms of eq. (3.10) as the non-linear effects of this model are expected tovanish for small cj , and thus to asymptotically yield the same rotation matrix as eq. (3.12).The impacts of the variations of the coefficients of the rotated basis c′ on the STXSregions and Higgs boson branching ratios are shown in figure 9, with the same parametergrouping as shown in figure 5. The figure clearly demonstrates that the basis c′ representsimpact variations across regions that are much less correlated than those represented bythe Warsaw basis c. The magnitude of the parameter variations shown in figure 9 are setto the expected uncertainty for each parameter in the linear SMEFT model, thus giving arealistic indication of the magnitude of variations that can be constrained from the data. Forcompleteness, the impact of the quadratic terms for the same values of the parameter basis isoverlaid, indicating the relative magnitude of the quadratic terms at the expected sensitivitylevel of the linear model. The impact of these expected sensitivities for the measured SMEFTparameters is discussed in section 3.2.3.– 24 –JHEP11(2024)09711110.031−0.110.99−0.030.990.110.22−0.490.850.640.730.250.74−0.49−0.470.01−0.020.02−0.02−0.010.22−0.320.210.90.08−0.340.87−0.350.66−0.58−0.39−0.270.720.660.190.02−0.02−0.02−0.05−0.02−0.03−0.08−0.08−0.01−0.02−0.06−0.060.020.030.080.80.57−0.15−0.340.460.95−0.230.17−0.13−0.290.45−0.08−0.160.27−0.08−0.150.27−0.03−0.050.16−0.03−0.060.16−0.17−0.20.14−0.04−0.110.06−0.02−0.030.05−0.01−0.020.03−0.01−0.010.02−0.010.64−0.48−0.480.360.540.54−0.39−0.390.27−0.14−0.13ATLAS√ s=13TeV,139fb−1−1−0.9−0.8−0.7−0.6−0.5−0.4−0.3−0.2−0.100.10.20.30.40.50.60.70.80.91c eH,22c eH,33c(3)Hqc bHc HGc tGc tHc HBc HWc HWBc tBc tWc Huc(1)Hqc Hdc(3)Hl,33c Htc He,33c(1)Hl,33c Hbc Gc(1,8)Qqc(3,1)Qqc(8)tqc(8)Quc(8)tuc(8)tdc(8)Qdc(3,8)Qqc(1,1)Qqc(1)tuc(1)tqc(1)Quc(1)Qdc H✷c(3)Hl,11c(3)Hl,22c ll ,1221c(1)Hl,11c(1)Hl,22c He,11c He,22c HDDc(3)HQc(1)HQe[1] Hlllle[1] globe[3] ttHe[2] ttHe[1] ttHe[4] ZHe[3] ZHe[2] ZHe[1] ZHe[3] Hγγ,Zγe[2] Hγγ,Zγe[1] Hγγ,Zγe[3] ggFe[2] ggFe[1] ggFc bHc(3) Hqc eH,33c eH,22Figure8.Definitionofthefitbasiscoefficientsc′intermsoftheWarsawbasiscoefficientsc.– 25 –JHEP11(2024)0970.51unc.0.2−00.20.40.60.811.2 B)(c')/SM × σ(∆=-0.003eH,22 c=-0.02eH,33 c=0.04(3)Hq c=-0.05bH c 1x0.2−00.20.40.60.811.2 B)(c')/SM × σ(∆=0.005[1]ggF e=-0.5[2]ggF e=8.0[3]ggF e 12x0.2−00.20.40.60.811.2 B)(c')/SM × σ(∆=-0.005[1]γ,ZγγH e=-0.04[2]γ,ZγγH e=0.7[3]γ,ZγγH e 2x0.2−00.20.40.60.811.2 B)(c')/SM × σ(∆=0.4[1]ZH e=4.0[2]ZH e=-10.0[3]ZH e=-11.0[4]ZH e 4000x0.2−00.20.40.60.811.2 B)(c')/SM × σ(∆=1.0[1]ttH e=5.0[2]ttH e=9.0[3]ttH e 400x0.2−00.20.40.60.811.2 B)(c')/SM × σ(∆=0.8[1]glob e 0.5x0.2−00.20.40.60.811.2 B)(c')/SM × σ(∆=1.0[1]Hllll e 0.3xATLAS-1 = 13 TeV, 139 fbsγγ →H γ Z→H ν lν l→ WW*→H 4l→ ZZ*→H b b→H µµ →H ττ →H < 10 GeVHTp 0-jet, H→gg < 200 GeVHTp ≤ 0-jet, 10 H→gg < 60 GeVHTp 1-jet, H→gg < 120 GeVHTp ≤ 1-jet, 60 H→gg < 200 GeVHTp ≤ 1-jet, 120 H→gg < 120 GeVHTp < 350 GeV, jjm 2-jet, ≥ H→gg < 200 GeVHTp ≤ < 350 GeV, 120 jjm 2-jet, ≥ H→gg < 200 GeVHTp 350 GeV, ≥ jjm 2-jet, ≥ H→gg < 300 GeVHTp ≤ 200 H→gg < 450 GeVHTp ≤ 300 H→gg 450 GeV≥ HTp H→gg-hadVH 2-jet, ≥ Hqq→qq < 200 GeVHTp < 700 GeV, jjm ≤ 2-jet, 350 ≥ Hqq→qq < 200 GeVHTp < 1000 GeV, jjm ≤ 2-jet, 700 ≥ Hqq→qq < 200 GeVHTp 1000 GeV, ≥ jjm 2-jet, ≥ Hqq→qq 200 GeV≥ HTp < 1000 GeV, jjm ≤ 2-jet, 350 ≥ Hqq→qq 200 GeV≥ HTp 1000 GeV, ≥ jjm 2-jet, ≥ Hqq→qq-vetoVH 1-jet and ≤ Hqq→qq < 150 GeVVTp νHl→qq > 150 GeVVTp νHl→qq < 150 GeVVTp Hll→gg/qq > 150 GeVVTp Hll→gg/qq < 60 GeVHTp Htt < 120 GeVHTp ≤ 60 Htt < 200 GeVHTp ≤ 120 Htt < 300 GeVHTp ≤ 200 Htt > 300 GeVHTp Htt tH ZYµ < 200 GeVHTp 0-jet, H→gg < 60 GeVHTp 1-jet, H→gg < 120 GeVHTp ≤ 1-jet, 60 H→gg < 200 GeVHTp ≤ 1-jet, 120 H→gg < 200 GeVHTp 2-jet, ≥ H→gg > 200 GeVHTp H→gg < 200 GeVHTp < 700 GeV, jjm ≤ 2-jet, 350 ≥ Hqq→qq < 200 GeVHTp < 1000 GeV, jjm ≤ 2-jet, 700 ≥ Hqq→qq < 200 GeVHTp < 1500 GeV, jjm ≤ 2-jet, 1000 ≥ Hqq→qq < 200 GeVHTp 1500 GeV, ≥ jjm 2-jet, ≥ Hqq→qq 200 GeV≥ HTp 350 GeV, ≥ jjm 2-jet, ≥ Hqq→qq < 10 GeVHTp 0-jet, H→gg < 200 GeVHTp ≤ 0-jet, 10 H→gg < 60 GeVHTp 1-jet, H→gg < 120 GeVHTp ≤ 1-jet, 60 H→gg < 200 GeVHTp ≤ 1-jet, 120 H→gg < 200 GeVHTp 2-jet, ≥ H→gg > 200 GeVHTp 2-jet, ≥ H→gg < 120 GeV,jjm 2-jet, 60 < ≥ Hqq→qq 200 GeV≥ HTp 350 GeV, ≥ jjm 2-jet, ≥ Hqq→qq VBFHqq→qq ZZVH-lep ZZHtt < 650 GeVHTp ≤ 450 H→gg > 650 GeVHTp H→ggHqq→qq < 250 GeVVTp ≤ 150 νHl→qq < 400 GeVVTp ≤ 250 νHl→qq 400 GeV≥ VTp νHl→qq < 150 GeVVTp ≤ 75 Hll→gg/qq < 250 GeVVTp ≤ 150 Hll→gg/qq < 400 GeVVTp ≤ 250 Hll→gg/qq 400 GeV≥ VTp Hll→gg/qq < 120 GeVHTp ≤ 0 Htt < 200 GeVHTp ≤ 120 Htt < 300 GeVHTp ≤ 200 Htt < 450 GeVHTp ≤ 300 Htt > 450 GeVHTp HttHtt, H→gg, VHHqq→qq < 200 GeVHTp ≤ 1-jet, 120 H→gg < 200 GeVHTp ≤ < 350 GeV, 120 jjm 2-jet, ≥ H→gg < 200 GeVHTp ≤ 350 GeV, 0 ≥ jjm 2-jet, ≥ H→gg < 300 GeVHTp ≤ 200 H→gg 300 GeV≥ HTp H→gg < 120 GeVHTp ≤ < 350 GeV, 60 jjm 2-jet, ≥ 1-jet or H→gg 350 GeV≥ jjm 2-jet, ≥ Hqq→qq 120 GeV≤ jjm ≤ 2-jet, 60 ≥ Hqq→qq HttFigure 9. Impact of coefficients of the rotated basis c′ on the STXS regions, relative to the SMcross-section, under the assumption of the linearised SMEFT model (shaded histogram) and theSMEFT model including quadratic terms (open histogram). For all coefficients, a variation equalto the expected uncertainty when using the linearised model is shown. Groupings in this figure areconsistent with those in figure 5, but vertical axis scales differ in order to completely show all quadraticimpact terms, which can occasionally be very large. To judge the experimental sensitivity to constrainthe operators from the data in the listed STXS regions, the total uncertainty in the correspondingregions is shown in the top panel. For presentational clarity, the uncertainty of low precision STXSregions is clipped off in the plot.– 26 –JHEP11(2024)0973.2.2 ResultsLinear model. Figure 10 compares the expected and observed results obtained usingthe linearised SMEFT model, showing good agreement of the observed data with the SMexpectation, corresponding to a p-value of 94.5%. The parameter value ranges shown in thebottom panel correspond to 68% and 95% confidence level (CL) intervals, where all othercoefficients and nuisance parameters are profiled. The observed uncertainties are generallyabout 10% smaller than the expected uncertainties, since the assumed Higgs boson width,when computed with the observed parameter values, is smaller than its SM expectation value.This effect is mostly driven by a high observed value of cbH , which corresponds to a reducedvalue of ΓH→bb¯. This reduction of the observed linear model uncertainties is comparable tothat of the reduced observed uncertainties in the κ model analysis of the same data reportedin ref. [9], due to an equivalently low measured value (< 1) of κb.Figure 10 also shows the contribution of each measured Higgs boson decay or productionmode to the sensitivity of each measurement of the coefficients of the rotated basis. Thecontribution of a measurement i to the sensitivity to a coefficient c′j is determined from theratio of the Fisher information Ii(c′j) of that measurement to the sum of the Fisher informationof all contributing components, i.e., ∑k Ik(c′j), where in all cases the Fisher information isestimated as the inverse of the covariance matrix VSMEFT, as defined in eq. (3.11). Thisbreakdown reveals that six parameters are (almost) exclusively measured by a single decaymode: the Yukawa coefficients cHe,22 and cHe,33 by the decay modes H → µµ and H → ττrespectively, the coefficient c(3)Hq by H → bb¯; coefficients e[1]Hγγ,Zγ and e[2]Hγγ,Zγ by H → γγand H → Zγ respectively and the coefficient e[1]Hllll by H → ZZ∗. Due to its large effect onthe Higgs boson width, the measurement of the Yukawa coefficient cbH is not dominatedby H → bb¯, but instead constrained by a combination of measured decays. Similarly, fiveparameters are measured (almost) exclusively by a single production mode: coefficient e[1]ggFby ggF production, e[1]ZH by ZH production, e[1]ttH and e[2]ttH by ttH production at high-pT andmedium-pT respectively, and e[3]ttH by tH production. No measured coefficient is predominantlysensitive to H → WW ∗ decays. The VBF or WH production modes each only dominatea single parameter measurement, cHe,33 and c(3)Hq, respectively.Generally, the tightest constraints on SMEFT coefficients are observed for processeswhere the SM amplitudes are suppressed by factors that do not enter in SMEFT operatorscontributing to the same measured final states. The most prominent example of these isthe OHe,22 operator, for which the corresponding SM H → µµ amplitude is so stronglysuppressed by the Yukawa factor that it is the most precisely measured coefficient, despitebeing constrained only by the very low-yieldH → µµ channel. Along similar lines, the preciselymeasured coefficients e[1]ggF, e[1]Hγγ,Zγ and e[2]Hγγ,Zγ benefit from suppressed SM amplitudes thatrequire loops at lowest order.Analysis of parameter uncertainty sources. Figure 11 illustrates the relative importanceof the various uncertainty components on the coefficients measured in the linearised model,where the top panel shows the relative contributions of the statistical and systematic com-ponents, and the bottom panel shows the relative contributions of the experimental, signaltheory and background theory contributions to the total systematic uncertainty, where signal– 27 –JHEP11(2024)097Symmetrizeduncertainty(σ)ProbedScale(Λ/√σ)[TeV]−4−2024Best Fit68 % CL95 % CLceH,22ceH,33c (3)HqcbHe [1]ggFe [2]ggFe [3]ggFe [1]Hγγ,Zγe [2]Hγγ,Zγe [3]Hγγ,Zγe [1]ZHe [2]ZHe [3]ZHe [4]ZHe [1]ttHe [2]ttHe [3]ttHe [1]globe [1]HllllpSM = 94.5%Parametervaluescaledbysymmetrizeduncertainty(c′ /σ)0.20.40.60.81ExpectedcontributionproductiondecayggFVBFWHZHtt¯HtHinclusive0.20.40.60.81H → γγH → ZγH → WW∗ → lνlνH → ZZ∗ → 4lH → bb¯H → ττH → µµATLASSMEFT Λ = 1 TeV√s =13 TeV, 139 fb−1,mH = 125.09 GeV10−310−210−110010132103.210.32Linear (obs.)Linear (exp.)Linear (obs.)Linear (exp.)Figure 10. Comparison of the expected (gray) and observed (blue) parameters of the rotated basisc′ with the SMEFT linearised model, where all other coefficients and nuisance parameters are profiled.The middle panel shows the symmetrised 68% CL uncertainty σ of each parameter measurement(left vertical axis) and the corresponding energy scale Λ/√σ that is probed (right vertical axis). Thebottom panel shows the measured parameter value (dot) and 68% (solid line) and 95% (dashedline) CL intervals, divided by the symmetrised uncertainty shown in the middle panel. The p-valuefor the compatibility of the data with the Standard Model expectation (all coefficients vanishing)is 94.5%. The top panel shows the expected breakdown of contributions to the sensitivity of eachmeasurement from the various measured Higgs boson decay and production modes. Green shadesrepresent production and decay modes with Higgs boson couplings to vector bosons, red shadesrepresent modes with Higgs boson couplings to fermions, and blue shades represent modes with loopcouplings. The production category labelled ‘inc’ collects final states for which the breakdown intoproduction modes is not available (H → µµ and H → Zγ). The 95% CL interval for e[3]ttH is truncatedat the boundary at which the logarithm of the likelihood function becomes undefined, resulting in asmall undercoverage.– 28 –JHEP11(2024)097ceH,22ceH,33c (3)HqcbHe [1]ggFe [2]ggFe [3]ggFe [1]Hγγ,Zγe [2]Hγγ,Zγe [3]Hγγ,Zγe [1]ZHe [2]ZHe [3]ZHe [4]ZHe [1]ttHe [2]ttHe [3]ttHe [1]globe [1]Hllll0.20.40.60.81Uncertaintybreakdownsystematictotalbkg. theorysig. theoryexperimental0.20.40.60.81systematicstatisticalATLASSMEFT Λ = 1 TeV√s =13 TeV, 139 fb−1,mH = 125.09 GeVFigure 11. Expected fractional contributions of the statistical (orange) and systematic (blue)uncertainties to the total uncertainty in the measurements of the parameters of the rotated basis c′with the SMEFT linearised model (top panel), and the corresponding expected fractional contributionsof experimental (cyan), signal theory (light blue) and background theory (dark blue) uncertainties tothe total systematic uncertainty (bottom panel).theory systematic uncertainties include both total cross-section uncertainties and acceptanceuncertainties. The breakdown of the total uncertainty into statistical and systematic com-ponents is performed as follows. The statistical uncertainty in each parameter is estimatedfrom the 68% confidence interval obtained when fixing to their best-fit values all nuisanceparameters associated with systematic uncertainties, and leaving unconstrained all otherparameters. The total systematic uncertainty is calculated as the square root of the differenceof the squares of the total uncertainty and the statistical uncertainty. The contributionfrom a group of systematic uncertainties is estimated as the difference of the squares of thetotal uncertainty and the uncertainty from a fit in which the associated nuisance parametersare fixed to their best-fit values.For parameters cHe,33, e[1]globand e[1]Hllll, the fractional contribution of systematic uncer-tainties is close to 50%; for parameters e[1]ggF, e[2]ggF, e[1]ttH and e[2]ttH, the fractional contributionof systematic uncertainties is around 40%; the remaining parameters have smaller relativesystematic uncertainties. In particular, the uncertainties in the cHe,22 and e[3]ttH parameters,probed by the measurements of the rare processes H → µµ decay and tH production, respec-tively, are almost completely dominated by the statistical component. The total systematicuncertainty in most parameters is dominated by experimental systematic uncertainties, excepte[1]ggF and e[1]glob, where signal theory systematic uncertainties dominate, and e[2]ggF, e[1]ttH ande[2]ttH, where background theory systematic uncertainties dominate. The breakdown of the un-certainty components, including a breakdown of the systematic uncertainty into experimental,signal theory and background theory components, is also given in tables 3 and 4.The expected and observed correlation matrices are shown in figure 12, and show areasonably good decorrelation achieved between the fit basis parameters: over half of theoff-diagonal elements are smaller than 0.1 and over 85% are smaller than 0.3 in both the– 29 –JHEP11(2024)097Parameter Value σtot σstat σsyst σexpsyst σth.sigsyst σth.bkgsystceH,22 −0.0002 0.0028 0.0026 0.0009 0.0006 0.00049 +0.0003−0.0005ceH,33 0.019 0.016 0.011 0.011 0.008 0.006 0.005c(3)Hq 0.039 0.040 0.034 0.021 0.015+0.011−0.005 0.012cbH 0.055 +0.039−0.058 +0.032−0.045 +0.023−0.037 +0.014−0.022 0.015 +0.013−0.025e[1]ggF 0.0003 0.0039 0.0029 0.0026 0.0013 0.0021+0.0013−0.0008e[2]ggF −0.07 0.38 0.29 0.25 0.13 0.11 0.18e[3]ggF 5.5 7.1 5.8 4.00 2.71+2.8−2.1 1.6e[1]Hγγ,Zγ 0.0048 0.0043 0.0034 0.0026 0.0017 0.0015 0.0012e[2]Hγγ,Zγ −0.042 0.041 0.037 +0.015−0.022 0.014 +0.006−0.011 +0.006−0.010e[3]Hγγ,Zγ −0.47 0.62 0.51 0.35 0.24 0.20 0.16e[1]ZH −0.14 0.34 0.29 0.19 0.16 0.09 +0.08−0.11e[2]ZH 3.7 3.9 3.3 2.1 1.6 0.9 1.0e[3]ZH 1.8 8.5 7.2 4.5 3.4 2.2 2.0e[4]ZH 4.8 9.8 8.2 5.2 4.0 2.5 2.2e[1]ttH −0.65 0.84 0.64 0.54 0.31 0.17 0.41e[2]ttH −0.05 3.7 2.8 2.4 0.94 +0.3−0.6 2.2e[3]ttH 8.6+13.4−9.2+12.1−8.8+5.73−2.91+3.9−2.1+3.8−1.5+2.0−1.2e[1]glob 0.13+0.83−0.57+0.57−0.42+0.60−0.38+0.30−0.20+0.42−0.29+0.29−0.17e[1]Hllll −0.349 1.1 0.76 0.74 0.44 0.38 0.46Table 3. Summary of the observed measurements of the parameters of the rotated basis c′ in theSMEFT linearised model, with a breakdown of the total uncertainty into statistical and systematiccomponents. A further breakdown of the systematic uncertainty into experimental and theoreticaluncertainties in the signal and background is also listed. All MC statistical uncertainties are classifiedas experimental systematic uncertainties in the breakdown. All uncertainties correspond to 68% CLintervals. The sum in quadrature of the systematic uncertainty components may differ from the totalsystematic uncertainty due to correlations.– 30 –JHEP11(2024)097Parameter Value σtot σstat σsyst σexpsyst σth.sigsyst σth.bkgsystceH,22 0.0 0.0031 0.0030 0.0010 0.0007 +0.0004−0.0005 +0.0004−0.0006ceH,33 0.0 0.019 0.013 0.014 0.010 0.007 0.007c(3)Hq 0.0 0.044 0.037 0.023 0.017 0.007 0.015cbH 0.0 +0.05−0.09 +0.04−0.07 +0.03−0.06 +0.02−0.03 +0.01−0.02 +0.02−0.04e[1]ggF 0.0 0.0046 0.0035 0.0029 0.0015 0.0022+0.0015−0.0011e[2]ggF 0.0 0.46 0.36 0.29 0.15 0.13 0.20e[3]ggF 0.0 8.4 7.1 4.4 3.1 2.5 1.9e[1]Hγγ,Zγ 0.0 0.0057 0.0043 0.0030 0.0021 0.0016+0.0012−0.0018e[2]Hγγ,Zγ 0.0 0.044 0.040 0.019 0.016+0.005−0.007 0.009e[3]Hγγ,Zγ 0.0 0.68 0.56 0.37 0.25+0.25−0.15 0.17e[1]ZH 0.0 0.40 0.34 0.21 0.15 0.10 0.10e[2]ZH 0.0 4.4 3.7 2.3 1.8 0.96 1.10e[3]ZH 0.0 9.8 8.4 5.0 3.7 2.5 2.3e[4]ZH 0.0 11 9.9 5.7 4.5 2.6 2.5e[1]ttH 0.0 1.0 0.79 0.68 0.40 0.22 0.49e[2]ttH 0.0 4.7 3.5 3.1 1.2 0.61 2.8e[3]ttH 0.0+10.4−7.6+10.0−7.0 3.02 2.25 +1.79−1.30 +0.97−1.51e[1]glob 0.0+0.93−0.60+0.64−0.46+0.67−0.39 0.28 +0.49−0.23 +0.35−0.18e[1]Hllll 0.0 1.23 0.89 0.85 0.54 0.39 0.53Table 4. Summary of the expected measurements of the parameters of the rotated basis c′ with theSMEFT linearised model, with a breakdown of the total uncertainty into a statistical and systematiccomponent. A further breakdown of the systematic uncertainty into experimental and theoreticaluncertainties in the signal and background is also listed. All MC statistical uncertainties are classifiedas experimental systematic uncertainties in the breakdown. All uncertainties correspond to 68% CLintervals. The sum in quadrature of the systematic uncertainty components may differ from the totalsystematic uncertainty due to correlations.– 31 –JHEP11(2024)097observed and expected matrix. A few exceptions stand out, notably the correlation betweene[2]ggF and e[1]ttH and between e[3]ggF and e[1]Hγγ,Zγ , which are caused by a common sensitivity tottH production and ggF H → γγ, respectively.Model including quadratic terms. Figure 13 compares the expected and observed resultsobtained using the SMEFT model including quadratic terms, again showing good agreementof the observed data with the SM expectation, corresponding to a p-value of 98.2%. For mostparameters, the observed uncertainty is noticeably smaller than the expected uncertainty. Thecause of this discrepancy is related to appearance of quadratic parameter terms in the cross-section predictions, which cause the likelihood function to generally have multiple minima ineach parameter. In the expected result, most nearby minima that are exactly degeneratewith the global minimum merge into a single wider uncertainty interval. Conversely, in theobserved result, the generally non-zero observed coefficient values lift some of these minimato become local minima, thereby resulting in a narrower interval around the remaining globalminimum. This effect can be clearly seen in more detail in the profile likelihood scans of eachparameter, shown in figures 14 and 15. Most secondary minima are raised by 1–2 units in−2 logL, thus narrowing the 68% confidence intervals, which are based on a unit threshold,but less so the 95% confidence intervals based on a 3.84 unit threshold. For all parameterswith multiple solutions, the global minimum in the observed result resolves to the minimumclosest to a coefficient value of zero, except parameter e[1]Hγγ,Zγ , where the minimum furthestfrom zero becomes the global minimum. For the parameter ceH,22, there are two exactlydegenerate minima. In that case, the minimum closest to that of the interpretation withthe linear model is quoted as the best-fit result.Almost all profile likelihood functions show Gaussian behaviour to a good approximationwithin the 95% CL range of each parameter, although this is masked by the appearanceof degenerate solutions. The only exception is the expected profile likelihood for the e[3]ttHparameter in the linearised model, where a boundary occurs at e[3]ttH = −10, just before thelikelihood threshold of the 95% CL is reached. The yield prediction in the high-pT regionof the ttH, H→ γγ channel becomes negative for very negative values of e[3]ttH, rendering thelikelihood undefined beyond that point. The 95% CL interval for e[3]ttH shown in figures 10and 16 is truncated at this boundary, resulting in a small undercoverage.3.2.3 Comparison between the linearised model and the model includingquadratic termsFigure 16 compares the results for the linearised model and the model with quadratic termsfor the observed data and shows that for several of the coefficients the constraints from themodel with the quadratic terms are significantly stronger than those observed for the linearmodel. In most cases, the stronger constraints arise from the relatively weak impact of theBSM-SM interference term on the cross-section compared to the quadratic BSM terms inspecific production or decay modes.Figure 9 illustrates the impact of both the linear model and the model with quadraticterms, where the impact strength visualised for both models corresponds to the expected 68%uncertainty of each fit basis parameter c′ under the linear model. The comparatively larger– 32 –JHEP11(2024)097c(3)HqcbHceH,22ceH,331 0.01 −0.06−0.170.01 1 0.11 0.34−0.06 0.11 1 0.13−0.17 0.34 0.13 1−0.07−0.03 0.10−0.33 0.02 0.020.02 −0.06−0.05 0.11 −0.09−0.02−0.20−0.460.35 0.04 0.030.08 0.030.33 0.08 −0.09−0.26 0.27 −0.16−0.210.18 0.10 0.28 0.250.07 0.03 0.10 0.110.20 0.07 0.36 0.34−0.020.06 0.03 −0.12−0.020.08 −0.03−0.17−0.340.060.280.17−0.19−0.12−0.33e[1]ggFe[2]ggFe[3]ggF−0.07−0.33 0.02 −0.05−0.03 0.02 0.110.10 0.02 −0.06−0.091 −0.18 0.25−0.18 1 −0.310.25 −0.31 10.35 0.02 −0.04−0.22−0.01−0.020.64 0.03−0.07 0.11 0.07 0.150.21 0.04 0.08 0.04−0.51−0.25−0.19−0.22−0.03−0.05 0.120.72 0.07−0.19−0.08 0.04−0.080.11−0.05−0.07−0.010.08e[1]Hγγ,Zγe[2]Hγγ,Zγe[3]Hγγ,Zγ−0.02 0.35 0.08 0.33−0.20 0.04 0.03 0.08−0.46 0.03 −0.090.35 −0.22 0.640.02 −0.01 0.03−0.04−0.021 0.06 −0.170.06 1 0.19−0.17 0.19 1−0.13 0.02 0.25 0.25−0.07−0.16−0.04−0.04−0.37−0.56−0.41−0.38−0.08−0.06 0.06−0.02−0.050.170.04−0.28−0.22−0.19−0.18e[1]ZHe[2]ZHe[3]ZHe[4]ZH−0.26 0.18 0.07 0.200.27 0.10 0.03 0.07−0.16 0.28 0.10 0.36−0.21 0.25 0.11 0.34−0.07 0.21 −0.510.11 0.04 −0.250.07 0.08 −0.190.15 0.04 −0.22−0.13−0.07−0.370.02 −0.16−0.560.25 −0.04−0.410.25 −0.04−0.381 0.38 0.46 0.480.38 1 0.33 0.350.46 0.33 1 0.530.48 0.35 0.53 10.15 0.04 −0.010.05 0.04 0.020.07 −0.020.05 0.020.09−0.060.250.24−0.010.23−0.04e[1]ttHe[2]ttHe[3]ttH−0.02 0.06 0.080.03−0.12−0.02−0.03−0.03 0.72 −0.19−0.05 0.07 −0.080.12 0.04−0.08−0.060.06 −0.02−0.050.15 0.05 0.07 0.050.04 0.04 0.02−0.01 0.02 −0.021 0.050.05 1 −0.01−0.01 1−0.02−0.010.03eglob −0.17−0.34 0.06 0.28 −0.08 0.11 −0.05 0.17 0.04 −0.28 0.09 −0.06 0.25 0.24 −0.02−0.01 0.03 1 −0.19c(3) Hqc bHc eH,22c eH,33e[1]Hllll0.17 −0.19−0.12−0.33e[1] ggFe[2] ggFe[3] ggF−0.07−0.01 0.08e[1] Hγγ,Zγe[2] Hγγ,Zγe[3] Hγγ,Zγ−0.22−0.19−0.18e[1] ZH e[2] ZH e[3] ZH e[4] ZH−0.01 0.23 −0.04e[1] ttH e[2] ttH e[3] ttHe glob−0.19e[1] Hllll1−1.0−0.50.00.51.0ρ(X,Y)ATLASExpected√s = 13TeV, 139 fb−1mH = 125.09GeV, |yH| < 2.5SMEFT Λ = 1TeV(a)c(3)HqcbHceH,22ceH,331 −0.12−0.07−0.19−0.12 1 0.15 0.26−0.07 0.15 1 0.14−0.19 0.26 0.14 1−0.02−0.03 0.11−0.35 0.02 −0.04−0.00 0.01 −0.050.00 0.14 −0.10−0.02−0.21−0.500.31 0.19 0.070.08 0.05 0.000.35 0.07 −0.14−0.30 0.31 −0.16−0.200.28 −0.01 0.35 0.260.08 0.02 0.11 0.120.22 0.06 0.38 0.37−0.04 0.00 0.030.16 0.03 −0.280.02 0.01 −0.040.09 0.01 −0.01−0.06−0.250.050.410.19−0.19−0.12−0.37e[1]ggFe[2]ggFe[3]ggF−0.02−0.35−0.00 0.00−0.03 0.02 0.01 0.140.11 −0.04−0.05−0.101 −0.20 0.26−0.20 1 −0.330.26 −0.33 10.34 −0.03−0.06−0.23−0.02−0.030.64 0.03 −0.01−0.09 0.12 0.07 0.150.22 0.05 0.08 0.05−0.54−0.26−0.20−0.24−0.07−0.05 0.180.74 0.11 −0.01−0.23−0.09 0.01−0.100.140.03−0.05−0.020.06e[1]Hγγ,Zγe[2]Hγγ,Zγe[3]Hγγ,Zγ−0.02 0.31 0.08 0.35−0.21 0.19 0.05 0.07−0.50 0.07 0.00 −0.140.34 −0.23 0.64−0.03−0.02 0.03−0.06−0.03−0.011 0.07 −0.210.07 1 0.23−0.21 0.23 1−0.13−0.01 0.27 0.26−0.03−0.18−0.02−0.04−0.32−0.60−0.39−0.40−0.10−0.06 0.040.02 0.00 −0.080.04 0.00 −0.110.27−0.09−0.37−0.24−0.19−0.16e[1]ZHe[2]ZHe[3]ZHe[4]ZH−0.30 0.28 0.08 0.220.31 −0.01 0.02 0.06−0.16 0.35 0.11 0.38−0.20 0.26 0.12 0.37−0.09 0.22 −0.540.12 0.05 −0.260.07 0.08 −0.200.15 0.05 −0.24−0.13−0.03−0.32−0.01−0.18−0.600.27 −0.02−0.390.26 −0.04−0.401 0.37 0.49 0.520.37 1 0.28 0.370.49 0.28 1 0.570.52 0.37 0.57 10.20 0.05 −0.030.05 0.04 0.050.10 0.01 −0.030.06 0.02 0.000.030.040.230.26−0.010.25−0.06−0.01e[1]ttHe[2]ttHe[3]ttH−0.04 0.16 0.02 0.090.00 0.03 0.01 0.010.03 −0.28−0.04−0.01−0.07 0.74 −0.23−0.05 0.11 −0.090.18 −0.01 0.01−0.10 0.02 0.04−0.06 0.00 0.000.04 −0.08−0.110.20 0.05 0.10 0.060.05 0.04 0.01 0.02−0.03 0.05 −0.03 0.001 0.10 −0.050.10 1 −0.12−0.05−0.12 1−0.10−0.010.16−0.010.02−0.02eglob −0.06−0.25 0.05 0.41 −0.10 0.14 0.03 0.27 −0.09−0.37 0.03 0.04 0.23 0.26 −0.10−0.01 0.16 1 −0.25c(3) Hqc bHc eH,22c eH,33e[1]Hllll0.19 −0.19−0.12−0.37e[1] ggFe[2] ggFe[3] ggF−0.05−0.02 0.06e[1] Hγγ,Zγe[2] Hγγ,Zγe[3] Hγγ,Zγ−0.24−0.19−0.16e[1] ZH e[2] ZH e[3] ZH e[4] ZH−0.01 0.25 −0.06−0.01e[1] ttH e[2] ttH e[3] ttH−0.01 0.02 −0.02e glob−0.25e[1] Hllll1−1.0−0.50.00.51.0ρ(X,Y)ATLAS√s = 13TeV, 139 fb−1mH = 125.09GeV, |yH| < 2.5SMEFT Λ = 1TeV(b)Figure 12. The (a) expected and (b) observed correlation matrix for the parameters of the rotatedbasis c′ obtained from a fit to the linearised SMEFT model.– 33 –JHEP11(2024)097Symmetrizeduncertainty(σ)ProbedScale(Λ/√σ)[TeV]−4−2024Best Fit68 % CL95 % CLceH,22ceH,33c (3)HqcbHe [1]ggFe [2]ggFe [3]ggFe [1]Hγγ,Zγe [2]Hγγ,Zγe [3]Hγγ,Zγe [1]ZHe [2]ZHe [3]ZHe [4]ZHe [1]ttHe [2]ttHe [3]ttHe [1]globe [1]HllllpSM = 98.2%Parametervaluescaledbysymmetrizeduncertainty(c′ /σ)ATLASSMEFT Λ = 1 TeV√s =13 TeV, 139 fb−1,mH = 125.09 GeV10−310−210−110010132103.210.32Linear+quad. (obs.)Linear+quad. (exp.)Figure 13. Comparison of the expected (gray) and observed (blue) parameters of the rotated basisc′ with the SMEFT model with quadratic terms, where all other coefficients and nuisance parametersare profiled. The top panel shows the symmetrised 68% uncertainty σ of each parameter measurement(left vertical axis) and the corresponding energy scale Λ/√σ that is probed (right vertical axis). Thebottom panel shows the measured parameter value and 68% (solid) and 95% (dashed) CL intervals,divided by the symmetrised uncertainty shown in the top panel. Some of the observed intervals shownare clipped off. Due to multiple minima, the likelihood curves from which these CL intervals arederived are non parabolic. For the parameter ceH,22, for which there are two degenerate minima inthe interpretation with the model including quadratic terms, the point corresponds to the best-fitvalue that is closest to that of the interpretation with the linear model.impact of the model including quadratic terms at these chosen parameter values identifiesSTXS regions where quadratic terms outweigh the linear terms at the measured scale andthus identifies regions that predominantly provide the extra constraining power of the modelsincluding quadratic terms. The strongest observed sensitivity enhancements occur in e[3]ggF,e[2]ttH and e[3]ttH. For coefficient e[3]ggF, the quadratic term significantly increases sensitivity in theggF, ZH and ttH production modes as well as in the H → γγ decay mode. For coefficientse[2]ttH and e[3]ttH, the quadratic term enhances sensitivity in high-pT ttH production and tHproduction, respectively. Conversely, for the coefficients e[2]ggF and e[3]Hγγ,Zγ , the effect of theincreased impact of the quadratic terms is limited, and the strong reduction in uncertaintiesis mostly driven by the lifting of degenerated solutions in the observed case compared withexpected, as visible in the profile likelihood scans in figure 14.– 34 –JHEP11(2024)097Operators in Warsaw basis: ceH,22, ceH,33, c(3)Hq and cbHATLAS√s =13 TeV, 139 fb−1mH = 125.09 GeVSMEFT Λ = 1 TeV−0.03 −0.02 −0.01 0 0.01 0.02 0.03024681012ceH,22−2log(L/L max)Linear (exp.)Linear (obs.)Linear + quad. (exp.)Linear + quad. (obs.)(a)ATLAS√s =13 TeV, 139 fb−1mH = 125.09 GeVSMEFT Λ = 1 TeV−0.1 −0.05 0 0.05 0.1024681012ceH,33−2log(L/L max)Linear (exp.)Linear (obs.)Linear + quad. (exp.)Linear + quad. (obs.)(b)ATLAS√s =13 TeV, 139 fb−1mH = 125.09 GeVSMEFT Λ = 1 TeV−0.2 −0.1 0 0.1 0.2024681012c (3)Hq−2log(L/L max)Linear (exp.)Linear (obs.)Linear + quad. (exp.)Linear + quad. (obs.)(c)ATLAS√s =13 TeV, 139 fb−1mH = 125.09 GeVSMEFT Λ = 1 TeV−0.6 −0.4 −0.2 0 0.2 0.4 0.6024681012cbH−2log(L/L max)Linear (exp.)Linear (obs.)Linear + quad. (exp.)Linear + quad. (obs.)(d)Eigenvector group ggFATLAS√s =13 TeV, 139 fb−1mH = 125.09 GeVSMEFT Λ = 1 TeV−0.03 −0.02 −0.01 0 0.01 0.02 0.03024681012e[1]ggF−2log(L/L max)Linear (exp.)Linear (obs.)Linear + quad. (exp.)Linear + quad. (obs.)(e)ATLAS√s =13 TeV, 139 fb−1mH = 125.09 GeVSMEFT Λ = 1 TeV−2 −1 0 1 2024681012e[2]ggF−2log(L/L max)Linear (exp.)Linear (obs.)Linear + quad. (exp.)Linear + quad. (obs.)(f)ATLAS√s =13 TeV, 139 fb−1mH = 125.09 GeVSMEFT Λ = 1 TeV−30 −20 −10 0 10 20 30024681012e[3]ggF−2log(L/L max)Linear (exp.)Linear (obs.)Linear + quad. (exp.)Linear + quad. (obs.)(g)Eigenvector group H → γγ,ZγATLAS√s =13 TeV, 139 fb−1mH = 125.09 GeVSMEFT Λ = 1 TeV−0.1 −0.05 0 0.05 0.1024681012e[1]Hγγ,Zγ−2log(L/L max)Linear (exp.)Linear (obs.)Linear + quad. (exp.)Linear + quad. (obs.)(h)ATLAS√s =13 TeV, 139 fb−1mH = 125.09 GeVSMEFT Λ = 1 TeV−0.4 −0.2 0 0.2 0.4024681012e[2]Hγγ,Zγ−2log(L/L max)Linear (exp.)Linear (obs.)Linear + quad. (exp.)Linear + quad. (obs.)(i)ATLAS√s =13 TeV, 139 fb−1mH = 125.09 GeVSMEFT Λ = 1 TeV−4 −2 0 2 4024681012e[3]Hγγ,Zγ−2log(L/L max)Linear (exp.)Linear (obs.)Linear + quad. (exp.)Linear + quad. (obs.)(j)Eigenvector group ZHATLAS√s =13 TeV, 139 fb−1mH = 125.09 GeVSMEFT Λ = 1 TeV−1.5 −1 −0.5 0 0.5 1 1.5024681012e[1]ZH−2log(L/L max)Linear (exp.)Linear (obs.)Linear + quad. (exp.)Linear + quad. (obs.)(k)ATLAS√s =13 TeV, 139 fb−1mH = 125.09 GeVSMEFT Λ = 1 TeV−20 −10 0 10 20024681012e[2]ZH−2log(L/L max)Linear (exp.)Linear (obs.)Linear + quad. (exp.)Linear + quad. (obs.)(l)ATLAS√s =13 TeV, 139 fb−1mH = 125.09 GeVSMEFT Λ = 1 TeV−40 −20 0 20 40024681012e[3]ZH−2log(L/L max)Linear (exp.)Linear (obs.)Linear + quad. (exp.)Linear + quad. (obs.)(m)ATLAS√s =13 TeV, 139 fb−1mH = 125.09 GeVSMEFT Λ = 1 TeV−40 −20 0 20 40024681012e[4]ZH−2log(L/L max)Linear (exp.)Linear (obs.)Linear + quad. (exp.)Linear + quad. (obs.)(n)Figure 14. Profile likelihood scans of the fitted coefficients of the rotated basis c′ obtained from fits tothe SM expectation (dashed lines) and to the observed data (solid lines), based on the SMEFT linearisedmodel (blue) and the SMEFT model with quadratic terms (orange). The horizontal dashed lines ineach plot correspond to the asymptotic threshold values for 68% and 95% CL intervals. The profilelikelihood scans of the SMEFT model with quadratic terms can exhibit two minima in the scannedparameter, whereas the scans of the linearised model have one minimum per parameter. Multipleminima in the coefficients that are profiled in each scan may furthermore result in discontinuousderivatives in the profile likelihood (e.g., prominently visible in the observed data in (e) and (l)).– 35 –JHEP11(2024)097Eigenvector group topATLAS√s =13 TeV, 139 fb−1mH = 125.09 GeVSMEFT Λ = 1 TeV−4 −2 0 2 4024681012e[1]ttH−2log(L/L max)Linear (exp.)Linear (obs.)Linear + quad. (exp.)Linear + quad. (obs.)(a)ATLAS√s =13 TeV, 139 fb−1mH = 125.09 GeVSMEFT Λ = 1 TeV−20 −10 0 10 20024681012e[2]ttH−2log(L/L max)Linear (exp.)Linear (obs.)Linear + quad. (exp.)Linear + quad. (obs.)(b)ATLAS√s =13 TeV, 139 fb−1mH = 125.09 GeVSMEFT Λ = 1 TeV−60 −40 −20 0 20 40 60024681012e[3]ttH−2log(L/L max)Linear (exp.)Linear (obs.)Linear + quad. (exp.)Linear + quad. (obs.)(c)Eigenvector group overall normalisationATLAS√s =13 TeV, 139 fb−1mH = 125.09 GeVSMEFT Λ = 1 TeV−10 −5 0 5 10024681012e[1]glob−2log(L/L max)Linear (exp.)Linear (obs.)Linear + quad. (exp.)Linear + quad. (obs.)(d)Eigenvector group H → ZZ∗ATLAS√s =13 TeV, 139 fb−1mH = 125.09 GeVSMEFT Λ = 1 TeV−30 −20 −10 0 10 20 30024681012e[1]Hllll−2log(L/L max)Linear (exp.)Linear (obs.)Linear + quad. (exp.)Linear + quad. (obs.)(e)Figure 15. Profile likelihood scans of the fitted coefficients of the rotated basis c′ obtained fromfits to the SM expected (dashed lines) and to the observed data (solid lines), based on the SMEFTlinearised model (blue) and the SMEFT model with quadratic terms (orange). The horizontal dashedlines in each plot correspond to the asymptotic threshold values for 68% and 95% CL intervals.The profile likelihood scans of the SMEFT model with quadratic terms can exhibit two minima inthe scanned parameter, whereas the scans of the linearised model can only have one minimum perparameter. Multiple minima in the coefficients that are profiled in each scan may furthermore resultin discontinuous derivatives in the profile likelihood (e.g., prominently visible in the observed datain (d)).– 36 –JHEP11(2024)097Symmetrizeduncertainty(σ)ProbedScale(Λ/√σ)[TeV]−4−2024Best Fit68 % CL95 % CLceH,22ceH,33c (3)HqcbHe [1]ggFe [2]ggFe [3]ggFe [1]Hγγ,Zγe [2]Hγγ,Zγe [3]Hγγ,Zγe [1]ZHe [2]ZHe [3]ZHe [4]ZHe [1]ttHe [2]ttHe [3]ttHe [1]globe [1]HllllParametervaluescaledbysymmetrizeduncertainty(c′ /σ)ATLASSMEFT Λ = 1 TeV√s =13 TeV, 139 fb−1,mH = 125.09 GeV10−310−210−110010132103.210.32Linear (obs.)Linear+quad. (obs.)Figure 16. Comparison of the observed parameters of the rotated basis c′ with the SMEFT linearisedmodel (blue) and the model including quadratic terms (orange), where all other coefficients andnuisance parameters are profiled. The top panel shows the symmetrised 68% CL uncertainty σ of eachparameter measurement (left vertical axis) and the corresponding energy scale Λ/√σ that is probed(right vertical axis). The bottom panel shows the measured parameter value and 68% (solid) and 95%(dashed) CL intervals, divided by the symmetrised uncertainty shown in the top panel. Some of theintervals shown for the model with quadratics terms are clipped off. Due to multiple minima thelikelihood curves from which these CL intervals are derived are non-parabolic. The 95% CL intervalfor e[3]ttH is truncated at the boundary at which the log likelihood becomes undefined, resulting in asmall undercoverage. For the parameter ceH,22, for which there are two degenerate minima in theinterpretation with the model including quadratic terms, the point corresponds to the best-fit valuethat is closest to that of the interpretation with the linear model.– 37 –JHEP11(2024)0973.3 Constraints from fiducial differential measurementsCoefficients of SMEFT operators can alternatively be constrained from fiducial cross-sectionmeasurements. Fiducial differential cross-section measurements are, unlike STXS measure-ments, explicitly unfolded to the particle level. The finer granularity of kinematic regionsdefined in differential measurements, compared to STXS measurements, offers an advantage inthe analysing power of differential distributions, but is counteracted by the inclusive treatmentof Higgs boson production processes, which are modelled separately in the STXS approach.For a comparison to the STXS approach, differential measurements in the pT of theHiggs boson are considered. Anomalous couplings of the Higgs boson to gluons and topquarks, as well as between gluons and top quarks, can affect the total Higgs boson productioncross-section and its dependence on the Higgs boson transverse momentum.The expected deviations from the SM predictions due to these anomalous couplingscan be relatively large in high Higgs boson pT regions, which are also characterised by abetter signal-to-background ratio, making the pHT -differential cross-section measurement moresensitive to these effects compared to a measurement of the inclusive rate.3.3.1 Sensitivity estimate and choice of parametersIn this study, constraints on anomalous Higgs boson couplings to gluons and top quarks areset from the observed transverse momentum differential spectra of the Higgs boson decayproducts in the H→ZZ∗→ 4ℓ and H→ γγ decay channels. The constraints are inferred usingan EFT approach in which the SM Lagrangian is augmented with the three dimension-6SMEFT operators OHG (Higgs-gluon point-like contact term), OtH (top quark Yukawacoupling modifier) and OtG (chromomagnetic dipole operator), that are defined in table 2.The operator OHG introduces an Hgg contact interaction that modifies the value and pT-dependence of the ggF production cross-section, as well as the H → gg partial decay width,thus affecting indirectly the H→ZZ∗→ 4ℓ and H→ γγ branching ratios. The operator OtHmodifies the tt¯H vertex and thus affects Higgs boson production through top-quark-loopmediated gluon-gluon fusion or in association with a tt¯ pair, as well as the top-quark-loopamplitude contributing to the H → γγ partial width. The operator OtG introduces a tt¯Hgvertex that leads to additional contributions to the amplitude for ggF or tt¯H Higgs bosonproduction, as well as for H → gg decays, affecting in turn the branching ratios for bothH → γγ and H→ZZ∗→ 4ℓ.The study presented in this section is performed in the scenario in which only theSM-BSM interference effects, linear in the Wilson coefficients, are considered. For simplicity,due to the statistical precision of the data sample and the very large correlations between theestimators for the three Wilson coefficients, the constraints are initially set on one Wilsoncoefficient at a time, while the values of the remaining coefficients are assumed to be equalto zero. Subsequently, similarly to the approach presented in section 3.2.1, a rotation inthe parameter space is performed to define a new set of coefficients that are decorrelatedand can be probed simultaneously. The new basis is formed by the three eigenvectors ev[i](i = 1..3) of the Fisher information matrix, which are related to the three Wilson coefficients– 38 –JHEP11(2024)0970.51unc.0.2−0.1−00.10.20.30.40.5 B)(c)/SM× σ(∆=0.003[1] ev=2.01[2] ev=3.93[3] evATLAS-1 = 13 TeV, 139 fbs0-5 5-10 10-15 15-20 20-25 25-30 30-35 35-45 45-60 60-80 80-100 100-120 120-140 140-170 170-200 200-250 250-300 300-450 450-650 650≥ 0-1010-2020-3030-4545-6060-8080-120120-200200-300 [GeV]γγTp [GeV]4lTpFigure 17. Impact of the rotated SMEFT operators on the fiducial cross-section differential in pHT inH→ γγ and H → ZZ∗ decays, relative to the SM cross-section, under the assumption of the linearisedSMEFT model. To judge the experimental sensitivity to constrain the operators from the data in thelisted fiducial regions, the total uncertainty in the corresponding regions is shown in the top panel.For presentational clarity, the uncertainty of low precision fiducial regions is clipped off in the plot.by the following rotation:ev[1] = 0.999cHG − 0.035ctG − 0.003ctH ,ev[2] = 0.035cHG + 0.978ctG + 0.205ctH ,ev[3] = −0.005cHG − 0.205ctG + 0.979ctH .The impact of the operators defining the new basis on the fiducial differential cross-sectionsis shown in figure 17.3.3.2 ResultsThe statistical interpretation is performed using a joint likelihood model of the data inthe two decay channels, built, as described in section 2.3, from the observed and expectedvalues of the fiducial differential cross-sections in each bin of the transverse momentum ofthe Higgs boson decay products for both H → 4ℓ and H → γγ decays. In the likelihoodfunction, the theoretical prediction for each decay channel and transverse momentum intervalis parameterised as a function of the Wilson coefficients, as summarised in section 3.1. Theprocedure assumes common higher-order corrections for the SMEFT and SM processes.The theoretical uncertainties are taken from the SM calculations in section 2.2, with theuncertainty associated with the SMEFT scaling assumed to be negligible.Figure 18 shows the 68% CL one-dimensional intervals in the linearised model for therotated parameters ev[i] with the other two parameters profiled. The constraint on thefirst rotated parameter, which is almost aligned with cHG, is of the order of 1%, while theconstraints on the other two rotated parameters are O(1). Figure 18 compares these resultsto those obtained from the STXS measurements performed with the same decay channelsusing a linearised model in which all Wilson coefficients except for ctH , ctG and cHG are set– 39 –JHEP11(2024)097−6 −4 −2 0 2 4 6ATLAS√s =13 TeV, 139 fb−1SMEFT Λ = 1 TeV3-parameter fit (Observed)1000× ev [1]ev [2]ev [3]Parameter ValueBest Fit68 % CLDifferential H → γγ + H → 4lSTXS H → γγ + H → 4l(a)−6 −4 −2 0 2 4 6ATLAS√s =13 TeV, 139 fb−1SMEFT Λ = 1 TeV3-parameter fit (Expected)ev [3]ev [2]1000× ev [1]Parameter ValueBest Fit68 % CLDifferential H → γγ + H → 4lSTXS H → γγ + H → 4l(b)Figure 18. The (a) observed and (b) expected 68% CL intervals on the three rotated parametersev[i] obtained with the SMEFT linearised model using either STXS (blue) or fiducial pT-differentialcross-section measurements (green) in the H → γγ and H → 4ℓ decay channels. The parameter ev[1]is almost aligned with cHG, which mainly affects ggF production, while the parameters ev[2] and ev[3]are close to ctG and ctH respectively, which impact both ggF and tt¯H production.to zero. The comparison illustrates that the differential cross-section measurements, whichhave a finer granularity compared to the STXS measurements but probe the distributionof a single observable inclusively in production mode, have less constraining power thanthe STXS measurements, which use information on the particles produced with the Higgsboson decay products to separate the different production modes whose cross-sections areaffected in different ways by the different operators, as shown in figure 5. In particular, thelarge sensitivity difference observed for ev[2] originates from the separate measurements ofggF and ttH production in the STXS framework.– 40 –JHEP11(2024)0974 Interpretations based on UV-complete BSM modelsIn this section, the measurements of Higgs boson cross-sections and decay rates are interpretedin two UV-complete extensions of the SM: a two-Higgs-doublet model near the alignmentlimit (section 4.1), and eight benchmark scenarios of the minimal supersymmetric extensionof the SM (section 4.2).4.1 Constraints on two-Higgs-doublet modelsIn two-Higgs-doublet models, the SM Higgs sector with one doublet of scalar complex fieldsΦ1 is extended by introducing a second doublet Φ2 [11–13]. The models considered hereassume CP conservation and a (softly broken) Z2 discrete symmetry that forbids quarticterms of the scalar field potential V (Φ1, Φ2) that contain odd powers of either Φ1 or Φ2. Thevacuum expectation values v1,2 of the scalar doublets Φ1,2 that minimise V are related bythe sum rule v21 + v22 = v2. These can be assumed to be both real and non-negative withoutloss of generality. Electroweak symmetry breaking leads to five physical scalar Higgs fields:two neutral CP-even Higgs bosons h and H, one neutral CP-odd Higgs boson A, and twocharged Higgs bosons H±. For the results presented in this section, the observed Higgs bosonis identified with the lightest CP-even neutral scalar particle h.The Z2 symmetry of the potential forbids tree-level flavour-changing neutral currents [108,109], which are strongly constrained by existing data, and implies that all fermions withthe same quantum numbers couple to only one Higgs doublet. Depending on which Higgsdoublet couples to the three groups of elementary fermions (up-type and down-type quarks,and leptons), four types of 2HDM are defined:• Type I: All fermions couple to the same Higgs doublet.• Type II: One Higgs doublet couples to up-type quarks while the other one couples todown-type quarks and charged leptons.• Lepton-specific: One Higgs doublet couples to leptons while the other one couples toup- and down-type quarks.• Flipped: One Higgs doublet couples to down-type quarks while the other one couplesto up-type quarks and leptons.The Higgs sector of these models contains seven free physical parameters: four Higgsboson masses (mh, mH , mA and mH±), two mixing angles α and β, and the coefficient m212of the (Φ†1Φ2 +Φ†2Φ1) term in the Higgs field potential that softly breaks the Z2 symmetry.The angle β is defined as tan β = v2v1 and can be assumed to be in the first quadrant. Themixing angle α of the neutral CP-even Higgs sector is defined, modulo a phase, equal toπ. It can thus be assumed that 0 ≤ β − α ≤ π.The values of α and β determine the couplings of the Higgs fields to the vector bosonsand to the fermions. In this section, the decoupling limit is assumed, in which mH ≫ v. Thisin turn implies the alignment limit, | cos(β − α)| ≪ 1, in which the light scalar Higgs bosonh has SM-like couplings. The mass of the light Higgs boson mh is assumed to be close to125 GeV, while all other Higgs bosons are assumed to be significantly heavier (and their– 41 –JHEP11(2024)097Coupling Type I Type II Lepton-specific Flippedu, c, t sβ−α + cβ−α/ tan βd, s, b sβ−α + cβ−α/ tan β sβ−α − cβ−α × tan β sβ−α + cβ−α/ tan β sβ−α − cβ−α × tan βe, µ, τ sβ−α + cβ−α/ tan β sβ−α − cβ−α × tan β sβ−α − cβ−α × tan β sβ−α + cβ−α/ tan βW , Z sβ−αh s3β−α +(3− 2 m¯2m2h)c2β−αsβ−α + 2 cot (2β)(1− m¯2m2h)c3β−αTable 5. Multiplicative factors predicted in the four 2HDM scenarios near the alignment limit, as afunction of tan β and cos(β−α), for the Higgs boson couplings to up-type quarks (1st row), down-typequarks (2nd row), charged leptons (3rd row), vector bosons (4th row), and to itself (5th row). Thesymbol cβ−α stands for cos(β − α), while sβ−α stands for sin(β − α). The definition of the parameterm¯ is given in the text.masses are assumed to be degenerate, mA ∼ mH± ∼ mH ∼ M). Near the alignment limit,i.e., for | cos(β − α)| small, the modifications of the tree-level couplings of the h boson withrespect to the SM predictions follow the expressions summarised in table 5 [13].In addition to the impact of the tree-level coupling modifications, the production anddecay rates of the h boson are modified through NLO EW corrections involving the trilinearhhh coupling λ [110]. In the 2HDM framework, this self-coupling is modified with respectto the SM expectation λSM by the scale factor (denoted by κλ) shown in the last row oftable 5 [111]. The parameter m¯ is m¯2 = m212sinβ cosβ = m2A + λ5v2, where λ5 is the coefficient ofthe (Φ†1Φ2)2 term of the Higgs potential. Near the alignment limit considered, the value ofm¯ is close to that of mA (λ5v2 ≪ m2A), and a value m¯ = mA = 1 TeV (λ5 = 0) is assumedin this section in all scenarios in which the effect of the self-coupling is considered in thecalculation of limits on cos(β − α) and tan β.In the following sections, limits on the 2HDM parameters cos(β − α) and tan β areinferred from studies of the ensemble of Higgs boson production and decay rate measurementsin two distinct scenarios: first by comparing the measured rates for each production modewith inclusive 2HDM predictions expressed in the ‘κ-framework’, and then by comparing themore fine-grained measurements described in section 2 with the 2HDM predictions expressedin the linearised statistical model of the EFT-based parameterisation described in section 3.4.1.1 Constraints based on the κ-frameworkIn the κ-framework [14], the Higgs boson production-mode cross-sections and decay branchingratios are parameterised in terms of multiplicative coupling strength modifiers κ [9]. In themodel considered in this study, the loop-induced processes (gluon-gluon fusion gg → H andgg → ZH production, as well as H → γγ, H → Zγ and H → gg decays) are expressedin terms of the strength factors for the couplings to the SM particles inside the loop. Themodel also assumes that there are no invisible or undetected Higgs boson decays beyond theSM. The impact of the trilinear hhh coupling modifier κλ on the Higgs boson productionand decay rates via NLO EW corrections to the LO amplitudes is also included in theparameterisations. Constraints on κλ from searches for Higgs boson pair production [112]are not taken into account. In the likelihood function in eq. (2.1), the signal strengths– 42 –JHEP11(2024)097µi,Xk are re-parametrised as µi,Xk = µi,X ({κ(tan β, cos(β − α))}) using the relations listed intable 5. Confidence regions for tan β and cos(β − α) can thus be inferred from the combinedmeasurements of Higgs boson production and decay rates.The resulting 95% CL contours in the (tan β, cos(β − α)) plane for 0.1 < tan β < 10 areshown in figure 19. All models exhibit similar exclusion regions in the (tan β, cos(β − α))plane at low values (≲ 1) of tan β, where only a narrow region of cos(β − α) around zero isconsistent with the measured values of the Higgs boson production and decay rates. Theinterval of allowed values of cos(β − α) increases in size with increasing tan β, up to a totalwidth of about 0.1–0.2 for tan β = 1, depending on the model. For higher values of tan β, inthe models in which at least one of the coupling strength modifiers is enhanced by a factortan β, i.e., all models except Type-I, the allowed range of cos(β − α) around zero shrinks astan β gets larger than one. This trend is observed also for the region tan β > 10, not shown infigure 19. For the Type-I model, the allowed range of cos(β − α) further increases with tan β,reaching a width of around 0.5 for tan β = 10. For tan β > 10, the allowed range of cos(β−α)remains approximately constant. This includes regions of the parameter space that deviatesignificantly from the alignment-limit hypothesis. When the constraint from the trilinearhhh coupling is included, the width of the 95% CL interval for cos(β − α) at large tan βfor the Type-I model is reduced by about 50%. An additional feature of the Type-I modelresult is that in the large tan β region, for positive cos(β − α), the observed exclusion regionis significantly larger than the expected one. This derives from the fact that the ATLASmeasurement of Higgs boson production and decay rates favours values of the couplingstrength modifiers to b-quarks, t-quarks and τ -leptons smaller than one and of the couplingsto W and Z bosons larger than one (κF = 0.95± 0.05 and κV = 1.035± 0.031 when assumingthat all fermions share the same modifier κF and that κW = κZ = κV [9]). In this scenario, themodel predicts sin(β−α) = κV ≈ 1 and cos(β−α) = tan β(κF − sin(β−α)) ≈ tan β(κF −1),disfavouring positive values of cos(β − α) for κF < 1.A second small region of allowed tan β and cos(β − α) values for large tan β and cos(β −α) ≈ 0.2 is present in the Type-II, Lepton-specific, and Flipped models. This corresponds toregions with cos(β+α) ≈ 0, for which some of the fermion couplings have the same magnitudeas in the SM but the opposite sign. In particular, this corresponds to a negative sign of thelepton couplings in the Lepton-specific model, of the down-type quark couplings in the Flippedmodel, or both in the Type-II model. Since the sign of these couplings is not sufficiently wellconstrained by current experimental measurements, this region is not excluded. The sameregion is however not allowed in the Type-I model, in which the coupling strength modifiersof down-type quarks and leptons have the same sign (and value) as for up-type quarks. Inthat case, a negative sign of the top-quark coupling strength modifier κt is experimentallyexcluded by the measurement of H → γγ decays, whose branching ratio depends linearly onκtκW because of the interference between W boson- and top-quark-mediated loop amplitudes.4.1.2 Constraints using an EFT-based approachThe modifications to the tree-level Higgs boson couplings to fermions near the alignmentlimit described in section 4.1 can be generated by the dimension-6 operators OuH , ObH , OtHand OeH of the SMEFT Lagrangian in the ‘top’ flavour scheme, with the following matching– 43 –JHEP11(2024)0970.3 0.2 0.1 0.0 0.1 0.2 0.3EQU  101100101VCP Obs. 95% CL Exp. 95% CL Obs. 95% CL (inc. ) Exp. 95% CL (inc. )SM-like coupling#6.#5s  6G8HD1mh )G8*&/6[RG+MA 6G8(a)0.3 0.2 0.1 0.0 0.1 0.2 0.3EQU  101100101VCP Obs. 95% CL Exp. 95% CLSM-like coupling#6.#5s  6G8HD1mh )G8*&/6[RG++(b)0.3 0.2 0.1 0.0 0.1 0.2 0.3EQU  101100101VCP Obs. 95% CL Exp. 95% CLSM-like coupling#6.#5s  6G8HD1mh )G8*&/6[RG.GRVQP5RGEKHKE(c)0.3 0.2 0.1 0.0 0.1 0.2 0.3EQU  101100101VCP Obs. 95% CL Exp. 95% CLSM-like coupling#6.#5s  6G8HD1mh )G8*&/6[RG(NKRRGF(d)Figure 19. Regions of the 2HDM (tan β, cos(β − α)) parameter plane excluded at 95% CL (lightyellow filled regions) in the κ-framework-based approach by the measured rates of Higgs bosonproduction and decays in the (a) Type-I, (b) Type-II, (c) Lepton-specific and (d) Flipped models.The dark yellow dashed lines show the borders of the corresponding expected exclusion regions for theSM hypothesis. For the Type-I model, the observed and expected regions excluded at 95% CL whenthe κλ constraint is considered are also shown (solid and dashed blue lines). The red dashed linescorrespond to the exact SM alignment limit (cos(β − α) = 0). Results derived in the κ-frameworkassume the decoupling limit, i.e., that the masses of the non-SM-like Higgs bosons are large comparedto the SM vev, which implies the assumption of the alignment limit, i.e., | cos(β − α)| ≪ 1.– 44 –JHEP11(2024)097between the Wilson coefficients and the 2HDM parameters [113]:v2ciHΛ2 = −Yiηicos(β − α)tan β , (4.1)with i = u, b, t, τ ,µ, and cµH and cτH referring to the ceH,22 and ceH,33 coefficients, respectively.In these formulae, computed to first order in cos(β − α), Yi =√2mi/v are the SM Higgsboson couplings and the values of ηi depend on the type of model (ηb = − tan2 β in theType-II and Flipped models, as are ηµ and ητ in the Type-II and the Lepton-specific models;ηb,t,µ,τ = 1 otherwise). The corrections to the HV V vertices are quadratic in cos(β − α)and are neglected. For the EFT to be valid, Λ≫ v and therefore | cos(β − α)| ∝ v2Λ2 shouldbe small, close to the alignment limit.The operator OH is also generated in the models under study, with a coefficient thatscales with cos2(β − α) but which can be significantly enhanced if the other scalar states aremuch heavier than the SM-like Higgs boson. In that case, cH is proportional to (M/v)2 [113]:v2cHΛ2 = cos(β − α)2(Mv)2.Non-zero values of cH modify the trilinear hhh coupling λ by a scale factor [114]:κλ = 1− v2cHλSMΛ2= 1− cos(β − α)2λSM(Mv)2.This in turn affects Higgs boson production and decay rates via NLO EW corrections tothe LO amplitudes, whose effect is included in the parameterisations used to obtain theresults. As in section 4.1.1, constraints on κλ from searches for Higgs boson pair productionare not taken into account. In the following, a value of M = 1 TeV is assumed for themasses of the heavy scalar particles, and thus κλ ≈ 1 − (11 cos(β − α))2. Given the largepredicted deviations of κλ from one for cos(β − α) different from zero, including κλ in theinterpretation is expected to affect significantly, for tan β 1, the results for the Type-Imodel, for which the impact of cos(β − α) ̸= 0 on the other Wilson coefficients, cbH , ctHand cτH , is suppressed by a 1/ tan β factor. Exclusion limits for all other types of 2HDMmodels are expected to be largely unaffected.Constraints on the values of tan β and cos(β − α) can thus be inferred from those seton cbH , ctH , cτH and cH using the SMEFT interpretation of the combined measurement ofproduction and decay rates in STXS bins. The likelihood model defined in section 3.2 isused, expressing the four Wilson coefficients cbH , ctH , cτH and cH in terms of the 2HDMparameters as in eq. (4.1) and fixing all the other Wilson coefficients to zero. The resultsare shown in figure 20.A comparison between the excluded regions from the two approaches is shown in figure 21.In the regions where the assumptions used in this study are valid, the excluded regions are verysimilar in the two approaches. In the Type-I model for large values of tan β, the EFT-basedapproach leads to looser constraints on cos(β − α) than the κ-framework-based approach.This difference stems from the fact that the EFT-based approach (i) does not exploit theconstraints from the HV V couplings, that only enter at dimension-8 in the SMEFT expansionand are not considered here, and (ii) retains only terms of O(cos(β − α)) in the expansion– 45 –JHEP11(2024)0970.3 0.2 0.1 0.0 0.1 0.2 0.3cos( )101100101tanEFT Obs. 95% CLEFT Exp. 95% CLEFT Obs. 95% CL (with cH)EFT Exp. 95% CL (with cH)SM-like couplingATLASs = 13 TeV, 139 fb1mh = 125.09 GeV2HDM Type-I, MA=1 TeV(a)0.3 0.2 0.1 0.0 0.1 0.2 0.3cos( )101100101tanEFT Obs. 95% CLEFT Exp. 95% CLSM-like couplingATLASs = 13 TeV, 36.1 - 139 fb1mh = 125.09 GeV2HDM Type-II(b)0.3 0.2 0.1 0.0 0.1 0.2 0.3cos( )101100101tanEFT Obs. 95% CLEFT Exp. 95% CLSM-like couplingATLASs = 13 TeV, 36.1 - 139 fb1mh = 125.09 GeV2HDM Type Lepton-Specific(c)0.3 0.2 0.1 0.0 0.1 0.2 0.3cos( )101100101tanEFT Obs. 95% CLEFT Exp. 95% CLSM-like couplingATLASs = 13 TeV, 36.1 - 139 fb1mh = 125.09 GeV2HDM Type Flipped(d)Figure 20. Regions of the 2HDM (tan β, cos(β−α)) parameter plane excluded at 95% CL (blue filledregions) in the EFT-based approach by the measured rates of Higgs boson production and decays inthe (a) Type-I, (b) Type-II, (c) Lepton-specific and (d) Flipped models. The dashed black lines showthe borders of the corresponding expected exclusion regions for the SM hypothesis. For the Type-Imodel, the observed and expected regions excluded at 95% CL when the cH constraint is consideredare also shown (solid and dashed green lines). Results are derived assuming that | cos(β − α)| ≪ 1,near the alignment limit represented by the red dashed lines, and that the masses of the non-SM-likeHiggs bosons are large compared to the SM vev. In particular, the limits on the Type-I model at hightan β are likely outside the validity range of the assumption made in the model.– 46 –JHEP11(2024)0970.3 0.2 0.1 0.0 0.1 0.2 0.3cos( )101100101tanEFT Exp. 95% CL (with cH)EFT Obs. 95% CL (with cH) Exp. 95% CL (with ) Obs. 95% CL (with )SM-like couplingATLASs = 13 TeV, 36.1 - 139 fb1mh = 125.09 GeV2HDM Type-I(a)0.3 0.2 0.1 0.0 0.1 0.2 0.3cos( )101100101tanEFT Exp. 95% CLEFT Obs. 95% CL Exp. 95% CL Obs. 95% CLSM-like couplingATLASs = 13 TeV, 36.1 - 139 fb1mh = 125.09 GeV2HDM Type-II(b)0.3 0.2 0.1 0.0 0.1 0.2 0.3cos( )101100101tanEFT Exp. 95% CLEFT Obs. 95% CL Exp. 95% CL Obs. 95% CLSM-like couplingATLASs = 13 TeV, 36.1 - 139 fb1mh = 125.09 GeV2HDM Type Lepton-Specific(c)0.3 0.2 0.1 0.0 0.1 0.2 0.3cos( )101100101tanEFT Exp. 95% CLEFT Obs. 95% CL Exp. 95% CL Obs. 95% CLSM-like couplingATLASs = 13 TeV, 36.1 - 139 fb1mh = 125.09 GeV2HDM Type Flipped(d)Figure 21. Comparison of the constraints from the approaches based on the κ- and EFT-frameworksin the tan β, cos(β − α) plane in the (a) Type-I, (b) Type-II, (c) Lepton-specific and (d) Flippedmodels. The κλ constraint is included in the Type-I model interpretation. Solid (dashed) lines indicatethe observed (expected) constraints. Results are derived assuming that | cos(β − α)| ≪ 1, near thealignment limit represented by the red dashed lines, and that the masses of the non-SM-like Higgsbosons are large compared to the SM vev. In particular, the EFT limits on the Type-I model at hightan β are likely outside the validity range of the assumption made in the model.of κλ, while in the κ-framework-based approach the constraint κV = sin(β − α) and thefull dependence of κλ on cos(β − α) are considered. However, part of the region of Type-Imodel parameter space allowed in the EFT-based approach but not in that based on theκ-framework is inconsistent with the alignment limit hypothesis of | cos(β − α)| ≪ 1.– 47 –JHEP11(2024)097A significant difference between the tan β, cos(β − α) constraints from the approachpresented in this section compared to those obtained using the κ-framework-based approachis the absence of the second small allowed region around tan β ≈ 10, cos(β − α) ≈ 0.2. Thisdifference follows from the fact that in the EFT-based approach only dimension-6 terms areconsidered in the SMEFT Lagrangian and a linear expansion of σ×B, which does not includeterms of second order in the Wilson coefficients, is performed. The likelihood function in theEFT-based approach is thus Gaussian and has a single maximum [115]. As a consequence,the region with a flipped coupling sign does not appear.4.2 Constraints on the MSSMSupersymmetry (SUSY) [116–124], a theoretically motivated framework for extending theSM, was conceived to address some of the SM’s unanswered questions. In particular, SUSYoffers a solution to the hierarchy problem [125–128], which is related to the fine tuning neededto obtain the relatively small value of the Higgs boson mass compared to the Planck scale.Supersymmetry can also provide credible dark matter candidates [129, 130] and can improvethe unification of the electroweak and strong interactions [131–139].Measurements of Higgs production and decay are interpreted in the context of the minimalsupersymmetric extension of the SM (MSSM) [15–19]. The Higgs sector of the MSSM is a2HDM with Type-II Yukawa couplings. At tree level, all Higgs boson masses and couplingscan be expressed in terms of two parameters, usually chosen to be tan β and the massof the pseudoscalar Higgs boson, mA. Radiative corrections, including contributions fromamplitudes mediated by loops of SM particles and their superpartners, lead to modificationsof the tree-level relations and can raise the lightest CP-even Higgs boson mass mh, boundedat tree level by mh ≤ mZ | cos 2β|, to the level of the mass of the Higgs boson discoveredby the ATLAS and CMS collaborations. The MSSM predicts a supersymmetric partner foreach SM state. In addition to the supersymmetric spin-one partners of the SM fermions(sfermions) and spin-half partners of the gluons (gluinos), there are a total of eight spin-halfpartners of the electroweak gauge and Higgs bosons: the neutral bino (superpartner of theU(1) gauge field), the winos, which are a charged pair and a neutral particle (superpartnersof the SU(2)L gauge fields) and the higgsinos, which are two neutral particles and a chargedpair (superpartners of the Higgs fields). Mixing between the bino, the neutral wino andthe neutral higgsinos leads to four neutralinos, while charginos arise from mixing betweenthe charged winos and the charged higgsinos.In the MSSM, SUSY is explicitly broken by some soft SUSY breaking operators resultingfrom a separate sector with unspecified dynamics. As a consequence, the MSSM has overa hundred parameters that describe the pattern of sparticle masses and their decays, andthe values of the quantum corrections that they induce vary significantly as a function ofthese parameters. The parameter space is thus too large to be probed exhaustively througha relatively small set of Higgs boson production and decay rate measurements. Therefore,several benchmark scenarios have been proposed in which the values of the MSSM parametersother than tan β and mA are fixed to provide a wide variety of phenomenologies of the MSSMHiggs sector. With only two free parameters left, tan β and mA, an MSSM interpretation ofthe Higgs boson production and decay rate measurements is simplified.– 48 –JHEP11(2024)097Scenario ReferenceM125h [39]M125h (τ˜) [39]M125h (χ˜) [39]M125h (alignment) [39]M125h1 (CPV) [39]M125h,EFT [40]M125h,EFT(χ˜) [40]hMSSM [38]Table 6. Benchmark scenarios considered for the MSSM interpretation.4.2.1 MSSM benchmark scenariosIn this study, the measured production and decay rates of the observed Higgs boson with massclose to 125 GeV are compared with the predictions of eight benchmark scenarios [38–40],assuming that the observed boson is the lightest CP-even Higgs boson h of the MSSM. Ineach benchmark scenario, constraints are set on mA (or mH±) and tan β after fixing thevalues of all the other MSSM parameters.One of the models considered is the hMSSM [38], which was also investigated in ourprevious publication [37]. The use of this model as a benchmark MSSM scenario suffersfrom theoretical limitations in regions with small mA or large tan β because its assumptionsmay not hold in these regions of parameter space [39]. For this reason, seven more recentbenchmark MSSM scenarios [39, 40] were also explored. These include two new scenarios [40]that were recently designed to be compatible with a low value of tan β (< 10). This parameterspace region is otherwise excluded in most MSSM scenarios, which predict for tan β ≲ 10 amass of the lightest neutral Higgs boson significantly lower than the observed Higgs bosonmass of 125.09 ± 0.24 GeV [48].The scenarios that are considered can be briefly summarised as follows, with detailsprovided in the references listed in table 6:• M125h scenario. All superparticles are assumed to be so heavy that they affect theproduction and decay rates of the MSSM Higgs bosons very slightly. The loop-inducedcontributions to the couplings of the light CP-even scalar are small. The largestones, enhanced with tan β, affect the b-quark Yukawa coupling but cancel out in thedecoupling limit mA ≫ mZ .• M125h (τ˜) scenario. The parameters related to the stop, sbottom and gluino massesare the same as in the previous case, but the soft-SUSY-breaking masses and trilinearinteraction term for the staus are significantly smaller. The resulting light staus andlight wino-like charginos can alter the amplitude for the decay of the SM-like Higgsboson into photons, with contributions that scale as 1/ tan β and tan2 β, respectively.As in the previous scenario, at low mA the hbb coupling is enhanced, leading to a– 49 –JHEP11(2024)097suppression of the branching ratios for all the other decay channels of the SM-like Higgsboson.• M125h (χ˜) scenario. The SUSY parameters in this scenario lead to all charginos andneutralinos being relatively light, with significant higgsino-gaugino mixing, and to acompressed electroweakino mass spectrum. The tan β-enhanced corrections to the hbbcoupling are suppressed. At low values of tan β, the partial width for the SM-like Higgsboson decay into two photons is significantly increased. The corresponding branchingratio for low tan β is larger (smaller) than the SM prediction for large (small) values ofmA.• M125h (alignment) scenario. In the ‘alignment without decoupling’ scenario, for agiven value of tan β, one of the two neutral CP-even scalars has SM-like couplingsindependent of the mass spectrum of the remaining Higgs bosons. In particular, fortan β ≈ 7 the lightest scalar Higgs boson h is SM-like, for relatively low values of mA.• M125h1 (CPV) scenario. This scenario is characterised by CP violation in the Higgssector, where mixing between the neutral CP-even scalar states h and H and the CP-oddscalar state A is induced by a non-zero phase ϕAt in the soft-SUSY-breaking Higgs-stopinteraction term. This causes significant interference effects in the production anddecay of the two heavier neutral states, which leads to weaker constraints from searchesfor resonances decaying into τ+τ−. The relevant parameters are chosen such that thestrongest interference region is located near the exclusion contour of the correspondingscenario with real parameters, the mass of the SM-like scalar is near the observed value,and all electric dipole moments are within the experimentally allowed ranges.• M125h,EFT scenario. In the previous scenarios, the sfermions have masses close to theTeV scale. As a consequence, values of tan β < 5 are automatically excluded as theywould lead to values of the Higgs boson mass mh that are significantly lower than theexperimental value of 125 GeV. To circumvent this problem, in this scenario all SUSYparticles, including sfermions, are relatively heavy, with masses close to the SUSY scalemSUSY, which is adjusted dynamically from 6 TeV to 1013 TeV to yield a Higgs bosonmass of 125 GeV for values of tan β between one and ten. As all SUSY particles are soheavy that production and decays of the MSSM Higgs bosons are only mildly affectedby their presence, their contribution to the Higgs boson properties is calculated with aneffective field theory. As in most of the previous scenarios, for low values of mA the hbbcoupling is enhanced with respect to the SM prediction and reduces to the SM valuefor large mA. At very small tan β, the model predicts a small suppression of the httcoupling, leading in turn to a slight suppression of the ggF production cross-section.• M125h,EFT(χ˜) scenario. Similarly to the previous scenario, the SUSY scale is adjusteddynamically to yield a light Higgs boson mass of mh ≈ 125 GeV at each point of theSUSY parameter space. In contrast to the M125h,EFT scenario, however, this scenariofeatures relatively light neutralinos and charginos. As a consequence, loop-inducedamplitudes mediated by these light states can induce modifications of the light Higgs– 50 –JHEP11(2024)097boson properties such as an enhancement of its partial decay width to two photons, inparticular for low tan β. The model therefore predicts a branching ratio for h → γγsignificantly larger than the SM prediction for large mA and low tan β. At low valuesof mA, the enhancement of the hbb coupling leads instead to an increase of the h→ bb¯branching ratio and a decrease of the h → γγ branching ratio relative to their SMexpectations.• hMSSM scenario. In this scenario, the lightest Higgs boson h is assumed to be theparticle discovered by the ATLAS and CMS collaborations in 2012. Its mass mh isassumed to be equal to the experimental value of 125.09 GeV, and it is used to fix thevalues of the dominant radiative corrections to the CP-even Higgs mass matrix from thestop-top sector. This hypothesis determines all other parameters of the Higgs sector,including α, mH , mH± , and the couplings between the Higgs bosons and the otherparticles, in terms of only the two parameters mA and tan β. Due to its assumptions,the hMSSM is a good approximation of the MSSM only for moderate values of tan β,1 ≲ tan β ≲ 10 [37].4.2.2 Interpretation procedureSince Higgs boson production cross-sections in the MSSM are not calculated for the full STXSStage-1.2 phase space partitioning of production cross-sections, only inclusive production-mode cross-sections are used in this analysis. The signal strength modifiers µi,X in the signalyield expression of eq. (2.2) are then written as:µi,X(mA, tan β) =σi(h)MSSM(mA, tan β)σiSM·BX(h)MSSM(mA, tan β)BXSM≡ ri(mA, tan β) · rX(mA, tan β), (4.2)where the index i enumerates the production processes (ggF, bbH, ttH, VBF, qq/qg→ZH,gg→ZH, qq→WH).The values of the production cross-section scale factors ri and branching ratio scalefactors rX are obtained using the procedures defined by the LHC Higgs Cross-section WorkingGroup, described in [49], as well as the calculations detailed in [140]. For all scenarios exceptthe hMSSM, Higgs boson masses and mixing (and effective Yukawa couplings) are calculatedwith FeynHiggs [141–147], and branching ratios are obtained combining the most preciseestimates of FeynHiggs, HDECAY [148, 149] and PROPHECY4f [150, 151]. In thehMSSM scenario, the Higgs boson mass is fixed at 125 GeV, the mixing is calculatedanalytically, and the branching ratios are calculated using the κ-framework. Inclusive cross-sections for ggF production are obtained with SusHi [152, 153], which includes NLO QCDcorrections [154], NNLO QCD corrections for the top-quark contribution in the effectivetheory of a heavy top quark [155–159] and EW corrections involving light quarks [160, 161].For the SM-like Higgs boson, SusHi adds N3LO corrections in the effective theory of a heavytop quark in a threshold expansion [61, 162, 163]. Cross-sections for b-quark-initiated Higgsboson production rely on matched predictions [164–167], which are based on the five flavourNNLO QCD calculation [168] and the four flavour NLO QCD calculation [169, 170]. The– 51 –JHEP11(2024)097values of the cross-sections of rare production modes, such as gg → Zh, pp → thW andpp→ thq, which are not calculated in refs. [140, 171], are determined through their relations,within the κ-framework, to κt, κb, κW , κZ , which are determined as either κ2t = σtt¯hMSSM/σtt¯HSMor κ2x = Γh→xxMSSM/Γh→xxSM , where x = b,W ,Z:rgg→Zh = 2.456κ2Z + 0.456κ2t − 1.903κZκt − 0.011κZκb + 0.003κtκb,rthW = 2.909κ2t + 2.310κ2W − 4.220κtκW ,rthq = 2.633κ2t + 3.578κ2W − 5.211κtκW .As the cross-section and branching ratio scale factors ri and rX are only calculated for adiscrete set of points in the two-dimensional benchmark parameter space, a likelihood based oneq. (4.2) is not differentially expressed in terms of its theory parameters (mA, tan β). Instead,the values of the profile likelihood ratio are calculated at fixed points in the (mA, tan β) plane,profiling only the nuisance parameters, and then numerically interpolated. Regions of thebenchmark scenario parameter space for which the mass mh of the lightest CP-even Higgsboson h predicted by the MSSM differs from the experimental value of 125.09 GeV by morethan 3 GeV, which is the estimated bound of allowed values of the calculated Higgs bosonmass in FeynHiggs [143, 172], are considered as excluded.4.2.3 ResultsFigure 22 shows the observed and expected 95% CL exclusion limits of the MSSM in thetwo-dimensional plane (mA, tan β) for the M125h , M125h (χ˜), M125h (τ˜), and M125h (alignment)benchmark scenarios. For all four scenarios, the regions excluded by the Higgs bosonmass requirement (|mh − 125.09 GeV| < 3 GeV) are separately indicated with gray shadedareas. For completeness, the constraints from previous searches for H/A → ττ [173] andH+ → tb¯ [174] are also overlaid.In the M125h and M125h (χ˜) scenarios, the low mA region, in which an enhancement ofthe h → bb¯ branching ratio and a suppression of the branching ratios of the other decaymodes such as h → γγ are predicted, is disfavoured. Since the data marginally preferB(h → bb¯)/BSM(h → bb¯) < 1 and B(h → γγ)/BSM(h → γγ) > 1, the observed constraintsare tighter than those expected under the SM hypothesis. In the M125h (τ˜) scenario, the regionat low mA and tan β < 53 is excluded for the same reason. The region tan β > 53, in whichthe τ˜ loop reduces the hbb coupling, leading to an enhanced prediction of B(h→ γγ), is alsolargely excluded. In the M125h (alignment) scenario, the limit of alignment without decouplingis only realised for tan β ≈ 7 and mA ≈ 200 GeV. For larger values of mA, MSSM couplingsare more similar to SM couplings, causing the allowed tan β region to broaden.In all four benchmark scenarios, the MSSM analysis generally excludes the low mA regimefor most of the scanned tan β range, while the requirement |mh − 125.09 GeV| < 3 GeVexcludes the low tan β range for all scanned values of mA, a range not fully covered by thedirect searches for H/A → ττ and H+ → tb¯ decays. The exclusion range due to the mhrequirement is qualitatively different in the M125h (alignment) scenario, as this scenario canonly realized for a value of tan(β) ≈ 7.Figure 23 shows the observed and expected 95% CL exclusion limits on the MSSM in thetwo-dimensional plane of mH± versus tan β for the M125h1 (CPV) scenario and of mA versus– 52 –JHEP11(2024)097250 500 750 1000 1250 1500 1750 2000mA=)G8?1102030405060VCP|mh125.09|> 3 GeVObs. 95% CL (h coupling)Exp. 95% CL (h coupling)Obs. 95% CL (H/A )Exp. 95% CL (H/A )Obs. 95% CL (H±tb)Exp. 95% CL (H±tb)#6.#5s  6G8HD1M125hUEGPCTKQ(a)250 500 750 1000 1250 1500 1750 2000mA=)G8?1102030405060VCP|mh125.09|> 3 GeVObs. 95% CL (h coupling)Exp. 95% CL (h coupling)Obs. 95% CL (H/A )Exp. 95% CL (H/A )Obs. 95% CL (H±tb)Exp. 95% CL (H±tb)#6.#5s  6G8HD1M125h( )UEGPCTKQ(b)250 500 750 1000 1250 1500 1750 2000mA=)G8?1102030405060VCP|mh125.09|> 3 GeVObs. 95% CL (h coupling)Exp. 95% CL (h coupling)Obs. 95% CL (H/A )Exp. 95% CL (H/A )Obs. 95% CL (H±tb)Exp. 95% CL (H±tb)#6.#5s  6G8HD1M125h( )UEGPCTKQ(c)200 300 400 500 600 700 800 900 1000mA=)G8?1.02.55.07.510.012.515.017.520.0VCP|mh125.09|> 3 GeVObs. 95% CLExp. 95% CLObs. 95% CL (H/A )Exp. 95% CL (H/A )#6.#5s  6G8HD1M125h(alignment)UEGPCTKQ(d)Figure 22. Observed (solid yellow area) and expected (dashed line) exclusion contours at 95% CL inthe (mA, tan β) plane for the (a) M125h , (b) M125h (τ˜), (c) M125h (χ˜) and (d) M125h (alignment) scenarios.The parameter space excluded by the condition |mh − 125.09 GeV| < 3 GeV is marked in gray. Forcomparison, the parameter space excluded by the searches for H/A→ ττ [173] and for H+ → tb¯ [174]are overlaid in blue and purple, respectively. For the M125h (alignment) scenario, no constraints fromthe search for H+ → tb¯ are available.– 53 –JHEP11(2024)097tan β for the M125h,EFT, M125h,EFT(χ˜) and hMSSM scenarios. The condition |mh− 125.09 GeV| <3 GeV excludes values of tan β ≲ 6 for all values of mH± in the M125h1 (CPV) scenario, while nopart of the parameter space is excluded in the M125h,EFT and M125h,EFT(χ˜) benchmark scenarios,in which mh = 125.09 GeV can be achieved through the flexible mSUSY scale. In thesefour models, the low mA region, where an enhancement of the hbb coupling is predicted,is excluded, and the excluded region is larger than expected in the SM hypothesis for thesame reason as for the previous four models. The similarity of the limits in the M125h,EFT andhMSSM scenarios stems from the fact that the M125h,EFT is a concrete realisation of an MSSMscenario that fulfils the assumptions of the hMSSM approach [40].– 54 –JHEP11(2024)097200 400 600 800 1000mH±=)G8?2.55.07.510.012.515.017.520.0VCP|mh125.09|> 3 GeVObs. 95% CLExp. 95% CL#6.#5s  6G8HD1M125h1(CPV)UEGPCTKQ(a)200 300 400 500 600 700 800mA=)G8?12345678910VCPObs. 95% CLExp. 95% CL#6.#5s  6G8HD1M125h, EFTUEGPCTKQ(b)250 500 750 1000 1250 1500 1750 2000mA=)G8?12345678910VCPObs. 95% CLExp. 95% CL#6.#5s  6G8HD1M125h, EFT( )UEGPCTKQ(c)200 300 400 500 600 700 800mA=)G8?100101VCPObs. 95% CLExp. 95% CL#6.#5s  6G8HD1J/55/(d)Figure 23. Observed (solid yellow area) and expected (dashed line) exclusion contours at 95% CLin (a) the (mH± , tan β) plane for the M125h1 (CPV) scenario and in the (mA, tan β) plane for the (b)M125h,EFT, (c) M125h,EFT(χ˜) and (d) hMSSM scenarios. In (a), the parameter space excluded by thecondition |mh − 125.09 GeV| < 3 GeV is marked in gray.– 55 –JHEP11(2024)0975 ConclusionsNovel interpretations of the recent combined ATLAS measurements of Higgs boson productionand decay rates and simplified template cross-sections in several final states are presented.Constraints on linear combinations of Wilson coefficients corresponding to SM effective fieldtheory operators in the Warsaw basis are reported. In this model-independent parameterisa-tion of BSM physics effects, no significant deviations from the SM are observed. A comparisonof results interpreted with a linearised SMEFT model that only considers terms suppressed byup to a factor Λ−2, and a variant including quadratic terms that considers all available termsincluding those with suppression factor Λ−4, shows that the effect of operators suppressed byΛ−4 can significantly affect constraints on Wilson coefficients for a mass scale of Λ = 1 TeV.Constraints on a subset of these operators have also been set through a joint interpretationof the fiducial cross-section measurements of Higgs boson production as a function of transversemomentum in the H → γγ and H → ZZ∗ → 4ℓ final states. Three linear combinations ofthe Wilson coefficients of operators affecting these spectra can be simultaneously constrained.For two of these combinations, the constraints are similar to those that can be derived fromthe interpretation of Higgs boson simplified template cross-section measurements in thesame channels. The constraint on the top-gluon coupling is significantly stronger in theinterpretation of simplified template cross-sections.Finally, the Higgs boson production and decay rate measurements are interpreted inthe context of two-Higgs-doublet models and of eight benchmark scenarios of the minimalsupersymmetric model. Constraints are set on the (cos(β −α), tan β) plane in 2HDM Type-I,Type-II, Lepton-specific and Flipped models, and on the parameters (mA, tan β) of theMSSM in eight benchmark scenarios. These results are complementary to limits from directsearches for additional Higgs bosons.AcknowledgmentsWe thank CERN for the very successful operation of the LHC and its injectors, as wellas the support staff at CERN and at our institutions worldwide without whom ATLAScould not be operated efficiently.The crucial computing support from all WLCG partners is acknowledged gratefully, inparticular from CERN, the ATLAS Tier-1 facilities at TRIUMF/SFU (Canada), NDGF(Denmark, Norway, Sweden), CC-IN2P3 (France), KIT/GridKA (Germany), INFN-CNAF(Italy), NL-T1 (Netherlands), PIC (Spain), RAL (UK) and BNL (USA), the Tier-2 facilitiesworldwide and large non-WLCG resource providers. Major contributors of computingresources are listed in ref. [175].We gratefully 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; IN2P3-CNRS 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;– 56 –JHEP11(2024)097MEiN, Poland; FCT, Portugal; MNE/IFA, Romania; MESTD, Serbia; MSSR, Slovakia;ARIS and MVZI, Slovenia; DSI/NRF, South Africa; MICINN, Spain; SRC and WallenbergFoundation, Sweden; SERI, SNSF and Cantons of Bern and Geneva, Switzerland; NSTC,Taipei; TENMAK, Türkiye; STFC/UKRI, United Kingdom; DOE and NSF, United Statesof America.Individual groups and members have received support from BCKDF, CANARIE, CRCand DRAC, Canada; CERN-CZ, PRIMUS 21/SCI/017 and UNCE SCI/013, Czech Republic;COST, ERC, ERDF, Horizon 2020, ICSC-NextGenerationEU and Marie Skłodowska-CurieActions, European Union; Investissements d’Avenir Labex, Investissements d’Avenir Idexand ANR, France; DFG and AvH Foundation, Germany; Herakleitos, Thales and Aristeiaprogrammes co-financed by EU-ESF and the Greek NSRF, Greece; BSF-NSF and MINERVA,Israel; Norwegian Financial Mechanism 2014–2021, Norway; NCN and NAWA, Poland; LaCaixa Banking Foundation, CERCA Programme Generalitat de Catalunya and PROMETEOand GenT Programmes Generalitat Valenciana, Spain; Göran Gustafssons Stiftelse, Sweden;The Royal Society and Leverhulme Trust, United Kingdom.In addition, individual members wish to acknowledge support from Chile: Agencia Na-cional de Investigación y Desarrollo (FONDECYT 1190886, FONDECYT 1210400, FONDE-CYT 1230812, FONDECYT 1230987); China: National Natural Science Foundation ofChina (NSFC - 12175119, NSFC 12275265, NSFC-12075060); Czech Republic: PRIMUSResearch Programme (PRIMUS/21/SCI/017); EU: H2020 European Research Council (ERC- 101002463); European Union: European Research Council (ERC - 948254), Horizon 2020Framework Programme (MUCCA - CHIST-ERA-19-XAI-00), European Union, Future Ar-tificial Intelligence Research (FAIR-NextGenerationEU PE00000013), Italian Center forHigh Performance Computing, Big Data and Quantum Computing (ICSC, NextGenera-tionEU), Marie Sklodowska-Curie Actions (EU H2020 MSC IF GRANT NO 101033496);France: Agence Nationale de la Recherche (ANR-20-CE31-0013, ANR-21-CE31-0013, ANR-21-CE31-0022, ANR-22-EDIR-0002), Investissements d’Avenir Idex (ANR-11-LABX-0012),Investissements d’Avenir Labex (ANR-11-LABX-0012); Germany: Baden-WürttembergStiftung (BW Stiftung-Postdoc Eliteprogramme), Deutsche Forschungsgemeinschaft (DFG -CR 312/5-1); Italy: Istituto Nazionale di Fisica Nucleare (FELLINI G.A. n. 754496, ICSC,NextGenerationEU); Japan: Japan Society for the Promotion of Science (JSPS KAKENHIJP21H05085, JSPS KAKENHI JP22H01227, JSPS KAKENHI JP22H04944); Netherlands:Netherlands Organisation for Scientific Research (NWO Veni 2020 - VI.Veni.202.179); Nor-way: Research Council of Norway (RCN-314472); Poland: Polish National Agency forAcademic Exchange (PPN/PPO/2020/1/00002/U/00001), Polish National Science Cen-tre (NCN 2021/42/E/ST2/00350, NCN OPUS nr 2022/47/B/ST2/03059, NCN UMO-2019/34/E/ST2/00393, UMO-2020/37/B/ST2/01043, UMO-2021/40/C/ST2/00187); Slove-nia: Slovenian Research Agency (ARIS grant J1-3010); Spain: BBVA Foundation (LEO22-1-603), Generalitat Valenciana (Artemisa, FEDER, IDIFEDER/2018/048), La Caixa Bank-ing Foundation (LCF/BQ/PI20/11760025), Ministry of Science and Innovation (MCIN &NextGenEU PCI2022-135018-2, MICIN & FEDER PID2021-125273NB, RYC2019-028510-I,RYC2020-030254-I, RYC2021-031273-I, RYC2022-038164-I), PROMETEO and GenT Pro-grammes Generalitat Valenciana (CIDEGENT/2019/023, CIDEGENT/2019/027); Sweden:– 57 –JHEP11(2024)097Swedish Research Council (VR 2018-00482, VR 2022-03845, VR 2022-04683, VR grant2021-03651), Knut and Alice Wallenberg Foundation (KAW 2017.0100, KAW 2018.0157,KAW 2018.0458, KAW 2019.0447); Switzerland: Swiss National Science Foundation (SNSF- PCEFP2_194658); United Kingdom: Leverhulme Trust (Leverhulme Trust RPG-2020-004); United States of America: U.S. Department of Energy (ECA DE-AC02-76SF00515),Neubauer Family Foundation.A Validity of Gaussian approximation of STXS measurements in theSMEFT interpretationThe STXS SMEFT interpretation model constructs the likelihood function in terms of thefit basis parameters c′ from three ingredients:1. The likelihood function of the STXS measurements, measuring 78 cross-section pa-rameters, and featuring over a thousand nuisance parameters expressing systematicuncertainties.2. A specification of the impact of all relevant CP-even Warsaw basis SMEFT operatorson the SM predictions of these cross-sections, including acceptance corrections wherenecessary, i.e., eqs. (3.9) and (3.10), using the coefficients Aσi,k′j , AΓH→Xj , Bσi,k′jl andBΓH→Xjl as defined in eqs. (3.5)–(3.8), and visualised in figure 5.3. A rotation matrix from the 50 Warsaw basis parameters c, which cannot be unambigu-ously constrained from the STXS data, to a fit basis c′ for which all 19 parameters canbe simultaneously constrained from the data, as shown in figure 8.An important upside of a likelihood model built this way is that all non-Gaussian effects inthe STXS measurements are accounted for, and that the correlated effects of all experimentaland theoretical systematic uncertainties are accounted at the level of detail implementedin the original underlying measurements. A downside of this likelihood model is that therequired complexity of its implementation prevents it from easily being made available.An alternative likelihood function, based on a multivariate Gaussian approximationof the STXS measurements instead of the full measurement, with an identical SMEFT re-parameterisation, can be constructed in a relatively straightforward way from the informationprovided and represents a reasonably good approximation of the full likelihood. A comparisonof the results obtained with this simplified Gaussian variant of the likelihood model and thoseobtained with the full likelihood function is shown in figure 24 for the linear SMEFT modeland in figure 25 for the SMEFT model including the quadratic terms. Both comparisonsindicate generally good agreement between expected and observed parameter estimates andtheir 68% and 95% uncertainty intervals.– 58 –JHEP11(2024)097Symmetrizeduncertainty(σ)ProbedScale(Λ/√σ)[TeV]−4−2024c c c c e [1] e [2] e [3] e [1] e [2] e [3] e [1] e [2] e [3] e [4] e [1] e [2] e [3] e [1] e [1]Best Fit68 % CL95 % CLeH,22eH,33(3)HqbH ggFggFggFHγγ,ZγHγγ,ZγHγγ,ZγZH ZH ZH ZH ttH ttH ttH globHllllParametervaluescaledbysymmetrizeduncertainty(c′ /σ)ATLASSMEFT Λ = 1 TeVLinear (Observed)√s =13 TeV, 139 fb−1,mH = 125.09 GeV10−310−210−110010132103.210.32full likelihoodsimplified likelihoodFigure 24. Comparison of the observed result from the full likelihood fit in the SMEFT fit basiswith only linear terms (blue) to a fit based on a simplified likelihood constructed from the covariancematrix of the STXS measurements rotated to the same SMEFT fit basis (purple).Symmetrizeduncertainty(σ)ProbedScale(Λ/√σ)[TeV]−4−2024c c c c e [1] e [2] e [3] e [1] e [2] e [3] e [1] e [2] e [3] e [4]Best Fit68 % CL95 % CLeH,22eH,33(3)HqbH ggFggFggFHγγ,ZγHγγ,ZγHγγ,ZγZH ZH ZH ZHe [1]ttHe [2]ttHe [3]ttHe [1]globe [1]HllllParametervaluescaledbysymmetrizeduncertainty(c′ /σ)ATLASSMEFT Λ = 1 TeVLinear+quad. (Observed)√s =13 TeV, 139 fb−1,mH = 125.09 GeV10−310−210−110010132103.210.32full likelihoodsimplified likelihoodFigure 25. Comparison of the observed result from the full likelihood fit in the SMEFT fit basiswith linear and quadratic terms (orange) to a fit based on a simplified likelihood constructed from thecovariance matrix of the STXS measurements rotated to the same SMEFT fit basis (dark red).– 59 –JHEP11(2024)097Open Access. This article is distributed under the terms of the Creative Commons Attri-bution License (CC-BY4.0), which permits any use, distribution and reproduction in anymedium, provided the original author(s) and source are credited.References[1] F. Englert and R. Brout, Broken Symmetry and the Mass of Gauge Vector Mesons, Phys. Rev.Lett. 13 (1964) 321 [INSPIRE].[2] P.W. Higgs, Broken symmetries, massless particles and gauge fields, Phys. Lett. 12 (1964) 132[INSPIRE].[3] P.W. Higgs, Broken Symmetries and the Masses of Gauge Bosons, Phys. Rev. Lett. 13 (1964)508 [INSPIRE].[4] G.S. Guralnik, C.R. Hagen and T.W.B. Kibble, Global Conservation Laws and MasslessParticles, Phys. Rev. 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Ekman 98, S. El Farkh 35b, Y. El Ghazali 35b,H. El Jarrari 36, A. El Moussaouy 108, V. Ellajosyula 161, M. Ellert 161, F. Ellinghaus 171,N. Ellis 36, J. Elmsheuser 29, M. Elsing 36, D. Emeliyanov 134, Y. Enari 153, I. Ene 17a,S. Epari 13, J. Erdmann 49, P.A. Erland 87, M. Errenst 171, M. Escalier 66, C. Escobar 163,E. Etzion 151, G. Evans 130a, H. Evans 68, L.S. Evans 95, M.O. Evans 146, A. Ezhilov 37,S. Ezzarqtouni 35a, F. Fabbri 59, L. Fabbri 23b,23a, G. Facini 96, V. Fadeyev 136,R.M. Fakhrutdinov 37, D. Fakoudis 100, S. Falciano 75a, L.F. Falda Ulhoa Coelho 36,P.J. Falke 24, J. Faltova 133, C. Fan 162, Y. Fan 14a, Y. Fang 14a,14e, M. Fanti 71a,71b,M. Faraj 69a,69b, Z. Farazpay 97, A. Farbin 8, A. Farilla 77a, T. Farooque 107,S.M. Farrington 52, F. Fassi 35e, D. Fassouliotis 9, M. Faucci Giannelli 76a,76b, W.J. Fawcett 32,L. Fayard 66, P. Federic 133, P. Federicova 131, O.L. Fedin 37,a, G. Fedotov 37,M. Feickert 170, L. Feligioni 102, D.E. Fellers 123, C. Feng 62b, M. Feng 14b, Z. Feng 114,M.J. Fenton 160, A.B. Fenyuk37, L. Ferencz 48, R.A.M. Ferguson 91, S.I. Fernandez Luengo 137f ,P. Fernandez Martinez 13, M.J.V. Fernoux 102, J. Ferrando 48, A. Ferrari 161, P. Ferrari 114,113,R. Ferrari 73a, D. Ferrere 56, C. Ferretti 106, F. Fiedler 100, P. Fiedler 132, A. Filipčič 93,E.K. Filmer 1, F. Filthaut 113, M.C.N. Fiolhais 130a,130c,c, L. Fiorini 163, W.C. Fisher 107,T. Fitschen 101, P.M. Fitzhugh135, I. Fleck 141, P. Fleischmann 106, T. Flick 171,M. Flores 33d,ad, L.R. Flores Castillo 64a, L. Flores Sanz De Acedo 36, F.M. Follega 78a,78b,N. Fomin 16, J.H. Foo 155, B.C. Forland68, A. Formica 135, A.C. Forti 101, E. Fortin 36,A.W. Fortman 61, M.G. Foti 17a, L. Fountas 9,j , D. Fournier 66, H. Fox 91,P. Francavilla 74a,74b, S. Francescato 61, S. Franchellucci 56, M. Franchini 23b,23a,S. Franchino 63a, D. Francis36, L. Franco 113, V. Franco Lima 36, L. Franconi 48,M. Franklin 61, G. Frattari 26, A.C. Freegard 94, W.S. Freund 83b, Y.Y. Frid 151, J. Friend 59,N. Fritzsche 50, A. Froch 54, D. Froidevaux 36, J.A. Frost 126, Y. Fu 62a,S. Fuenzalida Garrido 137f , M. Fujimoto 102, K.Y. Fung 64a, E. Furtado De Simas Filho 83b,M. Furukawa 153, J. Fuster 163, A. Gabrielli 23b,23a, A. Gabrielli 155, P. Gadow 36,G. Gagliardi 57b,57a, L.G. Gagnon 17a, E.J. Gallas 126, B.J. Gallop 134, K.K. Gan 119,S. Ganguly 153, Y. Gao 52, F.M. Garay Walls 137a,137b, B. Garcia29, C. García 163,A. Garcia Alonso 114, A.G. Garcia Caffaro 172, J.E. García Navarro 163, M. Garcia-Sciveres 17a,G.L. Gardner 128, R.W. Gardner 39, N. Garelli 158, D. Garg 80, R.B. Garg 143,n,J.M. Gargan 52, C.A. Garner155, C.M. Garvey 33a, P. Gaspar 83b, V.K. Gassmann158,G. Gaudio 73a, V. Gautam13, P. Gauzzi 75a,75b, I.L. Gavrilenko 37, A. Gavrilyuk 37,– 73 –JHEP11(2024)097C. Gay 164, G. Gaycken 48, E.N. Gazis 10, A.A. Geanta 27b, C.M. Gee 136, A. Gekow119,C. Gemme 57b, M.H. Genest 60, S. Gentile 75a,75b, A.D. Gentry 112, S. George 95,W.F. George 20, T. Geralis 46, P. Gessinger-Befurt 36, M.E. Geyik 171, M. Ghani 167,M. Ghneimat 141, K. Ghorbanian 94, A. Ghosal 141, A. Ghosh 160, A. Ghosh 7,B. Giacobbe 23b, S. Giagu 75a,75b, T. Giani 114, P. Giannetti 74a, A. Giannini 62a,S.M. Gibson 95, M. Gignac 136, D.T. Gil 86b, A.K. Gilbert 86a, B.J. Gilbert 41,D. Gillberg 34, G. Gilles 114, N.E.K. Gillwald 48, L. Ginabat 127, D.M. Gingrich 2,ag,M.P. Giordani 69a,69c, P.F. Giraud 135, G. Giugliarelli 69a,69c, D. Giugni 71a, F. Giuli 36,I. Gkialas 9,j , L.K. Gladilin 37, C. Glasman 99, G.R. Gledhill 123, G. Glemža 48, M. Glisic123,I. Gnesi 43b,f , Y. Go 29,aj , M. Goblirsch-Kolb 36, B. Gocke 49, D. Godin108, B. Gokturk 21a,S. Goldfarb 105, T. Golling 56, M.G.D. Gololo 33g, D. Golubkov 37, J.P. Gombas 107,A. Gomes 130a,130b, G. Gomes Da Silva 141, A.J. Gomez Delegido 163, R. Gonçalo 130a,130c,G. Gonella 123, L. Gonella 20, A. Gongadze 149c, F. Gonnella 20, J.L. Gonski 41,R.Y. González Andana 52, S. González de la Hoz 163, S. Gonzalez Fernandez 13,R. Gonzalez Lopez 92, C. Gonzalez Renteria 17a, M.V. Gonzalez Rodrigues 48,R. Gonzalez Suarez 161, S. Gonzalez-Sevilla 56, G.R. Gonzalvo Rodriguez 163, L. Goossens 36,B. Gorini 36, E. Gorini 70a,70b, A. Gorišek 93, T.C. Gosart 128, A.T. Goshaw 51,M.I. Gostkin 38, S. Goswami 121, C.A. Gottardo 36, S.A. Gotz 109, M. Gouighri 35b,V. Goumarre 48, A.G. Goussiou 138, N. Govender 33c, I. Grabowska-Bold 86a, K. Graham 34,E. Gramstad 125, S. Grancagnolo 70a,70b, M. Grandi 146, C.M. Grant1,135, P.M. Gravila 27f ,F.G. Gravili 70a,70b, H.M. Gray 17a, M. Greco 70a,70b, C. Grefe 24, I.M. Gregor 48,P. Grenier 143, S.G. Grewe110, C. Grieco 13, A.A. Grillo 136, K. Grimm 31, S. Grinstein 13,t,J.-F. Grivaz 66, E. Gross 169, J. Grosse-Knetter 55, C. Grud106, J.C. Grundy 126, L. Guan 106,W. Guan 29, C. Gubbels 164, J.G.R. Guerrero Rojas 163, G. Guerrieri 69a,69c, F. Guescini 110,R. Gugel 100, J.A.M. Guhit 106, A. Guida 18, E. Guilloton 167,134, S. Guindon 36,F. Guo 14a,14e, J. Guo 62c, L. Guo 48, Y. Guo 106, R. Gupta 48, R. Gupta 129, S. Gurbuz 24,S.S. Gurdasani 54, G. Gustavino 36, M. Guth 56, P. Gutierrez 120, L.F. Gutierrez Zagazeta 128,M. Gutsche 50, C. Gutschow 96, C. Gwenlan 126, C.B. Gwilliam 92, E.S. Haaland 125,A. Haas 117, M. Habedank 48, C. Haber 17a, H.K. Hadavand 8, A. Hadef 50, S. Hadzic 110,A.I. Hagan 91, J.J. Hahn 141, E.H. Haines 96, M. Haleem 166, J. Haley 121, J.J. Hall 139,G.D. Hallewell 102, L. Halser 19, K. Hamano 165, M. Hamer 24, G.N. Hamity 52,E.J. Hampshire 95, J. Han 62b, K. Han 62a, L. Han 14c, L. Han 62a, S. Han 17a,Y.F. Han 155, K. Hanagaki 84, M. Hance 136, D.A. Hangal 41,ac, H. Hanif 142, M.D. Hank 128,R. Hankache 101, J.B. Hansen 42, J.D. Hansen 42, P.H. Hansen 42, K. Hara 157, D. Harada 56,T. Harenberg 171, S. Harkusha 37, M.L. Harris 103, Y.T. Harris 126, J. Harrison 13,N.M. Harrison 119, P.F. Harrison167, N.M. Hartman 110, N.M. Hartmann 109, Y. Hasegawa 140,R. Hauser 107, C.M. Hawkes 20, R.J. Hawkings 36, Y. Hayashi 153, S. Hayashida 111,D. Hayden 107, C. Hayes 106, R.L. Hayes 114, C.P. Hays 126, J.M. Hays 94, H.S. Hayward 92,F. He 62a, M. He 14a,14e, Y. He 154, Y. He 48, N.B. Heatley 94, V. Hedberg 98,A.L. Heggelund 125, N.D. Hehir 94,∗, C. Heidegger 54, K.K. Heidegger 54, W.D. Heidorn 81,J. Heilman 34, S. Heim 48, T. Heim 17a, J.G. Heinlein 128, J.J. Heinrich 123,L. Heinrich 110,ae, J. Hejbal 131, L. Helary 48, A. Held 170, S. Hellesund 16, C.M. Helling 164,S. Hellman 47a,47b, R.C.W. Henderson91, L. Henkelmann 32, A.M. Henriques Correia36,– 74 –JHEP11(2024)097H. Herde 98, Y. Hernández Jiménez 145, L.M. Herrmann 24, T. Herrmann 50, G. Herten 54,R. Hertenberger 109, L. Hervas 36, M.E. Hesping 100, N.P. Hessey 156a, H. Hibi 85, E. Hill 155,S.J. Hillier 20, J.R. Hinds 107, F. Hinterkeuser 24, M. Hirose 124, S. Hirose 157,D. Hirschbuehl 171, T.G. Hitchings 101, B. Hiti 93, J. Hobbs 145, R. Hobincu 27e, N. Hod 169,M.C. Hodgkinson 139, B.H. Hodkinson 32, A. Hoecker 36, D.D. Hofer 106, J. Hofer 48,T. Holm 24, M. Holzbock 110, L.B.A.H. Hommels 32, B.P. Honan 101, J. Hong 62c,T.M. Hong 129, B.H. Hooberman 162, W.H. Hopkins 6, Y. Horii 111, S. Hou 148,A.S. Howard 93, J. Howarth 59, J. Hoya 6, M. Hrabovsky 122, A. Hrynevich 48, T. Hryn’ova 4,P.J. Hsu 65, S.-C. Hsu 138, Q. Hu 62a, Y.F. Hu 14a,14e, S. Huang 64b, X. Huang 14c,X. Huang 14a,14e, Y. Huang 139, Y. Huang 14a, Z. Huang 101, Z. Hubacek 132, M. Huebner 24,F. Huegging 24, T.B. Huffman 126, C.A. Hugli 48, M. Huhtinen 36, S.K. Huiberts 16,R. Hulsken 104, N. Huseynov 12, J. Huston 107, J. Huth 61, R. Hyneman 143, G. Iacobucci 56,G. Iakovidis 29, I. Ibragimov 141, L. Iconomidou-Fayard 66, P. Iengo 72a,72b, R. Iguchi 153,T. Iizawa 126, Y. Ikegami 84, N. Ilic 155, H. Imam 35a, M. Ince Lezki 56,T. Ingebretsen Carlson 47a,47b, G. Introzzi 73a,73b, M. Iodice 77a, V. Ippolito 75a,75b,R.K. Irwin 92, M. Ishino 153, W. Islam 170, C. Issever 18,48, S. Istin 21a,am, H. Ito 168,J.M. Iturbe Ponce 64a, R. Iuppa 78a,78b, A. Ivina 169, J.M. Izen 45, V. Izzo 72a,P. Jacka 131,132, P. Jackson 1, R.M. Jacobs 48, B.P. Jaeger 142, C.S. Jagfeld 109, G. Jain 156a,P. Jain 54, K. Jakobs 54, T. Jakoubek 169, J. Jamieson 59, K.W. Janas 86a, M. Javurkova 103,F. Jeanneau 135, L. Jeanty 123, J. Jejelava 149a,aa, P. Jenni 54,g, C.E. Jessiman 34,S. Jézéquel 4, C. Jia62b, J. Jia 145, X. Jia 61, X. Jia 14a,14e, Z. Jia 14c, S. Jiggins 48,J. Jimenez Pena 13, S. Jin 14c, A. Jinaru 27b, O. Jinnouchi 154, P. Johansson 139,K.A. Johns 7, J.W. Johnson 136, D.M. Jones 32, E. Jones 48, P. Jones 32, R.W.L. Jones 91,T.J. Jones 92, H.L. Joos 55,36, R. Joshi 119, J. Jovicevic 15, X. Ju 17a, J.J. Junggeburth 103,T. Junkermann 63a, A. Juste Rozas 13,t, M.K. Juzek 87, S. Kabana 137e, A. Kaczmarska 87,M. Kado 110, H. Kagan 119, M. Kagan 143, A. Kahn41, A. Kahn 128, C. Kahra 100,T. Kaji 153, E. Kajomovitz 150, N. Kakati 169, I. Kalaitzidou 54, C.W. Kalderon 29,A. Kamenshchikov 155, N.J. Kang 136, D. Kar 33g, K. Karava 126, M.J. Kareem 156b,E. Karentzos 54, I. Karkanias 152, O. Karkout 114, S.N. Karpov 38, Z.M. Karpova 38,V. Kartvelishvili 91, A.N. Karyukhin 37, E. Kasimi 152, J. Katzy 48, S. Kaur 34,K. Kawade 140, M.P. Kawale 120, C. Kawamoto 88, T. Kawamoto 62a, E.F. Kay 36,F.I. Kaya 158, S. Kazakos 107, V.F. Kazanin 37, Y. Ke 145, J.M. Keaveney 33a, R. Keeler 165,G.V. Kehris 61, J.S. Keller 34, A.S. Kelly96, J.J. Kempster 146, K.E. Kennedy 41,P.D. Kennedy 100, O. Kepka 131, B.P. Kerridge 167, S. Kersten 171, B.P. Kerševan 93,S. Keshri 66, L. Keszeghova 28a, S. Ketabchi Haghighat 155, R.A. Khan 129, M. Khandoga 127,A. Khanov 121, A.G. Kharlamov 37, T. Kharlamova 37, E.E. Khoda 138, M. Kholodenko 37,T.J. Khoo 18, G. Khoriauli 166, J. Khubua 149b,∗, Y.A.R. Khwaira 66, A. Kilgallon 123,D.W. Kim 47a,47b, Y.K. Kim 39, N. Kimura 96, M.K. Kingston 55, A. Kirchhoff 55,C. Kirfel 24, F. Kirfel 24, J. Kirk 134, A.E. Kiryunin 110, C. Kitsaki 10, O. Kivernyk 24,M. Klassen 63a, C. Klein 34, L. Klein 166, M.H. Klein 106, M. Klein 92,∗, S.B. Klein 56,U. Klein 92, P. Klimek 36, A. Klimentov 29, T. Klioutchnikova 36, P. Kluit 114, S. Kluth 110,E. Kneringer 79, T.M. Knight 155, A. Knue 49, R. Kobayashi 88, D. Kobylianskii 169,S.F. Koch 126, M. Kocian 143, P. Kodyš 133, D.M. Koeck 123, P.T. Koenig 24, T. Koffas 34,– 75 –JHEP11(2024)097O. Kolay 50, I. Koletsou 4, T. Komarek 122, K. Köneke 54, A.X.Y. Kong 1, T. Kono 118,N. Konstantinidis 96, P. Kontaxakis 56, B. Konya 98, R. Kopeliansky 68, S. Koperny 86a,K. Korcyl 87, K. Kordas 152,e, G. Koren 151, A. Korn 96, S. Korn 55, I. Korolkov 13,N. Korotkova 37, B. Kortman 114, O. Kortner 110, S. Kortner 110, W.H. Kostecka 115,V.V. Kostyukhin 141, A. Kotsokechagia 135, A. Kotwal 51, A. Koulouris 36,A. Kourkoumeli-Charalampidi 73a,73b, C. Kourkoumelis 9, E. Kourlitis 110,ae, O. Kovanda 146,R. Kowalewski 165, W. Kozanecki 135, A.S. Kozhin 37, V.A. Kramarenko 37, G. Kramberger 93,P. Kramer 100, M.W. Krasny 127, A. Krasznahorkay 36, J.W. Kraus 171, J.A. Kremer 48,T. Kresse 50, J. Kretzschmar 92, K. Kreul 18, P. Krieger 155, S. Krishnamurthy 103,M. Krivos 133, K. Krizka 20, K. Kroeninger 49, H. Kroha 110, J. Kroll 131, J. Kroll 128,K.S. Krowpman 107, U. Kruchonak 38, H. Krüger 24, N. Krumnack81, M.C. Kruse 51,O. Kuchinskaia 37, S. Kuday 3a, S. Kuehn 36, R. Kuesters 54, T. Kuhl 48, V. Kukhtin 38,Y. Kulchitsky 37,a, S. Kuleshov 137d,137b, M. Kumar 33g, N. Kumari 48, P. Kumari 156b,A. Kupco 131, T. Kupfer49, A. Kupich 37, O. Kuprash 54, H. Kurashige 85,L.L. Kurchaninov 156a, O. Kurdysh 66, Y.A. Kurochkin 37, A. Kurova 37, M. Kuze 154,A.K. Kvam 103, J. Kvita 122, T. Kwan 104, N.G. Kyriacou 106, L.A.O. Laatu 102,C. Lacasta 163, F. Lacava 75a,75b, H. Lacker 18, D. Lacour 127, N.N. Lad 96, E. Ladygin 38,B. Laforge 127, T. Lagouri 137e, F.Z. Lahbabi 35a, S. Lai 55, I.K. Lakomiec 86a, N. Lalloue 60,J.E. Lambert 165, S. Lammers 68, W. Lampl 7, C. Lampoudis 152,e, A.N. Lancaster 115,E. Lançon 29, U. Landgraf 54, M.P.J. Landon 94, V.S. Lang 54, R.J. Langenberg 103,O.K.B. Langrekken 125, A.J. Lankford 160, F. Lanni 36, K. Lantzsch 24, A. Lanza 73a,A. Lapertosa 57b,57a, J.F. Laporte 135, T. Lari 71a, F. Lasagni Manghi 23b, M. Lassnig 36,V. Latonova 131, A. Laudrain 100, A. Laurier 150, S.D. Lawlor 139, Z. Lawrence 101,R. Lazaridou167, M. Lazzaroni 71a,71b, B. Le101, E.M. Le Boulicaut 51, B. Leban 93,A. Lebedev 81, M. LeBlanc 101, F. Ledroit-Guillon 60, A.C.A. Lee96, S.C. Lee 148,S. Lee 47a,47b, T.F. Lee 92, L.L. Leeuw 33c, H.P. Lefebvre 95, M. Lefebvre 165, C. Leggett 17a,G. Lehmann Miotto 36, M. Leigh 56, W.A. Leight 103, W. Leinonen 113, A. Leisos 152,s,M.A.L. Leite 83c, C.E. Leitgeb 48, R. Leitner 133, K.J.C. Leney 44, T. Lenz 24, S. Leone 74a,C. Leonidopoulos 52, A. Leopold 144, C. Leroy 108, R. Les 107, C.G. Lester 32,M. Levchenko 37, J. Levêque 4, D. Levin 106, L.J. Levinson 169, M.P. Lewicki 87,D.J. Lewis 4, A. Li 5, B. Li 62b, C. Li62a, C-Q. Li 110, H. Li 62a, H. Li 62b, H. Li 14c,H. Li 14b, H. Li 62b, J. Li 62c, K. Li 138, L. Li 62c, M. Li 14a,14e, Q.Y. Li 62a, S. Li 14a,14e,S. Li 62d,62c,d, T. Li 5, X. Li 104, Z. Li 126, Z. Li 104, Z. Li 92, Z. Li 14a,14e, S. Liang 14a,14e,Z. Liang 14a, M. Liberatore 135, B. Liberti 76a, K. Lie 64c, J. Lieber Marin 83b, H. Lien 68,K. Lin 107, R.E. Lindley 7, J.H. Lindon 2, E. Lipeles 128, A. Lipniacka 16, A. Lister 164,J.D. Little 4, B. Liu 14a, B.X. Liu 142, D. Liu 62d,62c, J.B. Liu 62a, J.K.K. Liu 32,K. Liu 62d,62c, M. Liu 62a, M.Y. Liu 62a, P. Liu 14a, Q. Liu 62d,138,62c, X. Liu 62a,Y. Liu 14d,14e, Y.L. Liu 62b, Y.W. Liu 62a, J. Llorente Merino 142, S.L. Lloyd 94,E.M. Lobodzinska 48, P. Loch 7, T. Lohse 18, K. Lohwasser 139, E. Loiacono 48,M. Lokajicek 131,∗, J.D. Lomas 20, J.D. Long 162, I. Longarini 160, L. Longo 70a,70b,R. Longo 162, I. Lopez Paz 67, A. Lopez Solis 48, N. Lorenzo Martinez 4, A.M. Lory 109,G. Löschcke Centeno 146, O. Loseva 37, X. Lou 47a,47b, X. Lou 14a,14e, A. Lounis 66,J. Love 6, P.A. Love 91, G. Lu 14a,14e, M. Lu 80, S. Lu 128, Y.J. Lu 65, H.J. Lubatti 138,– 76 –JHEP11(2024)097C. Luci 75a,75b, F.L. Lucio Alves 14c, A. Lucotte 60, F. Luehring 68, I. Luise 145,O. Lukianchuk 66, O. Lundberg 144, B. Lund-Jensen 144,∗, N.A. Luongo 6, M.S. Lutz 151,A.B. Lux 25, D. Lynn 29, H. Lyons92, R. Lysak 131, E. Lytken 98, V. Lyubushkin 38,T. Lyubushkina 38, M.M. Lyukova 145, H. Ma 29, K. Ma 62a, L.L. Ma 62b, W. Ma 62a,Y. Ma 121, D.M. Mac Donell 165, G. Maccarrone 53, J.C. MacDonald 100,P.C. Machado De Abreu Farias 83b, R. Madar 40, W.F. Mader 50, T. Madula 96, J. Maeda 85,T. Maeno 29, H. Maguire 139, V. Maiboroda 135, A. Maio 130a,130b,130d, K. Maj 86a,O. Majersky 48, S. Majewski 123, N. Makovec 66, V. Maksimovic 15, B. Malaescu 127,Pa. Malecki 87, V.P. Maleev 37, F. Malek 60, M. Mali 93, D. Malito 95, U. Mallik 80,∗,S. Maltezos10, S. Malyukov38, J. Mamuzic 13, G. Mancini 53, G. Manco 73a,73b,J.P. Mandalia 94, I. Mandić 93, L. Manhaes de Andrade Filho 83a, I.M. Maniatis 169,J. Manjarres Ramos 102,ab, D.C. Mankad 169, A. Mann 109, B. Mansoulie 135, S. Manzoni 36,L. Mao 62c, X. Mapekula 33c, A. Marantis 152,s, G. Marchiori 5, M. Marcisovsky 131,C. Marcon 71a, M. Marinescu 20, S. Marium 48, M. Marjanovic 120, E.J. Marshall 91,Z. Marshall 17a, S. Marti-Garcia 163, T.A. Martin 167, V.J. Martin 52, B. Martin dit Latour 16,L. Martinelli 75a,75b, M. Martinez 13,t, P. Martinez Agullo 163, V.I. Martinez Outschoorn 103,P. Martinez Suarez 13, S. Martin-Haugh 134, V.S. Martoiu 27b, A.C. Martyniuk 96,A. Marzin 36, D. Mascione 78a,78b, L. Masetti 100, T. Mashimo 153, J. Masik 101,A.L. Maslennikov 37, L. Massa 23b, P. Massarotti 72a,72b, P. Mastrandrea 74a,74b,A. Mastroberardino 43b,43a, T. Masubuchi 153, T. Mathisen 161, J. Matousek 133,N. Matsuzawa153, J. Maurer 27b, B. Maček 93, D.A. Maximov 37, R. Mazini 148, I. Maznas 152,M. Mazza 107, S.M. Mazza 136, E. Mazzeo 71a,71b, C. Mc Ginn 29, J.P. Mc Gowan 104,S.P. Mc Kee 106, E.F. McDonald 105, A.E. McDougall 114, J.A. Mcfayden 146,R.P. McGovern 128, G. Mchedlidze 149b, R.P. Mckenzie 33g, T.C. Mclachlan 48,D.J. Mclaughlin 96, S.J. McMahon 134, C.M. Mcpartland 92, R.A. McPherson 165,x,S. Mehlhase 109, A. Mehta 92, D. Melini 150, B.R. Mellado Garcia 33g, A.H. Melo 55,F. Meloni 48, A.M. Mendes Jacques Da Costa 101, H.Y. Meng 155, L. Meng 91, S. Menke 110,M. Mentink 36, E. Meoni 43b,43a, G. Mercado 115, C. Merlassino 69a,69c, L. Merola 72a,72b,C. Meroni 71a,71b, G. Merz106, J. Metcalfe 6, A.S. Mete 6, C. Meyer 68, J-P. Meyer 135,R.P. Middleton 134, L. Mijović 52, G. Mikenberg 169, M. Mikestikova 131, M. Mikuž 93,H. Mildner 100, A. Milic 36, C.D. Milke 44, D.W. Miller 39, L.S. Miller 34, A. Milov 169,D.A. Milstead47a,47b, T. Min14c, A.A. Minaenko 37, I.A. Minashvili 149b, L. Mince 59,A.I. Mincer 117, B. Mindur 86a, M. Mineev 38, Y. Mino 88, L.M. Mir 13,M. Miralles Lopez 163, M. Mironova 17a, A. Mishima153, M.C. Missio 113, A. Mitra 167,V.A. Mitsou 163, Y. Mitsumori 111, O. Miu 155, P.S. Miyagawa 94, T. Mkrtchyan 63a,M. Mlinarevic 96, T. Mlinarevic 96, M. Mlynarikova 36, S. Mobius 19, P. Moder 48,P. Mogg 109, M.H. Mohamed Farook 112, A.F. Mohammed 14a,14e, S. Mohapatra 41,G. Mokgatitswane 33g, L. Moleri 169, B. Mondal 141, S. Mondal 132, K. Mönig 48,E. Monnier 102, L. Monsonis Romero163, J. Montejo Berlingen 13, M. Montella 119,F. Montereali 77a,77b, F. Monticelli 90, S. Monzani 69a,69c, N. Morange 66,A.L. Moreira De Carvalho 130a, M. Moreno Llácer 163, C. Moreno Martinez 56, P. Morettini 57b,S. Morgenstern 36, M. Morii 61, M. Morinaga 153, A.K. Morley 36, F. Morodei 75a,75b,L. Morvaj 36, P. Moschovakos 36, B. Moser 36, M. Mosidze 149b, T. Moskalets 54,– 77 –JHEP11(2024)097P. Moskvitina 113, J. Moss 31,l, E.J.W. Moyse 103, O. Mtintsilana 33g, S. Muanza 102,J. Mueller 129, D. Muenstermann 91, R. Müller 19, G.A. Mullier 161, A.J. Mullin32,J.J. Mullin128, D.P. Mungo 155, D. Munoz Perez 163, F.J. Munoz Sanchez 101, M. Murin 101,W.J. Murray 167,134, A. Murrone 71a,71b, M. Muškinja 17a, C. Mwewa 29, A.G. Myagkov 37,a,A.J. Myers 8, G. Myers 68, M. Myska 132, B.P. Nachman 17a, O. Nackenhorst 49, A. Nag 50,K. Nagai 126, K. Nagano 84, J.L. Nagle 29,aj , E. Nagy 102, A.M. Nairz 36, Y. Nakahama 84,K. Nakamura 84, K. Nakkalil 5, H. Nanjo 124, R. Narayan 44, E.A. Narayanan 112,I. Naryshkin 37, M. Naseri 34, S. Nasri 159, C. Nass 24, G. Navarro 22a,J. Navarro-Gonzalez 163, R. Nayak 151, A. Nayaz 18, P.Y. Nechaeva 37, F. Nechansky 48,L. Nedic 126, T.J. Neep 20, A. Negri 73a,73b, M. Negrini 23b, C. Nellist 114, C. Nelson 104,K. Nelson 106, S. Nemecek 131, M. Nessi 36,h, M.S. Neubauer 162, F. Neuhaus 100,J. Neundorf 48, R. Newhouse 164, P.R. Newman 20, C.W. Ng 129, Y.W.Y. Ng 48,B. Ngair 35e, H.D.N. Nguyen 108, R.B. Nickerson 126, R. Nicolaidou 135, J. Nielsen 136,M. Niemeyer 55, J. Niermann 55,36, N. Nikiforou 36, V. Nikolaenko 37,a, I. Nikolic-Audit 127,K. Nikolopoulos 20, P. Nilsson 29, I. Ninca 48, H.R. Nindhito 56, G. Ninio 151, A. Nisati 75a,N. Nishu 2, R. Nisius 110, J-E. Nitschke 50, E.K. Nkadimeng 33g, T. Nobe 153, D.L. Noel 32,T. Nommensen 147, M.B. Norfolk 139, R.R.B. Norisam 96, B.J. Norman 34, M. Noury 35a,J. Novak 93, T. Novak 48, L. Novotny 132, R. Novotny 112, L. Nozka 122, K. Ntekas 160,N.M.J. Nunes De Moura Junior 83b, E. Nurse96, J. Ocariz 127, A. Ochi 85, I. Ochoa 130a,S. Oerdek 48,u, J.T. Offermann 39, A. Ogrodnik 133, A. Oh 101, C.C. Ohm 144, H. Oide 84,R. Oishi 153, M.L. Ojeda 48, M.W. O’Keefe92, Y. Okumura 153, L.F. Oleiro Seabra 130a,S.A. Olivares Pino 137d, D. Oliveira Damazio 29, D. Oliveira Goncalves 83a, J.L. Oliver 160,Ö.O. Öncel 54, A.P. O’Neill 19, A. Onofre 130a,130e, P.U.E. Onyisi 11, M.J. Oreglia 39,G.E. Orellana 90, D. Orestano 77a,77b, N. Orlando 13, R.S. Orr 155, V. O’Shea 59,L.M. Osojnak 128, R. Ospanov 62a, G. Otero y Garzon 30, H. Otono 89, P.S. Ott 63a,G.J. Ottino 17a, M. Ouchrif 35d, J. Ouellette 29, F. Ould-Saada 125, M. Owen 59,R.E. Owen 134, K.Y. Oyulmaz 21a, V.E. Ozcan 21a, F. Ozturk 87, N. Ozturk 8, S. Ozturk 82,H.A. Pacey 126, A. Pacheco Pages 13, C. Padilla Aranda 13, G. Padovano 75a,75b,S. Pagan Griso 17a, G. Palacino 68, A. Palazzo 70a,70b, S. Palestini 36, J. Pan 172, T. Pan 64a,D.K. Panchal 11, C.E. Pandini 114, J.G. Panduro Vazquez 95, H.D. Pandya 1, H. Pang 14b,P. Pani 48, G. Panizzo 69a,69c, L. Paolozzi 56, C. Papadatos 108, S. Parajuli 44,A. Paramonov 6, C. Paraskevopoulos 10, D. Paredes Hernandez 64b, K.R. Park 41,T.H. Park 155, M.A. Parker 32, F. Parodi 57b,57a, E.W. Parrish 115, V.A. Parrish 52,J.A. Parsons 41, U. Parzefall 54, B. Pascual Dias 108, L. Pascual Dominguez 151,E. Pasqualucci 75a, S. Passaggio 57b, F. Pastore 95, P. Pasuwan 47a,47b, P. Patel 87,U.M. Patel 51, J.R. Pater 101, T. Pauly 36, J. Pearkes 143, M. Pedersen 125, R. Pedro 130a,S.V. Peleganchuk 37, O. Penc 36, E.A. Pender 52, K.E. Penski 109, M. Penzin 37,B.S. Peralva 83d, A.P. Pereira Peixoto 60, L. Pereira Sanchez 47a,47b, D.V. Perepelitsa 29,aj ,E. Perez Codina 156a, M. Perganti 10, L. Perini 71a,71b,∗, H. Pernegger 36, O. Perrin 40,K. Peters 48, R.F.Y. Peters 101, B.A. Petersen 36, T.C. Petersen 42, E. Petit 102,V. Petousis 132, C. Petridou 152,e, A. Petrukhin 141, M. Pettee 17a, N.E. Pettersson 36,A. Petukhov 37, K. Petukhova 133, R. Pezoa 137f , L. Pezzotti 36, G. Pezzullo 172,T.M. Pham 170, T. Pham 105, P.W. Phillips 134, G. Piacquadio 145, E. Pianori 17a,– 78 –JHEP11(2024)097F. Piazza 123, R. Piegaia 30, D. Pietreanu 27b, A.D. Pilkington 101, M. Pinamonti 69a,69c,J.L. Pinfold 2, B.C. Pinheiro Pereira 130a, A.E. Pinto Pinoargote 100,135, L. Pintucci 69a,69c,K.M. Piper 146, A. Pirttikoski 56, D.A. Pizzi 34, L. Pizzimento 64b, A. Pizzini 114,M.-A. Pleier 29, V. Plesanovs54, V. Pleskot 133, E. Plotnikova38, G. Poddar 4, R. Poettgen 98,L. Poggioli 127, I. Pokharel 55, S. Polacek 133, G. Polesello 73a, A. Poley 142,156a,R. Polifka 132, A. Polini 23b, C.S. Pollard 167, Z.B. Pollock 119, V. Polychronakos 29,E. Pompa Pacchi 75a,75b, D. Ponomarenko 113, L. Pontecorvo 36, S. Popa 27a,G.A. Popeneciu 27d, A. Poreba 36, D.M. Portillo Quintero 156a, S. Pospisil 132,M.A. Postill 139, P. Postolache 27c, K. Potamianos 167, P.A. Potepa 86a, I.N. Potrap 38,C.J. Potter 32, H. Potti 1, T. Poulsen 48, J. Poveda 163, M.E. Pozo Astigarraga 36,A. Prades Ibanez 163, J. Pretel 54, D. Price 101, M. Primavera 70a, M.A. Principe Martin 99,R. Privara 122, T. Procter 59, M.L. Proffitt 138, N. Proklova 128, K. Prokofiev 64c,G. Proto 110, S. Protopopescu 29, J. Proudfoot 6, M. Przybycien 86a, W.W. Przygoda 86b,J.E. Puddefoot 139, D. Pudzha 37, D. Pyatiizbyantseva 37, J. Qian 106, D. Qichen 101,Y. Qin 101, T. Qiu 52, A. Quadt 55, M. Queitsch-Maitland 101, G. Quetant 56, R.P. Quinn 164,G. Rabanal Bolanos 61, D. Rafanoharana 54, F. Ragusa 71a,71b, J.L. Rainbolt 39, J.A. Raine 56,S. Rajagopalan 29, E. Ramakoti 37, I.A. Ramirez-Berend 34, K. Ran 48,14e, N.P. Rapheeha 33g,H. Rasheed 27b, V. Raskina 127, D.F. Rassloff 63a, S. Rave 100, B. Ravina 55,I. Ravinovich 169, M. Raymond 36, A.L. Read 125, N.P. Readioff 139, D.M. Rebuzzi 73a,73b,G. Redlinger 29, A.S. Reed 110, K. Reeves 26, J.A. Reidelsturz 171, D. Reikher 151, A. Rej 49,C. Rembser 36, A. Renardi 48, M. Renda 27b, M.B. Rendel110, F. Renner 48, A.G. Rennie 160,A.L. Rescia 48, S. Resconi 71a, M. Ressegotti 57b,57a, S. Rettie 36, J.G. Reyes Rivera 107,E. Reynolds 17a, O.L. Rezanova 37, P. Reznicek 133, N. Ribaric 91, E. Ricci 78a,78b,R. Richter 110, S. Richter 47a,47b, E. Richter-Was 86b, M. Ridel 127, S. Ridouani 35d,P. Rieck 117, P. Riedler 36, E.M. Riefel 47a,47b, J.O. Rieger 114, M. Rijssenbeek 145,A. Rimoldi 73a,73b, M. Rimoldi 36, L. Rinaldi 23b,23a, T.T. Rinn 29, M.P. Rinnagel 109,G. Ripellino 161, I. Riu 13, P. Rivadeneira 48, J.C. Rivera Vergara 165, F. Rizatdinova 121,E. Rizvi 94, B.A. Roberts 167, B.R. Roberts 17a, S.H. Robertson 104,x, D. Robinson 32,C.M. Robles Gajardo137f , M. Robles Manzano 100, A. Robson 59, A. Rocchi 76a,76b,C. Roda 74a,74b, S. Rodriguez Bosca 63a, Y. Rodriguez Garcia 22a, A. Rodriguez Rodriguez 54,A.M. Rodríguez Vera 156b, S. Roe36, J.T. Roemer 160, A.R. Roepe-Gier 136, J. Roggel 171,O. Røhne 125, R.A. Rojas 103, C.P.A. Roland 127, J. Roloff 29, A. Romaniouk 37,E. Romano 73a,73b, M. Romano 23b, A.C. Romero Hernandez 162, N. Rompotis 92, L. Roos 127,S. Rosati 75a, B.J. Rosser 39, E. Rossi 126, E. Rossi 72a,72b, L.P. Rossi 57b, L. Rossini 54,R. Rosten 119, M. Rotaru 27b, B. Rottler 54, C. Rougier 102,ab, D. Rousseau 66, D. Rousso 32,A. Roy 162, S. Roy-Garand 155, A. Rozanov 102, Z.M.A. Rozario 59, Y. Rozen 150,X. Ruan 33g, A. Rubio Jimenez 163, A.J. Ruby 92, V.H. Ruelas Rivera 18, T.A. Ruggeri 1,A. Ruggiero 126, A. Ruiz-Martinez 163, A. Rummler 36, Z. Rurikova 54, N.A. Rusakovich 38,H.L. Russell 165, G. Russo 75a,75b, J.P. Rutherfoord 7, S. Rutherford Colmenares 32,K. Rybacki91, M. Rybar 133, E.B. Rye 125, A. Ryzhov 44, J.A. Sabater Iglesias 56,P. Sabatini 163, H.F-W. Sadrozinski 136, F. Safai Tehrani 75a, B. Safarzadeh Samani 134,M. Safdari 143, S. Saha 165, M. Sahinsoy 110, A. Saibel 163, M. Saimpert 135, M. Saito 153,T. Saito 153, D. Salamani 36, A. Salnikov 143, J. Salt 163, A. Salvador Salas 151,– 79 –JHEP11(2024)097D. Salvatore 43b,43a, F. Salvatore 146, A. Salzburger 36, D. Sammel 54, D. Sampsonidis 152,e,D. Sampsonidou 123, J. Sánchez 163, A. Sanchez Pineda 4, V. Sanchez Sebastian 163,H. Sandaker 125, C.O. Sander 48, J.A. Sandesara 103, M. Sandhoff 171, C. Sandoval 22b,D.P.C. Sankey 134, T. Sano 88, A. Sansoni 53, L. Santi 75a,75b, C. Santoni 40,H. Santos 130a,130b, S.N. Santpur 17a, A. Santra 169, K.A. Saoucha 116b, J.G. Saraiva 130a,130d,J. Sardain 7, O. Sasaki 84, K. Sato 157, C. Sauer63b, F. Sauerburger 54, E. Sauvan 4,P. Savard 155,ag, R. Sawada 153, C. Sawyer 134, L. Sawyer 97, I. Sayago Galvan163,C. Sbarra 23b, A. Sbrizzi 23b,23a, T. Scanlon 96, J. Schaarschmidt 138, P. Schacht 110,U. Schäfer 100, A.C. Schaffer 66,44, D. Schaile 109, R.D. Schamberger 145, C. Scharf 18,M.M. Schefer 19, V.A. Schegelsky 37, D. Scheirich 133, F. Schenck 18, M. Schernau 160,C. Scheulen 55, C. Schiavi 57b,57a, E.J. Schioppa 70a,70b, M. Schioppa 43b,43a, B. Schlag 143,n,K.E. Schleicher 54, S. Schlenker 36, J. Schmeing 171, M.A. Schmidt 171, K. Schmieden 100,C. Schmitt 100, N. Schmitt 100, S. Schmitt 48, L. Schoeffel 135, A. Schoening 63b,P.G. Scholer 54, E. Schopf 126, M. Schott 100, J. Schovancova 36, S. Schramm 56,F. Schroeder 171, T. Schroer 56, H-C. Schultz-Coulon 63a, M. Schumacher 54,B.A. Schumm 136, Ph. Schune 135, A.J. Schuy 138, H.R. Schwartz 136, A. Schwartzman 143,T.A. Schwarz 106, Ph. Schwemling 135, R. Schwienhorst 107, A. Sciandra 136, G. Sciolla 26,F. Scuri 74a, C.D. Sebastiani 92, K. Sedlaczek 115, P. Seema 18, S.C. Seidel 112, A. Seiden 136,B.D. Seidlitz 41, C. Seitz 48, J.M. Seixas 83b, G. Sekhniaidze 72a, S.J. Sekula 44, L. Selem 60,N. Semprini-Cesari 23b,23a, D. Sengupta 56, V. Senthilkumar 163, L. Serin 66, L. Serkin 69a,69b,M. Sessa 76a,76b, H. Severini 120, F. Sforza 57b,57a, A. Sfyrla 56, E. Shabalina 55,R. Shaheen 144, J.D. Shahinian 128, D. Shaked Renous 169, L.Y. Shan 14a, M. Shapiro 17a,A. Sharma 36, A.S. Sharma 164, P. Sharma 80, S. Sharma 48, P.B. Shatalov 37, K. Shaw 146,S.M. Shaw 101, A. Shcherbakova 37, Q. Shen 62c,5, D.J. Sheppard 142, P. Sherwood 96,L. Shi 96, X. Shi 14a, C.O. Shimmin 172, J.D. Shinner 95, I.P.J. Shipsey 126, S. Shirabe 56,h,M. Shiyakova 38,v, J. Shlomi 169, M.J. Shochet 39, J. Shojaii 105, D.R. Shope 125,B. Shrestha 120, S. Shrestha 119,al, E.M. Shrif 33g, M.J. Shroff 165, P. Sicho 131,A.M. Sickles 162, E. Sideras Haddad 33g, A. Sidoti 23b, F. Siegert 50, Dj. Sijacki 15, F. Sili 90,J.M. Silva 20, M.V. Silva Oliveira 29, S.B. Silverstein 47a, S. Simion66, R. Simoniello 36,E.L. Simpson 59, H. Simpson 146, L.R. Simpson 106, N.D. Simpson98, S. Simsek 82,S. Sindhu 55, P. Sinervo 155, S. Singh 155, S. Sinha 48, S. Sinha 101, M. Sioli 23b,23a,I. Siral 36, E. Sitnikova 48, S.Yu. Sivoklokov 37,∗, J. Sjölin 47a,47b, A. Skaf 55, E. Skorda 20,P. Skubic 120, M. Slawinska 87, V. Smakhtin169, B.H. Smart 134, J. Smiesko 36,S.Yu. Smirnov 37, Y. Smirnov 37, L.N. Smirnova 37,a, O. Smirnova 98, A.C. Smith 41,E.A. Smith 39, H.A. Smith 126, J.L. Smith 92, R. Smith143, M. Smizanska 91, K. Smolek 132,A.A. Snesarev 37, S.R. Snider 155, H.L. Snoek 114, S. Snyder 29, R. Sobie 165,x, A. Soffer 151,C.A. Solans Sanchez 36, E.Yu. Soldatov 37, U. Soldevila 163, A.A. Solodkov 37, S. Solomon 26,A. Soloshenko 38, K. Solovieva 54, O.V. Solovyanov 40, V. Solovyev 37, P. Sommer 36,A. Sonay 13, W.Y. Song 156b, J.M. Sonneveld 114, A. Sopczak 132, A.L. Sopio 96,F. Sopkova 28b, I.R. Sotarriva Alvarez 154, V. Sothilingam63a, O.J. Soto Sandoval 137c,137b,S. Sottocornola 68, R. Soualah 116b, Z. Soumaimi 35e, D. South 48, N. Soybelman 169,S. Spagnolo 70a,70b, M. Spalla 110, D. Sperlich 54, G. Spigo 36, S. Spinali 91, D.P. Spiteri 59,M. Spousta 133, E.J. Staats 34, A. Stabile 71a,71b, R. Stamen 63a, A. Stampekis 20,– 80 –JHEP11(2024)097M. Standke 24, E. Stanecka 87, M.V. Stange 50, B. Stanislaus 17a, M.M. Stanitzki 48,B. Stapf 48, E.A. Starchenko 37, G.H. Stark 136, J. Stark 102,ab, D.M. Starko156b,P. Staroba 131, P. Starovoitov 63a, S. Stärz 104, R. Staszewski 87, G. Stavropoulos 46,J. Steentoft 161, P. Steinberg 29, B. Stelzer 142,156a, H.J. Stelzer 129, O. Stelzer-Chilton 156a,H. Stenzel 58, T.J. Stevenson 146, G.A. Stewart 36, J.R. Stewart 121, M.C. Stockton 36,G. Stoicea 27b, M. Stolarski 130a, S. Stonjek 110, A. Straessner 50, J. Strandberg 144,S. Strandberg 47a,47b, M. Stratmann 171, M. Strauss 120, T. Strebler 102, P. Strizenec 28b,R. Ströhmer 166, D.M. Strom 123, R. Stroynowski 44, A. Strubig 47a,47b, S.A. Stucci 29,B. Stugu 16, J. Stupak 120, N.A. Styles 48, D. Su 143, S. Su 62a, W. Su 62d, X. Su 62a,66,K. Sugizaki 153, V.V. Sulin 37, M.J. Sullivan 92, D.M.S. Sultan 78a,78b, L. Sultanaliyeva 37,S. Sultansoy 3b, T. Sumida 88, S. Sun 106, S. Sun 170, O. Sunneborn Gudnadottir 161,N. Sur 102, M.R. Sutton 146, H. Suzuki 157, M. Svatos 131, M. Swiatlowski 156a,T. Swirski 166, I. Sykora 28a, M. Sykora 133, T. Sykora 133, D. Ta 100, K. Tackmann 48,u,A. Taffard 160, R. Tafirout 156a, J.S. Tafoya Vargas 66, E.P. Takeva 52, Y. Takubo 84,M. Talby 102, A.A. Talyshev 37, K.C. Tam 64b, N.M. Tamir151, A. Tanaka 153, J. Tanaka 153,R. Tanaka 66, M. Tanasini 57b,57a, Z. Tao 164, S. Tapia Araya 137f , S. Tapprogge 100,A. Tarek Abouelfadl Mohamed 107, S. Tarem 150, K. Tariq 14a, G. Tarna 102,27b,G.F. Tartarelli 71a, P. Tas 133, M. Tasevsky 131, E. Tassi 43b,43a, A.C. Tate 162,G. Tateno 153, Y. Tayalati 35e,w, G.N. Taylor 105, W. Taylor 156b, A.S. Tee 170,R. Teixeira De Lima 143, P. Teixeira-Dias 95, J.J. Teoh 155, K. Terashi 153, J. Terron 99,S. Terzo 13, M. Testa 53, R.J. Teuscher 155,x, A. Thaler 79, O. Theiner 56,N. Themistokleous 52, T. Theveneaux-Pelzer 102, O. Thielmann 171, D.W. Thomas95,J.P. Thomas 20, E.A. Thompson 17a, P.D. Thompson 20, E. Thomson 128, Y. Tian 55,V. Tikhomirov 37,a, Yu.A. Tikhonov 37, S. Timoshenko37, D. Timoshyn 133, E.X.L. Ting 1,P. Tipton 172, S.H. Tlou 33g, A. Tnourji 40, K. Todome 154, S. Todorova-Nova 133, S. Todt50,M. Togawa 84, J. Tojo 89, S. Tokár 28a, K. Tokushuku 84, O. Toldaiev 68, R. Tombs 32,M. Tomoto 84,111, L. Tompkins 143,n, K.W. Topolnicki 86b, E. Torrence 123, H. Torres 102,ab,E. Torró Pastor 163, M. Toscani 30, C. Tosciri 39, M. Tost 11, D.R. Tovey 139, A. Traeet16,I.S. Trandafir 27b, T. Trefzger 166, A. Tricoli 29, I.M. Trigger 156a, S. Trincaz-Duvoid 127,D.A. Trischuk 26, B. Trocmé 60, C. Troncon 71a, M.R. Trott ak, L. Truong 33c,M. Trzebinski 87, A. Trzupek 87, F. Tsai 145, M. Tsai 106, A. Tsiamis 152,e, P.V. Tsiareshka37,S. Tsigaridas 156a, A. Tsirigotis 152,s, V. Tsiskaridze 155, E.G. Tskhadadze 149a,M. Tsopoulou 152,e, Y. Tsujikawa 88, I.I. Tsukerman 37, V. Tsulaia 17a, S. Tsuno 84,K. Tsuri 118, D. Tsybychev 145, Y. Tu 64b, A. Tudorache 27b, V. Tudorache 27b, A.N. Tuna 61,S. Turchikhin 57b,57a, I. Turk Cakir 3a, R. Turra 71a, T. Turtuvshin 38,y, P.M. Tuts 41,S. Tzamarias 152,e, P. Tzanis 10, E. Tzovara 100, F. Ukegawa 157, P.A. Ulloa Poblete 137c,137b,E.N. Umaka 29, G. Unal 36, M. Unal 11, A. Undrus 29, G. Unel 160, J. Urban 28b,P. Urquijo 105, P. Urrejola 137a, G. Usai 8, R. Ushioda 154, M. Usman 108, Z. Uysal 21b,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, E. Valiente Moreno 163, A. Vallier 102,ab, J.A. Valls Ferrer 163,D.R. Van Arneman 114, T.R. Van Daalen 138, A. Van Der Graaf 49, P. Van Gemmeren 6,M. Van Rijnbach 125,36, S. Van Stroud 96, I. Van Vulpen 114, M. Vanadia 76a,76b,– 81 –JHEP11(2024)097W. Vandelli 36, M. Vandenbroucke 135, E.R. Vandewall 121, D. Vannicola 151,L. Vannoli 57b,57a, R. Vari 75a, E.W. Varnes 7, C. Varni 17b, T. Varol 148, D. Varouchas 66,L. Varriale 163, K.E. Varvell 147, M.E. Vasile 27b, L. Vaslin84, G.A. Vasquez 165,A. Vasyukov 38, 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, S. Ventura Gonzalez 135, A. Verbytskyi 110, M. Verducci 74a,74b,C. Vergis 24, M. Verissimo De Araujo 83b, W. Verkerke 114, J.C. Vermeulen 114,C. Vernieri 143, M. Vessella 103, M.C. Vetterli 142,ag, A. Vgenopoulos 152,e,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. Villhauer52, E. Vilucchi 53,M.G. Vincter 34, G.S. Virdee 20, A. Vishwakarma 52, A. Visibile114, C. Vittori 36,I. Vivarelli 146, E. Voevodina 110, F. Vogel 109, J.C. Voigt 50, P. Vokac 132,Yu. Volkotrub 86a, 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, N.K. Vu 62d,62c, R. Vuillermet 36,O. Vujinovic 100, I. Vukotic 39, S. Wada 157, C. Wagner103, J.M. Wagner 17a, W. Wagner 171,S. Wahdan 171, H. Wahlberg 90, M. Wakida 111, J. Walder 134, R. Walker 109,W. Walkowiak 141, A. Wall 128, T. Wamorkar 6, A.Z. Wang 136, C. Wang 100, C. Wang 62c,H. Wang 17a, J. Wang 64a, R.-J. Wang 100, R. Wang 61, R. Wang 6, S.M. Wang 148,S. Wang 62b, T. Wang 62a, W.T. Wang 80, W. Wang 14a, 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, E. Watton 59,134, G. Watts 138, B.M. Waugh 96, 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. Wenke110, N. Wermes 24, M. Wessels 63a,A.M. Wharton 91, A.S. White 61, A. White 8, M.J. White 1, D. Whiteson 160,L. Wickremasinghe 124, W. Wiedenmann 170, C. Wiel 50, M. Wielers 134, C. Wiglesworth 42,D.J. Wilbern120, H.G. Wilkens 36, D.M. Williams 41, H.H. Williams128, S. Williams 32,S. Willocq 103, B.J. Wilson 101, P.J. Windischhofer 39, F.I. Winkel 30, F. Winklmeier 123,B.T. Winter 54, J.K. Winter 101, M. Wittgen143, M. Wobisch 97, Z. Wolffs 114, J. Wollrath160,M.W. Wolter 87, H. Wolters 130a,130c, A.F. Wongel 48, E.L. Woodward 41, S.D. Worm 48,B.K. Wosiek 87, K.W. Woźniak 87, S. Wozniewski 55, K. Wraight 59, C. Wu 20, J. Wu 14a,14e,M. Wu 64a, M. Wu 113, S.L. Wu 170, X. Wu 56, Y. Wu 62a, Z. Wu 135, J. Wuerzinger 110,ae,T.R. Wyatt 101, B.M. Wynne 52, S. Xella 42, L. Xia 14c, M. Xia 14b, J. Xiang 64c,M. Xie 62a, X. Xie 62a, S. Xin 14a,14e, A. Xiong 123, J. Xiong 17a, D. Xu 14a, H. Xu 62a,L. Xu 62a, R. Xu 128, T. Xu 106, Y. Xu 14b, Z. Xu 52, Z. Xu14c, B. Yabsley 147,S. Yacoob 33a, Y. Yamaguchi 154, E. Yamashita 153, H. Yamauchi 157, T. Yamazaki 17a,Y. Yamazaki 85, J. Yan62c, S. Yan 126, Z. Yan 25, H.J. Yang 62c,62d, H.T. Yang 62a,S. Yang 62a, T. Yang 64c, X. Yang 36, X. Yang 14a, Y. Yang 44, Y. Yang62a, Z. Yang 62a,W-M. Yao 17a, Y.C. Yap 48, H. Ye 14c, H. Ye 55, J. Ye 14a, S. Ye 29, X. Ye 62a, Y. Yeh 96,I. Yeletskikh 38, B. Yeo 17b, M.R. Yexley 96, P. Yin 41, K. Yorita 168, S. Younas 27b,C.J.S. Young 36, C. Young 143, C. Yu 14a,14e,ai, Y. Yu 62a, M. Yuan 106, R. Yuan 62b,– 82 –JHEP11(2024)097L. Yue 96, M. Zaazoua 62a, B. Zabinski 87, E. Zaid52, Z.K. Zak 87, 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, H. Zeng 14a, 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,14e, B. Zhang 14c,D.F. Zhang 139, J. Zhang 62b, J. Zhang 6, K. Zhang 14a,14e, L. Zhang 14c, P. Zhang 14a,14e,R. Zhang 170, S. Zhang 106, S. Zhang 44, T. Zhang 153, X. Zhang 62c, X. Zhang 62b,Y. Zhang 62c,5, Y. Zhang 96, Y. Zhang 14c, Z. Zhang 17a, Z. Zhang 66, H. Zhao 138,T. Zhao 62b, Y. Zhao 136, Z. Zhao 62a, A. Zhemchugov 38, J. Zheng 14c, K. Zheng 162,X. Zheng 62a, Z. Zheng 143, D. Zhong 162, B. Zhou 106, H. Zhou 7, N. Zhou 62c, Y. Zhou7,C.G. Zhu 62b, 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 61, T.G. Zorbas 139, O. Zormpa 46, W. Zou 41, L. Zwalinski 361Department of Physics, University of Adelaide, Adelaide; Australia2Department of Physics, University of Alberta, Edmonton AB; Canada3 (a)Department of Physics, Ankara University, Ankara;(b)Division of Physics, TOBB University ofEconomics and Technology, Ankara; Türkiye4 LAPP, Université Savoie Mont Blanc, CNRS/IN2P3, Annecy; France5APC, Université Paris Cité, CNRS/IN2P3, Paris; France6High Energy Physics Division, Argonne National Laboratory, Argonne IL; United States of America7Department of Physics, University of Arizona, Tucson AZ; United States of America8Department of Physics, University of Texas at Arlington, Arlington TX; United States of America9 Physics Department, National and Kapodistrian University of Athens, Athens; Greece10 Physics Department, National Technical University of Athens, Zografou; Greece11Department of Physics, University of Texas at Austin, Austin TX; United States of America12 Institute of Physics, Azerbaijan Academy of Sciences, Baku; Azerbaijan13 Institut de Física d’Altes Energies (IFAE), Barcelona Institute of Science and Technology, Barcelona;Spain14 (a)Institute of High Energy Physics, Chinese Academy of Sciences, Beijing;(b)Physics Department,Tsinghua University, Beijing;(c)Department of Physics, Nanjing University, Nanjing;(d)School of Science,Shenzhen Campus of Sun Yat-sen University;(e)University of Chinese Academy of Science (UCAS),Beijing; China15 Institute of Physics, University of Belgrade, Belgrade; Serbia16Department for Physics and Technology, University of Bergen, Bergen; Norway17 (a)Physics Division, Lawrence Berkeley National Laboratory, Berkeley CA;(b)University of California,Berkeley CA; United States of America18 Institut für Physik, Humboldt Universität zu Berlin, Berlin; Germany19Albert Einstein Center for Fundamental Physics and Laboratory for High Energy Physics, University ofBern, Bern; Switzerland20 School of Physics and Astronomy, University of Birmingham, Birmingham; United Kingdom21 (a)Department of Physics, Bogazici University, Istanbul;(b)Department of Physics Engineering, GaziantepUniversity, Gaziantep;(c)Department of Physics, Istanbul University, Istanbul; Türkiye22 (a)Facultad de Ciencias y Centro de Investigaciónes, Universidad Antonio Nariño,Bogotá;(b)Departamento de Física, Universidad Nacional de Colombia, Bogotá; Colombia23 (a)Dipartimento di Fisica e Astronomia A. Righi, Università di Bologna, Bologna;(b)INFN Sezione diBologna; Italy24 Physikalisches Institut, Universität Bonn, Bonn; Germany25Department of Physics, Boston University, Boston MA; United States of America26Department of Physics, Brandeis University, Waltham MA; United States of America– 83 –JHEP11(2024)09727 (a)Transilvania University of Brasov, Brasov;(b)Horia Hulubei National Institute of Physics and NuclearEngineering, Bucharest;(c)Department of Physics, Alexandru Ioan Cuza University of Iasi, Iasi;(d)NationalInstitute for Research and Development of Isotopic and Molecular Technologies, Physics Department,Cluj-Napoca;(e)National University of Science and Technology Politechnica, Bucharest;(f)West Universityin Timisoara, Timisoara;(g)Faculty of Physics, University of Bucharest, Bucharest; Romania28 (a)Faculty of Mathematics, Physics and Informatics, Comenius University, Bratislava;(b)Department ofSubnuclear Physics, Institute of Experimental Physics of the Slovak Academy of Sciences, Kosice; SlovakRepublic29 Physics Department, Brookhaven National Laboratory, Upton NY; United States of America30Universidad de Buenos Aires, Facultad de Ciencias Exactas y Naturales, Departamento de Física, yCONICET, Instituto de Física de Buenos Aires (IFIBA), Buenos Aires; Argentina31California State University, CA; United States of America32Cavendish Laboratory, University of Cambridge, Cambridge; United Kingdom33 (a)Department of Physics, University of Cape Town, Cape Town;(b)iThemba Labs, WesternCape;(c)Department of Mechanical Engineering Science, University of Johannesburg,Johannesburg;(d)National Institute of Physics, University of the Philippines Diliman(Philippines);(e)University of South Africa, Department of Physics, Pretoria;(f)University of Zululand,KwaDlangezwa;(g)School of Physics, University of the Witwatersrand, Johannesburg; South Africa34Department of Physics, Carleton University, Ottawa ON; Canada35 (a)Faculté des Sciences Ain Chock, Université Hassan II de Casablanca;(b)Faculté des Sciences, UniversitéIbn-Tofail, Kénitra;(c)Faculté des Sciences Semlalia, Université Cadi Ayyad, LPHEA-Marrakech;(d)LPMR,Faculté des Sciences, Université Mohamed Premier, Oujda;(e)Faculté des sciences, Université MohammedV, Rabat;(f)Institute of Applied Physics, Mohammed VI Polytechnic University, Ben Guerir; Morocco36CERN, Geneva; Switzerland37Affiliated with an institute covered by a cooperation agreement with CERN38Affiliated with an international laboratory covered by a cooperation agreement with CERN39 Enrico Fermi Institute, University of Chicago, Chicago IL; United States of America40 LPC, Université Clermont Auvergne, CNRS/IN2P3, Clermont-Ferrand; France41Nevis Laboratory, Columbia University, Irvington NY; United States of America42Niels Bohr Institute, University of Copenhagen, Copenhagen; Denmark43 (a)Dipartimento di Fisica, Università della Calabria, Rende;(b)INFN Gruppo Collegato di Cosenza,Laboratori Nazionali di Frascati; Italy44 Physics Department, Southern Methodist University, Dallas TX; United States of America45 Physics Department, University of Texas at Dallas, Richardson TX; United States of America46National Centre for Scientific Research “Demokritos”, Agia Paraskevi; Greece47 (a)Department of Physics, Stockholm University;(b)Oskar Klein Centre, Stockholm; Sweden48Deutsches Elektronen-Synchrotron DESY, Hamburg and Zeuthen; Germany49 Fakultät Physik, Technische Universität Dortmund, Dortmund; Germany50 Institut für Kern- und Teilchenphysik, Technische Universität Dresden, Dresden; Germany51Department of Physics, Duke University, Durham NC; United States of America52 SUPA — School of Physics and Astronomy, University of Edinburgh, Edinburgh; United Kingdom53 INFN e Laboratori Nazionali di Frascati, Frascati; Italy54 Physikalisches Institut, Albert-Ludwigs-Universität Freiburg, Freiburg; Germany55 II. Physikalisches Institut, Georg-August-Universität Göttingen, Göttingen; Germany56Département de Physique Nucléaire et Corpusculaire, Université de Genève, Genève; Switzerland57 (a)Dipartimento di Fisica, Università di Genova, Genova;(b)INFN Sezione di Genova; Italy58 II. Physikalisches Institut, Justus-Liebig-Universität Giessen, Giessen; Germany59 SUPA — School of Physics and Astronomy, University of Glasgow, Glasgow; United Kingdom60 LPSC, Université Grenoble Alpes, CNRS/IN2P3, Grenoble INP, Grenoble; France61 Laboratory for Particle Physics and Cosmology, Harvard University, Cambridge MA; United States ofAmerica– 84 –JHEP11(2024)09762 (a)Department of Modern Physics and State Key Laboratory of Particle Detection and Electronics,University of Science and Technology of China, Hefei;(b)Institute of Frontier and Interdisciplinary Scienceand Key Laboratory of Particle Physics and Particle Irradiation (MOE), Shandong University,Qingdao;(c)School of Physics and Astronomy, Shanghai Jiao Tong University, Key Laboratory for ParticleAstrophysics and Cosmology (MOE), SKLPPC, Shanghai;(d)Tsung-Dao Lee Institute, Shanghai;(e)Schoolof Physics and Microelectronics, Zhengzhou University; China63 (a)Kirchhoff-Institut für Physik, Ruprecht-Karls-Universität Heidelberg, Heidelberg;(b)PhysikalischesInstitut, Ruprecht-Karls-Universität Heidelberg, Heidelberg; Germany64 (a)Department of Physics, Chinese University of Hong Kong, Shatin, N.T., Hong Kong;(b)Department ofPhysics, University of Hong Kong, Hong Kong;(c)Department of Physics and Institute for Advanced Study,Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong; China65Department of Physics, National Tsing Hua University, Hsinchu; Taiwan66 IJCLab, Université Paris-Saclay, CNRS/IN2P3, 91405, Orsay; France67Centro Nacional de Microelectrónica (IMB-CNM-CSIC), Barcelona; Spain68Department of Physics, Indiana University, Bloomington IN; United States of America69 (a)INFN Gruppo Collegato di Udine, Sezione di Trieste, Udine;(b)ICTP, Trieste;(c)DipartimentoPolitecnico di Ingegneria e Architettura, Università di Udine, Udine; Italy70 (a)INFN Sezione di Lecce;(b)Dipartimento di Matematica e Fisica, Università del Salento, Lecce; Italy71 (a)INFN Sezione di Milano;(b)Dipartimento di Fisica, Università di Milano, Milano; Italy72 (a)INFN Sezione di Napoli;(b)Dipartimento di Fisica, Università di Napoli, Napoli; Italy73 (a)INFN Sezione di Pavia;(b)Dipartimento di Fisica, Università di Pavia, Pavia; Italy74 (a)INFN Sezione di Pisa;(b)Dipartimento di Fisica E. Fermi, Università di Pisa, Pisa; Italy75 (a)INFN Sezione di Roma;(b)Dipartimento di Fisica, Sapienza Università di Roma, Roma; Italy76 (a)INFN Sezione di Roma Tor Vergata;(b)Dipartimento di Fisica, Università di Roma Tor Vergata, Roma;Italy77 (a)INFN Sezione di Roma Tre;(b)Dipartimento di Matematica e Fisica, Università Roma Tre, Roma; Italy78 (a)INFN-TIFPA;(b)Università degli Studi di Trento, Trento; Italy79Universität Innsbruck, Department of Astro and Particle Physics, Innsbruck; Austria80University of Iowa, Iowa City IA; United States of America81Department of Physics and Astronomy, Iowa State University, Ames IA; United States of America82 Istinye University, Sariyer, Istanbul; Türkiye83 (a)Departamento de Engenharia Elétrica, Universidade Federal de Juiz de Fora (UFJF), Juiz deFora;(b)Universidade Federal do Rio De Janeiro COPPE/EE/IF, Rio de Janeiro;(c)Instituto de Física,Universidade de São Paulo, São Paulo;(d)Rio de Janeiro State University, Rio de Janeiro; Brazil84KEK, High Energy Accelerator Research Organization, Tsukuba; Japan85Graduate School of Science, Kobe University, Kobe; Japan86 (a)AGH University of Krakow, Faculty of Physics and Applied Computer Science, Krakow;(b)MarianSmoluchowski Institute of Physics, Jagiellonian University, Krakow; Poland87 Institute of Nuclear Physics Polish Academy of Sciences, Krakow; Poland88 Faculty of Science, Kyoto University, Kyoto; Japan89Research Center for Advanced Particle Physics and Department of Physics, Kyushu University, Fukuoka;Japan90 Instituto de Física La Plata, Universidad Nacional de La Plata and CONICET, La Plata; Argentina91 Physics Department, Lancaster University, Lancaster; United Kingdom92Oliver Lodge Laboratory, University of Liverpool, Liverpool; United Kingdom93Department of Experimental Particle Physics, Jožef Stefan Institute and Department of Physics,University of Ljubljana, Ljubljana; Slovenia94 School of Physics and Astronomy, Queen Mary University of London, London; United Kingdom95Department of Physics, Royal Holloway University of London, Egham; United Kingdom96Department of Physics and Astronomy, University College London, London; United Kingdom97 Louisiana Tech University, Ruston LA; United States of America98 Fysiska institutionen, Lunds universitet, Lund; Sweden99Departamento de Física Teorica C-15 and CIAFF, Universidad Autónoma de Madrid, Madrid; Spain– 85 –JHEP11(2024)097100 Institut für Physik, Universität Mainz, Mainz; Germany101 School of Physics and Astronomy, University of Manchester, Manchester; United Kingdom102CPPM, Aix-Marseille Université, CNRS/IN2P3, Marseille; France103Department of Physics, University of Massachusetts, Amherst MA; United States of America104Department of Physics, McGill University, Montreal QC; Canada105 School of Physics, University of Melbourne, Victoria; Australia106Department of Physics, University of Michigan, Ann Arbor MI; United States of America107Department of Physics and Astronomy, Michigan State University, East Lansing MI; United States ofAmerica108Group of Particle Physics, University of Montreal, Montreal QC; Canada109 Fakultät für Physik, Ludwig-Maximilians-Universität München, München; Germany110Max-Planck-Institut für Physik (Werner-Heisenberg-Institut), München; Germany111Graduate School of Science and Kobayashi-Maskawa Institute, Nagoya University, Nagoya; Japan112Department of Physics and Astronomy, University of New Mexico, Albuquerque NM; United States ofAmerica113 Institute for Mathematics, Astrophysics and Particle Physics, Radboud University/Nikhef, Nijmegen;Netherlands114Nikhef National Institute for Subatomic Physics and University of Amsterdam, Amsterdam; Netherlands115Department of Physics, Northern Illinois University, DeKalb IL; United States of America116 (a)New York University Abu Dhabi, Abu Dhabi;(b)University of Sharjah, Sharjah; United Arab Emirates117Department of Physics, New York University, New York NY; United States of America118Ochanomizu University, Otsuka, Bunkyo-ku, Tokyo; Japan119Ohio State University, Columbus OH; United States of America120Homer L. Dodge Department of Physics and Astronomy, University of Oklahoma, Norman OK; UnitedStates of America121Department of Physics, Oklahoma State University, Stillwater OK; United States of America122 Palacký University, Joint Laboratory of Optics, Olomouc; Czech Republic123 Institute for Fundamental Science, University of Oregon, Eugene, OR; United States of America124Graduate School of Science, Osaka University, Osaka; Japan125Department of Physics, University of Oslo, Oslo; Norway126Department of Physics, Oxford University, Oxford; United Kingdom127 LPNHE, Sorbonne Université, Université Paris Cité, CNRS/IN2P3, Paris; France128Department of Physics, University of Pennsylvania, Philadelphia PA; United States of America129Department of Physics and Astronomy, University of Pittsburgh, Pittsburgh PA; United States of America130 (a)Laboratório de Instrumentação e Física Experimental de Partículas — LIP, Lisboa;(b)Departamento deFísica, Faculdade de Ciências, Universidade de Lisboa, Lisboa;(c)Departamento de Física, Universidade deCoimbra, Coimbra;(d)Centro de Física Nuclear da Universidade de Lisboa, Lisboa;(e)Departamento deFísica, Universidade do Minho, Braga;(f)Departamento de Física Teórica y del Cosmos, Universidad deGranada, Granada (Spain);(g)Departamento de Física, Instituto Superior Técnico, Universidade de Lisboa,Lisboa; Portugal131 Institute of Physics of the Czech Academy of Sciences, Prague; Czech Republic132Czech Technical University in Prague, Prague; Czech Republic133Charles University, Faculty of Mathematics and Physics, Prague; Czech Republic134 Particle Physics Department, Rutherford Appleton Laboratory, Didcot; United Kingdom135 IRFU, CEA, Université Paris-Saclay, Gif-sur-Yvette; France136 Santa Cruz Institute for Particle Physics, University of California Santa Cruz, Santa Cruz CA; UnitedStates of America137 (a)Departamento de Física, Pontificia Universidad Católica de Chile, Santiago;(b)Millennium Institute forSubatomic physics at high energy frontier (SAPHIR), Santiago;(c)Instituto de InvestigaciónMultidisciplinario en Ciencia y Tecnología, y Departamento de Física, Universidad de LaSerena;(d)Universidad Andres Bello, Department of Physics, Santiago;(e)Instituto de Alta Investigación,Universidad de Tarapacá, Arica;(f)Departamento de Física, Universidad Técnica Federico Santa María,Valparaíso; Chile– 86 –JHEP11(2024)097138Department of Physics, University of Washington, Seattle WA; United States of America139Department of Physics and Astronomy, University of Sheffield, Sheffield; United Kingdom140Department of Physics, Shinshu University, Nagano; Japan141Department Physik, Universität Siegen, Siegen; Germany142Department of Physics, Simon Fraser University, Burnaby BC; Canada143 SLAC National Accelerator Laboratory, Stanford CA; United States of America144Department of Physics, Royal Institute of Technology, Stockholm; Sweden145Departments of Physics and Astronomy, Stony Brook University, Stony Brook NY; United States ofAmerica146Department of Physics and Astronomy, University of Sussex, Brighton; United Kingdom147 School of Physics, University of Sydney, Sydney; Australia148 Institute of Physics, Academia Sinica, Taipei; Taiwan149 (a)E. Andronikashvili Institute of Physics, Iv. Javakhishvili Tbilisi State University, Tbilisi;(b)High EnergyPhysics Institute, Tbilisi State University, Tbilisi;(c)University of Georgia, Tbilisi; Georgia150Department of Physics, Technion, Israel Institute of Technology, Haifa; Israel151Raymond and Beverly Sackler School of Physics and Astronomy, Tel Aviv University, Tel Aviv; Israel152Department of Physics, Aristotle University of Thessaloniki, Thessaloniki; Greece153 International Center for Elementary Particle Physics and Department of Physics, University of Tokyo,Tokyo; Japan154Department of Physics, Tokyo Institute of Technology, Tokyo; Japan155Department of Physics, University of Toronto, Toronto ON; Canada156 (a)TRIUMF, Vancouver BC;(b)Department of Physics and Astronomy, York University, Toronto ON;Canada157Division of Physics and Tomonaga Center for the History of the Universe, Faculty of Pure and AppliedSciences, University of Tsukuba, Tsukuba; Japan158Department of Physics and Astronomy, Tufts University, Medford MA; United States of America159United Arab Emirates University, Al Ain; United Arab Emirates160Department of Physics and Astronomy, University of California Irvine, Irvine CA; United States ofAmerica161Department of Physics and Astronomy, University of Uppsala, Uppsala; Sweden162Department of Physics, University of Illinois, Urbana IL; United States of America163 Instituto de Física Corpuscular (IFIC), Centro Mixto Universidad de Valencia — CSIC, Valencia; Spain164Department of Physics, University of British Columbia, Vancouver BC; Canada165Department of Physics and Astronomy, University of Victoria, Victoria BC; Canada166 Fakultät für Physik und Astronomie, Julius-Maximilians-Universität Würzburg, Würzburg; Germany167Department of Physics, University of Warwick, Coventry; United Kingdom168Waseda University, Tokyo; Japan169Department of Particle Physics and Astrophysics, Weizmann Institute of Science, Rehovot; Israel170Department of Physics, University of Wisconsin, Madison WI; United States of America171 Fakultät für Mathematik und Naturwissenschaften, Fachgruppe Physik, Bergische Universität Wuppertal,Wuppertal; Germany172Department of Physics, Yale University, New Haven CT; United States of AmericaaAlso Affiliated with an institute covered by a cooperation agreement with CERNbAlso at An-Najah National University, Nablus; PalestinecAlso at Borough of Manhattan Community College, City University of New York, New York NY; UnitedStates of AmericadAlso at Center for High Energy Physics, Peking University; ChinaeAlso at Center for Interdisciplinary Research and Innovation (CIRI-AUTH), Thessaloniki; Greecef Also at Centro Studi e Ricerche Enrico Fermi; ItalygAlso at CERN, Geneva; SwitzerlandhAlso at Département de Physique Nucléaire et Corpusculaire, Université de Genève, Genève; SwitzerlandiAlso at Departament de Fisica de la Universitat Autonoma de Barcelona, Barcelona; Spainj Also at Department of Financial and Management Engineering, University of the Aegean, Chios; Greece– 87 –JHEP11(2024)097kAlso at Department of Physics, Ben Gurion University of the Negev, Beer Sheva; IsraellAlso at Department of Physics, California State University, Sacramento; United States of AmericamAlso at Department of Physics, King’s College London, London; United KingdomnAlso at Department of Physics, Stanford University, Stanford CA; United States of AmericaoAlso at Department of Physics, University of Fribourg, Fribourg; SwitzerlandpAlso at Department of Physics, University of Thessaly; GreeceqAlso at Department of Physics, Westmont College, Santa Barbara; United States of AmericarAlso at Faculty of Physics, Sofia University, ‘St. Kliment Ohridski’, Sofia; BulgariasAlso at Hellenic Open University, Patras; GreecetAlso at Institucio Catalana de Recerca i Estudis Avancats, ICREA, Barcelona; SpainuAlso at Institut für Experimentalphysik, Universität Hamburg, Hamburg; GermanyvAlso at Institute for Nuclear Research and Nuclear Energy (INRNE) of the Bulgarian Academy ofSciences, Sofia; BulgariawAlso at Institute of Applied Physics, Mohammed VI Polytechnic University, Ben Guerir; MoroccoxAlso at Institute of Particle Physics (IPP); CanadayAlso at Institute of Physics and Technology, Mongolian Academy of Sciences, Ulaanbaatar; MongoliazAlso at Institute of Physics, Azerbaijan Academy of Sciences, Baku; AzerbaijanaaAlso at Institute of Theoretical Physics, Ilia State University, Tbilisi; GeorgiaabAlso at L2IT, Université de Toulouse, CNRS/IN2P3, UPS, Toulouse; FranceacAlso at Lawrence Livermore National Laboratory, Livermore; United States of AmericaadAlso at National Institute of Physics, University of the Philippines Diliman (Philippines); PhilippinesaeAlso at Technical University of Munich, Munich; Germanyaf Also at The Collaborative Innovation Center of Quantum Matter (CICQM), Beijing; ChinaagAlso at TRIUMF, Vancouver BC; CanadaahAlso at Università di Napoli Parthenope, Napoli; ItalyaiAlso at University of Chinese Academy of Sciences (UCAS), Beijing; Chinaaj Also at University of Colorado Boulder, Department of Physics, Colorado; United States of AmericaakAssociated at University of Copenhagen, Copenhagen; DenmarkalAlso at Washington College, Chestertown, MD; United States of AmericaamAlso at Yeditepe University, Physics Department, Istanbul; Türkiye∗Deceased– 88 –
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Hadron-Hadron Scattering
Higgs Physics
Interpretations of the ATLAS measurements of Higgs boson production and decay rates and diferential cross-sections in pp collisions at √s = 13 TeV
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