Double Higgs boson production and Higgs self-coupling extraction at CLIC

The trilinear Higgs self-coupling has a central role in the understanding of electroweak symmetry breaking as it determines the shape of the Higgs potential. The future electron-positron collider CLIC will provide the opportunity to measure the trilinear Higgs self-coupling directly in double Higgs boson events produced at its high-energy stages with collision energies of $\sqrt{s}$ = 1.5 and 3 TeV. The main channel is double Higgs boson production through W-boson fusion where the Higgs bosons decay to bottom-quark pairs. Its cross section and the kinematics of the di-Higgs system are dependent on the trilinear Higgs self-coupling as well as the quartic HHWW coupling. The sensitivity is driven by the measurements of the HH${\nu_e}{\nu_e}$ cross section and of the invariant mass of the Higgs boson pair. It is enhanced by including the cross-section measurement of ZHH production at 1.5 TeV. The expected sensitivity of CLIC for Higgs pair production through W-boson fusion is studied for the decay channels bbbb and bbWW using full detector simulation including all relevant backgrounds. The energy stage at $\sqrt{s}$ = 1.5 TeV with $\mathcal{L}$ = 2.5 ab$^{-1}$ integrated luminosity allows the observation of the Higgsstrahlung process ZHH and provides evidence for the W-boson fusion process $e^+e^- \to $HH${\nu_e}{\nu_e}$. With an integrated luminosity of $\mathcal{L}$ = 5 ab$^{-1}$ at $\sqrt{s}$ = 3 TeV, CLIC will be able to measure the trilinear Higgs self-coupling with a relative uncertainty of -7 % and +11 % at 68 % C.L., assuming the Standard Model.


Introduction
The discovery of the Higgs boson [1,2] has initiated an era of investigations of its properties and of the nature of the mechanism that breaks the electroweak symmetry. Besides its mass and width, the Higgs properties of interest are the couplings of the Higgs boson to other Standard Model (SM) particles as well as the coupling to itself. While the couplings to other SM particles illustrate the way these particles obtain masses in the Higgs mechanism, the self-coupling determines the shape of the Higgs potential which has implications for the hierarchy problem, the vacuum metastability as well as the electroweak phase transition and baryogenesis. In the Standard Model, the Higgs potential is described by where µ is proportional to the Higgs mass and λ is the Higgs self-coupling. Theories beyond the SM can modify the self-coupling by up to tens of percent [3]. A measurement of the Higgs self-coupling with a precision below O(1) will not be possible at the High-Luminosity Large Hadron Collider (HL-LHC) [4]. The Compact Linear Collider (CLIC) is a mature option for a future linear electron-positron collider [5], which will allow the precise determination of the properties of the Higgs boson well beyond the precision of the HL-LHC. A detailed investigation of the CLIC prospects for the Higgs couplings to SM particles is given in [6] and an update of these results to a new luminosity and polarisation baseline is provided in [7].
Moreover, the high-energy stages of CLIC with centre-of-mass energies of 1.5 and 3 TeV provide the unique opportunity to access directly the trilinear Higgs self-coupling in double Higgs boson production. The main channels are double Higgsstrahlung ZHH production at 1.5 TeV and double Higgs boson production via W-boson fusion at 1.5 and 3 TeV. Both are directly sensitive to the trilinear Higgs selfcoupling g HHH , while the latter is also sensitive to the quartic Higgs-gauge coupling g HHWW . This paper explores the CLIC potential for extracting these couplings from measurements of double Higgs boson production.
The Higgs self-coupling also contributes in a model-dependent way through loops to single Higgs boson processes measured at CLIC [8]. However, in a full EFT approach, other operators apart from the one modifying the triple Higgs vertex can also contribute to the same final state. As these operators are themselves constrained by other measurements, e.g. single Higgs boson production channels, a global fit approach as studied in [9] is appropriate and results for CLIC are presented in [10]. This paper investigates the prospects for extracting the trilinear Higgs self-coupling at CLIC in double Higgs boson production at the high-energy stages of CLIC. It is structured as follows: Sec. 2 describes the strategy of the analysis and the various contributions to the sensitivity. In Sec. 3, the definition of the signal and background processes, as well as the simulation and reconstruction chain, are described. The event selection procedures for the analyses at 1.5 and 3 TeV for HHν e ν e → bbbb and bbWW * are explained in Sec. 4. This is followed by the results for the cross section measurement in Sec. 5 and for the differential measurement giving the most stringent constraints in Sec. 6. A summary is provided in Sec. 7.

Analysis strategy
At CLIC, the Higgs self-coupling can be directly accessed through the measurement of double Higgs boson production. Two main channels contribute: W-boson fusion (WBF) double Higgs boson production (e + e − → HHν e ν e ) and the double Higgsstrahlung process (e + e − → ZHH). The other process of vector boson fusion, namely Z-boson fusion (e + e − → HHe + e − ), has one order of magnitude smaller cross section and is therefore not considered here. As illustrated in Fig. 1, the highest cross section of ZHH production at CLIC is expected at the 1.5 TeV energy stage. In ZHH production, this energy stage also gives the best sensitivity to g HHH . The cross section of WBF double Higgs boson production grows with the collision energy. Therefore, the 3 TeV stage gives the largest rate of WBF double Higgs boson production at CLIC. In e + e − collisions at this energy, WBF is the dominant double Higgs boson production mode. Its total cross section, including effects of the luminosity spectrum, exceeds that of Higgsstrahlung at 1.5 TeV by a factor of 6. The single most sensitive measurement of Higgs boson pair production at CLIC is therefore the double Higgs boson production through WBF at 3 TeV, which is the focus of this work.    This analysis is focused on the two decay channels HH → bbbb (branching fraction 34 %) and HH → bbWW * → bbqqqq (branching fraction 8.4 %). Both channels benefit from the relatively clean environment in electron-positron collisions, the excellent jet energy resolution of the assumed CLIC detector concept using particle flow analysis, as well as from its very good flavour tagging capabilities. This allows accurate reconstruction of the kinematics of the Higgs boson pair.
The baseline scenario for CLIC sets the collision energy of the second stage to 1.5 TeV [7]. The earlier choice of 1.4 TeV [11] is used in the present study due to the availability of full simulation event samples. It is expected that prospects for 1.5 TeV will be very similar to those because from 1.4 TeV to 1.5 TeV collision energy the cross section only changes by -7 % for ZHH and +18 % for HHν e ν e . Results presented here are based on an integrated luminosity of 2.5 ab −1 at a centre-of-mass energy of 1.4 TeV and 5 ab −1 at √ s = 3 TeV. In both cases, the electron beam polarisation is set to -80 % (+80 %) for 80 % (20 %) of the run, which is denoted by "4:1 polarisation scheme" in the following.
The CLIC electron beam can be polarised with a polarisation of up to ±80 %. The negative polarisation of -80 % leads to an increase of the cross section for e + e − →HHν eνe by a factor of 1.8. The positive polarisation has the inverse effect of reducing the cross section to 20 %. For the process e + e − → ZHH, the cross-section scaling factors are 1.12 (0.88) for the electron beam polarisation of -80 % (+80 %). Running a fraction of the integrated luminosity with positive polarisation is, however, desirable for some other measurements including two-fermion production [10]. Therefore, a scheme of collecting 80 % (20 %) of the data with -80 % (+80 %) electron beam polarisation is envisaged, the so-called 4:1 polarisation scheme. This results in a scaling factor of f p = 1.48 for the e + e − →HHν eνe signal cross section and f p = 1.072 for ZHH. The total cross sections of WBF and Higgsstrahlung double Higgs boson production are sensitive to the value of the trilinear Higgs self-coupling. Figure 3 (a) shows the parabolic dependence of the WBF double Higgs boson production cross section on g HHH . The cross section at around 2.3 × g SM HHH is identical to the SM cross section. Therefore, only measuring the cross section of this process will not be sufficient to determine g HHH unambiguously. This can be resolved by measuring the double Higgsstrahlung cross section which has an unambiguous dependence on g HHH as illustrated in Fig. 3 (b). Another way to resolve the ambiguity is by making use of differential distributions: as Fig. 4 (a) shows, the di-Higgs invariant mass distributions between two points with similar, but opposite, variation of the g HHH coupling differ especially in the lower invariant mass region.
Differential distributions of the Higgs pair production process can also be exploited to distinguish whether a possible deviation from the SM originates from a modification of the HHH or of the HHWW vertex. Fig. 4 (b) illustrates how the invariant mass of the Higgs boson pair differs between modifications of the HHH and the HHWW vertex. The latter impacts also the higher invariant mass region. In this way, the kinematic observables provide a means to distinguish between the couplings.

Definition of signal and background processes and Monte Carlo generation
The process e + e − → HHν e ν e with a total cross section of 0.59 fb (0.149 fb) at √ s =3 TeV (1.4 TeV) in the decay channels bbbb and bbWW * defines the signal. The background consists of processes with multiple intermediate electroweak gauge bosons resulting in multiple jets, single Higgs boson production in association with electroweak gauge bosons decaying hadronically, as well as di-Higgs production with decays to other final states. In order to avoid overlap, Higgs boson pair production is removed from the other background samples.
Initial state radiation and beamstrahlung lead to a tail in the distribution of the effective centre-of-mass energy, which is included in the simulation. In addition to e + e − collisions, photon-initiated processes are also considered. The modeling of the latter can be separated into photons from beamstrahlung and "quasi-real" photons for which the Equivalent Photon Approximation (EPA) is used. The contributions of the most important background processes are presented in Tables 1, 2, 3 and 4.
All samples are generated with WHIZARD 1.95 [12,13] interfaced to PYTHIA6.4 [14] for parton shower and hadronisation as well as Higgs decays. TAUOLA [15,16] is used for τ lepton decays. The expected luminosity spectrum of CLIC [17] is applied. Unpolarised beams are used in the simulation samples.

Detector simulation
The detector simulation in this analysis uses the CLIC_ILD detector model [5]. It is based on the ILD detector concept [18] for the International Linear Collider (ILC) [19] adapted to the experimental conditions at CLIC. The CLIC_ILD detector has a cylindrical layout. The innermost subdetector is an ultra-light silicon vertex detector with a single point resolution of 3 µm. It is surrounded by a large tracking system consisting of a large central gaseous Time Projection Chamber (TPC) surrounded by several silicon strip layers. Highly granular electromagnetic and hadronic calorimeters are located around the tracker. They are optimised for particle flow analysis which aims at reconstructing the final-state particles within a jet using the information from the tracking detectors combined with that from the calorimeters. A solenoidal magnet generates a magnetic field of 4 T in the tracker and calorimeters. The outermost part of the detector consists of an iron return yoke, which is instrumented with muon chambers. The forward region is equipped with a system of two electromagnetic calorimeters specifically designed for the luminosity measurement and the identification of electromagnetic clusters from forward electrons or photons.
At CLIC, the bunch crossings are separated by 0.5 ns. In order to suppress the beam-induced background collected over the duration of a bunch train, the hit time resolution in the calorimeters is 1 ns and the tracking elements have a time-stamping capability of 10 ns.
Recently, a new detector model, CLICdet, has been optimised and validated for CLIC [20]. The performance of this analysis is expected to be similar if the CLICdet model had been used.
The detector simulation of the generated event samples is performed with GEANT4 [21,22] and the detector description toolkit MOKKA [23]. For all samples, the beam-induced background γγ → hadrons is overlaid according to the integration time of each subdetector [24].

Reconstruction
The reconstruction algorithms run in the MARLIN framework [25] which is a part of ILCSoft [26]. This includes the track reconstruction with the ILD track reconstruction software [27] and particle flow analysis based on tracks and calorimeter deposits with the PANDORAPFA program [28][29][30] resulting in Particle Flow Objects (PFOs). Tight cuts on the timing of the PFOs are applied to suppress beaminduced backgrounds. Muon and electron candidates within the tracker volume are identified among the PFOs based on the particle flow algorithm, which makes use of the highly granular calorimeters and the muon system. They are required to be isolated by applying quality criteria on their impact parameters and by restricting the energy in the surrounding cone in dependence on the track energy. The forward calorimeters BeamCal and LumiCal [31] are used to identify forward electrons occurring in background processes with a polar angle outside the tracker acceptance (θ < 7 • ).
Jets are reconstructed using the FASTJET [32] package via the MARLINFASTJET interface. In the bbbb channel, the VLC algorithm [33,34] 1 with a radius parameter R = 1.1 is used in exclusive mode with N = 4 jets, while the bbWW * channel uses jets reconstructed with the longitudinally invariant k t algorithm [35] with a radius parameter of R = 0.7. Vertex reconstruction and heavy-flavour tagging is performed using the LCFIPLUS program [36]. Hadronic tau decays are identified using the TauFinder [37].

Common preselection and definition of orthogonal samples
To select events originating from double Higgs production in the bbbb and bbWW * → bbqqqq decay channels, all events containing isolated leptons or hadronic τ lepton candidates are rejected. 1 Slightly differing from the definition given in [34], the beam distance is determined as In order to define orthogonal samples to be used for the bbbb and bbWW * channels, the events are clustered into four jets using the k t algorithm with a jet size parameter of R = 0.7. A flavour tagging algorithm is applied on these jets using the LCFIPLUS package, which determines a b-tag and a c-tag value for each jet [36]. The sample is then split into mutually exclusive samples with bbbb and bbWW * candidates in the following way: Events are chosen as bbWW * candidates if the sum of the b-tag values ∑ 4 b-tag of the jets is smaller than 1.5 (2.3) at 1.4 TeV (3 TeV). Otherwise, the events are considered as bbbb candidates. The ∑ 4 b-tag criterion is illustrated in Fig. 5. Further selection criteria are applied separately for the two channels.

Double Higgs production in the decay to bbWW *
In the bbWW * decay channel, the fully leptonic and semi-leptonic final states are dominated by background processes with leptons and missing transverse momentum [38]. Therefore, only the fully hadronic final state is considered here. The analysis is optimised separately for 1.4 and 3 TeV. After the initial classification, the bbWW * → bbqqqq candidate events are re-clustered into six jets which are grouped by minimising where σ H→bb , σ H→WW * , and σ W are the expected invariant mass resolutions for the respective decays [6] and i, j, k, l, m, n are the indices denoting the six jets. At 3 TeV, the highest b-tag value among those six jets has to be at least 0.7 while at 1.4 TeV, the second highest b-tag value is required to be at least 0.2 and the visible transverse momentum larger than 30 GeV. The signal selection is performed using Boosted Decision Trees (BDTs) trained on the following input variables [38]: Invariant masses of the bb system, of the WW * system, of the jets associated with the W decay, and of the bbWW * system, as well as the energy of the quarks associated with the W boson. A cut on the BDT response is applied to maximise the precision of the cross section measurement. The resulting event yields in the signal region for the HH→ bbWW * signal and the main background processes are listed in Table 1 Table 2: Selection efficiencies as well as expected number of events for L = 5 ab −1 and the 4:1 polarisation scheme with the selection optimised for the HH→ bbWW * process for the signal and the main backgrounds, at √ s =3 TeV.

Double Higgs production in the decay to bbbb
Candidate events for the final state bbbb at 3 TeV are pre-selected according to the orthogonality selection (Sec. 4.1). To enhance the signal fraction at √ s =1.4 TeV, if ∑ 4 b−tag < 2.3, events are required to have a sum of the jet energy of ∑ E jet > 150 GeV and the second highest jet transverse momentum must be p T ( jet 2 ) >25 GeV.
Since both Higgs bosons are expected to be on-shell, the four jets are then grouped as two Higgs candidates by minimising the absolute difference between the resulting di-jet masses |m i j − m kl |.
BDTs are trained based on the pre-selected events in order to optimise the signal selection efficiency and purity.
The following observables were chosen for the multivariate analyses: the sum of all b-tag weights, the ratio between the sum of all c-tag weights and the sum of all b-tag weights, the invariant mass of each jet pair, the cosine of the angle between the two paired jets for each jet pair evaluated in the centreof-mass system, the total invariant mass of the system, the missing transverse momentum computed as the opposite of the vectorial sum of the momenta of all jets, the number of photons with energy larger than 25 GeV, and the maximum absolute pseudorapidity among the four jets. The analyses are optimised separately for 1.4 and 3 TeV.
For the cross section measurement, the cut on the BDT response is optimised for the signal significance. The resulting expected event yields for the 1.4 TeV analysis are listed in Table 3. At 3 TeV, two selections are defined: the "tight BDT" region with a BDT cut of BDT > 0.12 which is optimised for signal significance, and the "loose BDT" region with a cut of BDT > 0.05. The expected event yields in the two signal regions at 3 TeV for a luminosity of L = 5 ab −1 are listed in Table 4. Both selection regions contain also a significant contribution from decays other than bbbb.   Table 4: Selection efficiencies as well as expected number of events after the tight and loose BDT selections of the bbbb analysis for L = 5 ab −1 and the 4:1 polarisation scheme for the HHν e ν e process and the main backgrounds, at √ s =3 TeV.
While the cross section is measured in the tight BDT region, the expected precision on g HHH and g HHWW is evaluated based on differential distributions in the loose BDT region to allow for a larger event sample. Fig. 6 shows the distribution of the BDT response in the loose BDT region for the SM contributions ( Fig. 6 (a)) as well as for selected samples with modified g HHH (Fig. 6 (b)). The distribution of the invariant mass of the double Higgs boson system for the SM contributions in the loose BDT region is presented in Fig. 7. Fig. 8 (a) and 8 (b) show the invariant di-Higgs mass distributions for selected values of g HHH and g HHWW .

Cross section measurement
The cross-section measurement is based on the nominal luminosity and polarisation scheme resulting in the event yields for the WBF Higgs pair production signal and the backgrounds listed in Tables 1 and 2 for the bbWW * analysis and in Tables 3 and 4 for the bbbb analysis. From this, the precision of the cross-section measurement assuming the SM value can be determined according to ∆σ σ = √ S+B S , where S (B) is the number of signal (background) events passing the selection.
Only statistical uncertainties are considered in this study. Systematic uncertainties for single H → bb from various potentially dominant sources of systematics are evaulated in [6]. They are shown to reach per mille of the H → bb cross section. As the Higgs bosons in the HHν e ν e → bbbb process are kinematically similar, the systematic uncertainties are expected to be of similar size. Compared with the almost two orders of magnitude higher statistical uncertainty, the systematic uncertainties are assumed This demonstrates that the contribution from the bbWW * analysis is very small. In the following, we therefore consider only the bbbb analysis.
As described in Sec. 2, the e + e − →HHν eνe cross section is influenced by the polarisation scheme. In the nominal 4:1 polarisation scheme, the cross section is scaled by a factor of f p = 1.48. Some of the backgrounds scale by the same factor, others are influenced less by the polarisation. As a conservative approximation, we scale the backgrounds by the same factor f p = 1.48. Table 5 shows the dependence of the bbbb cross-section measurement uncertainty on the luminosity and polarisation.
The dependence of the cross section on the value of the trilinear Higgs self-coupling (Fig. 3) is used to derive the prospective uncertainty for the extraction of the trilinear Higgs self-coupling from the measurement of the cross section.
In order to determine the expected precision for the measurement at CLIC, a template fit is used based on full detector simulation of event samples with different values of g HHH and g HHWW . A χ 2 minimisation is performed, using the SM sample as the observed data. For the cases with g HHWW =g SM HHWW , pseudo-experiments are drawn in order to determine the confidence interval at 68 % C.L. among the resulting measurements of g HHH . In the case of the 2-dimensional determination of g HHH and g HHWW simultaneously, the deviation of the nominal samples from the SM by ∆χ 2 = 2.3 is used as the 68 % C.L. constraints. Based on only the measurement of the HHνν production cross section at 3 TeV, the expected constraints at 68 % C.L. for g HHH , assuming the SM value for g HHWW , are [0.90, 1.12] ∪ [2.40, 2.61]. The corresponding ∆χ 2 curve is shown in Fig. 9 (a).

Precision in combination with double Higgsstrahlung and W-boson fusion Higgs pair production at 1.4 TeV
One approach which resolves the ambiguity on g HHH arising from the HHν e ν e cross-section measurement is the combination with a measurement of the double Higgsstrahlung cross section, as described in Sec. 2. The assumptions are based on √ s = 1.4 TeV as this is the energy stage of CLIC at which the ZHH cross section is largest. No dedicated full-simulation study has been conducted. However, with guidance from full-simulation studies of similar final states in [6], we assume that a signal efficiency of 50 % can be reached. Furthermore, we expect that the measurement is nearly background free: thanks to the low mis-identification rates, light jet final states will be highly suppressed by flavour tagging requirements. Background processes with four real b quarks and a Z-boson candidate in the final state originate mainly from multiboson production or top-quark pair production in association with a Z → bb decay. The latter is suppressed by requiring a visible Z-boson candidate in addition to the four b quarks. The good invariant mass separation [29] of W, Z, and H can be used to remove the remaining multiboson backgrounds. We therefore assume no background contribution. Based on these assumptions, the Higgsstrahlung process ZHH can be observed at √ s = 1.4 TeV with L = 2.5 ab −1 integrated luminosity with a significance of 5.9 σ . The resulting constraints on κ HHH at 68 % C.L. based on the combination of the cross-section measurements of HHν e ν e at 3 TeV and ZHH at 1.4 TeV are [0.90, 1.11]. Fig. 9 (b) shows the corresponding ∆χ 2 curve.
In addition we take into account the cross-section measurement of the HHν e ν e process in the bbbb final state at 1.4 TeV with a luminosity of 2.5 ab −1 and the 4:1 polarisation scheme applied, cf. Table 3. Standalone, such a measurement leads to the constraints [0.64, 2.3] at 68 % C.L. in κ HHH . Its overall contribution to the combination with the 3 TeV differential-based HHν e ν e and 1.4 TeV cross sectionbased ZHH measurements is very small. Using only the cross-section measurements of HHν e ν e and ZHH at 1.4 TeV results in the constraints [0.66, 1.36].

Self-coupling extraction based on sensitive kinematic observables
Differential distributions sensitive to new physics in the Higgs self-coupling can be used to measure more precisely the trilinear Higgs self-coupling g HHH and the quartic coupling to W bosons g HHWW [39]. Based on the bbbb selection, we make use of kinematic observables sensitive to the Higgs selfcoupling as described in Sec. 2. The highest sensitivity can be reached when combining the BDT score and the invariant di-Higgs mass. Fig. 10 shows the resulting kinematic bins which are used for a template fit to determine the expected confidence intervals on g HHH exclusively and on g HHH and g HHWW simultaneously.   Figure 11: ∆χ 2 curves based on differential distributions (a) without and (b) including a combination with the measurement of the ZHH production cross section at 1.4 TeV.
As Fig. 11 (a) illustrates, the resulting ∆χ 2 curve based on the kinematic bins lacks the second minimum exhibited in the case without differential information in Fig. 9 (a). The corresponding expected constraints for κ HHH at 68 % C.L. are [0.93, 1.12]. These constraints are improved to [0.93, 1.11] when making the combination with the σ ZHH measurement as described in Sec. 5.1, with the corresponding ∆χ 2 curve presented in Fig. 11 (b). This is the final resulting expectation for the sensitivity of the full CLIC programme to the trilinear Higgs self-coupling using the invariant di-Higgs mass and the BDT score as template.  Table 6: Constraints on κ HHH obtained in the full detector simulation study using a multivariate analysis for selection. The constraint from cross section only is obtained in the tight BDT selection. The constraints based on differential distributions are derived in the loose BDT selection.

Expected precision for simultaneous fit of g HHH and g HHWW
As described in Sec. 2, the Higgs-gauge vertex HHWW contributes to HHν e ν e as well. We can therefore extend the study of HHν e ν e production at 3 TeV and ZHH production at 1.4 TeV to fit simultaneously the modified couplings κ HHH and κ HHWW . Based on the template fit described above and using the same differential distribution and binning depicted in Fig. 10, we determine the 68 % and 95 % C.L. contours for two degrees of freedom. These are shown in Fig. 12. At 68 % C.L. the simultaneous fit leads to expected constraints of less than 20 % in κ HHH and less than 4 % in κ HHWW across the allowed range of the other coupling. Due to the anticorrelation illustrated in Fig. 12 Figure 12: Confidence contours at 68 % and 95 % C.L. for the simultaneous fit of κ HHH and κ HHWW based on differential measurement in HHν e ν e production at 3 TeV CLIC and the cross-section measurement of ZHH at 1.4 TeV.

Conclusions
The extraction of the trilinear Higgs self-coupling and the quartic HHWW coupling presented in this paper is based on the bbbb and bbWW * decay channels of HHν e ν e production at the second energy stage of CLIC, which in the full-simulation studies is assumed to be at 1.4 TeV, and the third energy stage at 3 TeV. Furthermore, ZHH production at 1.4 TeV is considered as well. The sensitivity is mainly driven by the bbbb decay of HHν e ν e production at 3 TeV and the use of differential information based on the invariant mass of the two Higgs bosons as well as a multivariate score. The second largest contribution is from the cross section measurement of double Higgsstrahlung ZHH production at 1.4 TeV while HHν e ν e production at 1.4 TeV has a negligible contribution. Taking into account only the 1.4 TeV stage of CLIC with cross-section measurements of HHν e ν e and ZHH allows the measurement of the Higgs self-coupling g HHH with relative uncertainties of −34 % and +36 % around the SM value at 68 % C.L. Based on events of double Higgs boson production at both high-energy stages, CLIC can be expected to measure the trilinear Higgs self-coupling g HHH with a relative uncertainty of −7 % and +11 % at 68 % C.L., assuming the Standard Model and setting the quartic HHWW coupling to its Standard Model value. Measuring simultaneously the trilinear Higgs self-coupling and the quartic Higgs-gauge coupling results in constraints below 4 % in g HHWW and below 20 % in g HHH for large modifications of g HHWW .
Generally, the measurement relies on the high accuracy of heavy flavour tagging and jet energy resolution realised in the CLIC detector models. In this case, the CLIC_ILD model was used. No significant change is expected for the application of this analysis to the current CLICdet model. This analysis benefits from the higher centre-of-mass energy due to the increase in cross section of the WBF double Higgs boson production. It therefore provides a strong motivation for the CLIC 3TeV energy stage.