CCLICdp-Note-2020-00311 August 2020
All-hadronic HHZ production at 3 TeV CLIC
Matthias Weber a , b On behalf of the CLICdp Collaboration a CERN, Geneva, Switzerland, b University of Glasgow, United Kingdom
Abstract
In this note, ZHH production in the all-hadronic final state is studied in e + e − collisionsat the Compact Linear Collider at the 3 TeV stage. At this stage this Higgs boson pairproduction mode is sub-leading to the W + W − fusion production cross-section of e + e − → HH νν . The events are characterised by a topology of six jets, where the masses of the threepair-wise combinations of two jets are compatible with originating from two H and one Zbosons. The event selection concentrates on the dominant H boson decays into two b-quarksby requiring a presence of multiple b-jets. The study is based on full simulation using theCLICdet model, including beam-induced backgrounds from γ γ → hadrons. Results on themeasurement of the total ZHH cross section are given. This work was carried out in the framework of the CLICdp Collaboration c (cid:13) a r X i v : . [ h e p - e x ] A ug Detector model and software chain
The Compact Linear Collider (CLIC) is a proposed option for a future electron-positron collider [1].The physics program will be performed in three stages [2], running at nominal centre-of-mass energiesbetween 380 GeV and 3 TeV. The CLIC Higgs physics programme has been discussed in detail in [3].The two energy stages of 1 . + e − → ZHH is thedominant double Higgs boson production mode at 1 . ( P ( e − ) = ± ) from Ref. [9]. This study is based on the new detector model CLICdet, which is designed to cope with experimentalconditions at 3 TeV CLIC. The superconducting solenoid with an internal diameter of 7 m in the centre ofthe detector provides a magnetic field of 4 T. Silicon pixel and strip trackers, the electromagnetic (ECAL)and hadronic calorimeters (HCAL) are situated within the solenoid. Each sub-detector consists of abarrel and two endcap parts. ECAL is a highly granular array of 40 layers of silicon sensors and tungstenplates. HCAL is made out of 60 layers of plastic scintillator tiles read out by silicon photomultipliers,and steel absorber plates. The solenoid is surrounded by the muon system consisting in the endcap of 6,in the barrel of 7 layers of resistive plate chambers interleaved with yoke steel plates. The very forwardregion of CLICdet is equipped on either side of the interaction point with two smaller electromagneticcalorimeters, LumiCal and BeamCal.CLICdet uses a right-handed coordinate system, with the origin at the nominal point of interaction.The z -axis is along the beam direction, with the electron pointing in the positive direction. The y -axispoints upwards along the vertical direction. The crossing angle between the electron and positron beamsis 20 mrad, with p − x > p + x >
0. The polar angle θ is measured from the positive z -axis.A new software chain for simulation and reconstruction has been developed, based on the DD4hepdetector description toolkit [10, 11]. The G EANT γ γ → hadrons are simulated with PYTHIA 6 [13] using thephoton spectra from G UINEA P IG [14] as input and CLIC beam parameters at 3 TeV. These backgroundcollisions are overlaid on the hard physics event. Tracks are reconstructed using the conformal trackingpattern recognition technique [15]. Software compensation is applied to hits in HCAL to improve theenergy measurement, using local energy density information [16]. Pandora particle flow algorithms [17,18] combine information from tracks, calorimeter clusters and muon hits for particle identification andreconstruction. Jet clustering and the jet resolution thresholds ( y , y , etc) are calculated using theFastJet 3.3.2 library [19] . The performance of track reconstruction, particle identification, and flavourtagging at CLICdet has been studied with the new software chain in [7]. Relative light flavour jet energyresolution values at 3 TeV CLIC are typically around 6–8% for jet energies around 50 GeV, decreasingto 4.5–6% for jet energies larger than 100 GeV, and about 3-4% for 1 TeV jets.2 HHZ signal reconstruction
In this study we consider all hadronic decays of the Z boson, while for the H boson the dominantStandard Model decay mode H → bb with a branching ratio of around 58.4% is considered. Thus inthe following the signal phase-space is about 24% of the total ZHH production. Typically the distancemeasure d q , q = − cos θ ( q , q ) is larger for the hadronic Z decays than the one from the H bosondecays considering all hadronic decays with HH → qqbbbb (Fig. 1 left). Here the angle θ refers to theopening angle between the momenta of the two quarks q q
2. The opening angle ∆ α between both Hbosons is larger than the angles between the Z and any of the H bosons as shown in the Fig. 1 middle. Onaverage the Z boson is the least boosted, while the H boson with the larger momentum carries typicallythe largest momentum of all bosons as displayed in Fig. 1 right. (q1,q2) θ =1 cos q1,q2 d0 0.5 1 1.5 2 E v en t s HHZ Events ij H1 d ij H2 d ij Z d
CLICdp pol 80% ,e L=4 ab ] ° (B1,B2) [ α∆ E v en t s HHZ Events(H1,H2) α∆ (H,Z) α∆ min (H,Z) α∆ max CLICdp pol 80% ,e L=4 ab p [GeV]0 500 1000 1500 E v en t s HHZ EventsZH1H2
CLICdp pol 80% ,e L=4 ab
Figure 1: The distance measure between the two quarks of the boson decay in all hadronic events withZHH → qqbbbb (left), the angles between the three bosons for all ZHH events (middle), andthe momenta p of the three bosons for all ZHH events (right).Inspired by a study of boosted hadronic HZ events, in a first attempt events are reconstructed usingthree large cone jets. These jets are reconstructed with the VLC algorithm [20] as implemented in theFastJet library [19] with a radius R = . γ = β = √ s agrees with the √ s calculated from the three MC truth particle level jets after adding the fourvector of the neutrinos, which are present in decays of B hadrons, confirming that the majority of thevisible event energy is collected in these three jets. While on detector level the total visible event energyis well reconstructed using three detector level jets, the mass reconstruction is not that satisfactory (seetop left Fig. 2). Clustering the event into three jets shows only a clear mass peak for the jet with thelargest jet mass, the jet with the lowest mass shows a peak around the Z-mass, but many more eventsappear at a second lower mass peak. A clear two-peak structure is observed for the jet with the secondhighest jet mass. The second peak at higher masses is spread spanning both the Z-mass and the H-mass.Jet clustering into three jets is not adequate for most events, particularly for the jet closest to the Zboson direction, which is on average the boson with smallest momentum. The exclusive jet clusteringis tested in three more configurations forcing the event into four, five, and six jets. In events with fourjet clustering two jets are combined into one H/Z boson candidate; in events where five jet clusteringis studied, four jets are pairwise combined into two H/Z boson candidates; and in six jet clustering allsix jets are pairwise combined into three final H/Z boson candidates. The combination is chosen byminimising the sumsum = min ∑ comb (( m ( H ) − m H ) + ( m ( H ) − m H ) + ( m ( Z ) − m Z ) ) , (1)where H H
2, and Z are the combined H and Z boson candidates, and m H and m Z are the H and Zboson masses. The best mass reconstruction is achieved by clustering the event into six jets (see Fig. 2).3 HHZ signal reconstruction
Increasing or decreasing the VLC jet radius in the jet clustering to R = . R = . R = . γ = β =
1, and N = jet mass [GeV]0 50 100 150 200 250 E v en t s =3 jet HHZ Events, Nj1j2j3
CLICdp pol 80% ,e L=4 ab boson candidate mass [GeV]0 50 100 150 200 250 E v en t s =4 jet HHZ Events, NH1H2Z
CLICdp pol 80% ,e L=4 ab boson candidate mass [GeV]0 50 100 150 200 250 E v en t s =5 jet HHZ Events, NH1H2Z
CLICdp pol 80% ,e L=4 ab boson candidate mass [GeV]0 50 100 150 200 250 E v en t s =6 jet HHZ Events, NH1H2Z
CLICdp pol 80% ,e L=4 ab
Figure 2: Masses of three boson candidates for for all hadronic ZHH decays with HH → bbbb in eventsusing exclusive jet clustering into three (top left), four (top right), five (bottom left), and six(bottom right) jets, using the VLC algorithm with β = γ = R = . → qqbbbb. In general each of the three bosons are close to one ofthe original partons, particularly for the reconstructed candidate with the largest mass, referred to as H1,which typically corresponds to the object with the largest momentum as well. Comparing the momentum p reco of the three boson candidates with the momentum of the matched boson on parton level p parton aclear peak at 1 can be observed for all candidates. The elongated tails of both H candidate objects tolower reconstructed momenta reflect the fact that neutrinos in B-hadron decays escape detection. Indecays of hadrons in the Z boson decay chain neutrinos play a less prominent role, and thus the recon-4 Monte Carlo simulation structed Z candidate response is more symmetric. While the combination procedure works well, futureimprovements could be achieved by modifying the summation in eq. 1 to reflect different resolutions forthe reconstructed invariant masses for the Z and Higgs bosons, taking into account the long tail to lowermasses for the H candidates as well. The jet clustering and the size of the jet cone impacts the means ofthe invariant mass distributions, which could be corrected for after a detailed study. ] ° (part,B) [ α∆ minimum 0 50 100 150 E v en t s =6 jet HHZ Events, NH1 candidateH2 candidateZ candidate
CLICdp pol 80% ,e L=4 ab parton /p reco p0 1 2 3 4 E v en t s =6 jet HHZ Events, NH1 candidateH2 candidateZ candidate
CLICdp pol 80% ,e L=4 ab
Figure 3: The angles between the boson candidates and the closest boson on parton level, (left) and theresponse of the boson candidate momentum and the matched boson parton level momentum(right) both for events with ZHH → qqbbbb.The identification of b -jets is performed by the linear collider flavour identification (LCFIPlus) tool [21].The identification starts with a primary vertex finder, and continues with the identification of secondaryvertices to identify b and c hadron decays. The secondary vertices are attached to jets. Isolated leptonswithin the jets are checked for compatibility with secondary vertices originating from semi-leptonic de-cays of heavy flavour hadrons. In the refined jet clustering step particles are combined into jets withthe VLC jet algorithm using the tracks and leptons originating from secondary vertices as seed. Valuesare attached to each jet reflecting its compatibility with originating from b (BTag), c (CTag), and lightflavour quarks (LTag). It is investigated if the pairwise jet combination can be improved using BTaginformation, since at least four b-quarks are involved in the decays of signal events. These attempts leadto no improvement of the mass resolution, energy and spatial agreement with the underlying bosons onparton level, thus BTagging information is not used as additional input in the combination. Both signal and backgrounds samples are produced by WHIZARD 2.7.0 [22], using luminosity spectrafrom G
UINEA P IG interfaced by CIRCE
HEP detector description toolkit has been used toimplement the simulated model of CLICdet in G
EANT
4, version 10.02p02, via the DDG4 package.Backgrounds to all-hadronic ZHH events originate from di-quark e + e − → qq, four-quark e + e − → qqqqand six-quark e + e − → qqqqqq final states, as well as triboson backgrounds from ZZH and WWH withhadronically decaying Z and W bosons. Table 1 lists the details of the produced samples for both negat-ive and positive polarisation of 80% of the electron beam. The weight of each event is calculated underthe assumption of luminosity sharing of the ratio 4:1 between the negative and positive polarisation of theelectron beam, thus L − = − and L + = − are used as values for the integrated luminosity.The polarisation has a moderate impact on the ZHH signal, decreasing the cross section by about 45%5 Preselection for positive compared to negative electron beam polarisation, a similar impact can be observed for thedi-quark sample. The four-quark production cross section is dominated by WW boson production andthus largely reduced for positive polarisation by a factor of about 7.5. The six-quark dataset is split into23 samples to cover all possible flavour combinations compatible with tt and tri-boson production. Intable 1 the six-quark flavour combinations with the largest cross sections are shown. For the six-quarkdataset positive polarisation reduces the cross section considerably as well.Table 1: Signal and background datasets with y = d , s , b, L = − for P(e − )=-80%, L = − forP(e − )=+80%:process = Events σ [fb] Polarisation event weighte + e − → HHqq 9600 4.18e-2 P(e − )=-80% 0.0174e + e − → HHqq 9552 2.30e-2 P(e − )=+80% 0.00303e + e − → HZ 114000 3.83 P(e − )=-80% 0.134e + e − → HZ 27840 2.76 P(e − )=+80% 0.0959e + e − → qq 1549464 1269 P(e − )=-80% 3.28e + e − → qq 388392 786 P(e − )=+80% 2.02e + e − → qqqq 1915464 902 P(e − )=-80% 1.88e + e − → qqqq 479040 120 P(e − )=+80% 0.251e + e − → ddu yy u 456336 14.5 P(e − )=-80% 0.127e + e − → ddu yy u 121200 5.01 P(e − )=+80% 0.0413e + e − → yy ubbc 428405 13.3 P(e − )=-80% 0.124e + e − → yy ubbc 123720 5.21 P(e − )=+80% 0.0421e + e − → sscbbc 330096 12.5 P(e − )=-80% 0.151e + e − → sscbbc 84240 4.89 P(e − )=+80% 0.0581e + e − → ZZH → qqqqH 5784 1.39e-01 P(e − )=-80% 0.0964e + e − → ZZH → qqqqH 2904 7.16e-02 P(e − )=+80% 0.0247e + e − → WWH → qqqqH 94608 4.116 P(e − )=-80% 0.0174e + e − → WWH → qqqqH 2424 5.176e-01 P(e − )=+80% 0.214 In a first attempt boosted decision trees are used to separate signal events and background events using thefull available MC statistics in the training. While backgrounds are reduced substantially, the signal cannotbe identified with sizeable significance. The MC statistics for backgrounds is limited, and the BDTtraining is insufficient under these circumstances. In order to facilitate the machine learning processing,different preselections are considered to achieve a larger discriminating power by concentrating on moresignal-like background events. Different preselection cuts are applied, based on BTagging information,mass selections on the reconstruction boson candidates, as well as cuts on the energy and polar anglesof jets. The preselection which leads to the best results after tuning of the Boosted Decision Trees is thefollowing: • mass selection on the Z candidate (third largest massive boson candidate): 50 GeV < M <
150 GeV • mass selection on the first and second H candidate (order by mass): M >
75 GeV, M >
75 GeV • the BTag sum of the three jets with the largest BTagging values: ∑ BTag ( max 3 ) > . • polar angles of the leading two jets in energy: 10 ◦ < θ ( j1 ) < ◦ , 10 ◦ < θ ( j2 ) < ◦ Preselection • energies of the leading four jets in energy: E ( j1 ) >
150 GeV, E ( j2 ) >
100 GeV, E ( j3 ) >
50 GeV,and E ( j4 ) >
50 GeVThe masses of the boson candidates are shown in Fig. 4 for signal and background events with a signalenhancement of 50 000 in order to emphasise on the shape difference. For the di-quark and four-quarkdatasets these distributions peak at low values, whereas most of the six-quark dataset appears at massvalues similar to the signal events. While for signal events the tail to higher values is significant forthe H boson candidates (most and second-most massive candidates), the tail to higher mass values isnegligible for the Z boson candidate. The polar angles for the two jets with the highest energy as wellas the BTag sum of the three jets with the largest BTag values are shown in Fig. 5 for background andsignal events with a signal enhancement of 50 000 in order to emphasise on the shape difference. Forthe signal for both jets the polar angle distributions peak in the central part of the detector, whereas fordi-quark, four-quark, and six-quark events the distributions are peaked very forward. For HZ events thepolar angle distribution of the leading jet is peaked forward as well. Since the signal includes at leastfour b-quarks, several jets contain B-hadrons in their decay chain, thus the BTag sum distribution ofthe leading three b-tagged jets peaks at a high value close to 3. Six-quark events from tt contain twob-jets as well, with a peak around 2. For WWH and ZZH events the presence of the H boson and itsdominant decay into two b-quarks leads to a peak in the BTag sum distribution around 2. While forWWH events the distribution drops at higher values, for ZZH another peak at higher values close to 3is present due to the fact that the Z boson can decay into two b-quarks as well. For di- and four-quarkevents the distributions peak around 0.5. The energy distributions of the four jets with the largest energyare displayed in Fig. 6. While for signal, but also for the six-quark background the jet energy is typicallybeyond the cuts of the preselection, for di- and four-quark events the jet energy distributions peak wellbelow the preselection cuts.
H1 candidate mass [GeV]0 50 100 150 200 250 E v en t s × bbbbqq x 50000 → HHZ qqqqqq → ee qqqq → ee Hqq → HZ qqqqH → WWH qqqqH → ZZH qq → ee CLICdp pol 80% ,e L=4 ab
H2 candidate mass [GeV]0 50 100 150 200 250 E v en t s × bbbbqq x 50000 → HHZ qqqqqq → ee qqqq → ee Hqq → HZ qqqqH → WWH qqqqH → ZZH qq → ee CLICdp pol 80% ,e L=4 ab
Z candidate mass [GeV]0 50 100 150 200 250 E v en t s × bbbbqq x 50000 → HHZ qqqqqq → ee qqqq → ee Hqq → HZ qqqqH → WWH qqqqH → ZZH qq → ee CLICdp pol 80% ,e L=4 ab
Figure 4: The mass distributions for the more massive (left) and less massive (middle) H boson can-didates, and the Z boson candidate (right) for all background events from HZ, e + e − → qq,e + e − → qqqq , and e + e − → qqqqqq combined and signal events ZHH → qqbbbb weightedby a factor of 50 000. The vertical lines and arrows indicate the signal selection.As shown in the figures, the preselection is most powerful in rejecting di- and four-quark events. Thepreselection efficiencies on background and signal datasets are listed in Tab. 2. About 22% of signalevents are rejected by the preselection, di- and four-boson events are rejected by over 99%, as well as96% of Higgsstrahlung events. Less than 5% of the six-quark events and less than 4% of the WWHevents remain after the preselection. About 11% of ZZH events survive the preselection. Starting fromthese background events the signal can be extracted with sufficient significance using boosted decisiontrees. 7 Preselection ] ° [ θ jet1 0 50 100 150 E v en t s × bbbbqq x 50000 → HHZ qqqqqq → ee qqqq → ee Hqq → HZ qqqqH → WWH qqqqH → ZZH qq → ee CLICdp pol 80% ,e L=4 ab ] ° [ θ jet2 0 50 100 150 E v en t s × bbbbqq x 50000 → HHZ qqqqqq → ee qqqq → ee Hqq → HZ qqqqH → WWH qqqqH → ZZH qq → ee CLICdp pol 80% ,e L=4 ab
BTag (max 3 jets) ∑ E v en t s × bbbbqq x 50000 → HHZ qqqqqq → ee qqqq → ee Hqq → HZ qqqqH → WWH qqqqH → ZZH qq → ee CLICdp pol 80% ,e L=4 ab
Figure 5: The polar angle distribution for background events from HZ, e + e − → qq, e + e − → qqqq , ande + e − → qqqqqq combined and signal events ZHH → qqbbbb weighted by a factor of 50 000,for the jet with largest energy (left) and the jet with second largest energy (middle), as wellas the BTag sum of the three jets with the largest BTag values (right). The vertical lines andarrows indicate the signal selection. jet1 E [GeV]0 500 1000 1500 E v en t s × bbbbqq x 50000 → HHZ qqqqqq → ee qqqq → ee Hqq → HZ qqqqH → WWH qqqqH → ZZH qq → ee CLICdp pol 80% ,e L=4 ab jet2 E [GeV]0 200 400 600 800 100012001400 E v en t s × bbbbqq x 50000 → HHZ qqqqqq → ee qqqq → ee Hqq → HZ qqqqH → WWH qqqqH → ZZH qq → ee CLICdp pol 80% ,e L=4 ab jet3 E [GeV]0 200 400 600 E v en t s × bbbbqq x 50000 → HHZ qqqqqq → ee qqqq → ee Hqq → HZ qqqqH → WWH qqqqH → ZZH qq → ee CLICdp pol 80% ,e L=4 ab jet4 E [GeV]0 100 200 300 400 500 600 E v en t s × bbbbqq x 50000 → HHZ qqqqqq → ee qqqq → ee Hqq → HZ qqqqH → WWH qqqqH → ZZH qq → ee CLICdp pol 80% ,e L=4 ab
Figure 6: The energy distribution for the four jets with the largest energies decreasing from left to rightfor backgrounds events from HZ, e + e − → qq, e + e − → qqqq , and e + e − → qqqqqq combinedand signal events ZHH → qqbbbb weighted by a factor of 50 000. The vertical lines andarrows indicate the signal selection.Table 2: Preselection efficiencies and event numbers for signal and background events, assuming anintegrated luminosity of L = − for runs with negative polarisation P(e − )=-80%, andL = − for runs with positive polarisation P(e − )=+80% for all different final states of thee + e − collisions:final state Events Evts after cut Efficiency Events Evts after cut Efficiency-80% -80% -80%, in [%] +80% +80% +80% [in%]HHqq, both H → bb 69 33 48 12 5.7 49HHqq, all H decays 167 55 33 29 9.5 33Hqq, all H 15300 621 4.1 2670 107 4.0qq 5 070 000 3310 0.065 786 000 257 0.033qqqq 3 610 000 1580 0.044 120 000 143 0.12qqqqqq 311 000 11000 3.5 23 900 1120 4.7WWH → qqqqH 16 500 420 2.6 518 17 3.3ZZH → qqqqH 558 61 11 72 8.1 118 Results
After the preselection the signal ZHH → qqbbbb is still a factor of about 500 smaller than the sum of allbackgrounds (300 for events with positive electron beam polarisation P(e − )=+80%). After the preselec-tion is applied, the six-quark final state is the dominant background. In order to extract the signal, BDTsare used. Two implementation are considered: BDTs as implemented in the Toolkit for MultiVariate dataAnalysis (TMVA) [23], integrated into ROOT [24], and the XGBoost (Extreme Gradient Boost) gradientboosting library [25] as interfaced with scikit-learn. The following variables are used to derive the BDTs: • the n-jet resolution thresholds y n − , n for up to six VLC jets: y , y , y , y , and y , which areall shifted to larger values for signal events, which are more multi-jet like than most backgroundevents. • the mass values of the three boson candidates M j , M j , and M j and the angle between the two jetswhich are combined into both H boson candidates ∆ α H ( j , j ) , ∆ α H ( j , j ) , which are largerfor background events. • the BTag of the jet with the larger BTag value for each of the boson candidates, as well as theLTag of the jet with the larger light flavour compatibility for each of the boson candidates. TheBTag max distribution peaks closer to 0 for background than for signal events; for the light flavor tagbackground events show a large peak around 0.8, while for signal a double peak structure appearswith a peak close to 0.8 and one around 0. For both H candidates the CTag value for the largerc-tagged jet is considered as well. • the sum of the BTag values of the two and the three largest b-tagged jets, which are shifted tolarger values for signal; the sum of LTag values of all six jets, which is shifted to considerablylarger values for background events. • the energy for all six VLC jets, which are higher for signal, and the polar angles for all six VLCjets, which are more central for signal.For TMVA the best results are achieved using the Gini-index for separation criteria and adaptiveboosting instead of gradient boosting. The agreement of the BDT score distributions from the trainingand the testing datasets for both polarisations in Fig. 7 shows that no strong overtraining is observed,despite the limited statistics of the background MC samples. While in TMVA the data is split into testingand training datasets with the ratio 1:1, in XGBoost this ratio is configurable and chosen to be 1:4. InXGBoost we use the gbtree booster and the exact greedy algorithm for split finding. Although a moreaggressive boosting was chosen in XGBoost (maximum depth of trees of six compared to four in TMVA)the level of overtraining in XGBoost is on a similar level to that observed for TMVA as Fig. 8 illustrates,using the default regularisation values, such as λ = The BDTs are trained separately for both polarisation runs, restricting the signal to the most prominentdecay channel ZHH → qqbbbb. For the final cross-section result the event numbers of both runs areadded up. Using TMVA, the event numbers for both polarisation runs as well as the sum of these num-bers are listed in Tab. 3, with a selection on the BDT score of BDT > .
385 for events with negativeelectron beam polarisation, and BDT > .
325 for events with positive electron beam polarisation. Withthis selection a significance of about 2.09 σ is achieved. Applying the analogous procedure for XGBoostbased on the untransformed BDT scores using a maximum tree depth of 6, the combined event numbersare listed in Tab. 4, with a selection on the BDT score of BDT > .
45 for events with negative electron9
Results
BDT Score0.5 − a . u . Signal,testBG,testSignal,trainBG,train
CLICdp pol +80% ,e L=1 ab
BDT Score0.5 − a . u . Signal,testBG,testSignal,trainBG,train
CLICdp pol 80% ,e L=4 ab
Figure 7: The distribution of the BDT score for positive (left) and negative (right) electron beam polar-isation for the training and testing samples using TMVA. A . U . Signal,testBG,testSignal,trainBG,train 4 2 0 2 4BDT Score0.00.51.01.52.02.53.0 A . U . Signal,testBG,testSignal,trainBG,train
Figure 8: The distribution of the BDT score for positive (left) and negative (right) electron beam polar-isation for the training and testing samples using XGBoost.beam polarisation, and BDT > .
23 for events with positive electron beam polarisation. With this selec-tion a significance of about 2.38 σ is achieved. Using trees with larger depth higher significances canbe achieved but at the cost of larger overtraining. The overtraining can be mitigated using more conser-vative values for other parameters, increasing for example the regularisation parameters α , λ , γ , or theminimum sum of weights needed to create a child node. Choosing values which keep overtraining onthe level observed for depth six or smaller, the achieved significance remains on the level of 2.2-2.4 σ .Fig. 9 (left) shows the significance as function of signal efficiency, where the signal is defined as the sumof all ZHH → qqbbbb events. Significances between 2.1 and 2.3 σ are achieved for a relatively broadband of signal efficiencies between 10% and 22%.Considering that the statistical uncertainty of the cross-section determination is more than 40% theimpact of systematic uncertainties on the final result e.g from the flavour tagging shapes, mass andjet scales and resolution is expected to be sub-leading. The significance is studied as function of theBDT score separately for the test and train dataset, scaling both of the event yields to the total eventyield. The difference in the significance is typically about 0.2 to 0.25 σ (see Fig. 9 (right)). This 15%difference can be considered as overtraining systematics, which is sub-leading compared to the statisticaluncertainty. BDT tuning on a relaxed preselection with ∑ BTag ( max 3 ) > . Results S i g n i f i c a n c e i n [ σ ] s i g n i f i c a n c e [ σ ] train+testtraintest Figure 9: The significance as function of the signal efficiency (left) and the significance as function of theBDT score using all data, the testing, or only the training data (right) in events with negativeelectron beam polarisation using XGBoost.larger light flavour tag of the jets of the boson candidates, or the energy ratio between the two jets ofeach boson candidate lead to slightly worse performances. While this result in the full hadronic channelis not sufficient for a standalone discovery of ZHH production at 3 TeV CLIC with a significance ofslightly above 2 σ , the sensitivity achieved can contribute to an inclusive double Higgs boson productionmeasurement, and help solving ambiguities in EFT fits using processes with sensitivity to the Higgsself coupling. This is one of the first physics studies using the new detector model and software chain,demonstrating the performance of jet reconstruction and flavour tagging in a complex multi-jet final stateat very high energy.Table 3: Final event numbers for signal and background events using TMVA, assuming an integratedluminosity of L = − for runs with negative polarisation P(e − )=-80%, and L = − forruns with positive polarisation P(e − )=+80% for all different final states of the e + e − collisions:final state Events Events Events-80% +80% -80% and +80%HHqq, all H decays 11 . ± .
22 1 . ± .
04 13 . ± . → bb 9 . ± .
20 1 . ± .
04 11 . ± . . ± .
38 0 . ± .
18 1 . ± . . ± .
00 2 . ± .
02 2 . ± . . ± .
88 0 . ± .
25 2 . ± . . ± . . ± .
36 15 . ± . → qqqqH 1 . ± .
52 0 . ± .
21 1 . ± . → qqqqH 4 . ± .
68 1 . ± .
16 5 . ± . Acknowledgements
This work benefited from services provided by the ILC Virtual Organisation, supported by the nationalresource providers of the EGI Federation. This research was done using resources provided by theOpen Science Grid, which is supported by the National Science Foundation and the U.S. Department ofEnergy’s Office of Science. This project has received funding from the European Union’s Horizon 2020Research and Innovation programme under Grant Agreement no. 654168.11 eferences
Table 4: Final event numbers for signal and background events using XGBoost, assuming an integratedluminosity of L = − for runs with negative polarisation P(e − )=-80%, and L = − forruns with positive polarisation P(e − )=+80% for all different final states of the e + e − collisions:final state Events Events Events-80% +80% -80% and +80%HHqq, all H decays 13 . ± .
25 3 . ± .
05 17 . ± . → bb 11 . ± .
23 2 . ± .
05 14 . ± . . ± .
57 0 . ± .
24 2 . ± . . ± .
00 0 . ± . . ± . . ± .
88 0 . ± .
25 2 . ± . . ± . . ± .
45 21 . ± . → qqqqH 1 . ± .
52 0 ± . . ± . → qqqqH 6 . ± .
80 1 . ± .
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