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| CMS-PAS-HIG-24-016 | ||
| Search for nonresonant $ \mathrm{t\bar{t}HH} $ production in the final state with four bottom quarks and one lepton in proton-proton collisions at $ \sqrt{s} = $ 13 TeV | ||
| CMS Collaboration | ||
| 2026-08-20 | ||
| Abstract: We present the first direct search at the CMS experiment for nonresonant associated production of a Higgs boson (H) pair, where each H decays into a bottom quark-antiquark pair, with a top quark-antiquark pair ($ {\mathrm{t\bar{t}HH}} $), which decays into a single lepton final state. The analysis is performed using proton-proton collision data recorded with the CMS detector at a centre of mass energy of $ \sqrt{s}= $ 13 TeV, corresponding to an integrated luminosity of 138 fb$ ^{-1} $. A method based on neural networks is used for categorizing the events and extracting the signal. A simultaneous fit is performed in the signal and background enriched regions on the neural network discriminant output distribution. The observed signal strength relative to the standard model expectation is $ \mu=- $ 9 $ ^{+26}_{-25} $. The observed (expected) upper limit on the $ {\mathrm{t\bar{t}HH}} $ production cross section is 49 (55) times the standard model prediction and corresponds to an observed (expected) cross section upper limit of 37 (42) fb at 95$ % $ confidence level (CL). The $ {\mathrm{t\bar{t}HH}} $ results are further interpreted within the Higgs Effective Field Theory framework, leading to a 95$ % $ CL interval on the $ {\mathrm{t\bar{t}HH}} $ quartic interaction parameter, $ c_{\mathrm{t\bar{t}HH}} $, of $ -6.6 < c_{\mathrm{t\bar{t}HH}} < $ 6.4. | ||
| Links: CDS record (PDF) ; CADI line (restricted) ; | ||
| Figures | |
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Figure 1:
Representative leading order SM diagrams for $ \mathrm{t\bar{t}HH} $ production, illustrating the two distinct physical subprocesses: (left) the top-Yukawa vertex and (right) the Higgs trilinear self-coupling. |
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Figure 2:
BSM $ \mathrm{t\bar{t}HH} $ production diagram via the HEFT ttHH $ c_2 $ coupling. |
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Figure 3:
Feynman diagram of the $ \mathrm{t\overline{t}HH} $ production process in the single lepton channel. |
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Figure 4:
Schematic of the sample--parton correspondence. The large arrows indicate generator-level matching. |
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Figure 5:
Distributions of the JABDT output score for correct and incorrect jet-to-parton assignments, evaluated on both training (shaded histograms) and testing (red dots) samples. Correct assignments are defined by geometric matching of jets to Monte Carlo generator-level partons with minimum sum of $ \Delta $R, while incorrect assignments refer to the remaining permutations of jets assignments. The BDT is trained on $ \mathrm{t\bar{t}HH} $, and $ \mathrm{t\bar{t}} $ simulations to construct discriminative features for the target events against others considered in this analysis, such as $ \mathrm{t\bar{t}H} $, $ \mathrm{t\bar{t}ZH} $ and $ \mathrm{t\bar{t}ZZ} $, etc. The excellent agreement in shape between the training and testing distributions indicates the absence of overtraining. Samples are split into even event number (shown) and odd (not shown) subsets for validation on each other. The test and training sample are matching in shape, so no overtraining is visible. |
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Figure 6:
Confusion matrix of the DNN categorization of events in the 2018 dataset. |
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Figure 7:
Data/MC comparison of selected DNN input features for the 2018 dataset in the signal region ($ \geq $ 5 jets and $ \geq $ 4 b-tagged jets). The distributions show: $ p_\mathrm{T} $ of the third leading jet (top left), loose jet multiplicity, where loose jets satisfy relaxed kinematic cuts of $ p_{\mathrm{T}} > 20\text{ GeV} $ and $ |\eta| < $ 4.0, while all other selection criteria follow the standard jet reconstruction described in Section 5 (top right), mean DeepJet score of $ b $-tagged jets (middle left), $ b $-tagging likelihood ratio discriminant (middle right), scalar sum of jet $ p_\mathrm{T} $ ($ H_\mathrm{T} $) (bottom left), and the best-fit $ t\bar{t}HH $ JABDT output score (bottom right). |
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Figure 7-a:
Data/MC comparison of selected DNN input features for the 2018 dataset in the signal region ($ \geq $ 5 jets and $ \geq $ 4 b-tagged jets). The distributions show: $ p_\mathrm{T} $ of the third leading jet (top left), loose jet multiplicity, where loose jets satisfy relaxed kinematic cuts of $ p_{\mathrm{T}} > 20\text{ GeV} $ and $ |\eta| < $ 4.0, while all other selection criteria follow the standard jet reconstruction described in Section 5 (top right), mean DeepJet score of $ b $-tagged jets (middle left), $ b $-tagging likelihood ratio discriminant (middle right), scalar sum of jet $ p_\mathrm{T} $ ($ H_\mathrm{T} $) (bottom left), and the best-fit $ t\bar{t}HH $ JABDT output score (bottom right). |
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Figure 7-b:
Data/MC comparison of selected DNN input features for the 2018 dataset in the signal region ($ \geq $ 5 jets and $ \geq $ 4 b-tagged jets). The distributions show: $ p_\mathrm{T} $ of the third leading jet (top left), loose jet multiplicity, where loose jets satisfy relaxed kinematic cuts of $ p_{\mathrm{T}} > 20\text{ GeV} $ and $ |\eta| < $ 4.0, while all other selection criteria follow the standard jet reconstruction described in Section 5 (top right), mean DeepJet score of $ b $-tagged jets (middle left), $ b $-tagging likelihood ratio discriminant (middle right), scalar sum of jet $ p_\mathrm{T} $ ($ H_\mathrm{T} $) (bottom left), and the best-fit $ t\bar{t}HH $ JABDT output score (bottom right). |
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Figure 7-c:
Data/MC comparison of selected DNN input features for the 2018 dataset in the signal region ($ \geq $ 5 jets and $ \geq $ 4 b-tagged jets). The distributions show: $ p_\mathrm{T} $ of the third leading jet (top left), loose jet multiplicity, where loose jets satisfy relaxed kinematic cuts of $ p_{\mathrm{T}} > 20\text{ GeV} $ and $ |\eta| < $ 4.0, while all other selection criteria follow the standard jet reconstruction described in Section 5 (top right), mean DeepJet score of $ b $-tagged jets (middle left), $ b $-tagging likelihood ratio discriminant (middle right), scalar sum of jet $ p_\mathrm{T} $ ($ H_\mathrm{T} $) (bottom left), and the best-fit $ t\bar{t}HH $ JABDT output score (bottom right). |
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Figure 7-d:
Data/MC comparison of selected DNN input features for the 2018 dataset in the signal region ($ \geq $ 5 jets and $ \geq $ 4 b-tagged jets). The distributions show: $ p_\mathrm{T} $ of the third leading jet (top left), loose jet multiplicity, where loose jets satisfy relaxed kinematic cuts of $ p_{\mathrm{T}} > 20\text{ GeV} $ and $ |\eta| < $ 4.0, while all other selection criteria follow the standard jet reconstruction described in Section 5 (top right), mean DeepJet score of $ b $-tagged jets (middle left), $ b $-tagging likelihood ratio discriminant (middle right), scalar sum of jet $ p_\mathrm{T} $ ($ H_\mathrm{T} $) (bottom left), and the best-fit $ t\bar{t}HH $ JABDT output score (bottom right). |
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Figure 7-e:
Data/MC comparison of selected DNN input features for the 2018 dataset in the signal region ($ \geq $ 5 jets and $ \geq $ 4 b-tagged jets). The distributions show: $ p_\mathrm{T} $ of the third leading jet (top left), loose jet multiplicity, where loose jets satisfy relaxed kinematic cuts of $ p_{\mathrm{T}} > 20\text{ GeV} $ and $ |\eta| < $ 4.0, while all other selection criteria follow the standard jet reconstruction described in Section 5 (top right), mean DeepJet score of $ b $-tagged jets (middle left), $ b $-tagging likelihood ratio discriminant (middle right), scalar sum of jet $ p_\mathrm{T} $ ($ H_\mathrm{T} $) (bottom left), and the best-fit $ t\bar{t}HH $ JABDT output score (bottom right). |
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Figure 7-f:
Data/MC comparison of selected DNN input features for the 2018 dataset in the signal region ($ \geq $ 5 jets and $ \geq $ 4 b-tagged jets). The distributions show: $ p_\mathrm{T} $ of the third leading jet (top left), loose jet multiplicity, where loose jets satisfy relaxed kinematic cuts of $ p_{\mathrm{T}} > 20\text{ GeV} $ and $ |\eta| < $ 4.0, while all other selection criteria follow the standard jet reconstruction described in Section 5 (top right), mean DeepJet score of $ b $-tagged jets (middle left), $ b $-tagging likelihood ratio discriminant (middle right), scalar sum of jet $ p_\mathrm{T} $ ($ H_\mathrm{T} $) (bottom left), and the best-fit $ t\bar{t}HH $ JABDT output score (bottom right). |
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Figure 8:
Final discriminant distributions for Run2 for the $ \mathrm{t\bar{t}HH} $ signal node, and for the background nodes $ \mathrm{t\bar{t}H} $, $ \mathrm{t\bar{t}Z} $, where Z stands for: Z $ \to $ bb, ZZ $ \to $ 4b and ZH $ \to $ 4b, $ \mathrm{t} \overline{\mathrm{t}} $ stands: for $ \mathrm{t\bar{t}} $+lf and $ \mathrm{t\bar{t}} $+cc, $ \mathrm{t\bar{t}} $ b stands for $ \mathrm{t\bar{t}} $+mb and $ \mathrm{t\bar{t}} $+nb. In each panel, the SM $ \mathrm{t\bar{t}HH} $ prediction is overlaid, scaled for visibility. |
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Figure 8-a:
Final discriminant distributions for Run2 for the $ \mathrm{t\bar{t}HH} $ signal node, and for the background nodes $ \mathrm{t\bar{t}H} $, $ \mathrm{t\bar{t}Z} $, where Z stands for: Z $ \to $ bb, ZZ $ \to $ 4b and ZH $ \to $ 4b, $ \mathrm{t} \overline{\mathrm{t}} $ stands: for $ \mathrm{t\bar{t}} $+lf and $ \mathrm{t\bar{t}} $+cc, $ \mathrm{t\bar{t}} $ b stands for $ \mathrm{t\bar{t}} $+mb and $ \mathrm{t\bar{t}} $+nb. In each panel, the SM $ \mathrm{t\bar{t}HH} $ prediction is overlaid, scaled for visibility. |
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Figure 8-b:
Final discriminant distributions for Run2 for the $ \mathrm{t\bar{t}HH} $ signal node, and for the background nodes $ \mathrm{t\bar{t}H} $, $ \mathrm{t\bar{t}Z} $, where Z stands for: Z $ \to $ bb, ZZ $ \to $ 4b and ZH $ \to $ 4b, $ \mathrm{t} \overline{\mathrm{t}} $ stands: for $ \mathrm{t\bar{t}} $+lf and $ \mathrm{t\bar{t}} $+cc, $ \mathrm{t\bar{t}} $ b stands for $ \mathrm{t\bar{t}} $+mb and $ \mathrm{t\bar{t}} $+nb. In each panel, the SM $ \mathrm{t\bar{t}HH} $ prediction is overlaid, scaled for visibility. |
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Figure 8-c:
Final discriminant distributions for Run2 for the $ \mathrm{t\bar{t}HH} $ signal node, and for the background nodes $ \mathrm{t\bar{t}H} $, $ \mathrm{t\bar{t}Z} $, where Z stands for: Z $ \to $ bb, ZZ $ \to $ 4b and ZH $ \to $ 4b, $ \mathrm{t} \overline{\mathrm{t}} $ stands: for $ \mathrm{t\bar{t}} $+lf and $ \mathrm{t\bar{t}} $+cc, $ \mathrm{t\bar{t}} $ b stands for $ \mathrm{t\bar{t}} $+mb and $ \mathrm{t\bar{t}} $+nb. In each panel, the SM $ \mathrm{t\bar{t}HH} $ prediction is overlaid, scaled for visibility. |
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Figure 8-d:
Final discriminant distributions for Run2 for the $ \mathrm{t\bar{t}HH} $ signal node, and for the background nodes $ \mathrm{t\bar{t}H} $, $ \mathrm{t\bar{t}Z} $, where Z stands for: Z $ \to $ bb, ZZ $ \to $ 4b and ZH $ \to $ 4b, $ \mathrm{t} \overline{\mathrm{t}} $ stands: for $ \mathrm{t\bar{t}} $+lf and $ \mathrm{t\bar{t}} $+cc, $ \mathrm{t\bar{t}} $ b stands for $ \mathrm{t\bar{t}} $+mb and $ \mathrm{t\bar{t}} $+nb. In each panel, the SM $ \mathrm{t\bar{t}HH} $ prediction is overlaid, scaled for visibility. |
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Figure 8-e:
Final discriminant distributions for Run2 for the $ \mathrm{t\bar{t}HH} $ signal node, and for the background nodes $ \mathrm{t\bar{t}H} $, $ \mathrm{t\bar{t}Z} $, where Z stands for: Z $ \to $ bb, ZZ $ \to $ 4b and ZH $ \to $ 4b, $ \mathrm{t} \overline{\mathrm{t}} $ stands: for $ \mathrm{t\bar{t}} $+lf and $ \mathrm{t\bar{t}} $+cc, $ \mathrm{t\bar{t}} $ b stands for $ \mathrm{t\bar{t}} $+mb and $ \mathrm{t\bar{t}} $+nb. In each panel, the SM $ \mathrm{t\bar{t}HH} $ prediction is overlaid, scaled for visibility. |
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Figure 9:
The expected (dashed vertical line) upper 95% CL limit on the $ \mathrm{t\bar{t}HH} $ signal strength modifier $ \mu = \sigma / \sigma_{\mathrm SM} $ for different years and their combination for the SL channel. The green (yellow) areas indicate the one (two) standard deviation confidence intervals on the expected limit. |
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Figure 10:
The 95% CL upper limits on the signal strength as a function of $ c_2 $. The yellow and blue bands indicate the one and two standard deviation of the median expected limit (dashed black line), respectively. The red line corresponds to the theoretical prediction for the $ \mathrm{t\bar{t}HH} $ production cross section. |
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Figure 11:
The 68% and 95% CL likehood contours in the ($ c_2 $, $ \kappa_{\mathrm{t}} $) plane. The yellow (blue) lines indicate the one (two) standard deviation contours, along with the 3$ \sigma $ (in red) and 5$ \sigma $ (purple) contours. The yellow cross shows the observed best fit value. The red diamond shows the SM expectation. |
| Tables | |
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Table 1:
Summary of simulated signal and background MC samples. |
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Table 2:
Baseline selection criteria. Leptons and jets are ordered in $ p_{\mathrm{T}} $. Where the criteria differ per year of data taking, they are quoted as three values, corresponding to 2016/2017/2018, respectively. |
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Table 3:
Reconstruction accuracies of the JABDT method and $ \chi^2 $ method, evaluated on $ \mathrm{t\bar{t}HH} $ simulated events. |
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Table 4:
Observables used as input variables to the DNN. |
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Table 5:
Cross sections at 13 TeV with the uncertainties $ \pm $QCD Scale (%) and $ \pm $(PDF$ +\alpha_s $) (%) for the signal and all the considered backgrounds. |
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Table 6:
Summary of systematic uncertainties. |
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Table 7:
Fit results for the Run 2 data signal strength. |
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Table 8:
Samples used in the analysis with the listed corresponding coupling modifiers within the HEFT framework for each considered sample. The $ \mathrm{H} \mathrm{H} \to \mathrm{b\bar{b}}\mathrm{b\bar{b}} $ branching ratio is $ (0.5824)^2 $. |
| Summary |
| We present the first CMS search for the associated production of a Higgs boson (H) pair, where each H decays into a bottom quark-antiquark pair, with a top quark--antiquark pair ($ \mathrm{t\bar{t}HH} $), in the single lepton channel. The analysis has been performed using proton proton collision data recorded with the CMS detector at a centre-of-mass energy of 13 TeV, corresponding to an integrated luminosity of 138 fb$ ^{-1} $. Neural network discriminants were used to further categorize the events according to the most probable process, targeting the signal and different backgrounds. A best fit value of the $ \mathrm{t\bar{t}HH} $ production cross section relative to the standard model (SM) expectation of -9 $ ^{+26}_{-25} $ is obtained. The upper limit on the $ \mathrm{t\bar{t}HH} $ production cross section is 49 (55) times the observed (expected) SM cross-section; it corresponds to an observed (expected) cross-section upper limit of 37 (42)fb, at 95% CL. The $ \mathrm{t\bar{t}HH} $ results are further interpreted within the Higgs effective field theory (HEFT) theory framework, leading to a 95% CL interval on the $ \mathrm{t\bar{t}HH} $ quartic interaction parameter of $ -6.6 < c_2 < $ 6.4. It is interesting to compare these results with those already produced by ATLAS and CMS. Whereas the analysis presented in this Note only considers one decay channel for the Higgs boson pair, both the ATLAS [23] and CMS [22] consider various $ \mathrm{t\bar{t}HH} $ signatures and combine the final results. ATLAS study includes: $ \mathrm{t\bar{t}HH} $ with either $ \mathrm{t\bar{t}} $ single lepton plus Higgs boson pair decay into 4 b-quarks; or same sign multilepton signatures with $ \mathrm{t\bar{t}} $ decay into 1 or 2 leptons, and one Higgs boson decays into $ \mathrm{b\bar{b}} $ while the other decays into WW, ZZ or a $ \tau $-lepton pair; or a diphoton signature with one Higgs boson decays into $ \mathrm{b\bar{b}} $, and the other one decays into a pair of photons. All analyses are performed with data recorded at Run 2 at 13 TeV plus the two first years of Run 3 at 13.6 TeV. It represents a total integrated luminosity of 196 fb$ ^{-1} $. CMS [22] considers the $ \mathrm{t\bar{t}HH} $ cases where one Higgs boson decays into a pair of photons while the other one decays into either a b-quark pair or a $ \tau $-lepton pair or a W boson pair, where the W bosons decay into leptons, with Run 2 data. On one hand, the case where one Higgs boson decays into a photon pair, even if combined with other Higgs boson decays, provides a much lower sensitivity for the considered integrated luminosities (138 or 196 fb$ ^{-1} $). This is due to the very low $ \mathrm{t\bar{t}HH} $ production cross-section combined to a very small branching decay of the Higgs boson into a pair of photons and although the Higgs boson decay into 2 photons strengthens the $ \mathrm{t\bar{t}HH} $ signature. This is shown by the results from CMS [22] and ATLAS [23]. The full Run 3 and moreover HL-LHC will make this case much more promising. On the other hand, for comparing the CMS-SL results reported here with the ones from a similar ATLAS-SL search, several facts have to be taken into account. The first one is the difference in statistics due to the increase in luminosity (138 fb$ ^{-1} $ to 196 fb$ ^{-1} $), and in the $ \mathrm{t\bar{t}HH} $ cross-section in Run 3 (0.756 to 0.860 fb) due to the increase from 13 TeV to 13.6 TeV. But also improvements on detector performances as well as triggering and analysis tools in Run 3, thanks to the experiments upgrades for Run 3. This brings a difference between ATLAS and CMS estimated to be about at least 40%. Apart from the statistics, slightly lower $ p_{\mathrm{T}} $ thresholds applied to Physics objects in ATLAS w.r.t. CMS, and also differences in jet assignment procedure and in the treatment of the dominant $ \mathrm{t\bar{t}} $ + X background are impacting as well the results. But both the results presented here as well as those from ATLAS, assuming the $ \mathrm{t\bar{t}} $ semileptonic decay and the $ \mathrm{b\bar{b}} $ decay of the two Higgs bosons, despite a still relatively low integrated luminosity, demonstrate the sensitivity to the SM study and the HEFT interpretation of the $ \mathrm{t\bar{t}HH} $ production process in this specific signature. |
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