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| CMS-HIG-24-012 ; CERN-EP-2026-157 | ||
| Search for nonresonant triple Higgs boson production in the final state with six bottom quarks in proton-proton collisions at $ \sqrt{s}= $ 13 TeV | ||
| CMS Collaboration | ||
| 6 July 2026 | ||
| Submitted to Physical Review Letters | ||
| Abstract: A search for nonresonant triple Higgs boson ($ {\mathrm{H}\mathrm{H}\mathrm{H}} $) production in the final state with six bottom quarks is performed using proton-proton collisions at $ \sqrt{s}= $ 13 TeV corresponding to an integrated luminosity of 138 fb$ ^{-1} $ recorded by the CMS experiment. No significant excess of events over the background prediction is seen. Observed (expected) 95% confidence level upper limits on the signal cross section are set at 44 (43) fb, corresponding to 588 (572) times the standard model expectation. The observed (expected) constraint on the trilinear coupling modifier $ \kappa_3 $ is $ -7.4 < \kappa_3 < $ 12.4 ($ -6.4 < \kappa_3 < $ 11.2), assuming the quartic coupling modifier $ \kappa_4= $ 1. The corresponding constraint on $ \kappa_4 $ is $ -177 < \kappa_4 < $ 185 ($ -180 < \kappa_4 < $ 190), assuming $ \kappa_3= $ 1. This analysis provides the most stringent constraint to date on nonresonant $ {\mathrm{H}\mathrm{H}\mathrm{H}} $ production and excludes, for the first time, part of the $ (\kappa_3,\kappa_4) $ space allowed by the perturbative unitarity bound. | ||
| Links: e-print arXiv:2607.05145 [hep-ex] (PDF) ; CDS record ; inSPIRE record ; HepData record ; CADI line (restricted) ; | ||
| Figures | Summary | Additional Figures & Tables | References | CMS Publications |
|---|
| Figures | |
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Figure 1:
Post-fit yields in the SR categories with three reconstructed H. Bins correspond to ten intervals per category of the SPANET score $ \mathrm{ProbMultiH} $ in the high-score range 0.8--1.0, ordered by increasing purity. |
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Figure 2:
Expected and observed ULs on the $ {\mathrm{H}\mathrm{H}\mathrm{H}} $ signal strength shown separately for merged, partially merged, and resolved event topologies, along with the combined result (left). The 68 and 95% CL contours in the $ (\kappa_3,\kappa_4) $ plane from the combined profile likelihood scan (right). The gray region denotes parameter space allowed by perturbative unitarity in $ \mathrm{H}\mathrm{H}\to\mathrm{H}\mathrm{H} $ scattering [47]. |
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Figure 2-a:
Expected and observed ULs on the $ {\mathrm{H}\mathrm{H}\mathrm{H}} $ signal strength shown separately for merged, partially merged, and resolved event topologies, along with the combined result (left). The 68 and 95% CL contours in the $ (\kappa_3,\kappa_4) $ plane from the combined profile likelihood scan (right). The gray region denotes parameter space allowed by perturbative unitarity in $ \mathrm{H}\mathrm{H}\to\mathrm{H}\mathrm{H} $ scattering [47]. |
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Figure 2-b:
Expected and observed ULs on the $ {\mathrm{H}\mathrm{H}\mathrm{H}} $ signal strength shown separately for merged, partially merged, and resolved event topologies, along with the combined result (left). The 68 and 95% CL contours in the $ (\kappa_3,\kappa_4) $ plane from the combined profile likelihood scan (right). The gray region denotes parameter space allowed by perturbative unitarity in $ \mathrm{H}\mathrm{H}\to\mathrm{H}\mathrm{H} $ scattering [47]. |
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Figure 3:
Representative leading-order Feynman diagrams for nonresonant $ {\mathrm{H}\mathrm{H}\mathrm{H}} $ production via gluon fusion. The last three diagrams provide direct sensitivity to the trilinear ($ \lambda_3 $) and quartic ($ \lambda_4 $) H self-couplings. |
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Figure 3-a:
Representative leading-order Feynman diagrams for nonresonant $ {\mathrm{H}\mathrm{H}\mathrm{H}} $ production via gluon fusion. The last three diagrams provide direct sensitivity to the trilinear ($ \lambda_3 $) and quartic ($ \lambda_4 $) H self-couplings. |
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Figure 3-b:
Representative leading-order Feynman diagrams for nonresonant $ {\mathrm{H}\mathrm{H}\mathrm{H}} $ production via gluon fusion. The last three diagrams provide direct sensitivity to the trilinear ($ \lambda_3 $) and quartic ($ \lambda_4 $) H self-couplings. |
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Figure 3-c:
Representative leading-order Feynman diagrams for nonresonant $ {\mathrm{H}\mathrm{H}\mathrm{H}} $ production via gluon fusion. The last three diagrams provide direct sensitivity to the trilinear ($ \lambda_3 $) and quartic ($ \lambda_4 $) H self-couplings. |
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Figure 3-d:
Representative leading-order Feynman diagrams for nonresonant $ {\mathrm{H}\mathrm{H}\mathrm{H}} $ production via gluon fusion. The last three diagrams provide direct sensitivity to the trilinear ($ \lambda_3 $) and quartic ($ \lambda_4 $) H self-couplings. |
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Figure 4:
Observed and expected 95% CL upper limits on the $ {\mathrm{H}\mathrm{H}\mathrm{H}} $ signal strength $ \mu_{{\mathrm{H}\mathrm{H}\mathrm{H}}} $. Results are shown for the analyzed dataset of 138 fb$ ^{-1} $ of pp collisions at $ \sqrt{s}= $ 13 TeV, along with projections for 14 TeV and an integrated luminosity of 3$ \text{ab}^{-1}$. |
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Figure 5:
Expected 68 and 95% CL constraints in the $ (\kappa_3,\kappa_4) $ plane for the $ \mathrm{H}\mathrm{H}\mathrm{H} \to 6\mathrm{b} $ analysis in the HL-LHC scenario ($ \sqrt{s}= $ 14 TeV, 3$ \text{ab}^{-1}$). The unitarity boundary is overlaid, and the best-fit point from the projection is indicated. |
| Summary |
| In summary, this Letter presents a search for nonresonant triple Higgs boson ($ {\mathrm{H}\mathrm{H}\mathrm{H}} $) production in the final state with six bottom quarks using 138 fb$ ^{-1} $ of proton-proton collision data at $\sqrt{s}=13$ TeV collected by the CMS experiment between 2016 and 2018. No significant deviation from the background prediction is observed. At 95% confidence level, the observed (expected) upper limit on the $ {\mathrm{H}\mathrm{H}\mathrm{H}} $ production cross section is 44 (43) fb, corresponding to 588 (572) times the standard model prediction. In the framework of Higgs boson self-coupling modifiers ($\kappa$), the search constrains the trilinear coupling modifier $\kappa_3$ to $-7.4 < \kappa_3 < 12.4$ for the quartic coupling modifier $\kappa_4=1$ and constrains $\kappa_4$ to $-177 < \kappa_4 < 185$ for $\kappa_3=1$. The two-dimensional $(\kappa_3,\kappa_4)$ scan constrains, for the first time in a direct search for nonresonant $ {\mathrm{H}\mathrm{H}\mathrm{H}} $ production, the perturbative unitarity boundary and excludes part of the allowed parameter space. These results are the most stringent constraints to date on nonresonant $ {\mathrm{H}\mathrm{H}\mathrm{H}} $ production and on $\kappa_4$. |
| Additional Figures | |
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Additional Figure 1:
Profile likelihood scans of the trilinear Higgs boson self-coupling modifier $\kappa_3$ ($\kappa_4=1$), shown separately for events with 2$\mathrm{H}$, 3$\mathrm{H}$, and their combination. Solid (dashed) curves correspond to the observed (expected) scan; horizontal lines indicate the $1\sigma$ and $2\sigma$ intervals. |
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Additional Figure 2:
Profile likelihood scans of the quartic Higgs boson self-coupling modifier $\kappa_4$ ($\kappa_3=1$), shown separately for events with 2$\mathrm{H}$, 3$\mathrm{H}$, and their combination. Solid (dashed) curves correspond to the observed (median expected) scan; horizontal lines indicate the $1\sigma$ and $2\sigma$ intervals. |
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Additional Figure 3:
Expected 68% and 95% CL constraints in the $(\kappa_3,\kappa_4)$ plane from the $ {\mathrm{H}\mathrm{H}\mathrm{H}} \to 6\mathrm{b} $analysis under alternative treatments of the $ {\mathrm{H}\mathrm{H}\mathrm{H}} $ contribution: the nominal modeling, a model excluding the $ {\mathrm{H}\mathrm{H}\mathrm{H}} $ process, and a model including $\kappa_4$-dependent electroweak corrections in $ {\mathrm{H}\mathrm{H}\mathrm{H}} $. The unitarity boundary and best-fit point are overlaid. |
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Additional Figure 4:
Observed 68% and 95% CL constraints in the $(\kappa_3,\kappa_4)$ plane from the $ {\mathrm{H}\mathrm{H}\mathrm{H}} \to 6\mathrm{b} $analysis under alternative treatments of the $ {\mathrm{H}\mathrm{H}\mathrm{H}} $ contribution (nominal; no $ {\mathrm{H}\mathrm{H}\mathrm{H}} $; $ {\mathrm{H}\mathrm{H}\mathrm{H}} $ with $\kappa_4$-dependent electroweak corrections). The unitarity boundary and best-fit point are shown. |
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Additional Figure 5:
Expected 68% and 95% CL constraints in the $(\kappa_3,\kappa_4)$ plane for integrated luminosities of 3 and 6 ab$ ^{-1} $. The unitarity boundary and the SM point are shown. |
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Additional Figure 6:
Expected and observed 95% CL upper limits on the $ {\mathrm{H}\mathrm{H}\mathrm{H}} $ signal strength $ \mu_{\mathrm{H}\mathrm{H}\mathrm{H}} $ for the 2$\mathrm{H}$ region (events with two reconstructed Higgs bosons) and its subcategories. Categories are labeled by the number of merged Higgs boson candidates (mh) and resolved Higgs boson candidates (h); the median expected limit and the $\pm1\sigma$ ($\pm2\sigma$) bands are shown. |
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Additional Figure 7:
Expected and observed 95% CL upper limits on the $ {\mathrm{H}\mathrm{H}\mathrm{H}} $ signal strength $ \mu_{\mathrm{H}\mathrm{H}\mathrm{H}} $ for the 3$\mathrm{H}$ region (events with three reconstructed Higgs bosons) and its subcategories, labeled by the number of merged (mh) and resolved (h) Higgs boson candidates. The median expected limit and the $\pm1\sigma$ ($\pm2\sigma$) bands are shown. |
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Additional Figure 8:
Expected and observed 95% CL upper limits on $ \mu_{\mathrm{H}\mathrm{H}\mathrm{H}} $ for each $ {\mathrm{H}\mathrm{H}\mathrm{H}} \to 6\mathrm{b} $analysis category (labeled by the number of merged and resolved Higgs boson candidates) and for their combination. The median expected limit and the $\pm1\sigma$ ($\pm2\sigma$) bands are shown. |
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Additional Figure 9:
Summary of the expected and observed 95% CL upper limits on the $ {\mathrm{H}\mathrm{H}\mathrm{H}} $ signal strength $ \mu_{\mathrm{H}\mathrm{H}\mathrm{H}} $ for the 2$\mathrm{H}$ and 3$\mathrm{H}$ regions and their combination. The median expected limit and the $\pm1\sigma$ ($\pm2\sigma$) bands are shown. |
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Additional Figure 10:
Impact of uncertainty groupings on the expected and observed 95% CL upper limits on $ \mu_{\mathrm{H}\mathrm{H}\mathrm{H}} $ in the $ {\mathrm{H}\mathrm{H}\mathrm{H}} \to 6\mathrm{b} $analysis. Limits are recomputed under alternative configurations (nominal; removing background uncertainties; background-only; MC-only; theory-only; and statistical-only), illustrating the relative contribution of each uncertainty class. |
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Additional Figure 11:
Post-fit distribution of the binned SPANET discriminant in the 0$\mathrm{H}$ (0mh0h) category of the $ {\mathrm{H}\mathrm{H}\mathrm{H}} \to 6\mathrm{b} $analysis at 13 TeV with 138fb$ ^{-1} $ , shown on a linear scale. The fitted background components (QCD multijet and $ {\mathrm{H}\mathrm{H}\mathrm{H}} $) are stacked and compared to data; the $ {\mathrm{H}\mathrm{H}\mathrm{H}} $ signal shape is overlaid for the SM expectation and scaled to the observed upper limit for visibility. The lower panel shows the data-to-prediction ratio with the post-fit uncertainty band. |
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Additional Figure 12:
Post-fit distribution of the binned SPANET discriminant in the 1$\mathrm{H}$ categories (1mh0h and 0mh1h), shown on a linear scale. Vertical dashed lines separate the category-specific bin ranges; the stacked post-fit backgrounds, overlaid $ {\mathrm{H}\mathrm{H}\mathrm{H}} $ signal reference, and data-to-prediction ratio are shown. |
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Additional Figure 13:
Post-fit distribution of the binned SPANET discriminant in the 2$\mathrm{H}$ categories (2mh0h, 1mh1h, and 0mh2h), shown on a linear scale. Vertical dashed lines separate the category-specific bin ranges; the stacked post-fit backgrounds, overlaid $ {\mathrm{H}\mathrm{H}\mathrm{H}} $ signal reference, and data-to-prediction ratio are shown. |
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Additional Figure 14:
Post-fit distribution of the binned SPANET discriminant in the 3$\mathrm{H}$ categories (3mh0h, 2mh1h, 1mh2h, and 0mh3h), shown on a linear scale. Vertical dashed lines separate the category-specific bin ranges; the stacked post-fit backgrounds, overlaid $ {\mathrm{H}\mathrm{H}\mathrm{H}} $ signal reference, and data-to-prediction ratio are shown. |
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Additional Figure 15:
Post-fit distribution of the binned SPANET discriminant in the 0$\mathrm{H}$ (0mh0h) category of the $ {\mathrm{H}\mathrm{H}\mathrm{H}} \to 6\mathrm{b} $analysis at 13 TeV with 138fb$ ^{-1} $ , shown with a logarithmic $y$-axis to emphasize the low-yield and high-discriminant regions. |
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Additional Figure 16:
Post-fit distribution of the binned SPANET discriminant in the 1$\mathrm{H}$ categories (1mh0h and 0mh1h), shown with a logarithmic $y$-axis to emphasize the low-yield and high-discriminant regions. |
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Additional Figure 17:
Post-fit distribution of the binned SPANET discriminant in the 2$\mathrm{H}$ categories (2mh0h, 1mh1h, and 0mh2h), shown with a logarithmic $y$-axis to emphasize the low-yield and high-discriminant regions. |
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Additional Figure 18:
Post-fit distribution of the binned SPANET discriminant in the 3$\mathrm{H}$ categories (3mh0h, 2mh1h, 1mh2h, and 0mh3h), shown with a logarithmic $y$-axis to emphasize the low-yield and high-discriminant regions. |
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Additional Figure 19:
Selection efficiency as a function of the trilinear coupling modifier $\kappa_3$ for simulated $ \mu_{\mathrm{H}\mathrm{H}\mathrm{H}} \to 6\mathrm{b} $ (solid) and $$\mathrm{H}$$\mathrm{H}$ \to 4\PQb$ (dashed) samples. Efficiencies are shown after baseline preselection (black), after the $ \mu_{\mathrm{H}\mathrm{H}\mathrm{H}} \to 6\mathrm{b} $ like categorization in the inclusive region (green) and signal region (blue), and after the final SPANET requirement (red). |
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Additional Figure 20:
Selection efficiency as a function of the quartic coupling modifier $\kappa_4$ for simulated $ \mu_{\mathrm{H}\mathrm{H}\mathrm{H}} \to 6\mathrm{b} $ events. Efficiencies are shown after baseline preselection (black), after the $ \mu_{\mathrm{H}\mathrm{H}\mathrm{H}} \to 6\mathrm{b} $ like categorization in the inclusive region (green) and signal region (blue), and after the final SPANET requirement (red). |
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Additional Figure 21:
Selection efficiency versus $\kappa_3$ for $\mathrm{H}\mathrm{H}\mathrm{H}$(solid) and $\mathrm{H}\mathrm{H}$(dashed) signals at successive selections: baseline, inclusive categorization, $ \mu_{\mathrm{H}\mathrm{H}\mathrm{H}} \to 6\mathrm{b} $ selection, and final SPANET requirement. |
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Additional Figure 22:
Selection efficiency versus $\kappa_4$ for $\mathrm{H}\mathrm{H}\mathrm{H}$(solid) and $\mathrm{H}\mathrm{H}$(dashed) signals at successive selections: baseline, inclusive categorization, $ \mu_{\mathrm{H}\mathrm{H}\mathrm{H}} \to 6\mathrm{b} $ selection, and final SPANET requirement. |
| Additional Tables | |
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Additional Table 1:
Summary of the Monte Carlo simulated processes used in the analysis, listing the event generator configuration, nominal perturbative accuracy of the generated samples, the cross-section normalization order, and the production cross section at $\sqrt{s}=13$ TeV in pb. |
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Additional Table 2:
Composition of reconstructible $\mathrm{H}$ boson candidates based on MC simulation. Columns list the number of candidates reconstructed in two small-radius jets (0h, 1h, 2h, 3h) and rows list the number of candidates reconstructed in one large-radius jet (3mh, 2mh, 1mh, 0mh). |
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Additional Table 3:
Benchmark cross sections for $gg \to {\mathrm{H}\mathrm{H}\mathrm{H}} $ and $gg \to {\mathrm{H}\mathrm{H}}$ as a function of $(\kappa_3,\kappa_4)$ (or $\kappa_3$ for $ {\mathrm{H}\mathrm{H}\mathrm{H}} $), including associated theoretical uncertainties. These values define the coupling-scan points used to map limits in the $(\kappa_3,\kappa_4)$ parameter space. |
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