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| CMS-PAS-HIG-25-014 | ||
| Combination of ATLAS and CMS searches for Higgs boson pair production at $ \sqrt{s} = $ 13 TeV | ||
| ATLAS and CMS Collaborations | ||
| 2025-10-30 | ||
| Abstract: This note presents a combination of searches for Higgs boson pair (HH) production performed by the ATLAS and CMS Collaborations using proton-proton collision data sets recorded at $ \sqrt{s} = $ 13 TeV at the LHC Run 2, corresponding to integrated luminosities ranging between 126 and 140 fb$^{-1}$. The upper limit at the 95% confidence level on the total HH production cross section corresponds to 2.5 times the standard model (SM) prediction with an expected value of 1.7 (2.8) assuming the absence (presence) of the SM HH signal. The strength of the HH signal is measured to be 0.8 $ ^{+0.9}_{-0.7} $ relative to the SM prediction. The observed significance is found to be 1.1 standard deviations when 1.3 are expected for the SM HH signal. Constraints are set on the Higgs boson trilinear self-coupling and on the couplings of two Higgs bosons to two vector bosons, both normalized to the SM predictions and denoted as $ \kappa_\lambda $ and $ \kappa_{2\mathrm{V}} $, respectively. The observed individual constraints at the 95% confidence level are $ -$0.71 $ < \kappa_\lambda < $ 6.1 and 0.73 $ < \kappa_{2\mathrm{V}} < $ 1.3, while the expected constraints assuming the presence of the SM HH signal are $ -1.3 < \kappa_\lambda < $ 6.7 and 0.66 $ < \kappa_{2\mathrm{V}} < $ 1.4. | ||
| Links: CDS record (PDF) ; CADI line (restricted) ; | ||
| Figures | |
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Figure 1:
Expected and observed 95% CL upper limits on the total HH signal strength, defined as the ratio of the measured cross section to the sum of the ggF and VBF HH SM production cross sections, for ATLAS, CMS, and the combination of both experiments. The median expected limits on $ \mu_{\mathrm{H}\mathrm{H}} $ are obtained under the hypotheses of no HH signal ($ \mu_{\mathrm{H}\mathrm{H}}^\text{Asimov}= $ 0) or assuming the presence of the SM HH signal ($ \mu_{\mathrm{H}\mathrm{H}}^\text{Asimov}= $ 1). The $ \pm 1\sigma $ and $ \pm 2\sigma $ bands are computed under the $ \mu_{\mathrm{H}\mathrm{H}}^\text{Asimov}= $ 0 hypothesis. |
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Figure 2:
Expected negative log-likelihood values as function of $ \kappa_\lambda $ (left) and $ \kappa_{2\text{V}} $ (right) for ATLAS, CMS, and their combination, and observed values for the combination. The result is obtained fixing all the other couplings to their SM values. |
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Figure 2-a:
Expected negative log-likelihood values as function of $ \kappa_\lambda $ (left) and $ \kappa_{2\text{V}} $ (right) for ATLAS, CMS, and their combination, and observed values for the combination. The result is obtained fixing all the other couplings to their SM values. |
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Figure 2-b:
Expected negative log-likelihood values as function of $ \kappa_\lambda $ (left) and $ \kappa_{2\text{V}} $ (right) for ATLAS, CMS, and their combination, and observed values for the combination. The result is obtained fixing all the other couplings to their SM values. |
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Figure 3:
Observed and expected 95% CL contours for the simultaneous scan of the profile likelihood as a function of $ \kappa_\lambda $ and $ \kappa_{2\text{V}} $. The expected constraints from the individual experiments are also shown. All other Higgs boson couplings are fixed to their SM value. |
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Figure 4:
Expected negative log-likelihood values as a function of the total signal strength parameter $ \mu_{\mathrm{H}\mathrm{H}} $ for ATLAS, CMS, and their combination. The observed value for the combination is also shown. All the couplings are assumed to be fixed to the SM values, but the overall ggF+VBF HH signal normalization is allowed to vary freely. |
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Figure 5:
Observed negative log-likelihood values as a function of the total signal strength parameter $ \mu_{\mathrm{H}\mathrm{H}} $ for ATLAS, CMS, and their combination. The expected value for the combination is also shown. All the couplings are assumed to be fixed to the SM values, but the overall ggF+VBF HH signal normalization is allowed to vary freely. |
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Figure 6:
Observed and expected negative log-likelihood values as a function of the total signal strength parameter $ \mu_{\mathrm{H}\mathrm{H}} $. All the couplings are assumed to be fixed to the SM values, but the overall ggF+VBF HH signal normalization is allowed to vary freely. |
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Figure 7:
Observed and expected negative log-likelihood values as a function of $ \kappa_\lambda $. All the other couplings are assumed to be fixed to the SM values. |
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Figure 8:
Observed negative log-likelihood values as a function of $ \kappa_\lambda $ for ATLAS, CMS, and their combination, and expected value for the combination. All the other couplings are assumed to be fixed to the SM values. |
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Figure 9:
Observed and expected negative log-likelihood values as a function of $ \kappa_{2\text{V}} $. All the other couplings are assumed to be fixed to the SM values. |
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Figure 10:
Observed negative log-likelihood values as a function of $ \kappa_{2\text{V}} $ for ATLAS, CMS, and their combination, and expected value for the combination. All the other couplings are assumed to be fixed to the SM values. |
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Figure 11:
Observed and expected 95% CL contours for a bidimensional likelihood scan in the $ (\kappa_\lambda, \kappa_{2\text{V}}) $ plane for ATLAS, CMS, and their combination. All other Higgs boson couplings are fixed to their SM value. |
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Figure 12:
Observed 95% CL contours for a bidimensional likelihood scan in the $ (\kappa_\lambda, \kappa_{2\text{V}}) $ plane for ATLAS, CMS, and their combination. The expected contour from the combination is also shown. All other Higgs boson couplings are fixed to their SM value. |
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Figure 13:
Exclusion limit at the 95% confidence level on the total HH cross section as a function of the value of $ \kappa_\lambda $. The expected exclusion is computed assuming no HH signal is present ($ \mu_{\mathrm{H}\mathrm{H}}^\text{Asimov} = $ 0). The individual results by ATLAS and CMS are indicated by the green and purple lines, respectively. Dashed and solid lines denote respectively the expected median and the observed limits. The theoretical prediction, corresponding to the sum of the ggF and VBF HH cross sections, is shown in red. |
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Figure 14:
Exclusion limit at the 95% confidence level on the total HH cross section as a function of the value of $ \kappa_{2\text{V}} $. The expected exclusion is computed assuming no HH signal is present ($ \mu_{\mathrm{H}\mathrm{H}}^\text{Asimov} = $ 0). The individual results by ATLAS and CMS are indicated by the green and purple lines, respectively. Dashed and solid lines denote respectively the expected median and the observed limits. The theoretical prediction, corresponding to the sum of the ggF and VBF HH cross sections, is shown in red. |
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Figure 15:
Expected and observed 95% CL upper limits on the total HH signal strength, defined as the ratio of the measured cross section to the sum of the ggF and VBF HH SM production cross sections, for ATLAS, CMS, and the combination of both experiments. The expected limits on $ \mu_{\mathrm{H}\mathrm{H}} $ are obtained assuming the absence of an HH signal ($ \mu_{\mathrm{H}\mathrm{H}}^\text{Asimov}= $ 0). |
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Figure 16:
Expected and observed 95% CL upper limits on the total HH cross section, defined as the sum of the ggF and VBF HH SM production cross sections, for ATLAS, CMS, and the combination of both experiments. The expected limits on $ \mu_{\mathrm{H}\mathrm{H}} $ are obtained assuming the absence of an HH signal ($ \mu_{\mathrm{H}\mathrm{H}}^\text{Asimov}= $ 0). The theoretical prediction is indicated in red. |
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Figure 17:
Expected and observed 95% CL upper limits on the signal strength of the VBF HH production $ \mu_{\mathrm{H}\mathrm{H}}^\text{VBF} $, defined as the ratio of the measured VBF HH cross section to the corresponding SM prediction, for ATLAS, CMS, and the combination of both experiments. The limits are obtained by fixing the ggF signal strength to the SM prediction ($ \mu_{\mathrm{H}\mathrm{H}}^\text{ggF} = $ 1). The expected limits assume the absence of the VBF HH signal. |
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Figure 18:
Observed and expected 95% CL contours for a bidimensional likelihood scan where the individual signal strengths for the ggF ($ \mu_{\mathrm{H}\mathrm{H}}^\text{ggF} $) and VBF ($ \mu_{\mathrm{H}\mathrm{H}}^\text{VBF} $) HH production modes are allowed to vary independently. All Higgs boson couplings are fixed to their SM value. The likelihood function is not well defined in regions with large negative values of either $ \mu_{\mathrm{H}\mathrm{H}}^\text{ggF} $ or $ \mu_{\mathrm{H}\mathrm{H}}^\text{VBF} $, where the total prediction for the sum of signal and backgrounds can become negative in some categories of the input analyses. This region is therefore not shown. |
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Figure 19:
Observed (top) and expected (bottom) negative log-likelihood values as a function of $ \kappa_\lambda $ for the input ATLAS (left) and CMS (right) analyses. All the other couplings are fixed to the SM values. |
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Figure 19-a:
Observed (top) and expected (bottom) negative log-likelihood values as a function of $ \kappa_\lambda $ for the input ATLAS (left) and CMS (right) analyses. All the other couplings are fixed to the SM values. |
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Figure 19-b:
Observed (top) and expected (bottom) negative log-likelihood values as a function of $ \kappa_\lambda $ for the input ATLAS (left) and CMS (right) analyses. All the other couplings are fixed to the SM values. |
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Figure 19-c:
Observed (top) and expected (bottom) negative log-likelihood values as a function of $ \kappa_\lambda $ for the input ATLAS (left) and CMS (right) analyses. All the other couplings are fixed to the SM values. |
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Figure 19-d:
Observed (top) and expected (bottom) negative log-likelihood values as a function of $ \kappa_\lambda $ for the input ATLAS (left) and CMS (right) analyses. All the other couplings are fixed to the SM values. |
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Figure 20:
Observed (top) and expected (bottom) negative log-likelihood values as a function of $ \kappa_{2\text{V}} $ for the input ATLAS (left) and CMS (right) analyses. All the other couplings are fixed to the SM values. |
png pdf |
Figure 20-a:
Observed (top) and expected (bottom) negative log-likelihood values as a function of $ \kappa_{2\text{V}} $ for the input ATLAS (left) and CMS (right) analyses. All the other couplings are fixed to the SM values. |
png pdf |
Figure 20-b:
Observed (top) and expected (bottom) negative log-likelihood values as a function of $ \kappa_{2\text{V}} $ for the input ATLAS (left) and CMS (right) analyses. All the other couplings are fixed to the SM values. |
png pdf |
Figure 20-c:
Observed (top) and expected (bottom) negative log-likelihood values as a function of $ \kappa_{2\text{V}} $ for the input ATLAS (left) and CMS (right) analyses. All the other couplings are fixed to the SM values. |
png pdf |
Figure 20-d:
Observed (top) and expected (bottom) negative log-likelihood values as a function of $ \kappa_{2\text{V}} $ for the input ATLAS (left) and CMS (right) analyses. All the other couplings are fixed to the SM values. |
| Tables | |
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Table 1:
Summary of the observed and expected results from the individual input analyses considered, the single experiment combination, and the LHC combination presented in this work. The upper limit on $ \mu_{\mathrm{H}\mathrm{H}}=\sigma_{\mathrm{H}\mathrm{H}}/\sigma_{\mathrm{H}\mathrm{H}}^\text{SM} $ and the constraints on $ \kappa_\lambda $ and $ \kappa_{2\text{V}} $ are reported. All values quoted are defined at the 95% CL. The expected limits on $ \mu_{\mathrm{H}\mathrm{H}} $ are computed assuming the absence of HH signal. The references indicate the original publication where the corresponding analyses are documented, and the results were recomputed following the modifications to input analyses described in the text. |
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Table 2:
Best fit values, 68%, and 95% CL intervals obtained from the likelihood values as a function of the coupling modifiers for the trilinear Higgs boson self-coupling $ \kappa_\lambda $ and the quartic coupling between two Higgs bosons and two vector bosons $ \kappa_{2\text{V}} $ for the ATLAS and CMS experiments and their combination. Results for $ \kappa_\lambda $ and $ \kappa_{2\text{V}} $ are computed from independent fits where all other Higgs boson couplings are set to their SM value. |
| Summary |
| In summary, this note presents the first combination of ATLAS and CMS searches for Higgs boson pair (HH) production. The searches are performed using the LHC Run 2 data set with integrated luminosities ranging between 126 and 140 fb$ ^{-1} $. The upper limit at the 95% confidence level on the total HH cross section, defined as the sum of the ggF and VBF production modes, corresponds to 2.5 times the SM prediction, compared to an expected value of 1.7 (2.8) in the absence (presence) of SM HH production. The best fit signal strength, defined as the ratio of the measured cross section to the SM prediction, is observed to be 0.8 $ ^{+0.9}_{-0.7} $, corresponding to a significance of 1.1 standard deviations. The observed 95% confidence level constraints on the $ \kappa_\lambda $ and $ \kappa_{2\text{V}} $ coupling modifiers are $ -$0.71 $ < \kappa_\lambda < $ 6.1 ($ -$1.3 $ < \kappa_\lambda < $ 6.7 expected) and 0.73 $ < \kappa_{2\text{V}} < $ 1.3 (0.66 $ < \kappa_{2\text{V}} < $ 1.4 expected). The results are compatible within their uncertainties with the SM predictions and provide the most comprehensive and most sensitive results on HH production to date. |
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