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| CMS-HIG-20-011 ; CERN-EP-2025-214 | ||
| Combination of searches for nonresonant Higgs boson pair production in proton-proton collisions at $ \sqrt{s}= $ 13 TeV | ||
| CMS Collaboration | ||
| 8 October 2025 | ||
| Submitted to Reports on Progress in Physics | ||
| Abstract: This paper presents a combination of searches for the nonresonant production of Higgs boson pairs (HH) in proton-proton collisions at a centre-of-mass energy of 13 TeV. The data set was collected by the CMS experiment at the LHC from 2016 to 2018 and corresponds to a total integrated luminosity of 138 fb$ ^{-1} $. The observed (expected) upper limit on the inclusive HH production cross section relative to the standard model (SM) prediction is found to be 3.5 (2.5). Assuming all other Higgs boson couplings are equal to their SM values, the Higgs boson trilinear self-coupling modifier $ \kappa_\lambda=\lambda_3/\lambda_{3}^\text{SM} $ is constrained in the range $ -$1.35 $\leq \kappa_\lambda \leq $ 6.37 at 95% confidence level. Similarly, for the coupling modifier $ \kappa_{2\mathrm{V}} $, which governs the interaction between two vector bosons and two Higgs bosons, we have excluded $ \kappa_{2\mathrm{V}}= $ 0 at more than 5 standard deviations for all values of $ \kappa_\lambda $. At 95% confidence level assuming other couplings are equal to their SM values, $ \kappa_{2\mathrm{V}} $ is constrained in the range 0.64 $ \leq \kappa_{2\mathrm{V}} \leq $ 1.40. This work also studies HH production in several new physics scenarios, using the Higgs effective field theory (HEFT) framework. The HEFT framework is further exploited to study various ultraviolet complete models with an extended Higgs sector and set constraints on specific parameters. An extrapolation of the results to the integrated luminosity expected after the high-luminosity upgrade of the LHC is reported as well. | ||
| Links: e-print arXiv:2510.07527 [hep-ex] (PDF) ; CDS record ; inSPIRE record ; CADI line (restricted) ; | ||
| Figures | |
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Figure 1:
Leading-order Feynman diagrams of nonresonant Higgs boson pair production via gluon-gluon fusion in the SM. The modifiers of the Higgs boson coupling with the top quark and the Higgs boson trilinear self-coupling are shown as $ \kappa_{\mathrm{t}} $ and $ \kappa_\lambda $, respectively. |
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Figure 1-a:
Leading-order Feynman diagrams of nonresonant Higgs boson pair production via gluon-gluon fusion in the SM. The modifiers of the Higgs boson coupling with the top quark and the Higgs boson trilinear self-coupling are shown as $ \kappa_{\mathrm{t}} $ and $ \kappa_\lambda $, respectively. |
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Figure 1-b:
Leading-order Feynman diagrams of nonresonant Higgs boson pair production via gluon-gluon fusion in the SM. The modifiers of the Higgs boson coupling with the top quark and the Higgs boson trilinear self-coupling are shown as $ \kappa_{\mathrm{t}} $ and $ \kappa_\lambda $, respectively. |
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Figure 2:
Leading-order Feynman diagrams of nonresonant Higgs boson pair production via vector boson fusion in the SM. The modifiers of the Higgs boson coupling with a vector boson, the Higgs boson trilinear self-coupling, and the coupling between two Higgs bosons and two vector bosons are shown as $ \kappa_\mathrm{V} $, $ \kappa_\lambda $, and $ \kappa_{2\mathrm{V}} $, respectively. |
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Figure 2-a:
Leading-order Feynman diagrams of nonresonant Higgs boson pair production via vector boson fusion in the SM. The modifiers of the Higgs boson coupling with a vector boson, the Higgs boson trilinear self-coupling, and the coupling between two Higgs bosons and two vector bosons are shown as $ \kappa_\mathrm{V} $, $ \kappa_\lambda $, and $ \kappa_{2\mathrm{V}} $, respectively. |
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Figure 2-b:
Leading-order Feynman diagrams of nonresonant Higgs boson pair production via vector boson fusion in the SM. The modifiers of the Higgs boson coupling with a vector boson, the Higgs boson trilinear self-coupling, and the coupling between two Higgs bosons and two vector bosons are shown as $ \kappa_\mathrm{V} $, $ \kappa_\lambda $, and $ \kappa_{2\mathrm{V}} $, respectively. |
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Figure 2-c:
Leading-order Feynman diagrams of nonresonant Higgs boson pair production via vector boson fusion in the SM. The modifiers of the Higgs boson coupling with a vector boson, the Higgs boson trilinear self-coupling, and the coupling between two Higgs bosons and two vector bosons are shown as $ \kappa_\mathrm{V} $, $ \kappa_\lambda $, and $ \kappa_{2\mathrm{V}} $, respectively. |
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Figure 3:
Leading-order Feynman diagrams of nonresonant Higgs boson pair production via associated production with a vector boson in the SM. The modifiers of the Higgs boson coupling with a vector boson, the Higgs boson trilinear self-coupling, and the coupling between two Higgs bosons and two vector bosons are shown as $ \kappa_\mathrm{V} $, $ \kappa_\lambda $, and $ \kappa_{2\mathrm{V}} $, respectively. |
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Figure 3-a:
Leading-order Feynman diagrams of nonresonant Higgs boson pair production via associated production with a vector boson in the SM. The modifiers of the Higgs boson coupling with a vector boson, the Higgs boson trilinear self-coupling, and the coupling between two Higgs bosons and two vector bosons are shown as $ \kappa_\mathrm{V} $, $ \kappa_\lambda $, and $ \kappa_{2\mathrm{V}} $, respectively. |
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Figure 3-b:
Leading-order Feynman diagrams of nonresonant Higgs boson pair production via associated production with a vector boson in the SM. The modifiers of the Higgs boson coupling with a vector boson, the Higgs boson trilinear self-coupling, and the coupling between two Higgs bosons and two vector bosons are shown as $ \kappa_\mathrm{V} $, $ \kappa_\lambda $, and $ \kappa_{2\mathrm{V}} $, respectively. |
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Figure 3-c:
Leading-order Feynman diagrams of nonresonant Higgs boson pair production via associated production with a vector boson in the SM. The modifiers of the Higgs boson coupling with a vector boson, the Higgs boson trilinear self-coupling, and the coupling between two Higgs bosons and two vector bosons are shown as $ \kappa_\mathrm{V} $, $ \kappa_\lambda $, and $ \kappa_{2\mathrm{V}} $, respectively. |
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Figure 4:
Leading-order Feynman diagrams of nonresonant Higgs boson pair production via gluon-gluon fusion with anomalous Higgs boson couplings $ \text{c}_2 $, $ \text{c}_\mathrm{g} $, and $ \text{c}_{2\mathrm{g}} $. The Higgs boson trilinear self-coupling modifier is shown as $ \kappa_\lambda $. |
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Figure 4-a:
Leading-order Feynman diagrams of nonresonant Higgs boson pair production via gluon-gluon fusion with anomalous Higgs boson couplings $ \text{c}_2 $, $ \text{c}_\mathrm{g} $, and $ \text{c}_{2\mathrm{g}} $. The Higgs boson trilinear self-coupling modifier is shown as $ \kappa_\lambda $. |
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Figure 4-b:
Leading-order Feynman diagrams of nonresonant Higgs boson pair production via gluon-gluon fusion with anomalous Higgs boson couplings $ \text{c}_2 $, $ \text{c}_\mathrm{g} $, and $ \text{c}_{2\mathrm{g}} $. The Higgs boson trilinear self-coupling modifier is shown as $ \kappa_\lambda $. |
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Figure 4-c:
Leading-order Feynman diagrams of nonresonant Higgs boson pair production via gluon-gluon fusion with anomalous Higgs boson couplings $ \text{c}_2 $, $ \text{c}_\mathrm{g} $, and $ \text{c}_{2\mathrm{g}} $. The Higgs boson trilinear self-coupling modifier is shown as $ \kappa_\lambda $. |
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Figure 5:
Illustrations of the resolved (upper left) and boosted (upper right) topologies of the $ \mathrm{b}\overline{\mathrm{b}}\mathrm{b}\overline{\mathrm{b}} $ decay channel. The topology of VHH production when all Higgs bosons decay to b jets and the vector boson is either a Z boson that decays into two leptons (lower left) or a W boson decaying into a lepton and a neutrino, giving missing transverse momentum (lower right). |
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Figure 5-a:
Illustrations of the resolved (upper left) and boosted (upper right) topologies of the $ \mathrm{b}\overline{\mathrm{b}}\mathrm{b}\overline{\mathrm{b}} $ decay channel. The topology of VHH production when all Higgs bosons decay to b jets and the vector boson is either a Z boson that decays into two leptons (lower left) or a W boson decaying into a lepton and a neutrino, giving missing transverse momentum (lower right). |
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Figure 5-b:
Illustrations of the resolved (upper left) and boosted (upper right) topologies of the $ \mathrm{b}\overline{\mathrm{b}}\mathrm{b}\overline{\mathrm{b}} $ decay channel. The topology of VHH production when all Higgs bosons decay to b jets and the vector boson is either a Z boson that decays into two leptons (lower left) or a W boson decaying into a lepton and a neutrino, giving missing transverse momentum (lower right). |
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Figure 5-c:
Illustrations of the resolved (upper left) and boosted (upper right) topologies of the $ \mathrm{b}\overline{\mathrm{b}}\mathrm{b}\overline{\mathrm{b}} $ decay channel. The topology of VHH production when all Higgs bosons decay to b jets and the vector boson is either a Z boson that decays into two leptons (lower left) or a W boson decaying into a lepton and a neutrino, giving missing transverse momentum (lower right). |
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Figure 5-d:
Illustrations of the resolved (upper left) and boosted (upper right) topologies of the $ \mathrm{b}\overline{\mathrm{b}}\mathrm{b}\overline{\mathrm{b}} $ decay channel. The topology of VHH production when all Higgs bosons decay to b jets and the vector boson is either a Z boson that decays into two leptons (lower left) or a W boson decaying into a lepton and a neutrino, giving missing transverse momentum (lower right). |
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Figure 6:
Illustrations of the resolved topology of the $ \mathrm{b}\overline{\mathrm{b}}\mathrm{W}\mathrm{W} $ decay channel in the final state with two leptons (upper left) and one lepton (upper right). The boosted topology of the fully hadronic $ \mathrm{b}\overline{\mathrm{b}}\mathrm{W}\mathrm{W} $ decay channel (lower). |
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Figure 6-a:
Illustrations of the resolved topology of the $ \mathrm{b}\overline{\mathrm{b}}\mathrm{W}\mathrm{W} $ decay channel in the final state with two leptons (upper left) and one lepton (upper right). The boosted topology of the fully hadronic $ \mathrm{b}\overline{\mathrm{b}}\mathrm{W}\mathrm{W} $ decay channel (lower). |
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Figure 6-b:
Illustrations of the resolved topology of the $ \mathrm{b}\overline{\mathrm{b}}\mathrm{W}\mathrm{W} $ decay channel in the final state with two leptons (upper left) and one lepton (upper right). The boosted topology of the fully hadronic $ \mathrm{b}\overline{\mathrm{b}}\mathrm{W}\mathrm{W} $ decay channel (lower). |
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Figure 6-c:
Illustrations of the resolved topology of the $ \mathrm{b}\overline{\mathrm{b}}\mathrm{W}\mathrm{W} $ decay channel in the final state with two leptons (upper left) and one lepton (upper right). The boosted topology of the fully hadronic $ \mathrm{b}\overline{\mathrm{b}}\mathrm{W}\mathrm{W} $ decay channel (lower). |
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Figure 7:
Distributions of the $ m_\text{reg}^{\mathrm{b}\overline{\mathrm{b}}} $ observable in the ggF (left) and VBF (right) signal regions of the all-hadronic $ \mathrm{b}\overline{\mathrm{b}}\mathrm{W}\mathrm{W} $ search, after a maximum likelihood fit of the background and SM HH signal to the data. |
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Figure 7-a:
Distributions of the $ m_\text{reg}^{\mathrm{b}\overline{\mathrm{b}}} $ observable in the ggF (left) and VBF (right) signal regions of the all-hadronic $ \mathrm{b}\overline{\mathrm{b}}\mathrm{W}\mathrm{W} $ search, after a maximum likelihood fit of the background and SM HH signal to the data. |
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Figure 7-b:
Distributions of the $ m_\text{reg}^{\mathrm{b}\overline{\mathrm{b}}} $ observable in the ggF (left) and VBF (right) signal regions of the all-hadronic $ \mathrm{b}\overline{\mathrm{b}}\mathrm{W}\mathrm{W} $ search, after a maximum likelihood fit of the background and SM HH signal to the data. |
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Figure 8:
The distributions of DNN scores for the signal and main backgrounds in the 1\ell (upper left) and fully hadronic (upper right) channels of the $ \mathrm{W}\mathrm{W}\gamma\gamma $ analysis. The signal-plus-background (red), single H plus continuum background (blue), and continuum background (dashed black) fits for all channels weighted by $ S/(S+B) $ (lower). |
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Figure 8-a:
The distributions of DNN scores for the signal and main backgrounds in the 1\ell (upper left) and fully hadronic (upper right) channels of the $ \mathrm{W}\mathrm{W}\gamma\gamma $ analysis. The signal-plus-background (red), single H plus continuum background (blue), and continuum background (dashed black) fits for all channels weighted by $ S/(S+B) $ (lower). |
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Figure 8-b:
The distributions of DNN scores for the signal and main backgrounds in the 1\ell (upper left) and fully hadronic (upper right) channels of the $ \mathrm{W}\mathrm{W}\gamma\gamma $ analysis. The signal-plus-background (red), single H plus continuum background (blue), and continuum background (dashed black) fits for all channels weighted by $ S/(S+B) $ (lower). |
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Figure 8-c:
The distributions of DNN scores for the signal and main backgrounds in the 1\ell (upper left) and fully hadronic (upper right) channels of the $ \mathrm{W}\mathrm{W}\gamma\gamma $ analysis. The signal-plus-background (red), single H plus continuum background (blue), and continuum background (dashed black) fits for all channels weighted by $ S/(S+B) $ (lower). |
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Figure 9:
The upper limits at 95% CL on the inclusive signal strength $ \mu = \sigma_{\mathrm{H}\mathrm{H}} /\sigma_{\mathrm{H}\mathrm{H}} ^\text{SM} $ for each channel and their combination. The inner (green) and outer (yellow) bands indicate the 68 and 95% CL intervals, respectively, under the background-only hypothesis. The individual contributions within the $ \mathrm{b}\overline{\mathrm{b}}\mathrm{b}\overline{\mathrm{b}} $ and $ \mathrm{b}\overline{\mathrm{b}}\mathrm{W}\mathrm{W} $ channels have been combined in order to simplify the presentation of results. |
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Figure 10:
The upper limits at 95% CL on the VBF signal strength $ \mu_{\text{VBF} {\mathrm{H}\mathrm{H}}} = \sigma_{\text{VBF} \mathrm{H}\mathrm{H}} /\sigma_{\text{VBF} \mathrm{H}\mathrm{H}} ^\text{SM} $ for each channel and their combination. The inner (green) and outer (yellow) bands indicate the 68 and 95% CL intervals, respectively, under the background-only hypothesis. The five contributing channels are indicated in the figure. The individual contributions within the $ \mathrm{b}\overline{\mathrm{b}}\mathrm{b}\overline{\mathrm{b}} $ and $ \mathrm{b}\overline{\mathrm{b}}\mathrm{W}\mathrm{W} $ channels have been combined in order to simplify the presentation of results. |
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Figure 11:
The $ -2\Delta\ln(L) $ scan as functions of coupling modifiers $ \kappa_\lambda $ (left) and $ \kappa_{2\mathrm{V}} $ (right) for the combination of all channels when all the other parameters are fixed to their SM values. |
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Figure 11-a:
The $ -2\Delta\ln(L) $ scan as functions of coupling modifiers $ \kappa_\lambda $ (left) and $ \kappa_{2\mathrm{V}} $ (right) for the combination of all channels when all the other parameters are fixed to their SM values. |
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Figure 11-b:
The $ -2\Delta\ln(L) $ scan as functions of coupling modifiers $ \kappa_\lambda $ (left) and $ \kappa_{2\mathrm{V}} $ (right) for the combination of all channels when all the other parameters are fixed to their SM values. |
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Figure 12:
The 95% CL upper limits on the inclusive HH cross section as functions of $ \kappa_\lambda $ (left) and $ \kappa_{2\mathrm{V}} $ (right). All other couplings are set to the values predicted by the SM. The theoretical uncertainties in the ggF and VBFHH signal cross sections are not considered because here we directly constrain the measured cross section. The inner (green) band and the outer (yellow) band indicate the 68 and 95% CL intervals, respectively, under the background-only hypothesis. The star shows the limit at the SM value for $ \kappa_\lambda $ and $ \kappa_{2\mathrm{V}} $. |
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Figure 12-a:
The 95% CL upper limits on the inclusive HH cross section as functions of $ \kappa_\lambda $ (left) and $ \kappa_{2\mathrm{V}} $ (right). All other couplings are set to the values predicted by the SM. The theoretical uncertainties in the ggF and VBFHH signal cross sections are not considered because here we directly constrain the measured cross section. The inner (green) band and the outer (yellow) band indicate the 68 and 95% CL intervals, respectively, under the background-only hypothesis. The star shows the limit at the SM value for $ \kappa_\lambda $ and $ \kappa_{2\mathrm{V}} $. |
png pdf |
Figure 12-b:
The 95% CL upper limits on the inclusive HH cross section as functions of $ \kappa_\lambda $ (left) and $ \kappa_{2\mathrm{V}} $ (right). All other couplings are set to the values predicted by the SM. The theoretical uncertainties in the ggF and VBFHH signal cross sections are not considered because here we directly constrain the measured cross section. The inner (green) band and the outer (yellow) band indicate the 68 and 95% CL intervals, respectively, under the background-only hypothesis. The star shows the limit at the SM value for $ \kappa_\lambda $ and $ \kappa_{2\mathrm{V}} $. |
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Figure 13:
The 68 and 95% CL contours of $ -2\Delta\ln(L) $ in the ($ \kappa_\lambda $, $ \kappa_{2\mathrm{V}} $) (upper left), ($ \kappa_\mathrm{V} $, $ \kappa_{2\mathrm{V}} $) (upper right), and ($ \kappa_\lambda $, $ \kappa_{\mathrm{t}} $) (lower) planes for the combination of all channels when all the other parameters are fixed to their SM values. In the ($ \kappa_\lambda $, $ \kappa_{2\mathrm{V}} $) and ($ \kappa_\mathrm{V} $, $ \kappa_{2\mathrm{V}} $) planes, the 5 standard deviation CL contours are also shown. |
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Figure 13-a:
The 68 and 95% CL contours of $ -2\Delta\ln(L) $ in the ($ \kappa_\lambda $, $ \kappa_{2\mathrm{V}} $) (upper left), ($ \kappa_\mathrm{V} $, $ \kappa_{2\mathrm{V}} $) (upper right), and ($ \kappa_\lambda $, $ \kappa_{\mathrm{t}} $) (lower) planes for the combination of all channels when all the other parameters are fixed to their SM values. In the ($ \kappa_\lambda $, $ \kappa_{2\mathrm{V}} $) and ($ \kappa_\mathrm{V} $, $ \kappa_{2\mathrm{V}} $) planes, the 5 standard deviation CL contours are also shown. |
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Figure 13-b:
The 68 and 95% CL contours of $ -2\Delta\ln(L) $ in the ($ \kappa_\lambda $, $ \kappa_{2\mathrm{V}} $) (upper left), ($ \kappa_\mathrm{V} $, $ \kappa_{2\mathrm{V}} $) (upper right), and ($ \kappa_\lambda $, $ \kappa_{\mathrm{t}} $) (lower) planes for the combination of all channels when all the other parameters are fixed to their SM values. In the ($ \kappa_\lambda $, $ \kappa_{2\mathrm{V}} $) and ($ \kappa_\mathrm{V} $, $ \kappa_{2\mathrm{V}} $) planes, the 5 standard deviation CL contours are also shown. |
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Figure 13-c:
The 68 and 95% CL contours of $ -2\Delta\ln(L) $ in the ($ \kappa_\lambda $, $ \kappa_{2\mathrm{V}} $) (upper left), ($ \kappa_\mathrm{V} $, $ \kappa_{2\mathrm{V}} $) (upper right), and ($ \kappa_\lambda $, $ \kappa_{\mathrm{t}} $) (lower) planes for the combination of all channels when all the other parameters are fixed to their SM values. In the ($ \kappa_\lambda $, $ \kappa_{2\mathrm{V}} $) and ($ \kappa_\mathrm{V} $, $ \kappa_{2\mathrm{V}} $) planes, the 5 standard deviation CL contours are also shown. |
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Figure 14:
The upper limits at 95% CL on the HH production cross section for the two sets of HEFT benchmarks. The theoretical uncertainties in the ggFHH signal cross section are not considered because we directly constrain the measured cross section. |
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Figure 15:
The upper limits at 95% CL on the HH cross section as a function of the $ \text{c}_2 $ coupling modifier (left). The theoretical uncertainties in the ggFHH signal cross section are not considered because we directly constrain the measured cross section. The $ -2\Delta\ln(L) $ scan as a function of the $ \text{c}_2 $ coupling modifier (right). |
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Figure 15-a:
The upper limits at 95% CL on the HH cross section as a function of the $ \text{c}_2 $ coupling modifier (left). The theoretical uncertainties in the ggFHH signal cross section are not considered because we directly constrain the measured cross section. The $ -2\Delta\ln(L) $ scan as a function of the $ \text{c}_2 $ coupling modifier (right). |
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Figure 15-b:
The upper limits at 95% CL on the HH cross section as a function of the $ \text{c}_2 $ coupling modifier (left). The theoretical uncertainties in the ggFHH signal cross section are not considered because we directly constrain the measured cross section. The $ -2\Delta\ln(L) $ scan as a function of the $ \text{c}_2 $ coupling modifier (right). |
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Figure 16:
The 68 and 95% CL contours of $ -2\Delta\ln(L) $ in the (c}_2, \kappa_{\mathrm{t}) (left) and $ (\text{c}_2, \kappa_\lambda) $ (right) planes for the combination of all channels when all the other parameters are fixed to their SM values. |
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Figure 16-a:
The 68 and 95% CL contours of $ -2\Delta\ln(L) $ in the (c}_2, \kappa_{\mathrm{t}) (left) and $ (\text{c}_2, \kappa_\lambda) $ (right) planes for the combination of all channels when all the other parameters are fixed to their SM values. |
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Figure 16-b:
The 68 and 95% CL contours of $ -2\Delta\ln(L) $ in the (c}_2, \kappa_{\mathrm{t}) (left) and $ (\text{c}_2, \kappa_\lambda) $ (right) planes for the combination of all channels when all the other parameters are fixed to their SM values. |
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Figure 17:
The $ -2\Delta\ln(L) $ scan for the combination of all channels as a function of $ |\cos{\alpha}| $ for singlet extensions of the SM with spontaneous $ Z_2 $ symmetry breaking (left). The $ |\cos{\alpha}| $ is constrained at 95% CL between 0.79 and 1. The 95% CL contour of $ -2\Delta\ln(L) $ in the ($ |\cos{\alpha}| $, $ \lambda_\text{eff} $) plane (right), where $ \lambda_\text{eff}=\lambda_\alpha-\tan{(\alpha)\frac{m_{2}}{\nu}} $ The ranges of $ |\cos{\alpha}| $ and $ \lambda_\text{eff} $ are chosen to guarantee the validity of the models. The excluded regions are below and to the left of the curves shown. |
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Figure 17-a:
The $ -2\Delta\ln(L) $ scan for the combination of all channels as a function of $ |\cos{\alpha}| $ for singlet extensions of the SM with spontaneous $ Z_2 $ symmetry breaking (left). The $ |\cos{\alpha}| $ is constrained at 95% CL between 0.79 and 1. The 95% CL contour of $ -2\Delta\ln(L) $ in the ($ |\cos{\alpha}| $, $ \lambda_\text{eff} $) plane (right), where $ \lambda_\text{eff}=\lambda_\alpha-\tan{(\alpha)\frac{m_{2}}{\nu}} $ The ranges of $ |\cos{\alpha}| $ and $ \lambda_\text{eff} $ are chosen to guarantee the validity of the models. The excluded regions are below and to the left of the curves shown. |
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Figure 17-b:
The $ -2\Delta\ln(L) $ scan for the combination of all channels as a function of $ |\cos{\alpha}| $ for singlet extensions of the SM with spontaneous $ Z_2 $ symmetry breaking (left). The $ |\cos{\alpha}| $ is constrained at 95% CL between 0.79 and 1. The 95% CL contour of $ -2\Delta\ln(L) $ in the ($ |\cos{\alpha}| $, $ \lambda_\text{eff} $) plane (right), where $ \lambda_\text{eff}=\lambda_\alpha-\tan{(\alpha)\frac{m_{2}}{\nu}} $ The ranges of $ |\cos{\alpha}| $ and $ \lambda_\text{eff} $ are chosen to guarantee the validity of the models. The excluded regions are below and to the left of the curves shown. |
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Figure 18:
The 95% CL contour of $ -2\Delta\ln(L) $ for the combination of all channels in the ($ m_{\mathrm{H}} $, $ \tan\beta $) plane for a fixed value of $ |\cos(\beta-\alpha)|= $ 0.2 in the 2HDM-I model (left) and the four considered 2HDM models (right). In these and all other cases considered in this paper, $ m_{\mathrm{H}}=m_{\mathrm{A}} $. The ranges of $ m_{\mathrm{H}} $ and $ \tan\beta $ are chosen to guarantee the validity of the models. The excluded regions are below the curves shown. The value $ \tan\beta= $ 0.5 is excluded for $ m_{\mathrm{H}} > $ 800 GeV for all models considered. |
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Figure 18-a:
The 95% CL contour of $ -2\Delta\ln(L) $ for the combination of all channels in the ($ m_{\mathrm{H}} $, $ \tan\beta $) plane for a fixed value of $ |\cos(\beta-\alpha)|= $ 0.2 in the 2HDM-I model (left) and the four considered 2HDM models (right). In these and all other cases considered in this paper, $ m_{\mathrm{H}}=m_{\mathrm{A}} $. The ranges of $ m_{\mathrm{H}} $ and $ \tan\beta $ are chosen to guarantee the validity of the models. The excluded regions are below the curves shown. The value $ \tan\beta= $ 0.5 is excluded for $ m_{\mathrm{H}} > $ 800 GeV for all models considered. |
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Figure 18-b:
The 95% CL contour of $ -2\Delta\ln(L) $ for the combination of all channels in the ($ m_{\mathrm{H}} $, $ \tan\beta $) plane for a fixed value of $ |\cos(\beta-\alpha)|= $ 0.2 in the 2HDM-I model (left) and the four considered 2HDM models (right). In these and all other cases considered in this paper, $ m_{\mathrm{H}}=m_{\mathrm{A}} $. The ranges of $ m_{\mathrm{H}} $ and $ \tan\beta $ are chosen to guarantee the validity of the models. The excluded regions are below the curves shown. The value $ \tan\beta= $ 0.5 is excluded for $ m_{\mathrm{H}} > $ 800 GeV for all models considered. |
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Figure 19:
The 95% CL contour of $ -2\Delta\ln(L) $ for the combination of all channels in the ($ \cos(\beta-\alpha) $, $ \tan\beta $) plane for a fixed value of $ m_{\mathrm{H}}= $ 1000 GeV in the 2HDM-I model (left) and the four considered 2HDM models (right). In these and all other cases considered in this paper, $ m_{\mathrm{H}}=m_{\mathrm{A}} $. The ranges of $ \cos(\beta-\alpha) $ and $ \tan\beta $ are chosen to guarantee the validity of the model. The excluded regions are below the curves shown. The value $ \tan\beta= $ 0.5 is excluded for $ \cos(\beta-\alpha) > $ 0.16 and $ \cos(\beta-\alpha) < - $ 0.13 for all models considered. |
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Figure 19-a:
The 95% CL contour of $ -2\Delta\ln(L) $ for the combination of all channels in the ($ \cos(\beta-\alpha) $, $ \tan\beta $) plane for a fixed value of $ m_{\mathrm{H}}= $ 1000 GeV in the 2HDM-I model (left) and the four considered 2HDM models (right). In these and all other cases considered in this paper, $ m_{\mathrm{H}}=m_{\mathrm{A}} $. The ranges of $ \cos(\beta-\alpha) $ and $ \tan\beta $ are chosen to guarantee the validity of the model. The excluded regions are below the curves shown. The value $ \tan\beta= $ 0.5 is excluded for $ \cos(\beta-\alpha) > $ 0.16 and $ \cos(\beta-\alpha) < - $ 0.13 for all models considered. |
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Figure 19-b:
The 95% CL contour of $ -2\Delta\ln(L) $ for the combination of all channels in the ($ \cos(\beta-\alpha) $, $ \tan\beta $) plane for a fixed value of $ m_{\mathrm{H}}= $ 1000 GeV in the 2HDM-I model (left) and the four considered 2HDM models (right). In these and all other cases considered in this paper, $ m_{\mathrm{H}}=m_{\mathrm{A}} $. The ranges of $ \cos(\beta-\alpha) $ and $ \tan\beta $ are chosen to guarantee the validity of the model. The excluded regions are below the curves shown. The value $ \tan\beta= $ 0.5 is excluded for $ \cos(\beta-\alpha) > $ 0.16 and $ \cos(\beta-\alpha) < - $ 0.13 for all models considered. |
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Figure 20:
The $ -2\Delta\ln(L) $ scan for the combination of all channels as a function of $ \xi $ for MCHM$ _4 $ (left) and MCHM$ _5 $ (right). The range of $ \xi $ is chosen to guarantee the validity of the model. At 95% CL, $ \xi $ is constrained to be between 0 and 0.45 in MCHM$ _4 $ and 0 and 0.26 in MCHM$ _5 $. |
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Figure 20-a:
The $ -2\Delta\ln(L) $ scan for the combination of all channels as a function of $ \xi $ for MCHM$ _4 $ (left) and MCHM$ _5 $ (right). The range of $ \xi $ is chosen to guarantee the validity of the model. At 95% CL, $ \xi $ is constrained to be between 0 and 0.45 in MCHM$ _4 $ and 0 and 0.26 in MCHM$ _5 $. |
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Figure 20-b:
The $ -2\Delta\ln(L) $ scan for the combination of all channels as a function of $ \xi $ for MCHM$ _4 $ (left) and MCHM$ _5 $ (right). The range of $ \xi $ is chosen to guarantee the validity of the model. At 95% CL, $ \xi $ is constrained to be between 0 and 0.45 in MCHM$ _4 $ and 0 and 0.26 in MCHM$ _5 $. |
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Figure 21:
The expected upper limits at 95% CL on the HH signal strength from the combination of all the considered channels projected to different integrated luminosities (left), and under different assumptions on the systematic uncertainties for an integrated luminosity of 3000 fb$ ^{-1} $ (right). |
png pdf |
Figure 21-a:
The expected upper limits at 95% CL on the HH signal strength from the combination of all the considered channels projected to different integrated luminosities (left), and under different assumptions on the systematic uncertainties for an integrated luminosity of 3000 fb$ ^{-1} $ (right). |
png pdf |
Figure 21-b:
The expected upper limits at 95% CL on the HH signal strength from the combination of all the considered channels projected to different integrated luminosities (left), and under different assumptions on the systematic uncertainties for an integrated luminosity of 3000 fb$ ^{-1} $ (right). |
png pdf |
Figure 22:
The expected $ -2\Delta\ln(L) $ scan as a function of coupling modifier $ \kappa_\lambda $ for the combination of all contributing channels, projected to different integrated luminosities (left), and under different assumptions on the systematic uncertainties for an integrated luminosity of 3000 fb$ ^{-1} $ (right). All other parameters are fixed to their SM values. |
png pdf |
Figure 22-a:
The expected $ -2\Delta\ln(L) $ scan as a function of coupling modifier $ \kappa_\lambda $ for the combination of all contributing channels, projected to different integrated luminosities (left), and under different assumptions on the systematic uncertainties for an integrated luminosity of 3000 fb$ ^{-1} $ (right). All other parameters are fixed to their SM values. |
png pdf |
Figure 22-b:
The expected $ -2\Delta\ln(L) $ scan as a function of coupling modifier $ \kappa_\lambda $ for the combination of all contributing channels, projected to different integrated luminosities (left), and under different assumptions on the systematic uncertainties for an integrated luminosity of 3000 fb$ ^{-1} $ (right). All other parameters are fixed to their SM values. |
png pdf |
Figure 23:
The expected signal significance as a function of integrated luminosity for the nominal systematic uncertainty scenario S2 and for the scenario with statistical uncertainties only (left). The expected signal significance as a function of $ \kappa_\lambda $ under different assumptions on the systematic uncertainties for an integrated luminosity of 3000 fb$ ^{-1} $ (right). |
png pdf |
Figure 23-a:
The expected signal significance as a function of integrated luminosity for the nominal systematic uncertainty scenario S2 and for the scenario with statistical uncertainties only (left). The expected signal significance as a function of $ \kappa_\lambda $ under different assumptions on the systematic uncertainties for an integrated luminosity of 3000 fb$ ^{-1} $ (right). |
png pdf |
Figure 23-b:
The expected signal significance as a function of integrated luminosity for the nominal systematic uncertainty scenario S2 and for the scenario with statistical uncertainties only (left). The expected signal significance as a function of $ \kappa_\lambda $ under different assumptions on the systematic uncertainties for an integrated luminosity of 3000 fb$ ^{-1} $ (right). |
png pdf |
Figure A1:
The 95% CL upper limits on the inclusive HH signal strength as functions of $ \kappa_\lambda $ (left) and $ \kappa_{2\mathrm{V}} $ (right). All other couplings are set to the values predicted by the SM. The theoretical uncertainties in the HH ggF and VBF signal cross sections are considered in this case. The inner (green) band and the outer (yellow) band indicate the 68 and 95% CL intervals, respectively, under the background-only hypothesis. |
png pdf |
Figure A1-a:
The 95% CL upper limits on the inclusive HH signal strength as functions of $ \kappa_\lambda $ (left) and $ \kappa_{2\mathrm{V}} $ (right). All other couplings are set to the values predicted by the SM. The theoretical uncertainties in the HH ggF and VBF signal cross sections are considered in this case. The inner (green) band and the outer (yellow) band indicate the 68 and 95% CL intervals, respectively, under the background-only hypothesis. |
png pdf |
Figure A1-b:
The 95% CL upper limits on the inclusive HH signal strength as functions of $ \kappa_\lambda $ (left) and $ \kappa_{2\mathrm{V}} $ (right). All other couplings are set to the values predicted by the SM. The theoretical uncertainties in the HH ggF and VBF signal cross sections are considered in this case. The inner (green) band and the outer (yellow) band indicate the 68 and 95% CL intervals, respectively, under the background-only hypothesis. |
png pdf |
Figure A2:
The $ -2\Delta\ln(L) $ scan as functions of $ \kappa_\lambda $ (left) and $ \kappa_{2\mathrm{V}} $ (right) for all channels, when all the other parameters are fixed to their SM value. |
png pdf |
Figure A2-a:
The $ -2\Delta\ln(L) $ scan as functions of $ \kappa_\lambda $ (left) and $ \kappa_{2\mathrm{V}} $ (right) for all channels, when all the other parameters are fixed to their SM value. |
png pdf |
Figure A2-b:
The $ -2\Delta\ln(L) $ scan as functions of $ \kappa_\lambda $ (left) and $ \kappa_{2\mathrm{V}} $ (right) for all channels, when all the other parameters are fixed to their SM value. |
png pdf |
Figure A3:
The expected $ -2\Delta\ln(L) $ scan as a function of coupling modifier $ \kappa_\lambda $ for all channels and an integrated luminosity of 3000 fb$ ^{-1} $. All the other parameters are fixed to their SM values. |
png pdf |
Figure A4:
The 95% CL upper limits on the inclusive (left) and VBF (right) HH cross section as functions of $ \kappa_\lambda $ and $ \kappa_{2\mathrm{V}} $, respectively, for all channels. All other couplings are set to the values predicted by the SM. The theoretical uncertainties in the HH ggF and VBF signal cross sections are not considered because we directly constrain the measured cross section. |
png pdf |
Figure A4-a:
The 95% CL upper limits on the inclusive (left) and VBF (right) HH cross section as functions of $ \kappa_\lambda $ and $ \kappa_{2\mathrm{V}} $, respectively, for all channels. All other couplings are set to the values predicted by the SM. The theoretical uncertainties in the HH ggF and VBF signal cross sections are not considered because we directly constrain the measured cross section. |
png pdf |
Figure A4-b:
The 95% CL upper limits on the inclusive (left) and VBF (right) HH cross section as functions of $ \kappa_\lambda $ and $ \kappa_{2\mathrm{V}} $, respectively, for all channels. All other couplings are set to the values predicted by the SM. The theoretical uncertainties in the HH ggF and VBF signal cross sections are not considered because we directly constrain the measured cross section. |
png pdf |
Figure A5:
The 95% CL upper limits on the inclusive (left) and VBF (right) HH signal strength as functions of $ \kappa_\lambda $ and $ \kappa_{2\mathrm{V}} $, respectively, for all channels. All other couplings are set to the values predicted by the SM. The theoretical uncertainties in the HH ggF and VBF signal cross sections are considered in this case. |
png pdf |
Figure A5-a:
The 95% CL upper limits on the inclusive (left) and VBF (right) HH signal strength as functions of $ \kappa_\lambda $ and $ \kappa_{2\mathrm{V}} $, respectively, for all channels. All other couplings are set to the values predicted by the SM. The theoretical uncertainties in the HH ggF and VBF signal cross sections are considered in this case. |
png pdf |
Figure A5-b:
The 95% CL upper limits on the inclusive (left) and VBF (right) HH signal strength as functions of $ \kappa_\lambda $ and $ \kappa_{2\mathrm{V}} $, respectively, for all channels. All other couplings are set to the values predicted by the SM. The theoretical uncertainties in the HH ggF and VBF signal cross sections are considered in this case. |
png pdf |
Figure A6:
The best fit value for $ \kappa_\lambda $ (left) and $ \kappa_{2\mathrm{V}} $ (right) compared to the SM expectation for all channels and their combination, when all the other parameters are fixed to their SM values. |
png pdf |
Figure A6-a:
The best fit value for $ \kappa_\lambda $ (left) and $ \kappa_{2\mathrm{V}} $ (right) compared to the SM expectation for all channels and their combination, when all the other parameters are fixed to their SM values. |
png pdf |
Figure A6-b:
The best fit value for $ \kappa_\lambda $ (left) and $ \kappa_{2\mathrm{V}} $ (right) compared to the SM expectation for all channels and their combination, when all the other parameters are fixed to their SM values. |
png pdf |
Figure A7:
The 68%, 95%, and 5 standard deviation contours of $ -2\Delta\ln(L) $ in the ($ \kappa_\mathrm{V} $, $ \kappa_{2\mathrm{V}} $) plane for the combination of all channels when all the other parameters are fixed to their SM values. |
png pdf |
Figure A8:
The 95% CL upper limits on the inclusive HH signal strength as a function of the $ \text{c}_2 $ coupling modifier. All other couplings are set to the values predicted by the SM. The theoretical uncertainties in the ggFHH signal cross sections are considered in this case. The inner (green) band and the outer (yellow) band indicate the 68 and 95% CL intervals, respectively, under the background-only hypothesis. |
png pdf |
Figure A9:
The $ -2\Delta\ln(L) $ scan as a function of the $ \text{c}_2 $ coupling modifier for all channels, when all the other parameters are fixed to their SM values. |
png pdf |
Figure A10:
The 95% CL upper limits on the inclusive HH cross section as a function of the $ \text{c}_2 $ coupling modifier for all channels. All other couplings are set to the values predicted by the SM. The theoretical uncertainties in the HH ggF signal cross sections are not considered because we directly constrain the measured cross section. |
png pdf |
Figure A11:
The 95% CL upper limits on the HH signal strength as a function of the $ \text{c}_2 $ coupling modifier for all channels. All other couplings are set to the values predicted by the SM. The theoretical uncertainties in the ggFHH signal cross sections are considered in this case. |
png pdf |
Figure A12:
The best fit value for the $ \text{c}_2 $ coupling modifier compared to the SM expectation for all channels and their combination, when all the other parameters are fixed to their SM values. |
png pdf |
Figure A13:
The observed 68 and 95% CL contours of $ -2\Delta\ln(L) $ in the ($ \text{c}_2 $, $ \kappa_{\mathrm{t}} $) plane for the combination of all channels when $ \kappa_\lambda $ is allowed to vary. The range of $ \kappa_\lambda $ is set between-15 and 15 to avoid unphysical areas of the phase space. All the other parameters are fixed to their SM values. |
png pdf |
Figure A14:
The observed 68 and 95% CL contours of $ -2\Delta\ln(L) $ in the ($ \text{c}_2 $, $ \kappa_\lambda $) plane for the combination of all channels when $ \kappa_{\mathrm{t}} $ is allowed to vary. The range of $ \kappa_{\mathrm{t}} $ is set between 0.5 and 1.5 to avoid unphysical areas of the phase space. All the other parameters are fixed to their SM values. |
png pdf |
Figure A15:
The observed 68% CL contours of $ -2\Delta\ln(L) $ in the ($ \text{c}_2 $, $ \kappa_\lambda $) plane for all channels when all the other parameters are fixed to their SM value. The best fit value and 68% CL contour for the $ \mathrm{b}\overline{\mathrm{b}}\tau\tau $ channel are not within the range of the figure. |
png pdf |
Figure A16:
A bar chart showing the fraction of all HH events that are selected in each analysis. The numbers shown, correspond to the total of selected events per analysis. The results are calculated inclusively and per production mode. |
png pdf |
Figure A17:
A bar chart showing the selection efficiency for the HH signal per channel. The number of selected events per channel is also shown. |
| Tables | |
png pdf |
Table 1:
Values of the effective Lagrangian couplings for the Higgs effective field theory benchmarks proposed in Ref. [50] and referred to in this paper as JHEP04(2016)126. |
png pdf |
Table 2:
Values of the effective Lagrangian couplings for the Higgs effective field theory benchmarks proposed in Ref. [51] and referred to in this paper as JHEP03(2020)091. |
png pdf |
Table 3:
Summary of results for the HH analyses included in this combination. The second column is the observed (expected) 95% CL upper limit on the inclusive signal strength $ \mu= \sigma_{\mathrm{H}\mathrm{H}} /\sigma_{\mathrm{H}\mathrm{H}} ^\text{SM} $, with one exception where $ \mu_{\mathrm{V}\mathrm{H}\mathrm{H}}= \sigma_{\mathrm{V}\mathrm{H}\mathrm{H}}/\sigma_{\mathrm{V}\mathrm{H}\mathrm{H}}^\text{SM} $ is shown. The third (fourth) column is the allowed 68% CL interval for the coupling modifier $ \kappa_\lambda $ ($ \kappa_{2\mathrm{V}} $). The last column indicates whether the analysis is included in the results using the HEFT parametrisation. |
png pdf |
Table 4:
Summary of results on constraints to the coupling modifiers $ \kappa_\lambda $ and $ \kappa_{2\mathrm{V}} $. The ranges are either extracted using either the $ -2\Delta\ln(L) $ scan at 68% and 95% CL, or upper limits on the signal strength $ \mu $ at 95% CL. The theoretical uncertainties in the ggF and VBFHH signal cross sections are considered in all results tabulated here. |
png pdf |
Table 5:
Treatment of most important common systematic uncertainties in the S2 scenario. |
png pdf |
Table 6:
Expected significance for the HH signal projected to 2000 or 3000 fb$ ^{-1} $ under different assumptions of systematic uncertainties. |
png pdf |
Table A1:
Upper limits on the HH production cross section at 95% CL for the JHEP03(2020)91 BM1 benchmark. The theoretical uncertainties in the ggFHH signal cross section are not considered because we directly constrain the measured cross section. |
png pdf |
Table A2:
Upper limits on the HH production cross section at 95% CL for the JHEP03(2020)91 BM2 benchmark. The theoretical uncertainties in the HH ggF signal cross section are not considered because we directly constrain the measured cross section. |
png pdf |
Table A3:
Upper limits on the HH production cross section at 95% CL for the JHEP03(2020)91 BM3 benchmark. The theoretical uncertainties in the ggFHH signal cross section are not considered because we directly constrain the measured cross section. |
png pdf |
Table A4:
Upper limits on the HH production cross section at 95% CL for the JHEP03(2020)91 BM4 benchmark. The theoretical uncertainties in the ggFHH signal cross section are not considered because we directly constrain the measured cross section. |
png pdf |
Table A5:
Upper limits on the HH production cross section at 95% CL for the JHEP03(2020)91 BM5 benchmark. The theoretical uncertainties in the ggFHH signal cross section are not considered because we directly constrain the measured cross section. |
png pdf |
Table A6:
Upper limits on the HH production cross section at 95% CL for the JHEP03(2020)91 BM6 benchmark. The theoretical uncertainties in the HH ggF signal cross section are not considered because we directly constrain the measured cross section. |
png pdf |
Table A7:
Upper limits on the HH production cross section at 95% CL for the JHEP03(2020)91 BM7 benchmark. The theoretical uncertainties in the HH ggF signal cross section are not considered because we directly constrain the measured cross section. |
png pdf |
Table A8:
Upper limits on the HH production cross section at 95% CL for the JHEP04(2016)126 BM1 benchmark. The theoretical uncertainties in the HH ggF signal cross section are not considered because we directly constrain the measured cross section. |
png pdf |
Table A9:
Upper limits on the HH production cross section at 95% CL for the JHEP04(2016)126 BM2 benchmark. The theoretical uncertainties in the HH ggF signal cross section are not considered because we directly constrain the measured cross section. |
png pdf |
Table A10:
Upper limits on the HH production cross section at 95% CL for the JHEP04(2016)126 BM3 benchmark. The theoretical uncertainties in the HH ggF signal cross section are not considered because we directly constrain the measured cross section. |
png pdf |
Table A11:
Upper limits on the HH production cross section at 95% CL for the JHEP04(2016)126 BM4 benchmark. The theoretical uncertainties in the HH ggF signal cross section are not considered because we directly constrain the measured cross section. |
png pdf |
Table A12:
Upper limits on the HH production cross section at 95% CL for the JHEP04(2016)126 BM5 benchmark. The theoretical uncertainties in the HH ggF signal cross section are not considered because we directly constrain the measured cross section. |
png pdf |
Table A13:
Upper limits on the HH production cross section at 95% CL for the JHEP04(2016)126 BM6 benchmark. The theoretical uncertainties in the HH ggF signal cross section are not considered because we directly constrain the measured cross section. |
png pdf |
Table A14:
Upper limits on the HH production cross section at 95% CL for the JHEP04(2016)126 BM7 benchmark. The theoretical uncertainties in the HH ggF signal cross section are not considered because we directly constrain the measured cross section. |
png pdf |
Table A15:
Upper limits on the HH production cross section at 95% CL for the JHEP04(2016)126 BM8 benchmark. The theoretical uncertainties in the HH ggF signal cross section are not considered because we directly constrain the measured cross section. |
png pdf |
Table A16:
Upper limits on the HH production cross section at 95% CL for the JHEP04(2016)126 BM8a benchmark. The theoretical uncertainties in the HH ggF signal cross section are not considered because we directly constrain the measured cross section. |
png pdf |
Table A17:
Upper limits on the HH production cross section at 95% CL for the JHEP04(2016)126 BM9 benchmark. The theoretical uncertainties in the HH ggF signal cross section are not considered because we directly constrain the measured cross section. |
png pdf |
Table A18:
Upper limits on the HH production cross section at 95% CL for the JHEP04(2016)126 BM10 benchmark. The theoretical uncertainties in the HH ggF signal cross section are not considered because we directly constrain the measured cross section. |
png pdf |
Table A19:
Upper limits on the HH production cross section at 95% CL for the JHEP04(2016)126 BM11 benchmark. The theoretical uncertainties in the HH ggF signal cross section are not considered because we directly constrain the measured cross section. |
png pdf |
Table A20:
Upper limits on the HH production cross section at 95% CL for the JHEP04(2016)126 BM12 benchmark. The theoretical uncertainties in the HH ggF signal cross section are not considered because we directly constrain the measured cross section. |
| Summary |
| A combined search for nonresonant Higgs boson pair (HH) production was performed using the proton-proton collision data set produced by the LHC at $ \sqrt{s} = $ 13 TeV, and collected by the CMS experiment from 2016 to 2018 (Run 2), which corresponds to an integrated luminosity of 138 fb$ ^{-1} $. Searches for HH production via gluon-gluon (ggF) and vector boson fusion (VBF) production, were carried out in the $ \mathrm{b}\overline{\mathrm{b}}\gamma\gamma $, $ \mathrm{b}\overline{\mathrm{b}}\tau\tau $, $ \mathrm{b}\overline{\mathrm{b}}\mathrm{b}\overline{\mathrm{b}} $, $ \mathrm{b}\overline{\mathrm{b}}\mathrm{W}\mathrm{W} $, and multilepton channels. Additionally, searches for ggFHH production were conducted in the $ \mathrm{b}\overline{\mathrm{b}}\mathrm{Z}\mathrm{Z} $ (with both Z bosons decaying to leptons), $ \mathrm{W}\mathrm{W}\gamma\gamma $, and $ \tau\tau\gamma\gamma $ final states, which have clean signatures but relatively small branching fractions. We searched for the associated production mechanism with a vector boson in the $ \mathrm{b}\overline{\mathrm{b}}\mathrm{b}\overline{\mathrm{b}} $ final state, which has the largest branching fraction. The analyses of these channels were combined to probe the Higgs boson trilinear self-coupling and the quartic coupling between two vector bosons and two Higgs bosons ($ \mathrm{V}\mathrm{V}\mathrm{H}\mathrm{H} $), and to search for beyond the standard model (SM) physics scenarios in the Higgs effective field theory (HEFT) approach. The observed and expected upper limits at 95% confidence level (CL) on the cross section of ggFHH production were found to be 3.5 and 2.5 times the SM expectation, respectively. For VBF production, the observed and expected 95% CL upper limits are 79 and 91 times the SM expectation, respectively. When all other parameters are set to their SM values, we constrain the Higgs boson trilinear self-coupling modifier $ \kappa_\lambda $ in the range from $-$1.35 to 6.37 at 95% CL (expected 95% CL range is $-$2.24 to 7.89). Likewise, the $ \mathrm{V}\mathrm{V}\mathrm{H}\mathrm{H} $ coupling modifier $ \kappa_{2\mathrm{V}} $ is constrained in the range from 0.64 to 1.40 (0.62 to 1.41 expected). Two-dimensional measurements were also performed, including simultaneous measurements of $ \kappa_\lambda $ and $ \kappa_{2\mathrm{V}} $, $ \kappa_\lambda $ and the modifier of the Higgs boson coupling to the top quark ($ \kappa_{\mathrm{t}} $), and $ \kappa_{2\mathrm{V}} $ and the modifier of the Higgs boson coupling to vector bosons ($ \kappa_\mathrm{V} $). The results are in agreement with the SM predictions. Under the HEFT framework, the cross section of the nonresonant ggFHH pair production was parametrized as a function of anomalous couplings of the Higgs boson, involving the contact interactions between two Higgs and two top quarks, between two gluons and two Higgs bosons, and between two gluons and a Higgs boson. We performed searches for benchmark signals under different anomalous coupling scenarios and set upper limits on their cross sections at 95% CL. We exclude HH production at 95% CL when the coupling modifier of the contact interaction between two Higgs bosons and two top quarks is outside the range from $-$0.28 to 0.59 (expected 95% CL range is-0.17 to 0.47). The HEFT parametrisation is also exploited to study various ultraviolet complete models with an extended Higgs sector and set constraints on specific parameters. These results constitute the most stringent limits and constraints obtained from the searches for nonresonant HH production using the LHC Run-2 data set collected by the CMS experiment. Extrapolating our current results to the integrated luminosity anticipated of the High-Luminosity LHC, it is expected to see first evidence for HH production with $ \approx $2000 fb$ ^{-1} $ of data. |
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