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| CMS-PAS-HIG-20-011 | ||
| Combination of searches for nonresonant Higgs boson pair production in proton-proton collisions at $ \sqrt{s}= $ 13 TeV | ||
| CMS Collaboration | ||
| 2024-11-15 | ||
| Abstract: This note presents a comprehensive overview and statistical combination of searches for the nonresonant production of Higgs boson pairs (HH) using data from proton-proton collisions collected by the CMS experiment at the LHC from 2016 to 2018 at a centre-of-mass energy of 13 TeV, corresponding to a total integrated luminosity of 138 fb$ ^{-1} $. Upper limits at 95% confidence level are set on the rate of the HH production. The observed (expected) upper limit on the inclusive production cross section relative to the standard model expectation is found to be 3.5 (2.5). Assuming all other Higgs boson couplings are equal to their values in the standard model, we exclude HH production at 95% confidence level for values of the Higgs boson trilinear self-coupling modifier $ \kappa_{\lambda} $ outside the range between $-$1.39 and 7.02. Similarly, for the coupling modifier $ \kappa_{2\mathrm{V}} $ affecting the interaction between two vector bosons and two Higgs bosons, we exclude HH production for values outside the range between 0.62 and 1.42. This work also studies HH production in new physics scenarios, using the Higgs effective field theory parametrisation. An extrapolation of the results to the integrated luminosity expected after the high-luminosity upgrade of the LHC is also presented. | ||
| Links: CDS record (PDF) ; 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 standard model. 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 standard model. 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 standard model. 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 standard model. 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_{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 standard model. 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_{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 standard model. 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_{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 standard model. 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_{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 standard model. 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_{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 standard model. 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_{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 standard model. 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_{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 standard model. 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_{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 $ c_{2} $, $ c_{\mathrm{g}} $, and $ 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 $ c_{2} $, $ c_{\mathrm{g}} $, and $ 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 $ c_{2} $, $ c_{\mathrm{g}} $, and $ 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 $ c_{2} $, $ c_{\mathrm{g}} $, and $ c_{2\mathrm{g}} $. The Higgs boson trilinear self-coupling modifier is shown as $ \kappa_{\lambda} $. |
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Figure 5:
The 95% CL upper limits on the inclusive signal strength $ r = \sigma_{\mathrm{H}\mathrm{H}} /\sigma_{\mathrm{H}\mathrm{H}} ^\text{SM} $ for each channel and their combination. The inner (green) band and the outer (yellow) band indicate the 68 and 95% CL intervals, respectively, under the background-only hypothesis. The $ \mathrm{b}\overline{\mathrm{b}}\mathrm{b}\overline{\mathrm{b}} $ and $ \mathrm{b}\overline{\mathrm{b}}\mathrm{W}\mathrm{W} $ contributions have been combined in order to simplify the presentation of results. |
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Figure 6:
The 95% CL upper limits on the VBF signal strength $ r_{{\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) band and the outer (yellow) band indicate the 68 and 95% CL intervals, respectively, under the background-only hypothesis. Not all of the eight channels are used to extract the combined VBF limit. The contributing channels are indicated in the figure. The $ \mathrm{b}\overline{\mathrm{b}}\mathrm{b}\overline{\mathrm{b}} $ and $ \mathrm{b}\overline{\mathrm{b}}\mathrm{W}\mathrm{W} $ contributions have been combined in order to simplify the presentation of results. |
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Figure 7:
The 95% CL upper limits on the inclusive HH cross section as a function of $ \kappa_{\lambda} $ (left) and $ \kappa_{2\mathrm{V}} $ (right), respectively. 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 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}} $, respectively. |
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Figure 7-a:
The 95% CL upper limits on the inclusive HH cross section as a function of $ \kappa_{\lambda} $ (left) and $ \kappa_{2\mathrm{V}} $ (right), respectively. 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 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}} $, respectively. |
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Figure 7-b:
The 95% CL upper limits on the inclusive HH cross section as a function of $ \kappa_{\lambda} $ (left) and $ \kappa_{2\mathrm{V}} $ (right), respectively. 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 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}} $, respectively. |
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Figure 8:
The profile likelihood ratio test statistic $ -2\Delta\log(L) $ as a function of coupling modifiers $ \kappa_{\lambda} $ (left) and $ \kappa_{2\mathrm{V}} $ (right) for the combination of all channels. |
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Figure 8-a:
The profile likelihood ratio test statistic $ -2\Delta\log(L) $ as a function of coupling modifiers $ \kappa_{\lambda} $ (left) and $ \kappa_{2\mathrm{V}} $ (right) for the combination of all channels. |
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Figure 8-b:
The profile likelihood ratio test statistic $ -2\Delta\log(L) $ as a function of coupling modifiers $ \kappa_{\lambda} $ (left) and $ \kappa_{2\mathrm{V}} $ (right) for the combination of all channels. |
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Figure 9:
Profile likelihood ratio test statistic $ -2\Delta\log(L) $ scans as a function of pairs of coupling modifiers ( $ \kappa_{\lambda} $, $ \kappa_{2\mathrm{V}} $) (top left), ($ \kappa_{V} $, $ \kappa_{2\mathrm{V}} $) (top right), and ( $ \kappa_{\lambda} $, $ \kappa_{\mathrm{t}} $) (bottom) for the combination of all channels when all the other parameters are fixed to their SM value. |
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Figure 9-a:
Profile likelihood ratio test statistic $ -2\Delta\log(L) $ scans as a function of pairs of coupling modifiers ( $ \kappa_{\lambda} $, $ \kappa_{2\mathrm{V}} $) (top left), ($ \kappa_{V} $, $ \kappa_{2\mathrm{V}} $) (top right), and ( $ \kappa_{\lambda} $, $ \kappa_{\mathrm{t}} $) (bottom) for the combination of all channels when all the other parameters are fixed to their SM value. |
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Figure 9-b:
Profile likelihood ratio test statistic $ -2\Delta\log(L) $ scans as a function of pairs of coupling modifiers ( $ \kappa_{\lambda} $, $ \kappa_{2\mathrm{V}} $) (top left), ($ \kappa_{V} $, $ \kappa_{2\mathrm{V}} $) (top right), and ( $ \kappa_{\lambda} $, $ \kappa_{\mathrm{t}} $) (bottom) for the combination of all channels when all the other parameters are fixed to their SM value. |
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Figure 9-c:
Profile likelihood ratio test statistic $ -2\Delta\log(L) $ scans as a function of pairs of coupling modifiers ( $ \kappa_{\lambda} $, $ \kappa_{2\mathrm{V}} $) (top left), ($ \kappa_{V} $, $ \kappa_{2\mathrm{V}} $) (top right), and ( $ \kappa_{\lambda} $, $ \kappa_{\mathrm{t}} $) (bottom) for the combination of all channels when all the other parameters are fixed to their SM value. |
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Figure 10:
Upper limits on the HH production cross section at 95% CL for the two sets of HEFT benchmarks. The theoretical uncertainties in the HH ggF signal cross section are not considered because we directly constrain the measured cross section. |
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Figure 11:
On the left, upper limits on the HH cross section as a function of the $ c_{2} $ coupling modifier. The theoretical uncertainties in the HH ggF signal cross section are not considered because we directly constrain the measured cross section. On the right, the profile likelihood ratio test statistic $ -2\Delta\log(L) $ as a function of the $ c_{2} $ coupling modifier. |
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Figure 11-a:
On the left, upper limits on the HH cross section as a function of the $ c_{2} $ coupling modifier. The theoretical uncertainties in the HH ggF signal cross section are not considered because we directly constrain the measured cross section. On the right, the profile likelihood ratio test statistic $ -2\Delta\log(L) $ as a function of the $ c_{2} $ coupling modifier. |
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Figure 11-b:
On the left, upper limits on the HH cross section as a function of the $ c_{2} $ coupling modifier. The theoretical uncertainties in the HH ggF signal cross section are not considered because we directly constrain the measured cross section. On the right, the profile likelihood ratio test statistic $ -2\Delta\log(L) $ as a function of the $ c_{2} $ coupling modifier. |
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Figure 12:
Expected upper limits on the HH signal strength from the combination of all the considered channels at different integrated luminosities (left), and under different assumptions on the systematic uncertainties for an integrated luminosity of 3000 fb$ ^{-1} $ (right). |
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Figure 12-a:
Expected upper limits on the HH signal strength from the combination of all the considered channels at different integrated luminosities (left), and under different assumptions on the systematic uncertainties for an integrated luminosity of 3000 fb$ ^{-1} $ (right). |
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Figure 12-b:
Expected upper limits on the HH signal strength from the combination of all the considered channels at different integrated luminosities (left), and under different assumptions on the systematic uncertainties for an integrated luminosity of 3000 fb$ ^{-1} $ (right). |
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Figure 13:
Expected $ \kappa_{\lambda} $ likelihood scan from the combination of all the considered channels projected at different integrated luminosities (left), and under different assumptions on the systematic uncertainties for an integrated luminosity of 3000 fb$ ^{-1} $ (right). |
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Figure 13-a:
Expected $ \kappa_{\lambda} $ likelihood scan from the combination of all the considered channels projected at different integrated luminosities (left), and under different assumptions on the systematic uncertainties for an integrated luminosity of 3000 fb$ ^{-1} $ (right). |
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Figure 13-b:
Expected $ \kappa_{\lambda} $ likelihood scan from the combination of all the considered channels projected at different integrated luminosities (left), and under different assumptions on the systematic uncertainties for an integrated luminosity of 3000 fb$ ^{-1} $ (right). |
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Figure 14:
Expected signal significance as a function of integrated luminosity for the nominal scenario of systematic uncertainties S2 and for the scenario with statistical uncertainties only (left). 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). |
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Figure 14-a:
Expected signal significance as a function of integrated luminosity for the nominal scenario of systematic uncertainties S2 and for the scenario with statistical uncertainties only (left). 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). |
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Figure 14-b:
Expected signal significance as a function of integrated luminosity for the nominal scenario of systematic uncertainties S2 and for the scenario with statistical uncertainties only (left). 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). |
| Tables | |
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Table 1:
Values of the effective Lagrangian couplings for the Higgs Effective field theory benchmarks proposed in Ref. [33]. |
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Table 2:
Values of the effective Lagrangian couplings for the Higgs effective field theory benchmarks proposed in Ref. [34]. |
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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 $ r $. The third (fourth) column is the allowed 68% CL interval for the coupling modifier $ \kappa_{\lambda} $ ($ \kappa_{2\mathrm{V}} $). The last column indicates whether the analysis is included in the results using the HEFT parametrisation. |
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Table 4:
Treatment of most important common systematic uncertainties in the S2 scenario. |
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Table 5:
Expected significance for the HH signal projected to 2000 or 3000 fb$ ^{-1} $ under different assumptions of systematic uncertainties. |
| Summary |
| A combined search for nonresonant Higgs boson pair (HH) production is performed using the proton-proton collision data set produced by the LHC at $ \sqrt{s} = $ 13 TeV, and collected by the CMS detector 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, are 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, the gluon-gluon fusion Higgs boson pair production is also searched for in the $ \mathrm{b}\overline{\mathrm{b}}\mathrm{Z}\mathrm{Z} $ with ZZ decaying to four leptons, $ \mathrm{W}\mathrm{W}\gamma\gamma $, and $ \tau\tau\gamma\gamma $ final states, which have clean signatures but relatively small branching fractions. The associated production mechanism with a vector boson is searched for in the $ \mathrm{b}\overline{\mathrm{b}}\mathrm{b}\overline{\mathrm{b}} $ final state with the largest branching fraction. The analyses of these channels are combined to probe the Higgs boson trilinear self-coupling, the quartic coupling between two vector bosons and two Higgs bosons (VVHH) and to search for beyond the standard model physics scenarios in the Higgs effective field theory approach. The observed and expected upper limits at 95% confidence level (CL) on the cross section of gluon-gluon fusion Higgs boson pair production are found to be 3.5 and 2.5 times the standard model expectations. For the vector boson fusion production, the observed and expected upper limit at 95% CL are 79 and 91 times the standard model expectations. One-dimensional scans of coupling modifiers are performed. When all other parameters are assumed to be as expected from the SM, we (expect to) exclude HH production at 95% CL when the Higgs boson trilinear self-coupling modifier $ \kappa_{\lambda} $ is outside the range from $- $1.39 to 7.02 ($-$1.02 to 7.19). Equivalently, HH production is excluded when the VVHH coupling modifier $ \kappa_{2\mathrm{V}} $ is outside the range from 0.62 to 1.42 (0.69 to 1.35 expected). Two-dimensional measurements are 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 standard model predictions. Under an effective field theory framework, the cross section of the nonresonant ggF HH pair production is parameterised 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 perform searches for benchmark signals under different anomalous coupling scenarios and set upper limits on their cross sections at 95% CL. We (expect to) exclude HH production at 95% CL when the coupling of the contact interaction between two Higgs and two top quarks is outside the range between $-$0.28 to 0.59 ($-$0.17 to 0.47). These results present the most stringent limits and constraints obtained from the searches for nonresonant Higgs boson pair production using the LHC Run 2 data set collected by the CMS detector. Extrapolating our current results to the luminosity of HL-LHC it can be expected to see first evidence for Higgs boson pair production with $ \approx $2000 fb$ ^{-1} $ of data. |
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