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| CMS-HIG-19-018 ; CERN-EP-2020-222 | ||
| Search for nonresonant Higgs boson pair production in final states with two bottom quarks and two photons in proton-proton collisions at $\sqrt{s} = $ 13 TeV | ||
| CMS Collaboration | ||
| 24 November 2020 | ||
| JHEP 03 (2021) 257 | ||
| Abstract: A search for nonresonant production of Higgs boson pairs via gluon-gluon and vector boson fusion processes in final states with two bottom quarks and two photons is presented. The search uses data from proton-proton collisions at a center-of-mass energy of $\sqrt{s} = $ 13 TeV recorded with the CMS detector at the LHC, corresponding to an integrated luminosity of 137 fb$^{-1}$. No significant deviation from the background-only hypothesis is observed. An upper limit at 95% confidence level is set on the product of the Higgs boson pair production cross section and branching fraction into ${\mathrm{b\bar{b}}} \gamma\gamma$. The observed (expected) upper limit is determined to be 0.67 (0.45) fb, which corresponds to 7.7 (5.2) times the standard model prediction. This search has the highest sensitivity to Higgs boson pair production to date. Assuming all other Higgs boson couplings are equal to their values in the standard model, the observed coupling modifiers of the trilinear Higgs boson self-coupling ${\kappa_{\lambda}} $ and the coupling between a pair of Higgs bosons and a pair of vector bosons ${c_{2V}}$ are constrained within the ranges $-3.3 < {\kappa_{\lambda}} < 8.5$ and $-1.3 < c_{2V} < 3.5$ at 95% confidence level. Constraints on ${\kappa_{\lambda}} $ are also set by combining this analysis with a search for single Higgs bosons decaying to two photons, produced in association with top quark-antiquark pairs, and by performing a simultaneous fit of ${\kappa_{\lambda}} $ and the top quark Yukawa coupling modifier ${\kappa_{\mathrm{t}}} $. | ||
| Links: e-print arXiv:2011.12373 [hep-ex] (PDF) ; CDS record ; inSPIRE record ; CADI line (restricted) ; | ||
| Figures & Tables | Summary | Additional Figures | References | CMS Publications |
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| Figures | |
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Figure 1:
Feynman diagrams of the processes contributing to the production of Higgs boson pairs via ggF at LO. The upper diagrams correspond to SM processes, involving the top Yukawa coupling ${y_{\mathrm{t}}}$ and the trilinear Higgs boson self-coupling ${\lambda _{\mathrm{H} \mathrm{H} \mathrm{H}}}$, respectively. The lower diagrams correspond to BSM processes: the diagram on the left involves the contact interaction of two Higgs bosons with two top quarks (${c_2}$), the middle diagram shows the quartic coupling between the Higgs bosons and two gluons (${c_{2\mathrm{g}}}$), and the diagram on the right describes the contact interactions between the Higgs boson and gluons (${c_{\mathrm{g}}}$). |
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Figure 1-a:
Feynman diagram of a SM process contributing to the production of Higgs boson pairs via ggF at LO, involving the top Yukawa coupling ${y_{\mathrm{t}}}$ and the trilinear Higgs boson self-coupling ${\lambda _{\mathrm{H} \mathrm{H} \mathrm{H}}}$. |
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Figure 1-b:
Feynman diagram of a SM process contributing to the production of Higgs boson pairs via ggF at LO, involving the top Yukawa coupling ${y_{\mathrm{t}}}$. |
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Figure 1-c:
Feynman diagram of a BSM process contributing to the production of Higgs boson pairs via ggF at LO, involving the contact interaction of two Higgs bosons with two top quarks (${c_2}$). |
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Figure 1-d:
Feynman diagram of a BSM process contributing to the production of Higgs boson pairs via ggF at LO, involving the quartic coupling between the Higgs boson and two gluons (${c_{2\mathrm{g}}}$). |
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Figure 1-e:
Feynman diagram of a BSM process contributing to the production of Higgs boson pairs via ggF at LO, involving the contact interactions between the Higgs boson and gluons (${c_{\mathrm{g}}}$). |
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Figure 2:
Feynman diagrams that contribute to the production of Higgs boson pairs via VBF at LO. On the left the diagram involving the HHH vertex (${\lambda _{\mathrm{H} \mathrm{H} \mathrm{H}}}$), in the middle the diagram with two HVV vertices ($ {c_{\mathrm{V}}} $), and on the right the diagram with the HHVV vertex ($ {c_{2\mathrm{V}}} $). |
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Figure 2-a:
Feynman diagram that contributes to the production of Higgs boson pairs via VBF at LO, involving the HHH vertex (${\lambda _{\mathrm{H} \mathrm{H} \mathrm{H}}}$). |
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Figure 2-b:
Feynman diagram that contributes to the production of Higgs boson pairs via VBF at LO, involving two HVV vertices ($ {c_{\mathrm{V}}} $). |
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Figure 2-c:
Feynman diagram that contributes to the production of Higgs boson pairs via VBF at LO, involving the HHVV vertex ($ {c_{2\mathrm{V}}} $). |
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Figure 3:
The invariant mass distributions of the reconstructed Higgs boson candidates $ {m_{\gamma \gamma}} $ (left) and $ {m_\text {jj}}$ (right) in data and simulated events. Data, dominated by the $ \gamma \gamma $+jets and $ \gamma $+jets backgrounds, are compared to the SM ggF HH signal samples and single H samples (ttH, ggH, VBF H, VH) after imposing the selection criteria described in Section 5. The error bars on the data points indicate statistical uncertainties. The HH signal has been scaled by a factor of 10$^{3}$ for display purposes. |
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Figure 3-a:
The invariant mass distribution of the reconstructed Higgs boson candidates $ {m_{\gamma \gamma}} $ in data and simulated events. Data, dominated by the $ \gamma \gamma $+jets and $ \gamma $+jets backgrounds, are compared to the SM ggF HH signal samples and single H samples (ttH, ggH, VBF H, VH) after imposing the selection criteria described in Section 5. The error bars on the data points indicate statistical uncertainties. The HH signal has been scaled by a factor of 10$^{3}$ for display purposes. |
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Figure 3-b:
The invariant mass distribution of the reconstructed Higgs boson candidates $ {m_\text {jj}}$ in data and simulated events. Data, dominated by the $ \gamma \gamma $+jets and $ \gamma $+jets backgrounds, are compared to the SM ggF HH signal samples and single H samples (ttH, ggH, VBF H, VH) after imposing the selection criteria described in Section 5. The error bars on the data points indicate statistical uncertainties. The HH signal has been scaled by a factor of 10$^{3}$ for display purposes. |
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Figure 4:
Distributions of $ {\tilde{M}_{\mathrm {X}}} $. The SM ggF HH signal is compared with several BSM hypotheses listed in Table 1 (left), and the SM VBF HH signal is compared with two different anomalous values of $ {c_{2\mathrm{V}}} $ (right). All distributions are normalized to unity. |
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Figure 4-a:
Distribution of $ {\tilde{M}_{\mathrm {X}}} $. The SM ggF HH signal is compared with several BSM hypotheses listed in Table. All distributions are normalized to unity. |
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Figure 4-b:
Distribution of $ {\tilde{M}_{\mathrm {X}}} $. The SM VBF HH signal is compared with two different anomalous values of $ {c_{2\mathrm{V}}} $. All distributions are normalized to unity. |
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Figure 5:
The distribution of the ttHScore (left) and MVA output (right) in data and simulated events. Data, dominated by $ \gamma \gamma $+jets and $ \gamma $+jets background, are compared to the SM ggF HH signal samples and single H samples (ttH, ggH, VBF H, VH) after imposing the selection criteria described in Section 5. The error bars on the data points indicate statistical uncertainties. The HH signal has been scaled by a factor of 10$^{3}$ for display purposes. |
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Figure 5-a:
The distribution of the ttHScore in data and simulated events. Data, dominated by $ \gamma \gamma $+jets and $ \gamma $+jets background, are compared to the SM ggF HH signal samples and single H samples (ttH, ggH, VBF H, VH) after imposing the selection criteria described in Section 5. The error bars on the data points indicate statistical uncertainties. The HH signal has been scaled by a factor of 10$^{3}$ for display purposes. |
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Figure 5-b:
The distribution of the MVA output in data and simulated events. Data, dominated by $ \gamma \gamma $+jets and $ \gamma $+jets background, are compared to the SM ggF HH signal samples and single H samples (ttH, ggH, VBF H, VH) after imposing the selection criteria described in Section 5. The error bars on the data points indicate statistical uncertainties. The HH signal has been scaled by a factor of 10$^{3}$ for display purposes. |
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Figure 6:
The distribution of the two MVA outputs is shown in data and simulated events in the two VBF $ {\tilde{M}_{\mathrm {X}}} $ regions: $ {\tilde{M}_{\mathrm {X}}} > $ 500 GeV (left) and $ {\tilde{M}_{\mathrm {X}}} < $ 500 GeV (right). Data, dominated by the $ \gamma \gamma $+jets and $ \gamma $+jets backgrounds, are compared to the VBF HH signal samples with SM couplings and $ {c_{2\mathrm{V}}} =$ 0, SM ggF HH and single H samples (ttH, ggH, VBF H, VH) after imposing the VBF selection criteria described in Section 5. The error bars on the data points indicate statistical uncertainties. The HH signal has been scaled by a factor of 10$^{3}$ for display purposes. |
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Figure 6-a:
The distribution of the MVA output is shown in data and simulated events in the VBF $ {\tilde{M}_{\mathrm {X}}} > $ 500 GeV region. Data, dominated by the $ \gamma \gamma $+jets and $ \gamma $+jets backgrounds, are compared to the VBF HH signal samples with SM couplings and $ {c_{2\mathrm{V}}} =$ 0, SM ggF HH and single H samples (ttH, ggH, VBF H, VH) after imposing the VBF selection criteria described in Section 5. The error bars on the data points indicate statistical uncertainties. The HH signal has been scaled by a factor of 10$^{3}$ for display purposes. |
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Figure 6-b:
The distribution of the MVA output is shown in data and simulated events in the VBF $ {\tilde{M}_{\mathrm {X}}} < $ 500 GeV region. Data, dominated by the $ \gamma \gamma $+jets and $ \gamma $+jets backgrounds, are compared to the VBF HH signal samples with SM couplings and $ {c_{2\mathrm{V}}} =$ 0, SM ggF HH and single H samples (ttH, ggH, VBF H, VH) after imposing the VBF selection criteria described in Section 5. The error bars on the data points indicate statistical uncertainties. The HH signal has been scaled by a factor of 10$^{3}$ for display purposes. |
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Figure 7:
Parametrized signal shape for $ {m_{\gamma \gamma}} $ (left) and ${m_\text {jj}}$ (right) in the best resolution ggF (upper) and VBF (lower) categories. The open squares represent simulated events and the blue lines are the corresponding models. Also shown are the $\sigma _{\text {eff}}$ value (half the width of the narrowest interval containing 68.3% of the invariant mass distribution) and the corresponding interval as a gray band, and the full width at half the maximum (FWHM) and the corresponding interval as a double arrow. |
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Figure 7-a:
Parametrized signal shape for $ {m_{\gamma \gamma}} $ in the best resolution ggF category. The open squares represent simulated events and the blue lines are the corresponding models. Also shown are the $\sigma _{\text {eff}}$ value (half the width of the narrowest interval containing 68.3% of the invariant mass distribution) and the corresponding interval as a gray band, and the full width at half the maximum (FWHM) and the corresponding interval as a double arrow. |
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Figure 7-b:
Parametrized signal shape for ${m_\text {jj}}$ in the best resolution VBF category. The open squares represent simulated events and the blue lines are the corresponding models. Also shown are the $\sigma _{\text {eff}}$ value (half the width of the narrowest interval containing 68.3% of the invariant mass distribution) and the corresponding interval as a gray band, and the full width at half the maximum (FWHM) and the corresponding interval as a double arrow. |
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Figure 7-c:
Parametrized signal shape for $ {m_{\gamma \gamma}} $ in the best resolution ggF category. The open squares represent simulated events and the blue lines are the corresponding models. Also shown are the $\sigma _{\text {eff}}$ value (half the width of the narrowest interval containing 68.3% of the invariant mass distribution) and the corresponding interval as a gray band, and the full width at half the maximum (FWHM) and the corresponding interval as a double arrow. |
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Figure 7-d:
Parametrized signal shape for ${m_\text {jj}}$ in the best resolution VBF category. The open squares represent simulated events and the blue lines are the corresponding models. Also shown are the $\sigma _{\text {eff}}$ value (half the width of the narrowest interval containing 68.3% of the invariant mass distribution) and the corresponding interval as a gray band, and the full width at half the maximum (FWHM) and the corresponding interval as a double arrow. |
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Figure 8:
Invariant mass distributions $ {m_{\gamma \gamma}} $ (upper) and $ {m_\text {jj}}$ (lower) for the selected events in data (black points) in the best resolution ggF (CAT0) and VBF (CAT0) categories. The solid red line shows the sum of the fitted signal and background (HH+H+B), the solid blue line shows the background component from the single Higgs boson and the nonresonant processes (H+B), and the dashed black line shows the nonresonant background component (B). The normalization of each component (HH, H, B) is extracted from the combined fit to the data in all analysis categories. The one (green) and two (yellow) standard deviation bands include the uncertainties in the background component of the fit. The lower panel in each plot shows the residual signal yield after the background (H+B) subtraction. |
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Figure 8-a:
Invariant mass distributions $ {m_{\gamma \gamma}} $ for the selected events in data (black points) in the best resolution ggF (CAT0) category. The solid red line shows the sum of the fitted signal and background (HH+H+B), the solid blue line shows the background component from the single Higgs boson and the nonresonant processes (H+B), and the dashed black line shows the nonresonant background component (B). The normalization of each component (HH, H, B) is extracted from the combined fit to the data in all analysis categories. The one (green) and two (yellow) standard deviation bands include the uncertainties in the background component of the fit. The lower panel shows the residual signal yield after the background (H+B) subtraction. |
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Figure 8-b:
Invariant mass distributions $ {m_{\gamma \gamma}} $ for the selected events in data (black points) in the best resolution VBF (CAT0) category. The solid red line shows the sum of the fitted signal and background (HH+H+B), the solid blue line shows the background component from the single Higgs boson and the nonresonant processes (H+B), and the dashed black line shows the nonresonant background component (B). The normalization of each component (HH, H, B) is extracted from the combined fit to the data in all analysis categories. The one (green) and two (yellow) standard deviation bands include the uncertainties in the background component of the fit. The lower panel shows the residual signal yield after the background (H+B) subtraction. |
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Figure 8-c:
Invariant mass distributions $ {m_\text {jj}}$ for the selected events in data (black points) in the best resolution ggF (CAT0) category. The solid red line shows the sum of the fitted signal and background (HH+H+B), the solid blue line shows the background component from the single Higgs boson and the nonresonant processes (H+B), and the dashed black line shows the nonresonant background component (B). The normalization of each component (HH, H, B) is extracted from the combined fit to the data in all analysis categories. The one (green) and two (yellow) standard deviation bands include the uncertainties in the background component of the fit. The lower panel shows the residual signal yield after the background (H+B) subtraction. |
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Figure 8-d:
Invariant mass distributions $ {m_\text {jj}}$ for the selected events in data (black points) in the best resolution VBF (CAT0) category. The solid red line shows the sum of the fitted signal and background (HH+H+B), the solid blue line shows the background component from the single Higgs boson and the nonresonant processes (H+B), and the dashed black line shows the nonresonant background component (B). The normalization of each component (HH, H, B) is extracted from the combined fit to the data in all analysis categories. The one (green) and two (yellow) standard deviation bands include the uncertainties in the background component of the fit. The lower panel shows the residual signal yield after the background (H+B) subtraction. |
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Figure 9:
Invariant mass distributions $ {m_{\gamma \gamma}} $ (left) and $ {m_\text {jj}}$ (right) for the selected events in data (black points) weighted by S/(S+B), where S (B) is the number of signal (background) events extracted from the signal-plus-background fit. The solid red line shows the sum of the fitted signal and background (HH+H+B), the solid blue line shows the background component from the single Higgs boson and the nonresonant processes (H+B), and the dashed black line shows the nonresonant background component (B). The normalization of each component (HH, H, B) is extracted from the combined fit to the data in all analysis categories. The one (green) and two (yellow) standard deviation bands include the uncertainties in the background component of the fit. The lower panel in each plot shows the residual signal yield after the background (H+B) subtraction. |
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Figure 9-a:
Invariant mass distributions $ {m_{\gamma \gamma}} $ for the selected events in data (black points) weighted by S/(S+B), where S (B) is the number of signal (background) events extracted from the signal-plus-background fit. The solid red line shows the sum of the fitted signal and background (HH+H+B), the solid blue line shows the background component from the single Higgs boson and the nonresonant processes (H+B), and the dashed black line shows the nonresonant background component (B). The normalization of each component (HH, H, B) is extracted from the combined fit to the data in all analysis categories. The one (green) and two (yellow) standard deviation bands include the uncertainties in the background component of the fit. The lower panel shows the residual signal yield after the background (H+B) subtraction. |
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Figure 9-b:
Invariant mass distributions $ {m_\text {jj}}$ for the selected events in data (black points) weighted by S/(S+B), where S (B) is the number of signal (background) events extracted from the signal-plus-background fit. The solid red line shows the sum of the fitted signal and background (HH+H+B), the solid blue line shows the background component from the single Higgs boson and the nonresonant processes (H+B), and the dashed black line shows the nonresonant background component (B). The normalization of each component (HH, H, B) is extracted from the combined fit to the data in all analysis categories. The one (green) and two (yellow) standard deviation bands include the uncertainties in the background component of the fit. The lower panel shows the residual signal yield after the background (H+B) subtraction. |
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Figure 10:
Expected and observed 95% CL upper limits on the product of the HH production cross section and $\mathcal {B}({{\mathrm{H} \mathrm{H}}} \to {\gamma \gamma \mathrm{b} {}\mathrm{\bar{b}}})$ obtained for different values of $ {\kappa _{\lambda}} $ assuming $ {\kappa _{\mathrm{t}}} $ = 1. The green and yellow bands represent, respectively, the one and two standard deviation extensions beyond the expected limit. The long-dashed red line shows the theoretical prediction. |
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Figure 11:
Negative log-likelihood, as a function of $ {\kappa _{\lambda}} $, evaluated with an Asimov data set assuming the SM hypothesis (left) and the observed data (right). The 68 and 95% CL intervals are shown with the dashed gray lines. The two curves are shown for the HH (blue) and HH+ttH (orange) analysis categories. All other couplings are set to their SM values. |
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Figure 11-a:
Negative log-likelihood, as a function of $ {\kappa _{\lambda}} $, evaluated with an Asimov data set assuming the SM hypothesis. The 68 and 95% CL intervals are shown with the dashed gray lines. The two curves are shown for the HH (blue) and HH+ttH (orange) analysis categories. All other couplings are set to their SM values. |
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Figure 11-b:
Negative log-likelihood, as a function of $ {\kappa _{\lambda}} $, evaluated with an Asimov data set assuming the observed data. The 68 and 95% CL intervals are shown with the dashed gray lines. The two curves are shown for the HH (blue) and HH+ttH (orange) analysis categories. All other couplings are set to their SM values. |
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Figure 12:
Negative log-likelihood contours at 68 and 95% CL in the ($ {\kappa _{\lambda}} $, $ {\kappa _{\mathrm{t}}} $) plane evaluated with an Asimov data set assuming the SM hypothesis (left) and the observed data (right). The contours obtained using the HH analysis categories only are shown in blue, and in orange when combined with the ttH categories. The best fit value for the HH categories only ($ {\kappa _{\lambda}} $ = 0.6, $ {\kappa _{\mathrm{t}}} $ = 1.2) is indicated by a blue circle, for the HH+ttH categories ($ {\kappa _{\lambda}} $ = 1.4, $ {\kappa _{\mathrm{t}}} $ = 1.3) by an orange diamond, and the SM prediction ($ {\kappa _{\lambda}} $ = 1.0, $ {\kappa _{\mathrm{t}}} $ = 1.0) by a black star. The regions of the 2D scan where the ${\kappa _{\mathrm{t}}}$ parametrization for anomalous values of ${\kappa _{\lambda}}$ at LO is not reliable are shown with a gray band. |
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Figure 12-a:
Negative log-likelihood contours at 68 and 95% CL in the ($ {\kappa _{\lambda}} $, $ {\kappa _{\mathrm{t}}} $) plane evaluated with an Asimov data set assuming the SM hypothesis. The contours obtained using the HH analysis categories only are shown in blue, and in orange when combined with the ttH categories. The best fit value for the HH categories only ($ {\kappa _{\lambda}} $ = 0.6, $ {\kappa _{\mathrm{t}}} $ = 1.2) is indicated by a blue circle, for the HH+ttH categories ($ {\kappa _{\lambda}} $ = 1.4, $ {\kappa _{\mathrm{t}}} $ = 1.3) by an orange diamond, and the SM prediction ($ {\kappa _{\lambda}} $ = 1.0, $ {\kappa _{\mathrm{t}}} $ = 1.0) by a black star. The regions of the 2D scan where the ${\kappa _{\mathrm{t}}}$ parametrization for anomalous values of ${\kappa _{\lambda}}$ at LO is not reliable are shown with a gray band. |
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Figure 12-b:
Negative log-likelihood contours at 68 and 95% CL in the ($ {\kappa _{\lambda}} $, $ {\kappa _{\mathrm{t}}} $) plane evaluated with an Asimov data set assuming the observed data. The contours obtained using the HH analysis categories only are shown in blue, and in orange when combined with the ttH categories. The best fit value for the HH categories only ($ {\kappa _{\lambda}} $ = 0.6, $ {\kappa _{\mathrm{t}}} $ = 1.2) is indicated by a blue circle, for the HH+ttH categories ($ {\kappa _{\lambda}} $ = 1.4, $ {\kappa _{\mathrm{t}}} $ = 1.3) by an orange diamond, and the SM prediction ($ {\kappa _{\lambda}} $ = 1.0, $ {\kappa _{\mathrm{t}}} $ = 1.0) by a black star. The regions of the 2D scan where the ${\kappa _{\mathrm{t}}}$ parametrization for anomalous values of ${\kappa _{\lambda}}$ at LO is not reliable are shown with a gray band. |
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Figure 13:
Negative log-likelihood scan, as a function of $ {\kappa _{\mathrm{t}}} $, evaluated with an Asimov data set assuming the SM hypothesis (left) and the observed data (right). The 68 and 95% CL intervals are shown with the dashed gray lines. The two curves are shown for the HH (blue) and the HH+ttH (orange) analysis categories. All other couplings are fixed to their SM values. |
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Figure 13-a:
Negative log-likelihood scan, as a function of $ {\kappa _{\mathrm{t}}} $, evaluated with an Asimov data set assuming the SM hypothesis. The 68 and 95% CL intervals are shown with the dashed gray lines. The two curves are shown for the HH (blue) and the HH+ttH (orange) analysis categories. All other couplings are fixed to their SM values. |
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Figure 13-b:
Negative log-likelihood scan, as a function of $ {\kappa _{\mathrm{t}}} $, evaluated with an Asimov data set assuming the observed data. The 68 and 95% CL intervals are shown with the dashed gray lines. The two curves are shown for the HH (blue) and the HH+ttH (orange) analysis categories. All other couplings are fixed to their SM values. |
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Figure 14:
Expected and observed 95% CL upper limits on the product of the VBF HH production cross section and $\mathcal {B}({{\mathrm{H} \mathrm{H}}} \to {\gamma \gamma \mathrm{b} {}\mathrm{\bar{b}}})$ obtained for different values of $ {c_{2\mathrm{V}}} $. The green and yellow bands represent, respectively, the one and two standard deviation extensions beyond the expected limit. The long-dashed red line shows the theoretical prediction. |
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Figure 15:
Negative log-likelihood contours at 68 and 95% CL in the ($ {\kappa _{\lambda}} $, $ {c_{2\mathrm{V}}} $) plane evaluated with an Asimov data set assuming the SM hypothesis (left) and with the observed data (right). The contours are obtained using the HH analysis categories only. The best fit value ($ {\kappa _{\lambda}} $ = 0.0, $ {c_{2\mathrm{V}}} $ = 0.3) is indicated by a blue circle, and the SM prediction ($ {\kappa _{\lambda}} $ = 1.0, $ {c_{2\mathrm{V}}} $ = 1.0) by a black star. |
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Figure 15-a:
Negative log-likelihood contours at 68 and 95% CL in the ($ {\kappa _{\lambda}} $, $ {c_{2\mathrm{V}}} $) plane evaluated with an Asimov data set assuming the SM hypothesis. The contours are obtained using the HH analysis categories only. The best fit value ($ {\kappa _{\lambda}} $ = 0.0, $ {c_{2\mathrm{V}}} $ = 0.3) is indicated by a blue circle, and the SM prediction ($ {\kappa _{\lambda}} $ = 1.0, $ {c_{2\mathrm{V}}} $ = 1.0) by a black star. |
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Figure 15-b:
Negative log-likelihood contours at 68 and 95% CL in the ($ {\kappa _{\lambda}} $, $ {c_{2\mathrm{V}}} $) plane evaluated with an Asimov data set assuming the observed data. The contours are obtained using the HH analysis categories only. The best fit value ($ {\kappa _{\lambda}} $ = 0.0, $ {c_{2\mathrm{V}}} $ = 0.3) is indicated by a blue circle, and the SM prediction ($ {\kappa _{\lambda}} $ = 1.0, $ {c_{2\mathrm{V}}} $ = 1.0) by a black star. |
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Figure 16:
Expected and observed 95% CL upper limits on the product of the ggF HH production cross section and $\mathcal {B}({{\mathrm{H} \mathrm{H}}} \to {\gamma \gamma \mathrm{b} {}\mathrm{\bar{b}}})$ obtained for different nonresonant benchmark models (defined in Table 1) (upper) and BSM coupling $ {c_2} $ (lower). In this fit, the yield of the VBF HH signal is constrained within uncertainties to the one predicted in the SM. The green and yellow bands represent, respectively, the one and two standard deviation extensions beyond the expected limit. On the lower plot the long-dashed red line shows the theoretical prediction. |
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Figure 16-a:
Expected and observed 95% CL upper limits on the product of the ggF HH production cross section and $\mathcal {B}({{\mathrm{H} \mathrm{H}}} \to {\gamma \gamma \mathrm{b} {}\mathrm{\bar{b}}})$ obtained for different nonresonant benchmark models (defined in Table 1). In this fit, the yield of the VBF HH signal is constrained within uncertainties to the one predicted in the SM. The green and yellow bands represent, respectively, the one and two standard deviation extensions beyond the expected limit. |
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Figure 16-b:
Expected and observed 95% CL upper limits on the product of the ggF HH production cross section and $\mathcal {B}({{\mathrm{H} \mathrm{H}}} \to {\gamma \gamma \mathrm{b} {}\mathrm{\bar{b}}})$ obtained for BSM coupling $ {c_2} $. In this fit, the yield of the VBF HH signal is constrained within uncertainties to the one predicted in the SM. The green and yellow bands represent, respectively, the one and two standard deviation extensions beyond the expected limit. The long-dashed red line shows the theoretical prediction. |
| Tables | |
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Table 1:
Coupling parameter values in the SM and in twelve BSM benchmark hypotheses identified using the method described in Ref. [43]. |
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Table 2:
Summary of the analysis categories. Two VBF- and twelve ggF-enriched categories are defined based on the output of the MVA classifier and the mass of the Higgs boson pair system $ {\tilde{M}_{\mathrm {X}}} $. The VBF and ggF categories are mutually exclusive. |
| Summary |
|
A search for nonresonant Higgs boson pair production (HH) has been presented, where one of the Higgs bosons decays to a pair of bottom quarks and the other to a pair of photons. This search uses proton-proton collision data collected at $\sqrt{s} = $ 13 TeV by the CMS experiment at the LHC, corresponding to a total integrated luminosity of 137 fb$^{-1}$. No significant deviation from the background-only hypothesis is observed. Upper limits at 95% confidence level (CL) on the product of the HH production cross section and the branching fraction into ${\mathrm{b\bar{b}}} \gamma\gamma$ are extracted for production in the standard model (SM) and in several scenarios beyond the SM. The expected upper limit at 95% CL on ${\sigma_{\mathrm{H}\mathrm{H}}} {\mathcal{B}({{\mathrm{H}\mathrm{H}}} \to\mathrm{b\bar{b}}\gamma\gamma)}$ is 0.45 fb, corresponding to about 5.2 times the SM prediction, while the observed upper limit is 0.67 fb, corresponding to 7.7 times the expected value for the SM process. The presented search has the highest sensitivity to the SM HH production to date. Upper limits at 95% CL on the SM HH production cross section are also derived as a function of the Higgs boson self-coupling modifier ${\kappa_{\lambda}} \equiv {\lambda_{\mathrm{H}\mathrm{H}\mathrm{H}}} /{\lambda^\mathrm{SM}_{\mathrm{H}\mathrm{H}\mathrm{H}}} $ assuming that the top quark Yukawa coupling is SM-like. The coupling modifier ${\kappa_{\lambda}} $ is constrained within a range $-3.3 < \kappa_{\lambda} < 8.5$, while the expected constraint is within a range $-2.5 < \kappa_{\lambda} < 8.2$ at 95% CL. This search is combined with an analysis that targets top quark-antiquark associated production of a single Higgs boson decaying to a diphoton pair. In the scenario in which the HH signal has the properties predicted by the SM, the coupling modifier ${\kappa_{\lambda}}$ has been constrained. In addition, a simultaneous constraint on ${\kappa_{\lambda}}$ and the modifier of the coupling between the Higgs boson and the top quark ${\kappa_{\mathrm{t}}}$ is presented when both the HH and single Higgs boson processes are considered as signals. Limits are also set on the cross section of nonresonant HH production via vector boson fusion (VBF). The most stringent limit to date is set on the product of the HH VBF production cross section and the branching fraction into ${\mathrm{b\bar{b}}} \gamma\gamma$. The observed (expected) upper limit at 95% CL amounts to 1.02 (0.94) fb, corresponding to 225 (208) times the SM prediction. Limits are also set as a function of the modifier of the coupling between two vector bosons and two Higgs bosons, ${c_{2V}}$. The observed excluded region corresponds to ${c_{2V}} < -1.3$ and ${c_{2V}} > 3.5$, while the expected exclusion is ${c_{2V}} < -0.9$ and ${c_{2V}} > 3.1$. Numerous hypotheses on coupling modifiers beyond the SM have been explored, both in the context of inclusive Higgs boson pair production and for HH production via gluon-gluon fusion and VBF. The production of Higgs boson pairs was also combined with the top quark-antiquark pair associated production of a single Higgs boson. Overall, all of the results are consistent with the SM predictions. |
| Additional Figures | |
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Additional Figure 1:
Impact of the b-jet energy corrections to the Higgs boson mass reconstruction obtained in the standard model process of HH production via ggF. The open squares are the distributions of the simulated di-jet invariant mass before (red) and after (blue) the application of the two-step b-jet energy regression. In both cases, the two distributions are fitted with a double sided-crystal ball parametric shape, and the average value ($\mu $) and core resolution ($\sigma $) are also shown. |
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