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| CMS-B2G-22-003 ; CERN-EP-2022-090 | ||
| Search for nonresonant pair production of highly energetic Higgs bosons decaying to bottom quarks | ||
| CMS Collaboration | ||
| 13 May 2022 | ||
| Phys. Rev. Lett. 131 (2023) 041803 | ||
| Abstract: A search for nonresonant Higgs boson (H) pair production via gluon and vector boson (V) fusion is performed in the four-bottom-quark final state, using proton-proton collision data at 13 TeV corresponding to 138 fb$^{-1}$ collected by the CMS experiment at the LHC. The analysis targets Lorentz-boosted H pairs identified using a graph neural network. It constrains the strengths relative to the standard model of the H self-coupling and the quartic VVHH couplings, ${\kappa_{2\mathrm{V}}} $, excluding ${\kappa_{2\mathrm{V}}} = $ 0 for the first time, with a significance of 6.3 standard deviations when other H couplings are fixed to their standard model values. | ||
| Links: e-print arXiv:2205.06667 [hep-ex] (PDF) ; CDS record ; inSPIRE record ; HepData record ; CADI line (restricted) ; | ||
| Figures | Summary | Additional Figures & Tables | References | CMS Publications |
|---|
| Figures | |
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Figure 1:
The data and fitted signal and background distributions for the ${D_{\mathrm{b} \mathrm{\bar{b}}}}$-subleading jet regressed mass are shown for the ggF BDT event category 1, the category accounting for most of the sensitivity to the ggF HH signal. The SM HH ($ {\kappa _{2{\mathrm{V}}}} = {\kappa _{\mathrm{V}}} = {\kappa _\lambda} =$ 1) signal is shown scaled to the best fit signal strength $\mu =$ 3.5. The lower panel shows the ratio of the data and the total prediction, with its uncertainty represented by the shaded band. The error bars on the data points represent the statistical uncertainties. |
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Figure 2:
The distributions of the invariant mass of the HH system after a background-only fit to the data, for the VBF low-purity (LP), medium-purity (MP), and high-purity (HP) categories. The VBF signal for $ {\kappa _{2{\mathrm{V}}}} =$ 0, $ {\kappa _{\mathrm{V}}} = {\kappa _\lambda} =$ 1, is shown in red with the vertical error bar indicating the prefit uncertainty. The lower panel shows the ratio of the data and the total background prediction, with its uncertainty represented by the shaded band. The error bars on the data points represent the statistical uncertainties. |
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Figure 3:
Two-parameter profile likelihood test statistic ($-2\Delta \ln\mathcal {L}$) scan in data as a function of ${\kappa _\lambda}$ and ${\kappa _{2{\mathrm{V}}}}$. The black cross indicates the minimum, while the red diamond marks the SM expectation ($ {\kappa _\lambda} = {\kappa _{2{\mathrm{V}}}} = $ 1). The gray solid, dashed, dotted, and dash-dotted contours enclose the 1, 2, 3, and 5$\sigma $ CL regions, respectively. |
| Summary |
| In summary, a search for nonresonant Higgs boson pair (HH) production via gluon fusion and vector boson (V) fusion in the final state with two bottom quark-antiquark ($\mathrm{b\bar{b}}$) pairs has been presented. The search is focused on the phase space region where both Higgs bosons are highly Lorentz boosted so that each Higgs boson is reconstructed as a large-radius jet. A novel algorithm based on a graph neural network is applied to identify the jets that correspond to $\mathrm{H \to b\bar{b}}$ decays. The data are found to agree with the background-only hypothesis, and an observed (expected) upper limit at 95% confidence level is set to 9.9 (5.1) relative to the standard model cross section. This represents a factor of 30 improvement over the previous best search for a pair of boosted $\mathrm{H \to b\bar{b}}$ jets, which used only data collected in 2016 (36 fb$^{-1}$) and less advanced methods for $\mathrm{H \to b\bar{b}}$ identification and event selection [93]. Upper limits on the production cross section are set as a function of the coupling modifier parameters $\kappa_\lambda$ and $\kappa_{2\mathrm{V}}$ , which parametrize the strengths of the Higgs boson self-coupling, and the quartic VVHH couplings, respectively, relative to their standard model values. The values of $\kappa_\lambda$ and $\kappa_{2\mathrm{V}}$ are observed (expected) to be in the ranges [$-$9.9, 16.9] ([-5.1, 12.2]) and [0.62, 1.41] ([0.66, 1.37]), respectively, excluding $ \kappa_{2\mathrm{V}} = $ 0 for the first time, with a significance of 6.3 standard deviations, when all the Higgs boson couplings, except for the one being scanned, are set to their standard model values. |
| Additional Figures | |
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Additional Figure 1:
Comparison of reconstruction efficiency for Higgs boson decays into bottom or charm quark-antiquark pairs, reconstructed using a pair of anti-$ k_{\mathrm{T}} $ jets clustered with $ R= $ 0.4 (AK4, red), using a single anti-$ k_{\mathrm{T}} $ jet with $ R= $ 0.8 (AK8, green) or a single anti-$ k_{\mathrm{T}} $ jet with $ R= $ 1.5 (blue). Only the matching efficiency between generator-level particles and the reconstructed jets is considered. |
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Additional Figure 2:
Comparison of the expected VBF HH signal yields, for a simulated VBF HH signal sample with $ \kappa_{2\mathrm{V}}= $ 0, entering the Medium Purity (MP) or High Purity (HP) event categories. The events are shown with an arbitrary normalization, accounting for the differences in selection efficiency between the three methods shown. The blue and red dashed lines correspond to using mass-decorrelated DeepAK8 or ParticleNet classifiers, respectively, to discriminate between signal jets and QCD multijet background. The soft-drop algorithm is used with angular exponent $ \beta= $ 0 and soft radiation fraction $ z= $ 0.1 for selections on Higgs boson candidate masses. The ParticleNet classifier is observed to improve the selection efficiency by $ \approx $50% compared to DeepAK8, at a similar background rejection rate. The solid red line corresponds to using the ParticleNet-based mass regression instead of the soft-drop algorithm, yielding another $ \approx $50% increase in selection efficiency (with the same cut values for the mass selections). More information on the training of the ParticleNet classifier and its performance can be found in CMS Detector Performance Note CMS-DP-2020-002 at CMS-DP-2020-002. Training and performance of the mass regression algorithm are detailed in CMS-DP-2021-017 in CMS-DP-2021-017. |
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Additional Figure 3:
Comparison of the ParticleNet discriminant ($ D_{\mathrm{b}\overline{\mathrm{b}}} $) shape between the VBF search region (SR, red) and its large-radius (AK8) jet mass sidebands (blue), using simulated QCD multijet events. The sidebands are used as a control region in the QCD background estimation to obtain transfer factors that correct for the difference in selection efficiency between the QCD-enriched low-$ D_{\mathrm{b}\overline{\mathrm{b}}} $ category and the high-$ D_{\mathrm{b}\overline{\mathrm{b}}} $ search categories. The agreement of the two shapes demonstrates that the transfer factors obtained from the sidebands can be applied to obtain a correct normalization in the SR. |
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Additional Figure 4:
The data and fitted signal and background distributions for the $ D_{\mathrm{b}\overline{\mathrm{b}}} $-subleading jet regressed mass are shown for the ggF BDT event categories 2 (upper left) and 3 (upper right), and the QCD multijet background control region (lower). The SM HH ($ \kappa_{2\mathrm{V}}=\kappa_\mathrm{V}=\kappa_\lambda= $ 1) signal is shown scaled to the best fit signal strength $ \mu= $ 3.5. The lower panel shows the ratio of the data and the total prediction, with its uncertainty represented by the shaded band. The error bars on the data points represent the statistical uncertainties. |
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Additional Figure 4-a:
The data and fitted signal and background distributions for the $ D_{\mathrm{b}\overline{\mathrm{b}}} $-subleading jet regressed mass are shown for the ggF BDT event category 2. The SM HH ($ \kappa_{2\mathrm{V}}=\kappa_\mathrm{V}=\kappa_\lambda= $ 1) signal is shown scaled to the best fit signal strength $ \mu= $ 3.5. The lower panel shows the ratio of the data and the total prediction, with its uncertainty represented by the shaded band. The error bars on the data points represent the statistical uncertainties. |
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Additional Figure 4-b:
The data and fitted signal and background distributions for the $ D_{\mathrm{b}\overline{\mathrm{b}}} $-subleading jet regressed mass are shown for the ggF BDT event category 3. The SM HH ($ \kappa_{2\mathrm{V}}=\kappa_\mathrm{V}=\kappa_\lambda= $ 1) signal is shown scaled to the best fit signal strength $ \mu= $ 3.5. The lower panel shows the ratio of the data and the total prediction, with its uncertainty represented by the shaded band. The error bars on the data points represent the statistical uncertainties. |
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Additional Figure 4-c:
The data and fitted signal and background distributions for the $ D_{\mathrm{b}\overline{\mathrm{b}}} $-subleading jet regressed mass are shown for the QCD multijet background control region. The SM HH ($ \kappa_{2\mathrm{V}}=\kappa_\mathrm{V}=\kappa_\lambda= $ 1) signal is shown scaled to the best fit signal strength $ \mu= $ 3.5. The lower panel shows the ratio of the data and the total prediction, with its uncertainty represented by the shaded band. The error bars on the data points represent the statistical uncertainties. |
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Additional Figure 5:
The data in the ggF BDT event categories 1 (upper), 2 (lower left), and 3 (lower right) after subtracting all background processes except the QCD multijet one compared to the QCD multijet background prediction derived from the dedicated control region. The fitted shape and uncertainty are derived from a simultaneous background-only fit of all four ggF analysis regions. |
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Additional Figure 5-a:
The data in the ggF BDT event category 1 after subtracting all background processes except the QCD multijet one compared to the QCD multijet background prediction derived from the dedicated control region. The fitted shape and uncertainty are derived from a simultaneous background-only fit of all four ggF analysis regions. |
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Additional Figure 5-b:
The data in the ggF BDT event category 2 after subtracting all background processes except the QCD multijet one compared to the QCD multijet background prediction derived from the dedicated control region. The fitted shape and uncertainty are derived from a simultaneous background-only fit of all four ggF analysis regions. |
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Additional Figure 5-c:
The data in the ggF BDT event category 3 after subtracting all background processes except the QCD multijet one compared to the QCD multijet background prediction derived from the dedicated control region. The fitted shape and uncertainty are derived from a simultaneous background-only fit of all four ggF analysis regions. |
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Additional Figure 6:
The data and expected background distributions from simulation in the $ {\mathrm{t}\overline{\mathrm{t}}} $ control region for some of the most discriminating BDT input variables, including the $ D_{\mathrm{b}\overline{\mathrm{b}}} $-leading jet $ m_\mathrm{SD} $ (upper left) and $ D_{\mathrm{b}\overline{\mathrm{b}}} $ (upper right), $ m_{\mathrm{H}\mathrm{H}} $ (lower left), and $ {p_{\mathrm{T}}}_{\text{j}_1}/m_{\mathrm{H}\mathrm{H}} $ (lower right). The lower panel shows the ratio of the data and the total background prediction, with its statistical uncertainty represented by the shaded band. The error bars on the data points represent the statistical uncertainties. |
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Additional Figure 6-a:
The data and expected background distributions from simulation in the $ {\mathrm{t}\overline{\mathrm{t}}} $ control region for the leading jet $ m_\mathrm{SD} $. The lower panel shows the ratio of the data and the total background prediction, with its statistical uncertainty represented by the shaded band. The error bars on the data points represent the statistical uncertainties. |
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Additional Figure 6-b:
The data and expected background distributions from simulation in the $ {\mathrm{t}\overline{\mathrm{t}}} $ control region for the leading jet $ D_{\mathrm{b}\overline{\mathrm{b}}} $. The lower panel shows the ratio of the data and the total background prediction, with its statistical uncertainty represented by the shaded band. The error bars on the data points represent the statistical uncertainties. |
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Additional Figure 6-c:
The data and expected background distributions from simulation in the $ {\mathrm{t}\overline{\mathrm{t}}} $ control region for $ m_{\mathrm{H}\mathrm{H}} $. The lower panel shows the ratio of the data and the total background prediction, with its statistical uncertainty represented by the shaded band. The error bars on the data points represent the statistical uncertainties. |
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Additional Figure 6-d:
The data and expected background distributions from simulation in the $ {\mathrm{t}\overline{\mathrm{t}}} $ control region for $ {p_{\mathrm{T}}}_{\text{j}_1}/m_{\mathrm{H}\mathrm{H}} $. The lower panel shows the ratio of the data and the total background prediction, with its statistical uncertainty represented by the shaded band. The error bars on the data points represent the statistical uncertainties. |
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Additional Figure 7:
Expected and observed 95% CL upper limits on HH production with respect to the SM expectation ($ \kappa_\lambda=\kappa_{\mathrm{t}}=\kappa_\mathrm{V}=\kappa_{2\mathrm{V}}= $ 1) in the individual ggF and VBF search categories and their combination. |
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Additional Figure 8:
Expected and observed 95% CL upper limits on HH production with respect to the expectation for $ \kappa_\lambda=\kappa_{\mathrm{t}}=\kappa_\mathrm{V}= $ 1, $ \kappa_{2\mathrm{V}}= $ 0 in the individual ggF and VBF search categories and their combination. |
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Additional Figure 9:
Observed (solid line) and expected (dashed line) 95% CL exclusion limit on the product of the inclusive HH production cross section and the branching fraction into $ \mathrm{b}\overline{\mathrm{b}}\mathrm{b}\overline{\mathrm{b}} $ as a function of $ \kappa_\lambda $ (upper), $ \kappa_{2\mathrm{V}} $ (lower left), and $ \kappa_\mathrm{V} $ (lower right) is shown with other couplings fixed to the SM values. The green and yellow bands correspond to one and two standard deviations, respectively, around the expected median. The red solid line depicts the theoretical prediction for the HH production cross section and the red band shows its uncertainty [60,109,61,110,5,111,112,113,114,8].The crossings of observed limit and the theoretical cross section indicate the ranges of the coupling values excluded at 95% CL. |
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Additional Figure 9-a:
Observed (solid line) and expected (dashed line) 95% CL exclusion limit on the product of the inclusive HH production cross section and the branching fraction into $ \mathrm{b}\overline{\mathrm{b}}\mathrm{b}\overline{\mathrm{b}} $ as a function of $ \kappa_\lambda $ is shown with other couplings fixed to the SM values. The green and yellow bands correspond to one and two standard deviations, respectively, around the expected median. The red solid line depicts the theoretical prediction for the HH production cross section and the red band shows its uncertainty [60,109,61,110,5,111,112,113,114,8].The crossings of observed limit and the theoretical cross section indicate the ranges of the coupling values excluded at 95% CL. |
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Additional Figure 9-b:
Observed (solid line) and expected (dashed line) 95% CL exclusion limit on the product of the inclusive HH production cross section and the branching fraction into $ \mathrm{b}\overline{\mathrm{b}}\mathrm{b}\overline{\mathrm{b}} $ as a function of $ \kappa_{2\mathrm{V}} $ is shown with other couplings fixed to the SM values. The green and yellow bands correspond to one and two standard deviations, respectively, around the expected median. The red solid line depicts the theoretical prediction for the HH production cross section and the red band shows its uncertainty [60,109,61,110,5,111,112,113,114,8].The crossings of observed limit and the theoretical cross section indicate the ranges of the coupling values excluded at 95% CL. |
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Additional Figure 9-c:
Observed (solid line) and expected (dashed line) 95% CL exclusion limit on the product of the inclusive HH production cross section and the branching fraction into $ \mathrm{b}\overline{\mathrm{b}}\mathrm{b}\overline{\mathrm{b}} $ as a function of $ \kappa_\mathrm{V} $ is shown with other couplings fixed to the SM values. The green and yellow bands correspond to one and two standard deviations, respectively, around the expected median. The red solid line depicts the theoretical prediction for the HH production cross section and the red band shows its uncertainty [60,109,61,110,5,111,112,113,114,8].The crossings of observed limit and the theoretical cross section indicate the ranges of the coupling values excluded at 95% CL. |
png pdf |
Additional Figure 10:
Observed (solid line) and expected (dashed line) 95% CL exclusion limit on the product of the VBF HH production cross section and the branching fraction into $ \mathrm{b}\overline{\mathrm{b}}\mathrm{b}\overline{\mathrm{b}} $ as a function of $ \kappa_{2\mathrm{V}} $ (left) and $ \kappa_\mathrm{V} $ (right) is shown with other couplings fixed to the SM values. The green and yellow bands correspond to one and two standard deviations, respectively, around the expected median. The red solid line depicts the theoretical prediction for the VBF HH production cross section and the red band shows its uncertainty [113,114,8]. The crossings of observed limit and the theoretical cross section indicate the ranges of the coupling values excluded at 95% CL. |
png pdf |
Additional Figure 10-a:
Observed (solid line) and expected (dashed line) 95% CL exclusion limit on the product of the VBF HH production cross section and the branching fraction into $ \mathrm{b}\overline{\mathrm{b}}\mathrm{b}\overline{\mathrm{b}} $ as a function of $ \kappa_{2\mathrm{V}} $ is shown with other couplings fixed to the SM values. The green and yellow bands correspond to one and two standard deviations, respectively, around the expected median. The red solid line depicts the theoretical prediction for the VBF HH production cross section and the red band shows its uncertainty [113,114,8]. The crossings of observed limit and the theoretical cross section indicate the ranges of the coupling values excluded at 95% CL. |
png pdf |
Additional Figure 10-b:
Observed (solid line) and expected (dashed line) 95% CL exclusion limit on the product of the VBF HH production cross section and the branching fraction into $ \mathrm{b}\overline{\mathrm{b}}\mathrm{b}\overline{\mathrm{b}} $ as a function of $ \kappa_\mathrm{V} $ is shown with other couplings fixed to the SM values. The green and yellow bands correspond to one and two standard deviations, respectively, around the expected median. The red solid line depicts the theoretical prediction for the VBF HH production cross section and the red band shows its uncertainty [113,114,8]. The crossings of observed limit and the theoretical cross section indicate the ranges of the coupling values excluded at 95% CL. |
png pdf |
Additional Figure 11:
Two-parameter profile likelihood test statistic ($ -2\Delta\ln\mathcal{L} $) scan in data as a function of $ \kappa_{2\mathrm{V}} $ and $ \kappa_\mathrm{V} $. The black cross indicates the minimum, while the red diamond marks the SM expectation ($ \kappa_\lambda = \kappa_{2\mathrm{V}} = $ 1). The gray solid, dashed, dotted, and dash-dotted contours enclose the 1, 2, 3, and 5 $ \,\sigma \text{CL} $ regions, respectively. |
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Additional Figure 12:
Two candidate events in which two Higgs bosons produced at large transverse momentum decay into collimated bottom quark-antiquark pairs, where both pairs are reconstructed as large-radius jets, represented by the orange cones. Two additional small-radius jets, represented by the yellow cones, are also measured in the forward segments of the detector in the event on the right. The energy deposits in the electromagnetic and hadron calorimeters are represented by green and blue boxes, respectively. In this visualization, only the former ones are displayed for the detector endcap regions. A muon (red line), potentially arising from a bottom hadron decay in one of the Higgs boson candidate jets, is measured in dedicated detectors (red boxes). The event signatures are consistent with gluon fusion (left) or vector boson fusion (right) production of a Higgs boson pair. |
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Additional Figure 12-a:
Candidate event in which two Higgs bosons produced at large transverse momentum decay into collimated bottom quark-antiquark pairs, where both pairs are reconstructed as large-radius jets, represented by the orange cones. The energy deposits in the electromagnetic and hadron calorimeters are represented by green and blue boxes, respectively. In this visualization, only the former ones are displayed for the detector endcap regions. A muon (red line), potentially arising from a bottom hadron decay in one of the Higgs boson candidate jets, is measured in dedicated detectors (red boxes). The event signature is consistent with vector boson fusion production of a Higgs boson pair. |
png |
Additional Figure 12-b:
Candidate event in which two Higgs bosons produced at large transverse momentum decay into collimated bottom quark-antiquark pairs, where both pairs are reconstructed as large-radius jets, represented by the orange cones. Two additional small-radius jets, represented by the yellow cones, are also measured in the forward segments of the detector. The energy deposits in the electromagnetic and hadron calorimeters are represented by green and blue boxes, respectively. In this visualization, only the former ones are displayed for the detector endcap regions. A muon (red line), potentially arising from a bottom hadron decay in one of the Higgs boson candidate jets, is measured in dedicated detectors (red boxes). The event signature is consistent with gluon fusion production of a Higgs boson pair. |
png |
Additional Figure 12-c:
Candidate event in which two Higgs bosons produced at large transverse momentum decay into collimated bottom quark-antiquark pairs, where both pairs are reconstructed as large-radius jets, represented by the orange cones. The energy deposits in the electromagnetic and hadron calorimeters are represented by green and blue boxes, respectively. In this visualization, only the former ones are displayed for the detector endcap regions. A muon (red line), potentially arising from a bottom hadron decay in one of the Higgs boson candidate jets, is measured in dedicated detectors (red boxes). The event signature is consistent with vector boson fusion production of a Higgs boson pair. |
png |
Additional Figure 12-d:
Candidate event in which two Higgs bosons produced at large transverse momentum decay into collimated bottom quark-antiquark pairs, where both pairs are reconstructed as large-radius jets, represented by the orange cones. Two additional small-radius jets, represented by the yellow cones, are also measured in the forward segments of the detector. The energy deposits in the electromagnetic and hadron calorimeters are represented by green and blue boxes, respectively. In this visualization, only the former ones are displayed for the detector endcap regions. A muon (red line), potentially arising from a bottom hadron decay in one of the Higgs boson candidate jets, is measured in dedicated detectors (red boxes). The event signature is consistent with gluon fusion production of a Higgs boson pair. |
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Additional Figure 13:
Leading-order Feynman diagrams for nonresonant HH production via gluon fusion (upper) and vector boson fusion (lower). |
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Additional Figure 13-a:
Leading-order Feynman diagram for nonresonant HH production via gluon fusion. |
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Additional Figure 13-b:
Leading-order Feynman diagram for nonresonant HH production via gluon fusion. |
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Additional Figure 13-c:
Leading-order Feynman diagram for nonresonant HH production via vector boson fusion. |
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Additional Figure 13-d:
Leading-order Feynman diagram for nonresonant HH production via vector boson fusion. |
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Additional Figure 13-e:
Leading-order Feynman diagram for nonresonant HH production via vector boson fusion. |
| Additional Tables | |
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Additional Table 1:
Major sources of uncertainty in the measurement of the signal strength modifier $ \mu $, and their observed impact ($ \Delta\mu $) from a fit to the combined data set. Decompositions of the statistical, systematic, and theoretical components of the total uncertainty are specified. The impact of each uncertainty is evaluated by computing the uncertainty excluding that source and subtracting it in quadrature from the total uncertainty. The sum in quadrature for each source does not in general equal the total uncertainty of each component because of correlations in the combined fit between nuisance parameters corresponding to different sources. |
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