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| CMS-HIG-21-019 ; CERN-EP-2024-210 | ||
| Measurement of the Higgs boson mass and width using the four-lepton final state in proton-proton collisions at $ \sqrt{s} = $ 13 TeV | ||
| CMS Collaboration | ||
| 20 September 2024 | ||
| Submitted to Phys. Rev. D | ||
| Abstract: A measurement of the Higgs boson mass and width via its decay to two Z bosons is presented. Proton-proton collision data collected by the CMS experiment, corresponding to an integrated luminosity of 138 fb$ ^{-1} $ at a center-of-mass energy of 13 TeV is used. The invariant mass distribution of four leptons in the on-shell Higgs boson decay is used to measure its mass and contrain its width. This yields the most precise single measurement of the Higgs boson mass to date, 125.04 $ \pm $ 0.12 GeV, and an upper limit on the width $ \Gamma_{\mathrm{H}} < $ 330 MeV at 95% confidence level. A combination of the on- and off-shell Higgs boson production decaying to four leptons is used to determine the Higgs boson width, assuming that no new virtual particles affect the production, a premise that is tested by adding new heavy particles in the gluon fusion loop model. This result is combined with a previous CMS analysis of the off-shell Higgs boson production with decay to two leptons and two neutrinos, giving a measured Higgs boson width of 3.0 $ ^{+2.0}_{-1.5} $ MeV, in agreement with the standard model prediction of 4.1 MeV. The strength of the off-shell Higgs boson production is also reported. The scenario of no off-shell Higgs boson production is excluded at a confidence level corresponding to 3.8 standard deviations. | ||
| Links: e-print arXiv:2409.13663 [hep-ex] (PDF) ; CDS record ; inSPIRE record ; CADI line (restricted) ; | ||
| Figures & Tables | Summary | Additional Figures & Tables | References | CMS Publications |
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| Figures | |
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Figure 1:
The observed (points) and predicted (stacked histograms) $ m_{4\ell} $ distributions in the inclusive (upper), 4$ \mu $ (middle left), 4e (middle right), 2e2$ \mu $ (lower left) and 2$ \mu$2e (lower right) final states, defined such that the first lepton pair is taken to be the one with the mass closest to the nominal Z boson mass. The predictions for the Higgs boson signal and the three main backgrounds are given by the different colors. The vertical bars on the points show the statistical uncertainties in the data. |
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Figure 1-a:
The observed (points) and predicted (stacked histograms) $ m_{4\ell} $ distributions in the inclusive (upper), 4$ \mu $ (middle left), 4e (middle right), 2e2$ \mu $ (lower left) and 2$ \mu$2e (lower right) final states, defined such that the first lepton pair is taken to be the one with the mass closest to the nominal Z boson mass. The predictions for the Higgs boson signal and the three main backgrounds are given by the different colors. The vertical bars on the points show the statistical uncertainties in the data. |
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Figure 1-b:
The observed (points) and predicted (stacked histograms) $ m_{4\ell} $ distributions in the inclusive (upper), 4$ \mu $ (middle left), 4e (middle right), 2e2$ \mu $ (lower left) and 2$ \mu$2e (lower right) final states, defined such that the first lepton pair is taken to be the one with the mass closest to the nominal Z boson mass. The predictions for the Higgs boson signal and the three main backgrounds are given by the different colors. The vertical bars on the points show the statistical uncertainties in the data. |
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Figure 1-c:
The observed (points) and predicted (stacked histograms) $ m_{4\ell} $ distributions in the inclusive (upper), 4$ \mu $ (middle left), 4e (middle right), 2e2$ \mu $ (lower left) and 2$ \mu$2e (lower right) final states, defined such that the first lepton pair is taken to be the one with the mass closest to the nominal Z boson mass. The predictions for the Higgs boson signal and the three main backgrounds are given by the different colors. The vertical bars on the points show the statistical uncertainties in the data. |
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Figure 1-d:
The observed (points) and predicted (stacked histograms) $ m_{4\ell} $ distributions in the inclusive (upper), 4$ \mu $ (middle left), 4e (middle right), 2e2$ \mu $ (lower left) and 2$ \mu$2e (lower right) final states, defined such that the first lepton pair is taken to be the one with the mass closest to the nominal Z boson mass. The predictions for the Higgs boson signal and the three main backgrounds are given by the different colors. The vertical bars on the points show the statistical uncertainties in the data. |
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Figure 1-e:
The observed (points) and predicted (stacked histograms) $ m_{4\ell} $ distributions in the inclusive (upper), 4$ \mu $ (middle left), 4e (middle right), 2e2$ \mu $ (lower left) and 2$ \mu$2e (lower right) final states, defined such that the first lepton pair is taken to be the one with the mass closest to the nominal Z boson mass. The predictions for the Higgs boson signal and the three main backgrounds are given by the different colors. The vertical bars on the points show the statistical uncertainties in the data. |
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Figure 2:
Distributions of the observed (points) and predicted (stacked histograms) relative per-event mass uncertainty of the four-lepton system, in the inclusive final state. The predictions for the Higgs boson signal and the three main backgrounds are given by the different colors. The vertical bars on the points show the statistical uncertainties in the data. |
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Figure 3:
Observed (points) and predicted (stacked histograms) yields of four-lepton events in each of the 9 $ \delta m_{4\ell}/m_{4\ell} $ bin categories for the inclusive final state. The bins are shown in the order of increasing $ \delta m_{4\ell}/m_{4\ell} $. The predictions for the Higgs boson signal and the three main backgrounds are given by the different colors. The vertical bars on the points show the statistical uncertainties in the data. |
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Figure 4:
Distributions of the observed (points) and predicted (stacked histograms) $ {\mathcal{D}}^{\text{kin}}_{\text{bkg}} $ of the four-lepton system, in the inclusive final state. The predictions for the Higgs boson signal and the three main backgrounds are given by the different colors. The vertical bars on the points show the statistical uncertainties in the data. |
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Figure 5:
Off-shell data (points) and pre-fit distributions (histograms) for the Untagged (left), $ \mathrm{VBF} $-tagged (middle), and VH-tagged (right) categories. The upper row shows $ m_{4\ell} $ distributions with a requirement on $ {\mathcal{D}}^{\text{kin}}_{\text{bkg}} > $ 0.6 (left), $ \mathcal{D}^{{\mathrm{VBF}}+{\text{dec}}}_\text{bkg} > $ 0.6 (middle), or $ \mathcal{D}^{{\mathrm{V}\mathrm{H}}+{\text{dec}}}_\text{bkg} > $ 0.6 (right) applied for illustration purposes to enhance signal over background contributions. The middle row shows $ \mathcal{D}^\text{kin}_\text{bkg} $ (left), $ \mathcal{D}^{{\mathrm{VBF}}+{\text{dec}}}_\text{bkg} $ (middle), $ \mathcal{D}^{{\mathrm{V}\mathrm{H}}+{\text{dec}}}_\text{bkg} $ (right) distributions, where an additional requirement $ m_{4\ell} > $ 340 GeV is applied to enhance signal-over-background contributions. The lower row plots the $ \mathcal{D}_\text{bsi} $ with both the $ m_{4\ell} $ and $ {\mathcal{D}}^{\text{kin}}_{\text{bkg}} $ requirements specified above. Contributions from the four processes are shown by the different colors, where ``s'', ``b'', and ``i'' refer to the signal, background, and interference contributions, respectively. The vertical bars on the points give the statistical uncertainties in the data, and the horizontal bars represent the bin widths. For the prefit distributions, the different cross sections are set to their SM values. |
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Figure 5-a:
Off-shell data (points) and pre-fit distributions (histograms) for the Untagged (left), $ \mathrm{VBF} $-tagged (middle), and VH-tagged (right) categories. The upper row shows $ m_{4\ell} $ distributions with a requirement on $ {\mathcal{D}}^{\text{kin}}_{\text{bkg}} > $ 0.6 (left), $ \mathcal{D}^{{\mathrm{VBF}}+{\text{dec}}}_\text{bkg} > $ 0.6 (middle), or $ \mathcal{D}^{{\mathrm{V}\mathrm{H}}+{\text{dec}}}_\text{bkg} > $ 0.6 (right) applied for illustration purposes to enhance signal over background contributions. The middle row shows $ \mathcal{D}^\text{kin}_\text{bkg} $ (left), $ \mathcal{D}^{{\mathrm{VBF}}+{\text{dec}}}_\text{bkg} $ (middle), $ \mathcal{D}^{{\mathrm{V}\mathrm{H}}+{\text{dec}}}_\text{bkg} $ (right) distributions, where an additional requirement $ m_{4\ell} > $ 340 GeV is applied to enhance signal-over-background contributions. The lower row plots the $ \mathcal{D}_\text{bsi} $ with both the $ m_{4\ell} $ and $ {\mathcal{D}}^{\text{kin}}_{\text{bkg}} $ requirements specified above. Contributions from the four processes are shown by the different colors, where ``s'', ``b'', and ``i'' refer to the signal, background, and interference contributions, respectively. The vertical bars on the points give the statistical uncertainties in the data, and the horizontal bars represent the bin widths. For the prefit distributions, the different cross sections are set to their SM values. |
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Figure 5-b:
Off-shell data (points) and pre-fit distributions (histograms) for the Untagged (left), $ \mathrm{VBF} $-tagged (middle), and VH-tagged (right) categories. The upper row shows $ m_{4\ell} $ distributions with a requirement on $ {\mathcal{D}}^{\text{kin}}_{\text{bkg}} > $ 0.6 (left), $ \mathcal{D}^{{\mathrm{VBF}}+{\text{dec}}}_\text{bkg} > $ 0.6 (middle), or $ \mathcal{D}^{{\mathrm{V}\mathrm{H}}+{\text{dec}}}_\text{bkg} > $ 0.6 (right) applied for illustration purposes to enhance signal over background contributions. The middle row shows $ \mathcal{D}^\text{kin}_\text{bkg} $ (left), $ \mathcal{D}^{{\mathrm{VBF}}+{\text{dec}}}_\text{bkg} $ (middle), $ \mathcal{D}^{{\mathrm{V}\mathrm{H}}+{\text{dec}}}_\text{bkg} $ (right) distributions, where an additional requirement $ m_{4\ell} > $ 340 GeV is applied to enhance signal-over-background contributions. The lower row plots the $ \mathcal{D}_\text{bsi} $ with both the $ m_{4\ell} $ and $ {\mathcal{D}}^{\text{kin}}_{\text{bkg}} $ requirements specified above. Contributions from the four processes are shown by the different colors, where ``s'', ``b'', and ``i'' refer to the signal, background, and interference contributions, respectively. The vertical bars on the points give the statistical uncertainties in the data, and the horizontal bars represent the bin widths. For the prefit distributions, the different cross sections are set to their SM values. |
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Figure 5-c:
Off-shell data (points) and pre-fit distributions (histograms) for the Untagged (left), $ \mathrm{VBF} $-tagged (middle), and VH-tagged (right) categories. The upper row shows $ m_{4\ell} $ distributions with a requirement on $ {\mathcal{D}}^{\text{kin}}_{\text{bkg}} > $ 0.6 (left), $ \mathcal{D}^{{\mathrm{VBF}}+{\text{dec}}}_\text{bkg} > $ 0.6 (middle), or $ \mathcal{D}^{{\mathrm{V}\mathrm{H}}+{\text{dec}}}_\text{bkg} > $ 0.6 (right) applied for illustration purposes to enhance signal over background contributions. The middle row shows $ \mathcal{D}^\text{kin}_\text{bkg} $ (left), $ \mathcal{D}^{{\mathrm{VBF}}+{\text{dec}}}_\text{bkg} $ (middle), $ \mathcal{D}^{{\mathrm{V}\mathrm{H}}+{\text{dec}}}_\text{bkg} $ (right) distributions, where an additional requirement $ m_{4\ell} > $ 340 GeV is applied to enhance signal-over-background contributions. The lower row plots the $ \mathcal{D}_\text{bsi} $ with both the $ m_{4\ell} $ and $ {\mathcal{D}}^{\text{kin}}_{\text{bkg}} $ requirements specified above. Contributions from the four processes are shown by the different colors, where ``s'', ``b'', and ``i'' refer to the signal, background, and interference contributions, respectively. The vertical bars on the points give the statistical uncertainties in the data, and the horizontal bars represent the bin widths. For the prefit distributions, the different cross sections are set to their SM values. |
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Figure 5-d:
Off-shell data (points) and pre-fit distributions (histograms) for the Untagged (left), $ \mathrm{VBF} $-tagged (middle), and VH-tagged (right) categories. The upper row shows $ m_{4\ell} $ distributions with a requirement on $ {\mathcal{D}}^{\text{kin}}_{\text{bkg}} > $ 0.6 (left), $ \mathcal{D}^{{\mathrm{VBF}}+{\text{dec}}}_\text{bkg} > $ 0.6 (middle), or $ \mathcal{D}^{{\mathrm{V}\mathrm{H}}+{\text{dec}}}_\text{bkg} > $ 0.6 (right) applied for illustration purposes to enhance signal over background contributions. The middle row shows $ \mathcal{D}^\text{kin}_\text{bkg} $ (left), $ \mathcal{D}^{{\mathrm{VBF}}+{\text{dec}}}_\text{bkg} $ (middle), $ \mathcal{D}^{{\mathrm{V}\mathrm{H}}+{\text{dec}}}_\text{bkg} $ (right) distributions, where an additional requirement $ m_{4\ell} > $ 340 GeV is applied to enhance signal-over-background contributions. The lower row plots the $ \mathcal{D}_\text{bsi} $ with both the $ m_{4\ell} $ and $ {\mathcal{D}}^{\text{kin}}_{\text{bkg}} $ requirements specified above. Contributions from the four processes are shown by the different colors, where ``s'', ``b'', and ``i'' refer to the signal, background, and interference contributions, respectively. The vertical bars on the points give the statistical uncertainties in the data, and the horizontal bars represent the bin widths. For the prefit distributions, the different cross sections are set to their SM values. |
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Figure 5-e:
Off-shell data (points) and pre-fit distributions (histograms) for the Untagged (left), $ \mathrm{VBF} $-tagged (middle), and VH-tagged (right) categories. The upper row shows $ m_{4\ell} $ distributions with a requirement on $ {\mathcal{D}}^{\text{kin}}_{\text{bkg}} > $ 0.6 (left), $ \mathcal{D}^{{\mathrm{VBF}}+{\text{dec}}}_\text{bkg} > $ 0.6 (middle), or $ \mathcal{D}^{{\mathrm{V}\mathrm{H}}+{\text{dec}}}_\text{bkg} > $ 0.6 (right) applied for illustration purposes to enhance signal over background contributions. The middle row shows $ \mathcal{D}^\text{kin}_\text{bkg} $ (left), $ \mathcal{D}^{{\mathrm{VBF}}+{\text{dec}}}_\text{bkg} $ (middle), $ \mathcal{D}^{{\mathrm{V}\mathrm{H}}+{\text{dec}}}_\text{bkg} $ (right) distributions, where an additional requirement $ m_{4\ell} > $ 340 GeV is applied to enhance signal-over-background contributions. The lower row plots the $ \mathcal{D}_\text{bsi} $ with both the $ m_{4\ell} $ and $ {\mathcal{D}}^{\text{kin}}_{\text{bkg}} $ requirements specified above. Contributions from the four processes are shown by the different colors, where ``s'', ``b'', and ``i'' refer to the signal, background, and interference contributions, respectively. The vertical bars on the points give the statistical uncertainties in the data, and the horizontal bars represent the bin widths. For the prefit distributions, the different cross sections are set to their SM values. |
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Figure 5-f:
Off-shell data (points) and pre-fit distributions (histograms) for the Untagged (left), $ \mathrm{VBF} $-tagged (middle), and VH-tagged (right) categories. The upper row shows $ m_{4\ell} $ distributions with a requirement on $ {\mathcal{D}}^{\text{kin}}_{\text{bkg}} > $ 0.6 (left), $ \mathcal{D}^{{\mathrm{VBF}}+{\text{dec}}}_\text{bkg} > $ 0.6 (middle), or $ \mathcal{D}^{{\mathrm{V}\mathrm{H}}+{\text{dec}}}_\text{bkg} > $ 0.6 (right) applied for illustration purposes to enhance signal over background contributions. The middle row shows $ \mathcal{D}^\text{kin}_\text{bkg} $ (left), $ \mathcal{D}^{{\mathrm{VBF}}+{\text{dec}}}_\text{bkg} $ (middle), $ \mathcal{D}^{{\mathrm{V}\mathrm{H}}+{\text{dec}}}_\text{bkg} $ (right) distributions, where an additional requirement $ m_{4\ell} > $ 340 GeV is applied to enhance signal-over-background contributions. The lower row plots the $ \mathcal{D}_\text{bsi} $ with both the $ m_{4\ell} $ and $ {\mathcal{D}}^{\text{kin}}_{\text{bkg}} $ requirements specified above. Contributions from the four processes are shown by the different colors, where ``s'', ``b'', and ``i'' refer to the signal, background, and interference contributions, respectively. The vertical bars on the points give the statistical uncertainties in the data, and the horizontal bars represent the bin widths. For the prefit distributions, the different cross sections are set to their SM values. |
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Figure 5-g:
Off-shell data (points) and pre-fit distributions (histograms) for the Untagged (left), $ \mathrm{VBF} $-tagged (middle), and VH-tagged (right) categories. The upper row shows $ m_{4\ell} $ distributions with a requirement on $ {\mathcal{D}}^{\text{kin}}_{\text{bkg}} > $ 0.6 (left), $ \mathcal{D}^{{\mathrm{VBF}}+{\text{dec}}}_\text{bkg} > $ 0.6 (middle), or $ \mathcal{D}^{{\mathrm{V}\mathrm{H}}+{\text{dec}}}_\text{bkg} > $ 0.6 (right) applied for illustration purposes to enhance signal over background contributions. The middle row shows $ \mathcal{D}^\text{kin}_\text{bkg} $ (left), $ \mathcal{D}^{{\mathrm{VBF}}+{\text{dec}}}_\text{bkg} $ (middle), $ \mathcal{D}^{{\mathrm{V}\mathrm{H}}+{\text{dec}}}_\text{bkg} $ (right) distributions, where an additional requirement $ m_{4\ell} > $ 340 GeV is applied to enhance signal-over-background contributions. The lower row plots the $ \mathcal{D}_\text{bsi} $ with both the $ m_{4\ell} $ and $ {\mathcal{D}}^{\text{kin}}_{\text{bkg}} $ requirements specified above. Contributions from the four processes are shown by the different colors, where ``s'', ``b'', and ``i'' refer to the signal, background, and interference contributions, respectively. The vertical bars on the points give the statistical uncertainties in the data, and the horizontal bars represent the bin widths. For the prefit distributions, the different cross sections are set to their SM values. |
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Figure 5-h:
Off-shell data (points) and pre-fit distributions (histograms) for the Untagged (left), $ \mathrm{VBF} $-tagged (middle), and VH-tagged (right) categories. The upper row shows $ m_{4\ell} $ distributions with a requirement on $ {\mathcal{D}}^{\text{kin}}_{\text{bkg}} > $ 0.6 (left), $ \mathcal{D}^{{\mathrm{VBF}}+{\text{dec}}}_\text{bkg} > $ 0.6 (middle), or $ \mathcal{D}^{{\mathrm{V}\mathrm{H}}+{\text{dec}}}_\text{bkg} > $ 0.6 (right) applied for illustration purposes to enhance signal over background contributions. The middle row shows $ \mathcal{D}^\text{kin}_\text{bkg} $ (left), $ \mathcal{D}^{{\mathrm{VBF}}+{\text{dec}}}_\text{bkg} $ (middle), $ \mathcal{D}^{{\mathrm{V}\mathrm{H}}+{\text{dec}}}_\text{bkg} $ (right) distributions, where an additional requirement $ m_{4\ell} > $ 340 GeV is applied to enhance signal-over-background contributions. The lower row plots the $ \mathcal{D}_\text{bsi} $ with both the $ m_{4\ell} $ and $ {\mathcal{D}}^{\text{kin}}_{\text{bkg}} $ requirements specified above. Contributions from the four processes are shown by the different colors, where ``s'', ``b'', and ``i'' refer to the signal, background, and interference contributions, respectively. The vertical bars on the points give the statistical uncertainties in the data, and the horizontal bars represent the bin widths. For the prefit distributions, the different cross sections are set to their SM values. |
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Figure 5-i:
Off-shell data (points) and pre-fit distributions (histograms) for the Untagged (left), $ \mathrm{VBF} $-tagged (middle), and VH-tagged (right) categories. The upper row shows $ m_{4\ell} $ distributions with a requirement on $ {\mathcal{D}}^{\text{kin}}_{\text{bkg}} > $ 0.6 (left), $ \mathcal{D}^{{\mathrm{VBF}}+{\text{dec}}}_\text{bkg} > $ 0.6 (middle), or $ \mathcal{D}^{{\mathrm{V}\mathrm{H}}+{\text{dec}}}_\text{bkg} > $ 0.6 (right) applied for illustration purposes to enhance signal over background contributions. The middle row shows $ \mathcal{D}^\text{kin}_\text{bkg} $ (left), $ \mathcal{D}^{{\mathrm{VBF}}+{\text{dec}}}_\text{bkg} $ (middle), $ \mathcal{D}^{{\mathrm{V}\mathrm{H}}+{\text{dec}}}_\text{bkg} $ (right) distributions, where an additional requirement $ m_{4\ell} > $ 340 GeV is applied to enhance signal-over-background contributions. The lower row plots the $ \mathcal{D}_\text{bsi} $ with both the $ m_{4\ell} $ and $ {\mathcal{D}}^{\text{kin}}_{\text{bkg}} $ requirements specified above. Contributions from the four processes are shown by the different colors, where ``s'', ``b'', and ``i'' refer to the signal, background, and interference contributions, respectively. The vertical bars on the points give the statistical uncertainties in the data, and the horizontal bars represent the bin widths. For the prefit distributions, the different cross sections are set to their SM values. |
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Figure 7:
Illustration of how the on-shell statistical model is constructed, combining the $ m_4\ell $ distributions from all data-taking years and all final states. The red, blue, and brown lines show the results of the fit to the signal, background, and their sum, respectively.. The solid black points with vertical bars show the data and the associated statistical uncertainties. |
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Figure 8:
The profile likelihood from the $ m_{\mathrm{H}} $ fit using the $ \mathcal{N} $-2D$ '_\text{BS} $ model for each of the 4$ \ell $ categories and combined. The change in likelihood corresponding to 68 and 95% CLs are shown by the dashed horizontal lines. Both statistical and systematic uncertainties are included in the fits. |
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Figure 9:
Summary of the CMS Higgs boson mass measurements using the four-lepton final state. The red vertical line and the gray column represent the best fit value and the total uncertainty, respectively, as measured by combining the Runs 1 and 2 data. The yellow band and horizontal black bars show the statistical and total uncertainties in each measurement, respectively. The value of each measurement is given, along with the total and statistical only (in parentheses) uncertainties. |
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Figure 10:
Distribution of 1 $ -\text{CL} $ vs. $ \Gamma_\mathrm{H} $ from the fit in the measurement of the Higgs boson width using on-shell production only. The CL values shown by the points are extracted using the Feldman-Cousins approach. The vertical bars on the points represent the spread of the simulated pseudo-experiment values. The 68 and 95% CL values are shown by the dashed horizontal lines. |
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Figure 11:
Observed (solid) and expected (dashed) profile likelihood projections from the Higgs boson width fit using on- and off-shell production from this analysis. The analysis of the off-shell $ \mathrm{H}\to\mathrm{Z}\mathrm{Z}\to4\ell $ channel combined with the on-shell $ \mathrm{H}\to\mathrm{Z}\mathrm{Z}\to4\ell $ channel [83] is shown in black. The full combination of $ \mathrm{H}\to\mathrm{Z}\mathrm{Z}\to4\ell $ with the off-shell $ \mathrm{H}\to\mathrm{Z}\mathrm{Z}\to2\ell2\nu $ [24] is given in red. The black horizontal dashed lines show the 68 and 95% CL values. |
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Figure 12:
Observed 2D profile likelihood projection of the off-shell signal strength parameters ($ \mu^\text{off-shell }_{\mathrm{F}} $, $ \mu^\text{off-shell }_{\mathrm{V}} $) from the fit to the combined off-shell $ \mathrm{H}\to\mathrm{Z}\mathrm{Z}\to4\ell $ and 2 $ \ell2\nu $ channels. The best fit value is shown by the black cross and the SM prediction by the red x. The 68 and 95% CL contours are given by the dashed and solid curves, respectively. The color scale to the right of the plot relates the quantitative values. |
| Tables | |
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Table 1:
Summary of the three production categories in the off-shell $ m_{4\ell} $ region and the observables used in the fits. |
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Table 2:
The observed and expected yields for the Higgs boson signal and background contributions in the on-shell region 105 $ < m_{4\ell} < $ 140 GeV, for each of the four-lepton categories and the total. |
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Table 3:
Observed and expected yields for the Higgs boson signal and background contributions in the off-shell region $ m_{4\ell} > $ 220 GeV, for each of the four-lepton categories and the total. The yields from interference of the signal and background and the ZH cross-feed are also shown. |
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Table 4:
Best fit values for the mass of the Higgs boson measured in the inclusive 4$ \ell $ final state and separately for different flavor categories using the 1D approach. Uncertainties are separated into statistical and systematic uncertainties. Expected uncertainties are also given assuming $ m_{\mathrm{H}} = $ 125.38 GeV [88]. |
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Table 5:
Best fit values for the mass of the Higgs boson measured in the inclusive 4$ \ell $ final state and separately for different flavor categories, using the final fit configuration ($ \mathcal{N} $-2D'$ _\text{BS} $). Uncertainties are separated into statistical and systematic uncertainties. Expected uncertainties are also given assuming $ m_{\mathrm{H}} = $ 125.38 GeV [88]. |
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Table 6:
Summary of the total Higgs boson width $ \Gamma_\mathrm{H} $ measurement, showing the 68% CL (central values with uncertainties) and 95% CL (in square brackets) intervals for the $ \mathrm{H}\to\mathrm{Z}\mathrm{Z}\to4\ell $ channel alone and in combination with the off-shell $ \mathrm{H}\to\mathrm{Z}\mathrm{Z}\to2\ell2\nu $ channel. |
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Table 7:
Measured values of the signal strengths $ \mu^\text{off-shell } $, $ \mu_{\mathrm{F}}^\text{off-shell } $, and $ \mu_{\mathrm{V}}^\text{off-shell } $, and their 68% and 95% (in square brackets) CL intervals from the combined fit to the off-shell $ \mathrm{H}\to\mathrm{Z}\mathrm{Z}\to4\ell $ and 2 $ \ell2\nu $ channels. |
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Table 8:
Summary of the Higgs boson mass and total width $ \Gamma_\mathrm{H} $ measurements, showing the allowed 68% CL (central values with uncertainties) and 95% CL (in square brackets) intervals. Uncertainties are reported as a combination of statistical and systematic uncertainties. The first two rows display the outcomes of the analysis conducted within the on-shell $ \mathrm{H}\to\mathrm{Z}\mathrm{Z}\to4\ell $ region, where the width is restricted to be positive. The third row incorporates results from the off-shell $ \mathrm{H}\to\mathrm{Z}\mathrm{Z}\to4\ell $ region combined with the on-shell $ \mathrm{H}\to\mathrm{Z}\mathrm{Z}\to4\ell $ [83] and off-shell $ \mathrm{H}\to\mathrm{Z}\mathrm{Z}\to2\ell2\nu $ [24]. |
| Summary |
| A measurement of the Higgs boson mass ($ m_{\mathrm{H}} $) and width ($ \Gamma_\mathrm{H} $) using the decays to two Z bosons is presented. The data sample comes from proton-proton collisions at the LHC recorded by the CMS experiment at a center-of-mass energy of 13 TeV, corresponding to an integrated luminosity of 138 fb$ ^{-1} $. On-shell Higgs boson production with the $ \mathrm{H}\to 4\ell $ decay ($ \ell = \mathrm{e} $, $ \mu $) is used to measure its mass and constrain its width. The mass measurement yields $ m_{\mathrm{H}}= $ 125.04 $ \pm $ 0.11 (stat) $ \pm $ 0.05 (syst) GeV $ = $ 125.04 $ \pm $ 0.12 GeV, in agreement with the expected precision of $ \pm $0.12 GeV. From on-shell production events, an upper limit of $ \Gamma_\mathrm{H} < $ 330 MeV is set at 95% confidence level. The mass measurement is further improved combining data from Runs 1 and 2, leading to the most precise single measurement of the mass to date in this channel, $ m_{\mathrm{H}}= $ 125.08 $ \pm $ 0.10 (stat) $ \pm $ 0.05 (syst) GeV $ = $ 125.08 $ \pm $ 0.12 GeV. Using on- and off-shell Higgs boson production with the decay to four leptons, and combining them with a separate analysis with Higgs boson decay to two leptons plus two neutrinos, we measure $ \Gamma_\mathrm{H}= $ 3.0 $ ^{+2.0}_{-1.5} $ MeV, consistent with the standard model prediction of 4.1 MeV. These results are summarized in Table 8. The strength of the off-shell Higgs boson production is also reported, and the scenario of no off-shell Higgs boson production is excluded at a confidence level corresponding to 3.8 standard deviations. Results of the measurements are tabulated in the HEPData record for this analysis [97]. |
| Additional Figures | |
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Additional Figure 1:
Comparison of the four-lepton invariant mass line shape with (red) and without (blue) the beam spot contraint, split per final state, merging all years. Top row: 4 $ \mu $ and 4e; bottom row: 2e2$ \mu $ and 2$ \mu $2e. $ \sigma^{68\%} $, defined as the Gaussian width used to fit the smallest invariant mass window containing 68% of the signal event, is also shown. |
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Additional Figure 1-a:
Comparison of the four-lepton invariant mass line shape with (red) and without (blue) the beam spot contraint, split per final state, merging all years. Top row: 4 $ \mu $ and 4e; bottom row: 2e2$ \mu $ and 2$ \mu $2e. $ \sigma^{68\%} $, defined as the Gaussian width used to fit the smallest invariant mass window containing 68% of the signal event, is also shown. |
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Additional Figure 1-b:
Comparison of the four-lepton invariant mass line shape with (red) and without (blue) the beam spot contraint, split per final state, merging all years. Top row: 4 $ \mu $ and 4e; bottom row: 2e2$ \mu $ and 2$ \mu $2e. $ \sigma^{68\%} $, defined as the Gaussian width used to fit the smallest invariant mass window containing 68% of the signal event, is also shown. |
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Additional Figure 1-c:
Comparison of the four-lepton invariant mass line shape with (red) and without (blue) the beam spot contraint, split per final state, merging all years. Top row: 4 $ \mu $ and 4e; bottom row: 2e2$ \mu $ and 2$ \mu $2e. $ \sigma^{68\%} $, defined as the Gaussian width used to fit the smallest invariant mass window containing 68% of the signal event, is also shown. |
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Additional Figure 1-d:
Comparison of the four-lepton invariant mass line shape with (red) and without (blue) the beam spot contraint, split per final state, merging all years. Top row: 4 $ \mu $ and 4e; bottom row: 2e2$ \mu $ and 2$ \mu $2e. $ \sigma^{68\%} $, defined as the Gaussian width used to fit the smallest invariant mass window containing 68% of the signal event, is also shown. |
png pdf |
Additional Figure 2:
Difference between data and simulation in $ Z(J/\psi) \rightarrow 2\ell $, normalized to simulation, as a function of $ p_{\mathrm{T}} $ and $ |\eta| $ for muons (left) and electron (right), regardless of the second lepton. From top to bottom: 2018, 2017, 2016 pre- and post-VFP. |
png pdf |
Additional Figure 2-a:
Difference between data and simulation in $ Z(J/\psi) \rightarrow 2\ell $, normalized to simulation, as a function of $ p_{\mathrm{T}} $ and $ |\eta| $ for muons (left) and electron (right), regardless of the second lepton. From top to bottom: 2018, 2017, 2016 pre- and post-VFP. |
png pdf |
Additional Figure 2-b:
Difference between data and simulation in $ Z(J/\psi) \rightarrow 2\ell $, normalized to simulation, as a function of $ p_{\mathrm{T}} $ and $ |\eta| $ for muons (left) and electron (right), regardless of the second lepton. From top to bottom: 2018, 2017, 2016 pre- and post-VFP. |
png pdf |
Additional Figure 2-c:
Difference between data and simulation in $ Z(J/\psi) \rightarrow 2\ell $, normalized to simulation, as a function of $ p_{\mathrm{T}} $ and $ |\eta| $ for muons (left) and electron (right), regardless of the second lepton. From top to bottom: 2018, 2017, 2016 pre- and post-VFP. |
png pdf |
Additional Figure 2-d:
Difference between data and simulation in $ Z(J/\psi) \rightarrow 2\ell $, normalized to simulation, as a function of $ p_{\mathrm{T}} $ and $ |\eta| $ for muons (left) and electron (right), regardless of the second lepton. From top to bottom: 2018, 2017, 2016 pre- and post-VFP. |
png pdf |
Additional Figure 2-e:
Difference between data and simulation in $ Z(J/\psi) \rightarrow 2\ell $, normalized to simulation, as a function of $ p_{\mathrm{T}} $ and $ |\eta| $ for muons (left) and electron (right), regardless of the second lepton. From top to bottom: 2018, 2017, 2016 pre- and post-VFP. |
png pdf |
Additional Figure 2-f:
Difference between data and simulation in $ Z(J/\psi) \rightarrow 2\ell $, normalized to simulation, as a function of $ p_{\mathrm{T}} $ and $ |\eta| $ for muons (left) and electron (right), regardless of the second lepton. From top to bottom: 2018, 2017, 2016 pre- and post-VFP. |
png pdf |
Additional Figure 2-g:
Difference between data and simulation in $ Z(J/\psi) \rightarrow 2\ell $, normalized to simulation, as a function of $ p_{\mathrm{T}} $ and $ |\eta| $ for muons (left) and electron (right), regardless of the second lepton. From top to bottom: 2018, 2017, 2016 pre- and post-VFP. |
png pdf |
Additional Figure 2-h:
Difference between data and simulation in $ Z(J/\psi) \rightarrow 2\ell $, normalized to simulation, as a function of $ p_{\mathrm{T}} $ and $ |\eta| $ for muons (left) and electron (right), regardless of the second lepton. From top to bottom: 2018, 2017, 2016 pre- and post-VFP. |
png pdf |
Additional Figure 3:
The observed (expected) likelihood scan as a function of $ m_{\mathrm{H}} $ is shown in black (red) using the $ \mathcal{N}--2D'_\text{BS} $ approach. The scans are shown both with (solid line) and without (dashed line) systematic uncertainties. Expected likelihood has been obtained with the hypothesis $ m_\mathrm{H} = $ 125.38 GeV and then shifted towards the observed central value of 125.04 GeV. |
png pdf |
Additional Figure 4:
Comparison of measured mass resolution with the predicted dilepton mass resolution using the event-by-event mass uncertainty for $ \mathrm{Z}\rightarrow\ell\ell $ events in data. The dashed lines denote the $ \pm$10%, the biggest value used as the systematic uncertainty on the resolution. Top row: 2016; bottom row 2017 (left) and 2018 (right). |
png pdf |
Additional Figure 4-a:
Comparison of measured mass resolution with the predicted dilepton mass resolution using the event-by-event mass uncertainty for $ \mathrm{Z}\rightarrow\ell\ell $ events in data. The dashed lines denote the $ \pm$10%, the biggest value used as the systematic uncertainty on the resolution. Top row: 2016; bottom row 2017 (left) and 2018 (right). |
png pdf |
Additional Figure 4-b:
Comparison of measured mass resolution with the predicted dilepton mass resolution using the event-by-event mass uncertainty for $ \mathrm{Z}\rightarrow\ell\ell $ events in data. The dashed lines denote the $ \pm$10%, the biggest value used as the systematic uncertainty on the resolution. Top row: 2016; bottom row 2017 (left) and 2018 (right). |
png pdf |
Additional Figure 4-c:
Comparison of measured mass resolution with the predicted dilepton mass resolution using the event-by-event mass uncertainty for $ \mathrm{Z}\rightarrow\ell\ell $ events in data. The dashed lines denote the $ \pm$10%, the biggest value used as the systematic uncertainty on the resolution. Top row: 2016; bottom row 2017 (left) and 2018 (right). |
png pdf |
Additional Figure 4-d:
Comparison of measured mass resolution with the predicted dilepton mass resolution using the event-by-event mass uncertainty for $ \mathrm{Z}\rightarrow\ell\ell $ events in data. The dashed lines denote the $ \pm$10%, the biggest value used as the systematic uncertainty on the resolution. Top row: 2016; bottom row 2017 (left) and 2018 (right). |
png pdf |
Additional Figure 5:
Observed (solid) and expected (dashed) profile likelihood projection on the Higgs boson width using on-shell and off-shell production. The analysis of $ \mathrm{H}\to\mathrm{Z}\mathrm{Z}\to4\ell $, considering an unconstrained (blue) coupling strength $ \kappa_\mathrm{Q} $, is presented alongside the same analysis with this coupling constrained to zero (black). |
png pdf |
Additional Figure 6:
Observed (solid) and expected (dashed) profile likelihood projection on the coupling strength terms using on-shell and off-shell production for both $ \mathrm{H}\to\mathrm{Z}\mathrm{Z}\to4\ell $ (black) and the combination with $ \mathrm{H}\to\mathrm{Z}\mathrm{Z}\to2\ell2\nu $ (red). |
png pdf |
Additional Figure 6-a:
Observed (solid) and expected (dashed) profile likelihood projection on the coupling strength terms using on-shell and off-shell production for both $ \mathrm{H}\to\mathrm{Z}\mathrm{Z}\to4\ell $ (black) and the combination with $ \mathrm{H}\to\mathrm{Z}\mathrm{Z}\to2\ell2\nu $ (red). |
png pdf |
Additional Figure 6-b:
Observed (solid) and expected (dashed) profile likelihood projection on the coupling strength terms using on-shell and off-shell production for both $ \mathrm{H}\to\mathrm{Z}\mathrm{Z}\to4\ell $ (black) and the combination with $ \mathrm{H}\to\mathrm{Z}\mathrm{Z}\to2\ell2\nu $ (red). |
png pdf |
Additional Figure 6-c:
Observed (solid) and expected (dashed) profile likelihood projection on the coupling strength terms using on-shell and off-shell production for both $ \mathrm{H}\to\mathrm{Z}\mathrm{Z}\to4\ell $ (black) and the combination with $ \mathrm{H}\to\mathrm{Z}\mathrm{Z}\to2\ell2\nu $ (red). |
| Additional Tables | |
png pdf |
Additional Table 1:
Features of the different approaches used in the on-shell analysis. |
png pdf |
Additional Table 2:
Systematic uncertainty table for the Higgs boson mass measurement. |
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