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The observed (points) and predicted (stacked histograms) $m_{4\Pell}$ distributions in the inclusive (upper), 4$\PGm$ (middle left), 4$\Pe$ (middle right), 2$\Pe$2$\PGm$ (lower left) and 2$\PGm2\Pe$ (lower right) final states, defined such that the first lepton pair is taken to be the one with the mass closest to the nominal $\PZ$ boson mass. The predictions for the \Hboson 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.

The observed (points) and predicted (stacked histograms) $m_{4\Pell}$ distributions in the inclusive (upper), 4$\PGm$ (middle left), 4$\Pe$ (middle right), 2$\Pe$2$\PGm$ (lower left) and 2$\PGm2\Pe$ (lower right) final states, defined such that the first lepton pair is taken to be the one with the mass closest to the nominal $\PZ$ boson mass. The predictions for the \Hboson 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.

The observed (points) and predicted (stacked histograms) $m_{4\Pell}$ distributions in the inclusive (upper), 4$\PGm$ (middle left), 4$\Pe$ (middle right), 2$\Pe$2$\PGm$ (lower left) and 2$\PGm2\Pe$ (lower right) final states, defined such that the first lepton pair is taken to be the one with the mass closest to the nominal $\PZ$ boson mass. The predictions for the \Hboson 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.

The observed (points) and predicted (stacked histograms) $m_{4\Pell}$ distributions in the inclusive (upper), 4$\PGm$ (middle left), 4$\Pe$ (middle right), 2$\Pe$2$\PGm$ (lower left) and 2$\PGm2\Pe$ (lower right) final states, defined such that the first lepton pair is taken to be the one with the mass closest to the nominal $\PZ$ boson mass. The predictions for the \Hboson 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.

The observed (points) and predicted (stacked histograms) $m_{4\Pell}$ distributions in the inclusive (upper), 4$\PGm$ (middle left), 4$\Pe$ (middle right), 2$\Pe$2$\PGm$ (lower left) and 2$\PGm2\Pe$ (lower right) final states, defined such that the first lepton pair is taken to be the one with the mass closest to the nominal $\PZ$ boson mass. The predictions for the \Hboson 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.

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 \Hboson 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.

Observed (points) and predicted (stacked histograms) yields of four-lepton events in each of the 9 \RelMassErr bin categories for the inclusive final state. The bins are shown in the order of increasing \RelMassErr. The predictions for the \Hboson 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.

Distributions of the observed (points) and predicted (stacked histograms) \Dbkgkin of the four-lepton system, in the inclusive final state. The predictions for the \Hboson 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.

Off-shell data (points) and pre-fit distributions (histograms) for the Untagged (left), \VBF-tagged (middle), and \VH-tagged (right) categories. The upper row shows $\mell$ distributions with a requirement on $\Dbkgkin>0.6$ (left), $\mathcal{D}^{{\VBF}+{\text{dec}}}_\text{bkg}>0.6$ (middle), or $\mathcal{D}^{{\VH}+{\text{dec}}}_\text{bkg}>0.6$ (right) applied for illustration purposes to enhance signal over background contributions. The middle row shows $\mathcal{D}^\text{kin}_\text{bkg}$ (left), $\mathcal{D}^{{\VBF}+{\text{dec}}}_\text{bkg}$ (middle), $\mathcal{D}^{{\VH}+{\text{dec}}}_\text{bkg}$ (right) distributions, where an additional requirement $\mell>340$\GeV is applied to enhance signal-over-background contributions. The lower row plots the $\mathcal{D}_\text{bsi}$ with both the \mell and \Dbkgkin 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.

Off-shell data (points) and pre-fit distributions (histograms) for the Untagged (left), \VBF-tagged (middle), and \VH-tagged (right) categories. The upper row shows $\mell$ distributions with a requirement on $\Dbkgkin>0.6$ (left), $\mathcal{D}^{{\VBF}+{\text{dec}}}_\text{bkg}>0.6$ (middle), or $\mathcal{D}^{{\VH}+{\text{dec}}}_\text{bkg}>0.6$ (right) applied for illustration purposes to enhance signal over background contributions. The middle row shows $\mathcal{D}^\text{kin}_\text{bkg}$ (left), $\mathcal{D}^{{\VBF}+{\text{dec}}}_\text{bkg}$ (middle), $\mathcal{D}^{{\VH}+{\text{dec}}}_\text{bkg}$ (right) distributions, where an additional requirement $\mell>340$\GeV is applied to enhance signal-over-background contributions. The lower row plots the $\mathcal{D}_\text{bsi}$ with both the \mell and \Dbkgkin 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.

Off-shell data (points) and pre-fit distributions (histograms) for the Untagged (left), \VBF-tagged (middle), and \VH-tagged (right) categories. The upper row shows $\mell$ distributions with a requirement on $\Dbkgkin>0.6$ (left), $\mathcal{D}^{{\VBF}+{\text{dec}}}_\text{bkg}>0.6$ (middle), or $\mathcal{D}^{{\VH}+{\text{dec}}}_\text{bkg}>0.6$ (right) applied for illustration purposes to enhance signal over background contributions. The middle row shows $\mathcal{D}^\text{kin}_\text{bkg}$ (left), $\mathcal{D}^{{\VBF}+{\text{dec}}}_\text{bkg}$ (middle), $\mathcal{D}^{{\VH}+{\text{dec}}}_\text{bkg}$ (right) distributions, where an additional requirement $\mell>340$\GeV is applied to enhance signal-over-background contributions. The lower row plots the $\mathcal{D}_\text{bsi}$ with both the \mell and \Dbkgkin 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.

Off-shell data (points) and pre-fit distributions (histograms) for the Untagged (left), \VBF-tagged (middle), and \VH-tagged (right) categories. The upper row shows $\mell$ distributions with a requirement on $\Dbkgkin>0.6$ (left), $\mathcal{D}^{{\VBF}+{\text{dec}}}_\text{bkg}>0.6$ (middle), or $\mathcal{D}^{{\VH}+{\text{dec}}}_\text{bkg}>0.6$ (right) applied for illustration purposes to enhance signal over background contributions. The middle row shows $\mathcal{D}^\text{kin}_\text{bkg}$ (left), $\mathcal{D}^{{\VBF}+{\text{dec}}}_\text{bkg}$ (middle), $\mathcal{D}^{{\VH}+{\text{dec}}}_\text{bkg}$ (right) distributions, where an additional requirement $\mell>340$\GeV is applied to enhance signal-over-background contributions. The lower row plots the $\mathcal{D}_\text{bsi}$ with both the \mell and \Dbkgkin 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.

Off-shell data (points) and pre-fit distributions (histograms) for the Untagged (left), \VBF-tagged (middle), and \VH-tagged (right) categories. The upper row shows $\mell$ distributions with a requirement on $\Dbkgkin>0.6$ (left), $\mathcal{D}^{{\VBF}+{\text{dec}}}_\text{bkg}>0.6$ (middle), or $\mathcal{D}^{{\VH}+{\text{dec}}}_\text{bkg}>0.6$ (right) applied for illustration purposes to enhance signal over background contributions. The middle row shows $\mathcal{D}^\text{kin}_\text{bkg}$ (left), $\mathcal{D}^{{\VBF}+{\text{dec}}}_\text{bkg}$ (middle), $\mathcal{D}^{{\VH}+{\text{dec}}}_\text{bkg}$ (right) distributions, where an additional requirement $\mell>340$\GeV is applied to enhance signal-over-background contributions. The lower row plots the $\mathcal{D}_\text{bsi}$ with both the \mell and \Dbkgkin 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.

Off-shell data (points) and pre-fit distributions (histograms) for the Untagged (left), \VBF-tagged (middle), and \VH-tagged (right) categories. The upper row shows $\mell$ distributions with a requirement on $\Dbkgkin>0.6$ (left), $\mathcal{D}^{{\VBF}+{\text{dec}}}_\text{bkg}>0.6$ (middle), or $\mathcal{D}^{{\VH}+{\text{dec}}}_\text{bkg}>0.6$ (right) applied for illustration purposes to enhance signal over background contributions. The middle row shows $\mathcal{D}^\text{kin}_\text{bkg}$ (left), $\mathcal{D}^{{\VBF}+{\text{dec}}}_\text{bkg}$ (middle), $\mathcal{D}^{{\VH}+{\text{dec}}}_\text{bkg}$ (right) distributions, where an additional requirement $\mell>340$\GeV is applied to enhance signal-over-background contributions. The lower row plots the $\mathcal{D}_\text{bsi}$ with both the \mell and \Dbkgkin 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.

Off-shell data (points) and pre-fit distributions (histograms) for the Untagged (left), \VBF-tagged (middle), and \VH-tagged (right) categories. The upper row shows $\mell$ distributions with a requirement on $\Dbkgkin>0.6$ (left), $\mathcal{D}^{{\VBF}+{\text{dec}}}_\text{bkg}>0.6$ (middle), or $\mathcal{D}^{{\VH}+{\text{dec}}}_\text{bkg}>0.6$ (right) applied for illustration purposes to enhance signal over background contributions. The middle row shows $\mathcal{D}^\text{kin}_\text{bkg}$ (left), $\mathcal{D}^{{\VBF}+{\text{dec}}}_\text{bkg}$ (middle), $\mathcal{D}^{{\VH}+{\text{dec}}}_\text{bkg}$ (right) distributions, where an additional requirement $\mell>340$\GeV is applied to enhance signal-over-background contributions. The lower row plots the $\mathcal{D}_\text{bsi}$ with both the \mell and \Dbkgkin 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.

Off-shell data (points) and pre-fit distributions (histograms) for the Untagged (left), \VBF-tagged (middle), and \VH-tagged (right) categories. The upper row shows $\mell$ distributions with a requirement on $\Dbkgkin>0.6$ (left), $\mathcal{D}^{{\VBF}+{\text{dec}}}_\text{bkg}>0.6$ (middle), or $\mathcal{D}^{{\VH}+{\text{dec}}}_\text{bkg}>0.6$ (right) applied for illustration purposes to enhance signal over background contributions. The middle row shows $\mathcal{D}^\text{kin}_\text{bkg}$ (left), $\mathcal{D}^{{\VBF}+{\text{dec}}}_\text{bkg}$ (middle), $\mathcal{D}^{{\VH}+{\text{dec}}}_\text{bkg}$ (right) distributions, where an additional requirement $\mell>340$\GeV is applied to enhance signal-over-background contributions. The lower row plots the $\mathcal{D}_\text{bsi}$ with both the \mell and \Dbkgkin 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.

Off-shell data (points) and pre-fit distributions (histograms) for the Untagged (left), \VBF-tagged (middle), and \VH-tagged (right) categories. The upper row shows $\mell$ distributions with a requirement on $\Dbkgkin>0.6$ (left), $\mathcal{D}^{{\VBF}+{\text{dec}}}_\text{bkg}>0.6$ (middle), or $\mathcal{D}^{{\VH}+{\text{dec}}}_\text{bkg}>0.6$ (right) applied for illustration purposes to enhance signal over background contributions. The middle row shows $\mathcal{D}^\text{kin}_\text{bkg}$ (left), $\mathcal{D}^{{\VBF}+{\text{dec}}}_\text{bkg}$ (middle), $\mathcal{D}^{{\VH}+{\text{dec}}}_\text{bkg}$ (right) distributions, where an additional requirement $\mell>340$\GeV is applied to enhance signal-over-background contributions. The lower row plots the $\mathcal{D}_\text{bsi}$ with both the \mell and \Dbkgkin 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.

Illustration of how the on-shell statistical model is constructed, combining the $m_4\Pell$ 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.

The profile likelihood from the \mH fit using the $\mathcal{N}$--2D$'_\text{BS}$ model for each of the 4$\Pell$ 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.

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.

Distribution of $1-\CL$ vs. \GH 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.

Observed (solid) and expected (dashed) profile likelihood projections from the \Hboson width fit using on- and off-shell production from this analysis. The analysis of the \offshell $\PH\to\PZ\PZ\to4\Pell$ channel combined with the \onshell $\PH\to\PZ\PZ\to4\Pell$ channel~\cite{CMS:2021nnc} is shown in black. The full combination of $\PH\to\PZ\PZ\to4\Pell$ with the \offshell $\PH\to\PZ\PZ\to2\Pell2\PGn$~\cite{CMS:2022ley} is given in red. The black horizontal dashed lines show the 68 and 95\% \CL values.

Observed 2D profile likelihood projection of the \offshell signal strength parameters ($\mu^\text{\offshell}_{\F}$, $\mu^\text{\offshell}_{\PV}$) from the fit to the combined \offshell $\PH\to\PZ\PZ\to4\Pell$ and $2\Pell2\PGn$ 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.