CMS-HIG-23-013

CMS-HIG-23-013 ; CERN-EP-2025-065
Combination and interpretation of differential Higgs boson production cross sections in proton-proton collisions at $\sqrt{s}=$ 13 TeV
CMS Collaboration
17 April 2025
Submitted to J. High Energy Phys.
Abstract: Precision measurements of Higgs boson differential production cross sections are a key tool to probe the properties of the Higgs boson and test the standard model. New physics can affect both Higgs boson production and decay, leading to deviations from the distributions that are expected in the standard model. In this paper, combined measurements of differential spectra in a fiducial region matching the experimental selections are performed, based on analyses of four Higgs boson decay channels ( $\gamma\gamma$ , $\mathrm{Z}\mathrm{Z}^{()}$ , $\mathrm{W}\mathrm{W}^{()}$ , and $\tau\tau$ ) using proton-proton collision data recorded with the CMS detector at $\sqrt{s}=$ 13 TeV, corresponding to an integrated luminosity of 138 fb $^{-1}$ . The differential measurements are extrapolated to the full phase space and combined to provide the differential spectra. A measurement of the total Higgs boson production cross section is also performed using the $\gamma\gamma$ and ZZ decay channels, with a result of 53.4 $^{+2.9}_{-2.9}$ (stat) $^{+1.9}_{-1.8}$ (syst) pb, consistent with the standard model prediction of 55.6 $\pm$ 2.5 pb. The fiducial measurements are used to compute limits on Higgs boson couplings using the $\kappa$ -framework and the SM effective field theory.
Links: e-print arXiv:2504.13081 [hep-ex] (PDF) ; CDS record ; inSPIRE record ; CADI line (restricted) ;

Figures & Tables	Summary	References	CMS Publications

Figures
png pdf	Figure 1: Measurement of the total differential cross section as a function of $p_{\mathrm{T}}^{\mathrm{H}}$ (upper left), $N_{\mathrm{jets}}$ (upper right), $p_{\mathrm{T}}^{\mathrm{j}_1}$ (lower left), and $\|y_{\mathrm{H}}\|$ (lower right). For $p_{\mathrm{T}}^{\mathrm{j}_1}$ , the first bin comprises all events with less than one jet, for which $p_{\mathrm{T}}^{\mathrm{j}_1}$ is undefined. The combined spectrum is shown as black points with error bars indicating the 68% confidence interval. The systematic component of the uncertainty is shown in gray. The SM prediction is reported for different generators. In the case of $p_{\mathrm{T}}^{\mathrm{H}}$ and $p_{\mathrm{T}}^{\mathrm{j}_1}$ , the rightmost bins of the distributions are overflow bins, and are normalized by the bin width of the last but one bin. In cases where the systematic uncertainty band covers only one side of the data point, the systematic uncertainty on the other side is negligible. The ratio between the measurements and the SM predictions is shown in the lower panel of each plot.
png pdf	Figure 1-a: Measurement of the total differential cross section as a function of $p_{\mathrm{T}}^{\mathrm{H}}$ (upper left), $N_{\mathrm{jets}}$ (upper right), $p_{\mathrm{T}}^{\mathrm{j}_1}$ (lower left), and $\|y_{\mathrm{H}}\|$ (lower right). For $p_{\mathrm{T}}^{\mathrm{j}_1}$ , the first bin comprises all events with less than one jet, for which $p_{\mathrm{T}}^{\mathrm{j}_1}$ is undefined. The combined spectrum is shown as black points with error bars indicating the 68% confidence interval. The systematic component of the uncertainty is shown in gray. The SM prediction is reported for different generators. In the case of $p_{\mathrm{T}}^{\mathrm{H}}$ and $p_{\mathrm{T}}^{\mathrm{j}_1}$ , the rightmost bins of the distributions are overflow bins, and are normalized by the bin width of the last but one bin. In cases where the systematic uncertainty band covers only one side of the data point, the systematic uncertainty on the other side is negligible. The ratio between the measurements and the SM predictions is shown in the lower panel of each plot.
png pdf	Figure 1-b: Measurement of the total differential cross section as a function of $p_{\mathrm{T}}^{\mathrm{H}}$ (upper left), $N_{\mathrm{jets}}$ (upper right), $p_{\mathrm{T}}^{\mathrm{j}_1}$ (lower left), and $\|y_{\mathrm{H}}\|$ (lower right). For $p_{\mathrm{T}}^{\mathrm{j}_1}$ , the first bin comprises all events with less than one jet, for which $p_{\mathrm{T}}^{\mathrm{j}_1}$ is undefined. The combined spectrum is shown as black points with error bars indicating the 68% confidence interval. The systematic component of the uncertainty is shown in gray. The SM prediction is reported for different generators. In the case of $p_{\mathrm{T}}^{\mathrm{H}}$ and $p_{\mathrm{T}}^{\mathrm{j}_1}$ , the rightmost bins of the distributions are overflow bins, and are normalized by the bin width of the last but one bin. In cases where the systematic uncertainty band covers only one side of the data point, the systematic uncertainty on the other side is negligible. The ratio between the measurements and the SM predictions is shown in the lower panel of each plot.
png pdf	Figure 1-c: Measurement of the total differential cross section as a function of $p_{\mathrm{T}}^{\mathrm{H}}$ (upper left), $N_{\mathrm{jets}}$ (upper right), $p_{\mathrm{T}}^{\mathrm{j}_1}$ (lower left), and $\|y_{\mathrm{H}}\|$ (lower right). For $p_{\mathrm{T}}^{\mathrm{j}_1}$ , the first bin comprises all events with less than one jet, for which $p_{\mathrm{T}}^{\mathrm{j}_1}$ is undefined. The combined spectrum is shown as black points with error bars indicating the 68% confidence interval. The systematic component of the uncertainty is shown in gray. The SM prediction is reported for different generators. In the case of $p_{\mathrm{T}}^{\mathrm{H}}$ and $p_{\mathrm{T}}^{\mathrm{j}_1}$ , the rightmost bins of the distributions are overflow bins, and are normalized by the bin width of the last but one bin. In cases where the systematic uncertainty band covers only one side of the data point, the systematic uncertainty on the other side is negligible. The ratio between the measurements and the SM predictions is shown in the lower panel of each plot.
png pdf	Figure 1-d: Measurement of the total differential cross section as a function of $p_{\mathrm{T}}^{\mathrm{H}}$ (upper left), $N_{\mathrm{jets}}$ (upper right), $p_{\mathrm{T}}^{\mathrm{j}_1}$ (lower left), and $\|y_{\mathrm{H}}\|$ (lower right). For $p_{\mathrm{T}}^{\mathrm{j}_1}$ , the first bin comprises all events with less than one jet, for which $p_{\mathrm{T}}^{\mathrm{j}_1}$ is undefined. The combined spectrum is shown as black points with error bars indicating the 68% confidence interval. The systematic component of the uncertainty is shown in gray. The SM prediction is reported for different generators. In the case of $p_{\mathrm{T}}^{\mathrm{H}}$ and $p_{\mathrm{T}}^{\mathrm{j}_1}$ , the rightmost bins of the distributions are overflow bins, and are normalized by the bin width of the last but one bin. In cases where the systematic uncertainty band covers only one side of the data point, the systematic uncertainty on the other side is negligible. The ratio between the measurements and the SM predictions is shown in the lower panel of each plot.
png pdf	Figure 2: Measurement of the total differential cross section as a function of $\|\Delta\eta_{\mathrm{jj}}\|$ (upper left), $m_{\mathrm{jj}}$ (upper right), and $\tau^{\mathrm{j}}_{\mathrm{C}}$ (lower). The combined spectrum is shown as black points with error bars indicating the 68% confidence interval. The systematic component of the uncertainty is shown in gray. The SM prediction is reported for different generators. The rightmost bins of the distributions are overflow bins, and are normalized by the bin width of the last but one bin. The ratio between the measurements and the SM predictions is shown in the lower panel of each plot.
png pdf	Figure 2-a: Measurement of the total differential cross section as a function of $\|\Delta\eta_{\mathrm{jj}}\|$ (upper left), $m_{\mathrm{jj}}$ (upper right), and $\tau^{\mathrm{j}}_{\mathrm{C}}$ (lower). The combined spectrum is shown as black points with error bars indicating the 68% confidence interval. The systematic component of the uncertainty is shown in gray. The SM prediction is reported for different generators. The rightmost bins of the distributions are overflow bins, and are normalized by the bin width of the last but one bin. The ratio between the measurements and the SM predictions is shown in the lower panel of each plot.
png pdf	Figure 2-b: Measurement of the total differential cross section as a function of $\|\Delta\eta_{\mathrm{jj}}\|$ (upper left), $m_{\mathrm{jj}}$ (upper right), and $\tau^{\mathrm{j}}_{\mathrm{C}}$ (lower). The combined spectrum is shown as black points with error bars indicating the 68% confidence interval. The systematic component of the uncertainty is shown in gray. The SM prediction is reported for different generators. The rightmost bins of the distributions are overflow bins, and are normalized by the bin width of the last but one bin. The ratio between the measurements and the SM predictions is shown in the lower panel of each plot.
png pdf	Figure 2-c: Measurement of the total differential cross section as a function of $\|\Delta\eta_{\mathrm{jj}}\|$ (upper left), $m_{\mathrm{jj}}$ (upper right), and $\tau^{\mathrm{j}}_{\mathrm{C}}$ (lower). The combined spectrum is shown as black points with error bars indicating the 68% confidence interval. The systematic component of the uncertainty is shown in gray. The SM prediction is reported for different generators. The rightmost bins of the distributions are overflow bins, and are normalized by the bin width of the last but one bin. The ratio between the measurements and the SM predictions is shown in the lower panel of each plot.
png pdf	Figure 3: Measurement of the total differential cross section as a function of $p_{\mathrm{T}}^{\mathrm{H}}$ (upper left), $N_{\mathrm{jets}}$ (upper right), $p_{\mathrm{T}}^{\mathrm{j}_1}$ (lower left), and $\|y_{\mathrm{H}}\|$ (lower right). The combined spectrum is shown in black points with error bars indicating the 68% interval. The systematic component of the uncertainty is shown in gray. The spectra for the analyses in $\mathrm{H} \to \gamma \gamma$ , $\mathrm{H} \to \mathrm{Z} \mathrm{Z}^{()} \to 4\ell$ , $\mathrm{H} \to \mathrm{W} \mathrm{W}^{()} \to \mathrm{e}^{\pm} \mu^{\mp} \nu_{\ell} \overline{\nu}_{\ell}$ , $\mathrm{H} \to \tau^{+} \tau^{-}$ , and $\mathrm{H} \to \tau^{+} \tau^{-}$ boosted are shown in red, blue, purple, green, and pink respectively. The SM prediction is reported in light gray for MadGraph-5_aMC@NLO NNLOPS. In the case of $p_{\mathrm{T}}^{\mathrm{H}}$ and $p_{\mathrm{T}}^{\mathrm{j}_1}$ , the rightmost bins of the distributions are overflow bins, and are normalized by the bin width of the last but one bin. Measurements or predictions with different binnings can be directly compared only in the ratio panels of the figures. In cases where individual contributions have finer bins than the combination, such as the last bin of the $p_{\mathrm{T}}^{\mathrm{H}}$ and $p_{\mathrm{T}}^{\mathrm{j}_1}$ spectra, a second, finer, SM prediction is shown in the upper panel.
png pdf	Figure 3-a: Measurement of the total differential cross section as a function of $p_{\mathrm{T}}^{\mathrm{H}}$ (upper left), $N_{\mathrm{jets}}$ (upper right), $p_{\mathrm{T}}^{\mathrm{j}_1}$ (lower left), and $\|y_{\mathrm{H}}\|$ (lower right). The combined spectrum is shown in black points with error bars indicating the 68% interval. The systematic component of the uncertainty is shown in gray. The spectra for the analyses in $\mathrm{H} \to \gamma \gamma$ , $\mathrm{H} \to \mathrm{Z} \mathrm{Z}^{()} \to 4\ell$ , $\mathrm{H} \to \mathrm{W} \mathrm{W}^{()} \to \mathrm{e}^{\pm} \mu^{\mp} \nu_{\ell} \overline{\nu}_{\ell}$ , $\mathrm{H} \to \tau^{+} \tau^{-}$ , and $\mathrm{H} \to \tau^{+} \tau^{-}$ boosted are shown in red, blue, purple, green, and pink respectively. The SM prediction is reported in light gray for MadGraph-5_aMC@NLO NNLOPS. In the case of $p_{\mathrm{T}}^{\mathrm{H}}$ and $p_{\mathrm{T}}^{\mathrm{j}_1}$ , the rightmost bins of the distributions are overflow bins, and are normalized by the bin width of the last but one bin. Measurements or predictions with different binnings can be directly compared only in the ratio panels of the figures. In cases where individual contributions have finer bins than the combination, such as the last bin of the $p_{\mathrm{T}}^{\mathrm{H}}$ and $p_{\mathrm{T}}^{\mathrm{j}_1}$ spectra, a second, finer, SM prediction is shown in the upper panel.
png pdf	Figure 3-b: Measurement of the total differential cross section as a function of $p_{\mathrm{T}}^{\mathrm{H}}$ (upper left), $N_{\mathrm{jets}}$ (upper right), $p_{\mathrm{T}}^{\mathrm{j}_1}$ (lower left), and $\|y_{\mathrm{H}}\|$ (lower right). The combined spectrum is shown in black points with error bars indicating the 68% interval. The systematic component of the uncertainty is shown in gray. The spectra for the analyses in $\mathrm{H} \to \gamma \gamma$ , $\mathrm{H} \to \mathrm{Z} \mathrm{Z}^{()} \to 4\ell$ , $\mathrm{H} \to \mathrm{W} \mathrm{W}^{()} \to \mathrm{e}^{\pm} \mu^{\mp} \nu_{\ell} \overline{\nu}_{\ell}$ , $\mathrm{H} \to \tau^{+} \tau^{-}$ , and $\mathrm{H} \to \tau^{+} \tau^{-}$ boosted are shown in red, blue, purple, green, and pink respectively. The SM prediction is reported in light gray for MadGraph-5_aMC@NLO NNLOPS. In the case of $p_{\mathrm{T}}^{\mathrm{H}}$ and $p_{\mathrm{T}}^{\mathrm{j}_1}$ , the rightmost bins of the distributions are overflow bins, and are normalized by the bin width of the last but one bin. Measurements or predictions with different binnings can be directly compared only in the ratio panels of the figures. In cases where individual contributions have finer bins than the combination, such as the last bin of the $p_{\mathrm{T}}^{\mathrm{H}}$ and $p_{\mathrm{T}}^{\mathrm{j}_1}$ spectra, a second, finer, SM prediction is shown in the upper panel.
png pdf	Figure 3-c: Measurement of the total differential cross section as a function of $p_{\mathrm{T}}^{\mathrm{H}}$ (upper left), $N_{\mathrm{jets}}$ (upper right), $p_{\mathrm{T}}^{\mathrm{j}_1}$ (lower left), and $\|y_{\mathrm{H}}\|$ (lower right). The combined spectrum is shown in black points with error bars indicating the 68% interval. The systematic component of the uncertainty is shown in gray. The spectra for the analyses in $\mathrm{H} \to \gamma \gamma$ , $\mathrm{H} \to \mathrm{Z} \mathrm{Z}^{()} \to 4\ell$ , $\mathrm{H} \to \mathrm{W} \mathrm{W}^{()} \to \mathrm{e}^{\pm} \mu^{\mp} \nu_{\ell} \overline{\nu}_{\ell}$ , $\mathrm{H} \to \tau^{+} \tau^{-}$ , and $\mathrm{H} \to \tau^{+} \tau^{-}$ boosted are shown in red, blue, purple, green, and pink respectively. The SM prediction is reported in light gray for MadGraph-5_aMC@NLO NNLOPS. In the case of $p_{\mathrm{T}}^{\mathrm{H}}$ and $p_{\mathrm{T}}^{\mathrm{j}_1}$ , the rightmost bins of the distributions are overflow bins, and are normalized by the bin width of the last but one bin. Measurements or predictions with different binnings can be directly compared only in the ratio panels of the figures. In cases where individual contributions have finer bins than the combination, such as the last bin of the $p_{\mathrm{T}}^{\mathrm{H}}$ and $p_{\mathrm{T}}^{\mathrm{j}_1}$ spectra, a second, finer, SM prediction is shown in the upper panel.
png pdf	Figure 3-d: Measurement of the total differential cross section as a function of $p_{\mathrm{T}}^{\mathrm{H}}$ (upper left), $N_{\mathrm{jets}}$ (upper right), $p_{\mathrm{T}}^{\mathrm{j}_1}$ (lower left), and $\|y_{\mathrm{H}}\|$ (lower right). The combined spectrum is shown in black points with error bars indicating the 68% interval. The systematic component of the uncertainty is shown in gray. The spectra for the analyses in $\mathrm{H} \to \gamma \gamma$ , $\mathrm{H} \to \mathrm{Z} \mathrm{Z}^{()} \to 4\ell$ , $\mathrm{H} \to \mathrm{W} \mathrm{W}^{()} \to \mathrm{e}^{\pm} \mu^{\mp} \nu_{\ell} \overline{\nu}_{\ell}$ , $\mathrm{H} \to \tau^{+} \tau^{-}$ , and $\mathrm{H} \to \tau^{+} \tau^{-}$ boosted are shown in red, blue, purple, green, and pink respectively. The SM prediction is reported in light gray for MadGraph-5_aMC@NLO NNLOPS. In the case of $p_{\mathrm{T}}^{\mathrm{H}}$ and $p_{\mathrm{T}}^{\mathrm{j}_1}$ , the rightmost bins of the distributions are overflow bins, and are normalized by the bin width of the last but one bin. Measurements or predictions with different binnings can be directly compared only in the ratio panels of the figures. In cases where individual contributions have finer bins than the combination, such as the last bin of the $p_{\mathrm{T}}^{\mathrm{H}}$ and $p_{\mathrm{T}}^{\mathrm{j}_1}$ spectra, a second, finer, SM prediction is shown in the upper panel.
png pdf	Figure 4: Measurement of the total differential cross section as a function of $\|\Delta\eta_{\mathrm{jj}}\|$ (upper left), $m_{\mathrm{jj}}$ (upper right), and $\tau^{\mathrm{j}}_{\mathrm{C}}$ (lower). The combined spectrum is shown in black points with error bars indicating the 68% interval. The systematic component of the uncertainty is shown in gray. The spectra for the analyses in $\mathrm{H} \to \gamma \gamma$ and $\mathrm{H} \to \mathrm{Z} \mathrm{Z}^{(*)} \to 4\ell$ are shown in red and blue, respectively. The SM prediction is reported in light gray for MadGraph-5_aMC@NLO NNLOPS. The rightmost bins of the distributions are overflow bins, and are normalized by the bin width of the last but one bin. Measurements or predictions with different binnings can be directly compared only in the ratio panels of the figures.
png pdf	Figure 4-a: Measurement of the total differential cross section as a function of $\|\Delta\eta_{\mathrm{jj}}\|$ (upper left), $m_{\mathrm{jj}}$ (upper right), and $\tau^{\mathrm{j}}_{\mathrm{C}}$ (lower). The combined spectrum is shown in black points with error bars indicating the 68% interval. The systematic component of the uncertainty is shown in gray. The spectra for the analyses in $\mathrm{H} \to \gamma \gamma$ and $\mathrm{H} \to \mathrm{Z} \mathrm{Z}^{(*)} \to 4\ell$ are shown in red and blue, respectively. The SM prediction is reported in light gray for MadGraph-5_aMC@NLO NNLOPS. The rightmost bins of the distributions are overflow bins, and are normalized by the bin width of the last but one bin. Measurements or predictions with different binnings can be directly compared only in the ratio panels of the figures.
png pdf	Figure 4-b: Measurement of the total differential cross section as a function of $\|\Delta\eta_{\mathrm{jj}}\|$ (upper left), $m_{\mathrm{jj}}$ (upper right), and $\tau^{\mathrm{j}}_{\mathrm{C}}$ (lower). The combined spectrum is shown in black points with error bars indicating the 68% interval. The systematic component of the uncertainty is shown in gray. The spectra for the analyses in $\mathrm{H} \to \gamma \gamma$ and $\mathrm{H} \to \mathrm{Z} \mathrm{Z}^{(*)} \to 4\ell$ are shown in red and blue, respectively. The SM prediction is reported in light gray for MadGraph-5_aMC@NLO NNLOPS. The rightmost bins of the distributions are overflow bins, and are normalized by the bin width of the last but one bin. Measurements or predictions with different binnings can be directly compared only in the ratio panels of the figures.
png pdf	Figure 4-c: Measurement of the total differential cross section as a function of $\|\Delta\eta_{\mathrm{jj}}\|$ (upper left), $m_{\mathrm{jj}}$ (upper right), and $\tau^{\mathrm{j}}_{\mathrm{C}}$ (lower). The combined spectrum is shown in black points with error bars indicating the 68% interval. The systematic component of the uncertainty is shown in gray. The spectra for the analyses in $\mathrm{H} \to \gamma \gamma$ and $\mathrm{H} \to \mathrm{Z} \mathrm{Z}^{(*)} \to 4\ell$ are shown in red and blue, respectively. The SM prediction is reported in light gray for MadGraph-5_aMC@NLO NNLOPS. The rightmost bins of the distributions are overflow bins, and are normalized by the bin width of the last but one bin. Measurements or predictions with different binnings can be directly compared only in the ratio panels of the figures.
png pdf	Figure 5: Negative log-likelihood scan of the total Higgs boson production cross section $\sigma_{\mathrm{tot}}$ for the $\mathrm{H} \to \gamma \gamma$ , $\mathrm{H} \to \mathrm{Z} \mathrm{Z}^{(*)} \to 4\ell$ , and combined analyses. The markers indicate the 68% confidence interval. The label \textitCYRM-2017-002 in the legend denotes Ref. [19].
png pdf	Figure 6: Observed and expected simultaneous fits for $\kappa_{\mathrm{b}}$ and $\kappa_{\mathrm{c}}$ , assuming a coupling dependence of the branching fractions (left) and with the branching fractions of the decay channels entering the combination implemented as nuisance parameters with no dependence on the couplings (right). The 68% and 95% CL contours are shown in solid and dashed lines for the observed data, with the expected contours indicated in blue.
png pdf	Figure 6-a: Observed and expected simultaneous fits for $\kappa_{\mathrm{b}}$ and $\kappa_{\mathrm{c}}$ , assuming a coupling dependence of the branching fractions (left) and with the branching fractions of the decay channels entering the combination implemented as nuisance parameters with no dependence on the couplings (right). The 68% and 95% CL contours are shown in solid and dashed lines for the observed data, with the expected contours indicated in blue.
png pdf	Figure 6-b: Observed and expected simultaneous fits for $\kappa_{\mathrm{b}}$ and $\kappa_{\mathrm{c}}$ , assuming a coupling dependence of the branching fractions (left) and with the branching fractions of the decay channels entering the combination implemented as nuisance parameters with no dependence on the couplings (right). The 68% and 95% CL contours are shown in solid and dashed lines for the observed data, with the expected contours indicated in blue.
png pdf	Figure 7: Simultaneous fit for $\kappa_{\mathrm{t}}$ and $c_{\mathrm{g}}$ , observed and expected, assuming a coupling dependence of the branching fractions (left) and with the branching fractions of the decay channels entering the combination implemented as nuisance parameters with no dependence on the couplings (right). The 68% and 95% CL contours are shown in solid and dashed lines for observed data, the expected contours are indicated by the blue shaded areas.
png pdf	Figure 7-a: Simultaneous fit for $\kappa_{\mathrm{t}}$ and $c_{\mathrm{g}}$ , observed and expected, assuming a coupling dependence of the branching fractions (left) and with the branching fractions of the decay channels entering the combination implemented as nuisance parameters with no dependence on the couplings (right). The 68% and 95% CL contours are shown in solid and dashed lines for observed data, the expected contours are indicated by the blue shaded areas.
png pdf	Figure 7-b: Simultaneous fit for $\kappa_{\mathrm{t}}$ and $c_{\mathrm{g}}$ , observed and expected, assuming a coupling dependence of the branching fractions (left) and with the branching fractions of the decay channels entering the combination implemented as nuisance parameters with no dependence on the couplings (right). The 68% and 95% CL contours are shown in solid and dashed lines for observed data, the expected contours are indicated by the blue shaded areas.
png pdf	Figure 8: Simultaneous fit for $\kappa_{\mathrm{t}}$ and $\kappa_{\mathrm{b}}$ , observed and expected, assuming a coupling dependence of the branching fractions (left) and with the branching fractions of the decay channels entering the combination implemented as nuisance parameters with no dependence on the couplings (right). The 68% and 95% CL contours are indicated by the solid and dashed lines for the observed data, the expected contours are indicated by the blue shaded regions.
png pdf	Figure 8-a: Simultaneous fit for $\kappa_{\mathrm{t}}$ and $\kappa_{\mathrm{b}}$ , observed and expected, assuming a coupling dependence of the branching fractions (left) and with the branching fractions of the decay channels entering the combination implemented as nuisance parameters with no dependence on the couplings (right). The 68% and 95% CL contours are indicated by the solid and dashed lines for the observed data, the expected contours are indicated by the blue shaded regions.
png pdf	Figure 8-b: Simultaneous fit for $\kappa_{\mathrm{t}}$ and $\kappa_{\mathrm{b}}$ , observed and expected, assuming a coupling dependence of the branching fractions (left) and with the branching fractions of the decay channels entering the combination implemented as nuisance parameters with no dependence on the couplings (right). The 68% and 95% CL contours are indicated by the solid and dashed lines for the observed data, the expected contours are indicated by the blue shaded regions.
png pdf	Figure 9: Observed and expected two-dimensional scans for the $c_{\mathrm{HG}}-\tilde{c}_{\mathrm{HG}}$ (upper left), $c_{\mathrm{HB}}-\tilde{c}_{\mathrm{HB}}$ (upper right), $c_{\mathrm{HW}}-\tilde{c}_{\mathrm{HW}}$ (lower left), and $c_{\mathrm{HWB}}-\tilde{c}_{\mathrm{HWB}}$ (lower right) pairs with $p_{\mathrm{T}}^{\mathrm{H}}$ spectra in all decay channels.
png pdf	Figure 9-a: Observed and expected two-dimensional scans for the $c_{\mathrm{HG}}-\tilde{c}_{\mathrm{HG}}$ (upper left), $c_{\mathrm{HB}}-\tilde{c}_{\mathrm{HB}}$ (upper right), $c_{\mathrm{HW}}-\tilde{c}_{\mathrm{HW}}$ (lower left), and $c_{\mathrm{HWB}}-\tilde{c}_{\mathrm{HWB}}$ (lower right) pairs with $p_{\mathrm{T}}^{\mathrm{H}}$ spectra in all decay channels.
png pdf	Figure 9-b: Observed and expected two-dimensional scans for the $c_{\mathrm{HG}}-\tilde{c}_{\mathrm{HG}}$ (upper left), $c_{\mathrm{HB}}-\tilde{c}_{\mathrm{HB}}$ (upper right), $c_{\mathrm{HW}}-\tilde{c}_{\mathrm{HW}}$ (lower left), and $c_{\mathrm{HWB}}-\tilde{c}_{\mathrm{HWB}}$ (lower right) pairs with $p_{\mathrm{T}}^{\mathrm{H}}$ spectra in all decay channels.
png pdf	Figure 9-c: Observed and expected two-dimensional scans for the $c_{\mathrm{HG}}-\tilde{c}_{\mathrm{HG}}$ (upper left), $c_{\mathrm{HB}}-\tilde{c}_{\mathrm{HB}}$ (upper right), $c_{\mathrm{HW}}-\tilde{c}_{\mathrm{HW}}$ (lower left), and $c_{\mathrm{HWB}}-\tilde{c}_{\mathrm{HWB}}$ (lower right) pairs with $p_{\mathrm{T}}^{\mathrm{H}}$ spectra in all decay channels.
png pdf	Figure 9-d: Observed and expected two-dimensional scans for the $c_{\mathrm{HG}}-\tilde{c}_{\mathrm{HG}}$ (upper left), $c_{\mathrm{HB}}-\tilde{c}_{\mathrm{HB}}$ (upper right), $c_{\mathrm{HW}}-\tilde{c}_{\mathrm{HW}}$ (lower left), and $c_{\mathrm{HWB}}-\tilde{c}_{\mathrm{HWB}}$ (lower right) pairs with $p_{\mathrm{T}}^{\mathrm{H}}$ spectra in all decay channels.
png pdf	Figure 10: The values of the diagonal entries of the Fisher information matrix, presented as rows, for each decay channel. The normalization is such that the sum of the entries associated with each decay channel is equal to 100.
png pdf	Figure 11: Graphical representation of the ten eigenvectors with the highest eigenvalues $\lambda$ of the expected combined Fisher information matrix in the SMEFT basis. Values lower than 10 $^{-3}$ are not shown. The intensity of the color represents the absolute value of the coefficient, going from-1 (blue) to 1 (red).
png pdf	Figure 12: Summary of observed and expected confidence intervals at 68% and 95% confidence level (CL) for the first ten eigenvectors. On the y-axis, the quantity being displayed is multiplied by the corresponding power of ten. The eigenvectors are ordered by decreasing eigenvalue.
png pdf	Figure 13: Correlation matrix of the linear combinations of Wilson coefficients obtained from the PCA, obtained by fitting the observed data to the $p_{\mathrm{T}}^{\mathrm{H}}$ spectra of all decay channels.
png pdf	Figure B1: Bin-to-bin correlation matrices for the $p_{\mathrm{T}}^{\mathrm{H}}$ (upper left), $N_{\mathrm{jets}}$ (upper right), $\|y_{\mathrm{H}}\|$ (lower left), and $p_{\mathrm{T}}^{\mathrm{j}_1}$ (lower right) spectra.
png pdf	Figure B1-a: Bin-to-bin correlation matrices for the $p_{\mathrm{T}}^{\mathrm{H}}$ (upper left), $N_{\mathrm{jets}}$ (upper right), $\|y_{\mathrm{H}}\|$ (lower left), and $p_{\mathrm{T}}^{\mathrm{j}_1}$ (lower right) spectra.
png pdf	Figure B1-b: Bin-to-bin correlation matrices for the $p_{\mathrm{T}}^{\mathrm{H}}$ (upper left), $N_{\mathrm{jets}}$ (upper right), $\|y_{\mathrm{H}}\|$ (lower left), and $p_{\mathrm{T}}^{\mathrm{j}_1}$ (lower right) spectra.
png pdf	Figure B1-c: Bin-to-bin correlation matrices for the $p_{\mathrm{T}}^{\mathrm{H}}$ (upper left), $N_{\mathrm{jets}}$ (upper right), $\|y_{\mathrm{H}}\|$ (lower left), and $p_{\mathrm{T}}^{\mathrm{j}_1}$ (lower right) spectra.
png pdf	Figure B1-d: Bin-to-bin correlation matrices for the $p_{\mathrm{T}}^{\mathrm{H}}$ (upper left), $N_{\mathrm{jets}}$ (upper right), $\|y_{\mathrm{H}}\|$ (lower left), and $p_{\mathrm{T}}^{\mathrm{j}_1}$ (lower right) spectra.
png pdf	Figure B2: Bin-to-bin correlation matrices for the $m_{\mathrm{jj}}$ (upper left), $\|\Delta\eta_{\mathrm{jj}}\|$ (upper right) and $\tau^{\mathrm{j}}_{\mathrm{C}}$ (lower) spectra.
png pdf	Figure B2-a: Bin-to-bin correlation matrices for the $m_{\mathrm{jj}}$ (upper left), $\|\Delta\eta_{\mathrm{jj}}\|$ (upper right) and $\tau^{\mathrm{j}}_{\mathrm{C}}$ (lower) spectra.
png pdf	Figure B2-b: Bin-to-bin correlation matrices for the $m_{\mathrm{jj}}$ (upper left), $\|\Delta\eta_{\mathrm{jj}}\|$ (upper right) and $\tau^{\mathrm{j}}_{\mathrm{C}}$ (lower) spectra.
png pdf	Figure B2-c: Bin-to-bin correlation matrices for the $m_{\mathrm{jj}}$ (upper left), $\|\Delta\eta_{\mathrm{jj}}\|$ (upper right) and $\tau^{\mathrm{j}}_{\mathrm{C}}$ (lower) spectra.
png pdf	Figure C1: Two-dimensional scans for the $c_{\mathrm{HG}}-\tilde{c}_{\mathrm{HG}}$ (upper left), $c_{\mathrm{HB}}-\tilde{c}_{\mathrm{HB}}$ (upper right), $c_{\mathrm{HW}}-\tilde{c}_{\mathrm{HW}}$ (lower left), and $c_{\mathrm{HWB}}-\tilde{c}_{\mathrm{HWB}}$ (lower right) pairs with $\Delta\phi_{\mathrm{jj}}$ spectra in $\mathrm{H} \to \gamma \gamma$ and $\mathrm{H} \to \mathrm{Z} \mathrm{Z}^{(*)} \to 4\ell$ .
png pdf	Figure C1-a: Two-dimensional scans for the $c_{\mathrm{HG}}-\tilde{c}_{\mathrm{HG}}$ (upper left), $c_{\mathrm{HB}}-\tilde{c}_{\mathrm{HB}}$ (upper right), $c_{\mathrm{HW}}-\tilde{c}_{\mathrm{HW}}$ (lower left), and $c_{\mathrm{HWB}}-\tilde{c}_{\mathrm{HWB}}$ (lower right) pairs with $\Delta\phi_{\mathrm{jj}}$ spectra in $\mathrm{H} \to \gamma \gamma$ and $\mathrm{H} \to \mathrm{Z} \mathrm{Z}^{(*)} \to 4\ell$ .
png pdf	Figure C1-b: Two-dimensional scans for the $c_{\mathrm{HG}}-\tilde{c}_{\mathrm{HG}}$ (upper left), $c_{\mathrm{HB}}-\tilde{c}_{\mathrm{HB}}$ (upper right), $c_{\mathrm{HW}}-\tilde{c}_{\mathrm{HW}}$ (lower left), and $c_{\mathrm{HWB}}-\tilde{c}_{\mathrm{HWB}}$ (lower right) pairs with $\Delta\phi_{\mathrm{jj}}$ spectra in $\mathrm{H} \to \gamma \gamma$ and $\mathrm{H} \to \mathrm{Z} \mathrm{Z}^{(*)} \to 4\ell$ .
png pdf	Figure C1-c: Two-dimensional scans for the $c_{\mathrm{HG}}-\tilde{c}_{\mathrm{HG}}$ (upper left), $c_{\mathrm{HB}}-\tilde{c}_{\mathrm{HB}}$ (upper right), $c_{\mathrm{HW}}-\tilde{c}_{\mathrm{HW}}$ (lower left), and $c_{\mathrm{HWB}}-\tilde{c}_{\mathrm{HWB}}$ (lower right) pairs with $\Delta\phi_{\mathrm{jj}}$ spectra in $\mathrm{H} \to \gamma \gamma$ and $\mathrm{H} \to \mathrm{Z} \mathrm{Z}^{(*)} \to 4\ell$ .
png pdf	Figure C1-d: Two-dimensional scans for the $c_{\mathrm{HG}}-\tilde{c}_{\mathrm{HG}}$ (upper left), $c_{\mathrm{HB}}-\tilde{c}_{\mathrm{HB}}$ (upper right), $c_{\mathrm{HW}}-\tilde{c}_{\mathrm{HW}}$ (lower left), and $c_{\mathrm{HWB}}-\tilde{c}_{\mathrm{HWB}}$ (lower right) pairs with $\Delta\phi_{\mathrm{jj}}$ spectra in $\mathrm{H} \to \gamma \gamma$ and $\mathrm{H} \to \mathrm{Z} \mathrm{Z}^{(*)} \to 4\ell$ .
png pdf	Figure D1: Observed and expected profile likelihood scans for eigenvectors 0 to 3.
png pdf	Figure D1-a: Observed and expected profile likelihood scans for eigenvectors 0 to 3.
png pdf	Figure D1-b: Observed and expected profile likelihood scans for eigenvectors 0 to 3.
png pdf	Figure D1-c: Observed and expected profile likelihood scans for eigenvectors 0 to 3.
png pdf	Figure D1-d: Observed and expected profile likelihood scans for eigenvectors 0 to 3.
png pdf	Figure D2: Observed and expected profile likelihood scans for eigenvectors 4 to 7.
png pdf	Figure D2-a: Observed and expected profile likelihood scans for eigenvectors 4 to 7.
png pdf	Figure D2-b: Observed and expected profile likelihood scans for eigenvectors 4 to 7.
png pdf	Figure D2-c: Observed and expected profile likelihood scans for eigenvectors 4 to 7.
png pdf	Figure D2-d: Observed and expected profile likelihood scans for eigenvectors 4 to 7.
png pdf	Figure D3: Observed and expected profile likelihood scans for eigenvectors 8 and 9.
png pdf	Figure D3-a: Observed and expected profile likelihood scans for eigenvectors 8 and 9.
png pdf	Figure D3-b: Observed and expected profile likelihood scans for eigenvectors 8 and 9.

Tables
png pdf	Table 1: The $p_{\mathrm{T}}^{\mathrm{H}}$ bin boundaries used in the analyses that are input to the combination.
png pdf	Table 2: The $N_{\text{jets}}$ bins used in the analyses that are input to the combination.
png pdf	Table 3: The $p_{\mathrm{T}}^{\mathrm{j}_1}$ bin boundaries used in the analyses that are input to the combination.
png pdf	Table 4: The $\|y_{\mathrm{H}}\|$ bin boundaries used in the analyses that are input to the combination.
png pdf	Table 5: The $\|\Delta\eta_{\mathrm{jj}}\|$ bin boundaries used in the analyses that are input to the combination.
png pdf	Table 6: The $m_{\mathrm{jj}}$ bin boundaries used in the analyses that are input to the combination.
png pdf	Table 7: The $\tau^{\mathrm{j}}_{\mathrm{C}}$ bin boundaries used in the analyses that are input to the combination.
png pdf	Table 8: The $\|\Delta\phi_{jj}\|$ ( $\mathrm{H} \to \gamma \gamma$ ) and $\Delta\phi_{jj}$ ( $\mathrm{H} \to \mathrm{Z} \mathrm{Z}^{(*)} \to 4\ell$ ) bin boundaries, used to set constraints on Wilson coefficients.
png pdf	Table 9: List of $X^2H^2$ operators and corresponding Wilson coefficients. Example Feynman diagrams of the processes affected by the operators are shown in the rightmost column.
png pdf	Table 10: Wilson coefficients used as input to the SMEFT interpretation (right column). In left and center column the class they belong to and the corresponding operator are reported.
png pdf	Table A1: Observed best fit differential cross section for the $p_{\mathrm{T}}^{\mathrm{H}}$ ( GeVns) observable
png pdf	Table A2: Observed best fit differential cross section for the $N_{\mathrm{jets}}$ observable
png pdf	Table A3: Observed best fit differential cross section for the $p_{\mathrm{T}}^{\mathrm{j}_1}$ ( GeVns) observable
png pdf	Table A4: Observed best fit differential cross section for the $\|y_{\mathrm{H}}\|$ observable
png pdf	Table A5: Observed best fit differential cross section for the $\|\Delta\eta_{\mathrm{jj}}\|$ observable
png pdf	Table A6: Observed best fit differential cross section for the $m_{\mathrm{jj}}$ ( GeVns) observable
png pdf	Table A7: Observed best fit differential cross section for the $\tau^{\mathrm{j}}_{\mathrm{C}}$ ( GeVns) observable

Summary

Combined measurements of differential Higgs boson production cross sections for the observables

$p_{\mathrm{T}}^{\mathrm{H}}$ ,

$N_{\mathrm{jets}}$ ,

$|y_{\mathrm{H}}|$ ,

$p_{\mathrm{T}}^{\mathrm{j}_1}$ ,

$m_{\mathrm{jj}}$ ,

$|\Delta\eta_{\mathrm{jj}}|$ , and

$\tau^{\mathrm{j}}_{\mathrm{C}}$ are presented, using proton-proton collision data collected at

$\sqrt{s} = 13\,\text{Te\hspace{-.08em}V}$ and corresponding to an integrated luminosity of 138 fb

$^{-1}$ . The spectra are obtained with data from the

$\mathrm{H} \to \gamma \gamma$ ,

$\mathrm{H} \to \mathrm{Z} \mathrm{Z}^{(*)} \to 4\ell$ ,

$\mathrm{H} \to \mathrm{W} \mathrm{W}^{(*)} \to \mathrm{e}^{\pm} \mu^{\mp} \nu_{\ell} \overline{\nu}_{\ell}$ , and

$\mathrm{H} \to \tau^{+} \tau^{-}$ (both in the small and large Lorentz-boost regimes) decay channels. The precision of the combined measurement of the

$p_{\mathrm{T}}^{\mathrm{H}}$ differential cross section is improved by about 23% with respect to the

$\mathrm{H} \to \gamma \gamma$ channel alone. The improvement is particularly significant in the low- and high-

$p_{\mathrm{T}}^{\mathrm{H}}$ regions. No significant deviations from the SM predictions are observed in the differential distributions. Additionally, the total cross section for Higgs boson production based on a combination of the

$\mathrm{H} \to \gamma \gamma$ and

$\mathrm{H} \to \mathrm{Z} \mathrm{Z}^{(*)} \to 4\ell$ channels is measured to be 53.4

$^{+2.9}_{-2.9}$ (stat)

$^{+1.9}_{-1.8}$ (syst) pb, consistent with the SM prediction. The obtained

$p_{\mathrm{T}}^{\mathrm{H}}$ spectra are interpreted using the

$\kappa$ and SM effective field theory frameworks. In the former, multiple couplings are varied using the models provided in Refs. [26,27,28]. In the latter, two-dimensional constraints are obtained for pairs of Wilson coefficients. A principal component analysis is then performed to identify nonflat directions of the likelihood. The studies performed in this context highlight that the differential fiducial cross section measurements are sensitive to a limited set of operators and related Wilson coefficients, with the most constrained ones being

$c_{\mathrm{HG}}$ ,

$c_{\mathrm{HB}}$ ,

$c_{\mathrm{HW}}$ , and

$c_{\mathrm{HWB}}$ . No significant deviations from the SM are observed in the results obtained with either framework.

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